Subgroups — #37548236

Order 23168.

1160 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26042025	C₂	1	2	yes	maximal, complemented
2	#26042021	C₂	1	2	yes	maximal, complemented
3	#26042014	C₂	1	1	yes	maximal, characteristic, complemented
4	#26042012	C₂	1	1	yes	maximal, characteristic, complemented
5	#26041941	C₂	1	1	yes	maximal, characteristic, complemented
6	#26041939	C₂	1	1	yes	maximal, characteristic, complemented
7	#26041926	C₂	1	1	yes	maximal, characteristic, complemented
8	#26041922	C₂	1	2	yes	maximal, complemented
9	#26041920	C₂	1	1	yes	maximal, characteristic, complemented
10	#26041920	C₂	1	2	yes	maximal, complemented
11	D₄×D₇₂₄	C₂	1	1	yes	maximal, characteristic, complemented
12	#26041913	C₂	1	1	yes	maximal, characteristic, complemented
13	#26041903	C₂	1	1	yes	maximal, characteristic, complemented
14	#26041868	C₂	1	2	yes	maximal, complemented
15	#26041868	C₂	1	2	yes	maximal, complemented
16	#26041865	C₂	1	2	yes	maximal, complemented
17	#26041848	C₂	1	1	yes	maximal, characteristic, complemented
18	#26041847	C₂	1	1	yes	maximal, characteristic, complemented
19	#26041840	C₂	1	2	yes	maximal, complemented
20	#26041830	C₂	1	1	yes	maximal, characteristic, complemented
21	#26041807	C₂	1	1	yes	maximal, characteristic, complemented
22	#124×D₁₈₁	C₂	1	1	yes	maximal, characteristic, complemented
23	#542×C₁₈₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#15668450	C₂²	1	2	yes	complemented
25	C₂×#15668450	C₂²	1	1	yes	characteristic, complemented
26	C₂×#15668449	C₂²	1	1	yes	characteristic, complemented
27	C₂×Q₈×D₁₈₁	C₂²	1	1	yes	characteristic, complemented
28	C₂²×D₇₂₄	C₂²	1	1	yes	characteristic, complemented
29	C₂²×D₇₂₄	C₂²	1	2	yes	complemented
30	C₂×D₄×D₁₈₁	C₂²	1	1	yes	characteristic
31	C₂×D₄×D₁₈₁	C₂²	1	2	yes	complemented
32	C₂×D₄×D₁₈₁	C₂²	1	1	yes	characteristic, complemented
33	#19153813	C₂²	1	1	yes	characteristic
34	#19153813	C₂²	1	1	yes	characteristic, complemented
35	#19153812	C₂²	1	1	yes	characteristic
36	#19153811	C₂²	1	2	yes	complemented
37	#19153811	C₂²	1	1	yes	characteristic, complemented
38	#19153809	C₂²	1	1	yes	characteristic, complemented
39	#19153806	C₂²	1	1	yes	characteristic, complemented
40	#19153805	C₂²	1	2	yes	complemented
41	#19153805	C₂²	1	1	yes	characteristic, complemented
42	#19153805	C₂²	1	1	yes	characteristic, complemented
43	#19153805	C₂²	1	2	yes	complemented
44	#19153804	C₂²	1	2	yes	complemented
45	#19153804	C₂²	1	2	yes	complemented
46	#19153804	C₂²	1	1	yes	characteristic, complemented
47	#19153804	C₂²	1	1	yes	characteristic, complemented
48	#19153803	C₂²	1	1	yes	characteristic, complemented
49	#19153802	C₂²	1	2	yes	complemented
50	#19153802	C₂²	1	2	yes	complemented
51	#19153802	C₂²	1	2	yes	complemented
52	#19153802	C₂²	1	1	yes	characteristic, complemented
53	#19153802	C₂²	1	2	yes	complemented
54	#19153801	C₂²	1	2	yes	complemented
55	#19153801	C₂²	1	2	yes	complemented
56	#19153801	C₂²	1	2	yes	complemented
57	#19153801	C₂²	1	1	yes	characteristic, complemented
58	#19153801	C₂²	1	2	yes	complemented
59	#19153799	C₂²	1	2	yes	complemented
60	#19153798	C₂²	1	2	yes	complemented
61	#19153798	C₂²	1	2	yes	complemented
62	#19153798	C₂²	1	1	yes	characteristic, complemented
63	#19153796	C₂²	1	2	yes	complemented
64	#19153796	C₂²	1	1	yes	characteristic, complemented
