Subgroups — C₆₇×#62773 #30742024

Order 17152.

7998 conjugacy classes of subgroups.

The subgroup lattice has 1190 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3520	C₂	1	4	yes	maximal, complemented
2	C₆₇×#3519	C₂	1	4	yes	maximal, complemented
3	C₆₇×#3513	C₂	1	8	yes	maximal, complemented
4	C₆₇×#3506	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3505	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3501	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#3496	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#3492	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3490	C₂	1	4	yes	maximal, complemented
10	C₆₇×#3484	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3481	C₂	1	8	yes	maximal, complemented
12	C₆₇×#3475	C₂	1	4	yes	maximal, complemented
13	D₄×#41×C₆₇	C₂	1	4	yes	maximal, complemented
14	C₆₇×#3460	C₂	1	2	yes	maximal, complemented
15	C₆₇×#3459	C₂	1	4	yes	maximal, complemented
16	C₆₇×#3444	C₂	1	2	yes	maximal, complemented
17	C₂×#525×C₆₇	C₂	1	4	yes	maximal, complemented
18	C₄×H(5,𝔽₂)×C₆₇	C₂	1	2	yes	maximal, complemented
19	C₂²×C₄×D₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	2	yes	—
21	C₂²×#41×C₆₇	C₂²	1	4	yes	complemented
22	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
23	C₂⁴×C₄×C₆₇	C₂²	1	2	yes	complemented
24	#559×C₆₇	C₂²	1	8	yes	complemented
25	#556×C₆₇	C₂²	1	4	yes	complemented
26	#555×C₆₇	C₂²	1	4	yes	complemented
27	#554×C₆₇	C₂²	1	8	yes	complemented
28	#554×C₆₇	C₂²	1	4	yes	complemented
29	#554×C₆₇	C₂²	1	8	yes	complemented
30	#553×C₆₇	C₂²	1	8	yes	complemented
31	#553×C₆₇	C₂²	1	8	yes	complemented
32	#553×C₆₇	C₂²	1	16	yes	complemented
33	#553×C₆₇	C₂²	1	8	yes	complemented
34	#552×C₆₇	C₂²	1	8	yes	complemented
35	#552×C₆₇	C₂²	1	8	yes	complemented
36	#551×C₆₇	C₂²	1	16	yes	complemented
37	#551×C₆₇	C₂²	1	16	yes	complemented
38	#551×C₆₇	C₂²	1	16	yes	complemented
39	#550×C₆₇	C₂²	1	4	yes	complemented
40	D₄×Q₈×C₆₇	C₂²	1	4	yes	complemented
41	#548×C₆₇	C₂²	1	8	yes	complemented
42	#547×C₆₇	C₂²	1	8	yes	complemented
43	#547×C₆₇	C₂²	1	4	yes	complemented
44	#547×C₆₇	C₂²	1	4	yes	complemented
45	#546×C₆₇	C₂²	1	8	yes	complemented
46	#546×C₆₇	C₂²	1	8	yes	complemented
47	#546×C₆₇	C₂²	1	16	yes	complemented
48	#546×C₆₇	C₂²	1	16	yes	complemented
49	#546×C₆₇	C₂²	1	8	yes	complemented
50	#546×C₆₇	C₂²	1	8	yes	complemented
51	D₄²×C₆₇	C₂²	1	8	yes	complemented
52	D₄²×C₆₇	C₂²	1	8	yes	complemented
53	D₄²×C₆₇	C₂²	1	4	yes	complemented
54	#544×C₆₇	C₂²	1	2	yes	complemented
55	#543×C₆₇	C₂²	1	4	yes	complemented
56	#542×C₆₇	C₂²	1	8	yes	complemented
57	#540×C₆₇	C₂²	1	8	yes	complemented
58	#539×C₆₇	C₂²	1	8	yes	complemented
59	#539×C₆₇	C₂²	1	16	yes	complemented
60	#538×C₆₇	C₂²	1	8	yes	complemented
61	#538×C₆₇	C₂²	1	8	yes	complemented
62	#538×C₆₇	C₂²	1	16	yes	complemented
63	#537×C₆₇	C₂²	1	2	yes	complemented
64	#535×C₆₇	C₂²	1	4	yes	complemented
65	#534×C₆₇	C₂²	1	8	yes	complemented
66	#534×C₆₇	C₂²	1	4	yes	complemented
67	#533×C₆₇	C₂²	1	2	yes	complemented
68	#533×C₆₇	C₂²	1	2	yes	complemented
69	#533×C₆₇	C₂²	1	2	yes	complemented
70	#532×C₆₇	C₂²	1	2	yes	complemented
71	#532×C₆₇	C₂²	1	2	yes	complemented
72	#532×C₆₇	C₂²	1	2	yes	complemented
73	#532×C₆₇	C₂²	1	8	yes	complemented
74	#529×C₆₇	C₂²	1	4	yes	complemented
75	#529×C₆₇	C₂²	1	4	yes	complemented
76	#529×C₆₇	C₂²	1	4	yes	complemented
77	#529×C₆₇	C₂²	1	4	yes	complemented
78	#529×C₆₇	C₂²	1	4	yes	complemented
79	#529×C₆₇	C₂²	1	4	yes	complemented
80	#529×C₆₇	C₂²	1	16	yes	complemented
81	#529×C₆₇	C₂²	1	8	yes	complemented
82	#525×C₆₇	C₂²	1	4	yes	complemented
83	#525×C₆₇	C₂²	1	8	yes	complemented
84	#525×C₆₇	C₂²	1	4	yes	complemented
85	#525×C₆₇	C₂²	1	4	yes	complemented
86	#525×C₆₇	C₂²	1	8	yes	complemented
87	#525×C₆₇	C₂²	1	8	yes	complemented
88	#525×C₆₇	C₂²	1	8	yes	complemented
89	#525×C₆₇	C₂²	1	8	yes	complemented
90	#525×C₆₇	C₂²	1	8	yes	complemented
91	#525×C₆₇	C₂²	1	8	yes	complemented
92	#525×C₆₇	C₂²	1	16	yes	complemented
93	C₂×#123×C₆₇	C₂²	1	8	yes	complemented
94	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	4	yes	complemented
95	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	4	yes	complemented
96	C₂×#121×C₆₇	C₂²	1	4	yes	complemented
97	C₂×#121×C₆₇	C₂²	1	4	yes	complemented
98	C₂×#120×C₆₇	C₂²	1	8	yes	complemented
99	#520×C₆₇	C₂²	1	4	yes	complemented
100	#520×C₆₇	C₂²	1	8	yes	complemented
101	#518×C₆₇	C₂²	1	2	yes	—
102	#518×C₆₇	C₂²	1	8	yes	complemented
103	#518×C₆₇	C₂²	1	8	yes	complemented
104	C₄×#41×C₆₇	C₂²	1	4	yes	complemented
105	C₄×#41×C₆₇	C₂²	1	4	yes	complemented
106	C₄×#41×C₆₇	C₂²	1	4	yes	complemented
107	C₄×#41×C₆₇	C₂²	1	8	yes	complemented
108	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
109	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
110	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
111	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
112	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	complemented
113	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	complemented
114	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
115	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
116	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	complemented
117	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	complemented
118	C₂×C₄×D₄×C₆₇	C₂²	1	8	yes	complemented
119	C₂×C₄×D₄×C₆₇	C₂²	1	8	yes	complemented
120	C₂×C₄×D₄×C₆₇	C₂²	1	8	yes	complemented
121	C₂×#117×C₆₇	C₂²	1	4	yes	complemented
122	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
123	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
124	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic, complemented
125	C₂⁵×C₆₇	C₂³	1	2	yes	—
126	H(5,𝔽₂)×C₆₇	—	2	16	no	—
127	C₂×#41×C₆₇	—	4	16	no	—
128	C₂×#41×C₆₇	C₂³	1	4	yes	—
129	C₂×#41×C₆₇	C₂³	1	8	yes	—
130	C₂×#41×C₆₇	C₂³	1	4	yes	—
131	C₂×#41×C₆₇	C₂³	1	4	yes	—
132	C₂×#41×C₆₇	C₂³	1	8	yes	—
133	C₂×#41×C₆₇	C₂³	1	8	yes	complemented
134	C₂×#41×C₆₇	C₂³	1	8	yes	complemented
135	C₂²×Q₈×C₆₇	C₂³	1	4	yes	complemented
136	C₂²×D₄×C₆₇	—	2	8	no	—
137	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
138	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
139	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
140	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
141	C₂²×D₄×C₆₇	C₂³	1	8	yes	—
142	C₂²×D₄×C₆₇	C₂³	1	8	yes	—
143	C₂²×D₄×C₆₇	C₂³	1	8	yes	—
144	C₂²×D₄×C₆₇	C₂³	1	8	yes	—
145	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
146	C₂²×D₄×C₆₇	C₂³	1	4	yes	complemented
147	C₂³×C₄×C₆₇	—	4	8	no	—
148	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
149	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
150	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
151	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
152	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
153	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
154	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
155	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
156	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
157	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
158	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
159	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
160	C₂³×C₄×C₆₇	C₂³	1	8	yes	complemented
161	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	complemented
162	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	complemented
163	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	complemented
164	C₄⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
165	#127×C₆₇	C₂³	1	8	yes	—
166	#127×C₆₇	C₂³	1	2	yes	complemented
167	#126×C₆₇	C₂³	1	8	yes	complemented
168	#126×C₆₇	C₂³	1	8	yes	complemented
169	#126×C₆₇	C₂³	1	16	yes	complemented
170	#126×C₆₇	C₂³	1	16	yes	complemented
171	#126×C₆₇	C₂³	1	16	yes	complemented
172	#125×C₆₇	C₂³	1	4	yes	complemented
173	#125×C₆₇	C₂³	1	4	yes	complemented
