Subgroups — C₆₇×#61078 #30740329

Order 17152.

2694 conjugacy classes of subgroups.

The subgroup lattice has 1402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#578×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#575×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3489	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3487	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#3285	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3284	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3278	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3275	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3271	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3270	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3269	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3268	C₂	1	2	yes	maximal, complemented
13	C₆₇×#3154	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3062	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3056	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3045	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3044	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#3013	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#3010	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#3002	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#452×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₇×#2947	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#2933	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	1	yes	characteristic, complemented
26	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
27	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
28	#578×C₆₇	—	2	8	no	—
29	#575×C₆₇	—	2	8	no	—
30	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×#137×C₆₇	C₂²	1	2	yes	—
32	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
34	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
35	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic, complemented
36	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	—
38	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic
39	C₂×#135×C₆₇	C₂²	1	2	yes	—
40	C₂×#135×C₆₇	C₂²	1	2	yes	—
41	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
43	C₂×#135×C₆₇	C₂²	1	2	yes	complemented
44	C₂²×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
45	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
46	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
47	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic, complemented
48	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
49	#550×C₆₇	—	2	1	no	—
50	#550×C₆₇	—	2	1	no	—
51	#550×C₆₇	C₂²	1	2	yes	—
52	#550×C₆₇	C₂²	1	2	yes	complemented
53	D₄×Q₈×C₆₇	C₂²	1	2	yes	complemented
54	#548×C₆₇	—	2	1	no	—
55	#548×C₆₇	—	2	1	no	—
56	#548×C₆₇	C₂²	1	2	yes	—
57	#548×C₆₇	C₂²	1	2	yes	complemented
58	#548×C₆₇	C₂²	1	2	yes	complemented
59	#547×C₆₇	—	2	2	no	—
60	#547×C₆₇	C₂²	1	2	yes	complemented
61	#546×C₆₇	—	2	2	no	—
62	#546×C₆₇	C₂²	1	2	yes	complemented
63	#537×C₆₇	—	2	1	no	—
64	#537×C₆₇	C₂²	1	1	yes	characteristic
65	#536×C₆₇	—	2	1	no	—
66	#536×C₆₇	C₂²	1	1	yes	characteristic
67	#535×C₆₇	—	2	2	no	—
68	#535×C₆₇	C₂²	1	1	yes	characteristic, complemented
69	#535×C₆₇	C₂²	1	1	yes	characteristic, complemented
70	#525×C₆₇	—	2	2	no	—
71	#525×C₆₇	—	2	1	no	—
72	#525×C₆₇	C₂²	1	1	yes	characteristic
73	#525×C₆₇	C₂²	1	1	yes	characteristic
74	C₂×C₂²⋊Q₈×C₆₇	—	2	1	no	—
75	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
76	#520×C₆₇	C₂²	1	1	yes	characteristic
77	#519×C₆₇	C₂²	1	1	yes	characteristic, complemented
78	#497×C₆₇	C₂²	1	2	yes	complemented
79	#496×C₆₇	C₂²	1	2	yes	complemented
80	#495×C₆₇	C₂²	1	2	yes	complemented
81	#492×C₆₇	C₂²	1	2	yes	complemented
82	#470×C₆₇	C₂²	1	2	yes	complemented
83	#469×C₆₇	C₂²	1	2	yes	complemented
84	#468×C₆₇	C₂²	1	2	yes	complemented
85	#468×C₆₇	C₂²	1	2	yes	complemented
86	#467×C₆₇	C₂²	1	2	yes	complemented
87	#466×C₆₇	C₂²	1	2	yes	complemented
88	#465×C₆₇	C₂²	1	2	yes	complemented
89	#465×C₆₇	C₂²	1	2	yes	complemented
90	#464×C₆₇	C₂²	1	2	yes	complemented
91	#464×C₆₇	C₂²	1	2	yes	complemented
92	#464×C₆₇	C₂²	1	2	yes	complemented
93	#463×C₆₇	C₂²	1	2	yes	complemented
94	#462×C₆₇	C₂²	1	2	yes	complemented
95	#462×C₆₇	C₂²	1	2	yes	complemented
96	#460×C₆₇	C₂²	1	2	yes	complemented
97	#459×C₆₇	C₂²	1	2	yes	complemented
98	#452×C₆₇	C₂²	1	2	yes	—
99	#452×C₆₇	C₂²	1	2	yes	—
100	#452×C₆₇	C₂²	1	2	yes	complemented
101	#452×C₆₇	C₂²	1	1	yes	characteristic, complemented
102	#452×C₆₇	C₂²	1	2	yes	complemented
103	#452×C₆₇	C₂²	1	2	yes	complemented
104	#452×C₆₇	C₂²	1	1	yes	characteristic, complemented
105	#451×C₆₇	C₂²	1	2	yes	complemented
106	#451×C₆₇	C₂²	1	1	yes	characteristic, complemented
107	#450×C₆₇	C₂²	1	1	yes	characteristic, complemented
108	#449×C₆₇	C₂²	1	2	yes	complemented
109	#449×C₆₇	C₂²	1	2	yes	complemented
110	#449×C₆₇	C₂²	1	2	yes	complemented
111	#449×C₆₇	C₂²	1	1	yes	characteristic, complemented
112	#449×C₆₇	C₂²	1	1	yes	characteristic, complemented
113	#448×C₆₇	C₂²	1	2	yes	complemented
114	#448×C₆₇	C₂²	1	2	yes	complemented
115	#448×C₆₇	C₂²	1	2	yes	complemented
116	#448×C₆₇	C₂²	1	1	yes	characteristic, complemented
117	#447×C₆₇	C₂²	1	1	yes	characteristic, complemented
118	#441×C₆₇	C₂²	1	2	yes	complemented
119	#440×C₆₇	C₂²	1	2	yes	complemented
120	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
121	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
122	#436×C₆₇	C₂²	1	2	yes	complemented
123	#435×C₆₇	C₂²	1	2	yes	complemented
124	#435×C₆₇	C₂²	1	2	yes	complemented
125	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
126	#428×C₆₇	C₂²	1	1	yes	characteristic, complemented
127	#424×C₆₇	C₂²	1	1	yes	characteristic, complemented
128	#419×C₆₇	C₂²	1	1	yes	characteristic, complemented
129	#417×C₆₇	C₂²	1	1	yes	characteristic, complemented
130	#416×C₆₇	C₂²	1	1	yes	characteristic
131	#416×C₆₇	C₂²	1	1	yes	characteristic
132	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic, complemented
133	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic, complemented
134	#408×C₆₇	C₂²	1	1	yes	characteristic, complemented
135	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
136	#405×C₆₇	C₂²	1	1	yes	characteristic, complemented
137	2₋¹⁺⁴×C₆₇	—	2	4	no	—
138	2₋¹⁺⁴×C₆₇	—	2	4	no	—
139	2₋¹⁺⁴×C₆₇	—	4	2	no	—
140	2₋¹⁺⁴×C₆₇	—	4	2	no	—
141	C₂×#41×C₆₇	—	2	2	no	—
142	C₂×#41×C₆₇	—	2	1	no	—
143	C₂×#41×C₆₇	—	2	2	no	—
144	C₂×#41×C₆₇	—	2	1	no	—
145	C₂×#41×C₆₇	—	2	1	no	—
146	C₂×#41×C₆₇	—	2	1	no	—
147	C₂×#41×C₆₇	—	2	1	no	—
148	C₂×#41×C₆₇	—	2	1	no	—
149	C₂×#41×C₆₇	—	2	4	no	—
150	C₂×#41×C₆₇	—	2	4	no	—
151	C₂×#41×C₆₇	—	4	2	no	—
152	C₂×#41×C₆₇	—	4	2	no	—
153	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
154	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
155	C₂×#41×C₆₇	C₂³	1	2	yes	—
156	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
