Subgroups — #22574008

Order 8576.

1100 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16864106	C₂	1	1	yes	maximal, characteristic, complemented
2	#16864105	C₂	1	1	yes	maximal, characteristic, complemented
3	#16864105	C₂	1	1	yes	maximal, characteristic, complemented
4	#16864102	C₂	1	1	yes	maximal, characteristic, complemented
5	#16864102	C₂	1	1	yes	maximal, characteristic, complemented
6	#16864101	C₂	1	2	yes	maximal, complemented
7	#16864100	C₂	1	2	yes	maximal, complemented
8	#16864100	C₂	1	2	yes	maximal, complemented
9	D₄×Dic₁₃₄	C₂	1	1	yes	maximal, characteristic, complemented
10	#16864061	C₂	1	1	yes	maximal, characteristic, complemented
11	#16864059	C₂	1	2	yes	maximal, complemented
12	#16864026	C₂	1	1	yes	maximal, characteristic, complemented
13	#16864023	C₂	1	1	yes	maximal, characteristic, complemented
14	#16864021	C₂	1	2	yes	maximal, complemented
15	#16864021	C₂	1	2	yes	maximal, complemented
16	#16863952	C₂	1	1	yes	maximal, characteristic, complemented
17	#16863950	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#14524021	C₂	1	2	yes	maximal, complemented
19	C₂²⋊Q₈×D₆₇	C₂	1	2	yes	maximal, complemented
20	#16863868	C₂	1	1	yes	maximal, characteristic
21	#16863868	C₂	1	1	yes	maximal, characteristic
22	C₄×D₄×D₆₇	C₂	1	1	yes	maximal, characteristic
23	#554×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×Dic₁₃₄	C₂²	1	2	yes	complemented
25	C₂×Q₈×D₆₇	C₂²	1	2	yes	complemented
26	C₂×D₄×D₆₇	C₂²	1	1	yes	characteristic
27	C₂²×C₄×D₆₇	C₂²	1	2	yes	—
28	#14524043	C₂²	1	1	yes	characteristic, complemented
29	#14524042	C₂²	1	1	yes	characteristic, complemented
30	#14524042	C₂²	1	2	yes	complemented
31	#14524042	C₂²	1	1	yes	characteristic, complemented
32	#14524042	C₂²	1	1	yes	characteristic, complemented
33	#14524042	C₂²	1	1	yes	characteristic, complemented
34	#14524042	C₂²	1	1	yes	characteristic, complemented
35	#14524041	C₂²	1	2	yes	complemented
36	#14524041	C₂²	1	1	yes	characteristic, complemented
37	#14524035	C₂²	1	1	yes	characteristic, complemented
38	#14524035	C₂²	1	1	yes	characteristic, complemented
39	#14524034	C₂²	1	1	yes	characteristic, complemented
40	#14524034	C₂²	1	1	yes	characteristic, complemented
41	#14524033	C₂²	1	2	yes	complemented
42	#14524033	C₂²	1	2	yes	complemented
43	#14524033	C₂²	1	1	yes	characteristic, complemented
44	#14524033	C₂²	1	1	yes	characteristic, complemented
45	#14524023	C₂²	1	1	yes	characteristic
46	#14524023	C₂²	1	2	yes	—
47	#14524023	C₂²	1	2	yes	complemented
48	#14524023	C₂²	1	2	yes	complemented
49	#14524022	C₂²	1	2	yes	complemented
50	#14524022	C₂²	1	2	yes	complemented
51	#14524022	C₂²	1	2	yes	complemented
52	#14524021	C₂²	1	2	yes	—
53	#14524021	C₂²	1	2	yes	—
54	#14524021	C₂²	1	2	yes	—
55	#14524021	C₂²	1	1	yes	characteristic
56	#14524021	C₂²	1	2	yes	—
57	#14524021	C₂²	1	1	yes	characteristic
58	#14524021	C₂²	1	2	yes	complemented
59	#14524021	C₂²	1	2	yes	complemented
60	#14524021	C₂²	1	2	yes	complemented