174	#125×C₆₇	C₂³	1	4	yes	complemented
175	#125×C₆₇	C₂³	1	16	yes	complemented
176	#125×C₆₇	C₂³	1	8	yes	complemented
177	#124×C₆₇	C₂³	1	8	yes	—
178	#124×C₆₇	C₂³	1	4	yes	complemented
179	#124×C₆₇	C₂³	1	4	yes	complemented
180	#124×C₆₇	C₂³	1	4	yes	complemented
181	#124×C₆₇	C₂³	1	16	yes	complemented
182	#124×C₆₇	C₂³	1	16	yes	complemented
183	#123×C₆₇	C₂³	1	8	yes	—
184	#123×C₆₇	C₂³	1	16	yes	—
185	#123×C₆₇	C₂³	1	8	yes	—
186	#123×C₆₇	C₂³	1	8	yes	—
187	#123×C₆₇	C₂³	1	16	yes	—
188	#123×C₆₇	C₂³	1	16	yes	complemented
189	#123×C₆₇	C₂³	1	16	yes	complemented
190	#123×C₆₇	C₂³	1	16	yes	complemented
191	#123×C₆₇	C₂³	1	16	yes	complemented
192	#123×C₆₇	C₂³	1	16	yes	complemented
193	#123×C₆₇	C₂³	1	16	yes	complemented
194	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
195	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
196	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	—
197	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	—
198	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
199	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
200	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
201	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
202	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
203	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
204	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
205	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
206	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	complemented
207	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	complemented
208	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
209	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	complemented
210	#121×C₆₇	C₂³	1	4	yes	—
211	#121×C₆₇	C₂³	1	4	yes	—
212	#121×C₆₇	C₂³	1	8	yes	—
213	#121×C₆₇	C₂³	1	8	yes	—
214	#121×C₆₇	C₂³	1	4	yes	—
215	#121×C₆₇	C₂³	1	4	yes	—
216	#121×C₆₇	C₂³	1	4	yes	—
217	#121×C₆₇	C₂³	1	4	yes	—
218	#121×C₆₇	C₂³	1	16	yes	—
219	#121×C₆₇	C₂³	1	16	yes	—
220	#121×C₆₇	C₂³	1	8	yes	—
221	#121×C₆₇	C₂³	1	8	yes	—
222	#121×C₆₇	C₂³	1	8	yes	complemented
223	#121×C₆₇	C₂³	1	8	yes	complemented
224	#121×C₆₇	C₂³	1	8	yes	complemented
225	#121×C₆₇	C₂³	1	8	yes	complemented
226	#121×C₆₇	C₂³	1	16	yes	complemented
227	#121×C₆₇	C₂³	1	8	yes	complemented
228	#121×C₆₇	C₂³	1	16	yes	complemented
229	#120×C₆₇	C₂³	1	8	yes	—
230	#120×C₆₇	C₂³	1	16	yes	—
231	#120×C₆₇	C₂³	1	16	yes	—
232	#120×C₆₇	C₂³	1	16	yes	—
233	#120×C₆₇	C₂³	1	16	yes	—
234	#120×C₆₇	C₂³	1	16	yes	complemented
235	C₄×Q₈×C₆₇	C₂³	1	4	yes	complemented
236	C₄×Q₈×C₆₇	C₂³	1	4	yes	complemented
237	C₄×Q₈×C₆₇	C₂³	1	8	yes	complemented
238	C₄×Q₈×C₆₇	C₂³	1	4	yes	complemented
239	C₄×Q₈×C₆₇	C₂³	1	4	yes	complemented
240	C₄×Q₈×C₆₇	C₂³	1	4	yes	complemented
241	C₄×Q₈×C₆₇	C₂³	1	4	yes	complemented
242	C₄×D₄×C₆₇	C₂³	1	4	yes	—
243	C₄×D₄×C₆₇	C₂³	1	4	yes	—
244	C₄×D₄×C₆₇	C₂³	1	4	yes	—
245	C₄×D₄×C₆₇	C₂³	1	4	yes	—
246	C₄×D₄×C₆₇	C₂³	1	8	yes	—
247	C₄×D₄×C₆₇	C₂³	1	4	yes	—
248	C₄×D₄×C₆₇	C₂³	1	8	yes	—
249	C₄×D₄×C₆₇	C₂³	1	4	yes	—
250	C₄×D₄×C₆₇	C₂³	1	8	yes	—
251	C₄×D₄×C₆₇	C₂³	1	4	yes	—
252	C₄×D₄×C₆₇	C₂³	1	8	yes	—
253	C₄×D₄×C₆₇	C₂³	1	4	yes	—
254	C₄×D₄×C₆₇	C₂³	1	8	yes	—
255	C₄×D₄×C₆₇	C₂³	1	8	yes	—
256	C₄×D₄×C₆₇	C₂³	1	8	yes	—
257	C₄×D₄×C₆₇	C₂³	1	16	yes	—
258	C₄×D₄×C₆₇	C₂³	1	16	yes	—
259	C₄×D₄×C₆₇	C₂³	1	8	yes	—
260	C₄×D₄×C₆₇	C₂³	1	8	yes	—
261	C₄×D₄×C₆₇	C₂³	1	8	yes	—
262	C₄×D₄×C₆₇	C₂³	1	8	yes	—
263	C₄×D₄×C₆₇	C₂³	1	8	yes	—
264	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
265	C₄×D₄×C₆₇	C₂³	1	4	yes	complemented
266	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
267	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
268	C₄×D₄×C₆₇	C₂³	1	8	yes	complemented
269	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
270	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
271	C₄×D₄×C₆₇	C₂³	1	4	yes	complemented
272	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
273	C₄×D₄×C₆₇	C₂³	1	4	yes	complemented
274	C₄×D₄×C₆₇	C₂³	1	4	yes	complemented
275	C₄×D₄×C₆₇	C₂³	1	4	yes	complemented
276	C₄×D₄×C₆₇	C₂³	1	4	yes	complemented
277	#117×C₆₇	C₂³	1	4	yes	—
278	#117×C₆₇	C₂³	1	8	yes	—
279	#117×C₆₇	C₂³	1	4	yes	—
280	#117×C₆₇	C₂³	1	4	yes	—
281	#117×C₆₇	C₂³	1	8	yes	complemented
282	#117×C₆₇	C₂³	1	8	yes	complemented
283	#117×C₆₇	C₂³	1	8	yes	complemented
284	#117×C₆₇	C₂³	1	16	yes	complemented
285	#117×C₆₇	C₂³	1	8	yes	complemented
286	#117×C₆₇	C₂³	1	8	yes	complemented
287	#117×C₆₇	C₂³	1	8	yes	complemented
288	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
289	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
290	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
291	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
292	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
293	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	complemented
294	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	complemented
295	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	complemented
296	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	complemented
297	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	complemented
298	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
299	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
300	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
301	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
302	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
303	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
304	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
305	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
306	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
307	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	complemented
308	C₂×C₂²⋊C₄×C₆₇	C₂³	1	16	yes	complemented
309	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	complemented
310	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
311	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
312	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
313	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
314	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
315	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
316	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
317	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
318	C₂×C₄²×C₆₇	C₂³	1	8	yes	complemented
319	C₂×C₄²×C₆₇	C₂³	1	8	yes	complemented
320	C₂⁴×C₆₇	—	2	8	no	—
321	C₂⁴×C₆₇	—	4	4	no	—
322	C₂⁴×C₆₇	—	4	4	no	—
323	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
324	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
325	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
326	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
327	C₂⁴×C₆₇	C₂⁴	1	8	yes	—
328	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
329	#41×C₆₇	—	2	32	no	—
330	#41×C₆₇	—	2	16	no	—
331	#41×C₆₇	—	2	16	no	—
332	#41×C₆₇	—	4	16	no	—
333	#41×C₆₇	—	4	16	no	—
334	#41×C₆₇	—	4	8	no	—
335	#41×C₆₇	—	4	16	no	—
336	C₂×Q₈×C₆₇	—	4	8	no	—
337	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
338	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
339	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
340	C₂×Q₈×C₆₇	C₂⁴	1	8	yes	—
341	C₂×D₄×C₆₇	—	2	8	no	—
342	C₂×D₄×C₆₇	—	2	32	no	—
343	C₂×D₄×C₆₇	—	2	16	no	—
344	C₂×D₄×C₆₇	—	2	16	no	—
345	C₂×D₄×C₆₇	—	2	32	no	—
346	C₂×D₄×C₆₇	—	2	4	no	—
347	C₂×D₄×C₆₇	—	4	8	no	—
348	C₂×D₄×C₆₇	—	4	16	no	—
349	C₂×D₄×C₆₇	—	4	16	no	—
350	C₂×D₄×C₆₇	#41	1	8	yes	complemented
351	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
352	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
353	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
354	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
355	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
356	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
357	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
