Subgroups — #22573937

Order 8576.

1142 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16864111	C₂	1	1	yes	maximal, characteristic, complemented
2	#16864110	C₂	1	1	yes	maximal, characteristic, complemented
3	#16864099	C₂	1	1	yes	maximal, characteristic, complemented
4	#16864093	C₂	1	1	yes	maximal, characteristic, complemented
5	#16864090	C₂	1	1	yes	maximal, characteristic, complemented
6	#16864075	C₂	1	2	yes	maximal, complemented
7	#16864071	C₂	1	2	yes	maximal, complemented
8	#16864051	C₂	1	1	yes	maximal, characteristic, complemented
9	#16864047	C₂	1	1	yes	maximal, characteristic, complemented
10	#16864043	C₂	1	2	yes	maximal, complemented
11	#16864038	C₂	1	2	yes	maximal, complemented
12	#16864026	C₂	1	1	yes	maximal, characteristic, complemented
13	#16864014	C₂	1	2	yes	maximal, complemented
14	#16863996	C₂	1	2	yes	maximal, complemented
15	#16863962	C₂	1	1	yes	maximal, characteristic, complemented
16	#16863943	C₂	1	2	yes	maximal, complemented
17	#16863929	C₂	1	2	yes	maximal, complemented
18	#16863905	C₂	1	1	yes	maximal, characteristic, complemented
19	#121×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	#16863877	C₂	1	1	yes	maximal, characteristic, complemented
21	#16863868	C₂	1	1	yes	maximal, characteristic, complemented
22	#117×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	#553×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#11761628	C₂²	1	1	yes	characteristic
25	C₂×#11761628	C₂²	1	2	yes	complemented
26	C₂×#11761628	C₂²	1	2	yes	complemented
27	C₂×D₄×D₆₇	C₂²	1	1	yes	characteristic
28	C₂×D₄×D₆₇	C₂²	1	2	yes	—
29	C₂²×C₄×D₆₇	C₂²	1	1	yes	characteristic
30	#14524043	C₂²	1	1	yes	characteristic, complemented
31	#14524042	C₂²	1	2	yes	complemented
32	#14524042	C₂²	1	1	yes	characteristic, complemented
33	#14524039	C₂²	1	2	yes	complemented
34	#14524038	C₂²	1	2	yes	complemented
35	#14524037	C₂²	1	2	yes	complemented
36	#14524036	C₂²	1	2	yes	complemented
37	#14524034	C₂²	1	1	yes	characteristic, complemented
38	#14524033	C₂²	1	2	yes	complemented
39	#14524030	C₂²	1	2	yes	complemented
40	#14524029	C₂²	1	2	yes	complemented
41	#14524029	C₂²	1	2	yes	complemented
42	#14524029	C₂²	1	2	yes	complemented
43	#14524029	C₂²	1	2	yes	complemented
44	#14524028	C₂²	1	1	yes	characteristic
45	#14524028	C₂²	1	2	yes	complemented
46	#14524028	C₂²	1	2	yes	complemented
47	#14524026	C₂²	1	2	yes	complemented
48	#14524025	C₂²	1	1	yes	characteristic
49	#14524025	C₂²	1	2	yes	complemented
50	#14524025	C₂²	1	2	yes	complemented
51	#14524025	C₂²	1	2	yes	complemented
52	#14524024	C₂²	1	2	yes	complemented
53	#14524023	C₂²	1	2	yes	—
54	#14524022	C₂²	1	2	yes	complemented
55	#14524021	C₂²	1	2	yes	—
56	#14524021	C₂²	1	2	yes	complemented
57	#14524021	C₂²	1	1	yes	characteristic, complemented
58	#14524020	C₂²	1	1	yes	characteristic, complemented
59	#14524018	C₂²	1	1	yes	characteristic
60	#14524018	C₂²	1	2	yes	complemented
61	#14524018	C₂²	1	1	yes	characteristic, complemented
62	#14524017	C₂²	1	1	yes	characteristic
63	#14524017	C₂²	1	1	yes	characteristic, complemented
64	#14524016	C₂²	1	2	yes	—
65	#14524016	C₂²	1	2	yes	complemented
66	#14524016	C₂²	1	1	yes	characteristic, complemented
67	#14524015	C₂²	1	2	yes	—
