Subgroups — #22574871

Order 8576.

954 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16864147	C₂	1	1	yes	maximal, characteristic, complemented
2	#16864143	C₂	1	1	yes	maximal, characteristic, complemented
3	#16864142	C₂	1	1	yes	maximal, characteristic, complemented
4	#16864135	C₂	1	1	yes	maximal, characteristic, complemented
5	#16864130	C₂	1	1	yes	maximal, characteristic, complemented
6	#16864113	C₂	1	1	yes	maximal, characteristic, complemented
7	#16864108	C₂	1	1	yes	maximal, characteristic, complemented
8	#16864097	C₂	1	1	yes	maximal, characteristic, complemented
9	#16864092	C₂	1	1	yes	maximal, characteristic, complemented
10	#16864091	C₂	1	1	yes	maximal, characteristic, complemented
11	#16864086	C₂	1	1	yes	maximal, characteristic, complemented
12	#16864085	C₂	1	1	yes	maximal, characteristic, complemented
13	#16864085	C₂	1	1	yes	maximal, characteristic, complemented
14	#16864072	C₂	1	1	yes	maximal, characteristic, complemented
15	#16864072	C₂	1	1	yes	maximal, characteristic, complemented
16	#16864019	C₂	1	1	yes	maximal, characteristic, complemented
17	#16864014	C₂	1	1	yes	maximal, characteristic, complemented
18	#16864011	C₂	1	1	yes	maximal, characteristic, complemented
19	#16864006	C₂	1	1	yes	maximal, characteristic, complemented
20	#16864003	C₂	1	1	yes	maximal, characteristic, complemented
21	#16863997	C₂	1	1	yes	maximal, characteristic, complemented
22	#16863990	C₂	1	1	yes	maximal, characteristic, complemented
23	#16863989	C₂	1	1	yes	maximal, characteristic, complemented
24	#16863987	C₂	1	1	yes	maximal, characteristic, complemented
25	#16863984	C₂	1	1	yes	maximal, characteristic, complemented
26	#16863984	C₂	1	1	yes	maximal, characteristic, complemented
27	#16863981	C₂	1	1	yes	maximal, characteristic, complemented
28	#16863925	C₂	1	1	yes	maximal, characteristic, complemented
29	#16863924	C₂	1	1	yes	maximal, characteristic, complemented
30	#16863924	C₂	1	1	yes	maximal, characteristic, complemented
31	#551×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
32	#14524042	C₂²	1	1	yes	characteristic, complemented
33	#14524042	C₂²	1	1	yes	characteristic, complemented
34	#14524041	C₂²	1	1	yes	characteristic, complemented
35	#14524039	C₂²	1	1	yes	characteristic
36	#14524038	C₂²	1	1	yes	characteristic, complemented
37	#14524038	C₂²	1	1	yes	characteristic, complemented
38	#14524038	C₂²	1	1	yes	characteristic, complemented
39	#14524038	C₂²	1	1	yes	characteristic, complemented
40	#14524038	C₂²	1	1	yes	characteristic, complemented
41	#14524036	C₂²	1	1	yes	characteristic
42	#14524036	C₂²	1	1	yes	characteristic
43	#14524036	C₂²	1	1	yes	characteristic
44	#14524036	C₂²	1	1	yes	characteristic
45	#14524036	C₂²	1	1	yes	characteristic
46	#14524036	C₂²	1	1	yes	characteristic
47	#14524036	C₂²	1	1	yes	characteristic
48	#14524036	C₂²	1	1	yes	characteristic
49	#14524036	C₂²	1	1	yes	characteristic
50	#14524036	C₂²	1	1	yes	characteristic
51	#14524036	C₂²	1	1	yes	characteristic
52	#14524036	C₂²	1	1	yes	characteristic
53	#14524036	C₂²	1	1	yes	characteristic, complemented
54	#14524035	C₂²	1	1	yes	characteristic, complemented
55	#14524035	C₂²	1	1	yes	characteristic, complemented
56	#14524035	C₂²	1	1	yes	characteristic, complemented
57	#14524034	C₂²	1	1	yes	characteristic, complemented
58	#14524034	C₂²	1	1	yes	characteristic, complemented
59	#14524034	C₂²	1	1	yes	characteristic, complemented
60	#14524034	C₂²	1	1	yes	characteristic, complemented
61	#14524033	C₂²	1	1	yes	characteristic, complemented
62	#14524033	C₂²	1	1	yes	characteristic, complemented
63	#14524033	C₂²	1	1	yes	characteristic, complemented
64	#14524033	C₂²	1	1	yes	characteristic, complemented
65	#14524033	C₂²	1	1	yes	characteristic, complemented
66	#14524032	C₂²	1	1	yes	characteristic, complemented
67	#14524030	C₂²	1	1	yes	characteristic
68	#14524029	C₂²	1	1	yes	characteristic
69	#14524029	C₂²	1	1	yes	characteristic
70	#14524029	C₂²	1	1	yes	characteristic
71	#14524029	C₂²	1	1	yes	characteristic
72	#14524029	C₂²	1	1	yes	characteristic
73	#14524029	C₂²	1	1	yes	characteristic
74	#14524029	C₂²	1	1	yes	characteristic
75	#14524029	C₂²	1	1	yes	characteristic, complemented
76	#14524029	C₂²	1	1	yes	characteristic, complemented
77	#14524028	C₂²	1	1	yes	characteristic, complemented
78	#14524028	C₂²	1	1	yes	characteristic, complemented
79	#14524028	C₂²	1	1	yes	characteristic, complemented
80	#14524027	C₂²	1	1	yes	characteristic
81	#14524027	C₂²	1	1	yes	characteristic
82	#14524026	C₂²	1	1	yes	characteristic
83	#14524026	C₂²	1	1	yes	characteristic
84	#14524026	C₂²	1	1	yes	characteristic, complemented
85	#14524025	C₂²	1	1	yes	characteristic
86	#14524025	C₂²	1	1	yes	characteristic
87	#14524025	C₂²	1	1	yes	characteristic
88	#14524025	C₂²	1	1	yes	characteristic
89	#14524025	C₂²	1	1	yes	characteristic
