Subgroups — #37547561

Order 23168.

1152 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26041982	C₂	1	2	yes	maximal, complemented
2	#26041982	C₂	1	1	yes	maximal, characteristic, complemented
3	#26041980	C₂	1	2	yes	maximal, complemented
4	#26041973	C₂	1	1	yes	maximal, characteristic, complemented
5	#26041964	C₂	1	1	yes	maximal, characteristic, complemented
6	#26041953	C₂	1	2	yes	maximal, complemented
7	#26041952	C₂	1	2	yes	maximal, complemented
8	#26041941	C₂	1	1	yes	maximal, characteristic, complemented
9	#26041939	C₂	1	1	yes	maximal, characteristic, complemented
10	#26041925	C₂	1	1	yes	maximal, characteristic, complemented
11	#26041920	C₂	1	1	yes	maximal, characteristic, complemented
12	#26041877	C₂	1	2	yes	maximal, complemented
13	#26041868	C₂	1	2	yes	maximal, complemented
14	#26041840	C₂	1	2	yes	maximal, complemented
15	#26041816	C₂	1	1	yes	maximal, characteristic, complemented
16	#26041814	C₂	1	1	yes	maximal, characteristic, complemented
17	#26041792	C₂	1	1	yes	maximal, characteristic, complemented
18	#26041791	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²⋊Q₈×D₁₈₁	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#19153791	C₂	1	1	yes	maximal, characteristic, complemented
21	#26041753	C₂	1	2	yes	maximal, complemented
22	C₄×D₄×D₁₈₁	C₂	1	1	yes	maximal, characteristic, complemented
23	#552×C₁₈₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#15668450	C₂²	1	1	yes	characteristic, complemented
25	C₂×#15668449	C₂²	1	1	yes	characteristic, complemented
26	C₂×Q₈×D₁₈₁	C₂²	1	1	yes	characteristic, complemented
27	C₂²×D₇₂₄	C₂²	1	2	yes	—
28	C₂²×D₇₂₄	C₂²	1	1	yes	characteristic, complemented
29	C₂×D₄×D₁₈₁	C₂²	1	1	yes	characteristic
30	C₂²×C₄×D₁₈₁	C₂²	1	1	yes	characteristic
31	C₂²×C₄×D₁₈₁	C₂²	1	1	yes	characteristic, complemented
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	#19153810	C₂²	1	2	yes	complemented
37	#19153807	C₂²	1	1	yes	characteristic, complemented
38	#19153806	C₂²	1	2	yes	complemented
39	#19153805	C₂²	1	1	yes	characteristic, complemented
40	#19153804	C₂²	1	2	yes	complemented
41	#19153804	C₂²	1	1	yes	characteristic, complemented
42	#19153802	C₂²	1	2	yes	complemented
43	#19153801	C₂²	1	2	yes	complemented
44	#19153801	C₂²	1	2	yes	complemented
45	#19153801	C₂²	1	2	yes	complemented
46	#19153801	C₂²	1	2	yes	complemented
47	#19153801	C₂²	1	2	yes	complemented
48	#19153801	C₂²	1	2	yes	complemented
49	#19153800	C₂²	1	2	yes	complemented
50	#19153799	C₂²	1	2	yes	—
51	#19153798	C₂²	1	2	yes	complemented
52	#19153796	C₂²	1	2	yes	complemented
53	#19153796	C₂²	1	1	yes	characteristic, complemented
54	#19153796	C₂²	1	1	yes	characteristic, complemented
55	#19153795	C₂²	1	1	yes	characteristic, complemented
56	#19153794	C₂²	1	2	yes	complemented
57	#19153794	C₂²	1	2	yes	complemented
58	#19153793	C₂²	1	2	yes	complemented
59	#19153792	C₂²	1	1	yes	characteristic, complemented
60	#19153791	C₂²	1	2	yes	—
61	#19153791	C₂²	1	1	yes	characteristic
62	#19153791	C₂²	1	1	yes	characteristic
63	#19153791	C₂²	1	2	yes	complemented
64	#19153791	C₂²	1	1	yes	characteristic, complemented
65	#19153791	C₂²	1	1	yes	characteristic, complemented
