Subgroups — C₆₇×#62762 #30742013

Order 17152.

6624 conjugacy classes of subgroups.

The subgroup lattice has 1400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3566	C₂	1	8	yes	maximal, complemented
2	C₆₇×#3565	C₂	1	4	yes	maximal, complemented
3	C₆₇×#3562	C₂	1	4	yes	maximal, complemented
4	C₆₇×#3555	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3554	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3547	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3546	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3540	C₂	1	4	yes	maximal, complemented
9	C₆₇×#3539	C₂	1	4	yes	maximal, complemented
10	C₆₇×#3529	C₂	1	4	yes	maximal, complemented
11	C₆₇×#3483	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3482	C₂	1	2	yes	maximal, complemented
13	C₆₇×#3481	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3480	C₂	1	4	yes	maximal, complemented
15	C₆₇×#3475	C₂	1	4	yes	maximal, complemented
16	C₆₇×#3461	C₂	1	4	yes	maximal, complemented
17	C₆₇×#3460	C₂	1	4	yes	maximal, complemented
18	C₆₇×#3455	C₂	1	4	yes	maximal, complemented
19	C₆₇×#3444	C₂	1	2	yes	maximal, complemented
20	C₆₇×#3444	C₂	1	1	yes	maximal, characteristic, complemented
21	#563×C₆₇	C₂²	1	8	yes	complemented
22	#563×C₆₇	C₂²	1	4	yes	complemented
23	#562×C₆₇	C₂²	1	8	yes	complemented
24	#562×C₆₇	C₂²	1	8	yes	complemented
25	#562×C₆₇	C₂²	1	8	yes	complemented
26	H(3,𝔽₄)×C₆₇	C₂²	1	4	yes	complemented
27	#560×C₆₇	C₂²	1	8	yes	—
28	#560×C₆₇	C₂²	1	4	yes	complemented
29	#560×C₆₇	C₂²	1	8	yes	complemented
30	#560×C₆₇	C₂²	1	4	yes	complemented
31	#559×C₆₇	C₂²	1	8	yes	complemented
32	#559×C₆₇	C₂²	1	1	yes	characteristic, complemented
33	#559×C₆₇	C₂²	1	4	yes	complemented
34	Q₈²×C₆₇	C₂²	1	1	yes	characteristic, complemented
35	#557×C₆₇	C₂²	1	2	yes	complemented
36	#557×C₆₇	C₂²	1	4	yes	complemented
37	#556×C₆₇	C₂²	1	4	yes	complemented
38	#556×C₆₇	C₂²	1	4	yes	complemented
39	#556×C₆₇	C₂²	1	2	yes	complemented
40	#556×C₆₇	C₂²	1	4	yes	complemented
41	#556×C₆₇	C₂²	1	8	yes	complemented
42	#555×C₆₇	C₂²	1	4	yes	—
43	#555×C₆₇	C₂²	1	4	yes	complemented
44	#555×C₆₇	C₂²	1	1	yes	characteristic, complemented
45	#555×C₆₇	C₂²	1	4	yes	complemented
46	#554×C₆₇	C₂²	1	2	yes	complemented
47	#554×C₆₇	C₂²	1	4	yes	complemented
48	#553×C₆₇	C₂²	1	4	yes	—
49	#553×C₆₇	C₂²	1	4	yes	complemented
50	#553×C₆₇	C₂²	1	8	yes	complemented
51	#553×C₆₇	C₂²	1	8	yes	complemented
52	#553×C₆₇	C₂²	1	4	yes	complemented
53	#553×C₆₇	C₂²	1	8	yes	complemented
54	#552×C₆₇	C₂²	1	4	yes	complemented
55	#552×C₆₇	C₂²	1	4	yes	complemented
56	#552×C₆₇	C₂²	1	4	yes	complemented
57	#552×C₆₇	C₂²	1	8	yes	complemented
58	#552×C₆₇	C₂²	1	8	yes	complemented
59	#551×C₆₇	C₂²	1	8	yes	complemented
60	#551×C₆₇	C₂²	1	8	yes	complemented
61	#551×C₆₇	C₂²	1	4	yes	complemented
62	#550×C₆₇	C₂²	1	4	yes	—
63	#550×C₆₇	C₂²	1	4	yes	complemented
64	#550×C₆₇	C₂²	1	2	yes	complemented
65	D₄×Q₈×C₆₇	C₂²	1	2	yes	complemented
66	#548×C₆₇	C₂²	1	4	yes	—
67	#548×C₆₇	C₂²	1	4	yes	complemented
68	#548×C₆₇	C₂²	1	4	yes	complemented
69	#547×C₆₇	C₂²	1	4	yes	complemented
70	#547×C₆₇	C₂²	1	4	yes	complemented
71	#547×C₆₇	C₂²	1	2	yes	complemented
72	#546×C₆₇	C₂²	1	4	yes	—
73	#546×C₆₇	C₂²	1	4	yes	—
74	#546×C₆₇	C₂²	1	4	yes	complemented
75	D₄²×C₆₇	C₂²	1	1	yes	characteristic, complemented
76	#544×C₆₇	C₂²	1	4	yes	complemented
77	#544×C₆₇	C₂²	1	4	yes	complemented
78	#542×C₆₇	C₂²	1	4	yes	—
79	#542×C₆₇	C₂²	1	4	yes	complemented
80	#542×C₆₇	C₂²	1	8	yes	complemented
81	#542×C₆₇	C₂²	1	8	yes	complemented
82	#542×C₆₇	C₂²	1	4	yes	complemented
83	#542×C₆₇	C₂²	1	8	yes	complemented
84	#542×C₆₇	C₂²	1	4	yes	complemented
85	#542×C₆₇	C₂²	1	8	yes	complemented
86	#541×C₆₇	C₂²	1	4	yes	complemented
87	#541×C₆₇	C₂²	1	4	yes	complemented
88	#541×C₆₇	C₂²	1	8	yes	complemented
89	#541×C₆₇	C₂²	1	8	yes	complemented
90	#540×C₆₇	C₂²	1	4	yes	complemented
91	#540×C₆₇	C₂²	1	8	yes	complemented
92	#540×C₆₇	C₂²	1	8	yes	complemented
93	#540×C₆₇	C₂²	1	4	yes	complemented
94	#539×C₆₇	C₂²	1	8	yes	complemented
95	#539×C₆₇	C₂²	1	8	yes	complemented
96	#539×C₆₇	C₂²	1	8	yes	complemented
97	#539×C₆₇	C₂²	1	8	yes	complemented
98	#538×C₆₇	C₂²	1	8	yes	complemented
99	#538×C₆₇	C₂²	1	8	yes	complemented
100	#538×C₆₇	C₂²	1	8	yes	complemented
101	#538×C₆₇	C₂²	1	8	yes	complemented
102	#537×C₆₇	C₂²	1	4	yes	—
103	#537×C₆₇	C₂²	1	4	yes	complemented
104	#536×C₆₇	C₂²	1	4	yes	complemented
105	#536×C₆₇	C₂²	1	4	yes	complemented
106	#535×C₆₇	C₂²	1	4	yes	—
107	#535×C₆₇	C₂²	1	4	yes	complemented
108	#533×C₆₇	C₂²	1	2	yes	complemented
109	#533×C₆₇	C₂²	1	2	yes	complemented
110	#533×C₆₇	C₂²	1	2	yes	complemented
111	#533×C₆₇	C₂²	1	2	yes	complemented
112	#533×C₆₇	C₂²	1	1	yes	characteristic, complemented
113	#533×C₆₇	C₂²	1	4	yes	complemented
114	#533×C₆₇	C₂²	1	4	yes	complemented
115	#532×C₆₇	C₂²	1	2	yes	—
116	#532×C₆₇	C₂²	1	2	yes	—
117	#532×C₆₇	C₂²	1	2	yes	—
118	#532×C₆₇	C₂²	1	2	yes	—
119	#532×C₆₇	C₂²	1	1	yes	characteristic
120	#532×C₆₇	C₂²	1	4	yes	complemented
121	#532×C₆₇	C₂²	1	8	yes	complemented
122	#532×C₆₇	C₂²	1	4	yes	complemented
123	#529×C₆₇	C₂²	1	2	yes	—
124	#529×C₆₇	C₂²	1	2	yes	—
125	#529×C₆₇	C₂²	1	8	yes	complemented
126	#529×C₆₇	C₂²	1	8	yes	complemented
127	#529×C₆₇	C₂²	1	8	yes	complemented
128	#529×C₆₇	C₂²	1	2	yes	complemented
129	#529×C₆₇	C₂²	1	4	yes	complemented
130	#529×C₆₇	C₂²	1	4	yes	complemented
131	#529×C₆₇	C₂²	1	4	yes	complemented
132	#529×C₆₇	C₂²	1	4	yes	complemented
133	#529×C₆₇	C₂²	1	4	yes	complemented
134	#529×C₆₇	C₂²	1	4	yes	complemented
135	#529×C₆₇	C₂²	1	4	yes	complemented
136	#529×C₆₇	C₂²	1	2	yes	complemented
137	#529×C₆₇	C₂²	1	8	yes	complemented
138	#529×C₆₇	C₂²	1	8	yes	complemented
139	#529×C₆₇	C₂²	1	4	yes	complemented
140	#529×C₆₇	C₂²	1	4	yes	complemented
141	#525×C₆₇	C₂²	1	4	yes	—
142	#525×C₆₇	C₂²	1	2	yes	—
143	#525×C₆₇	C₂²	1	4	yes	complemented
144	#525×C₆₇	C₂²	1	2	yes	complemented
145	#525×C₆₇	C₂²	1	8	yes	complemented
146	#525×C₆₇	C₂²	1	2	yes	complemented
147	#525×C₆₇	C₂²	1	4	yes	complemented
148	#525×C₆₇	C₂²	1	4	yes	complemented
149	#525×C₆₇	C₂²	1	4	yes	complemented
150	C₄×#41×C₆₇	C₂²	1	2	yes	—
151	C₄×#41×C₆₇	C₂²	1	2	yes	complemented
152	C₄×#41×C₆₇	C₂²	1	4	yes	complemented
153	C₄×#41×C₆₇	C₂²	1	4	yes	complemented
154	C₄×#41×C₆₇	C₂²	1	4	yes	complemented
155	C₄×#41×C₆₇	C₂²	1	2	yes	complemented
156	C₄×#41×C₆₇	C₂²	1	4	yes	complemented
157	C₄×#41×C₆₇	C₂²	1	4	yes	complemented
158	C₄×#41×C₆₇	C₂²	1	4	yes	complemented
159	C₂×C₄×Q₈×C₆₇	C₂²	1	4	yes	complemented
160	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	complemented
161	C₂×#117×C₆₇	C₂²	1	4	yes	complemented
162	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic, complemented
163	C₂×#41×C₆₇	C₂³	1	2	yes	—
164	C₂×#41×C₆₇	C₂³	1	2	yes	—
165	C₂×#41×C₆₇	C₂³	1	4	yes	—
166	C₂×#41×C₆₇	C₂³	1	4	yes	—
167	C₂×#41×C₆₇	C₂³	1	4	yes	—
168	C₂×#41×C₆₇	C₂³	1	2	yes	—
169	C₂×#41×C₆₇	C₂³	1	4	yes	—
170	C₂×#41×C₆₇	C₂³	1	4	yes	—
171	C₂×#41×C₆₇	C₂³	1	4	yes	—
172	C₂²×Q₈×C₆₇	C₂³	1	4	yes	—
173	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
174	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
175	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
176	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
177	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
178	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
179	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
180	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
181	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
182	C₄⋊Q₈×C₆₇	C₂³	1	4	yes	—
183	C₄⋊Q₈×C₆₇	C₂³	1	4	yes	—
184	C₄⋊Q₈×C₆₇	C₂³	1	8	yes	—
185	C₄⋊Q₈×C₆₇	C₂³	1	8	yes	—
186	C₄⋊Q₈×C₆₇	C₂³	1	4	yes	—
187	C₄⋊Q₈×C₆₇	C₂³	1	4	yes	—
188	#127×C₆₇	C₂³	1	2	yes	—
189	#127×C₆₇	C₂³	1	1	yes	characteristic
190	#127×C₆₇	C₂³	1	8	yes	—
191	#127×C₆₇	C₂³	1	4	yes	—
192	#127×C₆₇	C₂³	1	4	yes	—
193	#126×C₆₇	C₂³	1	4	yes	—
194	#126×C₆₇	C₂³	1	4	yes	—
195	#126×C₆₇	C₂³	1	8	yes	—
196	#126×C₆₇	C₂³	1	4	yes	—
197	#126×C₆₇	C₂³	1	4	yes	—
198	#126×C₆₇	C₂³	1	8	yes	—
199	#126×C₆₇	C₂³	1	8	yes	—
200	#126×C₆₇	C₂³	1	8	yes	—
201	#126×C₆₇	C₂³	1	8	yes	—