68	#14524015	C₂²	1	2	yes	complemented
69	#14524015	C₂²	1	1	yes	characteristic, complemented
70	#14524014	C₂²	1	1	yes	characteristic
71	#14524014	C₂²	1	2	yes	complemented
72	#14524014	C₂²	1	2	yes	complemented
73	#14524014	C₂²	1	1	yes	characteristic, complemented
74	#14524013	C₂²	1	1	yes	characteristic
75	#14524013	C₂²	1	2	yes	—
76	#14524011	C₂²	1	1	yes	characteristic
77	#14524011	C₂²	1	2	yes	—
78	#14524008	C₂²	1	2	yes	complemented
79	C₄×D₂₆₈	C₂²	1	1	yes	characteristic, complemented
80	C₄×D₂₆₈	C₂²	1	2	yes	complemented
81	C₄×D₂₆₈	C₂²	1	1	yes	characteristic, complemented
82	D₄×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
83	#14524005	C₂²	1	2	yes	—
84	#14524005	C₂²	1	2	yes	complemented
85	#14524005	C₂²	1	1	yes	characteristic, complemented
86	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	—
87	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
88	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic, complemented
89	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic, complemented
90	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
91	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	complemented
92	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	complemented
93	#14524002	C₂²	1	1	yes	characteristic, complemented
94	#14524002	C₂²	1	1	yes	characteristic, complemented
95	#14524001	C₂²	1	1	yes	characteristic
96	#14524001	C₂²	1	1	yes	characteristic
97	#14524001	C₂²	1	2	yes	complemented
98	#14524001	C₂²	1	1	yes	characteristic, complemented
99	#14524000	C₂²	1	1	yes	characteristic
100	#14524000	C₂²	1	2	yes	—
101	#14523999	C₂²	1	2	yes	complemented
102	#14523999	C₂²	1	2	yes	complemented
103	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
104	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
105	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
106	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
107	C₂×(C₂×D₆₇)⋊C₄	C₂²	1	2	yes	—
108	C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
109	C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
110	C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
111	C₄²×D₆₇	C₂²	1	2	yes	complemented
112	#126×C₆₇	C₂²	1	2	yes	complemented
113	#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
114	#123×C₆₇	C₂²	1	2	yes	complemented
115	#121×C₆₇	C₂²	1	1	yes	characteristic
116	#121×C₆₇	C₂²	1	2	yes	complemented
117	#121×C₆₇	C₂²	1	1	yes	characteristic, complemented
118	C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
120	C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
121	#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₆₇	C₂³	1	1	yes	characteristic
124	C₂³×D₆₇	C₂³	1	2	yes	—
125	#11761628	—	2	4	no	—
126	#11761628	—	4	4	no	—
127	#11761628	—	4	4	no	—
128	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
129	C₂×Dic₁₃₄	C₂³	1	2	yes	—
130	C₂×Dic₁₃₄	C₂³	1	2	yes	—
131	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
132	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
133	C₂×D₂₆₈	C₂³	1	2	yes	—
134	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
135	C₂×D₂₆₈	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
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	D₄×D₆₇	—	2	4	no	—
