Subgroups — #22574797

Order 8576.

1050 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16864142	C₂	1	2	yes	maximal, complemented
2	#16864134	C₂	1	2	yes	maximal, complemented
3	#16864131	C₂	1	1	yes	maximal, characteristic, complemented
4	#16864119	C₂	1	1	yes	maximal, characteristic, complemented
5	#16864097	C₂	1	2	yes	maximal, complemented
6	#16864071	C₂	1	2	yes	maximal, complemented
7	#16864067	C₂	1	1	yes	maximal, characteristic, complemented
8	#16864055	C₂	1	1	yes	maximal, characteristic, complemented
9	#16864055	C₂	1	1	yes	maximal, characteristic, complemented
10	#16864051	C₂	1	1	yes	maximal, characteristic, complemented
11	#16864042	C₂	1	1	yes	maximal, characteristic, complemented
12	#16864042	C₂	1	1	yes	maximal, characteristic, complemented
13	#16864008	C₂	1	1	yes	maximal, characteristic, complemented
14	#16864001	C₂	1	1	yes	maximal, characteristic, complemented
15	#16863998	C₂	1	2	yes	maximal, complemented
16	#16863994	C₂	1	2	yes	maximal, complemented
17	#16863982	C₂	1	2	yes	maximal, complemented
18	#16863980	C₂	1	2	yes	maximal, complemented
19	#16863972	C₂	1	1	yes	maximal, characteristic, complemented
20	#16863965	C₂	1	1	yes	maximal, characteristic, complemented
21	#16863946	C₂	1	1	yes	maximal, characteristic, complemented
22	#16863930	C₂	1	1	yes	maximal, characteristic, complemented
23	#529×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#11761628	C₂²	1	1	yes	characteristic
25	C₂×#11761628	C₂²	1	1	yes	characteristic
26	C₂×#11761628	C₂²	1	1	yes	characteristic
27	C₂×#11761628	C₂²	1	1	yes	characteristic, complemented
28	C₂²×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
29	C₂²×D₂₆₈	C₂²	1	1	yes	characteristic
30	#14524043	C₂²	1	1	yes	characteristic, complemented
31	#14524043	C₂²	1	1	yes	characteristic, complemented
32	#14524040	C₂²	1	1	yes	characteristic
33	#14524040	C₂²	1	1	yes	characteristic
34	#14524039	C₂²	1	2	yes	complemented
35	#14524038	C₂²	1	2	yes	complemented
36	#14524038	C₂²	1	2	yes	complemented
37	#14524037	C₂²	1	2	yes	complemented
38	#14524036	C₂²	1	2	yes	—
39	#14524036	C₂²	1	2	yes	—
40	#14524035	C₂²	1	1	yes	characteristic, complemented
41	#14524033	C₂²	1	2	yes	complemented
42	#14524033	C₂²	1	2	yes	complemented
43	#14524032	C₂²	1	2	yes	complemented
44	#14524031	C₂²	1	1	yes	characteristic
45	#14524031	C₂²	1	1	yes	characteristic
46	#14524031	C₂²	1	1	yes	characteristic
47	#14524031	C₂²	1	1	yes	characteristic
48	#14524031	C₂²	1	1	yes	characteristic, complemented
49	#14524029	C₂²	1	2	yes	—
50	#14524029	C₂²	1	2	yes	complemented
51	#14524028	C₂²	1	2	yes	—
52	#14524028	C₂²	1	2	yes	—
53	#14524028	C₂²	1	2	yes	complemented
54	#14524028	C₂²	1	2	yes	complemented
55	#14524028	C₂²	1	2	yes	complemented
56	#14524028	C₂²	1	2	yes	complemented
57	#14524027	C₂²	1	2	yes	complemented
58	#14524027	C₂²	1	2	yes	complemented
59	#14524026	C₂²	1	2	yes	complemented
60	#14524025	C₂²	1	2	yes	—
61	#14524025	C₂²	1	2	yes	complemented
62	#14524023	C₂²	1	2	yes	complemented
63	#14524023	C₂²	1	2	yes	complemented
64	#14524022	C₂²	1	1	yes	characteristic
65	#14524022	C₂²	1	1	yes	characteristic
66	#14524022	C₂²	1	1	yes	characteristic, complemented
67	#14524021	C₂²	1	2	yes	complemented