65	#19153794	C₂²	1	1	yes	characteristic, complemented
66	#19153794	C₂²	1	2	yes	complemented
67	#19153792	C₂²	1	2	yes	complemented
68	#19153791	C₂²	1	1	yes	characteristic
69	#19153791	C₂²	1	2	yes	complemented
70	#19153791	C₂²	1	2	yes	complemented
71	#19153791	C₂²	1	2	yes	complemented
72	#19153791	C₂²	1	1	yes	characteristic, complemented
73	#19153791	C₂²	1	1	yes	characteristic, complemented
74	#19153791	C₂²	1	2	yes	complemented
75	#19153791	C₂²	1	2	yes	complemented
76	#19153790	C₂²	1	2	yes	complemented
77	#19153789	C₂²	1	1	yes	characteristic
78	#19153789	C₂²	1	2	yes	complemented
79	#19153789	C₂²	1	2	yes	complemented
80	#19153789	C₂²	1	2	yes	complemented
81	#19153789	C₂²	1	2	yes	complemented
82	#19153787	C₂²	1	2	yes	complemented
83	#19153786	C₂²	1	2	yes	complemented
84	#19153786	C₂²	1	2	yes	complemented
85	#19153786	C₂²	1	2	yes	complemented
86	#19153786	C₂²	1	2	yes	complemented
87	#19153786	C₂²	1	2	yes	complemented
88	#19153786	C₂²	1	2	yes	complemented
89	#19153786	C₂²	1	2	yes	complemented
90	#19153786	C₂²	1	2	yes	complemented
91	#19153784	C₂²	1	2	yes	complemented
92	#19153784	C₂²	1	2	yes	complemented
93	C₄×Dic₃₆₂	C₂²	1	1	yes	characteristic, complemented
94	#19153781	C₂²	1	1	yes	characteristic, complemented
95	C₄×D₇₂₄	C₂²	1	2	yes	complemented
96	C₄×D₇₂₄	C₂²	1	2	yes	complemented
97	C₄×D₇₂₄	C₂²	1	1	yes	characteristic, complemented
98	#19153778	C₂²	1	2	yes	complemented
99	#19153778	C₂²	1	2	yes	complemented
100	#19153778	C₂²	1	1	yes	characteristic, complemented
101	#19153778	C₂²	1	1	yes	characteristic, complemented
102	#19153778	C₂²	1	1	yes	characteristic, complemented
103	C₄×C₂²⋊D₁₈₁	C₂²	1	2	yes	complemented
104	C₄×C₂²⋊D₁₈₁	C₂²	1	1	yes	characteristic, complemented
105	C₄×C₂²⋊D₁₈₁	C₂²	1	1	yes	characteristic, complemented
106	#19153773	C₂²	1	1	yes	characteristic, complemented
107	C₂²⋊C₄×D₁₈₁	C₂²	1	2	yes	complemented
108	C₂²⋊C₄×D₁₈₁	C₂²	1	2	yes	complemented
109	C₂²⋊C₄×D₁₈₁	C₂²	1	2	yes	complemented
110	C₂²⋊C₄×D₁₈₁	C₂²	1	2	yes	complemented
111	C₄²×D₁₈₁	C₂²	1	1	yes	characteristic, complemented
112	C₄⋊Q₈×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
113	#126×C₁₈₁	C₂²	1	2	yes	complemented
114	#124×C₁₈₁	C₂²	1	2	yes	complemented
115	#124×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
116	#123×C₁₈₁	C₂²	1	2	yes	complemented
117	C₂²⋊Q₈×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
118	C₂²⋊Q₈×C₁₈₁	C₂²	1	2	yes	complemented
119	#121×C₁₈₁	C₂²	1	1	yes	characteristic
120	C₄×Q₈×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₄×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
122	#117×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₈₁	C₂³	1	2	yes	—
124	C₂³×D₁₈₁	C₂³	1	2	yes	—
125	C₂³×D₁₈₁	C₂³	1	2	yes	—
126	#15668450	—	4	2	no	—
127	#15668450	—	4	4	no	—
128	#15668449	—	4	2	no	—
129	C₂×Dic₃₆₂	C₂³	1	1	yes	characteristic
130	C₂×Dic₃₆₂	C₂³	1	1	yes	characteristic
131	C₂×Dic₃₆₂	C₂³	1	2	yes	—
132	Q₈×D₁₈₁	—	4	2	no	—
133	C₂×D₇₂₄	—	4	2	no	—
134	C₂×D₇₂₄	—	4	4	no	—
135	C₂×D₇₂₄	C₂³	1	2	yes	—
136	C₂×D₇₂₄	C₂³	1	1	yes	characteristic
137	C₂×D₇₂₄	C₂³	1	1	yes	characteristic
138	C₂×D₇₂₄	C₂³	1	1	yes	characteristic
139	C₂×D₇₂₄	C₂³	1	2	yes	—
140	C₂×D₇₂₄	C₂³	1	1	yes	characteristic
141	C₂×D₇₂₄	C₂³	1	2	yes	—
142	C₂×D₇₂₄	C₂³	1	2	yes	—
143	C₂×D₇₂₄	C₂³	1	2	yes	—
144	C₂×D₇₂₄	C₂³	1	2	yes	—
145	C₂×D₇₂₄	C₂³	1	2	yes	—
146	C₂×D₇₂₄	C₂³	1	2	yes	—