146	D₄×D₆₇	—	4	4	no	—
147	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
148	C₂²×Dic₆₇	C₂³	1	2	yes	—
149	C₂×C₄×D₆₇	—	2	4	no	—
150	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₆₇	C₂³	1	2	yes	—
152	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₆₇	C₂³	1	2	yes	—
156	C₂×C₄×D₆₇	C₂³	1	2	yes	—
157	C₂×C₄×D₆₇	C₂³	1	2	yes	—
158	C₂×C₄×D₆₇	C₂³	1	2	yes	—
159	C₂×C₄×D₆₇	C₂³	1	2	yes	—
160	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
161	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
162	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
163	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
164	C₄⋊Dic₆₇	C₂³	1	2	yes	—
165	C₄⋊Dic₆₇	C₂³	1	2	yes	—
166	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
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	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
172	Dic₆₇⋊C₄	C₂³	1	2	yes	—
173	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
174	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
175	Dic₆₇⋊C₄	C₂³	1	2	yes	—
176	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
177	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
178	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
179	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
180	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
181	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
182	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
183	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
184	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
185	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
190	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
191	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
192	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
193	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
194	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
195	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
196	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
197	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
198	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
199	C₄×Dic₆₇	C₂³	1	2	yes	—
200	C₄×Dic₆₇	C₂³	1	2	yes	—
201	C₄×Dic₆₇	C₂³	1	2	yes	—
202	C₄×Dic₆₇	C₂³	1	2	yes	—
203	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
204	C₄×Dic₆₇	C₂³	1	2	yes	—
205	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
206	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
207	C₂×D₄×C₆₇	C₂³	1	2	yes	—
208	C₂×D₄×C₆₇	C₂³	1	2	yes	—
209	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
210	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
211	C₂²×C₄×C₆₇	C₂³	1	2	yes	—
212	C₂²×C₄×C₆₇	C₂³	1	2	yes	—
213	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
214	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
215	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
216	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
217	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
218	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
219	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
220	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