157	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
158	C₂×#41×C₆₇	C₂³	1	2	yes	—
159	C₂×#41×C₆₇	C₂³	1	2	yes	—
160	C₂×#41×C₆₇	C₂³	1	2	yes	—
161	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
162	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
163	C₂²×Q₈×C₆₇	—	2	1	no	—
164	C₂²×Q₈×C₆₇	—	2	1	no	—
165	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
166	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
167	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
168	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
169	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
170	C₂²×D₄×C₆₇	—	2	1	no	—
171	C₂²×D₄×C₆₇	—	2	1	no	—
172	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
173	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
174	C₂³×C₄×C₆₇	—	2	1	no	—
175	C₂³×C₄×C₆₇	—	2	1	no	—
176	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
177	#137×C₆₇	—	2	4	no	—
178	#137×C₆₇	—	2	8	no	—
179	#137×C₆₇	—	2	8	no	—
180	#137×C₆₇	—	2	8	no	—
181	#137×C₆₇	—	2	4	no	—
182	#137×C₆₇	D₄	1	8	yes	complemented
183	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
184	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
185	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
186	#135×C₆₇	—	2	4	no	—
187	#135×C₆₇	—	2	8	no	—
188	#135×C₆₇	—	2	8	no	—
189	#135×C₆₇	—	2	8	no	—
190	#135×C₆₇	—	4	2	no	—
191	C₂×Q₁₆×C₆₇	—	2	4	no	—
192	C₂×Q₁₆×C₆₇	—	2	8	no	—
193	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
194	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
195	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
196	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
197	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
198	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
199	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
200	C₂×SD₁₆×C₆₇	—	4	2	no	—
201	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
202	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
203	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
204	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
205	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
206	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
207	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
208	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
209	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
210	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
211	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
212	C₂×D₈×C₆₇	C₂³	1	2	yes	—
213	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
214	C₂×D₈×C₆₇	C₂³	1	2	yes	—
215	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
216	#131×C₆₇	—	2	4	no	—
217	C₂×M₁₆×C₆₇	—	2	4	no	—
218	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
219	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
220	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
221	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
222	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
223	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
224	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
225	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
226	C₄⋊Q₈×C₆₇	—	2	2	no	—
227	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
228	#127×C₆₇	—	2	2	no	—
229	#127×C₆₇	—	2	2	no	—
230	#127×C₆₇	—	2	1	no	—
231	#127×C₆₇	C₂³	1	2	yes	—
232	#124×C₆₇	—	2	1	no	—
233	#124×C₆₇	—	2	2	no	—
234	#124×C₆₇	—	2	2	no	—
235	#124×C₆₇	—	2	2	no	—
236	#124×C₆₇	C₂³	1	2	yes	—
237	#124×C₆₇	C₂³	1	2	yes	—
238	#123×C₆₇	—	2	1	no	—
239	#123×C₆₇	—	2	2	no	—
240	#123×C₆₇	—	2	2	no	—
241	#123×C₆₇	—	2	2	no	—
242	#123×C₆₇	—	2	2	no	—
243	#123×C₆₇	D₄	1	2	yes	—
244	C₂²⋊Q₈×C₆₇	—	2	1	no	—
245	C₂²⋊Q₈×C₆₇	—	2	1	no	—
246	C₂²⋊Q₈×C₆₇	—	2	1	no	—
247	C₂²⋊Q₈×C₆₇	—	2	1	no	—
248	C₂²⋊Q₈×C₆₇	—	2	2	no	—
249	C₂²⋊Q₈×C₆₇	—	2	1	no	—
250	C₂²⋊Q₈×C₆₇	—	2	2	no	—
251	C₂²⋊Q₈×C₆₇	—	2	2	no	—
252	C₂²⋊Q₈×C₆₇	—	2	2	no	—
253	C₂²⋊Q₈×C₆₇	—	2	2	no	—
254	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
255	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
256	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
257	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
258	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
259	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
260	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
261	#121×C₆₇	—	2	1	no	—
262	#121×C₆₇	—	2	2	no	—
263	#121×C₆₇	—	2	2	no	—
264	#121×C₆₇	—	2	2	no	—
265	#121×C₆₇	—	2	2	no	—
266	#121×C₆₇	—	2	2	no	—
267	#121×C₆₇	—	2	1	no	—
268	#121×C₆₇	—	2	1	no	—
269	#121×C₆₇	—	2	2	no	—
270	#121×C₆₇	—	2	2	no	—
271	#121×C₆₇	—	2	2	no	—
272	#121×C₆₇	—	2	2	no	—
273	#121×C₆₇	—	2	2	no	—
274	#121×C₆₇	D₄	1	1	yes	characteristic
275	#121×C₆₇	D₄	1	1	yes	characteristic
276	#121×C₆₇	C₂³	1	2	yes	—
277	#121×C₆₇	C₂³	1	2	yes	—
278	#121×C₆₇	C₂³	1	2	yes	—
279	#121×C₆₇	C₂³	1	1	yes	characteristic
280	#121×C₆₇	C₂³	1	1	yes	characteristic
281	#120×C₆₇	—	2	1	no	—
282	#120×C₆₇	—	2	2	no	—
283	#120×C₆₇	—	2	2	no	—
284	#120×C₆₇	—	2	2	no	—
285	#120×C₆₇	D₄	1	2	yes	—
286	C₄×Q₈×C₆₇	—	2	1	no	—
287	C₄×Q₈×C₆₇	—	2	1	no	—
288	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
289	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
290	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
291	C₄×D₄×C₆₇	—	2	2	no	—
292	C₄×D₄×C₆₇	—	2	1	no	—
293	C₄×D₄×C₆₇	—	2	1	no	—
294	C₄×D₄×C₆₇	—	2	2	no	—
295	C₄×D₄×C₆₇	—	2	2	no	—
296	C₄×D₄×C₆₇	—	2	2	no	—
297	C₄×D₄×C₆₇	—	2	2	no	—
298	C₄×D₄×C₆₇	—	2	2	no	—
299	C₄×D₄×C₆₇	—	2	2	no	—
300	C₄×D₄×C₆₇	C₂³	1	2	yes	—
301	C₄×D₄×C₆₇	C₂³	1	2	yes	—
302	C₄×D₄×C₆₇	C₂³	1	2	yes	—
303	#117×C₆₇	—	2	1	no	—
304	#117×C₆₇	—	2	2	no	—
305	#117×C₆₇	C₂³	1	1	yes	characteristic
306	#117×C₆₇	C₂³	1	1	yes	characteristic
307	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
308	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
309	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
310	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
311	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
312	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
313	#107×C₆₇	C₂³	1	2	yes	—
314	#106×C₆₇	C₂³	1	2	yes	—
315	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
316	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
317	#103×C₆₇	C₂³	1	1	yes	characteristic
318	#103×C₆₇	C₂³	1	1	yes	characteristic
319	#103×C₆₇	C₂³	1	2	yes	—
320	#103×C₆₇	C₂³	1	2	yes	—
321	#103×C₆₇	C₂³	1	2	yes	—
322	#103×C₆₇	C₂³	1	2	yes	—
323	#103×C₆₇	C₂³	1	1	yes	characteristic
324	#103×C₆₇	C₂³	1	2	yes	—
325	#103×C₆₇	C₂³	1	1	yes	characteristic
326	#102×C₆₇	C₂³	1	1	yes	characteristic
327	#102×C₆₇	C₂³	1	1	yes	characteristic
328	#102×C₆₇	C₂³	1	1	yes	characteristic
329	#102×C₆₇	C₂³	1	2	yes	—
330	#102×C₆₇	C₂³	1	2	yes	—
331	#102×C₆₇	C₂³	1	2	yes	—
332	#102×C₆₇	C₂³	1	1	yes	characteristic