147	C₂×D₇₂₄	C₂³	1	2	yes	—
148	C₂×C₂²⋊D₁₈₁	C₂³	1	1	yes	characteristic
149	C₂×C₂²⋊D₁₈₁	C₂³	1	1	yes	characteristic
150	C₂×C₂²⋊D₁₈₁	C₂³	1	2	yes	—
151	C₂×C₂²⋊D₁₈₁	C₂³	1	2	yes	—
152	C₂×C₂²⋊D₁₈₁	C₂³	1	2	yes	—
153	C₂×C₂²⋊D₁₈₁	C₂³	1	2	yes	—
154	C₂×C₂²⋊D₁₈₁	C₂³	1	2	yes	—
155	D₄×D₁₈₁	—	4	2	no	—
156	D₄×D₁₈₁	—	4	2	no	—
157	D₄×D₁₈₁	—	4	4	no	—
158	C₂×C₄×D₁₈₁	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₁₈₁	C₂³	1	1	yes	characteristic
160	C₂×C₄×D₁₈₁	C₂³	1	1	yes	characteristic
161	C₂×C₄×D₁₈₁	C₂³	1	1	yes	characteristic
162	C₂×C₄×D₁₈₁	C₂³	1	2	yes	—
163	C₂×C₄×D₁₈₁	C₂³	1	2	yes	—
164	C₂×C₄×D₁₈₁	C₂³	1	2	yes	—
165	C₂×C₄×D₁₈₁	C₂³	1	2	yes	—
166	C₂×C₄×D₁₈₁	C₂³	1	2	yes	—
167	C₂×C₄×D₁₈₁	C₂³	1	2	yes	—
168	C₄⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
169	C₄⋊Dic₁₈₁	C₂³	1	2	yes	—
170	C₄⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
171	#15668428	C₂³	1	1	yes	characteristic
172	#15668428	C₂³	1	1	yes	characteristic
173	#15668428	C₂³	1	1	yes	characteristic
174	#15668428	C₂³	1	1	yes	characteristic
175	#15668428	C₂³	1	1	yes	characteristic
176	#15668428	C₂³	1	2	yes	—
177	#15668428	C₂³	1	1	yes	characteristic
178	C₂²⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
179	C₂²⋊Dic₁₈₁	C₂³	1	2	yes	—
180	C₂²⋊Dic₁₈₁	C₂³	1	2	yes	—
181	C₂²⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
182	#15668426	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
190	#15668426	C₂³	1	1	yes	characteristic
191	#15668426	C₂³	1	1	yes	characteristic
192	#15668426	C₂³	1	2	yes	—
193	#15668426	C₂³	1	2	yes	—
194	#15668426	C₂³	1	2	yes	—
195	#15668426	C₂³	1	2	yes	—
196	#15668426	C₂³	1	2	yes	—
197	#15668426	C₂³	1	2	yes	—
198	#15668426	C₂³	1	2	yes	—
199	#15668426	C₂³	1	1	yes	characteristic
200	#15668426	C₂³	1	1	yes	characteristic
201	#15668426	C₂³	1	2	yes	—
202	#15668426	C₂³	1	2	yes	—
203	C₄×Dic₁₈₁	C₂³	1	1	yes	characteristic
204	C₄×Dic₁₈₁	C₂³	1	1	yes	characteristic
205	C₄×Dic₁₈₁	C₂³	1	1	yes	characteristic
206	C₄×Dic₁₈₁	C₂³	1	1	yes	characteristic
207	C₄×Dic₁₈₁	C₂³	1	2	yes	—
208	C₂×Q₈×C₁₈₁	C₂³	1	1	yes	characteristic
209	C₂×Q₈×C₁₈₁	C₂³	1	2	yes	—
210	C₂×D₄×C₁₈₁	C₂³	1	1	yes	characteristic
211	C₂×D₄×C₁₈₁	C₂³	1	2	yes	—
212	C₂²×C₄×C₁₈₁	C₂³	1	1	yes	characteristic
213	C₂²×C₄×C₁₈₁	C₂³	1	2	yes	—
214	C₄⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
215	C₄⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
216	C₄⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
217	C₄⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
218	C₄⋊C₄×C₁₈₁	C₂³	1	2	yes	—
219	C₄⋊C₄×C₁₈₁	C₂³	1	2	yes	—
220	C₄⋊C₄×C₁₈₁	C₂³	1	2	yes	—
221	C₂²⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
222	C₂²⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
223	C₂²⋊C₄×C₁₈₁	C₂³	1	2	yes	—
224	C₂²⋊C₄×C₁₈₁	C₂³	1	2	yes	—
225	C₂²⋊C₄×C₁₈₁	C₂³	1	2	yes	—
226	C₂²⋊C₄×C₁₈₁	C₂³	1	2	yes	—
227	C₂²⋊C₄×C₁₈₁	C₂³	1	2	yes	—
228	C₄²×C₁₈₁	C₂³	1	1	yes	characteristic
229	C₄²×C₁₈₁	C₂³	1	1	yes	characteristic
230	C₄²×C₁₈₁	C₂³	1	2	yes	—
231	C₂²×D₁₈₁	—	2	4	no	—
232	C₂²×D₁₈₁	—	4	2	no	—
233	C₂²×D₁₈₁	—	4	2	no	—
234	C₂²×D₁₈₁	—	4	2	no	—
235	C₂²×D₁₈₁	—	4	2	no	—
236	C₂²×D₁₈₁	—	4	2	no	—
237	C₂²×D₁₈₁	—	4	2	no	—
238	C₂²×D₁₈₁	—	4	2	no	—
239	C₂²×D₁₈₁	—	4	2	no	—
240	C₂²×D₁₈₁	C₂⁴	1	1	yes	characteristic
241	C₂²×D₁₈₁	C₂⁴	1	2	yes	—
242	C₂²×D₁₈₁	C₂⁴	1	2	yes	—
243	C₂²×D₁₈₁	C₂⁴	1	2	yes	—