90	#14524025	C₂²	1	1	yes	characteristic
91	#14524025	C₂²	1	1	yes	characteristic
92	#14524025	C₂²	1	1	yes	characteristic
93	#14524025	C₂²	1	1	yes	characteristic
94	#14524025	C₂²	1	1	yes	characteristic, complemented
95	#14524025	C₂²	1	1	yes	characteristic, complemented
96	#14524024	C₂²	1	1	yes	characteristic
97	#14524024	C₂²	1	1	yes	characteristic
98	#14524023	C₂²	1	1	yes	characteristic, complemented
99	#14524023	C₂²	1	1	yes	characteristic, complemented
100	#14524023	C₂²	1	1	yes	characteristic, complemented
101	#14524022	C₂²	1	1	yes	characteristic
102	#14524022	C₂²	1	1	yes	characteristic
103	#14524022	C₂²	1	1	yes	characteristic
104	#14524022	C₂²	1	1	yes	characteristic
105	#14524022	C₂²	1	1	yes	characteristic, complemented
106	#14524021	C₂²	1	1	yes	characteristic, complemented
107	#14524021	C₂²	1	1	yes	characteristic, complemented
108	#14524021	C₂²	1	1	yes	characteristic, complemented
109	#14524020	C₂²	1	1	yes	characteristic
110	#14524020	C₂²	1	1	yes	characteristic
111	#14524020	C₂²	1	1	yes	characteristic
112	#14524020	C₂²	1	1	yes	characteristic, complemented
113	#14524019	C₂²	1	1	yes	characteristic, complemented
114	#14524018	C₂²	1	1	yes	characteristic, complemented
115	#14524017	C₂²	1	1	yes	characteristic
116	#14524017	C₂²	1	1	yes	characteristic
117	#14524017	C₂²	1	1	yes	characteristic, complemented
118	#14524016	C₂²	1	1	yes	characteristic
119	#14524016	C₂²	1	1	yes	characteristic
120	#14524016	C₂²	1	1	yes	characteristic
121	#14524016	C₂²	1	1	yes	characteristic
122	#14524016	C₂²	1	1	yes	characteristic
123	#14524016	C₂²	1	1	yes	characteristic
124	#14524016	C₂²	1	1	yes	characteristic, complemented
125	#14524015	C₂²	1	1	yes	characteristic
126	#14524015	C₂²	1	1	yes	characteristic
127	#14524015	C₂²	1	1	yes	characteristic
128	#14524015	C₂²	1	1	yes	characteristic
129	#14524014	C₂²	1	1	yes	characteristic
130	#14524014	C₂²	1	1	yes	characteristic
131	#14524014	C₂²	1	1	yes	characteristic
132	#14524012	C₂²	1	1	yes	characteristic
133	#14524012	C₂²	1	1	yes	characteristic
134	#14524012	C₂²	1	1	yes	characteristic
135	Q₈×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
136	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
137	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
138	#14524008	C₂²	1	1	yes	characteristic, complemented
139	#14524008	C₂²	1	1	yes	characteristic, complemented
140	#14524008	C₂²	1	1	yes	characteristic, complemented
141	C₄×D₂₆₈	C₂²	1	1	yes	characteristic, complemented
142	C₄×D₂₆₈	C₂²	1	1	yes	characteristic, complemented
143	D₄×Dic₆₇	C₂²	1	1	yes	characteristic
144	#14524005	C₂²	1	1	yes	characteristic, complemented
145	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
146	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
147	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
148	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
149	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
150	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
151	(C₂²⋊D₆₇)⋊C₄	C₂²	1	1	yes	characteristic
152	(C₂²⋊D₆₇)⋊C₄	C₂²	1	1	yes	characteristic
153	(C₂²⋊D₆₇)⋊C₄	C₂²	1	1	yes	characteristic
154	(C₂²⋊D₆₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
155	(C₂²⋊D₆₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
156	(C₂²⋊D₆₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
157	#14524002	C₂²	1	1	yes	characteristic
158	#14524002	C₂²	1	1	yes	characteristic
159	#14524000	C₂²	1	1	yes	characteristic, complemented
160	#14524000	C₂²	1	1	yes	characteristic, complemented
161	#14524000	C₂²	1	1	yes	characteristic, complemented
162	#14524000	C₂²	1	1	yes	characteristic, complemented
163	#14523999	C₂²	1	1	yes	characteristic
164	#14523999	C₂²	1	1	yes	characteristic
165	#14523999	C₂²	1	1	yes	characteristic, complemented
166	#14523999	C₂²	1	1	yes	characteristic, complemented
167	C₂×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic, complemented
168	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
169	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
170	C₂×C₂²⋊Dic₆₇	C₂²	1	1	yes	characteristic
171	C₄²×D₆₇	C₂²	1	1	yes	characteristic, complemented
172	#126×C₆₇	C₂²	1	1	yes	characteristic
173	#126×C₆₇	C₂²	1	1	yes	characteristic
174	#124×C₆₇	C₂²	1	1	yes	characteristic
175	#123×C₆₇	C₂²	1	1	yes	characteristic
176	#123×C₆₇	C₂²	1	1	yes	characteristic
177	#123×C₆₇	C₂²	1	1	yes	characteristic
178	C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
179	C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
180	#120×C₆₇	C₂²	1	1	yes	characteristic
181	C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
182	C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
183	#117×C₆₇	C₂²	1	1	yes	characteristic
184	#117×C₆₇	C₂²	1	1	yes	characteristic
185	C₂×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