66	#19153791	C₂²	1	1	yes	characteristic, complemented
67	#19153791	C₂²	1	2	yes	complemented
68	#19153791	C₂²	1	2	yes	complemented
69	#19153791	C₂²	1	2	yes	complemented
70	#19153790	C₂²	1	1	yes	characteristic, complemented
71	#19153789	C₂²	1	2	yes	complemented
72	#19153789	C₂²	1	2	yes	complemented
73	#19153789	C₂²	1	2	yes	complemented
74	#19153786	C₂²	1	2	yes	—
75	#19153786	C₂²	1	2	yes	complemented
76	#19153786	C₂²	1	2	yes	complemented
77	#19153784	C₂²	1	2	yes	—
78	#19153781	C₂²	1	1	yes	characteristic, complemented
79	C₄×D₇₂₄	C₂²	1	2	yes	complemented
80	C₄×D₇₂₄	C₂²	1	2	yes	complemented
81	C₄×D₇₂₄	C₂²	1	1	yes	characteristic, complemented
82	C₄×D₇₂₄	C₂²	1	2	yes	complemented
83	C₄×D₇₂₄	C₂²	1	1	yes	characteristic, complemented
84	C₄×D₇₂₄	C₂²	1	2	yes	complemented
85	C₄×D₇₂₄	C₂²	1	2	yes	complemented
86	D₄×Dic₁₈₁	C₂²	1	1	yes	characteristic
87	#19153778	C₂²	1	2	yes	complemented
88	#19153778	C₂²	1	2	yes	complemented
89	#19153778	C₂²	1	1	yes	characteristic, complemented
90	#19153778	C₂²	1	2	yes	complemented
91	#19153778	C₂²	1	2	yes	complemented
92	#19153778	C₂²	1	1	yes	characteristic, complemented
93	C₄×C₂²⋊D₁₈₁	C₂²	1	1	yes	characteristic
94	C₄×C₂²⋊D₁₈₁	C₂²	1	1	yes	characteristic, complemented
95	#19153776	C₂²	1	1	yes	characteristic
96	#19153776	C₂²	1	2	yes	complemented
97	#19153776	C₂²	1	1	yes	characteristic, complemented
98	#19153775	C₂²	1	2	yes	complemented
99	#19153774	C₂²	1	2	yes	complemented
100	#19153774	C₂²	1	1	yes	characteristic, complemented
101	#19153773	C₂²	1	2	yes	complemented
102	C₄⋊C₄×D₁₈₁	C₂²	1	1	yes	characteristic, complemented
103	C₄⋊C₄×D₁₈₁	C₂²	1	1	yes	characteristic, complemented
104	C₄⋊C₄×D₁₈₁	C₂²	1	2	yes	complemented
105	C₂×#15668426	C₂²	1	2	yes	complemented
106	C₂²⋊C₄×D₁₈₁	C₂²	1	1	yes	characteristic
107	C₂²⋊C₄×D₁₈₁	C₂²	1	2	yes	—
108	C₂²⋊C₄×D₁₈₁	C₂²	1	1	yes	characteristic, 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	#126×C₁₈₁	C₂²	1	2	yes	complemented
113	#125×C₁₈₁	C₂²	1	2	yes	complemented
114	#125×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
115	#123×C₁₈₁	C₂²	1	2	yes	—
116	C₂²⋊Q₈×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
117	C₂²⋊Q₈×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
118	C₄×Q₈×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₄×C₁₈₁	C₂²	1	1	yes	characteristic
120	#117×C₁₈₁	C₂²	1	2	yes	complemented
121	#117×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₄⋊C₄×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₈₁	C₂³	1	2	yes	—
124	C₂³×D₁₈₁	C₂³	1	1	yes	characteristic
125	C₂³×D₁₈₁	C₂³	1	1	yes	characteristic
126	#15668450	—	4	2	no	—
127	#15668449	—	4	2	no	—
128	C₂×Dic₃₆₂	C₂³	1	1	yes	characteristic
129	C₂×Dic₃₆₂	C₂³	1	2	yes	—
130	Q₈×D₁₈₁	—	4	2	no	—
131	C₂×D₇₂₄	—	2	8	no	—
132	C₂×D₇₂₄	—	4	2	no	—
133	C₂×D₇₂₄	C₂³	1	2	yes	—
134	C₂×D₇₂₄	C₂³	1	2	yes	—
135	C₂×D₇₂₄	C₂³	1	1	yes	characteristic
136	C₂×D₇₂₄	C₂³	1	1	yes	characteristic
137	C₂×D₇₂₄	C₂³	1	2	yes	—
138	C₂×D₇₂₄	C₂³	1	2	yes	—
139	C₂×D₇₂₄	C₂³	1	1	yes	characteristic
140	C₂×D₇₂₄	C₂³	1	2	yes	—
141	C₂×D₇₂₄	C₂³	1	2	yes	—
142	C₂×D₇₂₄	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₁₈₁	C₂³	1	1	yes	characteristic
