Subgroups — #37547791

Order 23168.

1042 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26042002	C₂	1	1	yes	maximal, characteristic, complemented
2	#26042001	C₂	1	1	yes	maximal, characteristic, complemented
3	#26041986	C₂	1	1	yes	maximal, characteristic, complemented
4	#26041977	C₂	1	1	yes	maximal, characteristic, complemented
5	#26041975	C₂	1	2	yes	maximal, complemented
6	#26041964	C₂	1	1	yes	maximal, characteristic, complemented
7	#26041962	C₂	1	2	yes	maximal, complemented
8	#26041958	C₂	1	2	yes	maximal, complemented
9	#26041953	C₂	1	2	yes	maximal, complemented
10	#26041928	C₂	1	1	yes	maximal, characteristic, complemented
11	#26041924	C₂	1	1	yes	maximal, characteristic, complemented
12	#26041917	C₂	1	1	yes	maximal, characteristic, complemented
13	#26041900	C₂	1	1	yes	maximal, characteristic, complemented
14	#26041887	C₂	1	1	yes	maximal, characteristic, complemented
15	#26041876	C₂	1	2	yes	maximal, complemented
16	#26041862	C₂	1	2	yes	maximal, complemented
17	#26041816	C₂	1	1	yes	maximal, characteristic, complemented
18	#26041809	C₂	1	2	yes	maximal, complemented
19	#26041807	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#19153811	C₂	1	2	yes	maximal, complemented
21	#26041751	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#15668448	C₂	1	1	yes	maximal, characteristic, complemented
23	#520×C₁₈₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#15668448	C₂²	1	1	yes	characteristic
25	C₂×D₄×D₁₈₁	C₂²	1	1	yes	characteristic
26	#19153816	C₂²	1	1	yes	characteristic, complemented
27	#19153814	C₂²	1	1	yes	characteristic, complemented
28	#19153811	C₂²	1	2	yes	—
29	#19153811	C₂²	1	2	yes	—
30	#19153811	C₂²	1	2	yes	—
31	#19153811	C₂²	1	1	yes	characteristic
32	#19153811	C₂²	1	2	yes	complemented
33	#19153811	C₂²	1	2	yes	complemented
34	#19153811	C₂²	1	2	yes	complemented
35	#19153811	C₂²	1	2	yes	complemented
36	#19153811	C₂²	1	2	yes	complemented
37	#19153810	C₂²	1	2	yes	—
38	#19153810	C₂²	1	2	yes	complemented
39	#19153809	C₂²	1	1	yes	characteristic, complemented
40	#19153808	C₂²	1	2	yes	complemented
41	#19153807	C₂²	1	1	yes	characteristic, complemented
42	#19153807	C₂²	1	1	yes	characteristic, complemented
43	#19153806	C₂²	1	2	yes	complemented
44	#19153806	C₂²	1	2	yes	complemented
45	#19153806	C₂²	1	1	yes	characteristic, complemented
46	#19153805	C₂²	1	1	yes	characteristic
47	#19153804	C₂²	1	2	yes	—
48	#19153804	C₂²	1	1	yes	characteristic
49	#19153802	C₂²	1	1	yes	characteristic
50	#19153802	C₂²	1	2	yes	complemented
51	#19153801	C₂²	1	1	yes	characteristic
52	#19153801	C₂²	1	2	yes	complemented
53	#19153801	C₂²	1	2	yes	complemented
54	#19153800	C₂²	1	2	yes	—
55	#19153799	C₂²	1	2	yes	—
56	#19153799	C₂²	1	2	yes	—
57	#19153799	C₂²	1	2	yes	complemented
58	#19153798	C₂²	1	2	yes	complemented
59	#19153798	C₂²	1	1	yes	characteristic, complemented
60	#19153797	C₂²	1	2	yes	complemented
61	#19153796	C₂²	1	1	yes	characteristic
62	#19153795	C₂²	1	2	yes	complemented
63	#19153795	C₂²	1	1	yes	characteristic, complemented
