Subgroups — #37548092

Order 23168.

1150 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26042020	C₂	1	2	yes	maximal, complemented
2	#26042017	C₂	1	2	yes	maximal, complemented
3	#26041997	C₂	1	1	yes	maximal, characteristic, complemented
4	#26041982	C₂	1	1	yes	maximal, characteristic, complemented
5	#26041950	C₂	1	2	yes	maximal, complemented
6	#26041947	C₂	1	1	yes	maximal, characteristic, complemented
7	#26041930	C₂	1	1	yes	maximal, characteristic, complemented
8	#26041925	C₂	1	1	yes	maximal, characteristic, complemented
9	#26041924	C₂	1	1	yes	maximal, characteristic, complemented
10	#26041921	C₂	1	2	yes	maximal, complemented
11	#26041913	C₂	1	1	yes	maximal, characteristic, complemented
12	#26041895	C₂	1	2	yes	maximal, complemented
13	#26041865	C₂	1	2	yes	maximal, complemented
14	#26041862	C₂	1	2	yes	maximal, complemented
15	#26041860	C₂	1	1	yes	maximal, characteristic, complemented
16	#26041858	C₂	1	1	yes	maximal, characteristic, complemented
17	#26041848	C₂	1	1	yes	maximal, characteristic, complemented
18	#26041845	C₂	1	1	yes	maximal, characteristic, complemented
19	#26041845	C₂	1	2	yes	maximal, complemented
20	#26041826	C₂	1	1	yes	maximal, characteristic, complemented
21	#26041826	C₂	1	1	yes	maximal, characteristic, complemented
22	#26041814	C₂	1	1	yes	maximal, characteristic, complemented
23	#553×C₁₈₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#15668449	C₂²	1	1	yes	characteristic, complemented
25	C₂×#15668449	C₂²	1	1	yes	characteristic, complemented
26	C₂×#15668449	C₂²	1	1	yes	characteristic, complemented
27	C₂×#15668449	C₂²	1	2	yes	complemented
28	C₂×#15668449	C₂²	1	2	yes	complemented
29	C₂×#15668448	C₂²	1	1	yes	characteristic, complemented
30	C₂²×D₇₂₄	C₂²	1	1	yes	characteristic
31	C₂×D₄×D₁₈₁	C₂²	1	2	yes	—
32	C₂×D₄×D₁₈₁	C₂²	1	1	yes	characteristic
33	#19153815	C₂²	1	1	yes	characteristic, complemented
34	#19153815	C₂²	1	1	yes	characteristic, complemented
35	#19153813	C₂²	1	2	yes	complemented
36	#19153812	C₂²	1	1	yes	characteristic
37	#19153812	C₂²	1	1	yes	characteristic
38	#19153812	C₂²	1	2	yes	complemented
39	#19153812	C₂²	1	2	yes	complemented
40	#19153811	C₂²	1	2	yes	complemented
41	#19153811	C₂²	1	2	yes	complemented
42	#19153810	C₂²	1	2	yes	complemented
43	#19153809	C₂²	1	2	yes	complemented
44	#19153804	C₂²	1	1	yes	characteristic
45	#19153804	C₂²	1	2	yes	complemented
46	#19153802	C₂²	1	2	yes	—
47	#19153802	C₂²	1	1	yes	characteristic, complemented