68	#14524021	C₂²	1	2	yes	complemented
69	#14524019	C₂²	1	2	yes	complemented
70	#14524018	C₂²	1	2	yes	—
71	#14524018	C₂²	1	2	yes	—
72	#14524017	C₂²	1	1	yes	characteristic
73	#14524017	C₂²	1	1	yes	characteristic
74	#14524017	C₂²	1	1	yes	characteristic, complemented
75	#14524017	C₂²	1	2	yes	complemented
76	#14524017	C₂²	1	2	yes	complemented
77	#14524016	C₂²	1	2	yes	—
78	#14524016	C₂²	1	2	yes	—
79	#14524016	C₂²	1	2	yes	complemented
80	#14524016	C₂²	1	2	yes	complemented
81	#14524016	C₂²	1	2	yes	complemented
82	#14524016	C₂²	1	2	yes	complemented
83	#14524015	C₂²	1	2	yes	—
84	#14524015	C₂²	1	2	yes	complemented
85	#14524014	C₂²	1	2	yes	—
86	#14524013	C₂²	1	2	yes	—
87	#14524013	C₂²	1	2	yes	—
88	#14524011	C₂²	1	2	yes	—
89	#14524011	C₂²	1	2	yes	—
90	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
91	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
92	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
93	C₄×D₂₆₈	C₂²	1	1	yes	characteristic
94	C₄×D₂₆₈	C₂²	1	1	yes	characteristic
95	C₄×D₂₆₈	C₂²	1	1	yes	characteristic, complemented
96	C₄×D₂₆₈	C₂²	1	2	yes	complemented
97	C₄×D₂₆₈	C₂²	1	2	yes	complemented
98	#14524005	C₂²	1	2	yes	complemented
99	#14524005	C₂²	1	2	yes	complemented
100	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
101	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	complemented
102	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	complemented
103	#14524001	C₂²	1	2	yes	complemented
104	#14524000	C₂²	1	2	yes	complemented
105	C₄⋊C₄×D₆₇	C₂²	1	2	yes	complemented
106	C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
107	C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
108	#126×C₆₇	C₂²	1	1	yes	characteristic
109	#126×C₆₇	C₂²	1	1	yes	characteristic, complemented
110	#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
111	#124×C₆₇	C₂²	1	1	yes	characteristic
112	#123×C₆₇	C₂²	1	1	yes	characteristic
113	#123×C₆₇	C₂²	1	1	yes	characteristic, complemented
114	C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
115	#121×C₆₇	C₂²	1	1	yes	characteristic
116	C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
117	C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
118	C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
119	C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
120	#117×C₆₇	C₂²	1	1	yes	characteristic
121	#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₄²×C₆₇	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₆₇	C₂³	1	2	yes	—
124	#11761628	—	4	2	no	—
125	#11761628	—	4	2	no	—
126	#11761628	—	4	2	no	—
127	#11761628	—	4	2	no	—
128	C₂×Dic₁₃₄	—	4	2	no	—
129	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
130	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
131	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
132	C₂×Dic₁₃₄	C₂³	1	2	yes	—
133	C₂×D₂₆₈	—	4	2	no	—
134	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
135	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
136	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
137	C₂×D₂₆₈	C₂³	1	2	yes	—
138	C₂×D₂₆₈	C₂³	1	2	yes	—
139	C₂×D₂₆₈	C₂³	1	2	yes	—
140	C₂×D₂₆₈	C₂³	1	2	yes	—
141	C₂×D₂₆₈	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
145	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