186	C₂×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
187	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
188	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
189	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
190	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
191	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
192	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
193	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
194	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
195	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
196	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
197	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
199	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
200	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
201	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
202	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
207	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
208	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
209	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
210	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
211	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
212	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
213	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
214	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
215	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
216	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
217	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
218	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
219	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
220	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
221	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
222	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
223	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
224	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
225	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
226	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
227	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
228	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
229	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
230	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
231	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
232	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
233	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
234	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
235	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
236	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
237	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
238	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
239	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
240	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
241	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
242	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
243	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
244	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
245	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
246	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
247	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
248	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
249	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
250	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
251	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
252	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
253	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
254	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
255	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
256	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
257	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
258	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
259	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
260	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
261	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
262	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
263	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
264	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
265	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
266	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
267	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
268	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
269	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
270	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
271	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
272	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
273	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
274	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
275	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
276	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
277	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
278	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
279	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
280	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
281	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
282	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
283	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
284	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
285	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
286	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
287	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
288	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
289	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
290	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
291	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
292	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
293	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
294	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
295	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
296	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
297	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
298	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
299	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
300	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
301	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
302	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
303	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
304	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
305	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
306	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
307	C₂⁴×C₆₇	C₂³	1	1	yes	characteristic
308	C₂×Q₈×C₆₇	C₂³	1	1	yes	characteristic
309	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
310	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
311	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
312	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
313	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
314	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
315	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
316	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
317	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
318	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
319	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
320	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
321	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
322	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
323	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
324	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
325	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
326	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
327	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
328	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
329	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
330	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
331	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
332	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
333	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
334	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
335	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
336	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
337	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
338	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
339	C₄²×C₆₇	C₂³	1	1	yes	characteristic
340	C₄²×C₆₇	C₂³	1	1	yes	characteristic
341	C₄²×C₆₇	C₂³	1	1	yes	characteristic
342	C₂³×C₆₇	—	4	1	no	—
343	C₂³×C₆₇	—	4	1	no	—
344	C₂³×C₆₇	—	4	1	no	—
345	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
346	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
347	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
348	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
349	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
350	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
351	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
352	Q₈×C₆₇	—	4	1	no	—
353	D₄×C₆₇	—	4	1	no	—
354	D₄×C₆₇	—	4	1	no	—
355	D₄×C₆₇	—	4	1	no	—
356	C₂×C₄×C₆₇	—	4	1	no	—
357	C₂×C₄×C₆₇	—	4	1	no	—
358	C₂×C₄×C₆₇	—	4	1	no	—
359	C₂×C₄×C₆₇	—	4	1	no	—
360	C₂×C₄×C₆₇	—	4	1	no	—
361	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