61	#14524021	C₂²	1	2	yes	complemented
62	#14524021	C₂²	1	2	yes	complemented
63	#14524021	C₂²	1	2	yes	complemented
64	#14524021	C₂²	1	2	yes	complemented
65	#14524021	C₂²	1	2	yes	complemented
66	#14524020	C₂²	1	2	yes	complemented
67	#14524020	C₂²	1	2	yes	complemented
68	#14524020	C₂²	1	2	yes	complemented
69	#14524020	C₂²	1	2	yes	complemented
70	#14524020	C₂²	1	2	yes	complemented
71	#14524020	C₂²	1	2	yes	complemented
72	#14524019	C₂²	1	1	yes	characteristic
73	#14524019	C₂²	1	2	yes	—
74	#14524019	C₂²	1	2	yes	complemented
75	#14524019	C₂²	1	2	yes	complemented
76	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
77	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
78	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
79	#14524008	C₂²	1	2	yes	complemented
80	#14524008	C₂²	1	2	yes	complemented
81	C₄×D₂₆₈	C₂²	1	1	yes	characteristic
82	C₄×D₂₆₈	C₂²	1	1	yes	characteristic
83	C₄×D₂₆₈	C₂²	1	1	yes	characteristic
84	D₄×Dic₆₇	C₂²	1	1	yes	characteristic
85	D₄×Dic₆₇	C₂²	1	1	yes	characteristic
86	D₄×Dic₆₇	C₂²	1	1	yes	characteristic
87	#14524005	C₂²	1	1	yes	characteristic
88	#14524005	C₂²	1	1	yes	characteristic
89	#14524005	C₂²	1	1	yes	characteristic
90	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	—
91	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	—
92	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	—
93	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	—
94	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	—
95	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	—
96	#14524001	C₂²	1	1	yes	characteristic
97	#14524001	C₂²	1	1	yes	characteristic
98	#14524000	C₂²	1	1	yes	characteristic
99	#14524000	C₂²	1	1	yes	characteristic
100	C₂×Dic₆₇⋊C₄	C₂²	1	2	yes	complemented
101	C₂×Dic₆₇⋊C₄	C₂²	1	2	yes	complemented
102	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
103	C₄⋊C₄×D₆₇	C₂²	1	2	yes	complemented
104	C₄⋊C₄×D₆₇	C₂²	1	2	yes	complemented
105	C₄⋊C₄×D₆₇	C₂²	1	2	yes	complemented
106	C₂×(C₂×D₆₇)⋊C₄	C₂²	1	2	yes	—
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	1	yes	characteristic
112	C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
113	#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
114	#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
115	C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
116	C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
117	C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
118	C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
120	C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
121	C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
123	C₂³×D₆₇	C₂³	1	2	yes	—
124	C₂×Dic₁₃₄	—	4	4	no	—
125	C₂×Dic₁₃₄	C₂³	1	2	yes	—
126	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
127	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
128	C₂×Dic₁₃₄	C₂³	1	2	yes	—
129	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
130	C₂×Dic₁₃₄	C₂³	1	2	yes	—
131	C₂×Dic₁₃₄	C₂³	1	2	yes	—
132	C₂×Dic₁₃₄	C₂³	1	2	yes	—