144	C₂×C₂²⋊D₁₈₁	C₂³	1	1	yes	characteristic
145	C₂×C₂²⋊D₁₈₁	C₂³	1	2	yes	—
146	C₂×C₂²⋊D₁₈₁	C₂³	1	2	yes	—
147	D₄×D₁₈₁	—	2	4	no	—
148	C₂²×Dic₁₈₁	C₂³	1	1	yes	characteristic
149	C₂²×Dic₁₈₁	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₁₈₁	—	4	2	no	—
151	C₂×C₄×D₁₈₁	—	4	2	no	—
152	C₂×C₄×D₁₈₁	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₁₈₁	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₁₈₁	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₁₈₁	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₁₈₁	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₁₈₁	C₂³	1	2	yes	—
158	C₂×C₄×D₁₈₁	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₁₈₁	C₂³	1	2	yes	—
160	C₂×C₄×D₁₈₁	C₂³	1	1	yes	characteristic
161	C₂×C₄×D₁₈₁	C₂³	1	2	yes	—
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	1	yes	characteristic
166	C₂×C₄×D₁₈₁	C₂³	1	1	yes	characteristic
167	C₄⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
168	C₄⋊Dic₁₈₁	C₂³	1	2	yes	—
169	C₄⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
170	C₄⋊Dic₁₈₁	C₂³	1	2	yes	—
171	C₄⋊Dic₁₈₁	C₂³	1	2	yes	—
172	#15668428	C₂³	1	2	yes	—
173	#15668428	C₂³	1	1	yes	characteristic
174	#15668428	C₂³	1	1	yes	characteristic
175	#15668428	C₂³	1	2	yes	—
176	#15668428	C₂³	1	2	yes	—
177	#15668428	C₂³	1	2	yes	—
178	#15668428	C₂³	1	2	yes	—
179	C₂²⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
184	#15668426	C₂³	1	2	yes	—
185	#15668426	C₂³	1	2	yes	—
186	#15668426	C₂³	1	1	yes	characteristic
187	#15668426	C₂³	1	1	yes	characteristic
188	#15668426	C₂³	1	2	yes	—
189	#15668426	C₂³	1	2	yes	—
190	#15668426	C₂³	1	2	yes	—
191	#15668426	C₂³	1	2	yes	—
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	2	yes	—
200	#15668426	C₂³	1	2	yes	—
201	#15668426	C₂³	1	2	yes	—
202	C₄×Dic₁₈₁	C₂³	1	1	yes	characteristic
203	C₄×Dic₁₈₁	C₂³	1	1	yes	characteristic
204	C₄×Dic₁₈₁	C₂³	1	1	yes	characteristic
205	C₄×Dic₁₈₁	C₂³	1	2	yes	—
206	C₄×Dic₁₈₁	C₂³	1	2	yes	—
207	C₂×Q₈×C₁₈₁	C₂³	1	1	yes	characteristic
208	C₂×D₄×C₁₈₁	C₂³	1	1	yes	characteristic
209	C₂²×C₄×C₁₈₁	C₂³	1	2	yes	—
210	C₂²×C₄×C₁₈₁	C₂³	1	1	yes	characteristic
211	C₂²×C₄×C₁₈₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
216	C₄⋊C₄×C₁₈₁	C₂³	1	2	yes	—
217	C₄⋊C₄×C₁₈₁	C₂³	1	2	yes	—
218	C₄⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
219	C₄⋊C₄×C₁₈₁	C₂³	1	2	yes	—
220	C₄⋊C₄×C₁₈₁	C₂³	1	2	yes	—
221	C₄⋊C₄×C₁₈₁	C₂³	1	2	yes	—
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	1	yes	characteristic
226	C₂²⋊C₄×C₁₈₁	C₂³	1	2	yes	—
227	C₄²×C₁₈₁	C₂³	1	2	yes	—
228	C₄²×C₁₈₁	C₂³	1	2	yes	—
229	C₄²×C₁₈₁	C₂³	1	1	yes	characteristic
230	C₂²×D₁₈₁	—	2	4	no	—
231	C₂²×D₁₈₁	—	2	2	no	—
232	C₂²×D₁₈₁	—	4	1	no	—
233	C₂²×D₁₈₁	—	4	1	no	—
234	C₂²×D₁₈₁	—	4	1	no	—
235	C₂²×D₁₈₁	—	4	1	no	—
236	C₂²×D₁₈₁	—	4	2	no	—
237	C₂²×D₁₈₁	—	4	2	no	—
238	C₂²×D₁₈₁	#41	1	4	yes	complemented
239	C₂²×D₁₈₁	C₂⁴	1	1	yes	characteristic
240	C₂²×D₁₈₁	C₂⁴	1	2	yes	—
241	C₂²×D₁₈₁	C₂⁴	1	2	yes	—
242	C₂²×D₁₈₁	C₂⁴	1	1	yes	characteristic
243	C₂²×D₁₈₁	C₂⁴	1	1	yes	characteristic
244	Dic₃₆₂	—	2	2	no	—
245	Dic₃₆₂	—	4	2	no	—
246	D₇₂₄	—	2	2	no	—
247	D₇₂₄	—	2	4	no	—
248	D₇₂₄	—	2	4	no	—
249	D₇₂₄	—	2	4	no	—