64	#19153794	C₂²	1	1	yes	characteristic, complemented
65	#19153794	C₂²	1	2	yes	complemented
66	#19153794	C₂²	1	2	yes	complemented
67	#19153793	C₂²	1	2	yes	complemented
68	#19153793	C₂²	1	2	yes	complemented
69	#19153792	C₂²	1	1	yes	characteristic
70	#19153792	C₂²	1	1	yes	characteristic, complemented
71	#19153791	C₂²	1	1	yes	characteristic
72	#19153790	C₂²	1	2	yes	—
73	#19153790	C₂²	1	1	yes	characteristic
74	#19153790	C₂²	1	2	yes	complemented
75	#19153789	C₂²	1	1	yes	characteristic
76	#19153788	C₂²	1	2	yes	—
77	#19153788	C₂²	1	2	yes	complemented
78	#19153786	C₂²	1	2	yes	—
79	#19153784	C₂²	1	2	yes	—
80	C₄×Dic₃₆₂	C₂²	1	1	yes	characteristic, complemented
81	C₄×Dic₃₆₂	C₂²	1	2	yes	complemented
82	C₄×Dic₃₆₂	C₂²	1	1	yes	characteristic, complemented
83	#19153781	C₂²	1	1	yes	characteristic, complemented
84	C₄×D₇₂₄	C₂²	1	1	yes	characteristic
85	C₄×D₇₂₄	C₂²	1	1	yes	characteristic
86	C₄×D₇₂₄	C₂²	1	2	yes	complemented
87	D₄×Dic₁₈₁	C₂²	1	1	yes	characteristic
88	D₄×Dic₁₈₁	C₂²	1	1	yes	characteristic
89	#19153778	C₂²	1	1	yes	characteristic
90	C₄×C₂²⋊D₁₈₁	C₂²	1	2	yes	—
91	C₄×C₂²⋊D₁₈₁	C₂²	1	1	yes	characteristic
92	C₄×C₂²⋊D₁₈₁	C₂²	1	2	yes	complemented
93	C₄×C₂²⋊D₁₈₁	C₂²	1	1	yes	characteristic, complemented
94	C₄×C₂²⋊D₁₈₁	C₂²	1	2	yes	complemented
95	#19153776	C₂²	1	2	yes	—
96	#19153776	C₂²	1	2	yes	complemented
97	#19153775	C₂²	1	2	yes	complemented
98	#19153774	C₂²	1	1	yes	characteristic
99	#19153774	C₂²	1	1	yes	characteristic, complemented
100	#19153773	C₂²	1	1	yes	characteristic
101	#19153773	C₂²	1	2	yes	complemented
102	#19153773	C₂²	1	2	yes	complemented
103	#19153772	C₂²	1	2	yes	complemented
104	C₂×C₄⋊Dic₁₈₁	C₂²	1	2	yes	complemented
105	C₂×#15668428	C₂²	1	2	yes	complemented
106	C₂×#15668426	C₂²	1	2	yes	—
107	C₂×#15668426	C₂²	1	2	yes	—
108	C₂×#15668426	C₂²	1	2	yes	—
109	C₂²⋊C₄×D₁₈₁	C₂²	1	2	yes	—
110	C₂×C₄×Dic₁₈₁	C₂²	1	2	yes	complemented
111	C₄²×D₁₈₁	C₂²	1	1	yes	characteristic, complemented
112	C₂×#41×C₁₈₁	C₂²	1	1	yes	characteristic
113	C₄×Q₈×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
114	C₄×Q₈×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
115	C₄×D₄×C₁₈₁	C₂²	1	1	yes	characteristic
116	C₄×D₄×C₁₈₁	C₂²	1	1	yes	characteristic
117	C₄×D₄×C₁₈₁	C₂²	1	2	yes	complemented
118	C₄×D₄×C₁₈₁	C₂²	1	2	yes	complemented
119	#117×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
120	#117×C₁₈₁	C₂²	1	2	yes	complemented
121	C₂×C₄⋊C₄×C₁₈₁	C₂²	1	2	yes	complemented
122	C₂×C₄⋊C₄×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₈₁	C₂³	1	2	yes	—
124	#15668448	—	2	4	no	—
125	C₂×Dic₃₆₂	C₂³	1	1	yes	characteristic
126	C₂×Dic₃₆₂	C₂³	1	2	yes	—
127	C₂×Dic₃₆₂	C₂³	1	1	yes	characteristic
128	C₂×D₇₂₄	C₂³	1	1	yes	characteristic
129	C₂×D₇₂₄	C₂³	1	1	yes	characteristic
130	C₂×D₇₂₄	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₁₈₁	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₁₈₁	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₁₈₁	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊D₁₈₁	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₁₈₁	C₂³	1	1	yes	characteristic