244	C₂²×D₁₈₁	C₂⁴	1	1	yes	characteristic
245	Dic₃₆₂	—	2	2	no	—
246	Dic₃₆₂	—	4	2	no	—
247	Dic₃₆₂	—	4	1	no	—
248	D₇₂₄	—	2	4	no	—
249	D₇₂₄	—	2	2	no	—
250	D₇₂₄	—	2	4	no	—
251	D₇₂₄	—	2	2	no	—
252	D₇₂₄	—	2	2	no	—
253	D₇₂₄	—	2	2	no	—
254	D₇₂₄	—	4	2	no	—
255	D₇₂₄	—	4	2	no	—
256	D₇₂₄	—	4	2	no	—
257	D₇₂₄	—	4	2	no	—
258	D₇₂₄	—	4	2	no	—
259	D₇₂₄	—	4	2	no	—
260	D₇₂₄	—	4	2	no	—
261	C₂²⋊D₁₈₁	—	2	2	no	—
262	C₂²⋊D₁₈₁	—	4	2	no	—
263	C₂²⋊D₁₈₁	—	4	2	no	—
264	C₂²⋊D₁₈₁	—	4	2	no	—
265	C₂²⋊D₁₈₁	—	4	1	no	—
266	C₂²⋊D₁₈₁	—	4	2	no	—
267	C₂²⋊D₁₈₁	—	4	2	no	—
268	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
269	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
270	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
271	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
272	C₂×Dic₁₈₁	C₂⁴	1	2	yes	—
273	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
274	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
275	C₄×D₁₈₁	—	2	2	no	—
276	C₄×D₁₈₁	—	2	2	no	—
277	C₄×D₁₈₁	—	2	2	no	—
278	C₄×D₁₈₁	—	4	1	no	—
279	C₄×D₁₈₁	—	4	2	no	—
280	C₄×D₁₈₁	—	4	2	no	—
281	C₄×D₁₈₁	—	4	2	no	—
282	C₄×D₁₈₁	—	4	2	no	—
283	C₄×D₁₈₁	—	4	2	no	—
284	C₄×D₁₈₁	—	4	2	no	—
285	C₂³×C₁₈₁	C₂⁴	1	1	yes	characteristic
286	C₂³×C₁₈₁	C₂⁴	1	2	yes	—
287	Q₈×C₁₈₁	—	2	2	no	—
288	Q₈×C₁₈₁	—	4	2	no	—
289	D₄×C₁₈₁	—	2	2	no	—
290	D₄×C₁₈₁	—	4	2	no	—
291	C₂×C₄×C₁₈₁	—	2	2	no	—
292	C₂×C₄×C₁₈₁	—	4	2	no	—
293	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
294	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
295	C₂×C₄×C₁₈₁	C₂⁴	1	2	yes	—
296	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
297	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
298	C₂×C₄×C₁₈₁	C₂⁴	1	2	yes	—
299	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
300	C₂×C₄×C₁₈₁	C₂⁴	1	2	yes	—
301	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
302	C₂²×C₁₈₁	—	2	1	no	—
303	C₂²×C₁₈₁	—	2	2	no	—
304	C₂²×C₁₈₁	—	2	2	no	—
305	C₂²×C₁₈₁	—	2	1	no	—
306	C₂²×C₁₈₁	—	2	2	no	—
307	C₂²×C₁₈₁	—	2	1	no	—
308	C₂²×C₁₈₁	C₂⁵	1	1	yes	characteristic
309	C₂×D₁₈₁	—	2	1	no	—
310	C₂×D₁₈₁	—	2	1	no	—
311	C₂×D₁₈₁	—	2	1	no	—
312	C₂×D₁₈₁	—	2	2	no	—
313	C₂×D₁₈₁	—	2	2	no	—
314	C₂×D₁₈₁	—	2	2	no	—
315	C₂×D₁₈₁	—	2	2	no	—
316	C₂×D₁₈₁	—	2	2	no	—
317	C₂×D₁₈₁	—	2	2	no	—
318	C₂×D₁₈₁	—	2	1	no	—
319	C₂×D₁₈₁	—	2	2	no	—
320	C₂×D₁₈₁	—	2	1	no	—
321	C₂×D₁₈₁	—	2	2	no	—
322	C₂×D₁₈₁	—	2	2	no	—
323	C₂×D₁₈₁	—	8	4	no	—
324	C₂×D₁₈₁	—	8	4	no	—
325	C₂×D₁₈₁	—	8	4	no	—
326	C₂×D₁₈₁	H(5,𝔽₂)	1	2	yes	—
327	C₄×C₁₈₁	—	2	1	no	—
328	C₄×C₁₈₁	—	2	1	no	—
329	C₄×C₁₈₁	—	2	2	no	—
330	C₄×C₁₈₁	—	2	2	no	—
331	C₄×C₁₈₁	—	2	2	no	—
332	C₄×C₁₈₁	—	2	1	no	—
333	C₄×C₁₈₁	—	2	1	no	—
334	C₄×C₁₈₁	—	2	1	no	—
335	C₄×C₁₈₁	H(5,𝔽₂)	1	2	yes	—
336	Dic₁₈₁	—	2	1	no	—
337	Dic₁₈₁	—	2	1	no	—
338	Dic₁₈₁	—	2	1	no	—
339	Dic₁₈₁	—	2	1	no	—
340	Dic₁₈₁	—	2	2	no	—
341	Dic₁₈₁	—	2	1	no	—
342	Dic₁₈₁	—	2	1	no	—
343	C₂×C₁₈₁	—	4	2	no	—
344	C₂×C₁₈₁	—	4	1	no	—
345	C₂×C₁₈₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
346	C₂×C₁₈₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
347	C₂×C₁₈₁	#585	1	1	yes	characteristic
348	D₁₈₁	—	2	2	no	—
349	D₁₈₁	—	4	2	no	—
350	D₁₈₁	—	4	2	no	—
351	D₁₈₁	—	4	1	no	—
352	D₁₈₁	—	4	2	no	—
353	C₁₈₁	#3558	1	1	yes	characteristic, complemented, Sylow
354	#3558	—	181	1	no	maximal, Sylow
355	#562	—	181	2	no	—
356	H(3,𝔽₄)	—	181	2	no	—
357	#559	—	181	1	no	—
358	#559	—	181	1	no	—