202	#126×C₆₇	C₂³	1	8	yes	—
203	#126×C₆₇	C₂³	1	8	yes	—
204	#126×C₆₇	C₂³	1	8	yes	—
205	#126×C₆₇	C₂³	1	8	yes	—
206	#126×C₆₇	C₂³	1	8	yes	—
207	#126×C₆₇	C₂³	1	8	yes	—
208	#126×C₆₇	C₂³	1	8	yes	—
209	#126×C₆₇	C₂³	1	8	yes	—
210	#125×C₆₇	C₂³	1	2	yes	—
211	#125×C₆₇	C₂³	1	2	yes	—
212	#125×C₆₇	C₂³	1	4	yes	—
213	#125×C₆₇	C₂³	1	4	yes	—
214	#125×C₆₇	C₂³	1	4	yes	—
215	#125×C₆₇	C₂³	1	2	yes	—
216	#125×C₆₇	C₂³	1	8	yes	—
217	#125×C₆₇	C₂³	1	8	yes	—
218	#125×C₆₇	C₂³	1	8	yes	—
219	#125×C₆₇	C₂³	1	4	yes	—
220	#125×C₆₇	C₂³	1	8	yes	—
221	#125×C₆₇	C₂³	1	8	yes	—
222	#125×C₆₇	C₂³	1	4	yes	—
223	#125×C₆₇	C₂³	1	8	yes	—
224	#125×C₆₇	C₂³	1	8	yes	—
225	#124×C₆₇	C₂³	1	2	yes	—
226	#124×C₆₇	C₂³	1	4	yes	—
227	#124×C₆₇	C₂³	1	4	yes	—
228	#124×C₆₇	C₂³	1	4	yes	—
229	#124×C₆₇	C₂³	1	2	yes	—
230	#124×C₆₇	C₂³	1	2	yes	—
231	#124×C₆₇	C₂³	1	8	yes	—
232	#124×C₆₇	C₂³	1	4	yes	—
233	#124×C₆₇	C₂³	1	4	yes	—
234	#124×C₆₇	C₂³	1	8	yes	—
235	#124×C₆₇	C₂³	1	8	yes	—
236	#124×C₆₇	C₂³	1	8	yes	—
237	#124×C₆₇	C₂³	1	8	yes	—
238	#124×C₆₇	C₂³	1	8	yes	—
239	#124×C₆₇	C₂³	1	8	yes	—
240	#124×C₆₇	C₂³	1	8	yes	—
241	#124×C₆₇	C₂³	1	4	yes	—
242	#124×C₆₇	C₂³	1	4	yes	—
243	#123×C₆₇	C₂³	1	4	yes	—
244	#123×C₆₇	C₂³	1	4	yes	—
245	#123×C₆₇	C₂³	1	4	yes	—
246	#123×C₆₇	C₂³	1	4	yes	—
247	#123×C₆₇	C₂³	1	4	yes	—
248	#123×C₆₇	C₂³	1	8	yes	—
249	#123×C₆₇	C₂³	1	4	yes	—
250	#123×C₆₇	C₂³	1	4	yes	—
251	#123×C₆₇	C₂³	1	4	yes	—
252	#123×C₆₇	C₂³	1	4	yes	—
253	#123×C₆₇	C₂³	1	8	yes	—
254	#123×C₆₇	C₂³	1	8	yes	—
255	#123×C₆₇	C₂³	1	8	yes	—
256	#123×C₆₇	C₂³	1	8	yes	—
257	#123×C₆₇	C₂³	1	8	yes	—
258	#123×C₆₇	C₂³	1	8	yes	—
259	#123×C₆₇	C₂³	1	8	yes	—
260	#123×C₆₇	C₂³	1	8	yes	—
261	#123×C₆₇	C₂³	1	8	yes	—
262	#123×C₆₇	C₂³	1	8	yes	—
263	#123×C₆₇	C₂³	1	8	yes	—
264	#123×C₆₇	C₂³	1	8	yes	—
265	#123×C₆₇	C₂³	1	8	yes	—
266	#123×C₆₇	C₂³	1	8	yes	—
267	#123×C₆₇	C₂³	1	8	yes	—
268	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
269	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
270	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	—
271	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
272	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
273	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
274	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
275	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
276	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
277	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
278	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
279	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
280	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	—
281	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	—
282	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	—
283	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
284	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	—
285	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	—
286	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
287	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	—
288	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	—
289	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	—
290	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	—
291	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
292	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	—
293	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
294	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	—
295	#121×C₆₇	C₂³	1	2	yes	—
296	#121×C₆₇	C₂³	1	2	yes	—
297	#121×C₆₇	C₂³	1	8	yes	—
298	#121×C₆₇	C₂³	1	4	yes	—
299	#121×C₆₇	C₂³	1	2	yes	—
300	#121×C₆₇	C₂³	1	4	yes	—
301	#121×C₆₇	C₂³	1	4	yes	—
302	#121×C₆₇	C₂³	1	4	yes	—
303	#121×C₆₇	C₂³	1	2	yes	—
304	#121×C₆₇	C₂³	1	4	yes	—
305	#121×C₆₇	C₂³	1	4	yes	—
306	#121×C₆₇	C₂³	1	4	yes	—
307	#121×C₆₇	C₂³	1	8	yes	—
308	#121×C₆₇	C₂³	1	8	yes	—
309	#121×C₆₇	C₂³	1	8	yes	—
310	#121×C₆₇	C₂³	1	4	yes	—
311	#121×C₆₇	C₂³	1	8	yes	—
312	#121×C₆₇	C₂³	1	8	yes	—
313	#121×C₆₇	C₂³	1	4	yes	—
314	#121×C₆₇	C₂³	1	8	yes	—
315	#121×C₆₇	C₂³	1	8	yes	—
316	#121×C₆₇	C₂³	1	8	yes	—
317	#121×C₆₇	C₂³	1	4	yes	—
318	#121×C₆₇	C₂³	1	8	yes	—
319	#121×C₆₇	C₂³	1	4	yes	—
320	#121×C₆₇	C₂³	1	8	yes	—
321	#121×C₆₇	C₂³	1	8	yes	—
322	#121×C₆₇	C₂³	1	8	yes	—
323	#121×C₆₇	C₂³	1	8	yes	—
324	#121×C₆₇	C₂³	1	8	yes	—
325	#121×C₆₇	C₂³	1	8	yes	—
326	#120×C₆₇	C₂³	1	4	yes	—
327	#120×C₆₇	C₂³	1	4	yes	—
328	#120×C₆₇	C₂³	1	4	yes	—
329	#120×C₆₇	C₂³	1	4	yes	—
330	#120×C₆₇	C₂³	1	4	yes	—
331	#120×C₆₇	C₂³	1	8	yes	—
332	#120×C₆₇	C₂³	1	8	yes	—
333	#120×C₆₇	C₂³	1	8	yes	—
334	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
335	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
336	C₄×Q₈×C₆₇	C₂³	1	8	yes	—
337	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
338	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
339	C₄×Q₈×C₆₇	C₂³	1	8	yes	—
340	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
341	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
342	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
343	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
344	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
345	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
346	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
347	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
348	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
349	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
350	C₄×Q₈×C₆₇	C₂³	1	8	yes	—
351	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
352	C₄×D₄×C₆₇	C₂³	1	2	yes	—
353	C₄×D₄×C₆₇	C₂³	1	4	yes	—
354	C₄×D₄×C₆₇	C₂³	1	8	yes	—
355	C₄×D₄×C₆₇	C₂³	1	4	yes	—
356	C₄×D₄×C₆₇	C₂³	1	4	yes	—
357	C₄×D₄×C₆₇	C₂³	1	8	yes	—
358	C₄×D₄×C₆₇	C₂³	1	4	yes	—
359	C₄×D₄×C₆₇	C₂³	1	4	yes	—
360	C₄×D₄×C₆₇	C₂³	1	2	yes	—
361	C₄×D₄×C₆₇	C₂³	1	2	yes	—
362	C₄×D₄×C₆₇	C₂³	1	4	yes	—
363	C₄×D₄×C₆₇	C₂³	1	4	yes	—
364	C₄×D₄×C₆₇	C₂³	1	4	yes	—
365	C₄×D₄×C₆₇	C₂³	1	4	yes	—
366	C₄×D₄×C₆₇	C₂³	1	8	yes	—
367	C₄×D₄×C₆₇	C₂³	1	8	yes	—
368	C₄×D₄×C₆₇	C₂³	1	4	yes	—
369	C₄×D₄×C₆₇	C₂³	1	4	yes	—
370	C₄×D₄×C₆₇	C₂³	1	4	yes	—
371	C₄×D₄×C₆₇	C₂³	1	8	yes	—
372	C₄×D₄×C₆₇	C₂³	1	8	yes	—
373	C₄×D₄×C₆₇	C₂³	1	4	yes	—
374	C₄×D₄×C₆₇	C₂³	1	4	yes	—
375	C₄×D₄×C₆₇	C₂³	1	4	yes	—
376	C₄×D₄×C₆₇	C₂³	1	8	yes	—
377	C₄×D₄×C₆₇	C₂³	1	4	yes	—
378	C₄×D₄×C₆₇	C₂³	1	4	yes	—
379	C₄×D₄×C₆₇	C₂³	1	4	yes	—
380	C₄×D₄×C₆₇	C₂³	1	4	yes	—
381	C₄×D₄×C₆₇	C₂³	1	4	yes	—
382	C₄×D₄×C₆₇	C₂³	1	2	yes	—
383	C₄×D₄×C₆₇	C₂³	1	4	yes	—
384	C₄×D₄×C₆₇	C₂³	1	8	yes	—
385	C₄×D₄×C₆₇	C₂³	1	8	yes	—
386	C₄×D₄×C₆₇	C₂³	1	8	yes	—
387	C₄×D₄×C₆₇	C₂³	1	8	yes	—
388	C₄×D₄×C₆₇	C₂³	1	4	yes	—
389	C₄×D₄×C₆₇	C₂³	1	8	yes	—
390	C₄×D₄×C₆₇	C₂³	1	4	yes	—
391	#117×C₆₇	C₂³	1	4	yes	—
392	#117×C₆₇	C₂³	1	8	yes	—
393	#117×C₆₇	C₂³	1	8	yes	—
394	#117×C₆₇	C₂³	1	8	yes	—
395	#117×C₆₇	C₂³	1	2	yes	—
396	#117×C₆₇	C₂³	1	4	yes	—
397	#117×C₆₇	C₂³	1	4	yes	—
398	#117×C₆₇	C₂³	1	4	yes	—
399	#117×C₆₇	C₂³	1	2	yes	—
400	#117×C₆₇	C₂³	1	4	yes	—
401	#117×C₆₇	C₂³	1	2	yes	—
402	#117×C₆₇	C₂³	1	4	yes	—
403	#117×C₆₇	C₂³	1	4	yes	—
404	#117×C₆₇	C₂³	1	4	yes	—
405	#117×C₆₇	C₂³	1	4	yes	—
406	#117×C₆₇	C₂³	1	4	yes	—
407	#117×C₆₇	C₂³	1	8	yes	—
408	#117×C₆₇	C₂³	1	4	yes	—
409	#117×C₆₇	C₂³	1	4	yes	—
410	#117×C₆₇	C₂³	1	4	yes	—
411	#117×C₆₇	C₂³	1	8	yes	—
412	#117×C₆₇	C₂³	1	8	yes	—
413	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
414	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
415	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
416	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
417	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
418	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
419	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
420	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
421	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
422	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
423	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
424	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
425	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