146	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
147	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
148	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
149	C₂²×Dic₆₇	C₂³	1	2	yes	—
150	C₂×C₄×D₆₇	C₂³	1	2	yes	—
151	C₂×C₄×D₆₇	C₂³	1	2	yes	—
152	C₂×C₄×D₆₇	C₂³	1	2	yes	—
153	C₂×C₄×D₆₇	C₂³	1	2	yes	—
154	C₂×C₄×D₆₇	C₂³	1	2	yes	—
155	C₂×C₄×D₆₇	C₂³	1	2	yes	—
156	C₂×C₄×D₆₇	C₂³	1	2	yes	—
157	C₄⋊Dic₆₇	C₂³	1	2	yes	—
158	C₄⋊Dic₆₇	C₂³	1	2	yes	—
159	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
160	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
161	C₄⋊Dic₆₇	C₂³	1	2	yes	—
162	C₄⋊Dic₆₇	C₂³	1	2	yes	—
163	Dic₆₇⋊C₄	C₂³	1	2	yes	—
164	Dic₆₇⋊C₄	C₂³	1	2	yes	—
165	Dic₆₇⋊C₄	C₂³	1	2	yes	—
166	Dic₆₇⋊C₄	C₂³	1	2	yes	—
167	Dic₆₇⋊C₄	C₂³	1	2	yes	—
168	Dic₆₇⋊C₄	C₂³	1	2	yes	—
169	Dic₆₇⋊C₄	C₂³	1	2	yes	—
170	Dic₆₇⋊C₄	C₂³	1	2	yes	—
171	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
172	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
173	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
174	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
175	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
176	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
177	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
178	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
179	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
180	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
181	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
182	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
183	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
184	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
185	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
186	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
187	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
189	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
190	C₄×Dic₆₇	C₂³	1	2	yes	—
191	C₄×Dic₆₇	C₂³	1	2	yes	—
192	C₄×Dic₆₇	C₂³	1	2	yes	—
193	C₂×Q₈×C₆₇	C₂³	1	1	yes	characteristic
194	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
195	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
196	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
197	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
198	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
199	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
200	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
201	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
202	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
203	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
204	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
205	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
206	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
207	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
208	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
209	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
210	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
211	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
212	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