358	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
359	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
360	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
361	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
362	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
363	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
364	C₂²×C₄×C₆₇	—	2	4	no	—
365	C₂²×C₄×C₆₇	—	2	4	no	—
366	C₂²×C₄×C₆₇	—	2	16	no	—
367	C₂²×C₄×C₆₇	—	4	4	no	—
368	C₂²×C₄×C₆₇	—	4	8	no	—
369	C₂²×C₄×C₆₇	—	4	4	no	—
370	C₂²×C₄×C₆₇	—	4	8	no	—
371	C₂²×C₄×C₆₇	—	4	4	no	—
372	C₂²×C₄×C₆₇	—	4	4	no	—
373	C₂²×C₄×C₆₇	—	4	16	no	—
374	C₂²×C₄×C₆₇	—	4	8	no	—
375	C₂²×C₄×C₆₇	—	4	4	no	—
376	C₂²×C₄×C₆₇	—	4	2	no	—
377	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
378	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
379	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
380	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
381	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
382	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
383	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
384	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
385	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
386	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
387	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
388	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
389	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
390	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
391	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
392	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
393	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
394	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
395	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
396	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
397	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
398	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
399	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
400	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
401	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
402	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
403	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
404	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
405	C₂²×C₄×C₆₇	C₂⁴	1	16	yes	—
406	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
407	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
408	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
409	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
410	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
411	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
412	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
413	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
414	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
415	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
416	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
417	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
418	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
419	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
420	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
421	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
422	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
423	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
424	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
425	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
426	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
427	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
428	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
429	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
430	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
431	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
432	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
433	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
434	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
435	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
436	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
437	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
438	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
439	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
440	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
441	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
442	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
443	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
444	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
445	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
446	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
447	C₄²×C₆₇	C₂⁴	1	2	yes	—
448	C₄²×C₆₇	C₂⁴	1	2	yes	—
449	C₄²×C₆₇	C₂⁴	1	2	yes	—
450	C₄²×C₆₇	C₂⁴	1	2	yes	—
451	C₄²×C₆₇	C₂⁴	1	2	yes	—
452	C₄²×C₆₇	C₂⁴	1	2	yes	—
453	C₄²×C₆₇	C₂⁴	1	16	yes	—
454	C₄²×C₆₇	C₂⁴	1	8	yes	—
455	C₄²×C₆₇	C₂⁴	1	8	yes	—
456	C₄²×C₆₇	C₂⁴	1	2	yes	—
457	C₄²×C₆₇	C₂⁴	1	2	yes	—
458	C₄²×C₆₇	C₂⁴	1	8	yes	—
459	C₂³×C₆₇	—	2	2	no	—
460	C₂³×C₆₇	—	2	2	no	—
461	C₂³×C₆₇	—	2	2	no	—
462	C₂³×C₆₇	—	2	8	no	—
463	C₂³×C₆₇	—	2	8	no	—
464	C₂³×C₆₇	—	2	4	no	—
465	C₂³×C₆₇	—	2	8	no	—
466	C₂³×C₆₇	—	2	8	no	—
467	C₂³×C₆₇	—	2	16	no	—
468	C₂³×C₆₇	—	4	2	no	—
469	C₂³×C₆₇	—	4	4	no	—
470	C₂³×C₆₇	—	4	2	no	—
471	C₂³×C₆₇	—	4	2	no	—
472	C₂³×C₆₇	—	4	4	no	—
473	C₂³×C₆₇	—	4	2	no	—
474	C₂³×C₆₇	—	4	8	no	—
475	C₂³×C₆₇	—	4	8	no	—
476	C₂³×C₆₇	—	4	32	no	—
477	C₂³×C₆₇	C₂×#41	1	8	yes	complemented
478	C₂³×C₆₇	C₂⁵	1	4	yes	—
479	C₂³×C₆₇	C₂⁵	1	8	yes	—
480	C₂³×C₆₇	C₂⁵	1	4	yes	—
481	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
482	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
483	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
484	Q₈×C₆₇	—	2	8	no	—
485	Q₈×C₆₇	—	2	8	no	—
486	Q₈×C₆₇	—	4	8	no	—
487	Q₈×C₆₇	—	4	4	no	—
488	D₄×C₆₇	—	2	16	no	—
489	D₄×C₆₇	—	2	32	no	—
490	D₄×C₆₇	—	2	16	no	—
491	D₄×C₆₇	—	2	16	no	—
492	D₄×C₆₇	—	2	16	no	—
493	D₄×C₆₇	—	2	8	no	—
494	D₄×C₆₇	—	2	8	no	—
495	D₄×C₆₇	—	2	8	no	—
496	D₄×C₆₇	—	4	16	no	—
497	D₄×C₆₇	—	4	8	no	—
498	D₄×C₆₇	—	4	16	no	—
499	D₄×C₆₇	—	4	4	no	—
500	D₄×C₆₇	C₂×#41	1	16	yes	complemented
501	C₂×C₄×C₆₇	—	2	2	no	—
502	C₂×C₄×C₆₇	—	2	16	no	—
503	C₂×C₄×C₆₇	—	2	2	no	—
504	C₂×C₄×C₆₇	—	2	8	no	—
505	C₂×C₄×C₆₇	—	2	4	no	—
506	C₂×C₄×C₆₇	—	2	4	no	—
507	C₂×C₄×C₆₇	—	2	4	no	—
508	C₂×C₄×C₆₇	—	2	16	no	—
509	C₂×C₄×C₆₇	—	2	2	no	—
510	C₂×C₄×C₆₇	—	2	2	no	—
511	C₂×C₄×C₆₇	—	2	8	no	—
512	C₂×C₄×C₆₇	—	2	2	no	—
513	C₂×C₄×C₆₇	—	2	2	no	—
514	C₂×C₄×C₆₇	—	2	8	no	—
515	C₂×C₄×C₆₇	—	2	8	no	—
516	C₂×C₄×C₆₇	—	2	8	no	—
517	C₂×C₄×C₆₇	—	2	16	no	—
518	C₂×C₄×C₆₇	—	4	2	no	—
519	C₂×C₄×C₆₇	—	4	4	no	—
520	C₂×C₄×C₆₇	—	4	4	no	—
521	C₂×C₄×C₆₇	—	4	4	no	—
522	C₂×C₄×C₆₇	—	4	4	no	—
523	C₂×C₄×C₆₇	—	4	4	no	—
524	C₂×C₄×C₆₇	—	4	2	no	—
525	C₂×C₄×C₆₇	—	4	1	no	—
526	C₂×C₄×C₆₇	—	4	2	no	—
527	C₂×C₄×C₆₇	—	4	1	no	—
528	C₂×C₄×C₆₇	—	4	8	no	—
529	C₂×C₄×C₆₇	—	4	16	no	—
530	C₂×C₄×C₆₇	—	4	8	no	—
531	C₂×C₄×C₆₇	—	4	8	no	—
532	C₂×C₄×C₆₇	C₂×#41	1	4	yes	complemented
533	C₂×C₄×C₆₇	H(5,𝔽₂)	1	4	yes	complemented
534	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
535	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
536	C₂×C₄×C₆₇	C₂⁵	1	8	yes	—
537	C₂×C₄×C₆₇	C₂⁵	1	8	yes	—
538	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
539	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
540	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
541	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
542	C₂×C₄×C₆₇	C₂⁵	1	8	yes	—
543	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
544	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
545	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
546	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
547	C₂²×C₆₇	—	2	8	no	—