333	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
334	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
335	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
336	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
337	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
338	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
339	#97×C₆₇	C₂³	1	2	yes	—
340	C₄×C₈×C₆₇	C₂³	1	2	yes	—
341	C₂⁴×C₆₇	—	2	1	no	—
342	C₂⁴×C₆₇	—	2	1	no	—
343	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
344	#41×C₆₇	—	2	2	no	—
345	#41×C₆₇	—	2	2	no	—
346	#41×C₆₇	—	2	2	no	—
347	#41×C₆₇	—	2	2	no	—
348	#41×C₆₇	—	2	4	no	—
349	#41×C₆₇	—	2	4	no	—
350	#41×C₆₇	—	2	4	no	—
351	#41×C₆₇	—	2	2	no	—
352	#41×C₆₇	—	2	4	no	—
353	#41×C₆₇	—	2	2	no	—
354	#41×C₆₇	—	2	2	no	—
355	#41×C₆₇	—	2	2	no	—
356	#41×C₆₇	—	2	2	no	—
357	#41×C₆₇	—	4	4	no	—
358	#41×C₆₇	—	4	2	no	—
359	#41×C₆₇	—	4	1	no	—
360	#41×C₆₇	—	4	2	no	—
361	#41×C₆₇	—	4	1	no	—
362	#41×C₆₇	—	4	2	no	—
363	#41×C₆₇	—	4	2	no	—
364	#41×C₆₇	—	4	4	no	—
365	#41×C₆₇	—	4	8	no	—
366	#41×C₆₇	—	4	4	no	—
367	#41×C₆₇	—	4	4	no	—
368	#41×C₆₇	—	4	4	no	—
369	#41×C₆₇	—	4	8	no	—
370	#41×C₆₇	—	4	4	no	—
371	#41×C₆₇	C₂×D₄	1	4	yes	—
372	C₂×Q₈×C₆₇	—	2	1	no	—
373	C₂×Q₈×C₆₇	—	2	1	no	—
374	C₂×Q₈×C₆₇	—	2	2	no	—
375	C₂×Q₈×C₆₇	—	2	2	no	—
376	C₂×Q₈×C₆₇	—	2	1	no	—
377	C₂×Q₈×C₆₇	—	2	2	no	—
378	C₂×Q₈×C₆₇	—	2	4	no	—
379	C₂×Q₈×C₆₇	—	2	4	no	—
380	C₂×Q₈×C₆₇	—	2	2	no	—
381	C₂×Q₈×C₆₇	—	2	2	no	—
382	C₂×Q₈×C₆₇	—	2	2	no	—
383	C₂×Q₈×C₆₇	—	4	1	no	—
384	C₂×Q₈×C₆₇	—	4	2	no	—
385	C₂×Q₈×C₆₇	—	4	2	no	—
386	C₂×Q₈×C₆₇	—	4	4	no	—
387	C₂×Q₈×C₆₇	—	4	4	no	—
388	C₂×Q₈×C₆₇	C₂×D₄	1	4	yes	—
389	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
390	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
391	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
392	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
393	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
394	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
395	C₂×D₄×C₆₇	—	2	1	no	—
396	C₂×D₄×C₆₇	—	2	2	no	—
397	C₂×D₄×C₆₇	—	2	1	no	—
398	C₂×D₄×C₆₇	—	2	2	no	—
399	C₂×D₄×C₆₇	—	2	1	no	—
400	C₂×D₄×C₆₇	—	2	1	no	—
401	C₂×D₄×C₆₇	—	2	1	no	—
402	C₂×D₄×C₆₇	—	2	2	no	—
403	C₂×D₄×C₆₇	—	2	2	no	—
404	C₂×D₄×C₆₇	—	2	2	no	—
405	C₂×D₄×C₆₇	—	2	2	no	—
406	C₂×D₄×C₆₇	—	2	2	no	—
407	C₂×D₄×C₆₇	—	2	2	no	—
408	C₂×D₄×C₆₇	—	2	1	no	—
409	C₂×D₄×C₆₇	—	2	1	no	—
410	C₂×D₄×C₆₇	—	2	2	no	—
411	C₂×D₄×C₆₇	—	2	1	no	—
412	C₂×D₄×C₆₇	—	2	1	no	—
413	C₂×D₄×C₆₇	—	2	2	no	—
414	C₂×D₄×C₆₇	—	2	2	no	—
415	C₂×D₄×C₆₇	—	2	2	no	—
416	C₂×D₄×C₆₇	—	4	1	no	—
417	C₂×D₄×C₆₇	—	4	4	no	—
418	C₂×D₄×C₆₇	—	4	4	no	—
419	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
420	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
421	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
422	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
423	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
424	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
425	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
426	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
427	C₂²×C₄×C₆₇	—	2	1	no	—
428	C₂²×C₄×C₆₇	—	2	1	no	—
429	C₂²×C₄×C₆₇	—	2	2	no	—
430	C₂²×C₄×C₆₇	—	2	2	no	—
431	C₂²×C₄×C₆₇	—	2	1	no	—
432	C₂²×C₄×C₆₇	—	2	2	no	—
433	C₂²×C₄×C₆₇	—	2	2	no	—
434	C₂²×C₄×C₆₇	—	2	1	no	—
435	C₂²×C₄×C₆₇	—	2	1	no	—
436	C₂²×C₄×C₆₇	—	2	2	no	—
437	C₂²×C₄×C₆₇	—	2	1	no	—
438	C₂²×C₄×C₆₇	—	2	2	no	—
439	C₂²×C₄×C₆₇	—	2	1	no	—
440	C₂²×C₄×C₆₇	—	2	2	no	—
441	C₂²×C₄×C₆₇	—	2	2	no	—
442	C₂²×C₄×C₆₇	—	2	1	no	—
443	C₂²×C₄×C₆₇	—	2	1	no	—
444	C₂²×C₄×C₆₇	—	2	2	no	—
445	C₂²×C₄×C₆₇	—	4	4	no	—
446	C₂²×C₄×C₆₇	—	4	4	no	—
447	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
448	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
449	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
450	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
451	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
452	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
453	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
454	Q₁₆×C₆₇	—	2	2	no	—
455	Q₁₆×C₆₇	—	2	4	no	—
456	Q₁₆×C₆₇	—	2	4	no	—
457	Q₁₆×C₆₇	—	2	4	no	—
458	Q₁₆×C₆₇	—	2	4	no	—
459	Q₁₆×C₆₇	—	4	1	no	—
460	Q₁₆×C₆₇	C₂×D₄	1	8	yes	—
461	SD₁₆×C₆₇	—	2	4	no	—
462	SD₁₆×C₆₇	—	2	4	no	—
463	SD₁₆×C₆₇	—	2	2	no	—
464	SD₁₆×C₆₇	—	2	2	no	—
465	SD₁₆×C₆₇	—	2	4	no	—
466	SD₁₆×C₆₇	—	2	4	no	—
467	SD₁₆×C₆₇	—	4	2	no	—
468	SD₁₆×C₆₇	—	4	2	no	—
469	SD₁₆×C₆₇	—	4	1	no	—
470	SD₁₆×C₆₇	—	4	1	no	—
471	SD₁₆×C₆₇	C₂×D₄	1	8	yes	—
472	D₈×C₆₇	—	2	2	no	—
473	D₈×C₆₇	—	2	4	no	—
474	D₈×C₆₇	—	2	4	no	—
475	D₈×C₆₇	—	4	1	no	—
476	M₁₆×C₆₇	—	2	2	no	—
477	M₁₆×C₆₇	—	2	4	no	—
478	M₁₆×C₆₇	—	2	4	no	—
479	M₁₆×C₆₇	C₂×D₄	1	4	yes	—
480	C₂×C₈×C₆₇	—	2	2	no	—
481	C₂×C₈×C₆₇	—	2	2	no	—
482	C₂×C₈×C₆₇	—	2	4	no	—
483	C₂×C₈×C₆₇	—	2	4	no	—
484	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
485	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
486	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
487	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
488	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
489	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
490	C₄⋊C₄×C₆₇	—	2	2	no	—
491	C₄⋊C₄×C₆₇	—	2	1	no	—
492	C₄⋊C₄×C₆₇	—	2	2	no	—
493	C₄⋊C₄×C₆₇	—	2	2	no	—
494	C₄⋊C₄×C₆₇	—	2	2	no	—
495	C₄⋊C₄×C₆₇	—	2	2	no	—
496	C₄⋊C₄×C₆₇	—	2	2	no	—
497	C₄⋊C₄×C₆₇	—	2	2	no	—
498	C₄⋊C₄×C₆₇	—	2	1	no	—
499	C₄⋊C₄×C₆₇	—	2	1	no	—
500	C₄⋊C₄×C₆₇	—	2	2	no	—
501	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
502	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
503	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
504	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
505	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
506	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
507	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
508	C₂²⋊C₄×C₆₇	—	2	2	no	—
509	C₂²⋊C₄×C₆₇	—	2	2	no	—
510	C₂²⋊C₄×C₆₇	—	2	1	no	—
511	C₂²⋊C₄×C₆₇	—	2	1	no	—
512	C₂²⋊C₄×C₆₇	—	2	1	no	—
513	C₂²⋊C₄×C₆₇	—	2	2	no	—
514	C₂²⋊C₄×C₆₇	—	2	2	no	—
515	C₂²⋊C₄×C₆₇	—	2	2	no	—
516	C₂²⋊C₄×C₆₇	—	2	2	no	—
517	C₂²⋊C₄×C₆₇	—	2	1	no	—
518	C₂²⋊C₄×C₆₇	—	2	1	no	—
519	C₂²⋊C₄×C₆₇	—	2	2	no	—
520	C₂²⋊C₄×C₆₇	—	2	2	no	—
521	C₂²⋊C₄×C₆₇	—	2	2	no	—
522	C₂²⋊C₄×C₆₇	—	2	2	no	—
523	C₂²⋊C₄×C₆₇	—	2	2	no	—
524	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
525	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
526	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
527	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
528	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
529	C₄²×C₆₇	—	2	2	no	—
530	C₄²×C₆₇	—	2	2	no	—
531	C₄²×C₆₇	—	2	2	no	—
532	C₄²×C₆₇	—	2	1	no	—
533	C₄²×C₆₇	C₂⁴	1	2	yes	—
534	C₂³×C₆₇	—	2	1	no	—
535	C₂³×C₆₇	—	2	2	no	—
536	C₂³×C₆₇	—	2	1	no	—
537	C₂³×C₆₇	—	2	2	no	—
538	C₂³×C₆₇	—	2	1	no	—
539	C₂³×C₆₇	—	4	1	no	—
540	C₂³×C₆₇	—	4	1	no	—
541	C₂³×C₆₇	—	4	2	no	—