362	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
363	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
364	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
365	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
366	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
367	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
368	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
369	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
370	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
371	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
372	C₂²⋊D₆₇	—	4	1	no	—
373	C₂²⋊D₆₇	—	4	1	no	—
374	C₂²⋊D₆₇	—	4	1	no	—
375	C₂²⋊D₆₇	—	4	1	no	—
376	C₂²⋊D₆₇	—	4	1	no	—
377	C₂²⋊D₆₇	—	4	1	no	—
378	C₂²⋊D₆₇	—	4	1	no	—
379	C₂²⋊D₆₇	—	4	1	no	—
380	C₂²⋊D₆₇	—	4	1	no	—
381	C₂²⋊D₆₇	—	4	1	no	—
382	C₂²⋊D₆₇	—	4	1	no	—
383	C₂²⋊D₆₇	—	4	1	no	—
384	C₂×Dic₆₇	—	4	1	no	—
385	C₂×Dic₆₇	—	4	1	no	—
386	C₂×Dic₆₇	—	4	1	no	—
387	C₂×Dic₆₇	—	4	1	no	—
388	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
389	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
390	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
391	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
392	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
393	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
394	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
395	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
396	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
397	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
398	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
399	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
400	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
401	D₂₆₈	—	4	1	no	—
402	D₂₆₈	—	4	1	no	—
403	D₂₆₈	—	4	1	no	—
404	C₄×D₆₇	—	4	1	no	—
405	C₄×D₆₇	—	4	1	no	—
406	C₄×D₆₇	—	4	1	no	—
407	C₄×D₆₇	—	4	1	no	—
408	C₄×D₆₇	—	4	1	no	—
409	C₄×D₆₇	—	4	1	no	—
410	C₄×D₆₇	—	4	1	no	—
411	C₄×D₆₇	—	4	1	no	—
412	C₄×D₆₇	—	4	1	no	—
413	Dic₁₃₄	—	4	1	no	—
414	Dic₁₃₄	—	4	1	no	—
415	Dic₁₃₄	—	4	1	no	—
416	Dic₁₃₄	—	4	1	no	—
417	Dic₁₃₄	—	4	1	no	—
418	C₂²×C₆₇	—	2	1	no	—
419	C₂²×C₆₇	—	2	1	no	—
420	C₂²×C₆₇	—	2	1	no	—
421	C₂²×C₆₇	—	2	1	no	—
422	C₂²×C₆₇	—	2	1	no	—
423	C₂²×C₆₇	—	2	1	no	—
424	C₂²×C₆₇	—	2	1	no	—
425	C₂²×C₆₇	—	2	1	no	—
426	C₂²×C₆₇	—	2	1	no	—
427	C₂²×C₆₇	—	2	1	no	—
428	C₂²×C₆₇	—	2	1	no	—
429	C₂²×C₆₇	—	2	1	no	—
430	C₂²×C₆₇	—	8	2	no	—
431	C₂²×C₆₇	C₂⁵	1	1	yes	characteristic
432	C₂×D₆₇	—	2	1	no	—
433	C₂×D₆₇	—	2	1	no	—
434	C₂×D₆₇	—	2	1	no	—
435	C₂×D₆₇	—	2	1	no	—
436	C₂×D₆₇	—	2	1	no	—
437	C₂×D₆₇	—	2	1	no	—
438	C₂×D₆₇	—	2	1	no	—
439	C₂×D₆₇	—	2	1	no	—
440	C₂×D₆₇	—	2	1	no	—
441	C₄×C₆₇	—	2	1	no	—
442	C₄×C₆₇	—	2	1	no	—
443	C₄×C₆₇	—	2	1	no	—
444	C₄×C₆₇	—	2	1	no	—
445	C₄×C₆₇	—	2	1	no	—
446	C₄×C₆₇	—	2	1	no	—
447	C₄×C₆₇	—	2	1	no	—
448	C₄×C₆₇	—	2	1	no	—
449	C₄×C₆₇	—	2	1	no	—
450	C₄×C₆₇	—	2	1	no	—
451	C₄×C₆₇	—	2	1	no	—
452	Dic₆₇	—	2	1	no	—
453	Dic₆₇	—	2	1	no	—
454	Dic₆₇	—	2	1	no	—
455	Dic₆₇	—	2	1	no	—
456	Dic₆₇	—	2	1	no	—
457	Dic₆₇	—	2	1	no	—
458	Dic₆₇	—	2	1	no	—
459	Dic₆₇	—	2	1	no	—
460	Dic₆₇	—	2	1	no	—
461	Dic₆₇	—	2	1	no	—
462	Dic₆₇	—	2	1	no	—
463	Dic₆₇	—	2	1	no	—
464	Dic₆₇	—	2	1	no	—
465	C₂×C₆₇	—	4	1	no	—
466	C₂×C₆₇	—	4	1	no	—
467	C₂×C₆₇	—	4	1	no	—
468	C₂×C₆₇	—	4	1	no	—
469	C₂×C₆₇	#585	1	1	yes	characteristic
470	C₂×C₆₇	#585	1	1	yes	characteristic
471	C₂×C₆₇	#585	1	1	yes	characteristic
472	D₆₇	—	4	1	no	—
473	D₆₇	—	4	1	no	—
474	D₆₇	—	4	1	no	—
475	#3566	—	67	1	no	maximal, Sylow
476	C₆₇	#3566	1	1	yes	characteristic, complemented, Sylow
477	#563	—	67	1	no	—
478	#562	—	67	1	no	—
479	#562	—	67	1	no	—
480	#560	—	67	1	no	—
481	#559	—	67	1	no	—
482	#556	—	67	1	no	—
483	#555	—	67	1	no	—
484	#553	—	67	1	no	—
485	#553	—	67	1	no	—
486	#553	—	67	1	no	—
487	#552	—	67	1	no	—
488	#552	—	67	1	no	—
489	#552	—	67	1	no	—
490	#551	—	67	1	no	—
491	#551	—	67	1	no	—
492	#551	D₆₇	1	1	yes	characteristic, complemented
493	#542	—	67	1	no	—
494	#542	—	67	1	no	—
495	#542	—	67	1	no	—
496	#541	—	67	1	no	—
497	#541	—	67	1	no	—
498	#540	—	67	1	no	—
499	#539	—	67	1	no	—
500	#539	—	67	1	no	—
501	#539	—	67	1	no	—
502	#538	—	67	1	no	—
503	#538	—	67	1	no	—
504	#538	—	67	1	no	—
505	#529	—	67	1	no	—
506	#529	—	67	1	no	—
507	#529	—	67	1	no	—
508	C₄⋊Q₈	—	67	1	no	—
509	C₄⋊Q₈	—	67	1	no	—
510	C₄⋊Q₈	—	67	1	no	—
511	#127	—	67	1	no	—
512	#126	—	67	1	no	—
513	#126	—	67	1	no	—
514	#126	—	67	1	no	—
515	#126	—	67	1	no	—
516	#126	—	67	1	no	—
517	#126	—	67	1	no	—
518	#126	—	67	1	no	—
519	#126	—	67	1	no	—
520	#126	—	67	1	no	—
521	#126	—	67	1	no	—
522	#126	—	67	1	no	—
523	#126	—	67	1	no	—
524	#126	—	67	1	no	—
525	#126	—	67	1	no	—
526	#126	—	67	1	no	—
527	#126	—	67	1	no	—
528	#126	—	67	1	no	—
529	#126	—	67	1	no	—
530	#126	C₂×D₆₇	1	1	yes	characteristic