48	#19153802	C₂²	1	1	yes	characteristic, complemented
49	#19153802	C₂²	1	2	yes	complemented
50	#19153802	C₂²	1	2	yes	complemented
51	#19153801	C₂²	1	2	yes	complemented
52	#19153801	C₂²	1	2	yes	complemented
53	#19153801	C₂²	1	2	yes	complemented
54	#19153801	C₂²	1	2	yes	complemented
55	#19153800	C₂²	1	2	yes	complemented
56	#19153799	C₂²	1	2	yes	complemented
57	#19153796	C₂²	1	1	yes	characteristic, complemented
58	#19153796	C₂²	1	2	yes	complemented
59	#19153796	C₂²	1	1	yes	characteristic, complemented
60	#19153795	C₂²	1	1	yes	characteristic, complemented
61	#19153794	C₂²	1	2	yes	complemented
62	#19153793	C₂²	1	2	yes	complemented
63	#19153791	C₂²	1	1	yes	characteristic
64	#19153791	C₂²	1	1	yes	characteristic
65	#19153791	C₂²	1	1	yes	characteristic
66	#19153791	C₂²	1	2	yes	complemented
67	#19153791	C₂²	1	1	yes	characteristic, complemented
68	#19153791	C₂²	1	1	yes	characteristic, complemented
69	#19153791	C₂²	1	2	yes	complemented
70	#19153791	C₂²	1	1	yes	characteristic, complemented
71	#19153790	C₂²	1	1	yes	characteristic
72	#19153790	C₂²	1	2	yes	complemented
73	#19153790	C₂²	1	2	yes	complemented
74	#19153790	C₂²	1	2	yes	complemented
75	#19153789	C₂²	1	2	yes	—
76	#19153789	C₂²	1	1	yes	characteristic
77	#19153789	C₂²	1	2	yes	complemented
78	#19153789	C₂²	1	2	yes	complemented
79	#19153789	C₂²	1	2	yes	complemented
80	#19153789	C₂²	1	1	yes	characteristic, complemented
81	#19153789	C₂²	1	2	yes	complemented
82	#19153788	C₂²	1	2	yes	complemented
83	#19153788	C₂²	1	2	yes	complemented
84	#19153787	C₂²	1	2	yes	complemented
85	#19153787	C₂²	1	1	yes	characteristic, complemented
86	#19153787	C₂²	1	1	yes	characteristic, complemented
87	#19153786	C₂²	1	2	yes	—
88	#19153786	C₂²	1	2	yes	complemented
89	#19153786	C₂²	1	2	yes	complemented
90	#19153786	C₂²	1	2	yes	complemented
91	#19153786	C₂²	1	2	yes	complemented
92	#19153784	C₂²	1	2	yes	—
93	#19153784	C₂²	1	2	yes	complemented
94	#19153784	C₂²	1	2	yes	complemented
95	C₄×Dic₃₆₂	C₂²	1	2	yes	complemented
96	#19153781	C₂²	1	1	yes	characteristic, complemented
97	C₄×D₇₂₄	C₂²	1	1	yes	characteristic, complemented
98	C₄×D₇₂₄	C₂²	1	1	yes	characteristic, complemented
99	#19153778	C₂²	1	1	yes	characteristic
100	#19153778	C₂²	1	2	yes	complemented
101	#19153778	C₂²	1	2	yes	complemented
102	C₄×C₂²⋊D₁₈₁	C₂²	1	1	yes	characteristic
103	C₄×C₂²⋊D₁₈₁	C₂²	1	2	yes	complemented
104	C₄×C₂²⋊D₁₈₁	C₂²	1	1	yes	characteristic, complemented
105	#19153776	C₂²	1	2	yes	complemented
106	#19153774	C₂²	1	2	yes	complemented