426	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
427	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
428	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
429	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
430	C₂×C₄²×C₆₇	C₂³	1	8	yes	—
431	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
432	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
433	#41×C₆₇	—	4	8	no	—
434	#41×C₆₇	—	4	4	no	—
435	#41×C₆₇	—	4	8	no	—
436	#41×C₆₇	—	4	8	no	—
437	#41×C₆₇	—	4	4	no	—
438	#41×C₆₇	—	4	8	no	—
439	#41×C₆₇	—	4	4	no	—
440	#41×C₆₇	—	4	8	no	—
441	#41×C₆₇	—	4	8	no	—
442	C₂×Q₈×C₆₇	—	4	8	no	—
443	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
444	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
445	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
446	C₂×Q₈×C₆₇	C₂⁴	1	8	yes	—
447	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
448	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
449	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
450	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
451	C₂×D₄×C₆₇	—	4	8	no	—
452	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
453	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
454	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
455	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
456	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
457	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
458	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
459	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
460	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
461	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
462	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
463	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
464	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
465	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
466	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
467	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
468	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
469	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
470	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
471	C₂²×C₄×C₆₇	—	4	8	no	—
472	C₂²×C₄×C₆₇	—	4	4	no	—
473	C₂²×C₄×C₆₇	—	4	2	no	—
474	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
475	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
476	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
477	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
478	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
479	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
480	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
481	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
482	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
483	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
484	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
485	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
486	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
487	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
488	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
489	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
490	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
491	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
492	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
493	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
494	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
495	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
496	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
497	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
498	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
499	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
500	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
501	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
502	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
503	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
504	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
505	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
506	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
507	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
508	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
509	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
510	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
511	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
512	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
513	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
514	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
515	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
516	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
517	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
518	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
519	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
520	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
521	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
522	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
523	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
524	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
525	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
526	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
527	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
528	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
529	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
530	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
531	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
532	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
533	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
534	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
535	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
536	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
537	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
538	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
539	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
540	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
541	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
542	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
543	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
544	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
545	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
546	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
547	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
548	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
549	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
550	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
551	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
552	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
553	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
554	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
555	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
556	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
557	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
558	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
559	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
560	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
561	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
562	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
563	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
564	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
565	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
566	C₄²×C₆₇	C₂⁴	1	2	yes	—
567	C₄²×C₆₇	C₂⁴	1	2	yes	—
568	C₄²×C₆₇	C₂⁴	1	2	yes	—
569	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
570	C₄²×C₆₇	C₂⁴	1	2	yes	—
571	C₄²×C₆₇	C₂⁴	1	2	yes	—
572	C₄²×C₆₇	C₂⁴	1	4	yes	—
573	C₄²×C₆₇	C₂⁴	1	4	yes	—