548	C₂²×C₆₇	—	2	1	no	—
549	C₂²×C₆₇	—	2	1	no	—
550	C₂²×C₆₇	—	2	1	no	—
551	C₂²×C₆₇	—	2	1	no	—
552	C₂²×C₆₇	—	2	4	no	—
553	C₂²×C₆₇	—	2	1	no	—
554	C₂²×C₆₇	—	2	1	no	—
555	C₂²×C₆₇	—	2	4	no	—
556	C₂²×C₆₇	—	2	8	no	—
557	C₂²×C₆₇	—	2	4	no	—
558	C₂²×C₆₇	—	2	4	no	—
559	C₂²×C₆₇	—	2	8	no	—
560	C₂²×C₆₇	—	2	8	no	—
561	C₂²×C₆₇	—	2	4	no	—
562	C₂²×C₆₇	—	4	8	no	—
563	C₂²×C₆₇	—	4	16	no	—
564	C₂²×C₆₇	—	4	16	no	—
565	C₂²×C₆₇	—	4	8	no	—
566	C₂²×C₆₇	—	8	16	no	—
567	C₂²×C₆₇	C₂²×#41	1	8	yes	—
568	C₂²×C₆₇	C₂²×#41	1	2	yes	—
569	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
570	C₂²×C₆₇	#585	1	2	yes	—
571	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
572	C₄×C₆₇	—	2	2	no	—
573	C₄×C₆₇	—	2	8	no	—
574	C₄×C₆₇	—	2	1	no	—
575	C₄×C₆₇	—	2	1	no	—
576	C₄×C₆₇	—	2	4	no	—
577	C₄×C₆₇	—	2	4	no	—
578	C₄×C₆₇	—	2	8	no	—
579	C₄×C₆₇	—	2	2	no	—
580	C₄×C₆₇	—	2	2	no	—
581	C₄×C₆₇	—	2	8	no	—
582	C₄×C₆₇	C₂²×#41	1	4	yes	—
583	C₄×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
584	C₄×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
585	#62773	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
586	C₂×C₆₇	—	2	2	no	—
587	C₂×C₆₇	—	2	2	no	—
588	C₂×C₆₇	—	2	2	no	—
589	C₂×C₆₇	—	2	8	no	—
590	C₂×C₆₇	—	4	4	no	—
591	C₂×C₆₇	—	4	8	no	—
592	C₂×C₆₇	C₂³×#41	1	1	yes	characteristic
593	C₂×C₆₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
594	C₂×C₆₇	C₂×#585	1	1	yes	characteristic
595	#3520	C₂×C₆₇	1	4	yes	complemented
596	#3519	C₂×C₆₇	1	4	yes	complemented
597	#3513	C₂×C₆₇	1	8	yes	complemented
598	#3506	C₂×C₆₇	1	2	yes	complemented
599	#3505	C₂×C₆₇	1	4	yes	complemented
600	#3501	C₂×C₆₇	1	1	yes	characteristic, complemented
601	#3496	C₂×C₆₇	1	1	yes	characteristic, complemented
602	#3492	C₂×C₆₇	1	2	yes	complemented
603	#3490	C₂×C₆₇	1	4	yes	complemented
604	#3484	C₂×C₆₇	1	2	yes	complemented
605	#3481	C₂×C₆₇	1	8	yes	complemented
606	#3475	C₂×C₆₇	1	4	yes	complemented
607	D₄×#41	C₂×C₆₇	1	4	yes	complemented
608	#3460	C₂×C₆₇	1	2	yes	complemented
609	#3459	C₂×C₆₇	1	4	yes	complemented
610	#3444	C₂×C₆₇	1	2	yes	complemented
611	C₂×#525	C₂×C₆₇	1	4	yes	complemented
612	C₄×H(5,𝔽₂)	C₂×C₆₇	1	2	yes	complemented
613	C₂²×C₄×D₄	C₂×C₆₇	1	1	yes	characteristic, complemented
614	C₆₇	#62773	1	1	yes	characteristic, direct product factor, Sylow
615	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	2	yes	—
616	C₂²×#41	C₂²×C₆₇	1	4	yes	complemented
617	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
618	C₂⁴×C₄	C₂²×C₆₇	1	2	yes	complemented
619	#559	C₂²×C₆₇	1	8	yes	complemented
620	#556	C₂²×C₆₇	1	4	yes	complemented
621	#555	C₂²×C₆₇	1	4	yes	complemented
622	#554	C₂²×C₆₇	1	8	yes	complemented
623	#554	C₂²×C₆₇	1	4	yes	complemented
624	#554	C₂²×C₆₇	1	8	yes	complemented
625	#553	C₂²×C₆₇	1	8	yes	complemented
626	#553	C₂²×C₆₇	1	8	yes	complemented
627	#553	C₂²×C₆₇	1	16	yes	complemented
628	#553	C₂²×C₆₇	1	8	yes	complemented
629	#552	C₂²×C₆₇	1	8	yes	complemented
630	#552	C₂²×C₆₇	1	8	yes	complemented
631	#551	C₂²×C₆₇	1	16	yes	complemented
632	#551	C₂²×C₆₇	1	16	yes	complemented
633	#551	C₂²×C₆₇	1	16	yes	complemented
634	#550	C₂²×C₆₇	1	4	yes	complemented
635	D₄×Q₈	C₂²×C₆₇	1	4	yes	complemented
636	#548	C₂²×C₆₇	1	8	yes	complemented
637	#547	C₂²×C₆₇	1	8	yes	complemented
638	#547	C₂²×C₆₇	1	4	yes	complemented
639	#547	C₂²×C₆₇	1	4	yes	complemented
640	#546	C₂²×C₆₇	1	8	yes	complemented
641	#546	C₂²×C₆₇	1	8	yes	complemented
642	#546	C₂²×C₆₇	1	16	yes	complemented
643	#546	C₂²×C₆₇	1	16	yes	complemented
644	#546	C₂²×C₆₇	1	8	yes	complemented
645	#546	C₂²×C₆₇	1	8	yes	complemented
646	D₄²	C₂²×C₆₇	1	8	yes	complemented
647	D₄²	C₂²×C₆₇	1	8	yes	complemented
648	D₄²	C₂²×C₆₇	1	4	yes	complemented
649	#544	C₂²×C₆₇	1	2	yes	complemented
650	#543	C₂²×C₆₇	1	4	yes	complemented
651	#542	C₂²×C₆₇	1	8	yes	complemented
652	#540	C₂²×C₆₇	1	8	yes	complemented
653	#539	C₂²×C₆₇	1	8	yes	complemented
654	#539	C₂²×C₆₇	1	16	yes	complemented
655	#538	C₂²×C₆₇	1	8	yes	complemented
656	#538	C₂²×C₆₇	1	8	yes	complemented
657	#538	C₂²×C₆₇	1	16	yes	complemented
658	#537	C₂²×C₆₇	1	2	yes	complemented
659	#535	C₂²×C₆₇	1	4	yes	complemented
660	#534	C₂²×C₆₇	1	8	yes	complemented
661	#534	C₂²×C₆₇	1	4	yes	complemented
662	#533	C₂²×C₆₇	1	2	yes	complemented
663	#533	C₂²×C₆₇	1	2	yes	complemented
664	#533	C₂²×C₆₇	1	2	yes	complemented
665	#532	C₂²×C₆₇	1	2	yes	complemented
666	#532	C₂²×C₆₇	1	2	yes	complemented
667	#532	C₂²×C₆₇	1	2	yes	complemented
668	#532	C₂²×C₆₇	1	8	yes	complemented
669	#529	C₂²×C₆₇	1	4	yes	complemented
670	#529	C₂²×C₆₇	1	4	yes	complemented
671	#529	C₂²×C₆₇	1	4	yes	complemented
672	#529	C₂²×C₆₇	1	4	yes	complemented
673	#529	C₂²×C₆₇	1	4	yes	complemented
674	#529	C₂²×C₆₇	1	4	yes	complemented
675	#529	C₂²×C₆₇	1	16	yes	complemented
676	#529	C₂²×C₆₇	1	8	yes	complemented
677	#525	C₂²×C₆₇	1	4	yes	complemented
678	#525	C₂²×C₆₇	1	8	yes	complemented
679	#525	C₂²×C₆₇	1	4	yes	complemented
680	#525	C₂²×C₆₇	1	4	yes	complemented
681	#525	C₂²×C₆₇	1	8	yes	complemented
682	#525	C₂²×C₆₇	1	8	yes	complemented
683	#525	C₂²×C₆₇	1	8	yes	complemented
684	#525	C₂²×C₆₇	1	8	yes	complemented
685	#525	C₂²×C₆₇	1	8	yes	complemented
686	#525	C₂²×C₆₇	1	8	yes	complemented
687	#525	C₂²×C₆₇	1	16	yes	complemented
688	C₂×#123	C₂²×C₆₇	1	8	yes	complemented
689	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	4	yes	complemented
690	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	4	yes	complemented
691	C₂×#121	C₂²×C₆₇	1	4	yes	complemented
692	C₂×#121	C₂²×C₆₇	1	4	yes	complemented
693	C₂×#120	C₂²×C₆₇	1	8	yes	complemented
694	#520	C₂²×C₆₇	1	4	yes	complemented
695	#520	C₂²×C₆₇	1	8	yes	complemented
696	#518	C₂²×C₆₇	1	2	yes	—
697	#518	C₂²×C₆₇	1	8	yes	complemented
698	#518	C₂²×C₆₇	1	8	yes	complemented
699	C₄×#41	C₂²×C₆₇	1	4	yes	complemented
700	C₄×#41	C₂²×C₆₇	1	4	yes	complemented
701	C₄×#41	C₂²×C₆₇	1	4	yes	complemented
702	C₄×#41	C₂²×C₆₇	1	8	yes	complemented
703	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
704	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
705	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
706	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
707	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	complemented
708	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	complemented
709	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
710	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
711	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	complemented
712	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	complemented
713	C₂×C₄×D₄	C₂²×C₆₇	1	8	yes	complemented
714	C₂×C₄×D₄	C₂²×C₆₇	1	8	yes	complemented
715	C₂×C₄×D₄	C₂²×C₆₇	1	8	yes	complemented
716	C₂×#117	C₂²×C₆₇	1	4	yes	complemented
717	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
718	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
719	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic, complemented
720	C₂⁵	C₂³×C₆₇	1	2	yes	—
721	H(5,𝔽₂)	—	2	16	no	—
722	C₂×#41	—	4	16	no	—
723	C₂×#41	C₂³×C₆₇	1	4	yes	—
724	C₂×#41	C₂³×C₆₇	1	8	yes	—
725	C₂×#41	C₂³×C₆₇	1	4	yes	—
726	C₂×#41	C₂³×C₆₇	1	4	yes	—
727	C₂×#41	C₂³×C₆₇	1	8	yes	—
728	C₂×#41	C₂³×C₆₇	1	8	yes	complemented
729	C₂×#41	C₂³×C₆₇	1	8	yes	complemented
730	C₂²×Q₈	C₂³×C₆₇	1	4	yes	complemented
731	C₂²×D₄	—	2	8	no	—
732	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
733	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
734	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
735	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
736	C₂²×D₄	C₂³×C₆₇	1	8	yes	—
737	C₂²×D₄	C₂³×C₆₇	1	8	yes	—
738	C₂²×D₄	C₂³×C₆₇	1	8	yes	—
739	C₂²×D₄	C₂³×C₆₇	1	8	yes	—
740	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
741	C₂²×D₄	C₂³×C₆₇	1	4	yes	complemented
742	C₂³×C₄	—	4	8	no	—
743	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
744	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
745	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