136	D₄×D₁₈₁	—	2	4	no	—
137	C₂²×Dic₁₈₁	C₂³	1	2	yes	—
138	C₂²×Dic₁₈₁	C₂³	1	2	yes	—
139	C₂²×Dic₁₈₁	C₂³	1	2	yes	—
140	C₂×C₄×D₁₈₁	C₂³	1	1	yes	characteristic
141	C₂×C₄×D₁₈₁	C₂³	1	1	yes	characteristic
142	C₂×C₄×D₁₈₁	C₂³	1	1	yes	characteristic
143	C₂×C₄×D₁₈₁	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₁₈₁	C₂³	1	2	yes	—
145	C₂×C₄×D₁₈₁	C₂³	1	2	yes	—
146	C₄⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
147	C₄⋊Dic₁₈₁	C₂³	1	2	yes	—
148	C₄⋊Dic₁₈₁	C₂³	1	2	yes	—
149	C₄⋊Dic₁₈₁	C₂³	1	2	yes	—
150	C₄⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
151	C₄⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
152	C₄⋊Dic₁₈₁	C₂³	1	2	yes	—
153	C₄⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
154	#15668428	C₂³	1	1	yes	characteristic
155	#15668428	C₂³	1	2	yes	—
156	#15668428	C₂³	1	2	yes	—
157	#15668428	C₂³	1	2	yes	—
158	#15668428	C₂³	1	2	yes	—
159	#15668428	C₂³	1	2	yes	—
160	#15668428	C₂³	1	1	yes	characteristic
161	#15668428	C₂³	1	1	yes	characteristic
162	#15668428	C₂³	1	1	yes	characteristic
163	#15668428	C₂³	1	2	yes	—
164	#15668428	C₂³	1	2	yes	—
165	#15668428	C₂³	1	1	yes	characteristic
166	#15668428	C₂³	1	2	yes	—
167	#15668428	C₂³	1	2	yes	—
168	#15668428	C₂³	1	1	yes	characteristic
169	C₂²⋊Dic₁₈₁	C₂³	1	2	yes	—
170	C₂²⋊Dic₁₈₁	C₂³	1	2	yes	—
171	C₂²⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
172	C₂²⋊Dic₁₈₁	C₂³	1	2	yes	—
173	C₂²⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
174	#15668426	C₂³	1	1	yes	characteristic
175	#15668426	C₂³	1	2	yes	—
176	#15668426	C₂³	1	1	yes	characteristic
177	#15668426	C₂³	1	1	yes	characteristic
178	#15668426	C₂³	1	1	yes	characteristic
179	#15668426	C₂³	1	2	yes	—
180	#15668426	C₂³	1	2	yes	—
181	#15668426	C₂³	1	2	yes	—
182	#15668426	C₂³	1	2	yes	—
183	#15668426	C₂³	1	2	yes	—
184	#15668426	C₂³	1	2	yes	—
185	#15668426	C₂³	1	2	yes	—
186	#15668426	C₂³	1	2	yes	—
187	#15668426	C₂³	1	2	yes	—
188	#15668426	C₂³	1	2	yes	—
189	#15668426	C₂³	1	2	yes	—
190	#15668426	C₂³	1	1	yes	characteristic
191	#15668426	C₂³	1	1	yes	characteristic
192	#15668426	C₂³	1	2	yes	—
193	C₄×Dic₁₈₁	C₂³	1	1	yes	characteristic
194	C₄×Dic₁₈₁	C₂³	1	1	yes	characteristic
195	C₄×Dic₁₈₁	C₂³	1	1	yes	characteristic
196	C₄×Dic₁₈₁	C₂³	1	2	yes	—
197	C₄×Dic₁₈₁	C₂³	1	2	yes	—
198	C₄×Dic₁₈₁	C₂³	1	2	yes	—
199	C₄×Dic₁₈₁	C₂³	1	1	yes	characteristic
200	C₄×Dic₁₈₁	C₂³	1	2	yes	—
201	#41×C₁₈₁	—	2	4	no	—
202	C₂×Q₈×C₁₈₁	C₂³	1	1	yes	characteristic
203	C₂×D₄×C₁₈₁	C₂³	1	2	yes	—
204	C₂×D₄×C₁₈₁	C₂³	1	1	yes	characteristic
205	C₂²×C₄×C₁₈₁	C₂³	1	2	yes	—
206	C₂²×C₄×C₁₈₁	C₂³	1	1	yes	characteristic
207	C₂²×C₄×C₁₈₁	C₂³	1	2	yes	—
208	C₂²×C₄×C₁₈₁	C₂³	1	2	yes	—
209	C₂²×C₄×C₁₈₁	C₂³	1	2	yes	—
210	C₄⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
211	C₄⋊C₄×C₁₈₁	C₂³	1	2	yes	—
212	C₄⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
213	C₄⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
214	C₄⋊C₄×C₁₈₁	C₂³	1	2	yes	—
215	C₄⋊C₄×C₁₈₁	C₂³	1	2	yes	—
216	C₄⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