574	C₄²×C₆₇	C₂⁴	1	8	yes	—
575	C₄²×C₆₇	C₂⁴	1	4	yes	—
576	C₄²×C₆₇	C₂⁴	1	4	yes	—
577	C₄²×C₆₇	C₂⁴	1	4	yes	—
578	C₄²×C₆₇	C₂⁴	1	4	yes	—
579	C₄²×C₆₇	C₂⁴	1	8	yes	—
580	C₄²×C₆₇	C₂⁴	1	8	yes	—
581	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
582	C₄²×C₆₇	C₂⁴	1	2	yes	—
583	C₄²×C₆₇	C₂⁴	1	4	yes	—
584	C₄²×C₆₇	C₂⁴	1	4	yes	—
585	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
586	C₄²×C₆₇	C₂⁴	1	4	yes	—
587	C₂³×C₆₇	—	4	2	no	—
588	C₂³×C₆₇	—	4	1	no	—
589	C₂³×C₆₇	—	4	4	no	—
590	C₂³×C₆₇	—	4	8	no	—
591	C₂³×C₆₇	C₂⁵	1	4	yes	—
592	C₂³×C₆₇	C₂⁵	1	2	yes	—
593	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
594	C₂³×C₆₇	C₂⁵	1	4	yes	—
595	C₂³×C₆₇	C₂⁵	1	4	yes	—
596	Q₈×C₆₇	—	2	4	no	—
597	Q₈×C₆₇	—	2	8	no	—
598	Q₈×C₆₇	—	2	4	no	—
599	Q₈×C₆₇	—	4	8	no	—
600	Q₈×C₆₇	—	4	4	no	—
601	Q₈×C₆₇	—	4	4	no	—
602	Q₈×C₆₇	—	4	2	no	—
603	Q₈×C₆₇	—	4	4	no	—
604	D₄×C₆₇	—	2	4	no	—
605	D₄×C₆₇	—	2	8	no	—
606	D₄×C₆₇	—	2	4	no	—
607	D₄×C₆₇	—	4	8	no	—
608	D₄×C₆₇	—	4	4	no	—
609	D₄×C₆₇	—	4	4	no	—
610	D₄×C₆₇	—	4	4	no	—
611	D₄×C₆₇	—	4	4	no	—
612	D₄×C₆₇	—	4	4	no	—
613	D₄×C₆₇	—	4	2	no	—
614	D₄×C₆₇	—	4	4	no	—
615	D₄×C₆₇	—	4	4	no	—
616	D₄×C₆₇	—	4	4	no	—
617	D₄×C₆₇	—	4	8	no	—
618	D₄×C₆₇	—	4	8	no	—
619	D₄×C₆₇	—	4	4	no	—
620	D₄×C₆₇	—	4	8	no	—
621	D₄×C₆₇	—	4	8	no	—
622	D₄×C₆₇	—	4	4	no	—
623	C₂×C₄×C₆₇	—	2	8	no	—
624	C₂×C₄×C₆₇	—	2	4	no	—
625	C₂×C₄×C₆₇	—	2	4	no	—
626	C₂×C₄×C₆₇	—	2	2	no	—
627	C₂×C₄×C₆₇	—	2	4	no	—
628	C₂×C₄×C₆₇	—	2	8	no	—
629	C₂×C₄×C₆₇	—	2	4	no	—
630	C₂×C₄×C₆₇	—	2	8	no	—
631	C₂×C₄×C₆₇	—	2	8	no	—
632	C₂×C₄×C₆₇	—	2	8	no	—
633	C₂×C₄×C₆₇	—	4	2	no	—
634	C₂×C₄×C₆₇	—	4	2	no	—
635	C₂×C₄×C₆₇	—	4	2	no	—
636	C₂×C₄×C₆₇	—	4	4	no	—
637	C₂×C₄×C₆₇	—	4	8	no	—
638	C₂×C₄×C₆₇	—	4	2	no	—
639	C₂×C₄×C₆₇	—	4	1	no	—
640	C₂×C₄×C₆₇	—	4	8	no	—
641	C₂×C₄×C₆₇	—	4	4	no	—
642	C₂×C₄×C₆₇	—	4	8	no	—
643	C₂×C₄×C₆₇	—	4	4	no	—
644	C₂×C₄×C₆₇	—	4	8	no	—
645	C₂×C₄×C₆₇	—	4	8	no	—
646	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
647	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
648	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
649	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
650	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
651	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
652	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
653	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
654	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
655	C₂×C₄×C₆₇	C₂⁵	1	8	yes	—
656	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
657	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
658	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
659	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
660	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
661	C₂²×C₆₇	—	2	4	no	—
662	C₂²×C₆₇	—	2	4	no	—
663	C₂²×C₆₇	—	2	2	no	—
664	C₂²×C₆₇	—	2	2	no	—
665	C₂²×C₆₇	—	2	2	no	—
666	C₂²×C₆₇	—	2	2	no	—
667	C₂²×C₆₇	—	2	1	no	—
668	C₂²×C₆₇	—	2	4	no	—
669	C₂²×C₆₇	—	2	4	no	—
670	C₂²×C₆₇	—	2	4	no	—
671	C₂²×C₆₇	—	2	4	no	—
672	C₂²×C₆₇	—	2	8	no	—
673	C₂²×C₆₇	—	2	4	no	—
674	C₂²×C₆₇	—	4	4	no	—
675	C₂²×C₆₇	—	8	8	no	—
676	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
677	C₄×C₆₇	—	2	2	no	—
678	C₄×C₆₇	—	2	2	no	—
679	C₄×C₆₇	—	2	4	no	—
680	C₄×C₆₇	—	2	4	no	—
681	C₄×C₆₇	—	2	2	no	—
682	C₄×C₆₇	—	2	4	no	—
683	C₄×C₆₇	—	2	1	no	—
684	C₄×C₆₇	—	2	2	no	—
685	C₄×C₆₇	—	2	4	no	—
686	C₄×C₆₇	—	2	4	no	—
687	C₄×C₆₇	—	2	4	no	—
688	C₄×C₆₇	—	2	8	no	—
689	C₄×C₆₇	—	2	4	no	—
690	C₄×C₆₇	#585	1	2	yes	—
691	C₄×C₆₇	#585	1	4	yes	—
692	#62762	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
693	C₂×C₆₇	—	4	4	no	—
694	C₂×C₆₇	—	4	1	no	—
695	C₂×C₆₇	—	4	2	no	—
696	C₂×C₆₇	—	4	4	no	—
697	C₂×C₆₇	—	4	4	no	—
698	C₂×C₆₇	C₂×#585	1	2	yes	—
699	C₂×C₆₇	C₂×#585	1	1	yes	characteristic
700	#3566	C₂×C₆₇	1	8	yes	complemented
701	#3565	C₂×C₆₇	1	4	yes	complemented
702	#3562	C₂×C₆₇	1	4	yes	complemented
703	#3555	C₂×C₆₇	1	2	yes	complemented
704	#3554	C₂×C₆₇	1	2	yes	complemented
705	#3547	C₂×C₆₇	1	2	yes	complemented
706	#3546	C₂×C₆₇	1	2	yes	complemented
707	#3540	C₂×C₆₇	1	4	yes	complemented
708	#3539	C₂×C₆₇	1	4	yes	complemented
709	#3529	C₂×C₆₇	1	4	yes	complemented
710	#3483	C₂×C₆₇	1	1	yes	characteristic, complemented
711	#3482	C₂×C₆₇	1	2	yes	complemented
712	#3481	C₂×C₆₇	1	1	yes	characteristic, complemented
713	#3480	C₂×C₆₇	1	4	yes	complemented
714	#3475	C₂×C₆₇	1	4	yes	complemented
715	#3461	C₂×C₆₇	1	4	yes	complemented
716	#3460	C₂×C₆₇	1	4	yes	complemented
717	#3455	C₂×C₆₇	1	4	yes	complemented
718	#3444	C₂×C₆₇	1	2	yes	complemented
719	#3444	C₂×C₆₇	1	1	yes	characteristic, complemented
720	C₆₇	#62762	1	1	yes	characteristic, direct product factor, Sylow
721	#563	C₂²×C₆₇	1	8	yes	complemented
722	#563	C₂²×C₆₇	1	4	yes	complemented
723	#562	C₂²×C₆₇	1	8	yes	complemented
724	#562	C₂²×C₆₇	1	8	yes	complemented
725	#562	C₂²×C₆₇	1	8	yes	complemented
726	H(3,𝔽₄)	C₂²×C₆₇	1	4	yes	complemented
727	#560	C₂²×C₆₇	1	8	yes	—
728	#560	C₂²×C₆₇	1	4	yes	complemented
729	#560	C₂²×C₆₇	1	8	yes	complemented
730	#560	C₂²×C₆₇	1	4	yes	complemented
731	#559	C₂²×C₆₇	1	8	yes	complemented
732	#559	C₂²×C₆₇	1	4	yes	complemented
733	#559	C₂²×C₆₇	1	1	yes	characteristic, complemented
734	Q₈²	C₂²×C₆₇	1	1	yes	characteristic, complemented
735	#557	C₂²×C₆₇	1	4	yes	complemented
736	#557	C₂²×C₆₇	1	2	yes	complemented
737	#556	C₂²×C₆₇	1	4	yes	complemented
738	#556	C₂²×C₆₇	1	4	yes	complemented
739	#556	C₂²×C₆₇	1	8	yes	complemented
740	#556	C₂²×C₆₇	1	4	yes	complemented
741	#556	C₂²×C₆₇	1	2	yes	complemented
742	#555	C₂²×C₆₇	1	4	yes	—
743	#555	C₂²×C₆₇	1	4	yes	complemented
744	#555	C₂²×C₆₇	1	1	yes	characteristic, complemented
745	#555	C₂²×C₆₇	1	4	yes	complemented
746	#554	C₂²×C₆₇	1	4	yes	complemented
747	#554	C₂²×C₆₇	1	2	yes	complemented
748	#553	C₂²×C₆₇	1	4	yes	—
749	#553	C₂²×C₆₇	1	8	yes	complemented
750	#553	C₂²×C₆₇	1	4	yes	complemented
751	#553	C₂²×C₆₇	1	8	yes	complemented
752	#553	C₂²×C₆₇	1	4	yes	complemented
753	#553	C₂²×C₆₇	1	8	yes	complemented
754	#552	C₂²×C₆₇	1	4	yes	complemented
755	#552	C₂²×C₆₇	1	4	yes	complemented
756	#552	C₂²×C₆₇	1	8	yes	complemented
757	#552	C₂²×C₆₇	1	4	yes	complemented
758	#552	C₂²×C₆₇	1	8	yes	complemented
759	#551	C₂²×C₆₇	1	8	yes	complemented
760	#551	C₂²×C₆₇	1	8	yes	complemented
761	#551	C₂²×C₆₇	1	4	yes	complemented
762	#550	C₂²×C₆₇	1	4	yes	—
763	#550	C₂²×C₆₇	1	4	yes	complemented
764	#550	C₂²×C₆₇	1	2	yes	complemented
765	D₄×Q₈	C₂²×C₆₇	1	2	yes	complemented
766	#548	C₂²×C₆₇	1	4	yes	—
767	#548	C₂²×C₆₇	1	4	yes	complemented
768	#548	C₂²×C₆₇	1	4	yes	complemented
769	#547	C₂²×C₆₇	1	4	yes	complemented
770	#547	C₂²×C₆₇	1	4	yes	complemented
771	#547	C₂²×C₆₇	1	2	yes	complemented
772	#546	C₂²×C₆₇	1	4	yes	—
773	#546	C₂²×C₆₇	1	4	yes	—
774	#546	C₂²×C₆₇	1	4	yes	complemented
775	D₄²	C₂²×C₆₇	1	1	yes	characteristic, complemented
776	#544	C₂²×C₆₇	1	4	yes	complemented
777	#544	C₂²×C₆₇	1	4	yes	complemented
778	#542	C₂²×C₆₇	1	4	yes	—
779	#542	C₂²×C₆₇	1	8	yes	complemented
780	#542	C₂²×C₆₇	1	8	yes	complemented
781	#542	C₂²×C₆₇	1	4	yes	complemented
782	#542	C₂²×C₆₇	1	8	yes	complemented
783	#542	C₂²×C₆₇	1	4	yes	complemented
784	#542	C₂²×C₆₇	1	8	yes	complemented
785	#542	C₂²×C₆₇	1	4	yes	complemented
786	#541	C₂²×C₆₇	1	8	yes	complemented
787	#541	C₂²×C₆₇	1	4	yes	complemented
788	#541	C₂²×C₆₇	1	4	yes	complemented
789	#541	C₂²×C₆₇	1	8	yes	complemented
790	#540	C₂²×C₆₇	1	8	yes	complemented
791	#540	C₂²×C₆₇	1	4	yes	complemented
792	#540	C₂²×C₆₇	1	8	yes	complemented
793	#540	C₂²×C₆₇	1	4	yes	complemented
794	#539	C₂²×C₆₇	1	8	yes	complemented
795	#539	C₂²×C₆₇	1	8	yes	complemented
796	#539	C₂²×C₆₇	1	8	yes	complemented
797	#539	C₂²×C₆₇	1	8	yes	complemented
798	#538	C₂²×C₆₇	1	8	yes	complemented
799	#538	C₂²×C₆₇	1	8	yes	complemented
800	#538	C₂²×C₆₇	1	8	yes	complemented
801	#538	C₂²×C₆₇	1	8	yes	complemented
802	#537	C₂²×C₆₇	1	4	yes	—
803	#537	C₂²×C₆₇	1	4	yes	complemented
804	#536	C₂²×C₆₇	1	4	yes	complemented
805	#536	C₂²×C₆₇	1	4	yes	complemented
806	#535	C₂²×C₆₇	1	4	yes	—
807	#535	C₂²×C₆₇	1	4	yes	complemented
808	#533	C₂²×C₆₇	1	2	yes	complemented