107	#19153774	C₂²	1	1	yes	characteristic, complemented
108	C₄⋊C₄×D₁₈₁	C₂²	1	1	yes	characteristic, complemented
109	C₂×#15668426	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	1	yes	characteristic, complemented
114	#123×C₁₈₁	C₂²	1	2	yes	complemented
115	#121×C₁₈₁	C₂²	1	1	yes	characteristic
116	#121×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
117	#121×C₁₈₁	C₂²	1	2	yes	complemented
118	C₄×D₄×C₁₈₁	C₂²	1	2	yes	complemented
119	C₄×D₄×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₄×C₁₈₁	C₂²	1	1	yes	characteristic, 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	2	yes	—
125	#15668449	—	4	2	no	—
126	#15668449	—	4	2	no	—
127	#15668449	—	4	2	no	—
128	#15668449	—	4	4	no	—
129	#15668449	—	4	4	no	—
130	#15668448	—	4	2	no	—
131	C₂×Dic₃₆₂	C₂³	1	1	yes	characteristic
132	C₂×Dic₃₆₂	C₂³	1	2	yes	—
133	C₂×Dic₃₆₂	C₂³	1	1	yes	characteristic
134	C₂×Dic₃₆₂	C₂³	1	1	yes	characteristic
135	C₂×D₇₂₄	—	4	2	no	—
136	C₂×D₇₂₄	C₂³	1	1	yes	characteristic
137	C₂×D₇₂₄	C₂³	1	1	yes	characteristic
138	C₂×D₇₂₄	C₂³	1	2	yes	—
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	1	yes	characteristic
144	C₂×D₇₂₄	C₂³	1	2	yes	—
145	C₂×D₇₂₄	C₂³	1	2	yes	—
146	C₂×D₇₂₄	C₂³	1	1	yes	characteristic
147	C₂×C₂²⋊D₁₈₁	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	1	yes	characteristic
154	C₂×C₂²⋊D₁₈₁	C₂³	1	2	yes	—
155	C₂×C₂²⋊D₁₈₁	C₂³	1	1	yes	characteristic
156	C₂×C₂²⋊D₁₈₁	C₂³	1	1	yes	characteristic
157	C₂×C₂²⋊D₁₈₁	C₂³	1	2	yes	—
158	C₂×C₂²⋊D₁₈₁	C₂³	1	2	yes	—
159	C₂×C₂²⋊D₁₈₁	C₂³	1	1	yes	characteristic
160	D₄×D₁₈₁	—	4	2	no	—
161	D₄×D₁₈₁	—	4	4	no	—
162	C₂²×Dic₁₈₁	C₂³	1	2	yes	—
163	C₂×C₄×D₁₈₁	C₂³	1	1	yes	characteristic
164	C₂×C₄×D₁₈₁	C₂³	1	1	yes	characteristic
165	C₂×C₄×D₁₈₁	C₂³	1	1	yes	characteristic
166	C₂×C₄×D₁₈₁	C₂³	1	1	yes	characteristic
167	C₂×C₄×D₁₈₁	C₂³	1	2	yes	—
168	C₂×C₄×D₁₈₁	C₂³	1	1	yes	characteristic
169	C₂×C₄×D₁₈₁	C₂³	1	2	yes	—
170	C₂×C₄×D₁₈₁	C₂³	1	2	yes	—
171	C₂×C₄×D₁₈₁	C₂³	1	2	yes	—
172	C₄⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
173	C₄⋊Dic₁₈₁	C₂³	1	2	yes	—
174	C₄⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
175	C₄⋊Dic₁₈₁	C₂³	1	2	yes	—
176	#15668428	C₂³	1	2	yes	—
177	#15668428	C₂³	1	1	yes	characteristic
178	#15668428	C₂³	1	1	yes	characteristic
179	#15668428	C₂³	1	2	yes	—
180	#15668428	C₂³	1	2	yes	—
181	#15668428	C₂³	1	2	yes	—
182	C₂²⋊Dic₁₈₁	C₂³	1	2	yes	—
183	C₂²⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
184	C₂²⋊Dic₁₈₁	C₂³	1	2	yes	—