221	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
222	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
223	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
224	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
225	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
226	C₄²×C₆₇	C₂³	1	2	yes	—
227	C₄²×C₆₇	C₂³	1	1	yes	characteristic
228	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
229	C₂³×C₆₇	C₂⁴	1	2	yes	—
230	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
231	C₂²×D₆₇	—	2	2	no	—
232	C₂²×D₆₇	—	2	2	no	—
233	C₂²×D₆₇	—	2	4	no	—
234	C₂²×D₆₇	—	4	1	no	—
235	C₂²×D₆₇	—	4	2	no	—
236	C₂²×D₆₇	—	4	2	no	—
237	C₂²×D₆₇	C₂⁴	1	2	yes	—
238	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
239	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
240	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
241	D₄×C₆₇	—	2	2	no	—
242	D₄×C₆₇	—	4	1	no	—
243	D₄×C₆₇	—	4	2	no	—
244	D₄×C₆₇	—	4	2	no	—
245	C₂×C₄×C₆₇	—	2	2	no	—
246	C₂×C₄×C₆₇	—	2	2	no	—
247	C₂×C₄×C₆₇	—	4	2	no	—
248	C₂×C₄×C₆₇	—	4	2	no	—
249	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
251	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
252	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
253	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
255	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
256	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
257	C₂²⋊D₆₇	—	2	2	no	—
258	C₂²⋊D₆₇	—	2	4	no	—
259	C₂²⋊D₆₇	—	2	2	no	—
260	C₂²⋊D₆₇	—	2	4	no	—
261	C₂²⋊D₆₇	—	2	2	no	—
262	C₂²⋊D₆₇	—	4	2	no	—
263	C₂²⋊D₆₇	—	4	1	no	—
264	C₂²⋊D₆₇	—	4	2	no	—
265	C₂²⋊D₆₇	—	4	2	no	—
266	C₂×Dic₆₇	—	2	2	no	—
267	C₂×Dic₆₇	—	4	2	no	—
268	C₂×Dic₆₇	C₂⁴	1	2	yes	—
269	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
270	C₂×Dic₆₇	C₂⁴	1	2	yes	—
271	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
272	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
273	C₂×Dic₆₇	C₂⁴	1	2	yes	—
274	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
275	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
276	D₂₆₈	—	2	2	no	—
277	D₂₆₈	—	2	4	no	—
278	D₂₆₈	—	2	2	no	—
279	D₂₆₈	—	2	2	no	—
280	D₂₆₈	—	4	2	no	—
281	C₄×D₆₇	—	2	2	no	—
282	C₄×D₆₇	—	2	4	no	—
283	C₄×D₆₇	—	2	2	no	—
284	C₄×D₆₇	—	2	2	no	—
285	C₄×D₆₇	—	2	2	no	—
286	C₄×D₆₇	—	4	2	no	—
287	C₄×D₆₇	—	4	2	no	—
288	C₄×D₆₇	—	4	2	no	—
289	C₄×D₆₇	—	4	2	no	—
290	C₄×D₆₇	—	4	2	no	—
291	C₄×D₆₇	#41	1	4	yes	complemented
292	Dic₁₃₄	—	2	2	no	—
293	Dic₁₃₄	—	4	2	no	—
294	Dic₁₃₄	—	4	2	no	—
295	C₂²×C₆₇	—	2	1	no	—
296	C₂²×C₆₇	—	2	1	no	—
297	C₂²×C₆₇	—	2	2	no	—
298	C₂²×C₆₇	—	2	1	no	—
299	C₂²×C₆₇	—	2	2	no	—
300	C₂²×C₆₇	—	2	1	no	—
301	C₂²×C₆₇	—	2	2	no	—
302	C₂²×C₆₇	—	2	1	no	—
303	C₂²×C₆₇	—	2	1	no	—
304	C₂²×C₆₇	C₂⁵	1	1	yes	characteristic
305	C₂×D₆₇	—	2	1	no	—
306	C₂×D₆₇	—	2	1	no	—
307	C₂×D₆₇	—	2	1	no	—
308	C₂×D₆₇	—	2	1	no	—
309	C₂×D₆₇	—	2	1	no	—
310	C₂×D₆₇	—	2	2	no	—
311	C₂×D₆₇	—	2	1	no	—
312	C₂×D₆₇	—	2	2	no	—
313	C₂×D₆₇	—	2	2	no	—
314	C₂×D₆₇	—	2	1	no	—
315	C₂×D₆₇	—	4	4	no	—
316	C₂×D₆₇	—	8	4	no	—
317	C₂×D₆₇	C₂×#41	1	2	yes	—
318	C₂×D₆₇	H(5,𝔽₂)	1	2	yes	—
319	C₄×C₆₇	—	2	1	no	—
320	C₄×C₆₇	—	2	1	no	—
321	C₄×C₆₇	—	2	1	no	—
322	C₄×C₆₇	—	2	2	no	—
323	C₄×C₆₇	—	2	2	no	—
324	C₄×C₆₇	—	2	1	no	—
325	C₄×C₆₇	—	2	2	no	—