359	#548	—	181	1	no	—
360	#548	—	181	1	no	—
361	#546	—	181	2	no	—
362	#546	—	181	2	no	—
363	#546	—	181	1	no	—
364	#546	—	181	1	no	—
365	D₄²	—	181	1	no	—
366	D₄²	—	181	1	no	—
367	#542	—	181	1	no	—
368	#542	D₁₈₁	1	1	yes	characteristic, complemented
369	#538	—	181	2	no	—
370	#538	—	181	2	no	—
371	#538	—	181	2	no	—
372	#535	—	181	1	no	—
373	#535	—	181	1	no	—
374	#534	—	181	2	no	—
375	#532	—	181	1	no	—
376	#529	—	181	1	no	—
377	C₂×#124	—	181	1	no	—
378	C₂×#41	—	181	2	no	—
379	C₂×#41	—	181	1	no	—
380	C₂×#41	—	181	1	no	—
381	C₂²×Q₈	—	181	1	no	—
382	C₂²×D₄	—	181	1	no	—
383	C₂²×D₄	—	181	2	no	—
384	C₂²×D₄	—	181	1	no	—
385	C₂²×D₄	—	181	2	no	—
386	C₂²×D₄	—	181	1	no	—
387	C₄⋊Q₈	C₂×D₁₈₁	1	1	yes	characteristic, complemented
388	#127	—	181	1	no	—
389	#127	—	181	1	no	—
390	#127	—	181	1	no	—
391	#126	—	181	1	no	—
392	#126	—	181	2	no	—
393	#126	—	181	1	no	—
394	#126	C₂×D₁₈₁	1	2	yes	complemented
395	#125	—	181	1	no	—
396	#124	—	181	1	no	—
397	#124	—	181	2	no	—
398	#124	—	181	1	no	—
399	#124	—	181	2	no	—
400	#124	—	181	1	no	—
401	#124	—	181	2	no	—
402	#124	—	181	2	no	—
403	#124	—	181	1	no	—
404	#124	—	181	2	no	—
405	#124	—	181	2	no	—
406	#124	—	181	1	no	—
407	#124	—	181	1	no	—
408	#124	—	181	2	no	—
409	#124	—	181	2	no	—
410	#124	C₂×D₁₈₁	1	1	yes	characteristic, complemented
411	#124	C₂×D₁₈₁	1	2	yes	complemented
412	#123	—	181	2	no	—
413	#123	—	181	1	no	—
414	#123	—	181	2	no	—
415	#123	—	181	2	no	—
416	#123	—	181	2	no	—
417	#123	—	181	2	no	—
418	#123	—	181	1	no	—
419	#123	—	181	2	no	—
420	#123	—	181	2	no	—
421	#123	C₂×D₁₈₁	1	2	yes	complemented
422	C₂²⋊Q₈	—	181	2	no	—
423	C₂²⋊Q₈	—	181	1	no	—
424	C₂²⋊Q₈	—	181	2	no	—
425	C₂²⋊Q₈	—	181	2	no	—
426	C₂²⋊Q₈	—	181	1	no	—
427	C₂²⋊Q₈	C₂×D₁₈₁	1	1	yes	characteristic, complemented
428	C₂²⋊Q₈	C₂×D₁₈₁	1	2	yes	complemented
429	#121	—	181	2	no	—
430	#121	—	181	2	no	—
431	#121	—	181	2	no	—
432	#121	—	181	1	no	—
433	#121	—	181	1	no	—
434	#121	—	181	2	no	—
435	#121	—	181	2	no	—
436	#121	—	181	2	no	—
437	#121	—	181	2	no	—
438	#121	—	181	1	no	—
439	#121	—	181	1	no	—
440	#121	—	181	2	no	—
441	#121	—	181	2	no	—
442	#121	—	181	2	no	—
443	#121	—	181	2	no	—
444	#121	C₂×D₁₈₁	1	1	yes	characteristic
445	#120	—	181	2	no	—
446	#120	—	181	2	no	—
447	#120	—	181	2	no	—
448	#120	—	181	2	no	—
449	#120	—	181	2	no	—
450	#120	—	181	2	no	—
451	#120	—	181	2	no	—
452	#120	—	181	2	no	—
453	#120	—	181	2	no	—
454	#120	—	181	2	no	—
455	C₄×Q₈	—	181	1	no	—
456	C₄×Q₈	—	181	1	no	—
457	C₄×Q₈	C₂×D₁₈₁	1	1	yes	characteristic, complemented
458	C₄×D₄	—	181	1	no	—
459	C₄×D₄	—	181	1	no	—
460	C₄×D₄	—	181	2	no	—
461	C₄×D₄	—	181	2	no	—
462	C₄×D₄	—	181	1	no	—
463	C₄×D₄	—	181	1	no	—
464	C₄×D₄	—	181	2	no	—
465	C₄×D₄	—	181	1	no	—
466	C₄×D₄	—	181	1	no	—
467	C₄×D₄	—	181	2	no	—
468	C₄×D₄	—	181	2	no	—
469	C₄×D₄	C₂×D₁₈₁	1	1	yes	characteristic, complemented
470	#117	—	181	1	no	—
471	#117	C₂×D₁₈₁	1	1	yes	characteristic, complemented
472	C₂×C₂²⋊C₄	—	181	2	no	—
473	C₂×C₂²⋊C₄	—	181	2	no	—
474	C₂×C₂²⋊C₄	—	181	2	no	—
475	C₂×C₂²⋊C₄	—	181	2	no	—
476	C₂×C₄²	—	181	1	no	—
477	C₂⁴	—	181	2	no	—
478	C₂⁴	—	181	2	no	—
479	C₂⁴	—	181	2	no	—
480	#41	—	724	2	no	—
481	#41	—	724	4	no	—
482	#41	—	724	2	no	—
483	C₂×Q₈	—	181	1	no	—
484	C₂×Q₈	—	181	1	no	—
485	C₂×Q₈	—	181	2	no	—
486	C₂×Q₈	—	724	2	no	—
487	C₂×Q₈	C₂²×D₁₈₁	1	1	yes	characteristic
488	C₂×Q₈	C₂²×D₁₈₁	1	2	yes	—