809	#533	C₂²×C₆₇	1	1	yes	characteristic, complemented
810	#533	C₂²×C₆₇	1	2	yes	complemented
811	#533	C₂²×C₆₇	1	2	yes	complemented
812	#533	C₂²×C₆₇	1	2	yes	complemented
813	#533	C₂²×C₆₇	1	4	yes	complemented
814	#533	C₂²×C₆₇	1	4	yes	complemented
815	#532	C₂²×C₆₇	1	2	yes	—
816	#532	C₂²×C₆₇	1	1	yes	characteristic
817	#532	C₂²×C₆₇	1	2	yes	—
818	#532	C₂²×C₆₇	1	2	yes	—
819	#532	C₂²×C₆₇	1	2	yes	—
820	#532	C₂²×C₆₇	1	4	yes	complemented
821	#532	C₂²×C₆₇	1	4	yes	complemented
822	#532	C₂²×C₆₇	1	8	yes	complemented
823	#529	C₂²×C₆₇	1	2	yes	—
824	#529	C₂²×C₆₇	1	2	yes	—
825	#529	C₂²×C₆₇	1	4	yes	complemented
826	#529	C₂²×C₆₇	1	4	yes	complemented
827	#529	C₂²×C₆₇	1	2	yes	complemented
828	#529	C₂²×C₆₇	1	2	yes	complemented
829	#529	C₂²×C₆₇	1	4	yes	complemented
830	#529	C₂²×C₆₇	1	4	yes	complemented
831	#529	C₂²×C₆₇	1	4	yes	complemented
832	#529	C₂²×C₆₇	1	4	yes	complemented
833	#529	C₂²×C₆₇	1	4	yes	complemented
834	#529	C₂²×C₆₇	1	8	yes	complemented
835	#529	C₂²×C₆₇	1	8	yes	complemented
836	#529	C₂²×C₆₇	1	8	yes	complemented
837	#529	C₂²×C₆₇	1	4	yes	complemented
838	#529	C₂²×C₆₇	1	8	yes	complemented
839	#529	C₂²×C₆₇	1	4	yes	complemented
840	#529	C₂²×C₆₇	1	8	yes	complemented
841	#525	C₂²×C₆₇	1	2	yes	—
842	#525	C₂²×C₆₇	1	4	yes	—
843	#525	C₂²×C₆₇	1	4	yes	complemented
844	#525	C₂²×C₆₇	1	2	yes	complemented
845	#525	C₂²×C₆₇	1	2	yes	complemented
846	#525	C₂²×C₆₇	1	4	yes	complemented
847	#525	C₂²×C₆₇	1	4	yes	complemented
848	#525	C₂²×C₆₇	1	4	yes	complemented
849	#525	C₂²×C₆₇	1	8	yes	complemented
850	C₄×#41	C₂²×C₆₇	1	2	yes	—
851	C₄×#41	C₂²×C₆₇	1	2	yes	complemented
852	C₄×#41	C₂²×C₆₇	1	4	yes	complemented
853	C₄×#41	C₂²×C₆₇	1	4	yes	complemented
854	C₄×#41	C₂²×C₆₇	1	4	yes	complemented
855	C₄×#41	C₂²×C₆₇	1	2	yes	complemented
856	C₄×#41	C₂²×C₆₇	1	4	yes	complemented
857	C₄×#41	C₂²×C₆₇	1	4	yes	complemented
858	C₄×#41	C₂²×C₆₇	1	4	yes	complemented
859	C₂×C₄×Q₈	C₂²×C₆₇	1	4	yes	complemented
860	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	complemented
861	C₂×#117	C₂²×C₆₇	1	4	yes	complemented
862	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic, complemented
863	C₂×#41	C₂³×C₆₇	1	2	yes	—
864	C₂×#41	C₂³×C₆₇	1	2	yes	—
865	C₂×#41	C₂³×C₆₇	1	4	yes	—
866	C₂×#41	C₂³×C₆₇	1	4	yes	—
867	C₂×#41	C₂³×C₆₇	1	4	yes	—
868	C₂×#41	C₂³×C₆₇	1	2	yes	—
869	C₂×#41	C₂³×C₆₇	1	4	yes	—
870	C₂×#41	C₂³×C₆₇	1	4	yes	—
871	C₂×#41	C₂³×C₆₇	1	4	yes	—
872	C₂²×Q₈	C₂³×C₆₇	1	4	yes	—
873	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
874	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
875	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
876	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
877	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
878	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
879	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
880	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
881	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
882	C₄⋊Q₈	C₂³×C₆₇	1	4	yes	—
883	C₄⋊Q₈	C₂³×C₆₇	1	4	yes	—
884	C₄⋊Q₈	C₂³×C₆₇	1	8	yes	—
885	C₄⋊Q₈	C₂³×C₆₇	1	8	yes	—
886	C₄⋊Q₈	C₂³×C₆₇	1	4	yes	—
887	C₄⋊Q₈	C₂³×C₆₇	1	4	yes	—
888	#127	C₂³×C₆₇	1	2	yes	—
889	#127	C₂³×C₆₇	1	1	yes	characteristic
890	#127	C₂³×C₆₇	1	8	yes	—
891	#127	C₂³×C₆₇	1	4	yes	—
892	#127	C₂³×C₆₇	1	4	yes	—
893	#126	C₂³×C₆₇	1	4	yes	—
894	#126	C₂³×C₆₇	1	4	yes	—
895	#126	C₂³×C₆₇	1	8	yes	—
896	#126	C₂³×C₆₇	1	4	yes	—
897	#126	C₂³×C₆₇	1	4	yes	—
898	#126	C₂³×C₆₇	1	8	yes	—
899	#126	C₂³×C₆₇	1	8	yes	—
900	#126	C₂³×C₆₇	1	8	yes	—
901	#126	C₂³×C₆₇	1	8	yes	—
902	#126	C₂³×C₆₇	1	8	yes	—
903	#126	C₂³×C₆₇	1	8	yes	—
904	#126	C₂³×C₆₇	1	8	yes	—
905	#126	C₂³×C₆₇	1	8	yes	—
906	#126	C₂³×C₆₇	1	8	yes	—
907	#126	C₂³×C₆₇	1	8	yes	—
908	#126	C₂³×C₆₇	1	8	yes	—
909	#126	C₂³×C₆₇	1	8	yes	—
910	#125	C₂³×C₆₇	1	2	yes	—
911	#125	C₂³×C₆₇	1	2	yes	—
912	#125	C₂³×C₆₇	1	4	yes	—
913	#125	C₂³×C₆₇	1	4	yes	—
914	#125	C₂³×C₆₇	1	4	yes	—
915	#125	C₂³×C₆₇	1	2	yes	—
916	#125	C₂³×C₆₇	1	8	yes	—
917	#125	C₂³×C₆₇	1	8	yes	—
918	#125	C₂³×C₆₇	1	8	yes	—
919	#125	C₂³×C₆₇	1	4	yes	—
920	#125	C₂³×C₆₇	1	8	yes	—
921	#125	C₂³×C₆₇	1	8	yes	—
922	#125	C₂³×C₆₇	1	4	yes	—
923	#125	C₂³×C₆₇	1	8	yes	—
924	#125	C₂³×C₆₇	1	8	yes	—
925	#124	C₂³×C₆₇	1	2	yes	—
926	#124	C₂³×C₆₇	1	4	yes	—
927	#124	C₂³×C₆₇	1	4	yes	—
928	#124	C₂³×C₆₇	1	4	yes	—
929	#124	C₂³×C₆₇	1	2	yes	—
930	#124	C₂³×C₆₇	1	2	yes	—
931	#124	C₂³×C₆₇	1	8	yes	—
932	#124	C₂³×C₆₇	1	4	yes	—
933	#124	C₂³×C₆₇	1	4	yes	—
934	#124	C₂³×C₆₇	1	8	yes	—
935	#124	C₂³×C₆₇	1	8	yes	—
936	#124	C₂³×C₆₇	1	8	yes	—
937	#124	C₂³×C₆₇	1	8	yes	—
938	#124	C₂³×C₆₇	1	8	yes	—
939	#124	C₂³×C₆₇	1	8	yes	—
940	#124	C₂³×C₆₇	1	8	yes	—
941	#124	C₂³×C₆₇	1	4	yes	—
942	#124	C₂³×C₆₇	1	4	yes	—
943	#123	C₂³×C₆₇	1	4	yes	—
944	#123	C₂³×C₆₇	1	4	yes	—
945	#123	C₂³×C₆₇	1	4	yes	—
946	#123	C₂³×C₆₇	1	4	yes	—
947	#123	C₂³×C₆₇	1	4	yes	—
948	#123	C₂³×C₆₇	1	8	yes	—
949	#123	C₂³×C₆₇	1	4	yes	—
950	#123	C₂³×C₆₇	1	4	yes	—
951	#123	C₂³×C₆₇	1	4	yes	—
952	#123	C₂³×C₆₇	1	4	yes	—
953	#123	C₂³×C₆₇	1	8	yes	—
954	#123	C₂³×C₆₇	1	8	yes	—
955	#123	C₂³×C₆₇	1	8	yes	—
956	#123	C₂³×C₆₇	1	8	yes	—
957	#123	C₂³×C₆₇	1	8	yes	—
958	#123	C₂³×C₆₇	1	8	yes	—
959	#123	C₂³×C₆₇	1	8	yes	—
960	#123	C₂³×C₆₇	1	8	yes	—
961	#123	C₂³×C₆₇	1	8	yes	—
962	#123	C₂³×C₆₇	1	8	yes	—
963	#123	C₂³×C₆₇	1	8	yes	—
964	#123	C₂³×C₆₇	1	8	yes	—
965	#123	C₂³×C₆₇	1	8	yes	—
966	#123	C₂³×C₆₇	1	8	yes	—
967	#123	C₂³×C₆₇	1	8	yes	—
968	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
969	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
970	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	—
971	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
972	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
973	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
974	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
975	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
976	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
977	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
978	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
979	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
980	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	—
981	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	—
982	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	—
983	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
984	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	—
985	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	—
986	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
987	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	—
988	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	—
989	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	—
990	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	—
991	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
992	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	—
993	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
994	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	—
995	#121	C₂³×C₆₇	1	2	yes	—
996	#121	C₂³×C₆₇	1	2	yes	—
997	#121	C₂³×C₆₇	1	8	yes	—
998	#121	C₂³×C₆₇	1	4	yes	—
999	#121	C₂³×C₆₇	1	2	yes	—
1000	#121	C₂³×C₆₇	1	4	yes	—
1001	#121	C₂³×C₆₇	1	4	yes	—
1002	#121	C₂³×C₆₇	1	4	yes	—
1003	#121	C₂³×C₆₇	1	2	yes	—
1004	#121	C₂³×C₆₇	1	4	yes	—
1005	#121	C₂³×C₆₇	1	4	yes	—
1006	#121	C₂³×C₆₇	1	4	yes	—
1007	#121	C₂³×C₆₇	1	8	yes	—
1008	#121	C₂³×C₆₇	1	8	yes	—
1009	#121	C₂³×C₆₇	1	8	yes	—
1010	#121	C₂³×C₆₇	1	4	yes	—
1011	#121	C₂³×C₆₇	1	8	yes	—
1012	#121	C₂³×C₆₇	1	8	yes	—
1013	#121	C₂³×C₆₇	1	4	yes	—
1014	#121	C₂³×C₆₇	1	8	yes	—
1015	#121	C₂³×C₆₇	1	8	yes	—
1016	#121	C₂³×C₆₇	1	8	yes	—
1017	#121	C₂³×C₆₇	1	4	yes	—
1018	#121	C₂³×C₆₇	1	8	yes	—
1019	#121	C₂³×C₆₇	1	4	yes	—
1020	#121	C₂³×C₆₇	1	8	yes	—
1021	#121	C₂³×C₆₇	1	8	yes	—
1022	#121	C₂³×C₆₇	1	8	yes	—
1023	#121	C₂³×C₆₇	1	8	yes	—
1024	#121	C₂³×C₆₇	1	8	yes	—
1025	#121	C₂³×C₆₇	1	8	yes	—
1026	#120	C₂³×C₆₇	1	4	yes	—
1027	#120	C₂³×C₆₇	1	4	yes	—
1028	#120	C₂³×C₆₇	1	4	yes	—
1029	#120	C₂³×C₆₇	1	4	yes	—
1030	#120	C₂³×C₆₇	1	4	yes	—
1031	#120	C₂³×C₆₇	1	8	yes	—