133	Q₈×D₆₇	—	4	4	no	—
134	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
136	D₄×D₆₇	Q₈	1	8	yes	complemented
137	C₂²×Dic₆₇	C₂³	1	2	yes	—
138	C₂²×Dic₆₇	C₂³	1	2	yes	—
139	C₂²×Dic₆₇	C₂³	1	2	yes	—
140	C₂×C₄×D₆₇	—	4	4	no	—
141	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
142	C₂×C₄×D₆₇	C₂³	1	2	yes	—
143	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₆₇	C₂³	1	2	yes	—
145	C₂×C₄×D₆₇	C₂³	1	2	yes	—
146	C₂×C₄×D₆₇	C₂³	1	2	yes	—
147	C₂×C₄×D₆₇	C₂³	1	2	yes	—
148	C₂×C₄×D₆₇	C₂³	1	2	yes	—
149	C₂×C₄×D₆₇	C₂³	1	2	yes	—
150	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
151	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
152	C₄⋊Dic₆₇	C₂³	1	2	yes	—
153	C₄⋊Dic₆₇	C₂³	1	2	yes	—
154	C₄⋊Dic₆₇	C₂³	1	2	yes	—
155	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
156	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
157	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
158	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
159	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
160	Dic₆₇⋊C₄	C₂³	1	2	yes	—
161	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
162	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
168	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
169	Dic₆₇⋊C₄	C₂³	1	2	yes	—
170	Dic₆₇⋊C₄	C₂³	1	2	yes	—
171	Dic₆₇⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
176	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
177	Dic₆₇⋊C₄	C₂³	1	2	yes	—
178	Dic₆₇⋊C₄	C₂³	1	2	yes	—
179	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
180	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
181	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
182	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
183	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
184	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
190	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
191	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
192	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
193	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
194	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
195	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
196	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
197	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
198	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
199	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
200	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
201	C₄×Dic₆₇	C₂³	1	2	yes	—
202	C₄×Dic₆₇	C₂³	1	2	yes	—
203	C₂×Q₈×C₆₇	C₂³	1	1	yes	characteristic
204	C₂×Q₈×C₆₇	C₂³	1	2	yes	—
205	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
206	C₂²×C₄×C₆₇	C₂³	1	2	yes	—
207	C₂²×C₄×C₆₇	C₂³	1	2	yes	—
208	C₂²×C₄×C₆₇	C₂³	1	2	yes	—
209	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
210	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
211	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