217	C₂²⋊C₄×C₁₈₁	C₂³	1	2	yes	—
218	C₂²⋊C₄×C₁₈₁	C₂³	1	2	yes	—
219	C₂²⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
220	C₂²⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
221	C₄²×C₁₈₁	C₂³	1	1	yes	characteristic
222	C₄²×C₁₈₁	C₂³	1	1	yes	characteristic
223	C₄²×C₁₈₁	C₂³	1	2	yes	—
224	C₄²×C₁₈₁	C₂³	1	2	yes	—
225	C₂²×D₁₈₁	—	2	4	no	—
226	C₂²×D₁₈₁	—	4	2	no	—
227	C₂²×D₁₈₁	—	4	2	no	—
228	C₂²×D₁₈₁	C₂⁴	1	1	yes	characteristic
229	C₂²×D₁₈₁	C₂⁴	1	2	yes	—
230	C₂²×D₁₈₁	C₂⁴	1	1	yes	characteristic
231	Dic₃₆₂	—	2	2	no	—
232	Dic₃₆₂	—	4	1	no	—
233	Dic₃₆₂	—	4	2	no	—
234	D₇₂₄	—	2	2	no	—
235	D₇₂₄	—	4	2	no	—
236	D₇₂₄	—	4	1	no	—
237	C₂²⋊D₁₈₁	—	2	4	no	—
238	C₂²⋊D₁₈₁	—	2	4	no	—
239	C₂²⋊D₁₈₁	—	4	1	no	—
240	C₂²⋊D₁₈₁	—	4	1	no	—
241	C₂²⋊D₁₈₁	—	4	2	no	—
242	C₂×Dic₁₈₁	—	2	4	no	—
243	C₂×Dic₁₈₁	—	4	2	no	—
244	C₂×Dic₁₈₁	—	4	2	no	—
245	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
246	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
247	C₂×Dic₁₈₁	C₂⁴	1	2	yes	—
248	C₂×Dic₁₈₁	C₂⁴	1	2	yes	—
249	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
250	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
251	C₂×Dic₁₈₁	C₂⁴	1	2	yes	—
252	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
253	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
254	C₄×D₁₈₁	—	2	2	no	—
255	C₄×D₁₈₁	—	2	2	no	—
256	C₄×D₁₈₁	—	4	2	no	—
257	C₄×D₁₈₁	—	4	1	no	—
258	C₄×D₁₈₁	—	4	2	no	—
259	C₄×D₁₈₁	—	4	1	no	—
260	C₂³×C₁₈₁	C₂⁴	1	1	yes	characteristic
261	C₂³×C₁₈₁	C₂⁴	1	2	yes	—
262	Q₈×C₁₈₁	—	2	2	no	—
263	D₄×C₁₈₁	—	2	4	no	—
264	D₄×C₁₈₁	#41	1	4	yes	—
265	C₂×C₄×C₁₈₁	—	2	4	no	—
266	C₂×C₄×C₁₈₁	—	2	2	no	—
267	C₂×C₄×C₁₈₁	—	4	2	no	—
268	C₂×C₄×C₁₈₁	—	4	2	no	—
269	C₂×C₄×C₁₈₁	—	4	2	no	—
270	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
271	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
272	C₂×C₄×C₁₈₁	C₂⁴	1	2	yes	—
273	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
274	C₂×C₄×C₁₈₁	C₂⁴	1	2	yes	—
275	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
276	C₂×C₄×C₁₈₁	C₂⁴	1	2	yes	—
277	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
278	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
279	C₂²×C₁₈₁	—	2	2	no	—
280	C₂²×C₁₈₁	—	2	2	no	—
281	C₂²×C₁₈₁	—	2	1	no	—
282	C₂²×C₁₈₁	—	2	1	no	—
283	C₂²×C₁₈₁	—	2	1	no	—
284	C₂²×C₁₈₁	C₂×#41	1	4	yes	—
285	C₂²×C₁₈₁	C₂⁵	1	1	yes	characteristic
286	C₂×D₁₈₁	—	2	1	no	—
287	C₂×D₁₈₁	—	2	1	no	—
288	C₂×D₁₈₁	—	2	2	no	—
289	C₂×D₁₈₁	—	2	1	no	—
290	C₂×D₁₈₁	—	2	2	no	—
291	C₂×D₁₈₁	—	2	1	no	—
292	C₂×D₁₈₁	—	2	2	no	—
293	C₂×D₁₈₁	—	2	1	no	—
294	C₂×D₁₈₁	—	2	1	no	—
295	C₂×D₁₈₁	—	8	4	no	—
296	C₄×C₁₈₁	—	2	1	no	—
297	C₄×C₁₈₁	—	2	2	no	—
298	C₄×C₁₈₁	—	2	1	no	—
299	C₄×C₁₈₁	—	2	2	no	—
300	C₄×C₁₈₁	—	2	2	no	—
301	C₄×C₁₈₁	—	2	1	no	—
302	C₄×C₁₈₁	—	2	1	no	—
303	C₄×C₁₈₁	—	2	1	no	—
304	C₄×C₁₈₁	C₂×#41	1	2	yes	—
305	Dic₁₈₁	—	2	1	no	—
306	Dic₁₈₁	—	2	1	no	—
307	Dic₁₈₁	—	2	2	no	—
308	Dic₁₈₁	—	2	1	no	—
309	Dic₁₈₁	—	2	1	no	—
310	Dic₁₈₁	—	2	2	no	—
311	Dic₁₈₁	—	2	1	no	—
312	Dic₁₈₁	—	2	1	no	—
313	Dic₁₈₁	—	2	2	no	—
314	C₂×C₁₈₁	—	2	4	no	—