1032	#120	C₂³×C₆₇	1	8	yes	—
1033	#120	C₂³×C₆₇	1	8	yes	—
1034	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
1035	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
1036	C₄×Q₈	C₂³×C₆₇	1	8	yes	—
1037	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
1038	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
1039	C₄×Q₈	C₂³×C₆₇	1	8	yes	—
1040	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
1041	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
1042	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
1043	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
1044	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
1045	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
1046	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
1047	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
1048	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
1049	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
1050	C₄×Q₈	C₂³×C₆₇	1	8	yes	—
1051	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
1052	C₄×D₄	C₂³×C₆₇	1	2	yes	—
1053	C₄×D₄	C₂³×C₆₇	1	4	yes	—
1054	C₄×D₄	C₂³×C₆₇	1	8	yes	—
1055	C₄×D₄	C₂³×C₆₇	1	4	yes	—
1056	C₄×D₄	C₂³×C₆₇	1	4	yes	—
1057	C₄×D₄	C₂³×C₆₇	1	8	yes	—
1058	C₄×D₄	C₂³×C₆₇	1	4	yes	—
1059	C₄×D₄	C₂³×C₆₇	1	4	yes	—
1060	C₄×D₄	C₂³×C₆₇	1	2	yes	—
1061	C₄×D₄	C₂³×C₆₇	1	2	yes	—
1062	C₄×D₄	C₂³×C₆₇	1	4	yes	—
1063	C₄×D₄	C₂³×C₆₇	1	4	yes	—
1064	C₄×D₄	C₂³×C₆₇	1	4	yes	—
1065	C₄×D₄	C₂³×C₆₇	1	4	yes	—
1066	C₄×D₄	C₂³×C₆₇	1	8	yes	—
1067	C₄×D₄	C₂³×C₆₇	1	8	yes	—
1068	C₄×D₄	C₂³×C₆₇	1	4	yes	—
1069	C₄×D₄	C₂³×C₆₇	1	4	yes	—
1070	C₄×D₄	C₂³×C₆₇	1	4	yes	—
1071	C₄×D₄	C₂³×C₆₇	1	8	yes	—
1072	C₄×D₄	C₂³×C₆₇	1	8	yes	—
1073	C₄×D₄	C₂³×C₆₇	1	4	yes	—
1074	C₄×D₄	C₂³×C₆₇	1	4	yes	—
1075	C₄×D₄	C₂³×C₆₇	1	4	yes	—
1076	C₄×D₄	C₂³×C₆₇	1	8	yes	—
1077	C₄×D₄	C₂³×C₆₇	1	4	yes	—
1078	C₄×D₄	C₂³×C₆₇	1	4	yes	—
1079	C₄×D₄	C₂³×C₆₇	1	4	yes	—
1080	C₄×D₄	C₂³×C₆₇	1	4	yes	—
1081	C₄×D₄	C₂³×C₆₇	1	4	yes	—
1082	C₄×D₄	C₂³×C₆₇	1	2	yes	—
1083	C₄×D₄	C₂³×C₆₇	1	4	yes	—
1084	C₄×D₄	C₂³×C₆₇	1	8	yes	—
1085	C₄×D₄	C₂³×C₆₇	1	8	yes	—
1086	C₄×D₄	C₂³×C₆₇	1	8	yes	—
1087	C₄×D₄	C₂³×C₆₇	1	8	yes	—
1088	C₄×D₄	C₂³×C₆₇	1	4	yes	—
1089	C₄×D₄	C₂³×C₆₇	1	8	yes	—
1090	C₄×D₄	C₂³×C₆₇	1	4	yes	—
1091	#117	C₂³×C₆₇	1	4	yes	—
1092	#117	C₂³×C₆₇	1	8	yes	—
1093	#117	C₂³×C₆₇	1	8	yes	—
1094	#117	C₂³×C₆₇	1	8	yes	—
1095	#117	C₂³×C₆₇	1	2	yes	—
1096	#117	C₂³×C₆₇	1	4	yes	—
1097	#117	C₂³×C₆₇	1	4	yes	—
1098	#117	C₂³×C₆₇	1	4	yes	—
1099	#117	C₂³×C₆₇	1	2	yes	—
1100	#117	C₂³×C₆₇	1	4	yes	—
1101	#117	C₂³×C₆₇	1	2	yes	—
1102	#117	C₂³×C₆₇	1	4	yes	—
1103	#117	C₂³×C₆₇	1	4	yes	—
1104	#117	C₂³×C₆₇	1	4	yes	—
1105	#117	C₂³×C₆₇	1	4	yes	—
1106	#117	C₂³×C₆₇	1	4	yes	—
1107	#117	C₂³×C₆₇	1	8	yes	—
1108	#117	C₂³×C₆₇	1	4	yes	—
1109	#117	C₂³×C₆₇	1	4	yes	—
1110	#117	C₂³×C₆₇	1	4	yes	—
1111	#117	C₂³×C₆₇	1	8	yes	—
1112	#117	C₂³×C₆₇	1	8	yes	—
1113	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
1114	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
1115	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
1116	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
1117	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
1118	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
1119	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
1120	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
1121	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
1122	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
1123	C₂×C₄²	C₂³×C₆₇	1	8	yes	—
1124	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
1125	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
1126	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
1127	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
1128	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
1129	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
1130	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
1131	C₂⁴	C₂⁴×C₆₇	1	4	yes	—
1132	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
1133	#41	—	4	8	no	—
1134	#41	—	4	4	no	—
1135	#41	—	4	8	no	—
1136	#41	—	4	8	no	—
1137	#41	—	4	4	no	—
1138	#41	—	4	8	no	—
1139	#41	—	4	4	no	—
1140	#41	—	4	8	no	—
1141	#41	—	4	8	no	—
1142	C₂×Q₈	—	4	8	no	—
1143	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
1144	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
1145	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
1146	C₂×Q₈	C₂⁴×C₆₇	1	8	yes	—
1147	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
1148	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
1149	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
1150	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
1151	C₂×D₄	—	4	8	no	—
1152	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
1153	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
1154	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
1155	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
1156	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
1157	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
1158	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
1159	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
1160	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
1161	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
1162	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
1163	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
1164	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
1165	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
1166	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
1167	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
1168	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
1169	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
1170	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
1171	C₂²×C₄	—	4	8	no	—
1172	C₂²×C₄	—	4	4	no	—
1173	C₂²×C₄	—	4	2	no	—
1174	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
1175	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
1176	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1177	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1178	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1179	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1180	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1181	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
1182	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
1183	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
1184	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1185	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1186	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1187	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1188	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1189	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
1190	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
1191	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
1192	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
1193	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
1194	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
1195	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
1196	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