542	C₂³×C₆₇	—	4	2	no	—
543	C₂³×C₆₇	—	4	2	no	—
544	C₂³×C₆₇	—	8	1	no	—
545	C₂³×C₆₇	—	8	1	no	—
546	C₂³×C₆₇	—	8	1	no	—
547	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
548	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
549	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
550	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
551	Q₈×C₆₇	—	2	4	no	—
552	Q₈×C₆₇	—	2	2	no	—
553	Q₈×C₆₇	—	2	2	no	—
554	Q₈×C₆₇	—	2	1	no	—
555	Q₈×C₆₇	—	2	1	no	—
556	Q₈×C₆₇	—	2	1	no	—
557	Q₈×C₆₇	—	2	2	no	—
558	Q₈×C₆₇	—	2	2	no	—
559	Q₈×C₆₇	—	2	1	no	—
560	Q₈×C₆₇	—	2	1	no	—
561	Q₈×C₆₇	—	4	4	no	—
562	Q₈×C₆₇	—	4	4	no	—
563	Q₈×C₆₇	—	4	2	no	—
564	Q₈×C₆₇	—	4	2	no	—
565	Q₈×C₆₇	C₂²×D₄	1	2	yes	—
566	Q₈×C₆₇	C₂²×D₄	1	4	yes	—
567	D₄×C₆₇	—	2	4	no	—
568	D₄×C₆₇	—	2	4	no	—
569	D₄×C₆₇	—	2	2	no	—
570	D₄×C₆₇	—	2	2	no	—
571	D₄×C₆₇	—	2	1	no	—
572	D₄×C₆₇	—	2	1	no	—
573	D₄×C₆₇	—	2	1	no	—
574	D₄×C₆₇	—	2	1	no	—
575	D₄×C₆₇	—	2	1	no	—
576	D₄×C₆₇	—	2	2	no	—
577	D₄×C₆₇	—	4	2	no	—
578	D₄×C₆₇	—	4	2	no	—
579	D₄×C₆₇	—	4	2	no	—
580	D₄×C₆₇	—	4	2	no	—
581	D₄×C₆₇	—	4	4	no	—
582	D₄×C₆₇	—	4	4	no	—
583	D₄×C₆₇	—	4	4	no	—
584	D₄×C₆₇	—	4	2	no	—
585	D₄×C₆₇	—	4	4	no	—
586	D₄×C₆₇	—	4	2	no	—
587	D₄×C₆₇	—	4	2	no	—
588	D₄×C₆₇	—	4	2	no	—
589	D₄×C₆₇	—	8	2	no	—
590	D₄×C₆₇	—	8	2	no	—
591	D₄×C₆₇	—	8	2	no	—
592	D₄×C₆₇	—	8	2	no	—
593	D₄×C₆₇	—	8	1	no	—
594	D₄×C₆₇	—	8	2	no	—
595	D₄×C₆₇	—	8	1	no	—
596	D₄×C₆₇	C₂²×D₄	1	2	yes	—
597	C₂×C₄×C₆₇	—	2	2	no	—
598	C₂×C₄×C₆₇	—	2	4	no	—
599	C₂×C₄×C₆₇	—	2	2	no	—
600	C₂×C₄×C₆₇	—	2	1	no	—
601	C₂×C₄×C₆₇	—	2	2	no	—
602	C₂×C₄×C₆₇	—	2	2	no	—
603	C₂×C₄×C₆₇	—	2	4	no	—
604	C₂×C₄×C₆₇	—	2	1	no	—
605	C₂×C₄×C₆₇	—	2	2	no	—
606	C₂×C₄×C₆₇	—	2	1	no	—
607	C₂×C₄×C₆₇	—	2	1	no	—
608	C₂×C₄×C₆₇	—	2	1	no	—
609	C₂×C₄×C₆₇	—	2	2	no	—
610	C₂×C₄×C₆₇	—	2	1	no	—
611	C₂×C₄×C₆₇	—	2	1	no	—
612	C₂×C₄×C₆₇	—	2	2	no	—
613	C₂×C₄×C₆₇	—	2	1	no	—
614	C₂×C₄×C₆₇	—	2	2	no	—
615	C₂×C₄×C₆₇	—	2	1	no	—
616	C₂×C₄×C₆₇	—	4	2	no	—
617	C₂×C₄×C₆₇	—	4	4	no	—
618	C₂×C₄×C₆₇	—	4	4	no	—
619	C₂×C₄×C₆₇	—	4	4	no	—
620	C₂×C₄×C₆₇	—	4	2	no	—
621	C₂×C₄×C₆₇	—	4	2	no	—
622	C₂×C₄×C₆₇	—	4	4	no	—
623	C₂×C₄×C₆₇	—	4	4	no	—
624	C₂×C₄×C₆₇	—	4	4	no	—
625	C₂×C₄×C₆₇	—	4	2	no	—
626	C₂×C₄×C₆₇	—	4	2	no	—
627	C₂×C₄×C₆₇	—	4	2	no	—
628	C₂×C₄×C₆₇	—	8	2	no	—
629	C₂×C₄×C₆₇	—	8	1	no	—
630	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
631	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
632	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
633	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
634	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
635	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
636	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
637	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
638	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
639	C₈×C₆₇	—	2	1	no	—
640	C₈×C₆₇	—	2	2	no	—
641	C₈×C₆₇	—	2	1	no	—
642	C₈×C₆₇	—	2	1	no	—
643	C₈×C₆₇	—	2	1	no	—
644	C₈×C₆₇	C₂²×D₄	1	4	yes	—
645	C₂²×C₆₇	—	2	1	no	—
646	C₂²×C₆₇	—	2	1	no	—
647	C₂²×C₆₇	—	2	1	no	—
648	C₂²×C₆₇	—	2	2	no	—
649	C₂²×C₆₇	—	2	1	no	—
650	C₂²×C₆₇	—	2	1	no	—
651	C₂²×C₆₇	—	2	2	no	—
652	C₂²×C₆₇	—	2	1	no	—
653	C₂²×C₆₇	—	2	1	no	—
654	C₂²×C₆₇	—	2	1	no	—
655	C₂²×C₆₇	—	2	2	no	—
656	C₂²×C₆₇	—	2	2	no	—
657	C₂²×C₆₇	—	4	1	no	—
658	C₂²×C₆₇	—	4	1	no	—
659	C₂²×C₆₇	—	4	1	no	—
660	C₂²×C₆₇	—	4	2	no	—
661	C₂²×C₆₇	—	4	1	no	—
662	C₂²×C₆₇	—	4	1	no	—
663	C₂²×C₆₇	—	4	2	no	—
664	C₂²×C₆₇	—	4	1	no	—
665	C₂²×C₆₇	—	4	1	no	—
666	C₂²×C₆₇	—	4	2	no	—
667	C₂²×C₆₇	—	4	1	no	—
668	C₂²×C₆₇	—	8	2	no	—
669	C₂²×C₆₇	—	8	4	no	—
670	C₂²×C₆₇	—	8	4	no	—
671	C₂²×C₆₇	D₄²	1	2	yes	—
672	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
673	C₄×C₆₇	—	2	2	no	—
674	C₄×C₆₇	—	2	2	no	—
675	C₄×C₆₇	—	2	1	no	—
676	C₄×C₆₇	—	2	1	no	—
677	C₄×C₆₇	—	2	2	no	—
678	C₄×C₆₇	—	2	4	no	—
679	C₄×C₆₇	—	2	2	no	—
680	C₄×C₆₇	—	4	2	no	—
681	C₄×C₆₇	—	4	1	no	—
682	C₄×C₆₇	—	4	1	no	—
683	C₄×C₆₇	—	4	1	no	—
684	C₄×C₆₇	—	4	1	no	—
685	C₄×C₆₇	—	4	2	no	—
686	C₄×C₆₇	D₄²	1	2	yes	—
687	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
688	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
689	#61078	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
690	C₂×C₆₇	—	2	2	no	—
691	C₂×C₆₇	—	4	2	no	—
692	C₂×C₆₇	—	4	1	no	—
693	C₂×C₆₇	—	4	1	no	—
694	C₂×C₆₇	—	4	2	no	—
695	C₂×C₆₇	—	8	1	no	—
696	C₂×C₆₇	—	8	2	no	—
697	C₂×C₆₇	—	8	1	no	—
698	C₂×C₆₇	C₂×D₄²	1	1	yes	characteristic
699	C₂×C₆₇	#3584	1	1	yes	characteristic
700	C₂×C₆₇	#3586	1	1	yes	characteristic
701	C₂×#578	C₂×C₆₇	1	1	yes	characteristic, complemented
702	C₂×#575	C₂×C₆₇	1	1	yes	characteristic, complemented
703	#3489	C₂×C₆₇	1	1	yes	characteristic, complemented
704	#3487	C₂×C₆₇	1	1	yes	characteristic, complemented
705	#3285	C₂×C₆₇	1	2	yes	complemented
706	#3284	C₂×C₆₇	1	2	yes	complemented
707	#3278	C₂×C₆₇	1	2	yes	complemented
708	#3275	C₂×C₆₇	1	2	yes	complemented
709	#3271	C₂×C₆₇	1	2	yes	complemented
710	#3270	C₂×C₆₇	1	2	yes	complemented
711	#3269	C₂×C₆₇	1	2	yes	complemented
712	#3268	C₂×C₆₇	1	2	yes	complemented
713	#3154	C₂×C₆₇	1	1	yes	characteristic, complemented
714	#3062	C₂×C₆₇	1	1	yes	characteristic, complemented
715	#3056	C₂×C₆₇	1	1	yes	characteristic, complemented
716	#3045	C₂×C₆₇	1	1	yes	characteristic, complemented
717	#3044	C₂×C₆₇	1	1	yes	characteristic, complemented
718	#3013	C₂×C₆₇	1	1	yes	characteristic, complemented
719	#3010	C₂×C₆₇	1	1	yes	characteristic, complemented
720	#3002	C₂×C₆₇	1	1	yes	characteristic, complemented
721	C₂×#452	C₂×C₆₇	1	1	yes	characteristic, complemented
722	#2947	C₂×C₆₇	1	1	yes	characteristic, complemented
723	#2933	C₂×C₆₇	1	1	yes	characteristic, complemented
724	C₆₇	#61078	1	1	yes	characteristic, direct product factor, Sylow
725	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	1	yes	characteristic
726	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	1	yes	characteristic, complemented
727	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
728	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
729	#578	—	2	8	no	—
730	#575	—	2	8	no	—
731	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic
732	C₂×#137	C₂²×C₆₇	1	2	yes	—
733	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic
734	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic, complemented
735	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
736	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
737	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic
738	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic
739	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	—
740	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
741	C₂×#135	C₂²×C₆₇	1	2	yes	—
742	C₂×#135	C₂²×C₆₇	1	2	yes	—
743	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
744	C₂×#135	C₂²×C₆₇	1	2	yes	complemented
745	C₂²×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
746	C₂²×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