531	#126	C₂×D₆₇	1	1	yes	characteristic
532	#125	—	67	1	no	—
533	#125	—	67	1	no	—
534	#125	—	67	1	no	—
535	#125	—	67	1	no	—
536	#125	—	67	1	no	—
537	#125	—	67	1	no	—
538	#125	—	67	1	no	—
539	#125	—	67	1	no	—
540	#125	—	67	1	no	—
541	#125	—	67	1	no	—
542	#125	—	67	1	no	—
543	#125	—	67	1	no	—
544	#124	—	67	1	no	—
545	#124	—	67	1	no	—
546	#124	—	67	1	no	—
547	#124	—	67	1	no	—
548	#124	—	67	1	no	—
549	#124	—	67	1	no	—
550	#124	—	67	1	no	—
551	#124	—	67	1	no	—
552	#124	—	67	1	no	—
553	#124	—	67	1	no	—
554	#124	—	67	1	no	—
555	#124	C₂×D₆₇	1	1	yes	characteristic
556	#123	—	67	1	no	—
557	#123	—	67	1	no	—
558	#123	—	67	1	no	—
559	#123	—	67	1	no	—
560	#123	—	67	1	no	—
561	#123	—	67	1	no	—
562	#123	—	67	1	no	—
563	#123	—	67	1	no	—
564	#123	—	67	1	no	—
565	#123	—	67	1	no	—
566	#123	—	67	1	no	—
567	#123	—	67	1	no	—
568	#123	—	67	1	no	—
569	#123	—	67	1	no	—
570	#123	—	67	1	no	—
571	#123	—	67	1	no	—
572	#123	—	67	1	no	—
573	#123	—	67	1	no	—
574	#123	—	67	1	no	—
575	#123	—	67	1	no	—
576	#123	—	67	1	no	—
577	#123	C₂×D₆₇	1	1	yes	characteristic
578	#123	C₂×D₆₇	1	1	yes	characteristic
579	#123	C₂×D₆₇	1	1	yes	characteristic
580	C₂²⋊Q₈	—	67	1	no	—
581	C₂²⋊Q₈	—	67	1	no	—
582	C₂²⋊Q₈	—	67	1	no	—
583	C₂²⋊Q₈	—	67	1	no	—
584	C₂²⋊Q₈	—	67	1	no	—
585	C₂²⋊Q₈	—	67	1	no	—
586	C₂²⋊Q₈	—	67	1	no	—
587	C₂²⋊Q₈	—	67	1	no	—
588	C₂²⋊Q₈	—	67	1	no	—
589	C₂²⋊Q₈	—	67	1	no	—
590	C₂²⋊Q₈	—	67	1	no	—
591	C₂²⋊Q₈	—	67	1	no	—
592	C₂²⋊Q₈	—	67	1	no	—
593	C₂²⋊Q₈	—	67	1	no	—
594	C₂²⋊Q₈	—	67	1	no	—
595	C₂²⋊Q₈	—	67	1	no	—
596	C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic
597	C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic
598	#121	—	67	1	no	—
599	#121	—	67	1	no	—
600	#121	—	67	1	no	—
601	#121	—	67	1	no	—
602	#121	—	67	1	no	—
603	#121	—	67	1	no	—
604	#121	—	67	1	no	—
605	#121	—	67	1	no	—
606	#121	—	67	1	no	—
607	#121	—	67	1	no	—
608	#121	—	67	1	no	—
609	#121	—	67	1	no	—
610	#121	—	67	1	no	—
611	#121	—	67	1	no	—
612	#121	—	67	1	no	—
613	#121	—	67	1	no	—
614	#121	—	67	1	no	—
615	#121	—	67	1	no	—
616	#120	—	67	1	no	—
617	#120	—	67	1	no	—
618	#120	—	67	1	no	—
619	#120	C₂×D₆₇	1	1	yes	characteristic
620	C₄×Q₈	—	67	1	no	—
621	C₄×Q₈	—	67	1	no	—
622	C₄×Q₈	—	67	1	no	—
623	C₄×Q₈	—	67	1	no	—
624	C₄×Q₈	—	67	1	no	—
625	C₄×Q₈	—	67	1	no	—
626	C₄×D₄	—	67	1	no	—
627	C₄×D₄	—	67	1	no	—
628	C₄×D₄	—	67	1	no	—
629	C₄×D₄	—	67	1	no	—
630	C₄×D₄	—	67	1	no	—
631	C₄×D₄	—	67	1	no	—
632	C₄×D₄	—	67	1	no	—
633	C₄×D₄	—	67	1	no	—
634	C₄×D₄	—	67	1	no	—
635	C₄×D₄	—	67	1	no	—
636	C₄×D₄	—	67	1	no	—
637	C₄×D₄	—	67	1	no	—
638	C₄×D₄	—	67	1	no	—
639	C₄×D₄	—	67	1	no	—
640	C₄×D₄	—	67	1	no	—
641	C₄×D₄	—	67	1	no	—
642	C₄×D₄	C₂×D₆₇	1	1	yes	characteristic
643	C₄×D₄	C₂×D₆₇	1	1	yes	characteristic
644	#117	—	67	1	no	—
645	#117	—	67	1	no	—
646	#117	—	67	1	no	—
647	#117	—	67	1	no	—
648	#117	—	67	1	no	—
649	#117	—	67	1	no	—
650	#117	—	67	1	no	—
651	#117	—	67	1	no	—
652	#117	—	67	1	no	—
653	#117	—	67	1	no	—
654	#117	C₂×D₆₇	1	1	yes	characteristic
655	#117	C₂×D₆₇	1	1	yes	characteristic
656	C₂×C₄⋊C₄	—	67	1	no	—
657	C₂×C₄⋊C₄	—	67	1	no	—
658	C₂×C₄⋊C₄	—	67	1	no	—
659	C₂×C₂²⋊C₄	—	67	1	no	—
660	C₂×C₂²⋊C₄	C₂×D₆₇	1	1	yes	characteristic
661	C₂×C₂²⋊C₄	C₂×D₆₇	1	1	yes	characteristic
662	C₂×C₄²	—	67	1	no	—
663	C₂⁴	C₂²×D₆₇	1	1	yes	characteristic
664	C₂×Q₈	—	67	1	no	—
665	C₂×Q₈	—	67	1	no	—
666	C₂×Q₈	—	67	1	no	—
667	C₂×Q₈	—	67	1	no	—
668	C₂×Q₈	—	67	1	no	—
669	C₂×Q₈	C₂²×D₆₇	1	1	yes	characteristic
670	C₂×D₄	—	67	1	no	—
671	C₂×D₄	—	67	1	no	—
672	C₂×D₄	—	67	1	no	—
673	C₂×D₄	—	67	1	no	—
674	C₂×D₄	—	67	1	no	—
675	C₂×D₄	—	67	1	no	—
676	C₂×D₄	—	67	1	no	—
677	C₂×D₄	—	67	1	no	—
678	C₂×D₄	—	67	1	no	—
679	C₂×D₄	—	67	1	no	—
680	C₂×D₄	—	67	1	no	—
681	C₂×D₄	—	67	1	no	—
682	C₂×D₄	—	67	1	no	—
683	C₂×D₄	—	67	1	no	—
684	C₂×D₄	—	67	1	no	—
685	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
686	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
687	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
688	C₂²×C₄	—	67	1	no	—
689	C₂²×C₄	—	67	1	no	—
690	C₂²×C₄	—	67	1	no	—
691	C₂²×C₄	—	67	1	no	—
692	C₂²×C₄	—	67	1	no	—
693	C₂²×C₄	—	67	1	no	—
694	C₂²×C₄	—	67	1	no	—
695	C₂²×C₄	—	67	1	no	—
696	C₂²×C₄	—	67	1	no	—
697	C₂²×C₄	—	67	1	no	—
698	C₂²×C₄	—	67	1	no	—
699	C₂²×C₄	—	67	1	no	—
700	C₂²×C₄	—	67	1	no	—
701	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
702	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
703	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
704	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
705	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
706	C₄⋊C₄	—	67	1	no	—
707	C₄⋊C₄	—	67	1	no	—
708	C₄⋊C₄	—	67	1	no	—
709	C₄⋊C₄	—	67	1	no	—
710	C₄⋊C₄	—	67	1	no	—
711	C₄⋊C₄	—	67	1	no	—
712	C₄⋊C₄	—	67	1	no	—
713	C₄⋊C₄	—	67	1	no	—
714	C₄⋊C₄	—	67	1	no	—
715	C₄⋊C₄	—	67	1	no	—
716	C₄⋊C₄	—	67	1	no	—
717	C₄⋊C₄	—	67	1	no	—
718	C₄⋊C₄	—	67	1	no	—