250	D₇₂₄	—	2	4	no	—
251	D₇₂₄	—	2	2	no	—
252	D₇₂₄	—	2	2	no	—
253	D₇₂₄	—	4	2	no	—
254	D₇₂₄	—	4	2	no	—
255	D₇₂₄	—	4	2	no	—
256	C₂²⋊D₁₈₁	—	2	2	no	—
257	C₂²⋊D₁₈₁	—	2	2	no	—
258	C₂²⋊D₁₈₁	—	4	2	no	—
259	C₂²⋊D₁₈₁	—	4	2	no	—
260	C₂×Dic₁₈₁	—	4	1	no	—
261	C₂×Dic₁₈₁	—	4	1	no	—
262	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
263	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
264	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
265	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
266	C₂×Dic₁₈₁	C₂⁴	1	2	yes	—
267	C₂×Dic₁₈₁	C₂⁴	1	2	yes	—
268	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
269	C₄×D₁₈₁	—	2	2	no	—
270	C₄×D₁₈₁	—	2	2	no	—
271	C₄×D₁₈₁	—	2	2	no	—
272	C₄×D₁₈₁	—	2	2	no	—
273	C₄×D₁₈₁	—	4	1	no	—
274	C₄×D₁₈₁	—	4	1	no	—
275	C₄×D₁₈₁	—	4	1	no	—
276	C₄×D₁₈₁	—	4	1	no	—
277	C₄×D₁₈₁	—	4	1	no	—
278	C₄×D₁₈₁	—	4	2	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	C₂³×C₁₈₁	C₂⁴	1	1	yes	characteristic
285	C₂³×C₁₈₁	C₂⁴	1	1	yes	characteristic
286	Q₈×C₁₈₁	—	2	2	no	—
287	D₄×C₁₈₁	—	2	2	no	—
288	C₂×C₄×C₁₈₁	—	2	4	no	—
289	C₂×C₄×C₁₈₁	—	2	2	no	—
290	C₂×C₄×C₁₈₁	—	2	2	no	—
291	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
292	C₂×C₄×C₁₈₁	C₂⁴	1	2	yes	—
293	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
294	C₂×C₄×C₁₈₁	C₂⁴	1	2	yes	—
295	C₂×C₄×C₁₈₁	C₂⁴	1	2	yes	—
296	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
297	C₂×C₄×C₁₈₁	C₂⁴	1	2	yes	—
298	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
299	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
300	C₂²×C₁₈₁	—	2	1	no	—
301	C₂²×C₁₈₁	—	2	1	no	—
302	C₂²×C₁₈₁	—	2	1	no	—
303	C₂²×C₁₈₁	—	2	1	no	—
304	C₂²×C₁₈₁	—	2	1	no	—
305	C₂²×C₁₈₁	C₂×#41	1	2	yes	—
306	C₂²×C₁₈₁	C₂⁵	1	1	yes	characteristic
307	C₂×D₁₈₁	—	2	1	no	—
308	C₂×D₁₈₁	—	2	1	no	—
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	1	no	—
315	C₂×D₁₈₁	—	2	2	no	—
316	C₂×D₁₈₁	—	2	2	no	—
317	C₂×D₁₈₁	—	2	2	no	—
318	C₂×D₁₈₁	—	2	2	no	—
319	C₂×D₁₈₁	—	2	1	no	—
320	C₂×D₁₈₁	—	4	4	no	—
321	C₂×D₁₈₁	—	4	4	no	—
322	C₂×D₁₈₁	—	8	4	no	—
323	C₂×D₁₈₁	C₂×#41	1	2	yes	—
324	C₂×D₁₈₁	C₂×#41	1	2	yes	—
325	C₄×C₁₈₁	—	2	2	no	—
326	C₄×C₁₈₁	—	2	2	no	—
327	C₄×C₁₈₁	—	2	1	no	—
328	C₄×C₁₈₁	—	2	1	no	—
329	C₄×C₁₈₁	—	2	1	no	—
330	C₄×C₁₈₁	—	2	2	no	—
331	C₄×C₁₈₁	—	2	1	no	—
332	C₄×C₁₈₁	—	2	2	no	—
333	C₄×C₁₈₁	H(5,𝔽₂)	1	2	yes	—
334	Dic₁₈₁	—	2	1	no	—
335	Dic₁₈₁	—	2	1	no	—
336	Dic₁₈₁	—	2	1	no	—
337	Dic₁₈₁	—	2	1	no	—
338	Dic₁₈₁	—	2	2	no	—
339	Dic₁₈₁	—	2	1	no	—
340	Dic₁₈₁	—	2	2	no	—
341	C₂×C₁₈₁	—	2	2	no	—
342	C₂×C₁₈₁	—	4	1	no	—
343	C₂×C₁₈₁	C₂²×#41	1	1	yes	characteristic
344	C₂×C₁₈₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
345	C₂×C₁₈₁	#585	1	1	yes	characteristic
346	D₁₈₁	—	2	2	no	—
347	D₁₈₁	—	2	2	no	—
348	D₁₈₁	—	4	1	no	—
349	D₁₈₁	—	4	2	no	—
350	D₁₈₁	—	4	2	no	—
351	C₁₈₁	#3505	1	1	yes	characteristic, complemented, Sylow
352	#3505	—	181	1	no	maximal, Sylow
353	#553	—	181	2	no	—
354	#553	—	181	1	no	—
355	#553	—	181	2	no	—
356	#553	—	181	1	no	—
357	#552	—	181	1	no	—
358	#552	D₁₈₁	1	1	yes	characteristic, complemented
359	#551	—	181	2	no	—
360	#551	—	181	2	no	—
361	#548	—	181	1	no	—
362	#548	—	181	1	no	—
363	#546	—	181	1	no	—
364	#546	—	181	1	no	—