746	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
747	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
748	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
749	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
750	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
751	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
752	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
753	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
754	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
755	C₂³×C₄	C₂³×C₆₇	1	8	yes	complemented
756	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	complemented
757	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	complemented
758	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	complemented
759	C₄⋊Q₈	C₂³×C₆₇	1	8	yes	complemented
760	#127	C₂³×C₆₇	1	8	yes	—
761	#127	C₂³×C₆₇	1	2	yes	complemented
762	#126	C₂³×C₆₇	1	8	yes	complemented
763	#126	C₂³×C₆₇	1	8	yes	complemented
764	#126	C₂³×C₆₇	1	16	yes	complemented
765	#126	C₂³×C₆₇	1	16	yes	complemented
766	#126	C₂³×C₆₇	1	16	yes	complemented
767	#125	C₂³×C₆₇	1	4	yes	complemented
768	#125	C₂³×C₆₇	1	4	yes	complemented
769	#125	C₂³×C₆₇	1	4	yes	complemented
770	#125	C₂³×C₆₇	1	16	yes	complemented
771	#125	C₂³×C₆₇	1	8	yes	complemented
772	#124	C₂³×C₆₇	1	8	yes	—
773	#124	C₂³×C₆₇	1	4	yes	complemented
774	#124	C₂³×C₆₇	1	4	yes	complemented
775	#124	C₂³×C₆₇	1	4	yes	complemented
776	#124	C₂³×C₆₇	1	16	yes	complemented
777	#124	C₂³×C₆₇	1	16	yes	complemented
778	#123	C₂³×C₆₇	1	8	yes	—
779	#123	C₂³×C₆₇	1	16	yes	—
780	#123	C₂³×C₆₇	1	8	yes	—
781	#123	C₂³×C₆₇	1	8	yes	—
782	#123	C₂³×C₆₇	1	16	yes	—
783	#123	C₂³×C₆₇	1	16	yes	complemented
784	#123	C₂³×C₆₇	1	16	yes	complemented
785	#123	C₂³×C₆₇	1	16	yes	complemented
786	#123	C₂³×C₆₇	1	16	yes	complemented
787	#123	C₂³×C₆₇	1	16	yes	complemented
788	#123	C₂³×C₆₇	1	16	yes	complemented
789	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
790	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
791	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	—
792	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	—
793	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
794	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
795	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
796	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
797	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	complemented
798	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	complemented
799	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	complemented
800	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	complemented
801	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	complemented
802	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	complemented
803	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	complemented
804	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	complemented
805	#121	C₂³×C₆₇	1	4	yes	—
806	#121	C₂³×C₆₇	1	4	yes	—
807	#121	C₂³×C₆₇	1	8	yes	—
808	#121	C₂³×C₆₇	1	8	yes	—
809	#121	C₂³×C₆₇	1	4	yes	—
810	#121	C₂³×C₆₇	1	4	yes	—
811	#121	C₂³×C₆₇	1	4	yes	—
812	#121	C₂³×C₆₇	1	4	yes	—
813	#121	C₂³×C₆₇	1	16	yes	—
814	#121	C₂³×C₆₇	1	16	yes	—
815	#121	C₂³×C₆₇	1	8	yes	—
816	#121	C₂³×C₆₇	1	8	yes	—
817	#121	C₂³×C₆₇	1	8	yes	complemented
818	#121	C₂³×C₆₇	1	8	yes	complemented
819	#121	C₂³×C₆₇	1	8	yes	complemented
820	#121	C₂³×C₆₇	1	8	yes	complemented
821	#121	C₂³×C₆₇	1	16	yes	complemented
822	#121	C₂³×C₆₇	1	8	yes	complemented
823	#121	C₂³×C₆₇	1	16	yes	complemented
824	#120	C₂³×C₆₇	1	8	yes	—
825	#120	C₂³×C₆₇	1	16	yes	—
826	#120	C₂³×C₆₇	1	16	yes	—
827	#120	C₂³×C₆₇	1	16	yes	—
828	#120	C₂³×C₆₇	1	16	yes	—
829	#120	C₂³×C₆₇	1	16	yes	complemented
830	C₄×Q₈	C₂³×C₆₇	1	4	yes	complemented
831	C₄×Q₈	C₂³×C₆₇	1	4	yes	complemented
832	C₄×Q₈	C₂³×C₆₇	1	8	yes	complemented
833	C₄×Q₈	C₂³×C₆₇	1	4	yes	complemented
834	C₄×Q₈	C₂³×C₆₇	1	4	yes	complemented
835	C₄×Q₈	C₂³×C₆₇	1	4	yes	complemented
836	C₄×Q₈	C₂³×C₆₇	1	4	yes	complemented
837	C₄×D₄	C₂³×C₆₇	1	4	yes	—
838	C₄×D₄	C₂³×C₆₇	1	4	yes	—
839	C₄×D₄	C₂³×C₆₇	1	4	yes	—
840	C₄×D₄	C₂³×C₆₇	1	4	yes	—
841	C₄×D₄	C₂³×C₆₇	1	8	yes	—
842	C₄×D₄	C₂³×C₆₇	1	4	yes	—
843	C₄×D₄	C₂³×C₆₇	1	8	yes	—
844	C₄×D₄	C₂³×C₆₇	1	4	yes	—
845	C₄×D₄	C₂³×C₆₇	1	8	yes	—
846	C₄×D₄	C₂³×C₆₇	1	4	yes	—
847	C₄×D₄	C₂³×C₆₇	1	8	yes	—
848	C₄×D₄	C₂³×C₆₇	1	4	yes	—
849	C₄×D₄	C₂³×C₆₇	1	8	yes	—
850	C₄×D₄	C₂³×C₆₇	1	8	yes	—
851	C₄×D₄	C₂³×C₆₇	1	8	yes	—
852	C₄×D₄	C₂³×C₆₇	1	16	yes	—
853	C₄×D₄	C₂³×C₆₇	1	16	yes	—
854	C₄×D₄	C₂³×C₆₇	1	8	yes	—
855	C₄×D₄	C₂³×C₆₇	1	8	yes	—
856	C₄×D₄	C₂³×C₆₇	1	8	yes	—
857	C₄×D₄	C₂³×C₆₇	1	8	yes	—
858	C₄×D₄	C₂³×C₆₇	1	8	yes	—
859	C₄×D₄	C₂³×C₆₇	1	16	yes	complemented
860	C₄×D₄	C₂³×C₆₇	1	4	yes	complemented
861	C₄×D₄	C₂³×C₆₇	1	16	yes	complemented
862	C₄×D₄	C₂³×C₆₇	1	16	yes	complemented
863	C₄×D₄	C₂³×C₆₇	1	8	yes	complemented
864	C₄×D₄	C₂³×C₆₇	1	16	yes	complemented
865	C₄×D₄	C₂³×C₆₇	1	16	yes	complemented
866	C₄×D₄	C₂³×C₆₇	1	4	yes	complemented
867	C₄×D₄	C₂³×C₆₇	1	16	yes	complemented
868	C₄×D₄	C₂³×C₆₇	1	4	yes	complemented
869	C₄×D₄	C₂³×C₆₇	1	4	yes	complemented
870	C₄×D₄	C₂³×C₆₇	1	4	yes	complemented
871	C₄×D₄	C₂³×C₆₇	1	4	yes	complemented
872	#117	C₂³×C₆₇	1	4	yes	—
873	#117	C₂³×C₆₇	1	8	yes	—
874	#117	C₂³×C₆₇	1	4	yes	—
875	#117	C₂³×C₆₇	1	4	yes	—
876	#117	C₂³×C₆₇	1	8	yes	complemented
877	#117	C₂³×C₆₇	1	8	yes	complemented
878	#117	C₂³×C₆₇	1	8	yes	complemented
879	#117	C₂³×C₆₇	1	16	yes	complemented
880	#117	C₂³×C₆₇	1	8	yes	complemented
881	#117	C₂³×C₆₇	1	8	yes	complemented
882	#117	C₂³×C₆₇	1	8	yes	complemented
883	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
884	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
885	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
886	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
887	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
888	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	complemented
889	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	complemented
890	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	complemented
891	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	complemented
892	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	complemented
893	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
894	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
895	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
896	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
897	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
898	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
899	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
900	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
901	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
902	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	complemented
903	C₂×C₂²⋊C₄	C₂³×C₆₇	1	16	yes	complemented
904	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	complemented
905	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
906	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
907	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
908	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
909	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
910	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
911	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
912	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
913	C₂×C₄²	C₂³×C₆₇	1	8	yes	complemented
914	C₂×C₄²	C₂³×C₆₇	1	8	yes	complemented
915	C₂⁴	—	2	8	no	—
916	C₂⁴	—	4	4	no	—
917	C₂⁴	—	4	4	no	—
918	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
919	C₂⁴	C₂⁴×C₆₇	1	4	yes	—
920	C₂⁴	C₂⁴×C₆₇	1	4	yes	—
921	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
922	C₂⁴	C₂⁴×C₆₇	1	8	yes	—
923	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
924	#41	—	2	32	no	—
925	#41	—	2	16	no	—