212	C₄⋊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	1	yes	characteristic
216	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
217	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
218	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
219	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
220	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
221	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
222	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
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	C₂³×C₆₇	C₂⁴	1	2	yes	—
227	C₂²×D₆₇	—	4	2	no	—
228	C₂²×D₆₇	—	4	2	no	—
229	C₂²×D₆₇	C₂×Q₈	1	8	yes	complemented
230	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
231	C₂²×D₆₇	C₂⁴	1	2	yes	—
232	Q₈×C₆₇	—	4	1	no	—
233	Q₈×C₆₇	—	4	2	no	—
234	D₄×C₆₇	C₂×Q₈	1	4	yes	complemented
235	C₂×C₄×C₆₇	—	4	2	no	—
236	C₂×C₄×C₆₇	—	4	2	no	—
237	C₂×C₄×C₆₇	—	4	2	no	—
238	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
239	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
240	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
241	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
242	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
243	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
245	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
246	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
247	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
248	C₂²⋊D₆₇	C₂×Q₈	1	8	yes	complemented
249	C₂×Dic₆₇	—	2	4	no	—
250	C₂×Dic₆₇	—	4	2	no	—
251	C₂×Dic₆₇	—	4	2	no	—
252	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
253	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
254	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
255	C₂×Dic₆₇	C₂⁴	1	2	yes	—
256	C₂×Dic₆₇	C₂⁴	1	2	yes	—
257	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
258	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₆₇	C₂⁴	1	2	yes	—
260	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
261	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
262	D₂₆₈	C₂×Q₈	1	4	yes	complemented
263	C₄×D₆₇	—	2	2	no	—
264	C₄×D₆₇	—	2	4	no	—
265	C₄×D₆₇	—	4	2	no	—
266	C₄×D₆₇	—	4	2	no	—
267	C₄×D₆₇	—	4	1	no	—
268	C₄×D₆₇	—	4	2	no	—
269	C₄×D₆₇	—	4	2	no	—
270	C₄×D₆₇	—	4	2	no	—
271	C₄×D₆₇	—	4	2	no	—
272	C₄×D₆₇	C₂×Q₈	1	4	yes	complemented
273	Dic₁₃₄	—	2	2	no	—
274	Dic₁₃₄	—	2	4	no	—
275	Dic₁₃₄	—	2	2	no	—
276	Dic₁₃₄	—	4	2	no	—
277	Dic₁₃₄	—	4	2	no	—
278	Dic₁₃₄	—	4	2	no	—
279	Dic₁₃₄	—	4	2	no	—
280	Dic₁₃₄	—	4	1	no	—
281	C₂²×C₆₇	—	2	2	no	—
282	C₂²×C₆₇	—	2	2	no	—
283	C₂²×C₆₇	C₂²×Q₈	1	4	yes	—
284	C₂²×C₆₇	C₂⁵	1	1	yes	characteristic
285	C₂×D₆₇	—	2	2	no	—
286	C₂×D₆₇	—	2	1	no	—
287	C₂×D₆₇	—	2	2	no	—
288	C₂×D₆₇	—	2	1	no	—
289	C₂×D₆₇	—	4	8	no	—
290	C₂×D₆₇	C₂²×Q₈	1	2	yes	—
291	C₂×D₆₇	C₂²×Q₈	1	4	yes	—
292	C₄×C₆₇	—	2	1	no	—
293	C₄×C₆₇	—	2	2	no	—
294	C₄×C₆₇	—	2	1	no	—
295	C₄×C₆₇	—	2	2	no	—
296	C₄×C₆₇	—	2	1	no	—
297	C₄×C₆₇	—	2	2	no	—
298	C₄×C₆₇	—	2	1	no	—
299	C₄×C₆₇	—	2	1	no	—
300	C₄×C₆₇	—	2	1	no	—
301	C₄×C₆₇	C₂²×Q₈	1	2	yes	—