315	C₂×C₁₈₁	—	4	1	no	—
316	C₂×C₁₈₁	C₂²×#41	1	1	yes	characteristic
317	C₂×C₁₈₁	#585	1	1	yes	characteristic
318	C₂×C₁₈₁	#585	1	1	yes	characteristic
319	D₁₈₁	—	4	1	no	—
320	D₁₈₁	—	4	2	no	—
321	D₁₈₁	—	4	1	no	—
322	C₁₈₁	#3521	1	1	yes	characteristic, complemented, Sylow
323	#3521	—	181	1	no	maximal, Sylow
324	#556	—	181	1	no	—
325	#556	—	181	1	no	—
326	#554	—	181	1	no	—
327	#553	—	181	2	no	—
328	#553	—	181	1	no	—
329	#552	—	181	2	no	—
330	#552	—	181	1	no	—
331	#551	—	181	2	no	—
332	#551	—	181	2	no	—
333	#547	—	181	1	no	—
334	#546	—	181	1	no	—
335	#546	—	181	1	no	—
336	#542	—	181	1	no	—
337	#541	—	181	1	no	—
338	#539	—	181	2	no	—
339	#538	—	181	2	no	—
340	#529	—	181	1	no	—
341	#529	—	181	2	no	—
342	#529	—	181	1	no	—
343	C₂×#126	—	181	2	no	—
344	#520	D₁₈₁	1	1	yes	characteristic, complemented
345	#518	—	181	1	no	—
346	C₄×#41	—	181	1	no	—
347	C₂×#41	—	181	1	no	—
348	C₂×#41	C₂×D₁₈₁	1	1	yes	characteristic
349	C₂²×D₄	—	181	1	no	—
350	C₄⋊Q₈	—	181	1	no	—
351	C₄⋊Q₈	—	181	1	no	—
352	#126	—	181	1	no	—
353	#126	—	181	2	no	—
354	#126	—	181	2	no	—
355	#126	—	181	2	no	—
356	#126	—	181	2	no	—
357	#126	—	181	2	no	—
358	#126	—	181	2	no	—
359	#126	—	181	2	no	—
360	#126	—	181	2	no	—
361	#126	—	181	1	no	—
362	#126	—	181	2	no	—
363	#126	—	181	2	no	—
364	#125	—	181	2	no	—
365	#125	—	181	1	no	—
366	#125	—	181	1	no	—
367	#125	—	181	2	no	—
368	#125	—	181	1	no	—
369	#125	—	181	2	no	—
370	#124	—	181	1	no	—
371	#124	—	181	2	no	—
372	#124	—	181	1	no	—
373	#124	—	181	2	no	—
374	#124	—	181	1	no	—
375	#123	—	181	2	no	—
376	#123	—	181	2	no	—
377	#123	—	181	2	no	—
378	#123	—	181	2	no	—
379	#123	—	181	2	no	—
380	#123	—	181	1	no	—
381	#123	—	181	2	no	—
382	#123	—	181	2	no	—
383	#123	—	181	1	no	—
384	#123	—	181	2	no	—
385	C₂²⋊Q₈	—	181	1	no	—
386	C₂²⋊Q₈	—	181	1	no	—
387	C₂²⋊Q₈	—	181	2	no	—
388	C₂²⋊Q₈	—	181	1	no	—
389	C₂²⋊Q₈	—	181	1	no	—
390	C₂²⋊Q₈	—	181	2	no	—
391	C₂²⋊Q₈	—	181	1	no	—
392	C₂²⋊Q₈	—	181	2	no	—
393	C₂²⋊Q₈	—	181	2	no	—
394	C₂²⋊Q₈	—	181	2	no	—
395	#121	—	181	2	no	—
396	#121	—	181	2	no	—
397	#121	—	181	2	no	—
398	#121	—	181	2	no	—
399	#121	—	181	1	no	—
400	#121	—	181	1	no	—
401	#121	—	181	1	no	—
402	#120	—	181	2	no	—
403	#120	—	181	2	no	—
404	C₄×Q₈	—	181	1	no	—
405	C₄×Q₈	—	181	1	no	—
406	C₄×Q₈	—	181	2	no	—
407	C₄×Q₈	—	181	1	no	—
408	C₄×Q₈	C₂×D₁₈₁	1	1	yes	characteristic, complemented
409	C₄×Q₈	C₂×D₁₈₁	1	1	yes	characteristic, complemented
410	C₄×D₄	—	181	1	no	—
411	C₄×D₄	—	181	1	no	—
412	C₄×D₄	—	181	2	no	—
413	C₄×D₄	—	181	2	no	—
414	C₄×D₄	—	181	1	no	—
415	C₄×D₄	—	181	1	no	—
416	C₄×D₄	—	181	2	no	—
417	C₄×D₄	—	181	1	no	—
418	C₄×D₄	—	181	2	no	—
419	C₄×D₄	—	181	2	no	—
420	C₄×D₄	—	181	1	no	—
421	C₄×D₄	—	181	1	no	—
422	C₄×D₄	—	181	2	no	—
423	C₄×D₄	C₂×D₁₈₁	1	1	yes	characteristic
424	C₄×D₄	C₂×D₁₈₁	1	1	yes	characteristic
425	C₄×D₄	C₂×D₁₈₁	1	2	yes	complemented
426	C₄×D₄	C₂×D₁₈₁	1	2	yes	complemented
427	#117	—	181	2	no	—
428	#117	—	181	1	no	—
429	#117	—	181	1	no	—
430	#117	—	181	2	no	—
431	#117	—	181	1	no	—
432	#117	—	181	2	no	—
433	#117	—	181	2	no	—