747	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
748	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic, complemented
749	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
750	#550	—	2	1	no	—
751	#550	—	2	1	no	—
752	#550	C₂²×C₆₇	1	2	yes	—
753	#550	C₂²×C₆₇	1	2	yes	complemented
754	D₄×Q₈	C₂²×C₆₇	1	2	yes	complemented
755	#548	—	2	1	no	—
756	#548	—	2	1	no	—
757	#548	C₂²×C₆₇	1	2	yes	—
758	#548	C₂²×C₆₇	1	2	yes	complemented
759	#548	C₂²×C₆₇	1	2	yes	complemented
760	#547	—	2	2	no	—
761	#547	C₂²×C₆₇	1	2	yes	complemented
762	#546	—	2	2	no	—
763	#546	C₂²×C₆₇	1	2	yes	complemented
764	#537	—	2	1	no	—
765	#537	C₂²×C₆₇	1	1	yes	characteristic
766	#536	—	2	1	no	—
767	#536	C₂²×C₆₇	1	1	yes	characteristic
768	#535	—	2	2	no	—
769	#535	C₂²×C₆₇	1	1	yes	characteristic, complemented
770	#535	C₂²×C₆₇	1	1	yes	characteristic, complemented
771	#525	—	2	2	no	—
772	#525	—	2	1	no	—
773	#525	C₂²×C₆₇	1	1	yes	characteristic
774	#525	C₂²×C₆₇	1	1	yes	characteristic
775	C₂×C₂²⋊Q₈	—	2	1	no	—
776	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
777	#520	C₂²×C₆₇	1	1	yes	characteristic
778	#519	C₂²×C₆₇	1	1	yes	characteristic, complemented
779	#497	C₂²×C₆₇	1	2	yes	complemented
780	#496	C₂²×C₆₇	1	2	yes	complemented
781	#495	C₂²×C₆₇	1	2	yes	complemented
782	#492	C₂²×C₆₇	1	2	yes	complemented
783	#470	C₂²×C₆₇	1	2	yes	complemented
784	#469	C₂²×C₆₇	1	2	yes	complemented
785	#468	C₂²×C₆₇	1	2	yes	complemented
786	#468	C₂²×C₆₇	1	2	yes	complemented
787	#467	C₂²×C₆₇	1	2	yes	complemented
788	#466	C₂²×C₆₇	1	2	yes	complemented
789	#465	C₂²×C₆₇	1	2	yes	complemented
790	#465	C₂²×C₆₇	1	2	yes	complemented
791	#464	C₂²×C₆₇	1	2	yes	complemented
792	#464	C₂²×C₆₇	1	2	yes	complemented
793	#464	C₂²×C₆₇	1	2	yes	complemented
794	#463	C₂²×C₆₇	1	2	yes	complemented
795	#462	C₂²×C₆₇	1	2	yes	complemented
796	#462	C₂²×C₆₇	1	2	yes	complemented
797	#460	C₂²×C₆₇	1	2	yes	complemented
798	#459	C₂²×C₆₇	1	2	yes	complemented
799	#452	C₂²×C₆₇	1	2	yes	—
800	#452	C₂²×C₆₇	1	2	yes	—
801	#452	C₂²×C₆₇	1	2	yes	complemented
802	#452	C₂²×C₆₇	1	2	yes	complemented
803	#452	C₂²×C₆₇	1	1	yes	characteristic, complemented
804	#452	C₂²×C₆₇	1	1	yes	characteristic, complemented
805	#452	C₂²×C₆₇	1	2	yes	complemented
806	#451	C₂²×C₆₇	1	1	yes	characteristic, complemented
807	#451	C₂²×C₆₇	1	2	yes	complemented
808	#450	C₂²×C₆₇	1	1	yes	characteristic, complemented
809	#449	C₂²×C₆₇	1	1	yes	characteristic, complemented
810	#449	C₂²×C₆₇	1	1	yes	characteristic, complemented
811	#449	C₂²×C₆₇	1	2	yes	complemented
812	#449	C₂²×C₆₇	1	2	yes	complemented
813	#449	C₂²×C₆₇	1	2	yes	complemented
814	#448	C₂²×C₆₇	1	1	yes	characteristic, complemented
815	#448	C₂²×C₆₇	1	2	yes	complemented
816	#448	C₂²×C₆₇	1	2	yes	complemented
817	#448	C₂²×C₆₇	1	2	yes	complemented
818	#447	C₂²×C₆₇	1	1	yes	characteristic, complemented
819	#441	C₂²×C₆₇	1	2	yes	complemented
820	#440	C₂²×C₆₇	1	2	yes	complemented
821	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
822	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
823	#436	C₂²×C₆₇	1	2	yes	complemented
824	#435	C₂²×C₆₇	1	2	yes	complemented
825	#435	C₂²×C₆₇	1	2	yes	complemented
826	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
827	#428	C₂²×C₆₇	1	1	yes	characteristic, complemented
828	#424	C₂²×C₆₇	1	1	yes	characteristic, complemented
829	#419	C₂²×C₆₇	1	1	yes	characteristic, complemented
830	#417	C₂²×C₆₇	1	1	yes	characteristic, complemented
831	#416	C₂²×C₆₇	1	1	yes	characteristic
832	#416	C₂²×C₆₇	1	1	yes	characteristic
833	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic, complemented
834	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic, complemented
835	#408	C₂²×C₆₇	1	1	yes	characteristic, complemented
836	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
837	#405	C₂²×C₆₇	1	1	yes	characteristic, complemented
838	2₋¹⁺⁴	—	2	4	no	—
839	2₋¹⁺⁴	—	2	4	no	—
840	2₋¹⁺⁴	—	4	2	no	—
841	2₋¹⁺⁴	—	4	2	no	—
842	C₂×#41	—	2	2	no	—
843	C₂×#41	—	2	1	no	—
844	C₂×#41	—	2	2	no	—
845	C₂×#41	—	2	1	no	—
846	C₂×#41	—	2	1	no	—
847	C₂×#41	—	2	1	no	—
848	C₂×#41	—	2	1	no	—
849	C₂×#41	—	2	1	no	—
850	C₂×#41	—	2	4	no	—
851	C₂×#41	—	2	4	no	—
852	C₂×#41	—	4	2	no	—
853	C₂×#41	—	4	2	no	—
854	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
855	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
856	C₂×#41	C₂³×C₆₇	1	2	yes	—
857	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
858	C₂×#41	C₂³×C₆₇	1	2	yes	—
859	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
860	C₂×#41	C₂³×C₆₇	1	2	yes	—
861	C₂×#41	C₂³×C₆₇	1	2	yes	—
862	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
863	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
864	C₂²×Q₈	—	2	1	no	—
865	C₂²×Q₈	—	2	1	no	—
866	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
867	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
868	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
869	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
870	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
871	C₂²×D₄	—	2	1	no	—
872	C₂²×D₄	—	2	1	no	—
873	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
874	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
875	C₂³×C₄	—	2	1	no	—
876	C₂³×C₄	—	2	1	no	—
877	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
878	#137	—	2	4	no	—
879	#137	—	2	8	no	—
880	#137	—	2	8	no	—
881	#137	—	2	8	no	—
882	#137	—	2	4	no	—
883	#137	D₄×C₆₇	1	8	yes	complemented
884	AGL(1,ℤ/8)	—	2	4	no	—
885	AGL(1,ℤ/8)	—	2	8	no	—
886	AGL(1,ℤ/8)	—	2	4	no	—
887	#135	—	2	4	no	—
888	#135	—	2	8	no	—
889	#135	—	2	8	no	—
890	#135	—	2	8	no	—
891	#135	—	4	2	no	—
892	C₂×Q₁₆	—	2	4	no	—
893	C₂×Q₁₆	—	2	8	no	—
894	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
895	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
896	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
897	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
898	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
899	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
900	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
901	C₂×SD₁₆	—	4	2	no	—
902	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
903	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
904	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
905	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
906	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
907	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
908	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
909	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
910	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
911	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
912	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
913	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
914	C₂×D₈	C₂³×C₆₇	1	2	yes	—