185	C₂²⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
186	#15668426	C₂³	1	2	yes	—
187	#15668426	C₂³	1	2	yes	—
188	#15668426	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
196	#15668426	C₂³	1	2	yes	—
197	#15668426	C₂³	1	1	yes	characteristic
198	#15668426	C₂³	1	2	yes	—
199	#15668426	C₂³	1	1	yes	characteristic
200	#15668426	C₂³	1	2	yes	—
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	2	yes	—
207	C₄×Dic₁₈₁	C₂³	1	2	yes	—
208	C₂×D₄×C₁₈₁	C₂³	1	1	yes	characteristic
209	C₂×D₄×C₁₈₁	C₂³	1	1	yes	characteristic
210	C₂×D₄×C₁₈₁	C₂³	1	2	yes	—
211	C₂×D₄×C₁₈₁	C₂³	1	2	yes	—
212	C₂²×C₄×C₁₈₁	C₂³	1	1	yes	characteristic
213	C₂²×C₄×C₁₈₁	C₂³	1	1	yes	characteristic
214	C₂²×C₄×C₁₈₁	C₂³	1	2	yes	—
215	C₂²×C₄×C₁₈₁	C₂³	1	2	yes	—
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	1	yes	characteristic
220	C₄⋊C₄×C₁₈₁	C₂³	1	2	yes	—
221	C₄⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
222	C₄⋊C₄×C₁₈₁	C₂³	1	2	yes	—
223	C₂²⋊C₄×C₁₈₁	C₂³	1	2	yes	—
224	C₂²⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
225	C₂²⋊C₄×C₁₈₁	C₂³	1	2	yes	—
226	C₂²⋊C₄×C₁₈₁	C₂³	1	2	yes	—
227	C₂²⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
228	C₂²⋊C₄×C₁₈₁	C₂³	1	2	yes	—
229	C₄²×C₁₈₁	C₂³	1	2	yes	—
230	C₄²×C₁₈₁	C₂³	1	1	yes	characteristic
231	C₂²×D₁₈₁	—	4	2	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	C₂⁴	1	1	yes	characteristic
238	C₂²×D₁₈₁	C₂⁴	1	2	yes	—
239	C₂²×D₁₈₁	C₂⁴	1	2	yes	—
240	C₂²×D₁₈₁	C₂⁴	1	1	yes	characteristic
241	C₂²×D₁₈₁	C₂⁴	1	1	yes	characteristic
242	Dic₃₆₂	—	2	2	no	—
243	Dic₃₆₂	—	2	4	no	—
244	Dic₃₆₂	—	4	1	no	—
245	Dic₃₆₂	—	4	1	no	—
246	D₇₂₄	—	2	2	no	—
247	D₇₂₄	—	2	2	no	—
248	D₇₂₄	—	4	2	no	—
249	D₇₂₄	—	4	2	no	—
250	D₇₂₄	—	4	1	no	—
251	D₇₂₄	—	4	2	no	—
252	D₇₂₄	—	4	2	no	—
253	D₇₂₄	—	4	1	no	—
254	D₇₂₄	—	4	1	no	—
255	D₇₂₄	—	4	2	no	—
256	D₇₂₄	—	4	2	no	—
257	C₂²⋊D₁₈₁	—	2	2	no	—
258	C₂²⋊D₁₈₁	—	2	4	no	—
259	C₂²⋊D₁₈₁	—	2	2	no	—
260	C₂²⋊D₁₈₁	—	4	2	no	—
261	C₂²⋊D₁₈₁	—	4	2	no	—
262	C₂²⋊D₁₈₁	—	4	2	no	—
263	C₂²⋊D₁₈₁	—	4	1	no	—
264	C₂²⋊D₁₈₁	—	4	1	no	—
265	C₂²⋊D₁₈₁	—	4	1	no	—
266	C₂²⋊D₁₈₁	—	4	1	no	—
267	C₂²⋊D₁₈₁	—	4	2	no	—
268	C₂²⋊D₁₈₁	—	4	2	no	—
269	C₂²⋊D₁₈₁	—	4	2	no	—
270	C₂×Dic₁₈₁	—	4	2	no	—
271	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
272	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
273	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
274	C₂×Dic₁₈₁	C₂⁴	1	2	yes	—
275	C₂×Dic₁₈₁	C₂⁴	1	2	yes	—
276	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
277	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