365	#539	—	181	2	no	—
366	#538	—	181	2	no	—
367	#534	—	181	2	no	—
368	#529	—	181	1	no	—
369	#529	—	181	1	no	—
370	#525	—	181	1	no	—
371	#525	—	181	1	no	—
372	C₂×C₂²⋊Q₈	—	181	1	no	—
373	C₂×#121	—	181	1	no	—
374	#518	—	181	2	no	—
375	C₂×C₄×D₄	—	181	1	no	—
376	C₂×#41	—	181	1	no	—
377	C₂×#41	—	181	1	no	—
378	C₂²×Q₈	—	181	1	no	—
379	C₂²×D₄	—	181	1	no	—
380	C₂²×D₄	—	181	2	no	—
381	C₂²×D₄	—	181	1	no	—
382	C₂³×C₄	—	181	1	no	—
383	C₂³×C₄	—	181	1	no	—
384	#126	—	181	2	no	—
385	#126	—	181	2	no	—
386	#126	—	181	2	no	—
387	#126	—	181	2	no	—
388	#126	—	181	2	no	—
389	#126	C₂×D₁₈₁	1	2	yes	complemented
390	#125	—	181	1	no	—
391	#125	—	181	2	no	—
392	#125	C₂×D₁₈₁	1	1	yes	characteristic, complemented
393	#125	C₂×D₁₈₁	1	2	yes	complemented
394	#124	—	181	1	no	—
395	#124	—	181	2	no	—
396	#124	—	181	1	no	—
397	#124	—	181	2	no	—
398	#123	—	181	2	no	—
399	#123	—	181	2	no	—
400	#123	—	181	2	no	—
401	#123	—	181	2	no	—
402	#123	—	181	2	no	—
403	#123	—	181	2	no	—
404	#123	—	181	2	no	—
405	#123	—	181	2	no	—
406	#123	—	181	2	no	—
407	#123	C₂×D₁₈₁	1	2	yes	—
408	C₂²⋊Q₈	—	181	1	no	—
409	C₂²⋊Q₈	—	181	1	no	—
410	C₂²⋊Q₈	—	181	1	no	—
411	C₂²⋊Q₈	—	181	2	no	—
412	C₂²⋊Q₈	—	181	1	no	—
413	C₂²⋊Q₈	—	181	2	no	—
414	C₂²⋊Q₈	—	181	2	no	—
415	C₂²⋊Q₈	—	181	2	no	—
416	C₂²⋊Q₈	C₂×D₁₈₁	1	1	yes	characteristic, complemented
417	C₂²⋊Q₈	C₂×D₁₈₁	1	1	yes	characteristic, complemented
418	#121	—	181	1	no	—
419	#121	—	181	1	no	—
420	#121	—	181	1	no	—
421	#121	—	181	2	no	—
422	#121	—	181	1	no	—
423	#121	—	181	1	no	—
424	#121	—	181	2	no	—
425	#121	—	181	1	no	—
426	#121	—	181	2	no	—
427	#121	—	181	2	no	—
428	#121	—	181	2	no	—
429	#121	—	181	2	no	—
430	#121	—	181	2	no	—
431	#121	—	181	2	no	—
432	#120	—	181	2	no	—
433	#120	—	181	2	no	—
434	#120	—	181	2	no	—
435	#120	—	181	2	no	—
436	C₄×Q₈	—	181	1	no	—
437	C₄×Q₈	C₂×D₁₈₁	1	1	yes	characteristic, complemented
438	C₄×D₄	—	181	1	no	—
439	C₄×D₄	—	181	1	no	—
440	C₄×D₄	—	181	1	no	—
441	C₄×D₄	—	181	1	no	—
442	C₄×D₄	—	181	2	no	—
443	C₄×D₄	—	181	2	no	—
444	C₄×D₄	—	181	2	no	—
445	C₄×D₄	—	181	2	no	—
446	C₄×D₄	—	181	1	no	—
447	C₄×D₄	—	181	1	no	—
448	C₄×D₄	—	181	1	no	—
449	C₄×D₄	—	181	2	no	—
450	C₄×D₄	—	181	1	no	—
451	C₄×D₄	—	181	2	no	—
452	C₄×D₄	—	181	2	no	—
453	C₄×D₄	—	181	2	no	—
454	C₄×D₄	—	181	2	no	—
455	C₄×D₄	—	181	2	no	—
456	C₄×D₄	—	181	1	no	—
457	C₄×D₄	C₂×D₁₈₁	1	1	yes	characteristic
458	#117	—	181	2	no	—
459	#117	—	181	1	no	—
460	#117	—	181	2	no	—
461	#117	—	181	2	no	—
462	#117	C₂×D₁₈₁	1	2	yes	complemented
463	#117	C₂×D₁₈₁	1	1	yes	characteristic, complemented
464	C₂×C₄⋊C₄	—	181	1	no	—
465	C₂×C₄⋊C₄	—	181	1	no	—
466	C₂×C₄⋊C₄	—	181	2	no	—
467	C₂×C₄⋊C₄	C₂×D₁₈₁	1	1	yes	characteristic, complemented
468	C₂×C₂²⋊C₄	—	181	2	no	—
469	C₂×C₂²⋊C₄	—	181	1	no	—
470	C₂×C₂²⋊C₄	—	181	1	no	—
471	C₂×C₂²⋊C₄	—	181	2	no	—
472	C₂×C₂²⋊C₄	—	181	2	no	—
473	C₂×C₂²⋊C₄	—	181	2	no	—
474	C₂×C₄²	—	181	1	no	—
475	C₂⁴	—	181	2	no	—
476	C₂⁴	—	181	1	no	—
477	C₂⁴	—	181	1	no	—
478	#41	—	724	2	no	—
479	#41	—	724	2	no	—
480	C₂×Q₈	—	181	1	no	—
481	C₂×Q₈	—	181	2	no	—
482	C₂×Q₈	—	724	2	no	—
483	C₂×Q₈	C₂²×D₁₈₁	1	1	yes	characteristic
484	C₂×D₄	—	362	8	no	—
485	C₂×D₄	—	362	4	no	—