915	C₂×D₈	C₂³×C₆₇	1	2	yes	—
916	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
917	#131	—	2	4	no	—
918	C₂×M₁₆	—	2	4	no	—
919	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
920	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
921	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
922	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
923	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
924	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
925	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
926	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
927	C₄⋊Q₈	—	2	2	no	—
928	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
929	#127	—	2	2	no	—
930	#127	—	2	2	no	—
931	#127	—	2	1	no	—
932	#127	C₂³×C₆₇	1	2	yes	—
933	#124	—	2	1	no	—
934	#124	—	2	2	no	—
935	#124	—	2	2	no	—
936	#124	—	2	2	no	—
937	#124	C₂³×C₆₇	1	2	yes	—
938	#124	C₂³×C₆₇	1	2	yes	—
939	#123	—	2	1	no	—
940	#123	—	2	2	no	—
941	#123	—	2	2	no	—
942	#123	—	2	2	no	—
943	#123	—	2	2	no	—
944	#123	D₄×C₆₇	1	2	yes	—
945	C₂²⋊Q₈	—	2	1	no	—
946	C₂²⋊Q₈	—	2	1	no	—
947	C₂²⋊Q₈	—	2	1	no	—
948	C₂²⋊Q₈	—	2	1	no	—
949	C₂²⋊Q₈	—	2	2	no	—
950	C₂²⋊Q₈	—	2	1	no	—
951	C₂²⋊Q₈	—	2	2	no	—
952	C₂²⋊Q₈	—	2	2	no	—
953	C₂²⋊Q₈	—	2	2	no	—
954	C₂²⋊Q₈	—	2	2	no	—
955	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
956	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
957	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
958	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
959	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
960	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
961	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
962	#121	—	2	1	no	—
963	#121	—	2	2	no	—
964	#121	—	2	2	no	—
965	#121	—	2	2	no	—
966	#121	—	2	2	no	—
967	#121	—	2	2	no	—
968	#121	—	2	1	no	—
969	#121	—	2	1	no	—
970	#121	—	2	2	no	—
971	#121	—	2	2	no	—
972	#121	—	2	2	no	—
973	#121	—	2	2	no	—
974	#121	—	2	2	no	—
975	#121	D₄×C₆₇	1	1	yes	characteristic
976	#121	D₄×C₆₇	1	1	yes	characteristic
977	#121	C₂³×C₆₇	1	1	yes	characteristic
978	#121	C₂³×C₆₇	1	1	yes	characteristic
979	#121	C₂³×C₆₇	1	2	yes	—
980	#121	C₂³×C₆₇	1	2	yes	—
981	#121	C₂³×C₆₇	1	2	yes	—
982	#120	—	2	1	no	—
983	#120	—	2	2	no	—
984	#120	—	2	2	no	—
985	#120	—	2	2	no	—
986	#120	D₄×C₆₇	1	2	yes	—
987	C₄×Q₈	—	2	1	no	—
988	C₄×Q₈	—	2	1	no	—
989	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
990	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
991	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
992	C₄×D₄	—	2	2	no	—
993	C₄×D₄	—	2	1	no	—
994	C₄×D₄	—	2	1	no	—
995	C₄×D₄	—	2	2	no	—
996	C₄×D₄	—	2	2	no	—
997	C₄×D₄	—	2	2	no	—
998	C₄×D₄	—	2	2	no	—
999	C₄×D₄	—	2	2	no	—
1000	C₄×D₄	—	2	2	no	—
1001	C₄×D₄	C₂³×C₆₇	1	2	yes	—
1002	C₄×D₄	C₂³×C₆₇	1	2	yes	—
1003	C₄×D₄	C₂³×C₆₇	1	2	yes	—
1004	#117	—	2	1	no	—
1005	#117	—	2	2	no	—
1006	#117	C₂³×C₆₇	1	1	yes	characteristic
1007	#117	C₂³×C₆₇	1	1	yes	characteristic
1008	C₂×C₄⋊C₄	—	2	1	no	—
1009	C₂×C₄⋊C₄	—	2	1	no	—
1010	C₂×C₄⋊C₄	—	2	2	no	—
1011	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
1012	C₂×C₂²⋊C₄	—	2	1	no	—
1013	C₂×C₂²⋊C₄	—	2	2	no	—
1014	#107	C₂³×C₆₇	1	2	yes	—
1015	#106	C₂³×C₆₇	1	2	yes	—
1016	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
1017	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
1018	#103	C₂³×C₆₇	1	2	yes	—
1019	#103	C₂³×C₆₇	1	2	yes	—
1020	#103	C₂³×C₆₇	1	1	yes	characteristic
1021	#103	C₂³×C₆₇	1	1	yes	characteristic
1022	#103	C₂³×C₆₇	1	1	yes	characteristic
1023	#103	C₂³×C₆₇	1	1	yes	characteristic
1024	#103	C₂³×C₆₇	1	2	yes	—
1025	#103	C₂³×C₆₇	1	2	yes	—
1026	#103	C₂³×C₆₇	1	2	yes	—
1027	#102	C₂³×C₆₇	1	2	yes	—
1028	#102	C₂³×C₆₇	1	2	yes	—
1029	#102	C₂³×C₆₇	1	1	yes	characteristic
1030	#102	C₂³×C₆₇	1	1	yes	characteristic
1031	#102	C₂³×C₆₇	1	1	yes	characteristic
1032	#102	C₂³×C₆₇	1	1	yes	characteristic
1033	#102	C₂³×C₆₇	1	2	yes	—
1034	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
1035	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
1036	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
1037	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
1038	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
1039	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
1040	#97	C₂³×C₆₇	1	2	yes	—
1041	C₄×C₈	C₂³×C₆₇	1	2	yes	—
1042	C₂⁴	—	2	1	no	—
1043	C₂⁴	—	2	1	no	—
1044	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
1045	#41	—	2	2	no	—
1046	#41	—	2	2	no	—
1047	#41	—	2	2	no	—
1048	#41	—	2	2	no	—
1049	#41	—	2	4	no	—
1050	#41	—	2	4	no	—
1051	#41	—	2	4	no	—
1052	#41	—	2	2	no	—
1053	#41	—	2	4	no	—
1054	#41	—	2	2	no	—
1055	#41	—	2	2	no	—
1056	#41	—	2	2	no	—
1057	#41	—	2	2	no	—
1058	#41	—	4	4	no	—
1059	#41	—	4	2	no	—
1060	#41	—	4	1	no	—
1061	#41	—	4	2	no	—
1062	#41	—	4	1	no	—
1063	#41	—	4	2	no	—
1064	#41	—	4	2	no	—
1065	#41	—	4	4	no	—
1066	#41	—	4	8	no	—
1067	#41	—	4	4	no	—
1068	#41	—	4	4	no	—
1069	#41	—	4	4	no	—
1070	#41	—	4	8	no	—
1071	#41	—	4	4	no	—
1072	#41	C₂×D₄×C₆₇	1	4	yes	—
1073	C₂×Q₈	—	2	1	no	—
1074	C₂×Q₈	—	2	1	no	—
1075	C₂×Q₈	—	2	2	no	—
1076	C₂×Q₈	—	2	2	no	—
1077	C₂×Q₈	—	2	1	no	—
1078	C₂×Q₈	—	2	2	no	—
1079	C₂×Q₈	—	2	4	no	—
1080	C₂×Q₈	—	2	4	no	—
1081	C₂×Q₈	—	2	2	no	—
1082	C₂×Q₈	—	2	2	no	—
1083	C₂×Q₈	—	2	2	no	—
1084	C₂×Q₈	—	4	1	no	—
1085	C₂×Q₈	—	4	2	no	—
1086	C₂×Q₈	—	4	2	no	—
1087	C₂×Q₈	—	4	4	no	—
1088	C₂×Q₈	—	4	4	no	—
1089	C₂×Q₈	C₂×D₄×C₆₇	1	4	yes	—
1090	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
1091	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
1092	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
1093	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
1094	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
1095	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
1096	C₂×D₄	—	2	1	no	—
1097	C₂×D₄	—	2	2	no	—
1098	C₂×D₄	—	2	1	no	—
1099	C₂×D₄	—	2	2	no	—
1100	C₂×D₄	—	2	1	no	—
1101	C₂×D₄	—	2	1	no	—
1102	C₂×D₄	—	2	1	no	—
1103	C₂×D₄	—	2	2	no	—
1104	C₂×D₄	—	2	2	no	—
1105	C₂×D₄	—	2	2	no	—
1106	C₂×D₄	—	2	2	no	—
1107	C₂×D₄	—	2	2	no	—
1108	C₂×D₄	—	2	2	no	—
1109	C₂×D₄	—	2	1	no	—
1110	C₂×D₄	—	2	1	no	—
1111	C₂×D₄	—	2	2	no	—
1112	C₂×D₄	—	2	1	no	—
1113	C₂×D₄	—	2	1	no	—
1114	C₂×D₄	—	2	2	no	—
1115	C₂×D₄	—	2	2	no	—
1116	C₂×D₄	—	2	2	no	—
1117	C₂×D₄	—	4	1	no	—
1118	C₂×D₄	—	4	4	no	—
1119	C₂×D₄	—	4	4	no	—
1120	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
1121	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1122	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
1123	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
1124	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1125	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
1126	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1127	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1128	C₂²×C₄	—	2	1	no	—
1129	C₂²×C₄	—	2	1	no	—
1130	C₂²×C₄	—	2	2	no	—
1131	C₂²×C₄	—	2	2	no	—