213	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
214	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
215	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
216	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
217	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
218	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
219	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
220	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
221	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
222	C₄²×C₆₇	C₂³	1	1	yes	characteristic
223	C₄²×C₆₇	C₂³	1	1	yes	characteristic
224	C₄²×C₆₇	C₂³	1	1	yes	characteristic
225	C₄²×C₆₇	C₂³	1	1	yes	characteristic
226	C₄²×C₆₇	C₂³	1	1	yes	characteristic
227	C₄²×C₆₇	C₂³	1	1	yes	characteristic
228	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
229	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
230	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
231	C₂²×D₆₇	—	4	2	no	—
232	C₂²×D₆₇	—	4	2	no	—
233	C₂²×D₆₇	—	4	2	no	—
234	C₂²×D₆₇	C₂⁴	1	2	yes	—
235	C₂²×D₆₇	C₂⁴	1	2	yes	—
236	C₂²×D₆₇	C₂⁴	1	2	yes	—
237	Q₈×C₆₇	—	4	1	no	—
238	D₄×C₆₇	—	4	1	no	—
239	D₄×C₆₇	—	4	1	no	—
240	D₄×C₆₇	—	4	1	no	—
241	C₂×C₄×C₆₇	—	2	2	no	—
242	C₂×C₄×C₆₇	—	2	2	no	—
243	C₂×C₄×C₆₇	—	2	2	no	—
244	C₂×C₄×C₆₇	—	4	1	no	—
245	C₂×C₄×C₆₇	—	4	1	no	—
246	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
247	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
251	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
252	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
253	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
255	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
256	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
257	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
258	C₂²⋊D₆₇	—	4	2	no	—
259	C₂²⋊D₆₇	—	4	2	no	—
260	C₂²⋊D₆₇	—	4	2	no	—
261	C₂²⋊D₆₇	—	4	2	no	—
262	C₂²⋊D₆₇	—	4	2	no	—
263	C₂²⋊D₆₇	—	4	2	no	—
264	C₂²⋊D₆₇	—	4	2	no	—
265	C₂×Dic₆₇	—	4	2	no	—
266	C₂×Dic₆₇	C₂⁴	1	2	yes	—
267	C₂×Dic₆₇	C₂⁴	1	2	yes	—
268	C₂×Dic₆₇	C₂⁴	1	2	yes	—
269	C₂×Dic₆₇	C₂⁴	1	2	yes	—
270	C₂×Dic₆₇	C₂⁴	1	2	yes	—
271	D₂₆₈	—	2	2	no	—
272	D₂₆₈	—	2	2	no	—
273	D₂₆₈	—	2	2	no	—
274	D₂₆₈	—	4	2	no	—
275	D₂₆₈	—	4	2	no	—
276	D₂₆₈	—	4	2	no	—
277	D₂₆₈	—	4	2	no	—
278	D₂₆₈	—	4	2	no	—
279	C₄×D₆₇	—	4	2	no	—
280	C₄×D₆₇	—	4	2	no	—
281	C₄×D₆₇	—	4	2	no	—
282	C₄×D₆₇	—	4	2	no	—
283	C₄×D₆₇	—	4	2	no	—
284	C₄×D₆₇	—	4	2	no	—
285	C₄×D₆₇	—	4	2	no	—
286	Dic₁₃₄	—	2	2	no	—
287	Dic₁₃₄	—	2	2	no	—
288	Dic₁₃₄	—	2	2	no	—
289	Dic₁₃₄	—	4	2	no	—
290	C₂²×C₆₇	—	2	1	no	—
291	C₂²×C₆₇	—	2	1	no	—
292	C₂²×C₆₇	—	2	1	no	—
293	C₂²×C₆₇	—	2	1	no	—
294	C₂²×C₆₇	—	2	1	no	—
295	C₂²×C₆₇	—	2	1	no	—
296	C₂²×C₆₇	—	2	1	no	—
297	C₂²×C₆₇	—	2	1	no	—
298	C₂²×C₆₇	—	2	1	no	—
299	C₂²×C₆₇	C₂⁵	1	1	yes	characteristic
300	C₂×D₆₇	—	2	2	no	—
301	C₂×D₆₇	—	2	2	no	—
302	C₂×D₆₇	—	2	2	no	—
303	C₂×D₆₇	—	2	2	no	—
304	C₂×D₆₇	—	2	2	no	—
305	C₂×D₆₇	—	2	2	no	—
306	C₂×D₆₇	—	2	2	no	—
307	C₂×D₆₇	—	2	2	no	—
308	C₂×D₆₇	—	2	2	no	—
309	C₂×D₆₇	—	8	4	no	—
310	C₄×C₆₇	—	2	1	no	—
311	C₄×C₆₇	—	2	1	no	—
312	C₄×C₆₇	—	2	1	no	—
313	C₄×C₆₇	—	2	1	no	—
314	C₄×C₆₇	—	2	1	no	—
315	C₄×C₆₇	—	2	1	no	—
316	C₄×C₆₇	—	2	1	no	—
317	C₄×C₆₇	—	2	1	no	—
318	C₄×C₆₇	—	2	1	no	—
319	C₄×C₆₇	—	2	1	no	—