486	C₂×D₄	—	181	1	no	—
487	C₂×D₄	—	181	1	no	—
488	C₂×D₄	—	181	2	no	—
489	C₂×D₄	—	181	2	no	—
490	C₂×D₄	—	181	2	no	—
491	C₂×D₄	—	181	2	no	—
492	C₂×D₄	—	181	2	no	—
493	C₂×D₄	—	181	1	no	—
494	C₂×D₄	—	181	2	no	—
495	C₂×D₄	—	181	1	no	—
496	C₂×D₄	—	181	1	no	—
497	C₂×D₄	—	181	2	no	—
498	C₂×D₄	—	181	2	no	—
499	C₂×D₄	—	181	2	no	—
500	C₂×D₄	—	724	2	no	—
501	C₂×D₄	C₂²×D₁₈₁	1	1	yes	characteristic
502	C₂²×C₄	—	181	1	no	—
503	C₂²×C₄	—	181	1	no	—
504	C₂²×C₄	—	181	1	no	—
505	C₂²×C₄	—	181	1	no	—
506	C₂²×C₄	—	181	1	no	—
507	C₂²×C₄	—	181	1	no	—
508	C₂²×C₄	—	181	1	no	—
509	C₂²×C₄	—	181	2	no	—
510	C₂²×C₄	—	181	1	no	—
511	C₂²×C₄	—	181	2	no	—
512	C₂²×C₄	—	181	1	no	—
513	C₂²×C₄	—	181	2	no	—
514	C₂²×C₄	—	181	2	no	—
515	C₂²×C₄	—	181	2	no	—
516	C₂²×C₄	—	181	2	no	—
517	C₂²×C₄	—	181	1	no	—
518	C₂²×C₄	—	181	1	no	—
519	C₂²×C₄	—	724	2	no	—
520	C₂²×C₄	—	724	2	no	—
521	C₂²×C₄	C₂²×D₁₈₁	1	2	yes	—
522	C₂²×C₄	C₂²×D₁₈₁	1	1	yes	characteristic
523	C₂²×C₄	C₂²×D₁₈₁	1	1	yes	characteristic
524	C₄⋊C₄	—	181	1	no	—
525	C₄⋊C₄	—	181	2	no	—
526	C₄⋊C₄	—	181	2	no	—
527	C₄⋊C₄	—	181	1	no	—
528	C₄⋊C₄	—	181	1	no	—
529	C₄⋊C₄	—	181	1	no	—
530	C₄⋊C₄	—	181	2	no	—
531	C₄⋊C₄	—	181	2	no	—
532	C₄⋊C₄	—	181	2	no	—
533	C₄⋊C₄	—	181	2	no	—
534	C₄⋊C₄	—	181	2	no	—
535	C₄⋊C₄	—	181	2	no	—
536	C₄⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
537	C₄⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
538	C₄⋊C₄	C₂²×D₁₈₁	1	2	yes	—
539	C₄⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
540	C₄⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
541	C₄⋊C₄	C₂²×D₁₈₁	1	2	yes	—
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	C₄⋊C₄	C₂²×D₁₈₁	1	2	yes	—
546	C₂²⋊C₄	—	181	1	no	—
547	C₂²⋊C₄	—	181	2	no	—
548	C₂²⋊C₄	—	181	1	no	—
549	C₂²⋊C₄	—	181	2	no	—
550	C₂²⋊C₄	—	181	2	no	—
551	C₂²⋊C₄	—	181	1	no	—
552	C₂²⋊C₄	—	181	1	no	—
553	C₂²⋊C₄	—	181	2	no	—
554	C₂²⋊C₄	—	181	2	no	—
555	C₂²⋊C₄	—	181	1	no	—
556	C₂²⋊C₄	—	181	2	no	—
557	C₂²⋊C₄	—	181	2	no	—
558	C₂²⋊C₄	—	181	2	no	—
559	C₂²⋊C₄	—	181	2	no	—
560	C₂²⋊C₄	—	181	1	no	—
561	C₂²⋊C₄	—	181	2	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	C₂²×D₁₈₁	1	1	yes	characteristic
570	C₂²⋊C₄	C₂²×D₁₈₁	1	2	yes	—
571	C₂²⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
572	C₂²⋊C₄	C₂²×D₁₈₁	1	2	yes	—
573	C₂²⋊C₄	C₂²×D₁₈₁	1	2	yes	—
574	C₄²	—	181	1	no	—
575	C₄²	—	181	1	no	—
576	C₄²	—	181	1	no	—
577	C₄²	—	181	2	no	—
578	C₄²	—	181	2	no	—
579	C₄²	C₂²×D₁₈₁	1	1	yes	characteristic
580	C₄²	C₂²×D₁₈₁	1	2	yes	—
581	C₄²	C₂²×D₁₈₁	1	2	yes	—
582	C₂³	—	362	2	no	—
583	C₂³	—	362	4	no	—
584	C₂³	—	181	2	no	—
585	C₂³	—	181	2	no	—
586	C₂³	—	181	1	no	—
587	C₂³	—	181	1	no	—
588	C₂³	—	181	1	no	—
589	C₂³	—	181	4	no	—
590	C₂³	—	724	2	no	—
591	C₂³	—	724	2	no	—
592	C₂³	—	724	1	no	—
593	C₂³	—	724	1	no	—
594	C₂³	—	724	1	no	—
595	C₂³	—	724	1	no	—
596	C₂³	C₂³×D₁₈₁	1	1	yes	characteristic
597	C₂³	C₂³×D₁₈₁	1	1	yes	characteristic
598	Q₈	—	2	2	no	—
599	Q₈	—	362	2	no	—
600	Q₈	—	724	2	no	—
601	D₄	—	2	2	no	—
602	D₄	—	362	4	no	—
603	D₄	—	362	4	no	—
604	D₄	—	362	4	no	—
605	D₄	—	362	4	no	—
606	D₄	—	362	2	no	—
607	D₄	—	362	2	no	—
608	D₄	—	362	2	no	—
609	D₄	—	362	2	no	—
610	D₄	—	362	2	no	—
611	D₄	—	724	2	no	—