434	#117	C₂×D₁₈₁	1	1	yes	characteristic, complemented
435	#117	C₂×D₁₈₁	1	2	yes	complemented
436	C₂×C₄⋊C₄	—	181	2	no	—
437	C₂×C₄⋊C₄	—	181	2	no	—
438	C₂×C₄⋊C₄	C₂×D₁₈₁	1	2	yes	complemented
439	C₂×C₄⋊C₄	C₂×D₁₈₁	1	1	yes	characteristic, complemented
440	C₂×C₂²⋊C₄	—	181	2	no	—
441	C₂×C₂²⋊C₄	—	181	2	no	—
442	C₂×C₂²⋊C₄	—	181	2	no	—
443	C₂×C₂²⋊C₄	—	181	2	no	—
444	C₂×C₄²	—	181	2	no	—
445	C₂×C₄²	—	181	1	no	—
446	C₂⁴	—	181	2	no	—
447	#41	—	2	4	no	—
448	#41	—	362	4	no	—
449	C₂×Q₈	—	181	1	no	—
450	C₂×Q₈	—	181	1	no	—
451	C₂×Q₈	—	181	2	no	—
452	C₂×Q₈	C₂²×D₁₈₁	1	1	yes	characteristic
453	C₂×D₄	—	362	4	no	—
454	C₂×D₄	—	181	2	no	—
455	C₂×D₄	—	181	2	no	—
456	C₂×D₄	—	181	1	no	—
457	C₂×D₄	—	181	2	no	—
458	C₂×D₄	—	181	1	no	—
459	C₂×D₄	—	181	1	no	—
460	C₂×D₄	—	181	1	no	—
461	C₂×D₄	—	181	2	no	—
462	C₂×D₄	C₂²×D₁₈₁	1	2	yes	—
463	C₂×D₄	C₂²×D₁₈₁	1	1	yes	characteristic
464	C₂²×C₄	—	181	2	no	—
465	C₂²×C₄	—	181	1	no	—
466	C₂²×C₄	—	181	1	no	—
467	C₂²×C₄	—	181	2	no	—
468	C₂²×C₄	—	181	2	no	—
469	C₂²×C₄	—	181	1	no	—
470	C₂²×C₄	—	181	1	no	—
471	C₂²×C₄	—	181	2	no	—
472	C₂²×C₄	—	181	2	no	—
473	C₂²×C₄	C₂²×D₁₈₁	1	2	yes	—
474	C₂²×C₄	C₂²×D₁₈₁	1	1	yes	characteristic
475	C₂²×C₄	C₂²×D₁₈₁	1	2	yes	—
476	C₂²×C₄	C₂²×D₁₈₁	1	2	yes	—
477	C₂²×C₄	C₂²×D₁₈₁	1	2	yes	—
478	C₄⋊C₄	—	181	1	no	—
479	C₄⋊C₄	—	181	1	no	—
480	C₄⋊C₄	—	181	2	no	—
481	C₄⋊C₄	—	181	2	no	—
482	C₄⋊C₄	—	181	2	no	—
483	C₄⋊C₄	—	181	2	no	—
484	C₄⋊C₄	—	181	2	no	—
485	C₄⋊C₄	—	181	2	no	—
486	C₄⋊C₄	—	181	1	no	—
487	C₄⋊C₄	—	181	1	no	—
488	C₄⋊C₄	—	181	1	no	—
489	C₄⋊C₄	—	181	1	no	—
490	C₄⋊C₄	—	181	1	no	—
491	C₄⋊C₄	—	181	2	no	—
492	C₄⋊C₄	—	181	2	no	—
493	C₄⋊C₄	—	181	2	no	—
494	C₄⋊C₄	—	181	2	no	—
495	C₄⋊C₄	—	181	2	no	—
496	C₄⋊C₄	—	181	1	no	—
497	C₄⋊C₄	—	181	2	no	—
498	C₄⋊C₄	—	181	1	no	—
499	C₄⋊C₄	—	181	1	no	—
500	C₄⋊C₄	—	181	2	no	—
501	C₄⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
502	C₄⋊C₄	C₂²×D₁₈₁	1	2	yes	—
503	C₄⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
504	C₄⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
505	C₄⋊C₄	C₂²×D₁₈₁	1	2	yes	—
506	C₄⋊C₄	C₂²×D₁₈₁	1	2	yes	—
507	C₄⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
508	C₂²⋊C₄	—	181	2	no	—
509	C₂²⋊C₄	—	181	1	no	—
510	C₂²⋊C₄	—	181	2	no	—
511	C₂²⋊C₄	—	181	2	no	—
512	C₂²⋊C₄	—	181	1	no	—
513	C₂²⋊C₄	—	181	1	no	—
514	C₂²⋊C₄	—	181	2	no	—
515	C₂²⋊C₄	—	181	1	no	—
516	C₂²⋊C₄	—	181	1	no	—
517	C₂²⋊C₄	—	181	1	no	—
518	C₂²⋊C₄	—	181	2	no	—
519	C₂²⋊C₄	—	181	2	no	—
520	C₂²⋊C₄	—	181	2	no	—
521	C₂²⋊C₄	—	181	2	no	—
522	C₂²⋊C₄	—	181	2	no	—
523	C₂²⋊C₄	—	181	2	no	—
524	C₂²⋊C₄	—	181	2	no	—
525	C₂²⋊C₄	—	181	2	no	—
526	C₂²⋊C₄	—	181	2	no	—
527	C₂²⋊C₄	—	181	2	no	—
528	C₂²⋊C₄	—	181	2	no	—
529	C₂²⋊C₄	—	181	1	no	—
530	C₂²⋊C₄	—	181	2	no	—
531	C₂²⋊C₄	—	181	1	no	—
532	C₂²⋊C₄	C₂²×D₁₈₁	1	2	yes	—
533	C₂²⋊C₄	C₂²×D₁₈₁	1	2	yes	—
534	C₂²⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
535	C₂²⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
536	C₄²	—	181	1	no	—
537	C₄²	—	181	1	no	—
538	C₄²	—	181	2	no	—
539	C₄²	—	181	2	no	—
540	C₄²	—	181	1	no	—
541	C₄²	—	181	2	no	—