320	C₄×C₆₇	—	2	1	no	—
321	C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
322	Dic₆₇	—	2	2	no	—
323	Dic₆₇	—	2	2	no	—
324	Dic₆₇	—	2	2	no	—
325	Dic₆₇	—	2	2	no	—
326	Dic₆₇	—	2	2	no	—
327	C₂×C₆₇	—	4	1	no	—
328	C₂×C₆₇	—	4	1	no	—
329	C₂×C₆₇	—	4	1	no	—
330	C₂×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
331	C₂×C₆₇	#585	1	1	yes	characteristic
332	C₂×C₆₇	#585	1	1	yes	characteristic
333	D₆₇	—	4	2	no	—
334	D₆₇	—	4	2	no	—
335	D₆₇	—	4	2	no	—
336	#3562	—	67	1	no	maximal, Sylow
337	C₆₇	#3562	1	1	yes	characteristic, complemented, Sylow
338	#562	—	67	2	no	—
339	#560	—	67	2	no	—
340	#559	—	67	1	no	—
341	#556	—	67	1	no	—
342	#553	—	67	2	no	—
343	#551	—	67	2	no	—
344	#550	—	67	1	no	—
345	#548	—	67	1	no	—
346	#548	—	67	1	no	—
347	#547	—	67	1	no	—
348	#546	—	67	1	no	—
349	#546	—	67	1	no	—
350	#541	—	67	1	no	—
351	#540	—	67	2	no	—
352	#540	—	67	1	no	—
353	#539	—	67	2	no	—
354	#538	—	67	2	no	—
355	#538	—	67	2	no	—
356	#536	—	67	1	no	—
357	#535	—	67	1	no	—
358	#532	—	67	1	no	—
359	#529	—	67	1	no	—
360	#529	D₆₇	1	1	yes	characteristic, complemented
361	C₂×#41	—	67	1	no	—
362	C₂×#41	—	67	1	no	—
363	C₂×#41	—	67	1	no	—
364	C₂×#41	—	67	1	no	—
365	C₂²×Q₈	—	67	1	no	—
366	C₂²×D₄	—	67	1	no	—
367	C₄⋊Q₈	—	67	1	no	—
368	C₄⋊Q₈	—	67	1	no	—
369	#127	—	67	2	no	—
370	#127	—	67	1	no	—
371	#127	—	67	1	no	—
372	#126	—	67	2	no	—
373	#126	—	67	2	no	—
374	#126	—	67	2	no	—
375	#126	—	67	2	no	—
376	#126	—	67	2	no	—
377	#126	C₂×D₆₇	1	1	yes	characteristic
378	#126	C₂×D₆₇	1	1	yes	characteristic, complemented
379	#125	—	67	2	no	—
380	#125	—	67	2	no	—
381	#125	—	67	1	no	—
382	#125	C₂×D₆₇	1	1	yes	characteristic, complemented
383	#124	—	67	2	no	—
384	#124	—	67	2	no	—
385	#124	—	67	2	no	—
386	#124	—	67	1	no	—
387	#124	—	67	1	no	—
388	#124	—	67	1	no	—
389	#124	—	67	1	no	—
390	#124	—	67	1	no	—
391	#124	C₂×D₆₇	1	1	yes	characteristic
392	#123	—	67	2	no	—
393	#123	—	67	2	no	—
394	#123	—	67	2	no	—
395	#123	—	67	2	no	—
396	#123	—	67	2	no	—
397	#123	—	67	2	no	—
398	#123	—	67	2	no	—
399	#123	—	67	2	no	—
400	#123	—	67	2	no	—
401	#123	—	67	2	no	—
402	#123	—	67	2	no	—
403	#123	C₂×D₆₇	1	1	yes	characteristic
404	#123	C₂×D₆₇	1	1	yes	characteristic, complemented
405	C₂²⋊Q₈	—	67	2	no	—
406	C₂²⋊Q₈	—	67	1	no	—
407	C₂²⋊Q₈	—	67	1	no	—
408	C₂²⋊Q₈	—	67	1	no	—
409	C₂²⋊Q₈	—	67	2	no	—
410	C₂²⋊Q₈	—	67	2	no	—
411	C₂²⋊Q₈	—	67	2	no	—
412	C₂²⋊Q₈	—	67	2	no	—
413	C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
414	#121	—	67	2	no	—
415	#121	—	67	2	no	—
416	#121	—	67	2	no	—
417	#121	—	67	1	no	—
418	#121	—	67	2	no	—
419	#121	—	67	2	no	—
420	#121	—	67	1	no	—
421	#121	—	67	1	no	—
422	#121	—	67	2	no	—
423	#121	—	67	2	no	—
424	#121	—	67	2	no	—
425	#121	—	67	2	no	—
426	#121	—	67	2	no	—
427	#121	—	67	2	no	—
428	#121	—	67	2	no	—
429	#121	—	67	2	no	—
430	#121	C₂×D₆₇	1	1	yes	characteristic
431	#120	—	67	2	no	—
432	#120	—	67	2	no	—
433	#120	—	67	2	no	—
434	#120	—	67	2	no	—
435	C₄×Q₈	—	67	1	no	—
436	C₄×Q₈	—	67	1	no	—
437	C₄×Q₈	—	67	1	no	—
438	C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
439	C₄×D₄	—	67	2	no	—
440	C₄×D₄	—	67	2	no	—
441	C₄×D₄	—	67	2	no	—
442	C₄×D₄	—	67	2	no	—
443	C₄×D₄	—	67	2	no	—
444	C₄×D₄	—	67	1	no	—
445	C₄×D₄	—	67	2	no	—
446	C₄×D₄	—	67	2	no	—