612	D₄	—	724	2	no	—
613	D₄	—	724	2	no	—
614	D₄	—	724	2	no	—
615	D₄	—	724	2	no	—
616	C₂×C₄	—	2	4	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	362	2	no	—
620	C₂×C₄	—	362	2	no	—
621	C₂×C₄	—	362	2	no	—
622	C₂×C₄	—	362	2	no	—
623	C₂×C₄	—	181	1	no	—
624	C₂×C₄	—	181	1	no	—
625	C₂×C₄	—	181	1	no	—
626	C₂×C₄	—	181	1	no	—
627	C₂×C₄	—	181	2	no	—
628	C₂×C₄	—	181	2	no	—
629	C₂×C₄	—	181	1	no	—
630	C₂×C₄	—	724	1	no	—
631	C₂×C₄	—	724	1	no	—
632	C₂×C₄	—	724	1	no	—
633	C₂×C₄	—	724	1	no	—
634	C₂×C₄	—	724	2	no	—
635	C₂×C₄	—	724	2	no	—
636	C₂×C₄	—	724	2	no	—
637	C₂×C₄	—	724	1	no	—
638	C₂×C₄	—	724	2	no	—
639	C₂×C₄	—	724	2	no	—
640	C₂×C₄	—	724	2	no	—
641	C₂×C₄	—	724	1	no	—
642	C₂×C₄	—	724	1	no	—
643	C₂×C₄	C₂³×D₁₈₁	1	2	yes	—
644	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
645	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
646	C₂×C₄	C₂³×D₁₈₁	1	2	yes	—
647	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
648	C₂×C₄	C₂³×D₁₈₁	1	2	yes	—
649	C₂×C₄	C₂³×D₁₈₁	1	2	yes	—
650	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
651	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
652	C₂²	—	2	1	no	—
653	C₂²	—	2	1	no	—
654	C₂²	—	2	1	no	—
655	C₂²	—	2	1	no	—
656	C₂²	—	2	1	no	—
657	C₂²	—	362	1	no	—
658	C₂²	—	362	1	no	—
659	C₂²	—	362	1	no	—
660	C₂²	—	362	1	no	—
661	C₂²	—	362	2	no	—
662	C₂²	—	362	2	no	—
663	C₂²	—	362	1	no	—
664	C₂²	—	362	2	no	—
665	C₂²	—	362	2	no	—
666	C₂²	—	362	1	no	—
667	C₂²	—	362	1	no	—
668	C₂²	—	362	2	no	—
669	C₂²	—	362	2	no	—
670	C₂²	—	1448	4	no	—
671	C₂²	—	181	2	no	—
672	C₂²	—	181	2	no	—
673	C₂²	—	724	4	no	—
674	C₂²	—	724	4	no	—
675	C₂²	#41×D₁₈₁	1	2	yes	—
676	C₂²	C₂⁴×D₁₈₁	1	1	yes	characteristic
677	C₄	—	2	1	no	—
678	C₄	—	2	2	no	—
679	C₄	—	2	2	no	—
680	C₄	—	2	2	no	—
681	C₄	—	2	1	no	—
682	C₄	—	2	1	no	—
683	C₄	—	2	1	no	—
684	C₄	—	2	2	no	—
685	C₄	—	362	1	no	—
686	C₄	—	362	2	no	—
687	C₄	—	362	1	no	—
688	C₄	—	362	1	no	—
689	C₄	—	362	1	no	—
690	C₄	—	362	1	no	—
691	C₄	—	362	2	no	—
692	C₄	#19153862	1	2	yes	—
693	C₂	—	2	2	no	—
694	C₂	—	4	1	no	—
695	C₂	—	362	2	no	—
696	C₂	—	362	2	no	—
697	C₂	—	724	2	no	—
698	C₂	—	724	2	no	—
699	C₂	—	724	1	no	—
700	C₂	C₂×#41×D₁₈₁	1	1	yes	characteristic
701	C₂	C₂×#19153862	1	1	yes	characteristic
702	C₂	#26042116	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₈₁
commutator, socle, cosocle	C₂²×C₁₈₁	C₂⁵
Fitting	#552×C₁₈₁	C₂
hypercenter	#552	D₁₈₁
hypocenter	C₁₈₁	#3505
LCS	G ▷ C₂²×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂² ◁ #552

Complements

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

N	H ≅ G/N	type
1. #26041982	C₂	semidirect
2. #26041982	C₂	semidirect
3. #26041980	C₂	semidirect
4. #26041973	C₂	semidirect
5. #26041964	C₂	semidirect
6. #26041953	C₂	semidirect
7. #26041952	C₂	semidirect
8. #26041941	C₂	semidirect
9. #26041939	C₂	semidirect
10. #26041925	C₂	semidirect
11. #26041920	C₂	semidirect
12. #26041877	C₂	semidirect
13. #26041868	C₂	semidirect
14. #26041840	C₂	semidirect
15. #26041816	C₂	semidirect
16. #26041814	C₂	semidirect
17. #26041792	C₂	semidirect
18. #26041791	C₂	semidirect
19. C₂²⋊Q₈×D₁₈₁	C₂	semidirect
20. C₂×#19153791	C₂	semidirect
21. #26041753	C₂	semidirect