489	C₂×D₄	—	181	1	no	—
490	C₂×D₄	—	181	1	no	—
491	C₂×D₄	—	181	2	no	—
492	C₂×D₄	—	181	2	no	—
493	C₂×D₄	—	181	2	no	—
494	C₂×D₄	—	181	2	no	—
495	C₂×D₄	—	181	2	no	—
496	C₂×D₄	—	181	2	no	—
497	C₂×D₄	—	181	2	no	—
498	C₂×D₄	—	181	1	no	—
499	C₂×D₄	—	181	1	no	—
500	C₂×D₄	—	181	1	no	—
501	C₂×D₄	—	181	1	no	—
502	C₂×D₄	—	181	2	no	—
503	C₂×D₄	—	181	2	no	—
504	C₂×D₄	—	181	2	no	—
505	C₂×D₄	—	181	2	no	—
506	C₂×D₄	—	181	2	no	—
507	C₂×D₄	—	181	2	no	—
508	C₂×D₄	—	181	2	no	—
509	C₂×D₄	—	724	2	no	—
510	C₂×D₄	—	724	4	no	—
511	C₂×D₄	—	724	2	no	—
512	C₂×D₄	—	724	2	no	—
513	C₂×D₄	—	724	4	no	—
514	C₂×D₄	C₂²×D₁₈₁	1	1	yes	characteristic
515	C₂×D₄	C₂²×D₁₈₁	1	2	yes	—
516	C₂²×C₄	—	181	1	no	—
517	C₂²×C₄	—	181	1	no	—
518	C₂²×C₄	—	181	1	no	—
519	C₂²×C₄	—	181	1	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	C₂²×D₁₈₁	1	1	yes	characteristic
527	C₂²×C₄	C₂²×D₁₈₁	1	2	yes	—
528	C₄⋊C₄	—	181	1	no	—
529	C₄⋊C₄	—	181	1	no	—
530	C₄⋊C₄	—	181	1	no	—
531	C₄⋊C₄	—	181	1	no	—
532	C₄⋊C₄	—	181	1	no	—
533	C₄⋊C₄	—	181	1	no	—
534	C₄⋊C₄	—	181	2	no	—
535	C₄⋊C₄	—	181	1	no	—
536	C₄⋊C₄	—	181	2	no	—
537	C₄⋊C₄	—	181	1	no	—
538	C₄⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
539	C₄⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
540	C₄⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
541	C₄⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
542	C₄⋊C₄	C₂²×D₁₈₁	1	2	yes	—
543	C₄⋊C₄	C₂²×D₁₈₁	1	2	yes	—
544	C₄⋊C₄	C₂²×D₁₈₁	1	2	yes	—
545	C₂²⋊C₄	—	181	1	no	—
546	C₂²⋊C₄	—	181	2	no	—
547	C₂²⋊C₄	—	181	2	no	—
548	C₂²⋊C₄	—	181	1	no	—
549	C₂²⋊C₄	—	181	1	no	—
550	C₂²⋊C₄	—	181	2	no	—
551	C₂²⋊C₄	—	181	2	no	—
552	C₂²⋊C₄	—	181	2	no	—
553	C₂²⋊C₄	—	181	2	no	—
554	C₂²⋊C₄	—	181	2	no	—
555	C₂²⋊C₄	—	181	2	no	—
556	C₂²⋊C₄	—	181	1	no	—
557	C₂²⋊C₄	—	181	1	no	—
558	C₂²⋊C₄	—	181	1	no	—
559	C₂²⋊C₄	—	181	1	no	—
560	C₂²⋊C₄	—	181	2	no	—
561	C₂²⋊C₄	—	181	1	no	—
562	C₂²⋊C₄	—	181	2	no	—
563	C₂²⋊C₄	—	181	2	no	—
564	C₂²⋊C₄	—	181	2	no	—
565	C₂²⋊C₄	—	181	2	no	—
566	C₂²⋊C₄	—	181	2	no	—
567	C₂²⋊C₄	—	181	2	no	—
568	C₂²⋊C₄	—	181	2	no	—
569	C₂²⋊C₄	—	181	2	no	—
570	C₂²⋊C₄	C₂²×D₁₈₁	1	2	yes	—
571	C₂²⋊C₄	C₂²×D₁₈₁	1	2	yes	—
572	C₂²⋊C₄	C₂²×D₁₈₁	1	2	yes	—
573	C₂²⋊C₄	C₂²×D₁₈₁	1	2	yes	—
574	C₂²⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
575	C₂²⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
576	C₂²⋊C₄	C₂²×D₁₈₁	1	2	yes	—
577	C₄²	—	181	1	no	—
578	C₄²	—	181	1	no	—
579	C₄²	—	181	1	no	—
580	C₄²	—	181	1	no	—
581	C₄²	—	181	2	no	—
582	C₄²	C₂²×D₁₈₁	1	1	yes	characteristic
583	C₄²	C₂²×D₁₈₁	1	1	yes	characteristic
584	C₄²	C₂²×D₁₈₁	1	2	yes	—
585	C₂³	—	362	4	no	—
586	C₂³	—	181	2	no	—
587	C₂³	—	181	1	no	—
588	C₂³	—	181	2	no	—
589	C₂³	—	181	2	no	—
590	C₂³	—	181	1	no	—
591	C₂³	—	724	2	no	—
592	C₂³	—	724	2	no	—
593	C₂³	—	724	2	no	—
594	C₂³	—	724	2	no	—
595	C₂³	—	724	2	no	—
596	C₂³	—	724	2	no	—
597	C₂³	—	724	2	no	—
598	C₂³	—	724	2	no	—
599	C₂³	C₂³×D₁₈₁	1	2	yes	—
600	C₂³	C₂³×D₁₈₁	1	1	yes	characteristic
601	Q₈	—	2	2	no	—
602	Q₈	—	4	2	no	—
603	Q₈	—	362	2	no	—
604	Q₈	—	724	2	no	—
605	Q₈	—	724	1	no	—
606	D₄	—	2	2	no	—
607	D₄	—	4	2	no	—
608	D₄	—	362	2	no	—
609	D₄	—	362	4	no	—
610	D₄	—	362	4	no	—
611	D₄	—	362	2	no	—
612	D₄	—	362	2	no	—
613	D₄	—	362	2	no	—
614	D₄	—	362	2	no	—
615	D₄	—	724	2	no	—
616	D₄	—	724	2	no	—
617	D₄	—	724	2	no	—
618	D₄	—	724	2	no	—
619	D₄	—	724	2	no	—
620	D₄	—	724	2	no	—