447	C₄×D₄	—	67	1	no	—
448	C₄×D₄	—	67	1	no	—
449	C₄×D₄	C₂×D₆₇	1	1	yes	characteristic
450	C₄×D₄	C₂×D₆₇	1	1	yes	characteristic
451	C₄×D₄	C₂×D₆₇	1	1	yes	characteristic, complemented
452	#117	—	67	2	no	—
453	#117	—	67	2	no	—
454	#117	C₂×D₆₇	1	1	yes	characteristic
455	#117	C₂×D₆₇	1	1	yes	characteristic, complemented
456	C₂×C₄⋊C₄	—	67	2	no	—
457	C₂×C₂²⋊C₄	—	67	2	no	—
458	C₂×C₂²⋊C₄	—	67	2	no	—
459	C₂×C₄²	C₂×D₆₇	1	1	yes	characteristic, complemented
460	C₂⁴	—	67	2	no	—
461	#41	—	268	2	no	—
462	#41	—	268	2	no	—
463	#41	—	268	2	no	—
464	#41	—	268	2	no	—
465	C₂×Q₈	—	268	2	no	—
466	C₂×Q₈	—	67	2	no	—
467	C₂×Q₈	—	67	1	no	—
468	C₂×Q₈	—	67	1	no	—
469	C₂×Q₈	—	67	1	no	—
470	C₂×Q₈	C₂²×D₆₇	1	1	yes	characteristic
471	C₂×D₄	—	268	2	no	—
472	C₂×D₄	—	67	2	no	—
473	C₂×D₄	—	67	2	no	—
474	C₂×D₄	—	67	2	no	—
475	C₂×D₄	—	67	2	no	—
476	C₂×D₄	—	67	2	no	—
477	C₂×D₄	—	67	2	no	—
478	C₂×D₄	—	67	2	no	—
479	C₂×D₄	—	67	2	no	—
480	C₂×D₄	—	67	2	no	—
481	C₂×D₄	—	67	2	no	—
482	C₂×D₄	—	67	2	no	—
483	C₂×D₄	—	67	2	no	—
484	C₂×D₄	—	67	1	no	—
485	C₂×D₄	—	67	1	no	—
486	C₂×D₄	—	67	1	no	—
487	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
488	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
489	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
490	C₂²×C₄	—	67	2	no	—
491	C₂²×C₄	—	67	2	no	—
492	C₂²×C₄	—	67	2	no	—
493	C₂²×C₄	—	67	2	no	—
494	C₂²×C₄	—	67	2	no	—
495	C₂²×C₄	—	67	2	no	—
496	C₂²×C₄	—	67	2	no	—
497	C₂²×C₄	—	67	2	no	—
498	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
499	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
500	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
501	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
502	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
503	C₄⋊C₄	—	67	2	no	—
504	C₄⋊C₄	—	67	2	no	—
505	C₄⋊C₄	—	67	2	no	—
506	C₄⋊C₄	—	67	2	no	—
507	C₄⋊C₄	—	67	2	no	—
508	C₄⋊C₄	—	67	1	no	—
509	C₄⋊C₄	—	67	1	no	—
510	C₄⋊C₄	—	67	2	no	—
511	C₄⋊C₄	—	67	2	no	—
512	C₄⋊C₄	—	67	2	no	—
513	C₄⋊C₄	—	67	2	no	—
514	C₄⋊C₄	—	67	2	no	—
515	C₄⋊C₄	—	67	2	no	—
516	C₄⋊C₄	—	67	2	no	—
517	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
518	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
519	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
520	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
521	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
522	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
523	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
524	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
525	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
526	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
527	C₂²⋊C₄	—	67	2	no	—
528	C₂²⋊C₄	—	67	2	no	—
529	C₂²⋊C₄	—	67	2	no	—
530	C₂²⋊C₄	—	67	2	no	—
531	C₂²⋊C₄	—	67	2	no	—
532	C₂²⋊C₄	—	67	2	no	—
533	C₂²⋊C₄	—	67	2	no	—
534	C₂²⋊C₄	—	67	2	no	—
535	C₂²⋊C₄	—	67	2	no	—
536	C₂²⋊C₄	—	67	2	no	—
537	C₂²⋊C₄	—	67	2	no	—
538	C₂²⋊C₄	—	67	2	no	—
539	C₂²⋊C₄	—	67	2	no	—
540	C₂²⋊C₄	—	67	2	no	—
541	C₂²⋊C₄	—	67	2	no	—
542	C₂²⋊C₄	—	67	2	no	—
543	C₂²⋊C₄	—	67	2	no	—
544	C₂²⋊C₄	—	67	2	no	—
545	C₂²⋊C₄	—	67	2	no	—
546	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
547	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