22. C₄×D₄×D₁₈₁	C₂	semidirect
23. #552×C₁₈₁	C₂	semidirect
24. C₂×#15668450	C₂²	semidirect
25. C₂×#15668449	C₂²	semidirect
26. C₂×Q₈×D₁₈₁	C₂²	semidirect
28. C₂²×D₇₂₄	C₂²	semidirect
31. C₂²×C₄×D₁₈₁	C₂²	semidirect
32. #19153811	C₂²	semidirect
33. #19153811	C₂²	semidirect
34. #19153811	C₂²	semidirect
35. #19153811	C₂²	semidirect
36. #19153810	C₂²	semidirect
37. #19153807	C₂²	semidirect
38. #19153806	C₂²	semidirect
39. #19153805	C₂²	semidirect
40. #19153804	C₂²	semidirect
41. #19153804	C₂²	semidirect
42. #19153802	C₂²	semidirect
43. #19153801	C₂²	semidirect
44. #19153801	C₂²	semidirect
45. #19153801	C₂²	semidirect
46. #19153801	C₂²	semidirect
47. #19153801	C₂²	semidirect
48. #19153801	C₂²	semidirect
49. #19153800	C₂²	semidirect
51. #19153798	C₂²	semidirect
52. #19153796	C₂²	semidirect
53. #19153796	C₂²	semidirect
54. #19153796	C₂²	semidirect
55. #19153795	C₂²	semidirect
56. #19153794	C₂²	semidirect
57. #19153794	C₂²	semidirect
58. #19153793	C₂²	semidirect
59. #19153792	C₂²	semidirect
63. #19153791	C₂²	semidirect
64. #19153791	C₂²	semidirect
65. #19153791	C₂²	semidirect
66. #19153791	C₂²	semidirect
67. #19153791	C₂²	semidirect
68. #19153791	C₂²	semidirect
69. #19153791	C₂²	semidirect
70. #19153790	C₂²	semidirect
71. #19153789	C₂²	semidirect
72. #19153789	C₂²	semidirect
73. #19153789	C₂²	semidirect
75. #19153786	C₂²	semidirect
76. #19153786	C₂²	semidirect
78. #19153781	C₂²	semidirect
79. C₄×D₇₂₄	C₂²	semidirect
80. C₄×D₇₂₄	C₂²	semidirect
81. C₄×D₇₂₄	C₂²	semidirect
82. C₄×D₇₂₄	C₂²	semidirect
83. C₄×D₇₂₄	C₂²	semidirect
84. C₄×D₇₂₄	C₂²	semidirect
85. C₄×D₇₂₄	C₂²	semidirect
87. #19153778	C₂²	semidirect
88. #19153778	C₂²	semidirect
89. #19153778	C₂²	semidirect
90. #19153778	C₂²	semidirect
91. #19153778	C₂²	semidirect
92. #19153778	C₂²	semidirect
94. C₄×C₂²⋊D₁₈₁	C₂²	semidirect
96. #19153776	C₂²	semidirect
97. #19153776	C₂²	semidirect
98. #19153775	C₂²	semidirect
99. #19153774	C₂²	semidirect
100. #19153774	C₂²	semidirect
101. #19153773	C₂²	semidirect
102. C₄⋊C₄×D₁₈₁	C₂²	semidirect
103. C₄⋊C₄×D₁₈₁	C₂²	semidirect
104. C₄⋊C₄×D₁₈₁	C₂²	semidirect
105. C₂×#15668426	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. #126×C₁₈₁	C₂²	semidirect
113. #125×C₁₈₁	C₂²	semidirect
114. #125×C₁₈₁	C₂²	semidirect
116. C₂²⋊Q₈×C₁₈₁	C₂²	semidirect
117. C₂²⋊Q₈×C₁₈₁	C₂²	semidirect
118. C₄×Q₈×C₁₈₁	C₂²	semidirect
120. #117×C₁₈₁	C₂²	semidirect
121. #117×C₁₈₁	C₂²	semidirect
122. C₂×C₄⋊C₄×C₁₈₁	C₂²	semidirect
238. C₂²×D₁₈₁	#41	semidirect
351. C₁₈₁	#3505	semidirect
358. #552	D₁₈₁	semidirect
389. #126	C₂×D₁₈₁	semidirect
392. #125	C₂×D₁₈₁	semidirect
393. #125	C₂×D₁₈₁	semidirect
416. C₂²⋊Q₈	C₂×D₁₈₁	semidirect
417. C₂²⋊Q₈	C₂×D₁₈₁	semidirect
437. C₄×Q₈	C₂×D₁₈₁	semidirect
462. #117	C₂×D₁₈₁	semidirect
463. #117	C₂×D₁₈₁	semidirect
467. 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
#26041982	2
#26041980	2
#26041973	2
#26041964	2
#26041953	2
#26041952	2
#26041941	2
#26041939	2
#26041925	2
#26041920	2
#26041877	2
#26041868	2
#26041840	2
#26041816	2
#26041814	2
#26041792	2
#26041791	2
C₂²⋊Q₈×D₁₈₁	2
C₂×#19153791	2
#26041753	2
C₄×D₄×D₁₈₁	2
#552×C₁₈₁	2
#3505	181