302	Dic₆₇	—	2	1	no	—
303	Dic₆₇	—	2	2	no	—
304	Dic₆₇	—	2	1	no	—
305	Dic₆₇	—	2	2	no	—
306	Dic₆₇	—	2	1	no	—
307	Dic₆₇	—	2	1	no	—
308	Dic₆₇	—	2	2	no	—
309	Dic₆₇	—	2	1	no	—
310	Dic₆₇	C₂²×Q₈	1	2	yes	—
311	Dic₆₇	H(5,𝔽₂)	1	2	yes	—
312	C₂×C₆₇	—	2	4	no	—
313	C₂×C₆₇	C₂³×Q₈	1	1	yes	characteristic
314	C₂×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
315	C₂×C₆₇	#585	1	1	yes	characteristic
316	D₆₇	—	2	2	no	—
317	D₆₇	—	2	4	no	—
318	#3501	—	67	1	no	maximal, Sylow
319	C₆₇	#3501	1	1	yes	characteristic, complemented, Sylow
320	#554	—	67	1	no	—
321	#554	—	67	1	no	—
322	#554	—	67	2	no	—
323	#554	—	67	2	no	—
324	#554	—	67	1	no	—
325	#554	—	67	1	no	—
326	#554	—	67	1	no	—
327	#554	—	67	2	no	—
328	#554	D₆₇	1	1	yes	characteristic, complemented
329	D₄×Q₈	—	67	1	no	—
330	D₄×Q₈	—	67	2	no	—
331	D₄×Q₈	—	67	1	no	—
332	#544	—	67	1	no	—
333	#544	—	67	1	no	—
334	#543	—	67	2	no	—
335	#543	—	67	2	no	—
336	#533	—	67	1	no	—
337	#533	—	67	1	no	—
338	C₂×C₂²⋊Q₈	—	67	2	no	—
339	C₂×C₂²⋊Q₈	—	67	2	no	—
340	#518	—	67	1	no	—
341	#518	—	67	1	no	—
342	C₂×C₄×D₄	—	67	1	no	—
343	C₂²×Q₈	—	67	2	no	—
344	C₂²×Q₈	—	67	2	no	—
345	C₂²×D₄	—	67	1	no	—
346	C₂³×C₄	—	67	2	no	—
347	C₄⋊Q₈	—	67	1	no	—
348	C₄⋊Q₈	—	67	2	no	—
349	C₄⋊Q₈	—	67	1	no	—
350	C₄⋊Q₈	—	67	1	no	—
351	C₄⋊Q₈	—	67	1	no	—
352	C₄⋊Q₈	—	67	2	no	—
353	C₄⋊Q₈	—	67	1	no	—
354	C₄⋊Q₈	—	67	1	no	—
355	C₄⋊Q₈	—	67	1	no	—
356	C₄⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
357	#125	—	67	1	no	—
358	#125	—	67	1	no	—
359	#125	—	67	2	no	—
360	#125	—	67	2	no	—
361	#125	—	67	1	no	—
362	#125	—	67	1	no	—
363	#125	—	67	1	no	—
364	#125	—	67	1	no	—
365	#125	C₂×D₆₇	1	1	yes	characteristic, complemented
366	#125	C₂×D₆₇	1	1	yes	characteristic, complemented
367	C₂²⋊Q₈	—	67	2	no	—
368	C₂²⋊Q₈	—	67	1	no	—
369	C₂²⋊Q₈	—	67	2	no	—
370	C₂²⋊Q₈	—	67	2	no	—
371	C₂²⋊Q₈	—	67	2	no	—
372	C₂²⋊Q₈	—	67	2	no	—
373	C₂²⋊Q₈	—	67	2	no	—
374	C₂²⋊Q₈	—	67	1	no	—
375	C₂²⋊Q₈	—	67	2	no	—
376	C₂²⋊Q₈	—	67	1	no	—
377	C₂²⋊Q₈	—	67	2	no	—
378	C₂²⋊Q₈	—	67	2	no	—
379	C₂²⋊Q₈	—	67	2	no	—
380	C₂²⋊Q₈	—	67	2	no	—
381	C₂²⋊Q₈	—	67	2	no	—
382	C₂²⋊Q₈	—	67	2	no	—
383	C₂²⋊Q₈	—	67	2	no	—
384	C₂²⋊Q₈	—	67	2	no	—
385	C₂²⋊Q₈	—	67	1	no	—
386	C₂²⋊Q₈	—	67	2	no	—
387	C₂²⋊Q₈	—	67	2	no	—
388	C₂²⋊Q₈	—	67	2	no	—
389	C₂²⋊Q₈	—	67	2	no	—
390	C₂²⋊Q₈	—	67	2	no	—
391	C₂²⋊Q₈	—	67	2	no	—
392	C₂²⋊Q₈	—	67	2	no	—
393	C₂²⋊Q₈	—	67	2	no	—
394	C₂²⋊Q₈	—	67	2	no	—
395	C₂²⋊Q₈	—	67	2	no	—
396	C₂²⋊Q₈	—	67	2	no	—
397	C₂²⋊Q₈	—	67	2	no	—
398	C₂²⋊Q₈	C₂×D₆₇	1	2	yes	complemented
399	C₂²⋊Q₈	C₂×D₆₇	1	2	yes	complemented
400	C₂²⋊Q₈	C₂×D₆₇	1	2	yes	complemented
401	C₄×Q₈	—	67	2	no	—
402	C₄×Q₈	—	67	2	no	—
403	C₄×Q₈	—	67	1	no	—
404	C₄×Q₈	—	67	1	no	—
405	C₄×Q₈	—	67	1	no	—
406	C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
407	C₄×D₄	—	67	1	no	—
408	C₄×D₄	—	67	1	no	—
409	C₄×D₄	—	67	1	no	—
410	C₄×D₄	—	67	2	no	—
411	C₄×D₄	—	67	2	no	—
412	C₄×D₄	—	67	2	no	—
413	C₄×D₄	—	67	1	no	—
414	C₄×D₄	—	67	1	no	—
415	C₄×D₄	—	67	1	no	—
416	C₄×D₄	—	67	2	no	—
417	C₄×D₄	—	67	2	no	—