548	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
549	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
550	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
551	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
552	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
553	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
554	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
555	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
556	C₄²	—	67	2	no	—
557	C₄²	—	67	2	no	—
558	C₄²	—	67	2	no	—
559	C₄²	C₂²×D₆₇	1	1	yes	characteristic
560	C₄²	C₂²×D₆₇	1	1	yes	characteristic
561	C₄²	C₂²×D₆₇	1	1	yes	characteristic
562	C₄²	C₂²×D₆₇	1	1	yes	characteristic
563	C₄²	C₂²×D₆₇	1	1	yes	characteristic
564	C₄²	C₂²×D₆₇	1	1	yes	characteristic
565	C₂³	—	268	2	no	—
566	C₂³	—	268	2	no	—
567	C₂³	—	268	2	no	—
568	C₂³	—	67	2	no	—
569	C₂³	—	67	2	no	—
570	C₂³	—	67	2	no	—
571	C₂³	C₂³×D₆₇	1	1	yes	characteristic
572	C₂³	C₂³×D₆₇	1	1	yes	characteristic
573	C₂³	C₂³×D₆₇	1	1	yes	characteristic
574	Q₈	—	4	1	no	—
575	Q₈	—	268	2	no	—
576	Q₈	—	134	2	no	—
577	Q₈	—	134	2	no	—
578	Q₈	—	134	2	no	—
579	D₄	—	4	1	no	—
580	D₄	—	4	1	no	—
581	D₄	—	4	1	no	—
582	D₄	—	268	2	no	—
583	D₄	—	268	2	no	—
584	D₄	—	268	2	no	—
585	D₄	—	268	2	no	—
586	D₄	—	268	2	no	—
587	D₄	—	268	2	no	—
588	D₄	—	268	2	no	—
589	D₄	—	268	2	no	—
590	D₄	—	268	2	no	—
591	D₄	—	268	2	no	—
592	D₄	—	268	2	no	—
593	D₄	—	268	2	no	—
594	D₄	—	134	2	no	—
595	D₄	—	134	2	no	—
596	D₄	—	134	2	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	268	2	no	—
603	C₂×C₄	—	268	2	no	—
604	C₂×C₄	—	268	2	no	—
605	C₂×C₄	—	268	2	no	—
606	C₂×C₄	—	268	2	no	—
607	C₂×C₄	—	268	2	no	—
608	C₂×C₄	—	268	2	no	—
609	C₂×C₄	—	268	2	no	—
610	C₂×C₄	—	67	2	no	—
611	C₂×C₄	—	67	2	no	—
612	C₂×C₄	—	67	2	no	—
613	C₂×C₄	—	67	2	no	—
614	C₂×C₄	—	67	2	no	—
615	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
616	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
617	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
618	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
619	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
620	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
621	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
622	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
623	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
624	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
625	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
626	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
627	C₂²	—	2	1	no	—
628	C₂²	—	2	1	no	—
629	C₂²	—	2	1	no	—
630	C₂²	—	2	1	no	—
631	C₂²	—	2	1	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	1	no	—
634	C₂²	—	2	1	no	—
635	C₂²	—	2	1	no	—
636	C₂²	—	536	4	no	—
637	C₂²	—	134	2	no	—
638	C₂²	—	134	2	no	—
639	C₂²	—	134	2	no	—
640	C₂²	—	134	2	no	—
641	C₂²	—	134	2	no	—
642	C₂²	—	134	2	no	—
643	C₂²	—	134	2	no	—
644	C₂²	—	134	2	no	—
645	C₂²	—	134	2	no	—
646	C₂²	C₂⁴×D₆₇	1	1	yes	characteristic
647	C₄	—	2	1	no	—
648	C₄	—	2	1	no	—
649	C₄	—	2	1	no	—
650	C₄	—	2	1	no	—
651	C₄	—	2	1	no	—
652	C₄	—	2	1	no	—
653	C₄	—	2	1	no	—
654	C₄	—	2	1	no	—
655	C₄	—	2	1	no	—
656	C₄	—	2	1	no	—
657	C₄	—	2	1	no	—
658	C₄	—	134	2	no	—
659	C₄	—	134	2	no	—