1132	C₂²×C₄	—	2	1	no	—
1133	C₂²×C₄	—	2	2	no	—
1134	C₂²×C₄	—	2	2	no	—
1135	C₂²×C₄	—	2	1	no	—
1136	C₂²×C₄	—	2	1	no	—
1137	C₂²×C₄	—	2	2	no	—
1138	C₂²×C₄	—	2	1	no	—
1139	C₂²×C₄	—	2	2	no	—
1140	C₂²×C₄	—	2	1	no	—
1141	C₂²×C₄	—	2	2	no	—
1142	C₂²×C₄	—	2	2	no	—
1143	C₂²×C₄	—	2	1	no	—
1144	C₂²×C₄	—	2	1	no	—
1145	C₂²×C₄	—	2	2	no	—
1146	C₂²×C₄	—	4	4	no	—
1147	C₂²×C₄	—	4	4	no	—
1148	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1149	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1150	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1151	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1152	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1153	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1154	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1155	Q₁₆	—	2	2	no	—
1156	Q₁₆	—	2	4	no	—
1157	Q₁₆	—	2	4	no	—
1158	Q₁₆	—	2	4	no	—
1159	Q₁₆	—	2	4	no	—
1160	Q₁₆	—	4	1	no	—
1161	Q₁₆	C₂×D₄×C₆₇	1	8	yes	—
1162	SD₁₆	—	2	4	no	—
1163	SD₁₆	—	2	4	no	—
1164	SD₁₆	—	2	2	no	—
1165	SD₁₆	—	2	2	no	—
1166	SD₁₆	—	2	4	no	—
1167	SD₁₆	—	2	4	no	—
1168	SD₁₆	—	4	2	no	—
1169	SD₁₆	—	4	2	no	—
1170	SD₁₆	—	4	1	no	—
1171	SD₁₆	—	4	1	no	—
1172	SD₁₆	C₂×D₄×C₆₇	1	8	yes	—
1173	D₈	—	2	2	no	—
1174	D₈	—	2	4	no	—
1175	D₈	—	2	4	no	—
1176	D₈	—	4	1	no	—
1177	M₁₆	—	2	2	no	—
1178	M₁₆	—	2	4	no	—
1179	M₁₆	—	2	4	no	—
1180	M₁₆	C₂×D₄×C₆₇	1	4	yes	—
1181	C₂×C₈	—	2	2	no	—
1182	C₂×C₈	—	2	2	no	—
1183	C₂×C₈	—	2	4	no	—
1184	C₂×C₈	—	2	4	no	—
1185	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1186	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1187	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1188	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1189	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1190	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1191	C₄⋊C₄	—	2	2	no	—
1192	C₄⋊C₄	—	2	1	no	—
1193	C₄⋊C₄	—	2	2	no	—
1194	C₄⋊C₄	—	2	2	no	—
1195	C₄⋊C₄	—	2	2	no	—
1196	C₄⋊C₄	—	2	2	no	—
1197	C₄⋊C₄	—	2	2	no	—
1198	C₄⋊C₄	—	2	2	no	—
1199	C₄⋊C₄	—	2	1	no	—
1200	C₄⋊C₄	—	2	1	no	—
1201	C₄⋊C₄	—	2	2	no	—
1202	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1203	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1204	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1205	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1206	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1207	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1208	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1209	C₂²⋊C₄	—	2	2	no	—
1210	C₂²⋊C₄	—	2	2	no	—
1211	C₂²⋊C₄	—	2	1	no	—
1212	C₂²⋊C₄	—	2	1	no	—
1213	C₂²⋊C₄	—	2	1	no	—
1214	C₂²⋊C₄	—	2	2	no	—
1215	C₂²⋊C₄	—	2	2	no	—
1216	C₂²⋊C₄	—	2	2	no	—
1217	C₂²⋊C₄	—	2	2	no	—
1218	C₂²⋊C₄	—	2	1	no	—
1219	C₂²⋊C₄	—	2	1	no	—
1220	C₂²⋊C₄	—	2	2	no	—
1221	C₂²⋊C₄	—	2	2	no	—
1222	C₂²⋊C₄	—	2	2	no	—
1223	C₂²⋊C₄	—	2	2	no	—
1224	C₂²⋊C₄	—	2	2	no	—
1225	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1226	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1227	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1228	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1229	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1230	C₄²	—	2	2	no	—
1231	C₄²	—	2	2	no	—
1232	C₄²	—	2	2	no	—
1233	C₄²	—	2	1	no	—
1234	C₄²	C₂⁴×C₆₇	1	2	yes	—
1235	C₂³	—	2	1	no	—
1236	C₂³	—	2	2	no	—
1237	C₂³	—	2	1	no	—
1238	C₂³	—	2	2	no	—
1239	C₂³	—	2	1	no	—
1240	C₂³	—	4	1	no	—
1241	C₂³	—	4	1	no	—
1242	C₂³	—	4	2	no	—
1243	C₂³	—	4	2	no	—
1244	C₂³	—	4	2	no	—
1245	C₂³	—	8	1	no	—
1246	C₂³	—	8	1	no	—
1247	C₂³	—	8	1	no	—
1248	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1249	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1250	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1251	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1252	Q₈	—	2	4	no	—
1253	Q₈	—	2	2	no	—
1254	Q₈	—	2	2	no	—
1255	Q₈	—	2	1	no	—
1256	Q₈	—	2	1	no	—
1257	Q₈	—	2	1	no	—
1258	Q₈	—	2	2	no	—
1259	Q₈	—	2	2	no	—
1260	Q₈	—	2	1	no	—
1261	Q₈	—	2	1	no	—
1262	Q₈	—	4	4	no	—
1263	Q₈	—	4	4	no	—
1264	Q₈	—	4	2	no	—
1265	Q₈	—	4	2	no	—
1266	Q₈	C₂²×D₄×C₆₇	1	2	yes	—
1267	Q₈	C₂²×D₄×C₆₇	1	4	yes	—
1268	D₄	—	2	4	no	—
1269	D₄	—	2	4	no	—
1270	D₄	—	2	2	no	—
1271	D₄	—	2	2	no	—
1272	D₄	—	2	1	no	—
1273	D₄	—	2	1	no	—
1274	D₄	—	2	1	no	—
1275	D₄	—	2	1	no	—
1276	D₄	—	2	1	no	—
1277	D₄	—	2	2	no	—
1278	D₄	—	4	2	no	—
1279	D₄	—	4	2	no	—
1280	D₄	—	4	2	no	—
1281	D₄	—	4	2	no	—
1282	D₄	—	4	4	no	—
1283	D₄	—	4	4	no	—
1284	D₄	—	4	4	no	—
1285	D₄	—	4	2	no	—
1286	D₄	—	4	4	no	—
1287	D₄	—	4	2	no	—
1288	D₄	—	4	2	no	—
1289	D₄	—	4	2	no	—
1290	D₄	—	8	2	no	—
1291	D₄	—	8	2	no	—
1292	D₄	—	8	2	no	—
1293	D₄	—	8	2	no	—
1294	D₄	—	8	1	no	—
1295	D₄	—	8	2	no	—
1296	D₄	—	8	1	no	—
1297	D₄	C₂²×D₄×C₆₇	1	2	yes	—
1298	C₂×C₄	—	2	2	no	—
1299	C₂×C₄	—	2	4	no	—
1300	C₂×C₄	—	2	2	no	—
1301	C₂×C₄	—	2	1	no	—
1302	C₂×C₄	—	2	2	no	—
1303	C₂×C₄	—	2	2	no	—
1304	C₂×C₄	—	2	4	no	—
1305	C₂×C₄	—	2	1	no	—
1306	C₂×C₄	—	2	2	no	—
1307	C₂×C₄	—	2	1	no	—
1308	C₂×C₄	—	2	1	no	—
1309	C₂×C₄	—	2	1	no	—
1310	C₂×C₄	—	2	2	no	—
1311	C₂×C₄	—	2	1	no	—
1312	C₂×C₄	—	2	1	no	—
1313	C₂×C₄	—	2	2	no	—
1314	C₂×C₄	—	2	1	no	—
1315	C₂×C₄	—	2	2	no	—
1316	C₂×C₄	—	2	1	no	—
1317	C₂×C₄	—	4	2	no	—
1318	C₂×C₄	—	4	4	no	—
1319	C₂×C₄	—	4	4	no	—
1320	C₂×C₄	—	4	4	no	—
1321	C₂×C₄	—	4	2	no	—
1322	C₂×C₄	—	4	2	no	—
1323	C₂×C₄	—	4	4	no	—
1324	C₂×C₄	—	4	4	no	—
1325	C₂×C₄	—	4	4	no	—
1326	C₂×C₄	—	4	2	no	—
1327	C₂×C₄	—	4	2	no	—
1328	C₂×C₄	—	4	2	no	—
1329	C₂×C₄	—	8	2	no	—
1330	C₂×C₄	—	8	1	no	—
1331	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1332	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1333	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1334	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1335	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1336	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1337	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1338	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1339	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1340	C₈	—	2	1	no	—
1341	C₈	—	2	2	no	—
1342	C₈	—	2	1	no	—
1343	C₈	—	2	1	no	—
1344	C₈	—	2	1	no	—
1345	C₈	C₂²×D₄×C₆₇	1	4	yes	—
1346	C₂²	—	2	1	no	—
1347	C₂²	—	2	1	no	—
1348	C₂²	—	2	1	no	—
1349	C₂²	—	2	2	no	—
1350	C₂²	—	2	1	no	—
1351	C₂²	—	2	1	no	—
1352	C₂²	—	2	2	no	—
1353	C₂²	—	2	1	no	—
1354	C₂²	—	2	1	no	—
1355	C₂²	—	2	1	no	—
1356	C₂²	—	2	2	no	—
1357	C₂²	—	2	2	no	—
1358	C₂²	—	4	1	no	—
1359	C₂²	—	4	1	no	—
1360	C₂²	—	4	1	no	—
1361	C₂²	—	4	2	no	—
1362	C₂²	—	4	1	no	—
1363	C₂²	—	4	1	no	—
1364	C₂²	—	4	2	no	—
1365	C₂²	—	4	1	no	—
1366	C₂²	—	4	1	no	—
1367	C₂²	—	4	2	no	—
1368	C₂²	—	4	1	no	—
1369	C₂²	—	8	2	no	—
1370	C₂²	—	8	4	no	—
1371	C₂²	—	8	4	no	—
1372	C₂²	D₄²×C₆₇	1	2	yes	—
1373	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1374	C₄	—	2	2	no	—
1375	C₄	—	2	2	no	—
1376	C₄	—	2	1	no	—
1377	C₄	—	2	1	no	—
1378	C₄	—	2	2	no	—
1379	C₄	—	2	4	no	—
1380	C₄	—	2	2	no	—