326	C₄×C₆₇	C₂×#41	1	2	yes	—
327	Dic₆₇	—	2	1	no	—
328	Dic₆₇	—	2	1	no	—
329	Dic₆₇	—	2	2	no	—
330	Dic₆₇	—	2	1	no	—
331	Dic₆₇	—	2	2	no	—
332	Dic₆₇	—	2	2	no	—
333	Dic₆₇	—	2	1	no	—
334	Dic₆₇	C₂×#41	1	2	yes	—
335	C₂×C₆₇	—	4	1	no	—
336	C₂×C₆₇	—	4	2	no	—
337	C₂×C₆₇	—	4	1	no	—
338	C₂×C₆₇	C₂²×#41	1	1	yes	characteristic
339	C₂×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
340	C₂×C₆₇	#585	1	1	yes	characteristic
341	D₆₇	—	2	2	no	—
342	D₆₇	—	2	2	no	—
343	D₆₇	—	4	1	no	—
344	D₆₇	—	4	2	no	—
345	#3494	—	67	1	no	maximal, Sylow
346	C₆₇	#3494	1	1	yes	characteristic, complemented, Sylow
347	#555	—	67	1	no	—
348	#555	—	67	1	no	—
349	#553	—	67	1	no	—
350	#553	—	67	1	no	—
351	#553	—	67	1	no	—
352	#553	D₆₇	1	1	yes	characteristic, complemented
353	#551	—	67	2	no	—
354	#551	—	67	2	no	—
355	#547	—	67	1	no	—
356	#547	—	67	1	no	—
357	#546	—	67	2	no	—
358	#546	—	67	2	no	—
359	#544	—	67	1	no	—
360	#542	—	67	2	no	—
361	#540	—	67	2	no	—
362	#535	—	67	1	no	—
363	#532	—	67	2	no	—
364	#529	—	67	2	no	—
365	#525	—	67	1	no	—
366	C₂×#121	—	67	1	no	—
367	#520	—	67	1	no	—
368	#518	—	67	1	no	—
369	C₂×#117	—	67	1	no	—
370	C₂×#41	—	67	2	no	—
371	C₂×#41	—	67	2	no	—
372	C₂×#41	—	67	1	no	—
373	C₂²×D₄	—	67	2	no	—
374	C₂²×D₄	—	67	1	no	—
375	C₂³×C₄	—	67	1	no	—
376	C₄⋊Q₈	—	67	2	no	—
377	C₄⋊Q₈	—	67	1	no	—
378	C₄⋊Q₈	—	67	1	no	—
379	#127	—	67	2	no	—
380	#126	—	67	2	no	—
381	#126	—	67	2	no	—
382	#126	—	67	2	no	—
383	#126	C₂×D₆₇	1	2	yes	complemented
384	#125	—	67	2	no	—
385	#125	—	67	1	no	—
386	#125	C₂×D₆₇	1	1	yes	characteristic, complemented
387	#124	—	67	2	no	—
388	#124	—	67	2	no	—
389	#124	—	67	2	no	—
390	#124	—	67	2	no	—
391	#124	—	67	2	no	—
392	#123	—	67	2	no	—
393	#123	—	67	2	no	—
394	#123	—	67	1	no	—
395	#123	—	67	2	no	—
396	#123	—	67	2	no	—
397	#123	—	67	1	no	—
398	#123	—	67	2	no	—
399	#123	—	67	2	no	—
400	#123	—	67	2	no	—
401	#123	C₂×D₆₇	1	2	yes	complemented
402	C₂²⋊Q₈	—	67	2	no	—
403	C₂²⋊Q₈	—	67	1	no	—
404	C₂²⋊Q₈	—	67	2	no	—
405	C₂²⋊Q₈	—	67	2	no	—
406	C₂²⋊Q₈	—	67	2	no	—
407	C₂²⋊Q₈	—	67	1	no	—
408	#121	—	67	2	no	—
409	#121	—	67	1	no	—
410	#121	—	67	1	no	—
411	#121	—	67	2	no	—
412	#121	—	67	1	no	—
413	#121	—	67	2	no	—
414	#121	—	67	2	no	—
415	#121	—	67	1	no	—
416	#121	—	67	1	no	—
417	#121	—	67	1	no	—
418	#121	—	67	2	no	—
419	#121	—	67	1	no	—
420	#121	—	67	2	no	—
421	#121	—	67	1	no	—
422	#121	—	67	2	no	—
423	#121	C₂×D₆₇	1	1	yes	characteristic
424	#121	C₂×D₆₇	1	1	yes	characteristic, complemented
425	#121	C₂×D₆₇	1	2	yes	complemented
426	#120	—	67	1	no	—
427	#120	—	67	2	no	—
428	#120	—	67	1	no	—
429	#120	—	67	2	no	—
430	C₄×Q₈	—	67	2	no	—
431	C₄×D₄	—	67	1	no	—
432	C₄×D₄	—	67	2	no	—
433	C₄×D₄	—	67	2	no	—
434	C₄×D₄	—	67	2	no	—
435	C₄×D₄	—	67	1	no	—
436	C₄×D₄	—	67	1	no	—
437	C₄×D₄	—	67	1	no	—
438	C₄×D₄	—	67	2	no	—
439	C₄×D₄	—	67	2	no	—
440	C₄×D₄	—	67	2	no	—
441	C₄×D₄	—	67	2	no	—
442	C₄×D₄	—	67	1	no	—
443	C₄×D₄	—	67	1	no	—
444	C₄×D₄	—	67	2	no	—
445	C₄×D₄	C₂×D₆₇	1	1	yes	characteristic, complemented
446	C₄×D₄	C₂×D₆₇	1	1	yes	characteristic, complemented
447	C₄×D₄	C₂×D₆₇	1	2	yes	complemented
448	#117	—	67	1	no	—
449	#117	—	67	1	no	—
450	#117	—	67	1	no	—
451	#117	—	67	1	no	—
452	#117	—	67	1	no	—
453	#117	—	67	2	no	—