660	C₄	—	134	2	no	—
661	C₄	—	134	2	no	—
662	C₄	—	134	2	no	—
663	C₄	#14524089	1	2	yes	—
664	C₂	—	4	1	no	—
665	C₂	—	4	1	no	—
666	C₂	—	4	1	no	—
667	C₂	—	268	2	no	—
668	C₂	—	268	2	no	—
669	C₂	—	268	2	no	—
670	C₂	C₂×#14524089	1	1	yes	characteristic
671	C₂	#16864232	1	1	yes	characteristic
672	C₂	#16864232	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁵
Fitting	#529×C₆₇	C₂
hypercenter	#529	D₆₇
hypocenter	C₆₇	#3562
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
1. #16864142	C₂	semidirect
2. #16864134	C₂	semidirect
3. #16864131	C₂	semidirect
4. #16864119	C₂	semidirect
5. #16864097	C₂	semidirect
6. #16864071	C₂	semidirect
7. #16864067	C₂	semidirect
8. #16864055	C₂	semidirect
9. #16864055	C₂	semidirect
10. #16864051	C₂	semidirect
11. #16864042	C₂	semidirect
12. #16864042	C₂	semidirect
13. #16864008	C₂	semidirect
14. #16864001	C₂	semidirect
15. #16863998	C₂	semidirect
16. #16863994	C₂	semidirect
17. #16863982	C₂	semidirect
18. #16863980	C₂	semidirect
19. #16863972	C₂	semidirect
20. #16863965	C₂	semidirect
21. #16863946	C₂	semidirect
22. #16863930	C₂	semidirect
23. #529×C₆₇	C₂	semidirect
27. C₂×#11761628	C₂²	semidirect
28. C₂²×Dic₁₃₄	C₂²	semidirect
30. #14524043	C₂²	semidirect
31. #14524043	C₂²	semidirect
34. #14524039	C₂²	semidirect
35. #14524038	C₂²	semidirect
36. #14524038	C₂²	semidirect
37. #14524037	C₂²	semidirect
40. #14524035	C₂²	semidirect
41. #14524033	C₂²	semidirect
42. #14524033	C₂²	semidirect
43. #14524032	C₂²	semidirect
48. #14524031	C₂²	semidirect
50. #14524029	C₂²	semidirect
53. #14524028	C₂²	semidirect
54. #14524028	C₂²	semidirect
55. #14524028	C₂²	semidirect
56. #14524028	C₂²	semidirect
57. #14524027	C₂²	semidirect
58. #14524027	C₂²	semidirect
59. #14524026	C₂²	semidirect
61. #14524025	C₂²	semidirect
62. #14524023	C₂²	semidirect
63. #14524023	C₂²	semidirect
66. #14524022	C₂²	semidirect
67. #14524021	C₂²	semidirect
68. #14524021	C₂²	semidirect
69. #14524019	C₂²	semidirect
74. #14524017	C₂²	semidirect
75. #14524017	C₂²	semidirect
76. #14524017	C₂²	semidirect
79. #14524016	C₂²	semidirect
80. #14524016	C₂²	semidirect
81. #14524016	C₂²	semidirect
82. #14524016	C₂²	semidirect
84. #14524015	C₂²	semidirect
90. C₄×Dic₁₃₄	C₂²	semidirect
91. C₄×Dic₁₃₄	C₂²	semidirect
92. C₄×Dic₁₃₄	C₂²	semidirect
95. C₄×D₂₆₈	C₂²	semidirect
96. C₄×D₂₆₈	C₂²	semidirect
97. C₄×D₂₆₈	C₂²	semidirect
98. #14524005	C₂²	semidirect
99. #14524005	C₂²	semidirect
100. C₄×C₂²⋊D₆₇	C₂²	semidirect
101. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
102. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
103. #14524001	C₂²	semidirect
104. #14524000	C₂²	semidirect
105. C₄⋊C₄×D₆₇	C₂²	semidirect
109. #126×C₆₇	C₂²	semidirect
110. #125×C₆₇	C₂²	semidirect
113. #123×C₆₇	C₂²	semidirect
114. C₂²⋊Q₈×C₆₇	C₂²	semidirect
116. C₄×Q₈×C₆₇	C₂²	semidirect
119. C₄×D₄×C₆₇	C₂²	semidirect
121. #117×C₆₇	C₂²	semidirect
122. C₂×C₄²×C₆₇	C₂²	semidirect
337. C₆₇	#3562	semidirect
360. #529	D₆₇	semidirect
378. #126	C₂×D₆₇	semidirect
382. #125	C₂×D₆₇	semidirect
404. #123	C₂×D₆₇	semidirect
413. C₂²⋊Q₈	C₂×D₆₇	semidirect
438. C₄×Q₈	C₂×D₆₇	semidirect
451. C₄×D₄	C₂×D₆₇	semidirect
455. #117	C₂×D₆₇	semidirect
459. C₂×C₄²	C₂×D₆₇	semidirect