418	C₄×D₄	—	67	2	no	—
419	C₄×D₄	—	67	1	no	—
420	C₄×D₄	—	67	1	no	—
421	C₄×D₄	—	67	1	no	—
422	C₄×D₄	C₂×D₆₇	1	1	yes	characteristic
423	C₄×D₄	C₂×D₆₇	1	1	yes	characteristic
424	C₄×D₄	C₂×D₆₇	1	1	yes	characteristic
425	#117	—	67	1	no	—
426	#117	—	67	1	no	—
427	#117	—	67	1	no	—
428	#117	—	67	1	no	—
429	C₂×C₄⋊C₄	—	67	2	no	—
430	C₂×C₄⋊C₄	—	67	2	no	—
431	C₂×C₄⋊C₄	—	67	1	no	—
432	C₂×C₄⋊C₄	—	67	2	no	—
433	C₂×C₄⋊C₄	—	67	2	no	—
434	C₂×C₄⋊C₄	—	67	2	no	—
435	C₂×C₄⋊C₄	C₂×D₆₇	1	2	yes	complemented
436	C₂×C₂²⋊C₄	—	67	2	no	—
437	C₂×C₂²⋊C₄	—	67	2	no	—
438	C₂×C₂²⋊C₄	—	67	2	no	—
439	C₂×C₂²⋊C₄	—	67	2	no	—
440	C₂×C₂²⋊C₄	—	67	2	no	—
441	C₂×C₄²	—	67	1	no	—
442	C₂⁴	—	67	2	no	—
443	C₂×Q₈	—	268	4	no	—
444	C₂×Q₈	—	268	4	no	—
445	C₂×Q₈	—	67	2	no	—
446	C₂×Q₈	—	67	1	no	—
447	C₂×Q₈	—	67	2	no	—
448	C₂×Q₈	—	67	2	no	—
449	C₂×Q₈	—	67	2	no	—
450	C₂×Q₈	—	67	2	no	—
451	C₂×Q₈	—	67	1	no	—
452	C₂×Q₈	—	67	1	no	—
453	C₂×Q₈	C₂²×D₆₇	1	1	yes	characteristic
454	C₂×Q₈	C₂²×D₆₇	1	2	yes	—
455	C₂×D₄	—	67	2	no	—
456	C₂×D₄	—	67	8	no	—
457	C₂×D₄	—	67	1	no	—
458	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
459	C₂²×C₄	—	268	4	no	—
460	C₂²×C₄	—	67	2	no	—
461	C₂²×C₄	—	67	2	no	—
462	C₂²×C₄	—	67	1	no	—
463	C₂²×C₄	—	67	2	no	—
464	C₂²×C₄	—	67	2	no	—
465	C₂²×C₄	—	67	2	no	—
466	C₂²×C₄	—	67	2	no	—
467	C₂²×C₄	—	67	2	no	—
468	C₂²×C₄	—	67	2	no	—
469	C₂²×C₄	—	67	1	no	—
470	C₂²×C₄	—	67	2	no	—
471	C₂²×C₄	—	67	1	no	—
472	C₂²×C₄	—	67	2	no	—
473	C₂²×C₄	C₂²×D₆₇	1	2	yes	—
474	C₂²×C₄	C₂²×D₆₇	1	2	yes	—
475	C₂²×C₄	C₂²×D₆₇	1	2	yes	—
476	C₄⋊C₄	—	67	1	no	—
477	C₄⋊C₄	—	67	2	no	—
478	C₄⋊C₄	—	67	1	no	—
479	C₄⋊C₄	—	67	2	no	—
480	C₄⋊C₄	—	67	1	no	—
481	C₄⋊C₄	—	67	1	no	—
482	C₄⋊C₄	—	67	2	no	—
483	C₄⋊C₄	—	67	1	no	—
484	C₄⋊C₄	—	67	2	no	—
485	C₄⋊C₄	—	67	2	no	—
486	C₄⋊C₄	—	67	2	no	—
487	C₄⋊C₄	—	67	2	no	—
488	C₄⋊C₄	—	67	2	no	—
489	C₄⋊C₄	—	67	2	no	—
490	C₄⋊C₄	—	67	2	no	—
491	C₄⋊C₄	—	67	2	no	—
492	C₄⋊C₄	—	67	2	no	—
493	C₄⋊C₄	—	67	1	no	—
494	C₄⋊C₄	—	67	1	no	—
495	C₄⋊C₄	—	67	1	no	—
496	C₄⋊C₄	—	67	1	no	—
497	C₄⋊C₄	—	67	1	no	—
498	C₄⋊C₄	—	67	1	no	—
499	C₄⋊C₄	—	67	1	no	—
500	C₄⋊C₄	—	67	1	no	—
501	C₄⋊C₄	—	67	2	no	—
502	C₄⋊C₄	—	67	1	no	—
503	C₄⋊C₄	—	67	1	no	—
504	C₄⋊C₄	—	67	2	no	—
505	C₄⋊C₄	—	67	1	no	—
506	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
507	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
508	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
509	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
510	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
511	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
512	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
513	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
514	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
515	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
516	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
517	C₂²⋊C₄	—	67	2	no	—
518	C₂²⋊C₄	—	67	2	no	—
519	C₂²⋊C₄	—	67	2	no	—
520	C₂²⋊C₄	—	67	2	no	—
521	C₂²⋊C₄	—	67	1	no	—