454	#117	—	67	2	no	—
455	#117	—	67	2	no	—
456	#117	—	67	2	no	—
457	#117	—	67	1	no	—
458	#117	C₂×D₆₇	1	1	yes	characteristic, complemented
459	C₂×C₄⋊C₄	—	67	1	no	—
460	C₂×C₄⋊C₄	—	67	1	no	—
461	C₂×C₄⋊C₄	—	67	1	no	—
462	C₂×C₄⋊C₄	—	67	1	no	—
463	C₂×C₄⋊C₄	C₂×D₆₇	1	1	yes	characteristic, complemented
464	C₂×C₂²⋊C₄	—	67	2	no	—
465	C₂×C₂²⋊C₄	—	67	2	no	—
466	C₂×C₂²⋊C₄	—	67	2	no	—
467	C₂×C₂²⋊C₄	—	67	2	no	—
468	C₂×C₄²	—	67	2	no	—
469	C₂⁴	—	67	2	no	—
470	C₂⁴	—	67	1	no	—
471	#41	—	268	4	no	—
472	#41	—	268	4	no	—
473	#41	—	134	4	no	—
474	C₂×Q₈	—	67	2	no	—
475	C₂×Q₈	—	67	2	no	—
476	C₂×Q₈	—	67	1	no	—
477	C₂×D₄	—	268	4	no	—
478	C₂×D₄	—	67	1	no	—
479	C₂×D₄	—	67	2	no	—
480	C₂×D₄	—	67	2	no	—
481	C₂×D₄	—	67	2	no	—
482	C₂×D₄	—	67	1	no	—
483	C₂×D₄	—	67	2	no	—
484	C₂×D₄	—	67	1	no	—
485	C₂×D₄	—	67	1	no	—
486	C₂×D₄	—	67	2	no	—
487	C₂×D₄	—	67	2	no	—
488	C₂×D₄	—	67	1	no	—
489	C₂×D₄	—	67	1	no	—
490	C₂×D₄	—	67	1	no	—
491	C₂×D₄	—	67	2	no	—
492	C₂×D₄	—	134	4	no	—
493	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
494	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
495	C₂×D₄	C₂²×D₆₇	1	2	yes	—
496	C₂×D₄	C₂²×D₆₇	1	2	yes	—
497	C₂²×C₄	—	67	2	no	—
498	C₂²×C₄	—	67	2	no	—
499	C₂²×C₄	—	67	2	no	—
500	C₂²×C₄	—	67	2	no	—
501	C₂²×C₄	—	67	2	no	—
502	C₂²×C₄	—	67	2	no	—
503	C₂²×C₄	—	67	1	no	—
504	C₂²×C₄	—	67	1	no	—
505	C₂²×C₄	—	67	1	no	—
506	C₂²×C₄	—	67	2	no	—
507	C₂²×C₄	—	67	1	no	—
508	C₂²×C₄	—	67	1	no	—
509	C₂²×C₄	—	67	1	no	—
510	C₂²×C₄	—	134	4	no	—
511	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
512	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
513	C₂²×C₄	C₂²×D₆₇	1	2	yes	—
514	C₂²×C₄	C₂²×D₆₇	1	2	yes	—
515	C₄⋊C₄	—	67	1	no	—
516	C₄⋊C₄	—	67	1	no	—
517	C₄⋊C₄	—	67	1	no	—
518	C₄⋊C₄	—	67	2	no	—
519	C₄⋊C₄	—	67	2	no	—
520	C₄⋊C₄	—	67	2	no	—
521	C₄⋊C₄	—	67	2	no	—
522	C₄⋊C₄	—	67	1	no	—
523	C₄⋊C₄	—	67	1	no	—
524	C₄⋊C₄	—	67	1	no	—
525	C₄⋊C₄	—	67	2	no	—
526	C₄⋊C₄	—	67	2	no	—
527	C₄⋊C₄	—	67	2	no	—
528	C₄⋊C₄	—	67	2	no	—
529	C₄⋊C₄	—	67	1	no	—
530	C₄⋊C₄	—	67	1	no	—
531	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
532	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
533	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
534	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
535	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
536	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
537	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
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	1	no	—
544	C₂²⋊C₄	—	67	1	no	—
545	C₂²⋊C₄	—	67	2	no	—
546	C₂²⋊C₄	—	67	1	no	—
547	C₂²⋊C₄	—	67	1	no	—
548	C₂²⋊C₄	—	67	2	no	—
549	C₂²⋊C₄	—	67	2	no	—
550	C₂²⋊C₄	—	67	2	no	—
551	C₂²⋊C₄	—	67	2	no	—
552	C₂²⋊C₄	—	67	2	no	—
553	C₂²⋊C₄	—	67	2	no	—
554	C₂²⋊C₄	—	67	2	no	—
555	C₂²⋊C₄	—	67	1	no	—
556	C₂²⋊C₄	—	67	1	no	—
557	C₂²⋊C₄	—	67	1	no	—
558	C₂²⋊C₄	—	67	2	no	—
559	C₂²⋊C₄	—	67	1	no	—
560	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
561	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
562	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
563	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
564	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
565	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