542	C₄²	—	181	2	no	—
543	C₄²	—	181	1	no	—
544	C₄²	C₂²×D₁₈₁	1	1	yes	characteristic
545	C₄²	C₂²×D₁₈₁	1	2	yes	—
546	C₄²	C₂²×D₁₈₁	1	2	yes	—
547	C₄²	C₂²×D₁₈₁	1	1	yes	characteristic
548	C₂³	—	362	4	no	—
549	C₂³	—	181	1	no	—
550	C₂³	—	181	2	no	—
551	C₂³	—	181	1	no	—
552	C₂³	—	724	2	no	—
553	C₂³	—	724	2	no	—
554	C₂³	C₂³×D₁₈₁	1	1	yes	characteristic
555	C₂³	C₂³×D₁₈₁	1	2	yes	—
556	Q₈	—	2	2	no	—
557	Q₈	—	362	2	no	—
558	Q₈	—	724	1	no	—
559	Q₈	—	724	2	no	—
560	D₄	—	2	4	no	—
561	D₄	—	362	4	no	—
562	D₄	—	362	4	no	—
563	D₄	—	362	2	no	—
564	D₄	—	724	2	no	—
565	D₄	—	724	1	no	—
566	D₄	—	724	1	no	—
567	D₄	—	724	1	no	—
568	D₄	—	724	2	no	—
569	D₄	#15668449	1	4	yes	—
570	C₂×C₄	—	2	4	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	4	2	no	—
573	C₂×C₄	—	4	2	no	—
574	C₂×C₄	—	4	2	no	—
575	C₂×C₄	—	362	4	no	—
576	C₂×C₄	—	362	2	no	—
577	C₂×C₄	—	362	2	no	—
578	C₂×C₄	—	181	1	no	—
579	C₂×C₄	—	181	1	no	—
580	C₂×C₄	—	181	1	no	—
581	C₂×C₄	—	181	2	no	—
582	C₂×C₄	—	181	2	no	—
583	C₂×C₄	—	181	1	no	—
584	C₂×C₄	—	181	1	no	—
585	C₂×C₄	—	181	2	no	—
586	C₂×C₄	—	181	1	no	—
587	C₂×C₄	—	724	2	no	—
588	C₂×C₄	—	724	1	no	—
589	C₂×C₄	—	724	1	no	—
590	C₂×C₄	—	724	2	no	—
591	C₂×C₄	—	724	2	no	—
592	C₂×C₄	—	724	2	no	—
593	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
594	C₂×C₄	C₂³×D₁₈₁	1	2	yes	—
595	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
596	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
597	C₂×C₄	C₂³×D₁₈₁	1	2	yes	—
598	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
599	C₂×C₄	C₂³×D₁₈₁	1	2	yes	—
600	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
601	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
602	C₂²	—	2	2	no	—
603	C₂²	—	2	2	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	2	1	no	—
607	C₂²	—	362	1	no	—
608	C₂²	—	362	2	no	—
609	C₂²	—	362	1	no	—
610	C₂²	—	362	1	no	—
611	C₂²	—	362	2	no	—
612	C₂²	—	362	1	no	—
613	C₂²	—	362	1	no	—
614	C₂²	—	362	1	no	—
615	C₂²	—	362	2	no	—
616	C₂²	—	1448	4	no	—
617	C₂²	C₂×#15668449	1	4	yes	—
618	C₂²	C₂⁴×D₁₈₁	1	1	yes	characteristic
619	C₄	—	2	1	no	—
620	C₄	—	2	2	no	—
621	C₄	—	2	2	no	—
622	C₄	—	2	1	no	—
623	C₄	—	2	1	no	—
624	C₄	—	2	1	no	—
625	C₄	—	2	1	no	—
626	C₄	—	2	2	no	—
627	C₄	—	362	1	no	—
628	C₄	—	362	1	no	—
629	C₄	—	362	1	no	—
630	C₄	—	362	1	no	—
631	C₄	—	362	2	no	—
632	C₄	—	362	2	no	—
633	C₄	—	362	1	no	—
634	C₄	—	362	1	no	—
635	C₄	—	362	2	no	—
636	C₄	C₂×#15668449	1	2	yes	—
637	C₂	—	2	4	no	—
638	C₂	—	4	1	no	—
639	C₂	—	724	1	no	—
640	C₂	—	724	2	no	—
641	C₂	—	724	1	no	—
642	C₂	C₂²×#15668449	1	1	yes	characteristic
643	C₂	#26042114	1	1	yes	characteristic
644	C₂	#26042116	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₈₁
commutator, socle, cosocle	C₂²×C₁₈₁	C₂⁵
Fitting	#520×C₁₈₁	C₂
hypercenter	#520	D₁₈₁
hypocenter	C₁₈₁	#3521
LCS	G ▷ C₂²×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂² ◁ #520

Complements

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

N	H ≅ G/N	type
1. #26042002	C₂	semidirect
2. #26042001	C₂	semidirect
3. #26041986	C₂	semidirect