719	C₄⋊C₄	—	67	1	no	—
720	C₄⋊C₄	—	67	1	no	—
721	C₄⋊C₄	—	67	1	no	—
722	C₄⋊C₄	—	67	1	no	—
723	C₄⋊C₄	—	67	1	no	—
724	C₄⋊C₄	—	67	1	no	—
725	C₄⋊C₄	—	67	1	no	—
726	C₄⋊C₄	—	67	1	no	—
727	C₄⋊C₄	—	67	1	no	—
728	C₄⋊C₄	—	67	1	no	—
729	C₄⋊C₄	—	67	1	no	—
730	C₄⋊C₄	—	67	1	no	—
731	C₄⋊C₄	—	67	1	no	—
732	C₄⋊C₄	—	67	1	no	—
733	C₄⋊C₄	—	67	1	no	—
734	C₄⋊C₄	—	67	1	no	—
735	C₄⋊C₄	—	67	1	no	—
736	C₄⋊C₄	—	67	1	no	—
737	C₄⋊C₄	—	67	1	no	—
738	C₄⋊C₄	—	67	1	no	—
739	C₄⋊C₄	—	67	1	no	—
740	C₄⋊C₄	—	67	1	no	—
741	C₄⋊C₄	—	67	1	no	—
742	C₄⋊C₄	—	67	1	no	—
743	C₄⋊C₄	—	67	1	no	—
744	C₄⋊C₄	—	67	1	no	—
745	C₄⋊C₄	—	67	1	no	—
746	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
747	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
748	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
749	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
750	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
751	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
752	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
753	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
754	C₂²⋊C₄	—	67	1	no	—
755	C₂²⋊C₄	—	67	1	no	—
756	C₂²⋊C₄	—	67	1	no	—
757	C₂²⋊C₄	—	67	1	no	—
758	C₂²⋊C₄	—	67	1	no	—
759	C₂²⋊C₄	—	67	1	no	—
760	C₂²⋊C₄	—	67	1	no	—
761	C₂²⋊C₄	—	67	1	no	—
762	C₂²⋊C₄	—	67	1	no	—
763	C₂²⋊C₄	—	67	1	no	—
764	C₂²⋊C₄	—	67	1	no	—
765	C₂²⋊C₄	—	67	1	no	—
766	C₂²⋊C₄	—	67	1	no	—
767	C₂²⋊C₄	—	67	1	no	—
768	C₂²⋊C₄	—	67	1	no	—
769	C₂²⋊C₄	—	67	1	no	—
770	C₂²⋊C₄	—	67	1	no	—
771	C₂²⋊C₄	—	67	1	no	—
772	C₂²⋊C₄	—	67	1	no	—
773	C₂²⋊C₄	—	67	1	no	—
774	C₂²⋊C₄	—	67	1	no	—
775	C₂²⋊C₄	—	67	1	no	—
776	C₂²⋊C₄	—	67	1	no	—
777	C₂²⋊C₄	—	67	1	no	—
778	C₂²⋊C₄	—	67	1	no	—
779	C₂²⋊C₄	—	67	1	no	—
780	C₂²⋊C₄	—	67	1	no	—
781	C₂²⋊C₄	—	67	1	no	—
782	C₂²⋊C₄	—	67	1	no	—
783	C₂²⋊C₄	—	67	1	no	—
784	C₂²⋊C₄	—	67	1	no	—
785	C₂²⋊C₄	—	67	1	no	—
786	C₂²⋊C₄	—	67	1	no	—
787	C₂²⋊C₄	—	67	1	no	—
788	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
789	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
790	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
791	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
792	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
793	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
794	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
795	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
796	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
797	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
798	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
799	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
800	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
801	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
802	C₄²	—	67	1	no	—
803	C₄²	—	67	1	no	—
804	C₄²	—	67	1	no	—
805	C₄²	—	67	1	no	—
806	C₄²	—	67	1	no	—
807	C₄²	—	67	1	no	—
808	C₄²	—	67	1	no	—
809	C₄²	—	67	1	no	—
810	C₄²	—	67	1	no	—
811	C₄²	—	67	1	no	—
812	C₄²	—	67	1	no	—
813	C₄²	—	67	1	no	—
814	C₄²	—	67	1	no	—
815	C₄²	C₂²×D₆₇	1	1	yes	characteristic
816	C₄²	C₂²×D₆₇	1	1	yes	characteristic
817	C₄²	C₂²×D₆₇	1	1	yes	characteristic
818	C₂³	—	4	1	no	—
819	C₂³	—	4	1	no	—
820	C₂³	—	4	1	no	—
821	C₂³	—	67	1	no	—
822	C₂³	—	67	1	no	—
823	C₂³	—	67	1	no	—
824	C₂³	C₂³×D₆₇	1	1	yes	characteristic
825	C₂³	C₂³×D₆₇	1	1	yes	characteristic
826	C₂³	C₂³×D₆₇	1	1	yes	characteristic
827	C₂³	C₂³×D₆₇	1	1	yes	characteristic
828	Q₈	—	4	1	no	—
829	Q₈	—	268	1	no	—
830	Q₈	—	268	1	no	—
831	Q₈	—	268	1	no	—
832	Q₈	—	268	1	no	—
833	Q₈	—	268	1	no	—
834	D₄	—	4	1	no	—
835	D₄	—	4	1	no	—
836	D₄	—	4	1	no	—
837	D₄	—	268	1	no	—
838	D₄	—	268	1	no	—
839	D₄	—	268	1	no	—
840	D₄	—	268	1	no	—
841	D₄	—	268	1	no	—
842	D₄	—	268	1	no	—
843	D₄	—	268	1	no	—
844	D₄	—	268	1	no	—
845	D₄	—	268	1	no	—
846	D₄	—	268	1	no	—
847	D₄	—	268	1	no	—
848	D₄	—	268	1	no	—
849	D₄	—	268	1	no	—
850	D₄	—	268	1	no	—
851	D₄	—	268	1	no	—
852	C₂×C₄	—	4	1	no	—
853	C₂×C₄	—	4	1	no	—
854	C₂×C₄	—	4	1	no	—
855	C₂×C₄	—	4	1	no	—
856	C₂×C₄	—	4	1	no	—
857	C₂×C₄	—	268	1	no	—
858	C₂×C₄	—	268	1	no	—
859	C₂×C₄	—	268	1	no	—
860	C₂×C₄	—	268	1	no	—
861	C₂×C₄	—	268	1	no	—
862	C₂×C₄	—	268	1	no	—
863	C₂×C₄	—	268	1	no	—
864	C₂×C₄	—	268	1	no	—
865	C₂×C₄	—	268	1	no	—
866	C₂×C₄	—	268	1	no	—
867	C₂×C₄	—	268	1	no	—
868	C₂×C₄	—	268	1	no	—
869	C₂×C₄	—	268	1	no	—
870	C₂×C₄	—	67	1	no	—
871	C₂×C₄	—	67	1	no	—
872	C₂×C₄	—	67	1	no	—
873	C₂×C₄	—	67	1	no	—
874	C₂×C₄	—	67	1	no	—
875	C₂×C₄	—	67	1	no	—
876	C₂×C₄	—	67	1	no	—
877	C₂×C₄	—	67	1	no	—
878	C₂×C₄	—	67	1	no	—
879	C₂×C₄	—	67	1	no	—
880	C₂×C₄	—	67	1	no	—
881	C₂×C₄	—	67	1	no	—
882	C₂×C₄	—	67	1	no	—
883	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
884	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
885	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
886	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