1197	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1198	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1199	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1200	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1201	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1202	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1203	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1204	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1205	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1206	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1207	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1208	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1209	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1210	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1211	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1212	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1213	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1214	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1215	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1216	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1217	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1218	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1219	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1220	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1221	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1222	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1223	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1224	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1225	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1226	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1227	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1228	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1229	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1230	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1231	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1232	C₂²⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1233	C₂²⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1234	C₂²⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1235	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1236	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1237	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1238	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1239	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1240	C₂²⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1241	C₂²⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1242	C₂²⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1243	C₂²⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1244	C₂²⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1245	C₂²⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1246	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1247	C₂²⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1248	C₂²⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1249	C₂²⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1250	C₂²⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1251	C₂²⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1252	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1253	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1254	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1255	C₂²⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1256	C₂²⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1257	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1258	C₂²⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1259	C₂²⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1260	C₂²⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1261	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1262	C₂²⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1263	C₂²⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1264	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1265	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1266	C₄²	C₂⁴×C₆₇	1	2	yes	—
1267	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1268	C₄²	C₂⁴×C₆₇	1	4	yes	—
1269	C₄²	C₂⁴×C₆₇	1	4	yes	—
1270	C₄²	C₂⁴×C₆₇	1	4	yes	—
1271	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1272	C₄²	C₂⁴×C₆₇	1	2	yes	—
1273	C₄²	C₂⁴×C₆₇	1	2	yes	—
1274	C₄²	C₂⁴×C₆₇	1	2	yes	—
1275	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1276	C₄²	C₂⁴×C₆₇	1	2	yes	—
1277	C₄²	C₂⁴×C₆₇	1	2	yes	—
1278	C₄²	C₂⁴×C₆₇	1	4	yes	—
1279	C₄²	C₂⁴×C₆₇	1	4	yes	—
1280	C₄²	C₂⁴×C₆₇	1	8	yes	—
1281	C₄²	C₂⁴×C₆₇	1	4	yes	—
1282	C₄²	C₂⁴×C₆₇	1	4	yes	—
1283	C₄²	C₂⁴×C₆₇	1	4	yes	—
1284	C₄²	C₂⁴×C₆₇	1	4	yes	—
1285	C₄²	C₂⁴×C₆₇	1	8	yes	—
1286	C₄²	C₂⁴×C₆₇	1	8	yes	—
1287	C₂³	—	4	2	no	—
1288	C₂³	—	4	1	no	—
1289	C₂³	—	4	4	no	—
1290	C₂³	—	4	8	no	—
1291	C₂³	C₂⁵×C₆₇	1	4	yes	—
1292	C₂³	C₂⁵×C₆₇	1	2	yes	—
1293	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
1294	C₂³	C₂⁵×C₆₇	1	4	yes	—
1295	C₂³	C₂⁵×C₆₇	1	4	yes	—
1296	Q₈	—	2	4	no	—
1297	Q₈	—	2	8	no	—
1298	Q₈	—	2	4	no	—
1299	Q₈	—	4	8	no	—
1300	Q₈	—	4	4	no	—
1301	Q₈	—	4	4	no	—
1302	Q₈	—	4	2	no	—
1303	Q₈	—	4	4	no	—
1304	D₄	—	2	4	no	—
1305	D₄	—	2	8	no	—
1306	D₄	—	2	4	no	—
1307	D₄	—	4	8	no	—
1308	D₄	—	4	4	no	—
1309	D₄	—	4	4	no	—
1310	D₄	—	4	4	no	—
1311	D₄	—	4	4	no	—
1312	D₄	—	4	4	no	—
1313	D₄	—	4	2	no	—
1314	D₄	—	4	4	no	—
1315	D₄	—	4	4	no	—
1316	D₄	—	4	4	no	—
1317	D₄	—	4	8	no	—
1318	D₄	—	4	8	no	—
1319	D₄	—	4	4	no	—
1320	D₄	—	4	8	no	—
1321	D₄	—	4	8	no	—
1322	D₄	—	4	4	no	—
1323	C₂×C₄	—	2	8	no	—
1324	C₂×C₄	—	2	4	no	—
1325	C₂×C₄	—	2	4	no	—
1326	C₂×C₄	—	2	2	no	—
1327	C₂×C₄	—	2	4	no	—
1328	C₂×C₄	—	2	8	no	—
1329	C₂×C₄	—	2	4	no	—
1330	C₂×C₄	—	2	8	no	—
1331	C₂×C₄	—	2	8	no	—
1332	C₂×C₄	—	2	8	no	—
1333	C₂×C₄	—	4	2	no	—
1334	C₂×C₄	—	4	2	no	—
1335	C₂×C₄	—	4	2	no	—
1336	C₂×C₄	—	4	4	no	—
1337	C₂×C₄	—	4	8	no	—
1338	C₂×C₄	—	4	2	no	—
1339	C₂×C₄	—	4	1	no	—
1340	C₂×C₄	—	4	8	no	—
1341	C₂×C₄	—	4	4	no	—
1342	C₂×C₄	—	4	8	no	—
1343	C₂×C₄	—	4	4	no	—
1344	C₂×C₄	—	4	8	no	—
1345	C₂×C₄	—	4	8	no	—
1346	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
1347	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
1348	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
1349	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
1350	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
1351	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1352	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
1353	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
1354	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
1355	C₂×C₄	C₂⁵×C₆₇	1	8	yes	—
1356	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
1357	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
1358	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
1359	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1360	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
1361	C₂²	—	2	4	no	—
1362	C₂²	—	2	4	no	—
1363	C₂²	—	2	2	no	—
1364	C₂²	—	2	2	no	—
1365	C₂²	—	2	2	no	—
1366	C₂²	—	2	2	no	—
1367	C₂²	—	2	1	no	—
1368	C₂²	—	2	4	no	—
1369	C₂²	—	2	4	no	—
1370	C₂²	—	2	4	no	—
1371	C₂²	—	2	4	no	—
1372	C₂²	—	2	8	no	—
1373	C₂²	—	2	4	no	—
1374	C₂²	—	4	4	no	—
1375	C₂²	—	8	8	no	—
1376	C₂²	C₂⁶×C₆₇	1	1	yes	characteristic
1377	C₄	—	2	2	no	—
1378	C₄	—	2	2	no	—
1379	C₄	—	2	4	no	—
1380	C₄	—	2	4	no	—
1381	C₄	—	2	2	no	—
1382	C₄	—	2	4	no	—
1383	C₄	—	2	1	no	—
1384	C₄	—	2	2	no	—
1385	C₄	—	2	4	no	—
1386	C₄	—	2	4	no	—
1387	C₄	—	2	4	no	—
1388	C₄	—	2	8	no	—
1389	C₄	—	2	4	no	—
1390	C₄	#585×C₆₇	1	2	yes	—
1391	C₄	#585×C₆₇	1	4	yes	—
1392	C₂	—	4	1	no	—
1393	C₂	—	4	2	no	—
1394	C₂	—	4	4	no	—
1395	C₂	—	4	4	no	—
1396	C₂	—	4	4	no	—
1397	C₂	C₂×#585×C₆₇	1	2	yes	—
1398	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×#3566	C₂	semidirect
2. C₆₇×#3565	C₂	semidirect
3. C₆₇×#3562	C₂	semidirect
4. C₆₇×#3555	C₂	semidirect
5. C₆₇×#3554	C₂	semidirect
6. C₆₇×#3547	C₂	semidirect
7. C₆₇×#3546	C₂	semidirect
8. C₆₇×#3540	C₂	semidirect
9. C₆₇×#3539	C₂	semidirect
10. C₆₇×#3529	C₂	semidirect
11. C₆₇×#3483	C₂	semidirect
12. C₆₇×#3482	C₂	semidirect
13. C₆₇×#3481	C₂	semidirect
14. C₆₇×#3480	C₂	semidirect
15. C₆₇×#3475	C₂	semidirect
16. C₆₇×#3461	C₂	semidirect
17. C₆₇×#3460	C₂	semidirect
18. C₆₇×#3455	C₂	semidirect
19. C₆₇×#3444	C₂	semidirect
20. C₆₇×#3444	C₂	semidirect
21. #563×C₆₇	C₂²	semidirect
22. #563×C₆₇	C₂²	semidirect
23. #562×C₆₇	C₂²	semidirect
24. #562×C₆₇	C₂²	semidirect
25. #562×C₆₇	C₂²	semidirect
26. H(3,𝔽₄)×C₆₇	C₂²	semidirect
28. #560×C₆₇	C₂²	semidirect
29. #560×C₆₇	C₂²	semidirect
30. #560×C₆₇	C₂²	semidirect
31. #559×C₆₇	C₂²	semidirect
32. #559×C₆₇	C₂²	semidirect