621	D₄	—	724	2	no	—
622	D₄	—	724	2	no	—
623	D₄	—	724	2	no	—
624	D₄	—	724	2	no	—
625	D₄	—	724	2	no	—
626	D₄	—	724	1	no	—
627	D₄	—	724	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	4	2	no	—
630	C₂×C₄	—	362	2	no	—
631	C₂×C₄	—	362	2	no	—
632	C₂×C₄	—	362	2	no	—
633	C₂×C₄	—	181	1	no	—
634	C₂×C₄	—	181	1	no	—
635	C₂×C₄	—	181	1	no	—
636	C₂×C₄	—	181	1	no	—
637	C₂×C₄	—	181	2	no	—
638	C₂×C₄	—	181	1	no	—
639	C₂×C₄	—	181	1	no	—
640	C₂×C₄	—	724	2	no	—
641	C₂×C₄	—	724	2	no	—
642	C₂×C₄	—	724	2	no	—
643	C₂×C₄	—	724	2	no	—
644	C₂×C₄	—	724	2	no	—
645	C₂×C₄	—	724	2	no	—
646	C₂×C₄	—	724	1	no	—
647	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
648	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
649	C₂×C₄	C₂³×D₁₈₁	1	2	yes	—
650	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
651	C₂×C₄	C₂³×D₁₈₁	1	2	yes	—
652	C₂×C₄	C₂³×D₁₈₁	1	2	yes	—
653	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
654	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
655	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
656	C₂²	—	2	2	no	—
657	C₂²	—	2	1	no	—
658	C₂²	—	2	2	no	—
659	C₂²	—	2	1	no	—
660	C₂²	—	2	1	no	—
661	C₂²	—	2	2	no	—
662	C₂²	—	362	1	no	—
663	C₂²	—	362	1	no	—
664	C₂²	—	362	2	no	—
665	C₂²	—	362	2	no	—
666	C₂²	—	362	2	no	—
667	C₂²	—	362	1	no	—
668	C₂²	—	362	2	no	—
669	C₂²	—	362	2	no	—
670	C₂²	—	362	2	no	—
671	C₂²	—	362	1	no	—
672	C₂²	—	362	1	no	—
673	C₂²	—	362	2	no	—
674	C₂²	—	362	2	no	—
675	C₂²	—	362	2	no	—
676	C₂²	—	1448	4	no	—
677	C₂²	—	1448	4	no	—
678	C₂²	—	1448	4	no	—
679	C₂²	—	181	2	no	—
680	C₂²	C₂⁴×D₁₈₁	1	1	yes	characteristic
681	C₄	—	2	1	no	—
682	C₄	—	2	1	no	—
683	C₄	—	2	1	no	—
684	C₄	—	2	2	no	—
685	C₄	—	2	1	no	—
686	C₄	—	2	2	no	—
687	C₄	—	2	1	no	—
688	C₄	—	2	2	no	—
689	C₄	—	362	1	no	—
690	C₄	—	362	1	no	—
691	C₄	—	362	1	no	—
692	C₄	—	362	1	no	—
693	C₄	—	362	1	no	—
694	C₄	—	362	1	no	—
695	C₄	—	362	2	no	—
696	C₄	#19153862	1	2	yes	—
697	C₂	—	4	2	no	—
698	C₂	—	4	1	no	—
699	C₂	—	362	2	no	—
700	C₂	—	724	2	no	—
701	C₂	—	724	1	no	—
702	C₂	—	724	2	no	—
703	C₂	—	724	2	no	—
704	C₂	H(5,𝔽₂)×D₁₈₁	1	1	yes	characteristic
705	C₂	C₂×#19153862	1	1	yes	characteristic
706	C₂	#26042116	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₈₁
commutator, socle, cosocle	C₂²×C₁₈₁	C₂⁵
Fitting	#542×C₁₈₁	C₂
hypercenter	#542	D₁₈₁
hypocenter	C₁₈₁	#3558
LCS	G ▷ C₂²×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂² ◁ #542

Complements

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

N	H ≅ G/N	type
1. #26042025	C₂	semidirect
2. #26042021	C₂	semidirect
3. #26042014	C₂	semidirect
4. #26042012	C₂	semidirect
5. #26041941	C₂	semidirect
6. #26041939	C₂	semidirect
7. #26041926	C₂	semidirect
8. #26041922	C₂	semidirect
9. #26041920	C₂	semidirect
10. #26041920	C₂	semidirect
11. D₄×D₇₂₄	C₂	semidirect
12. #26041913	C₂	semidirect
13. #26041903	C₂	semidirect
14. #26041868	C₂	semidirect
15. #26041868	C₂	semidirect
16. #26041865	C₂	semidirect
17. #26041848	C₂	semidirect
18. #26041847	C₂	semidirect
19. #26041840	C₂	semidirect
20. #26041830	C₂	semidirect
21. #26041807	C₂	semidirect
22. #124×D₁₈₁	C₂	semidirect
23. #542×C₁₈₁	C₂	semidirect
24. C₂×#15668450	C₂²	semidirect
25. C₂×#15668450	C₂²	semidirect
26. C₂×#15668449	C₂²	semidirect
27. C₂×Q₈×D₁₈₁	C₂²	semidirect
28. C₂²×D₇₂₄	C₂²	semidirect
29. C₂²×D₇₂₄	C₂²	semidirect