926	#41	—	2	16	no	—
927	#41	—	4	16	no	—
928	#41	—	4	16	no	—
929	#41	—	4	8	no	—
930	#41	—	4	16	no	—
931	C₂×Q₈	—	4	8	no	—
932	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
933	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
934	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
935	C₂×Q₈	C₂⁴×C₆₇	1	8	yes	—
936	C₂×D₄	—	2	8	no	—
937	C₂×D₄	—	2	32	no	—
938	C₂×D₄	—	2	16	no	—
939	C₂×D₄	—	2	16	no	—
940	C₂×D₄	—	2	32	no	—
941	C₂×D₄	—	2	4	no	—
942	C₂×D₄	—	4	8	no	—
943	C₂×D₄	—	4	16	no	—
944	C₂×D₄	—	4	16	no	—
945	C₂×D₄	#41×C₆₇	1	8	yes	complemented
946	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
947	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
948	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
949	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
950	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
951	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
952	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
953	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
954	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
955	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
956	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
957	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
958	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
959	C₂²×C₄	—	2	4	no	—
960	C₂²×C₄	—	2	4	no	—
961	C₂²×C₄	—	2	16	no	—
962	C₂²×C₄	—	4	4	no	—
963	C₂²×C₄	—	4	8	no	—
964	C₂²×C₄	—	4	4	no	—
965	C₂²×C₄	—	4	8	no	—
966	C₂²×C₄	—	4	4	no	—
967	C₂²×C₄	—	4	4	no	—
968	C₂²×C₄	—	4	16	no	—
969	C₂²×C₄	—	4	8	no	—
970	C₂²×C₄	—	4	4	no	—
971	C₂²×C₄	—	4	2	no	—
972	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
973	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
974	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
975	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
976	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
977	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
978	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
979	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
980	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
981	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
982	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
983	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
984	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
985	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
986	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
987	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
988	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
989	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
990	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
991	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
992	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
993	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
994	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
995	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
996	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
997	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
998	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
999	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
1000	C₂²×C₄	C₂⁴×C₆₇	1	16	yes	—
1001	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
1002	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
1003	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1004	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1005	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1006	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1007	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1008	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1009	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1010	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1011	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1012	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
1013	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1014	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1015	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1016	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
1017	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1018	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1019	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1020	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1021	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1022	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1023	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1024	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1025	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1026	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1027	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1028	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1029	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1030	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1031	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
1032	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
1033	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
1034	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1035	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
1036	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1037	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1038	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
1039	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1040	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1041	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1042	C₄²	C₂⁴×C₆₇	1	2	yes	—
1043	C₄²	C₂⁴×C₆₇	1	2	yes	—
1044	C₄²	C₂⁴×C₆₇	1	2	yes	—
1045	C₄²	C₂⁴×C₆₇	1	2	yes	—
1046	C₄²	C₂⁴×C₆₇	1	2	yes	—
1047	C₄²	C₂⁴×C₆₇	1	2	yes	—
1048	C₄²	C₂⁴×C₆₇	1	2	yes	—
1049	C₄²	C₂⁴×C₆₇	1	2	yes	—
1050	C₄²	C₂⁴×C₆₇	1	8	yes	—
1051	C₄²	C₂⁴×C₆₇	1	16	yes	—
1052	C₄²	C₂⁴×C₆₇	1	8	yes	—
1053	C₄²	C₂⁴×C₆₇	1	8	yes	—
1054	C₂³	—	2	2	no	—
1055	C₂³	—	2	2	no	—
1056	C₂³	—	2	2	no	—
1057	C₂³	—	2	8	no	—
1058	C₂³	—	2	8	no	—
1059	C₂³	—	2	4	no	—
1060	C₂³	—	2	8	no	—
1061	C₂³	—	2	8	no	—
1062	C₂³	—	2	16	no	—
1063	C₂³	—	4	2	no	—
1064	C₂³	—	4	4	no	—
1065	C₂³	—	4	2	no	—
1066	C₂³	—	4	2	no	—
1067	C₂³	—	4	4	no	—
1068	C₂³	—	4	2	no	—
1069	C₂³	—	4	8	no	—
1070	C₂³	—	4	8	no	—
1071	C₂³	—	4	32	no	—
1072	C₂³	C₂×#41×C₆₇	1	8	yes	complemented
1073	C₂³	C₂⁵×C₆₇	1	4	yes	—
1074	C₂³	C₂⁵×C₆₇	1	8	yes	—
1075	C₂³	C₂⁵×C₆₇	1	4	yes	—
1076	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
1077	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
1078	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
1079	Q₈	—	2	8	no	—
1080	Q₈	—	2	8	no	—
1081	Q₈	—	4	8	no	—
1082	Q₈	—	4	4	no	—
1083	D₄	—	2	16	no	—
1084	D₄	—	2	32	no	—
1085	D₄	—	2	16	no	—
1086	D₄	—	2	16	no	—
1087	D₄	—	2	16	no	—
1088	D₄	—	2	8	no	—
1089	D₄	—	2	8	no	—
1090	D₄	—	2	8	no	—
1091	D₄	—	4	8	no	—
1092	D₄	—	4	16	no	—
1093	D₄	—	4	16	no	—
1094	D₄	—	4	4	no	—
1095	D₄	C₂×#41×C₆₇	1	16	yes	complemented
1096	C₂×C₄	—	2	2	no	—
1097	C₂×C₄	—	2	16	no	—
1098	C₂×C₄	—	2	2	no	—
1099	C₂×C₄	—	2	8	no	—
1100	C₂×C₄	—	2	4	no	—
1101	C₂×C₄	—	2	4	no	—
1102	C₂×C₄	—	2	4	no	—
1103	C₂×C₄	—	2	16	no	—
1104	C₂×C₄	—	2	2	no	—
1105	C₂×C₄	—	2	2	no	—
1106	C₂×C₄	—	2	8	no	—
1107	C₂×C₄	—	2	2	no	—
1108	C₂×C₄	—	2	2	no	—
1109	C₂×C₄	—	2	8	no	—
1110	C₂×C₄	—	2	8	no	—
1111	C₂×C₄	—	2	8	no	—
1112	C₂×C₄	—	2	16	no	—
1113	C₂×C₄	—	4	2	no	—
1114	C₂×C₄	—	4	4	no	—
1115	C₂×C₄	—	4	4	no	—
1116	C₂×C₄	—	4	4	no	—
1117	C₂×C₄	—	4	4	no	—
1118	C₂×C₄	—	4	4	no	—
1119	C₂×C₄	—	4	2	no	—
1120	C₂×C₄	—	4	8	no	—
1121	C₂×C₄	—	4	16	no	—
1122	C₂×C₄	—	4	1	no	—
1123	C₂×C₄	—	4	2	no	—
1124	C₂×C₄	—	4	1	no	—
1125	C₂×C₄	—	4	8	no	—
1126	C₂×C₄	—	4	8	no	—