1381	C₄	—	4	2	no	—
1382	C₄	—	4	1	no	—
1383	C₄	—	4	1	no	—
1384	C₄	—	4	1	no	—
1385	C₄	—	4	1	no	—
1386	C₄	—	4	2	no	—
1387	C₄	D₄²×C₆₇	1	2	yes	—
1388	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
1389	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1390	C₂	—	2	2	no	—
1391	C₂	—	4	1	no	—
1392	C₂	—	4	1	no	—
1393	C₂	—	4	2	no	—
1394	C₂	—	4	2	no	—
1395	C₂	—	8	2	no	—
1396	C₂	—	8	1	no	—
1397	C₂	—	8	1	no	—
1398	C₂	C₂×D₄²×C₆₇	1	1	yes	characteristic
1399	C₂	C₆₇×#3584	1	1	yes	characteristic
1400	C₂	C₆₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ #525×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#578×C₆₇	C₂	semidirect
2. C₂×#575×C₆₇	C₂	semidirect
3. C₆₇×#3489	C₂	semidirect
4. C₆₇×#3487	C₂	semidirect
5. C₆₇×#3285	C₂	semidirect
6. C₆₇×#3284	C₂	semidirect
7. C₆₇×#3278	C₂	semidirect
8. C₆₇×#3275	C₂	semidirect
9. C₆₇×#3271	C₂	semidirect
10. C₆₇×#3270	C₂	semidirect
11. C₆₇×#3269	C₂	semidirect
12. C₆₇×#3268	C₂	semidirect
13. C₆₇×#3154	C₂	semidirect
14. C₆₇×#3062	C₂	semidirect
15. C₆₇×#3056	C₂	semidirect
16. C₆₇×#3045	C₂	semidirect
17. C₆₇×#3044	C₂	semidirect
18. C₆₇×#3013	C₂	semidirect
19. C₆₇×#3010	C₂	semidirect
20. C₆₇×#3002	C₂	semidirect
21. C₂×#452×C₆₇	C₂	semidirect
22. C₆₇×#2947	C₂	semidirect
23. C₆₇×#2933	C₂	semidirect
25. C₂×2₋¹⁺⁴×C₆₇	C₂²	semidirect
33. C₂×#137×C₆₇	C₂²	semidirect
34. C₂×#137×C₆₇	C₂²	semidirect
35. C₂×#137×C₆₇	C₂²	semidirect
43. C₂×#135×C₆₇	C₂²	semidirect
44. C₂²×Q₁₆×C₆₇	C₂²	semidirect
45. C₂²×Q₁₆×C₆₇	C₂²	semidirect
46. C₂²×SD₁₆×C₆₇	C₂²	semidirect
47. C₂×#131×C₆₇	C₂²	semidirect
52. #550×C₆₇	C₂²	semidirect
53. D₄×Q₈×C₆₇	C₂²	semidirect
57. #548×C₆₇	C₂²	semidirect
58. #548×C₆₇	C₂²	semidirect
60. #547×C₆₇	C₂²	semidirect
62. #546×C₆₇	C₂²	semidirect
68. #535×C₆₇	C₂²	semidirect
69. #535×C₆₇	C₂²	semidirect
77. #519×C₆₇	C₂²	semidirect
78. #497×C₆₇	C₂²	semidirect
79. #496×C₆₇	C₂²	semidirect
80. #495×C₆₇	C₂²	semidirect
81. #492×C₆₇	C₂²	semidirect
82. #470×C₆₇	C₂²	semidirect
83. #469×C₆₇	C₂²	semidirect
84. #468×C₆₇	C₂²	semidirect
85. #468×C₆₇	C₂²	semidirect
86. #467×C₆₇	C₂²	semidirect
87. #466×C₆₇	C₂²	semidirect
88. #465×C₆₇	C₂²	semidirect
89. #465×C₆₇	C₂²	semidirect
90. #464×C₆₇	C₂²	semidirect
91. #464×C₆₇	C₂²	semidirect
92. #464×C₆₇	C₂²	semidirect
93. #463×C₆₇	C₂²	semidirect
94. #462×C₆₇	C₂²	semidirect
95. #462×C₆₇	C₂²	semidirect
96. #460×C₆₇	C₂²	semidirect
97. #459×C₆₇	C₂²	semidirect
100. #452×C₆₇	C₂²	semidirect
101. #452×C₆₇	C₂²	semidirect
102. #452×C₆₇	C₂²	semidirect
103. #452×C₆₇	C₂²	semidirect
104. #452×C₆₇	C₂²	semidirect
105. #451×C₆₇	C₂²	semidirect
106. #451×C₆₇	C₂²	semidirect
107. #450×C₆₇	C₂²	semidirect
108. #449×C₆₇	C₂²	semidirect
109. #449×C₆₇	C₂²	semidirect
110. #449×C₆₇	C₂²	semidirect
111. #449×C₆₇	C₂²	semidirect
112. #449×C₆₇	C₂²	semidirect
113. #448×C₆₇	C₂²	semidirect
114. #448×C₆₇	C₂²	semidirect
115. #448×C₆₇	C₂²	semidirect
116. #448×C₆₇	C₂²	semidirect
117. #447×C₆₇	C₂²	semidirect
118. #441×C₆₇	C₂²	semidirect
119. #440×C₆₇	C₂²	semidirect
120. C₄×Q₁₆×C₆₇	C₂²	semidirect
121. C₄×SD₁₆×C₆₇	C₂²	semidirect
122. #436×C₆₇	C₂²	semidirect
123. #435×C₆₇	C₂²	semidirect
124. #435×C₆₇	C₂²	semidirect
125. C₈×D₄×C₆₇	C₂²	semidirect
126. #428×C₆₇	C₂²	semidirect
127. #424×C₆₇	C₂²	semidirect
128. #419×C₆₇	C₂²	semidirect
129. #417×C₆₇	C₂²	semidirect
132. C₂×#103×C₆₇	C₂²	semidirect
133. C₂×#102×C₆₇	C₂²	semidirect
134. #408×C₆₇	C₂²	semidirect
136. #405×C₆₇	C₂²	semidirect
182. #137×C₆₇	D₄	semidirect
689. #61078	C₆₇	direct (N × H)
701. C₂×#578	C₂×C₆₇	semidirect
702. C₂×#575	C₂×C₆₇	semidirect
703. #3489	C₂×C₆₇	semidirect
704. #3487	C₂×C₆₇	semidirect
705. #3285	C₂×C₆₇	semidirect
706. #3284	C₂×C₆₇	semidirect
707. #3278	C₂×C₆₇	semidirect
708. #3275	C₂×C₆₇	semidirect
709. #3271	C₂×C₆₇	semidirect
710. #3270	C₂×C₆₇	semidirect
711. #3269	C₂×C₆₇	semidirect
712. #3268	C₂×C₆₇	semidirect
713. #3154	C₂×C₆₇	semidirect
714. #3062	C₂×C₆₇	semidirect
715. #3056	C₂×C₆₇	semidirect
716. #3045	C₂×C₆₇	semidirect
717. #3044	C₂×C₆₇	semidirect
718. #3013	C₂×C₆₇	semidirect
719. #3010	C₂×C₆₇	semidirect
720. #3002	C₂×C₆₇	semidirect
721. C₂×#452	C₂×C₆₇	semidirect
722. #2947	C₂×C₆₇	semidirect
723. #2933	C₂×C₆₇	semidirect
724. C₆₇	#61078	direct (N × H)
726. C₂×2₋¹⁺⁴	C₂²×C₆₇	semidirect
734. C₂×#137	C₂²×C₆₇	semidirect
735. C₂×#137	C₂²×C₆₇	semidirect
736. C₂×#137	C₂²×C₆₇	semidirect
744. C₂×#135	C₂²×C₆₇	semidirect
745. C₂²×Q₁₆	C₂²×C₆₇	semidirect
746. C₂²×Q₁₆	C₂²×C₆₇	semidirect
747. C₂²×SD₁₆	C₂²×C₆₇	semidirect
748. C₂×#131	C₂²×C₆₇	semidirect
753. #550	C₂²×C₆₇	semidirect
754. D₄×Q₈	C₂²×C₆₇	semidirect
758. #548	C₂²×C₆₇	semidirect
759. #548	C₂²×C₆₇	semidirect
761. #547	C₂²×C₆₇	semidirect
763. #546	C₂²×C₆₇	semidirect
769. #535	C₂²×C₆₇	semidirect
770. #535	C₂²×C₆₇	semidirect
778. #519	C₂²×C₆₇	semidirect
779. #497	C₂²×C₆₇	semidirect
780. #496	C₂²×C₆₇	semidirect
781. #495	C₂²×C₆₇	semidirect
782. #492	C₂²×C₆₇	semidirect
783. #470	C₂²×C₆₇	semidirect
784. #469	C₂²×C₆₇	semidirect
785. #468	C₂²×C₆₇	semidirect
786. #468	C₂²×C₆₇	semidirect
787. #467	C₂²×C₆₇	semidirect
788. #466	C₂²×C₆₇	semidirect
789. #465	C₂²×C₆₇	semidirect
790. #465	C₂²×C₆₇	semidirect
791. #464	C₂²×C₆₇	semidirect
792. #464	C₂²×C₆₇	semidirect
793. #464	C₂²×C₆₇	semidirect
794. #463	C₂²×C₆₇	semidirect
795. #462	C₂²×C₆₇	semidirect
796. #462	C₂²×C₆₇	semidirect
797. #460	C₂²×C₆₇	semidirect
798. #459	C₂²×C₆₇	semidirect
801. #452	C₂²×C₆₇	semidirect
802. #452	C₂²×C₆₇	semidirect
803. #452	C₂²×C₆₇	semidirect
804. #452	C₂²×C₆₇	semidirect
805. #452	C₂²×C₆₇	semidirect
806. #451	C₂²×C₆₇	semidirect
807. #451	C₂²×C₆₇	semidirect
808. #450	C₂²×C₆₇	semidirect
809. #449	C₂²×C₆₇	semidirect
810. #449	C₂²×C₆₇	semidirect
811. #449	C₂²×C₆₇	semidirect
812. #449	C₂²×C₆₇	semidirect
813. #449	C₂²×C₆₇	semidirect
814. #448	C₂²×C₆₇	semidirect
815. #448	C₂²×C₆₇	semidirect
816. #448	C₂²×C₆₇	semidirect
817. #448	C₂²×C₆₇	semidirect
818. #447	C₂²×C₆₇	semidirect
819. #441	C₂²×C₆₇	semidirect
820. #440	C₂²×C₆₇	semidirect
821. C₄×Q₁₆	C₂²×C₆₇	semidirect
822. C₄×SD₁₆	C₂²×C₆₇	semidirect
823. #436	C₂²×C₆₇	semidirect
824. #435	C₂²×C₆₇	semidirect
825. #435	C₂²×C₆₇	semidirect
826. C₈×D₄	C₂²×C₆₇	semidirect
827. #428	C₂²×C₆₇	semidirect
828. #424	C₂²×C₆₇	semidirect
829. #419	C₂²×C₆₇	semidirect
830. #417	C₂²×C₆₇	semidirect
833. C₂×#103	C₂²×C₆₇	semidirect
834. C₂×#102	C₂²×C₆₇	semidirect
835. #408	C₂²×C₆₇	semidirect
837. #405	C₂²×C₆₇	semidirect
883. #137	D₄×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#578×C₆₇	2
C₂×#575×C₆₇	2
C₆₇×#3489	2
C₆₇×#3487	2
C₆₇×#3285	2
C₆₇×#3284	2
C₆₇×#3278	2
C₆₇×#3275	2
C₆₇×#3271	2
C₆₇×#3270	2
C₆₇×#3269	2
C₆₇×#3268	2
C₆₇×#3154	2
C₆₇×#3062	2
C₆₇×#3056	2
C₆₇×#3045	2
C₆₇×#3044	2
C₆₇×#3013	2
C₆₇×#3010	2
C₆₇×#3002	2
C₂×#452×C₆₇	2
C₆₇×#2947	2
C₆₇×#2933	2
#61078	67

Subgroups — C67×#61078 #30740329

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61078 #30740329