566	C₄²	—	67	2	no	—
567	C₄²	—	67	2	no	—
568	C₄²	—	67	2	no	—
569	C₄²	—	67	2	no	—
570	C₄²	—	67	2	no	—
571	C₄²	—	67	1	no	—
572	C₄²	C₂²×D₆₇	1	2	yes	—
573	C₄²	C₂²×D₆₇	1	1	yes	characteristic
574	C₂³	—	268	1	no	—
575	C₂³	—	268	2	no	—
576	C₂³	—	268	2	no	—
577	C₂³	—	67	1	no	—
578	C₂³	—	67	1	no	—
579	C₂³	—	67	2	no	—
580	C₂³	—	67	1	no	—
581	C₂³	—	134	2	no	—
582	C₂³	—	134	2	no	—
583	C₂³	—	134	4	no	—
584	C₂³	C₂³×D₆₇	1	1	yes	characteristic
585	C₂³	C₂³×D₆₇	1	2	yes	—
586	C₂³	C₂³×D₆₇	1	1	yes	characteristic
587	Q₈	—	268	2	no	—
588	Q₈	—	268	2	no	—
589	Q₈	—	134	2	no	—
590	D₄	—	2	2	no	—
591	D₄	—	4	2	no	—
592	D₄	—	4	1	no	—
593	D₄	—	4	2	no	—
594	D₄	—	268	2	no	—
595	D₄	—	268	2	no	—
596	D₄	—	268	2	no	—
597	D₄	—	268	2	no	—
598	D₄	—	268	1	no	—
599	D₄	—	134	4	no	—
600	D₄	—	134	2	no	—
601	D₄	—	134	2	no	—
602	D₄	—	134	4	no	—
603	D₄	—	134	2	no	—
604	D₄	—	134	4	no	—
605	D₄	—	134	2	no	—
606	D₄	—	134	2	no	—
607	D₄	—	134	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	4	2	no	—
611	C₂×C₄	—	4	2	no	—
612	C₂×C₄	—	268	2	no	—
613	C₂×C₄	—	268	2	no	—
614	C₂×C₄	—	268	2	no	—
615	C₂×C₄	—	268	2	no	—
616	C₂×C₄	—	268	2	no	—
617	C₂×C₄	—	268	2	no	—
618	C₂×C₄	—	67	1	no	—
619	C₂×C₄	—	67	4	no	—
620	C₂×C₄	—	67	2	no	—
621	C₂×C₄	—	67	1	no	—
622	C₂×C₄	—	67	2	no	—
623	C₂×C₄	—	67	1	no	—
624	C₂×C₄	—	67	1	no	—
625	C₂×C₄	—	67	2	no	—
626	C₂×C₄	—	67	1	no	—
627	C₂×C₄	—	134	2	no	—
628	C₂×C₄	—	134	2	no	—
629	C₂×C₄	—	134	4	no	—
630	C₂×C₄	—	134	2	no	—
631	C₂×C₄	—	134	2	no	—
632	C₂×C₄	—	134	2	no	—
633	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
634	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
635	C₂×C₄	C₂³×D₆₇	1	2	yes	—
636	C₂×C₄	C₂³×D₆₇	1	2	yes	—
637	C₂×C₄	C₂³×D₆₇	1	2	yes	—
638	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
639	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
640	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
641	C₂²	—	2	1	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	1	no	—
645	C₂²	—	2	2	no	—
646	C₂²	—	2	1	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	2	1	no	—
649	C₂²	—	2	1	no	—
650	C₂²	—	268	4	no	—
651	C₂²	—	536	4	no	—
652	C₂²	—	67	2	no	—
653	C₂²	—	67	2	no	—
654	C₂²	—	134	1	no	—
655	C₂²	—	134	2	no	—
656	C₂²	—	134	1	no	—
657	C₂²	—	134	2	no	—
658	C₂²	—	134	2	no	—
659	C₂²	—	134	1	no	—
660	C₂²	—	134	1	no	—
661	C₂²	—	134	1	no	—
662	C₂²	—	134	1	no	—
663	C₂²	—	134	1	no	—
664	C₂²	C₂⁴×D₆₇	1	1	yes	characteristic
665	C₄	—	2	1	no	—
666	C₄	—	2	1	no	—
667	C₄	—	2	2	no	—
668	C₄	—	2	1	no	—
669	C₄	—	2	2	no	—
670	C₄	—	2	1	no	—
671	C₄	—	2	2	no	—
672	C₄	—	67	2	no	—
673	C₄	—	134	1	no	—
674	C₄	—	134	1	no	—
675	C₄	—	134	2	no	—
676	C₄	—	134	1	no	—
677	C₄	—	134	2	no	—
678	C₄	—	134	2	no	—
679	C₄	—	134	1	no	—
680	C₄	#41×D₆₇	1	2	yes	—
681	C₂	—	4	1	no	—
682	C₂	—	4	2	no	—
683	C₂	—	4	1	no	—
684	C₂	—	268	2	no	—
685	C₂	—	268	1	no	—
686	C₂	—	134	2	no	—
687	C₂	—	134	2	no	—
688	C₂	C₂×#41×D₆₇	1	1	yes	characteristic
689	C₂	H(5,𝔽₂)×D₆₇	1	1	yes	characteristic
690	C₂	#16864232	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁵
Fitting	#553×C₆₇	C₂
hypercenter	#553	D₆₇
hypocenter	C₆₇	#3494
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ #553

Complements

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