278	C₄×D₁₈₁	—	2	2	no	—
279	C₄×D₁₈₁	—	2	2	no	—
280	C₄×D₁₈₁	—	2	2	no	—
281	C₄×D₁₈₁	—	2	4	no	—
282	C₄×D₁₈₁	—	2	2	no	—
283	C₄×D₁₈₁	—	4	1	no	—
284	C₄×D₁₈₁	—	4	2	no	—
285	C₄×D₁₈₁	—	4	2	no	—
286	C₄×D₁₈₁	—	4	2	no	—
287	C₂³×C₁₈₁	C₂⁴	1	1	yes	characteristic
288	C₂³×C₁₈₁	C₂⁴	1	2	yes	—
289	C₂³×C₁₈₁	C₂⁴	1	1	yes	characteristic
290	D₄×C₁₈₁	—	2	2	no	—
291	D₄×C₁₈₁	—	4	1	no	—
292	D₄×C₁₈₁	—	4	2	no	—
293	D₄×C₁₈₁	—	4	2	no	—
294	C₂×C₄×C₁₈₁	—	2	2	no	—
295	C₂×C₄×C₁₈₁	—	2	2	no	—
296	C₂×C₄×C₁₈₁	—	4	2	no	—
297	C₂×C₄×C₁₈₁	—	4	2	no	—
298	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
299	C₂×C₄×C₁₈₁	C₂⁴	1	2	yes	—
300	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
301	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
302	C₂×C₄×C₁₈₁	C₂⁴	1	2	yes	—
303	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
304	C₂×C₄×C₁₈₁	C₂⁴	1	2	yes	—
305	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
306	C₂²×C₁₈₁	—	2	1	no	—
307	C₂²×C₁₈₁	—	2	1	no	—
308	C₂²×C₁₈₁	—	2	1	no	—
309	C₂²×C₁₈₁	—	2	2	no	—
310	C₂²×C₁₈₁	—	2	2	no	—
311	C₂²×C₁₈₁	—	2	1	no	—
312	C₂²×C₁₈₁	—	2	1	no	—
313	C₂²×C₁₈₁	—	2	2	no	—
314	C₂²×C₁₈₁	—	2	1	no	—
315	C₂²×C₁₈₁	C₂⁵	1	1	yes	characteristic
316	C₂×D₁₈₁	—	2	1	no	—
317	C₂×D₁₈₁	—	2	1	no	—
318	C₂×D₁₈₁	—	2	1	no	—
319	C₂×D₁₈₁	—	2	2	no	—
320	C₂×D₁₈₁	—	2	1	no	—
321	C₂×D₁₈₁	—	2	1	no	—
322	C₂×D₁₈₁	—	2	2	no	—
323	C₂×D₁₈₁	—	2	2	no	—
324	C₂×D₁₈₁	—	2	1	no	—
325	C₂×D₁₈₁	—	2	2	no	—
326	C₂×D₁₈₁	—	2	1	no	—
327	C₂×D₁₈₁	—	2	2	no	—
328	C₂×D₁₈₁	—	2	1	no	—
329	C₂×D₁₈₁	—	2	1	no	—
330	C₂×D₁₈₁	—	2	2	no	—
331	C₂×D₁₈₁	—	8	4	no	—
332	C₂×D₁₈₁	—	8	4	no	—
333	C₄×C₁₈₁	—	2	1	no	—
334	C₄×C₁₈₁	—	2	1	no	—
335	C₄×C₁₈₁	—	2	1	no	—
336	C₄×C₁₈₁	—	2	2	no	—
337	C₄×C₁₈₁	—	2	2	no	—
338	C₄×C₁₈₁	—	2	1	no	—
339	C₄×C₁₈₁	—	2	2	no	—
340	C₄×C₁₈₁	H(5,𝔽₂)	1	2	yes	—
341	Dic₁₈₁	—	2	1	no	—
342	Dic₁₈₁	—	2	1	no	—
343	Dic₁₈₁	—	2	1	no	—
344	Dic₁₈₁	—	2	2	no	—
345	Dic₁₈₁	—	2	2	no	—
346	Dic₁₈₁	—	2	1	no	—
347	Dic₁₈₁	H(5,𝔽₂)	1	2	yes	—
348	C₂×C₁₈₁	—	4	1	no	—
349	C₂×C₁₈₁	—	4	2	no	—
350	C₂×C₁₈₁	—	4	1	no	—
351	C₂×C₁₈₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
352	C₂×C₁₈₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
353	C₂×C₁₈₁	#585	1	1	yes	characteristic
354	D₁₈₁	—	4	1	no	—
355	D₁₈₁	—	4	1	no	—
356	D₁₈₁	—	4	2	no	—
357	D₁₈₁	—	4	1	no	—
358	D₁₈₁	—	4	2	no	—
359	C₁₈₁	#3546	1	1	yes	characteristic, complemented, Sylow
360	#3546	—	181	1	no	maximal, Sylow
361	#560	—	181	2	no	—
362	#560	—	181	2	no	—
363	#556	—	181	1	no	—
364	#553	—	181	1	no	—