522	C₂²⋊C₄	—	67	1	no	—
523	C₂²⋊C₄	—	67	2	no	—
524	C₂²⋊C₄	—	67	1	no	—
525	C₂²⋊C₄	—	67	1	no	—
526	C₂²⋊C₄	—	67	2	no	—
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	C₂²×D₆₇	1	2	yes	—
533	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
534	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
535	C₄²	—	67	1	no	—
536	C₄²	—	67	1	no	—
537	C₄²	—	67	1	no	—
538	C₄²	—	67	2	no	—
539	C₄²	—	67	2	no	—
540	C₄²	—	67	1	no	—
541	C₄²	—	67	1	no	—
542	C₄²	C₂²×D₆₇	1	1	yes	characteristic
543	C₄²	C₂²×D₆₇	1	1	yes	characteristic
544	C₄²	C₂²×D₆₇	1	1	yes	characteristic
545	C₂³	—	268	2	no	—
546	C₂³	—	268	2	no	—
547	C₂³	—	67	8	no	—
548	C₂³	—	67	1	no	—
549	C₂³	—	67	2	no	—
550	C₂³	C₂³×D₆₇	1	2	yes	—
551	Q₈	—	4	2	no	—
552	Q₈	—	4	1	no	—
553	Q₈	—	268	2	no	—
554	Q₈	—	268	2	no	—
555	Q₈	—	268	2	no	—
556	Q₈	—	268	2	no	—
557	Q₈	—	268	1	no	—
558	Q₈	—	134	2	no	—
559	Q₈	—	134	4	no	—
560	Q₈	—	134	2	no	—
561	D₄	—	67	8	no	—
562	D₄	—	67	4	no	—
563	D₄	Q₈×D₆₇	1	4	yes	complemented
564	C₂×C₄	—	4	2	no	—
565	C₂×C₄	—	4	2	no	—
566	C₂×C₄	—	4	2	no	—
567	C₂×C₄	—	268	2	no	—
568	C₂×C₄	—	268	2	no	—
569	C₂×C₄	—	268	2	no	—
570	C₂×C₄	—	268	2	no	—
571	C₂×C₄	—	268	2	no	—
572	C₂×C₄	—	268	2	no	—
573	C₂×C₄	—	268	1	no	—
574	C₂×C₄	—	268	2	no	—
575	C₂×C₄	—	268	2	no	—
576	C₂×C₄	—	67	1	no	—
577	C₂×C₄	—	67	1	no	—
578	C₂×C₄	—	67	4	no	—
579	C₂×C₄	—	67	1	no	—
580	C₂×C₄	—	67	1	no	—
581	C₂×C₄	—	67	2	no	—
582	C₂×C₄	—	67	1	no	—
583	C₂×C₄	—	67	1	no	—
584	C₂×C₄	—	67	2	no	—
585	C₂×C₄	—	67	1	no	—
586	C₂×C₄	—	67	2	no	—
587	C₂×C₄	—	134	2	no	—
588	C₂×C₄	—	134	4	no	—
589	C₂×C₄	—	134	4	no	—
590	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
591	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
592	C₂×C₄	C₂³×D₆₇	1	2	yes	—
593	C₂×C₄	C₂³×D₆₇	1	2	yes	—
594	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
595	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
596	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
597	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
598	C₂×C₄	C₂³×D₆₇	1	2	yes	—
599	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
600	C₂²	—	2	2	no	—
601	C₂²	—	2	2	no	—
602	C₂²	—	268	8	no	—
603	C₂²	—	67	2	no	—
604	C₂²	—	67	4	no	—
605	C₂²	—	134	2	no	—
606	C₂²	—	134	1	no	—
607	C₂²	—	134	2	no	—
608	C₂²	—	134	1	no	—
609	C₂²	C₂×Q₈×D₆₇	1	4	yes	—
610	C₂²	C₂⁴×D₆₇	1	1	yes	characteristic
611	C₄	—	2	1	no	—
612	C₄	—	2	1	no	—
613	C₄	—	2	2	no	—
614	C₄	—	2	2	no	—
615	C₄	—	2	1	no	—
616	C₄	—	2	1	no	—
617	C₄	—	2	2	no	—
618	C₄	—	2	1	no	—
619	C₄	—	2	1	no	—
620	C₄	—	67	2	no	—
621	C₄	—	67	2	no	—
622	C₄	—	134	2	no	—
623	C₄	—	134	1	no	—
624	C₄	—	134	2	no	—
625	C₄	—	134	1	no	—
626	C₄	—	134	1	no	—
627	C₄	—	134	2	no	—
628	C₄	—	134	1	no	—
629	C₄	—	134	1	no	—
630	C₄	C₂×Q₈×D₆₇	1	2	yes	—
631	C₂	—	2	4	no	—
632	C₂	—	134	2	no	—
633	C₂	—	134	4	no	—
634	C₂	C₂²×Q₈×D₆₇	1	1	yes	characteristic
635	C₂	H(5,𝔽₂)×D₆₇	1	1	yes	characteristic
636	C₂	#16864232	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁵
Fitting	#554×C₆₇	C₂
hypercenter	#554	D₆₇