N	H ≅ G/N	type
1. #16864111	C₂	semidirect
2. #16864110	C₂	semidirect
3. #16864099	C₂	semidirect
4. #16864093	C₂	semidirect
5. #16864090	C₂	semidirect
6. #16864075	C₂	semidirect
7. #16864071	C₂	semidirect
8. #16864051	C₂	semidirect
9. #16864047	C₂	semidirect
10. #16864043	C₂	semidirect
11. #16864038	C₂	semidirect
12. #16864026	C₂	semidirect
13. #16864014	C₂	semidirect
14. #16863996	C₂	semidirect
15. #16863962	C₂	semidirect
16. #16863943	C₂	semidirect
17. #16863929	C₂	semidirect
18. #16863905	C₂	semidirect
19. #121×D₆₇	C₂	semidirect
20. #16863877	C₂	semidirect
21. #16863868	C₂	semidirect
22. #117×D₆₇	C₂	semidirect
23. #553×C₆₇	C₂	semidirect
25. C₂×#11761628	C₂²	semidirect
26. C₂×#11761628	C₂²	semidirect
30. #14524043	C₂²	semidirect
31. #14524042	C₂²	semidirect
32. #14524042	C₂²	semidirect
33. #14524039	C₂²	semidirect
34. #14524038	C₂²	semidirect
35. #14524037	C₂²	semidirect
36. #14524036	C₂²	semidirect
37. #14524034	C₂²	semidirect
38. #14524033	C₂²	semidirect
39. #14524030	C₂²	semidirect
40. #14524029	C₂²	semidirect
41. #14524029	C₂²	semidirect
42. #14524029	C₂²	semidirect
43. #14524029	C₂²	semidirect
45. #14524028	C₂²	semidirect
46. #14524028	C₂²	semidirect
47. #14524026	C₂²	semidirect
49. #14524025	C₂²	semidirect
50. #14524025	C₂²	semidirect
51. #14524025	C₂²	semidirect
52. #14524024	C₂²	semidirect
54. #14524022	C₂²	semidirect
56. #14524021	C₂²	semidirect
57. #14524021	C₂²	semidirect
58. #14524020	C₂²	semidirect
60. #14524018	C₂²	semidirect
61. #14524018	C₂²	semidirect
63. #14524017	C₂²	semidirect
65. #14524016	C₂²	semidirect
66. #14524016	C₂²	semidirect
68. #14524015	C₂²	semidirect
69. #14524015	C₂²	semidirect
71. #14524014	C₂²	semidirect
72. #14524014	C₂²	semidirect
73. #14524014	C₂²	semidirect
78. #14524008	C₂²	semidirect
79. C₄×D₂₆₈	C₂²	semidirect
80. C₄×D₂₆₈	C₂²	semidirect
81. C₄×D₂₆₈	C₂²	semidirect
82. D₄×Dic₆₇	C₂²	semidirect
84. #14524005	C₂²	semidirect
85. #14524005	C₂²	semidirect
87. C₄×C₂²⋊D₆₇	C₂²	semidirect
88. C₄×C₂²⋊D₆₇	C₂²	semidirect
89. C₄×C₂²⋊D₆₇	C₂²	semidirect
90. C₄×C₂²⋊D₆₇	C₂²	semidirect
91. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
92. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
93. #14524002	C₂²	semidirect
94. #14524002	C₂²	semidirect
97. #14524001	C₂²	semidirect
98. #14524001	C₂²	semidirect
101. #14523999	C₂²	semidirect
102. #14523999	C₂²	semidirect
104. C₄⋊C₄×D₆₇	C₂²	semidirect
105. C₄⋊C₄×D₆₇	C₂²	semidirect
106. C₄⋊C₄×D₆₇	C₂²	semidirect
111. C₄²×D₆₇	C₂²	semidirect
112. #126×C₆₇	C₂²	semidirect
113. #125×C₆₇	C₂²	semidirect
114. #123×C₆₇	C₂²	semidirect
116. #121×C₆₇	C₂²	semidirect
117. #121×C₆₇	C₂²	semidirect
118. C₄×D₄×C₆₇	C₂²	semidirect
119. C₄×D₄×C₆₇	C₂²	semidirect
120. C₄×D₄×C₆₇	C₂²	semidirect
121. #117×C₆₇	C₂²	semidirect
122. C₂×C₄⋊C₄×C₆₇	C₂²	semidirect
291. C₄×D₆₇	#41	semidirect
346. C₆₇	#3494	semidirect
352. #553	D₆₇	semidirect
383. #126	C₂×D₆₇	semidirect
386. #125	C₂×D₆₇	semidirect
401. #123	C₂×D₆₇	semidirect
424. #121	C₂×D₆₇	semidirect
425. #121	C₂×D₆₇	semidirect
445. C₄×D₄	C₂×D₆₇	semidirect
446. C₄×D₄	C₂×D₆₇	semidirect
447. C₄×D₄	C₂×D₆₇	semidirect
458. #117	C₂×D₆₇	semidirect
463. C₂×C₄⋊C₄	C₂×D₆₇	semidirect