365	#553	D₁₈₁	1	1	yes	characteristic, complemented
366	#550	—	181	1	no	—
367	#550	—	181	2	no	—
368	#547	—	181	1	no	—
369	#546	—	181	2	no	—
370	#546	—	181	1	no	—
371	#546	—	181	1	no	—
372	D₄²	—	181	1	no	—
373	#542	—	181	2	no	—
374	#538	—	181	2	no	—
375	#538	—	181	2	no	—
376	#537	—	181	1	no	—
377	#537	—	181	1	no	—
378	#535	—	181	2	no	—
379	#535	—	181	1	no	—
380	#535	—	181	1	no	—
381	#532	—	181	1	no	—
382	#532	—	181	1	no	—
383	#529	—	181	1	no	—
384	C₂×#41	—	181	1	no	—
385	C₂×#41	—	181	1	no	—
386	C₂×#41	—	181	1	no	—
387	C₂×#41	—	181	2	no	—
388	C₂×#41	—	181	2	no	—
389	C₂×#41	—	181	1	no	—
390	C₂²×D₄	—	181	2	no	—
391	C₂²×D₄	—	181	1	no	—
392	C₂²×D₄	—	181	1	no	—
393	C₄⋊Q₈	—	181	1	no	—
394	C₄⋊Q₈	—	181	1	no	—
395	#127	—	181	1	no	—
396	#127	—	181	1	no	—
397	#127	—	181	2	no	—
398	#127	—	181	2	no	—
399	#127	—	181	2	no	—
400	#126	—	181	2	no	—
401	#126	—	181	2	no	—
402	#126	—	181	2	no	—
403	#126	—	181	2	no	—
404	#126	C₂×D₁₈₁	1	2	yes	complemented
405	#125	C₂×D₁₈₁	1	1	yes	characteristic, complemented
406	#124	—	181	2	no	—
407	#124	—	181	1	no	—
408	#124	—	181	1	no	—
409	#124	—	181	2	no	—
410	#124	—	181	2	no	—
411	#124	—	181	1	no	—
412	#124	—	181	2	no	—
413	#123	—	181	2	no	—
414	#123	—	181	2	no	—
415	#123	—	181	2	no	—
416	#123	—	181	2	no	—
417	#123	—	181	2	no	—
418	#123	—	181	2	no	—
419	#123	C₂×D₁₈₁	1	2	yes	complemented
420	C₂²⋊Q₈	—	181	1	no	—
421	C₂²⋊Q₈	—	181	1	no	—
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	#121	—	181	1	no	—
427	#121	—	181	1	no	—
428	#121	—	181	2	no	—
429	#121	—	181	2	no	—
430	#121	—	181	2	no	—
431	#121	—	181	2	no	—
432	#121	—	181	1	no	—
433	#121	—	181	2	no	—
434	#121	—	181	2	no	—
435	#121	—	181	1	no	—
436	#121	—	181	1	no	—
437	#121	—	181	1	no	—
438	#121	—	181	1	no	—
439	#121	—	181	1	no	—
440	#121	—	181	2	no	—
441	#121	—	181	1	no	—
442	#121	—	181	2	no	—
443	#121	—	181	1	no	—
444	#121	—	181	1	no	—
445	#121	—	181	2	no	—
446	#121	—	181	2	no	—
447	#121	—	181	2	no	—
448	#121	—	181	2	no	—
449	#121	—	181	2	no	—
450	#121	C₂×D₁₈₁	1	1	yes	characteristic
451	#121	C₂×D₁₈₁	1	1	yes	characteristic, complemented
452	#121	C₂×D₁₈₁	1	2	yes	complemented
453	#120	—	181	2	no	—
454	#120	—	181	2	no	—
455	#120	—	181	2	no	—
456	#120	—	181	2	no	—
457	#120	—	181	2	no	—
458	#120	—	181	2	no	—
459	#120	—	181	2	no	—
460	#120	—	181	2	no	—
461	C₄×Q₈	—	181	1	no	—
462	C₄×Q₈	—	181	2	no	—
463	C₄×D₄	—	181	2	no	—
464	C₄×D₄	—	181	1	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	—	181	2	no	—
470	C₄×D₄	—	181	1	no	—