31. C₂×D₄×D₁₈₁	C₂²	semidirect
32. C₂×D₄×D₁₈₁	C₂²	semidirect
34. #19153813	C₂²	semidirect
36. #19153811	C₂²	semidirect
37. #19153811	C₂²	semidirect
38. #19153809	C₂²	semidirect
39. #19153806	C₂²	semidirect
40. #19153805	C₂²	semidirect
41. #19153805	C₂²	semidirect
42. #19153805	C₂²	semidirect
43. #19153805	C₂²	semidirect
44. #19153804	C₂²	semidirect
45. #19153804	C₂²	semidirect
46. #19153804	C₂²	semidirect
47. #19153804	C₂²	semidirect
48. #19153803	C₂²	semidirect
49. #19153802	C₂²	semidirect
50. #19153802	C₂²	semidirect
51. #19153802	C₂²	semidirect
52. #19153802	C₂²	semidirect
53. #19153802	C₂²	semidirect
54. #19153801	C₂²	semidirect
55. #19153801	C₂²	semidirect
56. #19153801	C₂²	semidirect
57. #19153801	C₂²	semidirect
58. #19153801	C₂²	semidirect
59. #19153799	C₂²	semidirect
60. #19153798	C₂²	semidirect
61. #19153798	C₂²	semidirect
62. #19153798	C₂²	semidirect
63. #19153796	C₂²	semidirect
64. #19153796	C₂²	semidirect
65. #19153794	C₂²	semidirect
66. #19153794	C₂²	semidirect
67. #19153792	C₂²	semidirect
69. #19153791	C₂²	semidirect
70. #19153791	C₂²	semidirect
71. #19153791	C₂²	semidirect
72. #19153791	C₂²	semidirect
73. #19153791	C₂²	semidirect
74. #19153791	C₂²	semidirect
75. #19153791	C₂²	semidirect
76. #19153790	C₂²	semidirect
78. #19153789	C₂²	semidirect
79. #19153789	C₂²	semidirect
80. #19153789	C₂²	semidirect
81. #19153789	C₂²	semidirect
82. #19153787	C₂²	semidirect
83. #19153786	C₂²	semidirect
84. #19153786	C₂²	semidirect
85. #19153786	C₂²	semidirect
86. #19153786	C₂²	semidirect
87. #19153786	C₂²	semidirect
88. #19153786	C₂²	semidirect
89. #19153786	C₂²	semidirect
90. #19153786	C₂²	semidirect
91. #19153784	C₂²	semidirect
92. #19153784	C₂²	semidirect
93. C₄×Dic₃₆₂	C₂²	semidirect
94. #19153781	C₂²	semidirect
95. C₄×D₇₂₄	C₂²	semidirect
96. C₄×D₇₂₄	C₂²	semidirect
97. C₄×D₇₂₄	C₂²	semidirect
98. #19153778	C₂²	semidirect
99. #19153778	C₂²	semidirect
100. #19153778	C₂²	semidirect
101. #19153778	C₂²	semidirect
102. #19153778	C₂²	semidirect
103. C₄×C₂²⋊D₁₈₁	C₂²	semidirect
104. C₄×C₂²⋊D₁₈₁	C₂²	semidirect
105. C₄×C₂²⋊D₁₈₁	C₂²	semidirect
106. #19153773	C₂²	semidirect
107. C₂²⋊C₄×D₁₈₁	C₂²	semidirect
108. C₂²⋊C₄×D₁₈₁	C₂²	semidirect
109. C₂²⋊C₄×D₁₈₁	C₂²	semidirect
110. C₂²⋊C₄×D₁₈₁	C₂²	semidirect
111. C₄²×D₁₈₁	C₂²	semidirect
112. C₄⋊Q₈×C₁₈₁	C₂²	semidirect
113. #126×C₁₈₁	C₂²	semidirect
114. #124×C₁₈₁	C₂²	semidirect
115. #124×C₁₈₁	C₂²	semidirect
116. #123×C₁₈₁	C₂²	semidirect
117. C₂²⋊Q₈×C₁₈₁	C₂²	semidirect
118. C₂²⋊Q₈×C₁₈₁	C₂²	semidirect
120. C₄×Q₈×C₁₈₁	C₂²	semidirect
121. C₄×D₄×C₁₈₁	C₂²	semidirect
122. #117×C₁₈₁	C₂²	semidirect
353. C₁₈₁	#3558	semidirect
368. #542	D₁₈₁	semidirect
387. C₄⋊Q₈	C₂×D₁₈₁	semidirect
394. #126	C₂×D₁₈₁	semidirect
410. #124	C₂×D₁₈₁	semidirect
411. #124	C₂×D₁₈₁	semidirect
421. #123	C₂×D₁₈₁	semidirect
427. C₂²⋊Q₈	C₂×D₁₈₁	semidirect
428. C₂²⋊Q₈	C₂×D₁₈₁	semidirect
457. C₄×Q₈	C₂×D₁₈₁	semidirect
469. C₄×D₄	C₂×D₁₈₁	semidirect
471. #117	C₂×D₁₈₁	semidirect

Maximal subgroups

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

subgroup	index
#26042025	2
#26042021	2
#26042014	2
#26042012	2
#26041941	2
#26041939	2
#26041926	2
#26041922	2
#26041920	2
D₄×D₇₂₄	2
#26041913	2
#26041903	2
#26041868	2
#26041865	2
#26041848	2
#26041847	2
#26041840	2
#26041830	2
#26041807	2
#124×D₁₈₁	2
#542×C₁₈₁	2
#3558	181