33. #559×C₆₇	C₂²	semidirect
34. Q₈²×C₆₇	C₂²	semidirect
35. #557×C₆₇	C₂²	semidirect
36. #557×C₆₇	C₂²	semidirect
37. #556×C₆₇	C₂²	semidirect
38. #556×C₆₇	C₂²	semidirect
39. #556×C₆₇	C₂²	semidirect
40. #556×C₆₇	C₂²	semidirect
41. #556×C₆₇	C₂²	semidirect
43. #555×C₆₇	C₂²	semidirect
44. #555×C₆₇	C₂²	semidirect
45. #555×C₆₇	C₂²	semidirect
46. #554×C₆₇	C₂²	semidirect
47. #554×C₆₇	C₂²	semidirect
49. #553×C₆₇	C₂²	semidirect
50. #553×C₆₇	C₂²	semidirect
51. #553×C₆₇	C₂²	semidirect
52. #553×C₆₇	C₂²	semidirect
53. #553×C₆₇	C₂²	semidirect
54. #552×C₆₇	C₂²	semidirect
55. #552×C₆₇	C₂²	semidirect
56. #552×C₆₇	C₂²	semidirect
57. #552×C₆₇	C₂²	semidirect
58. #552×C₆₇	C₂²	semidirect
59. #551×C₆₇	C₂²	semidirect
60. #551×C₆₇	C₂²	semidirect
61. #551×C₆₇	C₂²	semidirect
63. #550×C₆₇	C₂²	semidirect
64. #550×C₆₇	C₂²	semidirect
65. D₄×Q₈×C₆₇	C₂²	semidirect
67. #548×C₆₇	C₂²	semidirect
68. #548×C₆₇	C₂²	semidirect
69. #547×C₆₇	C₂²	semidirect
70. #547×C₆₇	C₂²	semidirect
71. #547×C₆₇	C₂²	semidirect
74. #546×C₆₇	C₂²	semidirect
75. D₄²×C₆₇	C₂²	semidirect
76. #544×C₆₇	C₂²	semidirect
77. #544×C₆₇	C₂²	semidirect
79. #542×C₆₇	C₂²	semidirect
80. #542×C₆₇	C₂²	semidirect
81. #542×C₆₇	C₂²	semidirect
82. #542×C₆₇	C₂²	semidirect
83. #542×C₆₇	C₂²	semidirect
84. #542×C₆₇	C₂²	semidirect
85. #542×C₆₇	C₂²	semidirect
86. #541×C₆₇	C₂²	semidirect
87. #541×C₆₇	C₂²	semidirect
88. #541×C₆₇	C₂²	semidirect
89. #541×C₆₇	C₂²	semidirect
90. #540×C₆₇	C₂²	semidirect
91. #540×C₆₇	C₂²	semidirect
92. #540×C₆₇	C₂²	semidirect
93. #540×C₆₇	C₂²	semidirect
94. #539×C₆₇	C₂²	semidirect
95. #539×C₆₇	C₂²	semidirect
96. #539×C₆₇	C₂²	semidirect
97. #539×C₆₇	C₂²	semidirect
98. #538×C₆₇	C₂²	semidirect
99. #538×C₆₇	C₂²	semidirect
100. #538×C₆₇	C₂²	semidirect
101. #538×C₆₇	C₂²	semidirect
103. #537×C₆₇	C₂²	semidirect
104. #536×C₆₇	C₂²	semidirect
105. #536×C₆₇	C₂²	semidirect
107. #535×C₆₇	C₂²	semidirect
108. #533×C₆₇	C₂²	semidirect
109. #533×C₆₇	C₂²	semidirect
110. #533×C₆₇	C₂²	semidirect
111. #533×C₆₇	C₂²	semidirect
112. #533×C₆₇	C₂²	semidirect
113. #533×C₆₇	C₂²	semidirect
114. #533×C₆₇	C₂²	semidirect
120. #532×C₆₇	C₂²	semidirect
121. #532×C₆₇	C₂²	semidirect
122. #532×C₆₇	C₂²	semidirect
125. #529×C₆₇	C₂²	semidirect
126. #529×C₆₇	C₂²	semidirect
127. #529×C₆₇	C₂²	semidirect
128. #529×C₆₇	C₂²	semidirect
129. #529×C₆₇	C₂²	semidirect
130. #529×C₆₇	C₂²	semidirect
131. #529×C₆₇	C₂²	semidirect
132. #529×C₆₇	C₂²	semidirect
133. #529×C₆₇	C₂²	semidirect
134. #529×C₆₇	C₂²	semidirect
135. #529×C₆₇	C₂²	semidirect
136. #529×C₆₇	C₂²	semidirect
137. #529×C₆₇	C₂²	semidirect
138. #529×C₆₇	C₂²	semidirect
139. #529×C₆₇	C₂²	semidirect
140. #529×C₆₇	C₂²	semidirect
143. #525×C₆₇	C₂²	semidirect
144. #525×C₆₇	C₂²	semidirect
145. #525×C₆₇	C₂²	semidirect
146. #525×C₆₇	C₂²	semidirect
147. #525×C₆₇	C₂²	semidirect
148. #525×C₆₇	C₂²	semidirect
149. #525×C₆₇	C₂²	semidirect
151. C₄×#41×C₆₇	C₂²	semidirect
152. C₄×#41×C₆₇	C₂²	semidirect
153. C₄×#41×C₆₇	C₂²	semidirect
154. C₄×#41×C₆₇	C₂²	semidirect
155. C₄×#41×C₆₇	C₂²	semidirect
156. C₄×#41×C₆₇	C₂²	semidirect
157. C₄×#41×C₆₇	C₂²	semidirect
158. C₄×#41×C₆₇	C₂²	semidirect
159. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
160. C₂×C₄×D₄×C₆₇	C₂²	semidirect
161. C₂×#117×C₆₇	C₂²	semidirect
162. C₂²×C₄²×C₆₇	C₂²	semidirect
692. #62762	C₆₇	direct (N × H)
700. #3566	C₂×C₆₇	semidirect
701. #3565	C₂×C₆₇	semidirect
702. #3562	C₂×C₆₇	semidirect
703. #3555	C₂×C₆₇	semidirect
704. #3554	C₂×C₆₇	semidirect
705. #3547	C₂×C₆₇	semidirect
706. #3546	C₂×C₆₇	semidirect
707. #3540	C₂×C₆₇	semidirect
708. #3539	C₂×C₆₇	semidirect
709. #3529	C₂×C₆₇	semidirect
710. #3483	C₂×C₆₇	semidirect
711. #3482	C₂×C₆₇	semidirect
712. #3481	C₂×C₆₇	semidirect
713. #3480	C₂×C₆₇	semidirect
714. #3475	C₂×C₆₇	semidirect
715. #3461	C₂×C₆₇	semidirect
716. #3460	C₂×C₆₇	semidirect
717. #3455	C₂×C₆₇	semidirect
718. #3444	C₂×C₆₇	semidirect
719. #3444	C₂×C₆₇	semidirect
720. C₆₇	#62762	direct (N × H)
721. #563	C₂²×C₆₇	semidirect
722. #563	C₂²×C₆₇	semidirect
723. #562	C₂²×C₆₇	semidirect
724. #562	C₂²×C₆₇	semidirect
725. #562	C₂²×C₆₇	semidirect
726. H(3,𝔽₄)	C₂²×C₆₇	semidirect
728. #560	C₂²×C₆₇	semidirect
729. #560	C₂²×C₆₇	semidirect
730. #560	C₂²×C₆₇	semidirect
731. #559	C₂²×C₆₇	semidirect
732. #559	C₂²×C₆₇	semidirect
733. #559	C₂²×C₆₇	semidirect
734. Q₈²	C₂²×C₆₇	semidirect
735. #557	C₂²×C₆₇	semidirect
736. #557	C₂²×C₆₇	semidirect
737. #556	C₂²×C₆₇	semidirect
738. #556	C₂²×C₆₇	semidirect
739. #556	C₂²×C₆₇	semidirect
740. #556	C₂²×C₆₇	semidirect
741. #556	C₂²×C₆₇	semidirect
743. #555	C₂²×C₆₇	semidirect
744. #555	C₂²×C₆₇	semidirect
745. #555	C₂²×C₆₇	semidirect
746. #554	C₂²×C₆₇	semidirect
747. #554	C₂²×C₆₇	semidirect
749. #553	C₂²×C₆₇	semidirect
750. #553	C₂²×C₆₇	semidirect
751. #553	C₂²×C₆₇	semidirect
752. #553	C₂²×C₆₇	semidirect
753. #553	C₂²×C₆₇	semidirect
754. #552	C₂²×C₆₇	semidirect
755. #552	C₂²×C₆₇	semidirect
756. #552	C₂²×C₆₇	semidirect
757. #552	C₂²×C₆₇	semidirect
758. #552	C₂²×C₆₇	semidirect
759. #551	C₂²×C₆₇	semidirect
760. #551	C₂²×C₆₇	semidirect
761. #551	C₂²×C₆₇	semidirect
763. #550	C₂²×C₆₇	semidirect
764. #550	C₂²×C₆₇	semidirect
765. D₄×Q₈	C₂²×C₆₇	semidirect
767. #548	C₂²×C₆₇	semidirect
768. #548	C₂²×C₆₇	semidirect
769. #547	C₂²×C₆₇	semidirect
770. #547	C₂²×C₆₇	semidirect
771. #547	C₂²×C₆₇	semidirect
774. #546	C₂²×C₆₇	semidirect
775. D₄²	C₂²×C₆₇	semidirect
776. #544	C₂²×C₆₇	semidirect
777. #544	C₂²×C₆₇	semidirect
779. #542	C₂²×C₆₇	semidirect
780. #542	C₂²×C₆₇	semidirect
781. #542	C₂²×C₆₇	semidirect
782. #542	C₂²×C₆₇	semidirect
783. #542	C₂²×C₆₇	semidirect
784. #542	C₂²×C₆₇	semidirect
785. #542	C₂²×C₆₇	semidirect
786. #541	C₂²×C₆₇	semidirect
787. #541	C₂²×C₆₇	semidirect
788. #541	C₂²×C₆₇	semidirect
789. #541	C₂²×C₆₇	semidirect
790. #540	C₂²×C₆₇	semidirect
791. #540	C₂²×C₆₇	semidirect
792. #540	C₂²×C₆₇	semidirect
793. #540	C₂²×C₆₇	semidirect
794. #539	C₂²×C₆₇	semidirect
795. #539	C₂²×C₆₇	semidirect
796. #539	C₂²×C₆₇	semidirect
797. #539	C₂²×C₆₇	semidirect
798. #538	C₂²×C₆₇	semidirect
799. #538	C₂²×C₆₇	semidirect
800. #538	C₂²×C₆₇	semidirect
801. #538	C₂²×C₆₇	semidirect
803. #537	C₂²×C₆₇	semidirect
804. #536	C₂²×C₆₇	semidirect
805. #536	C₂²×C₆₇	semidirect
807. #535	C₂²×C₆₇	semidirect
808. #533	C₂²×C₆₇	semidirect
809. #533	C₂²×C₆₇	semidirect
810. #533	C₂²×C₆₇	semidirect
811. #533	C₂²×C₆₇	semidirect
812. #533	C₂²×C₆₇	semidirect
813. #533	C₂²×C₆₇	semidirect
814. #533	C₂²×C₆₇	semidirect
820. #532	C₂²×C₆₇	semidirect
821. #532	C₂²×C₆₇	semidirect
822. #532	C₂²×C₆₇	semidirect
825. #529	C₂²×C₆₇	semidirect
826. #529	C₂²×C₆₇	semidirect
827. #529	C₂²×C₆₇	semidirect
828. #529	C₂²×C₆₇	semidirect
829. #529	C₂²×C₆₇	semidirect
830. #529	C₂²×C₆₇	semidirect
831. #529	C₂²×C₆₇	semidirect
832. #529	C₂²×C₆₇	semidirect
833. #529	C₂²×C₆₇	semidirect
834. #529	C₂²×C₆₇	semidirect
835. #529	C₂²×C₆₇	semidirect
836. #529	C₂²×C₆₇	semidirect
837. #529	C₂²×C₆₇	semidirect
838. #529	C₂²×C₆₇	semidirect
839. #529	C₂²×C₆₇	semidirect
840. #529	C₂²×C₆₇	semidirect
843. #525	C₂²×C₆₇	semidirect
844. #525	C₂²×C₆₇	semidirect
845. #525	C₂²×C₆₇	semidirect
846. #525	C₂²×C₆₇	semidirect
847. #525	C₂²×C₆₇	semidirect
848. #525	C₂²×C₆₇	semidirect
849. #525	C₂²×C₆₇	semidirect
851. C₄×#41	C₂²×C₆₇	semidirect
852. C₄×#41	C₂²×C₆₇	semidirect
853. C₄×#41	C₂²×C₆₇	semidirect
854. C₄×#41	C₂²×C₆₇	semidirect
855. C₄×#41	C₂²×C₆₇	semidirect
856. C₄×#41	C₂²×C₆₇	semidirect
857. C₄×#41	C₂²×C₆₇	semidirect
858. C₄×#41	C₂²×C₆₇	semidirect
859. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
860. C₂×C₄×D₄	C₂²×C₆₇	semidirect
861. C₂×#117	C₂²×C₆₇	semidirect
862. C₂²×C₄²	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3566	2
C₆₇×#3565	2
C₆₇×#3562	2
C₆₇×#3555	2
C₆₇×#3554	2
C₆₇×#3547	2
C₆₇×#3546	2
C₆₇×#3540	2
C₆₇×#3539	2
C₆₇×#3529	2
C₆₇×#3483	2
C₆₇×#3482	2
C₆₇×#3481	2
C₆₇×#3480	2
C₆₇×#3475	2
C₆₇×#3461	2
C₆₇×#3460	2
C₆₇×#3455	2
C₆₇×#3444	2
#62762	67

Subgroups — C67×#62762 #30742013

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#62762 #30742013