1127	C₂×C₄	C₂×#41×C₆₇	1	4	yes	complemented
1128	C₂×C₄	H(5,𝔽₂)×C₆₇	1	4	yes	complemented
1129	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
1130	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
1131	C₂×C₄	C₂⁵×C₆₇	1	8	yes	—
1132	C₂×C₄	C₂⁵×C₆₇	1	8	yes	—
1133	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
1134	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1135	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1136	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
1137	C₂×C₄	C₂⁵×C₆₇	1	8	yes	—
1138	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
1139	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
1140	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1141	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1142	C₂²	—	2	8	no	—
1143	C₂²	—	2	1	no	—
1144	C₂²	—	2	1	no	—
1145	C₂²	—	2	1	no	—
1146	C₂²	—	2	1	no	—
1147	C₂²	—	2	4	no	—
1148	C₂²	—	2	1	no	—
1149	C₂²	—	2	1	no	—
1150	C₂²	—	2	4	no	—
1151	C₂²	—	2	8	no	—
1152	C₂²	—	2	4	no	—
1153	C₂²	—	2	4	no	—
1154	C₂²	—	2	8	no	—
1155	C₂²	—	2	8	no	—
1156	C₂²	—	2	4	no	—
1157	C₂²	—	4	8	no	—
1158	C₂²	—	4	16	no	—
1159	C₂²	—	4	16	no	—
1160	C₂²	—	4	8	no	—
1161	C₂²	—	8	16	no	—
1162	C₂²	C₂²×#41×C₆₇	1	8	yes	—
1163	C₂²	C₂²×#41×C₆₇	1	2	yes	—
1164	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
1165	C₂²	#585×C₆₇	1	2	yes	—
1166	C₂²	C₂⁶×C₆₇	1	1	yes	characteristic
1167	C₄	—	2	2	no	—
1168	C₄	—	2	8	no	—
1169	C₄	—	2	1	no	—
1170	C₄	—	2	1	no	—
1171	C₄	—	2	4	no	—
1172	C₄	—	2	4	no	—
1173	C₄	—	2	8	no	—
1174	C₄	—	2	2	no	—
1175	C₄	—	2	2	no	—
1176	C₄	—	2	8	no	—
1177	C₄	C₂²×#41×C₆₇	1	4	yes	—
1178	C₄	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
1179	C₄	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
1180	C₂	—	2	2	no	—
1181	C₂	—	2	2	no	—
1182	C₂	—	2	2	no	—
1183	C₂	—	2	8	no	—
1184	C₂	—	4	4	no	—
1185	C₂	—	4	8	no	—
1186	C₂	C₂³×#41×C₆₇	1	1	yes	characteristic
1187	C₂	C₂²×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1188	C₂	C₂×#585×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₆₇
socle	C₂²×C₆₇	C₂⁶
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₆₇×#3520	C₂	semidirect
2. C₆₇×#3519	C₂	semidirect
3. C₆₇×#3513	C₂	semidirect
4. C₆₇×#3506	C₂	semidirect
5. C₆₇×#3505	C₂	semidirect
6. C₆₇×#3501	C₂	semidirect
7. C₆₇×#3496	C₂	semidirect
8. C₆₇×#3492	C₂	semidirect
9. C₆₇×#3490	C₂	semidirect
10. C₆₇×#3484	C₂	semidirect
11. C₆₇×#3481	C₂	semidirect
12. C₆₇×#3475	C₂	semidirect
13. D₄×#41×C₆₇	C₂	semidirect
14. C₆₇×#3460	C₂	semidirect
15. C₆₇×#3459	C₂	semidirect
16. C₆₇×#3444	C₂	semidirect
17. C₂×#525×C₆₇	C₂	semidirect
18. C₄×H(5,𝔽₂)×C₆₇	C₂	semidirect
19. C₂²×C₄×D₄×C₆₇	C₂	semidirect
21. C₂²×#41×C₆₇	C₂²	semidirect
23. C₂⁴×C₄×C₆₇	C₂²	semidirect
24. #559×C₆₇	C₂²	semidirect
25. #556×C₆₇	C₂²	semidirect
26. #555×C₆₇	C₂²	semidirect
27. #554×C₆₇	C₂²	semidirect
28. #554×C₆₇	C₂²	semidirect
29. #554×C₆₇	C₂²	semidirect
30. #553×C₆₇	C₂²	semidirect
31. #553×C₆₇	C₂²	semidirect
32. #553×C₆₇	C₂²	semidirect
33. #553×C₆₇	C₂²	semidirect
34. #552×C₆₇	C₂²	semidirect
35. #552×C₆₇	C₂²	semidirect
36. #551×C₆₇	C₂²	semidirect
37. #551×C₆₇	C₂²	semidirect
38. #551×C₆₇	C₂²	semidirect
39. #550×C₆₇	C₂²	semidirect
40. D₄×Q₈×C₆₇	C₂²	semidirect
41. #548×C₆₇	C₂²	semidirect
42. #547×C₆₇	C₂²	semidirect
43. #547×C₆₇	C₂²	semidirect
44. #547×C₆₇	C₂²	semidirect
45. #546×C₆₇	C₂²	semidirect
46. #546×C₆₇	C₂²	semidirect
47. #546×C₆₇	C₂²	semidirect
48. #546×C₆₇	C₂²	semidirect
49. #546×C₆₇	C₂²	semidirect
50. #546×C₆₇	C₂²	semidirect
51. D₄²×C₆₇	C₂²	semidirect
52. D₄²×C₆₇	C₂²	semidirect
53. D₄²×C₆₇	C₂²	semidirect
54. #544×C₆₇	C₂²	semidirect
55. #543×C₆₇	C₂²	semidirect
56. #542×C₆₇	C₂²	semidirect
57. #540×C₆₇	C₂²	semidirect
58. #539×C₆₇	C₂²	semidirect
59. #539×C₆₇	C₂²	semidirect
60. #538×C₆₇	C₂²	semidirect
61. #538×C₆₇	C₂²	semidirect
62. #538×C₆₇	C₂²	semidirect
63. #537×C₆₇	C₂²	semidirect
64. #535×C₆₇	C₂²	semidirect
65. #534×C₆₇	C₂²	semidirect
66. #534×C₆₇	C₂²	semidirect
67. #533×C₆₇	C₂²	semidirect
68. #533×C₆₇	C₂²	semidirect
69. #533×C₆₇	C₂²	semidirect
70. #532×C₆₇	C₂²	semidirect
71. #532×C₆₇	C₂²	semidirect
72. #532×C₆₇	C₂²	semidirect
73. #532×C₆₇	C₂²	semidirect
74. #529×C₆₇	C₂²	semidirect
75. #529×C₆₇	C₂²	semidirect
76. #529×C₆₇	C₂²	semidirect
77. #529×C₆₇	C₂²	semidirect
78. #529×C₆₇	C₂²	semidirect
79. #529×C₆₇	C₂²	semidirect
80. #529×C₆₇	C₂²	semidirect
81. #529×C₆₇	C₂²	semidirect
82. #525×C₆₇	C₂²	semidirect
83. #525×C₆₇	C₂²	semidirect
84. #525×C₆₇	C₂²	semidirect
85. #525×C₆₇	C₂²	semidirect
86. #525×C₆₇	C₂²	semidirect
87. #525×C₆₇	C₂²	semidirect
88. #525×C₆₇	C₂²	semidirect
89. #525×C₆₇	C₂²	semidirect
90. #525×C₆₇	C₂²	semidirect
91. #525×C₆₇	C₂²	semidirect
92. #525×C₆₇	C₂²	semidirect
93. C₂×#123×C₆₇	C₂²	semidirect
94. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
95. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
96. C₂×#121×C₆₇	C₂²	semidirect
97. C₂×#121×C₆₇	C₂²	semidirect
98. C₂×#120×C₆₇	C₂²	semidirect
99. #520×C₆₇	C₂²	semidirect
100. #520×C₆₇	C₂²	semidirect
102. #518×C₆₇	C₂²	semidirect
103. #518×C₆₇	C₂²	semidirect
104. C₄×#41×C₆₇	C₂²	semidirect
105. C₄×#41×C₆₇	C₂²	semidirect
106. C₄×#41×C₆₇	C₂²	semidirect
107. C₄×#41×C₆₇	C₂²	semidirect
110. C₂×C₄×D₄×C₆₇	C₂²	semidirect
111. C₂×C₄×D₄×C₆₇	C₂²	semidirect
112. C₂×C₄×D₄×C₆₇	C₂²	semidirect
113. C₂×C₄×D₄×C₆₇	C₂²	semidirect
114. C₂×C₄×D₄×C₆₇	C₂²	semidirect
115. C₂×C₄×D₄×C₆₇	C₂²	semidirect
116. C₂×C₄×D₄×C₆₇	C₂²	semidirect
117. C₂×C₄×D₄×C₆₇	C₂²	semidirect
118. C₂×C₄×D₄×C₆₇	C₂²	semidirect
119. C₂×C₄×D₄×C₆₇	C₂²	semidirect
120. C₂×C₄×D₄×C₆₇	C₂²	semidirect
121. C₂×#117×C₆₇	C₂²	semidirect
122. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
123. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
124. C₂²×C₄²×C₆₇	C₂²	semidirect
133. C₂×#41×C₆₇	C₂³	semidirect
134. C₂×#41×C₆₇	C₂³	semidirect
135. C₂²×Q₈×C₆₇	C₂³	semidirect
146. C₂²×D₄×C₆₇	C₂³	semidirect
160. C₂³×C₄×C₆₇	C₂³	semidirect
161. C₄⋊Q₈×C₆₇	C₂³	semidirect
162. C₄⋊Q₈×C₆₇	C₂³	semidirect
163. C₄⋊Q₈×C₆₇	C₂³	semidirect
164. C₄⋊Q₈×C₆₇	C₂³	semidirect
166. #127×C₆₇	C₂³	semidirect
167. #126×C₆₇	C₂³	semidirect
168. #126×C₆₇	C₂³	semidirect
169. #126×C₆₇	C₂³	semidirect
170. #126×C₆₇	C₂³	semidirect
171. #126×C₆₇	C₂³	semidirect
172. #125×C₆₇	C₂³	semidirect
173. #125×C₆₇	C₂³	semidirect
174. #125×C₆₇	C₂³	semidirect
175. #125×C₆₇	C₂³	semidirect
176. #125×C₆₇	C₂³	semidirect
178. #124×C₆₇	C₂³	semidirect
179. #124×C₆₇	C₂³	semidirect
180. #124×C₆₇	C₂³	semidirect
181. #124×C₆₇	C₂³	semidirect
182. #124×C₆₇	C₂³	semidirect
188. #123×C₆₇	C₂³	semidirect
189. #123×C₆₇	C₂³	semidirect
190. #123×C₆₇	C₂³	semidirect
191. #123×C₆₇	C₂³	semidirect
192. #123×C₆₇	C₂³	semidirect
193. #123×C₆₇	C₂³	semidirect
202. C₂²⋊Q₈×C₆₇	C₂³	semidirect
203. C₂²⋊Q₈×C₆₇	C₂³	semidirect
204. C₂²⋊Q₈×C₆₇	C₂³	semidirect
205. C₂²⋊Q₈×C₆₇	C₂³	semidirect
206. C₂²⋊Q₈×C₆₇	C₂³	semidirect
207. C₂²⋊Q₈×C₆₇	C₂³	semidirect
208. C₂²⋊Q₈×C₆₇	C₂³	semidirect
209. C₂²⋊Q₈×C₆₇	C₂³	semidirect
222. #121×C₆₇	C₂³	semidirect
223. #121×C₆₇	C₂³	semidirect
224. #121×C₆₇	C₂³	semidirect
225. #121×C₆₇	C₂³	semidirect
226. #121×C₆₇	C₂³	semidirect
227. #121×C₆₇	C₂³	semidirect
228. #121×C₆₇	C₂³	semidirect
234. #120×C₆₇	C₂³	semidirect
235. C₄×Q₈×C₆₇	C₂³	semidirect
236. C₄×Q₈×C₆₇	C₂³	semidirect
237. C₄×Q₈×C₆₇	C₂³	semidirect
238. C₄×Q₈×C₆₇	C₂³	semidirect
239. C₄×Q₈×C₆₇	C₂³	semidirect
240. C₄×Q₈×C₆₇	C₂³	semidirect
241. C₄×Q₈×C₆₇	C₂³	semidirect
264. C₄×D₄×C₆₇	C₂³	semidirect
265. C₄×D₄×C₆₇	C₂³	semidirect
266. C₄×D₄×C₆₇	C₂³	semidirect
267. C₄×D₄×C₆₇	C₂³	semidirect
268. C₄×D₄×C₆₇	C₂³	semidirect
269. C₄×D₄×C₆₇	C₂³	semidirect
270. C₄×D₄×C₆₇	C₂³	semidirect
271. C₄×D₄×C₆₇	C₂³	semidirect
272. C₄×D₄×C₆₇	C₂³	semidirect
273. C₄×D₄×C₆₇	C₂³	semidirect
274. C₄×D₄×C₆₇	C₂³	semidirect
275. C₄×D₄×C₆₇	C₂³	semidirect
276. C₄×D₄×C₆₇	C₂³	semidirect
281. #117×C₆₇	C₂³	semidirect
282. #117×C₆₇	C₂³	semidirect
283. #117×C₆₇	C₂³	semidirect