hypocenter	C₆₇	#3501
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ #554

Complements

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

N	H ≅ G/N	type
1. #16864106	C₂	semidirect
2. #16864105	C₂	semidirect
3. #16864105	C₂	semidirect
4. #16864102	C₂	semidirect
5. #16864102	C₂	semidirect
6. #16864101	C₂	semidirect
7. #16864100	C₂	semidirect
8. #16864100	C₂	semidirect
9. D₄×Dic₁₃₄	C₂	semidirect
10. #16864061	C₂	semidirect
11. #16864059	C₂	semidirect
12. #16864026	C₂	semidirect
13. #16864023	C₂	semidirect
14. #16864021	C₂	semidirect
15. #16864021	C₂	semidirect
16. #16863952	C₂	semidirect
17. #16863950	C₂	semidirect
18. C₂×#14524021	C₂	semidirect
19. C₂²⋊Q₈×D₆₇	C₂	semidirect
23. #554×C₆₇	C₂	semidirect
24. C₂²×Dic₁₃₄	C₂²	semidirect
25. C₂×Q₈×D₆₇	C₂²	semidirect
28. #14524043	C₂²	semidirect
29. #14524042	C₂²	semidirect
30. #14524042	C₂²	semidirect
31. #14524042	C₂²	semidirect
32. #14524042	C₂²	semidirect
33. #14524042	C₂²	semidirect
34. #14524042	C₂²	semidirect
35. #14524041	C₂²	semidirect
36. #14524041	C₂²	semidirect
37. #14524035	C₂²	semidirect
38. #14524035	C₂²	semidirect
39. #14524034	C₂²	semidirect
40. #14524034	C₂²	semidirect
41. #14524033	C₂²	semidirect
42. #14524033	C₂²	semidirect
43. #14524033	C₂²	semidirect
44. #14524033	C₂²	semidirect
47. #14524023	C₂²	semidirect
48. #14524023	C₂²	semidirect
49. #14524022	C₂²	semidirect
50. #14524022	C₂²	semidirect
51. #14524022	C₂²	semidirect
58. #14524021	C₂²	semidirect
59. #14524021	C₂²	semidirect
60. #14524021	C₂²	semidirect
61. #14524021	C₂²	semidirect
62. #14524021	C₂²	semidirect
63. #14524021	C₂²	semidirect
64. #14524021	C₂²	semidirect
65. #14524021	C₂²	semidirect
66. #14524020	C₂²	semidirect
67. #14524020	C₂²	semidirect
68. #14524020	C₂²	semidirect
69. #14524020	C₂²	semidirect
70. #14524020	C₂²	semidirect
71. #14524020	C₂²	semidirect
74. #14524019	C₂²	semidirect
75. #14524019	C₂²	semidirect
76. C₄×Dic₁₃₄	C₂²	semidirect
77. C₄×Dic₁₃₄	C₂²	semidirect
78. C₄×Dic₁₃₄	C₂²	semidirect
79. #14524008	C₂²	semidirect
80. #14524008	C₂²	semidirect
100. C₂×Dic₆₇⋊C₄	C₂²	semidirect
101. C₂×Dic₆₇⋊C₄	C₂²	semidirect
103. C₄⋊C₄×D₆₇	C₂²	semidirect
104. C₄⋊C₄×D₆₇	C₂²	semidirect
105. C₄⋊C₄×D₆₇	C₂²	semidirect
112. C₄⋊Q₈×C₆₇	C₂²	semidirect
113. #125×C₆₇	C₂²	semidirect
114. #125×C₆₇	C₂²	semidirect
115. C₂²⋊Q₈×C₆₇	C₂²	semidirect
116. C₂²⋊Q₈×C₆₇	C₂²	semidirect
117. C₂²⋊Q₈×C₆₇	C₂²	semidirect
118. C₄×Q₈×C₆₇	C₂²	semidirect
122. C₂×C₄⋊C₄×C₆₇	C₂²	semidirect
136. D₄×D₆₇	Q₈	semidirect
229. C₂²×D₆₇	C₂×Q₈	semidirect
234. D₄×C₆₇	C₂×Q₈	semidirect
248. C₂²⋊D₆₇	C₂×Q₈	semidirect
262. D₂₆₈	C₂×Q₈	semidirect
272. C₄×D₆₇	C₂×Q₈	semidirect
319. C₆₇	#3501	semidirect
328. #554	D₆₇	semidirect
356. C₄⋊Q₈	C₂×D₆₇	semidirect
365. #125	C₂×D₆₇	semidirect
366. #125	C₂×D₆₇	semidirect
398. C₂²⋊Q₈	C₂×D₆₇	semidirect
399. C₂²⋊Q₈	C₂×D₆₇	semidirect
400. C₂²⋊Q₈	C₂×D₆₇	semidirect
406. C₄×Q₈	C₂×D₆₇	semidirect
435. C₂×C₄⋊C₄	C₂×D₆₇	semidirect
563. D₄	Q₈×D₆₇	semidirect