887	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
888	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
889	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
890	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
891	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
892	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
893	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
894	C₂²	—	2	1	no	—
895	C₂²	—	2	1	no	—
896	C₂²	—	2	1	no	—
897	C₂²	—	2	1	no	—
898	C₂²	—	2	1	no	—
899	C₂²	—	2	1	no	—
900	C₂²	—	2	1	no	—
901	C₂²	—	2	1	no	—
902	C₂²	—	2	1	no	—
903	C₂²	—	2	1	no	—
904	C₂²	—	2	1	no	—
905	C₂²	—	2	1	no	—
906	C₂²	—	8	2	no	—
907	C₂²	—	134	1	no	—
908	C₂²	—	134	1	no	—
909	C₂²	—	134	1	no	—
910	C₂²	—	134	1	no	—
911	C₂²	—	134	1	no	—
912	C₂²	—	134	1	no	—
913	C₂²	—	134	1	no	—
914	C₂²	—	134	1	no	—
915	C₂²	—	134	1	no	—
916	C₂²	C₂⁴×D₆₇	1	1	yes	characteristic
917	C₄	—	2	1	no	—
918	C₄	—	2	1	no	—
919	C₄	—	2	1	no	—
920	C₄	—	2	1	no	—
921	C₄	—	2	1	no	—
922	C₄	—	2	1	no	—
923	C₄	—	2	1	no	—
924	C₄	—	2	1	no	—
925	C₄	—	2	1	no	—
926	C₄	—	2	1	no	—
927	C₄	—	2	1	no	—
928	C₄	—	134	1	no	—
929	C₄	—	134	1	no	—
930	C₄	—	134	1	no	—
931	C₄	—	134	1	no	—
932	C₄	—	134	1	no	—
933	C₄	—	134	1	no	—
934	C₄	—	134	1	no	—
935	C₄	—	134	1	no	—
936	C₄	—	134	1	no	—
937	C₄	—	134	1	no	—
938	C₄	—	134	1	no	—
939	C₄	—	134	1	no	—
940	C₄	—	134	1	no	—
941	C₂	—	4	1	no	—
942	C₂	—	4	1	no	—
943	C₂	—	4	1	no	—
944	C₂	—	4	1	no	—
945	C₂	—	268	1	no	—
946	C₂	—	268	1	no	—
947	C₂	—	268	1	no	—
948	C₂	#16864231	1	1	yes	characteristic
949	C₂	#16864232	1	1	yes	characteristic
950	C₂	#16864232	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁵
Fitting	#551×C₆₇	C₂
hypercenter	#551	D₆₇
hypocenter	C₆₇	#3566
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ #551

Complements

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

N	H ≅ G/N	type
1. #16864147	C₂	semidirect
2. #16864143	C₂	semidirect
3. #16864142	C₂	semidirect
4. #16864135	C₂	semidirect
5. #16864130	C₂	semidirect
6. #16864113	C₂	semidirect
7. #16864108	C₂	semidirect
8. #16864097	C₂	semidirect
9. #16864092	C₂	semidirect
10. #16864091	C₂	semidirect
11. #16864086	C₂	semidirect
12. #16864085	C₂	semidirect
13. #16864085	C₂	semidirect
14. #16864072	C₂	semidirect
15. #16864072	C₂	semidirect
16. #16864019	C₂	semidirect
17. #16864014	C₂	semidirect
18. #16864011	C₂	semidirect
19. #16864006	C₂	semidirect
20. #16864003	C₂	semidirect
21. #16863997	C₂	semidirect
22. #16863990	C₂	semidirect
23. #16863989	C₂	semidirect
24. #16863987	C₂	semidirect
25. #16863984	C₂	semidirect
26. #16863984	C₂	semidirect
27. #16863981	C₂	semidirect
28. #16863925	C₂	semidirect
29. #16863924	C₂	semidirect
30. #16863924	C₂	semidirect
31. #551×C₆₇	C₂	semidirect
32. #14524042	C₂²	semidirect
33. #14524042	C₂²	semidirect
34. #14524041	C₂²	semidirect
36. #14524038	C₂²	semidirect
37. #14524038	C₂²	semidirect
38. #14524038	C₂²	semidirect
39. #14524038	C₂²	semidirect
40. #14524038	C₂²	semidirect
53. #14524036	C₂²	semidirect
54. #14524035	C₂²	semidirect
55. #14524035	C₂²	semidirect
56. #14524035	C₂²	semidirect
57. #14524034	C₂²	semidirect
58. #14524034	C₂²	semidirect
59. #14524034	C₂²	semidirect
60. #14524034	C₂²	semidirect
61. #14524033	C₂²	semidirect
62. #14524033	C₂²	semidirect
63. #14524033	C₂²	semidirect
64. #14524033	C₂²	semidirect
65. #14524033	C₂²	semidirect
66. #14524032	C₂²	semidirect
75. #14524029	C₂²	semidirect
76. #14524029	C₂²	semidirect
77. #14524028	C₂²	semidirect
78. #14524028	C₂²	semidirect
79. #14524028	C₂²	semidirect
84. #14524026	C₂²	semidirect
94. #14524025	C₂²	semidirect
95. #14524025	C₂²	semidirect
98. #14524023	C₂²	semidirect
99. #14524023	C₂²	semidirect
100. #14524023	C₂²	semidirect
105. #14524022	C₂²	semidirect
106. #14524021	C₂²	semidirect
107. #14524021	C₂²	semidirect
108. #14524021	C₂²	semidirect
112. #14524020	C₂²	semidirect
113. #14524019	C₂²	semidirect
114. #14524018	C₂²	semidirect
117. #14524017	C₂²	semidirect
124. #14524016	C₂²	semidirect
135. Q₈×Dic₆₇	C₂²	semidirect
136. C₄×Dic₁₃₄	C₂²	semidirect
137. C₄×Dic₁₃₄	C₂²	semidirect
138. #14524008	C₂²	semidirect
139. #14524008	C₂²	semidirect
140. #14524008	C₂²	semidirect
141. C₄×D₂₆₈	C₂²	semidirect
142. C₄×D₂₆₈	C₂²	semidirect
144. #14524005	C₂²	semidirect
154. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
155. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
156. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
159. #14524000	C₂²	semidirect
160. #14524000	C₂²	semidirect
161. #14524000	C₂²	semidirect
162. #14524000	C₂²	semidirect
165. #14523999	C₂²	semidirect
166. #14523999	C₂²	semidirect
167. C₂×C₄⋊Dic₆₇	C₂²	semidirect
168. C₄⋊C₄×D₆₇	C₂²	semidirect
169. C₄⋊C₄×D₆₇	C₂²	semidirect
171. C₄²×D₆₇	C₂²	semidirect
476. C₆₇	#3566	semidirect
492. #551	D₆₇	semidirect