284. #117×C₆₇	C₂³	semidirect
285. #117×C₆₇	C₂³	semidirect
286. #117×C₆₇	C₂³	semidirect
287. #117×C₆₇	C₂³	semidirect
293. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
294. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
295. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
296. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
297. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
307. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
308. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
309. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
318. C₂×C₄²×C₆₇	C₂³	semidirect
319. C₂×C₄²×C₆₇	C₂³	semidirect
350. C₂×D₄×C₆₇	#41	semidirect
477. C₂³×C₆₇	C₂×#41	semidirect
500. D₄×C₆₇	C₂×#41	semidirect
532. C₂×C₄×C₆₇	C₂×#41	semidirect
533. C₂×C₄×C₆₇	H(5,𝔽₂)	semidirect
585. #62773	C₆₇	direct (N × H)
595. #3520	C₂×C₆₇	semidirect
596. #3519	C₂×C₆₇	semidirect
597. #3513	C₂×C₆₇	semidirect
598. #3506	C₂×C₆₇	semidirect
599. #3505	C₂×C₆₇	semidirect
600. #3501	C₂×C₆₇	semidirect
601. #3496	C₂×C₆₇	semidirect
602. #3492	C₂×C₆₇	semidirect
603. #3490	C₂×C₆₇	semidirect
604. #3484	C₂×C₆₇	semidirect
605. #3481	C₂×C₆₇	semidirect
606. #3475	C₂×C₆₇	semidirect
607. D₄×#41	C₂×C₆₇	semidirect
608. #3460	C₂×C₆₇	semidirect
609. #3459	C₂×C₆₇	semidirect
610. #3444	C₂×C₆₇	semidirect
611. C₂×#525	C₂×C₆₇	semidirect
612. C₄×H(5,𝔽₂)	C₂×C₆₇	semidirect
613. C₂²×C₄×D₄	C₂×C₆₇	semidirect
614. C₆₇	#62773	direct (N × H)
616. C₂²×#41	C₂²×C₆₇	semidirect
618. C₂⁴×C₄	C₂²×C₆₇	semidirect
619. #559	C₂²×C₆₇	semidirect
620. #556	C₂²×C₆₇	semidirect
621. #555	C₂²×C₆₇	semidirect
622. #554	C₂²×C₆₇	semidirect
623. #554	C₂²×C₆₇	semidirect
624. #554	C₂²×C₆₇	semidirect
625. #553	C₂²×C₆₇	semidirect
626. #553	C₂²×C₆₇	semidirect
627. #553	C₂²×C₆₇	semidirect
628. #553	C₂²×C₆₇	semidirect
629. #552	C₂²×C₆₇	semidirect
630. #552	C₂²×C₆₇	semidirect
631. #551	C₂²×C₆₇	semidirect
632. #551	C₂²×C₆₇	semidirect
633. #551	C₂²×C₆₇	semidirect
634. #550	C₂²×C₆₇	semidirect
635. D₄×Q₈	C₂²×C₆₇	semidirect
636. #548	C₂²×C₆₇	semidirect
637. #547	C₂²×C₆₇	semidirect
638. #547	C₂²×C₆₇	semidirect
639. #547	C₂²×C₆₇	semidirect
640. #546	C₂²×C₆₇	semidirect
641. #546	C₂²×C₆₇	semidirect
642. #546	C₂²×C₆₇	semidirect
643. #546	C₂²×C₆₇	semidirect
644. #546	C₂²×C₆₇	semidirect
645. #546	C₂²×C₆₇	semidirect
646. D₄²	C₂²×C₆₇	semidirect
647. D₄²	C₂²×C₆₇	semidirect
648. D₄²	C₂²×C₆₇	semidirect
649. #544	C₂²×C₆₇	semidirect
650. #543	C₂²×C₆₇	semidirect
651. #542	C₂²×C₆₇	semidirect
652. #540	C₂²×C₆₇	semidirect
653. #539	C₂²×C₆₇	semidirect
654. #539	C₂²×C₆₇	semidirect
655. #538	C₂²×C₆₇	semidirect
656. #538	C₂²×C₆₇	semidirect
657. #538	C₂²×C₆₇	semidirect
658. #537	C₂²×C₆₇	semidirect
659. #535	C₂²×C₆₇	semidirect
660. #534	C₂²×C₆₇	semidirect
661. #534	C₂²×C₆₇	semidirect
662. #533	C₂²×C₆₇	semidirect
663. #533	C₂²×C₆₇	semidirect
664. #533	C₂²×C₆₇	semidirect
665. #532	C₂²×C₆₇	semidirect
666. #532	C₂²×C₆₇	semidirect
667. #532	C₂²×C₆₇	semidirect
668. #532	C₂²×C₆₇	semidirect
669. #529	C₂²×C₆₇	semidirect
670. #529	C₂²×C₆₇	semidirect
671. #529	C₂²×C₆₇	semidirect
672. #529	C₂²×C₆₇	semidirect
673. #529	C₂²×C₆₇	semidirect
674. #529	C₂²×C₆₇	semidirect
675. #529	C₂²×C₆₇	semidirect
676. #529	C₂²×C₆₇	semidirect
677. #525	C₂²×C₆₇	semidirect
678. #525	C₂²×C₆₇	semidirect
679. #525	C₂²×C₆₇	semidirect
680. #525	C₂²×C₆₇	semidirect
681. #525	C₂²×C₆₇	semidirect
682. #525	C₂²×C₆₇	semidirect
683. #525	C₂²×C₆₇	semidirect
684. #525	C₂²×C₆₇	semidirect
685. #525	C₂²×C₆₇	semidirect
686. #525	C₂²×C₆₇	semidirect
687. #525	C₂²×C₆₇	semidirect
688. C₂×#123	C₂²×C₆₇	semidirect
689. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
690. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
691. C₂×#121	C₂²×C₆₇	semidirect
692. C₂×#121	C₂²×C₆₇	semidirect
693. C₂×#120	C₂²×C₆₇	semidirect
694. #520	C₂²×C₆₇	semidirect
695. #520	C₂²×C₆₇	semidirect
697. #518	C₂²×C₆₇	semidirect
698. #518	C₂²×C₆₇	semidirect
699. C₄×#41	C₂²×C₆₇	semidirect
700. C₄×#41	C₂²×C₆₇	semidirect
701. C₄×#41	C₂²×C₆₇	semidirect
702. C₄×#41	C₂²×C₆₇	semidirect
705. C₂×C₄×D₄	C₂²×C₆₇	semidirect
706. C₂×C₄×D₄	C₂²×C₆₇	semidirect
707. C₂×C₄×D₄	C₂²×C₆₇	semidirect
708. C₂×C₄×D₄	C₂²×C₆₇	semidirect
709. C₂×C₄×D₄	C₂²×C₆₇	semidirect
710. C₂×C₄×D₄	C₂²×C₆₇	semidirect
711. C₂×C₄×D₄	C₂²×C₆₇	semidirect
712. C₂×C₄×D₄	C₂²×C₆₇	semidirect
713. C₂×C₄×D₄	C₂²×C₆₇	semidirect
714. C₂×C₄×D₄	C₂²×C₆₇	semidirect
715. C₂×C₄×D₄	C₂²×C₆₇	semidirect
716. C₂×#117	C₂²×C₆₇	semidirect
717. C₂²×C₄⋊C₄	C₂²×C₆₇	semidirect
718. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
719. C₂²×C₄²	C₂²×C₆₇	semidirect
728. C₂×#41	C₂³×C₆₇	semidirect
729. C₂×#41	C₂³×C₆₇	semidirect
730. C₂²×Q₈	C₂³×C₆₇	semidirect
741. C₂²×D₄	C₂³×C₆₇	semidirect
755. C₂³×C₄	C₂³×C₆₇	semidirect
756. C₄⋊Q₈	C₂³×C₆₇	semidirect
757. C₄⋊Q₈	C₂³×C₆₇	semidirect
758. C₄⋊Q₈	C₂³×C₆₇	semidirect
759. C₄⋊Q₈	C₂³×C₆₇	semidirect
761. #127	C₂³×C₆₇	semidirect
762. #126	C₂³×C₆₇	semidirect
763. #126	C₂³×C₆₇	semidirect
764. #126	C₂³×C₆₇	semidirect
765. #126	C₂³×C₆₇	semidirect
766. #126	C₂³×C₆₇	semidirect
767. #125	C₂³×C₆₇	semidirect
768. #125	C₂³×C₆₇	semidirect
769. #125	C₂³×C₆₇	semidirect
770. #125	C₂³×C₆₇	semidirect
771. #125	C₂³×C₆₇	semidirect
773. #124	C₂³×C₆₇	semidirect
774. #124	C₂³×C₆₇	semidirect
775. #124	C₂³×C₆₇	semidirect
776. #124	C₂³×C₆₇	semidirect
777. #124	C₂³×C₆₇	semidirect
783. #123	C₂³×C₆₇	semidirect
784. #123	C₂³×C₆₇	semidirect
785. #123	C₂³×C₆₇	semidirect
786. #123	C₂³×C₆₇	semidirect
787. #123	C₂³×C₆₇	semidirect
788. #123	C₂³×C₆₇	semidirect
797. C₂²⋊Q₈	C₂³×C₆₇	semidirect
798. C₂²⋊Q₈	C₂³×C₆₇	semidirect
799. C₂²⋊Q₈	C₂³×C₆₇	semidirect
800. C₂²⋊Q₈	C₂³×C₆₇	semidirect
801. C₂²⋊Q₈	C₂³×C₆₇	semidirect
802. C₂²⋊Q₈	C₂³×C₆₇	semidirect
803. C₂²⋊Q₈	C₂³×C₆₇	semidirect
804. C₂²⋊Q₈	C₂³×C₆₇	semidirect
817. #121	C₂³×C₆₇	semidirect
818. #121	C₂³×C₆₇	semidirect
819. #121	C₂³×C₆₇	semidirect
820. #121	C₂³×C₆₇	semidirect
821. #121	C₂³×C₆₇	semidirect
822. #121	C₂³×C₆₇	semidirect
823. #121	C₂³×C₆₇	semidirect
829. #120	C₂³×C₆₇	semidirect
830. C₄×Q₈	C₂³×C₆₇	semidirect
831. C₄×Q₈	C₂³×C₆₇	semidirect
832. C₄×Q₈	C₂³×C₆₇	semidirect
833. C₄×Q₈	C₂³×C₆₇	semidirect
834. C₄×Q₈	C₂³×C₆₇	semidirect
835. C₄×Q₈	C₂³×C₆₇	semidirect
836. C₄×Q₈	C₂³×C₆₇	semidirect
859. C₄×D₄	C₂³×C₆₇	semidirect
860. C₄×D₄	C₂³×C₆₇	semidirect
861. C₄×D₄	C₂³×C₆₇	semidirect
862. C₄×D₄	C₂³×C₆₇	semidirect
863. C₄×D₄	C₂³×C₆₇	semidirect
864. C₄×D₄	C₂³×C₆₇	semidirect
865. C₄×D₄	C₂³×C₆₇	semidirect
866. C₄×D₄	C₂³×C₆₇	semidirect
867. C₄×D₄	C₂³×C₆₇	semidirect
868. C₄×D₄	C₂³×C₆₇	semidirect
869. C₄×D₄	C₂³×C₆₇	semidirect
870. C₄×D₄	C₂³×C₆₇	semidirect
871. C₄×D₄	C₂³×C₆₇	semidirect
876. #117	C₂³×C₆₇	semidirect
877. #117	C₂³×C₆₇	semidirect
878. #117	C₂³×C₆₇	semidirect
879. #117	C₂³×C₆₇	semidirect
880. #117	C₂³×C₆₇	semidirect
881. #117	C₂³×C₆₇	semidirect
882. #117	C₂³×C₆₇	semidirect
888. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
889. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
890. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
891. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
892. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
902. C₂×C₂²⋊C₄	C₂³×C₆₇	semidirect
903. C₂×C₂²⋊C₄	C₂³×C₆₇	semidirect
904. C₂×C₂²⋊C₄	C₂³×C₆₇	semidirect
913. C₂×C₄²	C₂³×C₆₇	semidirect
914. C₂×C₄²	C₂³×C₆₇	semidirect
945. C₂×D₄	#41×C₆₇	semidirect
1072. C₂³	C₂×#41×C₆₇	semidirect
1095. D₄	C₂×#41×C₆₇	semidirect
1127. C₂×C₄	C₂×#41×C₆₇	semidirect
1128. C₂×C₄	H(5,𝔽₂)×C₆₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₆₇×#3520	2
C₆₇×#3519	2
C₆₇×#3513	2
C₆₇×#3506	2
C₆₇×#3505	2
C₆₇×#3501	2
C₆₇×#3496	2
C₆₇×#3492	2
C₆₇×#3490	2
C₆₇×#3484	2
C₆₇×#3481	2
C₆₇×#3475	2
D₄×#41×C₆₇	2
C₆₇×#3460	2
C₆₇×#3459	2
C₆₇×#3444	2
C₂×#525×C₆₇	2
C₄×H(5,𝔽₂)×C₆₇	2
C₂²×C₄×D₄×C₆₇	2
#62773	67

Subgroups — C67×#62773 #30742024

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#62773 #30742024