4. #26041977	C₂	semidirect
5. #26041975	C₂	semidirect
6. #26041964	C₂	semidirect
7. #26041962	C₂	semidirect
8. #26041958	C₂	semidirect
9. #26041953	C₂	semidirect
10. #26041928	C₂	semidirect
11. #26041924	C₂	semidirect
12. #26041917	C₂	semidirect
13. #26041900	C₂	semidirect
14. #26041887	C₂	semidirect
15. #26041876	C₂	semidirect
16. #26041862	C₂	semidirect
17. #26041816	C₂	semidirect
18. #26041809	C₂	semidirect
19. #26041807	C₂	semidirect
20. C₂×#19153811	C₂	semidirect
21. #26041751	C₂	semidirect
22. C₄×#15668448	C₂	semidirect
23. #520×C₁₈₁	C₂	semidirect
26. #19153816	C₂²	semidirect
27. #19153814	C₂²	semidirect
32. #19153811	C₂²	semidirect
33. #19153811	C₂²	semidirect
34. #19153811	C₂²	semidirect
35. #19153811	C₂²	semidirect
36. #19153811	C₂²	semidirect
38. #19153810	C₂²	semidirect
39. #19153809	C₂²	semidirect
40. #19153808	C₂²	semidirect
41. #19153807	C₂²	semidirect
42. #19153807	C₂²	semidirect
43. #19153806	C₂²	semidirect
44. #19153806	C₂²	semidirect
45. #19153806	C₂²	semidirect
50. #19153802	C₂²	semidirect
52. #19153801	C₂²	semidirect
53. #19153801	C₂²	semidirect
57. #19153799	C₂²	semidirect
58. #19153798	C₂²	semidirect
59. #19153798	C₂²	semidirect
60. #19153797	C₂²	semidirect
62. #19153795	C₂²	semidirect
63. #19153795	C₂²	semidirect
64. #19153794	C₂²	semidirect
65. #19153794	C₂²	semidirect
66. #19153794	C₂²	semidirect
67. #19153793	C₂²	semidirect
68. #19153793	C₂²	semidirect
70. #19153792	C₂²	semidirect
74. #19153790	C₂²	semidirect
77. #19153788	C₂²	semidirect
80. C₄×Dic₃₆₂	C₂²	semidirect
81. C₄×Dic₃₆₂	C₂²	semidirect
82. C₄×Dic₃₆₂	C₂²	semidirect
83. #19153781	C₂²	semidirect
86. C₄×D₇₂₄	C₂²	semidirect
92. C₄×C₂²⋊D₁₈₁	C₂²	semidirect
93. C₄×C₂²⋊D₁₈₁	C₂²	semidirect
94. C₄×C₂²⋊D₁₈₁	C₂²	semidirect
96. #19153776	C₂²	semidirect
97. #19153775	C₂²	semidirect
99. #19153774	C₂²	semidirect
101. #19153773	C₂²	semidirect
102. #19153773	C₂²	semidirect
103. #19153772	C₂²	semidirect
104. C₂×C₄⋊Dic₁₈₁	C₂²	semidirect
105. C₂×#15668428	C₂²	semidirect
110. C₂×C₄×Dic₁₈₁	C₂²	semidirect
111. C₄²×D₁₈₁	C₂²	semidirect
113. C₄×Q₈×C₁₈₁	C₂²	semidirect
114. C₄×Q₈×C₁₈₁	C₂²	semidirect
117. C₄×D₄×C₁₈₁	C₂²	semidirect
118. C₄×D₄×C₁₈₁	C₂²	semidirect
119. #117×C₁₈₁	C₂²	semidirect
120. #117×C₁₈₁	C₂²	semidirect
121. C₂×C₄⋊C₄×C₁₈₁	C₂²	semidirect
122. C₂×C₄⋊C₄×C₁₈₁	C₂²	semidirect
322. C₁₈₁	#3521	semidirect
344. #520	D₁₈₁	semidirect
408. C₄×Q₈	C₂×D₁₈₁	semidirect
409. C₄×Q₈	C₂×D₁₈₁	semidirect
425. C₄×D₄	C₂×D₁₈₁	semidirect
426. C₄×D₄	C₂×D₁₈₁	semidirect
434. #117	C₂×D₁₈₁	semidirect
435. #117	C₂×D₁₈₁	semidirect
438. C₂×C₄⋊C₄	C₂×D₁₈₁	semidirect
439. C₂×C₄⋊C₄	C₂×D₁₈₁	semidirect

Maximal subgroups

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

subgroup	index
#26042002	2
#26042001	2
#26041986	2
#26041977	2
#26041975	2
#26041964	2
#26041962	2
#26041958	2
#26041953	2
#26041928	2
#26041924	2
#26041917	2
#26041900	2
#26041887	2
#26041876	2
#26041862	2
#26041816	2
#26041809	2
#26041807	2
C₂×#19153811	2
#26041751	2
C₄×#15668448	2
#520×C₁₈₁	2
#3521	181