471	C₄×D₄	—	181	1	no	—
472	C₄×D₄	C₂×D₁₈₁	1	1	yes	characteristic, complemented
473	C₄×D₄	C₂×D₁₈₁	1	1	yes	characteristic, complemented
474	C₄×D₄	C₂×D₁₈₁	1	2	yes	complemented
475	#117	—	181	2	no	—
476	#117	—	181	1	no	—
477	#117	C₂×D₁₈₁	1	1	yes	characteristic, complemented
478	C₂×C₄⋊C₄	—	181	1	no	—
479	C₂×C₄⋊C₄	C₂×D₁₈₁	1	1	yes	characteristic, complemented
480	C₂×C₂²⋊C₄	—	181	2	no	—
481	C₂×C₂²⋊C₄	—	181	2	no	—
482	C₂×C₄²	—	181	1	no	—
483	C₂⁴	—	181	2	no	—
484	C₂⁴	—	181	2	no	—
485	#41	—	724	2	no	—
486	#41	—	724	2	no	—
487	#41	—	724	2	no	—
488	#41	—	724	4	no	—
489	#41	—	724	4	no	—
490	#41	—	724	2	no	—
491	C₂×Q₈	—	181	1	no	—
492	C₂×Q₈	—	181	2	no	—
493	C₂×Q₈	—	181	1	no	—
494	C₂×Q₈	—	181	1	no	—
495	C₂×D₄	—	181	1	no	—
496	C₂×D₄	—	181	2	no	—
497	C₂×D₄	—	181	1	no	—
498	C₂×D₄	—	181	2	no	—
499	C₂×D₄	—	181	1	no	—
500	C₂×D₄	—	181	2	no	—
501	C₂×D₄	—	181	1	no	—
502	C₂×D₄	—	181	1	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	1	no	—
508	C₂×D₄	—	181	1	no	—
509	C₂×D₄	—	181	1	no	—
510	C₂×D₄	—	181	1	no	—
511	C₂×D₄	—	181	2	no	—
512	C₂×D₄	—	181	2	no	—
513	C₂×D₄	—	181	1	no	—
514	C₂×D₄	—	181	2	no	—
515	C₂×D₄	—	181	2	no	—
516	C₂×D₄	—	181	2	no	—
517	C₂×D₄	—	181	2	no	—
518	C₂×D₄	—	181	1	no	—
519	C₂×D₄	—	724	2	no	—
520	C₂×D₄	—	724	2	no	—
521	C₂×D₄	—	724	4	no	—
522	C₂×D₄	C₂²×D₁₈₁	1	1	yes	characteristic
523	C₂×D₄	C₂²×D₁₈₁	1	1	yes	characteristic
524	C₂×D₄	C₂²×D₁₈₁	1	2	yes	—
525	C₂×D₄	C₂²×D₁₈₁	1	2	yes	—
526	C₂²×C₄	—	181	1	no	—
527	C₂²×C₄	—	181	1	no	—
528	C₂²×C₄	—	181	1	no	—
529	C₂²×C₄	—	181	2	no	—
530	C₂²×C₄	—	181	1	no	—
531	C₂²×C₄	—	181	2	no	—
532	C₂²×C₄	—	181	1	no	—
533	C₂²×C₄	—	181	2	no	—
534	C₂²×C₄	—	181	2	no	—
535	C₂²×C₄	—	181	2	no	—
536	C₂²×C₄	C₂²×D₁₈₁	1	1	yes	characteristic
537	C₂²×C₄	C₂²×D₁₈₁	1	1	yes	characteristic
538	C₂²×C₄	C₂²×D₁₈₁	1	2	yes	—
539	C₂²×C₄	C₂²×D₁₈₁	1	2	yes	—
540	C₄⋊C₄	—	181	1	no	—
541	C₄⋊C₄	—	181	2	no	—
542	C₄⋊C₄	—	181	2	no	—
543	C₄⋊C₄	—	181	1	no	—
544	C₄⋊C₄	—	181	1	no	—
545	C₄⋊C₄	—	181	2	no	—
546	C₄⋊C₄	—	181	1	no	—
547	C₄⋊C₄	—	181	2	no	—
548	C₄⋊C₄	—	181	2	no	—
549	C₄⋊C₄	—	181	2	no	—
550	C₄⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
551	C₄⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
552	C₄⋊C₄	C₂²×D₁₈₁	1	2	yes	—
553	C₄⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
554	C₄⋊C₄	C₂²×D₁₈₁	1	2	yes	—
555	C₄⋊C₄	C₂²×D₁₈₁	1	2	yes	—
556	C₄⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
557	C₂²⋊C₄	—	181	2	no	—
558	C₂²⋊C₄	—	181	1	no	—
559	C₂²⋊C₄	—	181	2	no	—
560	C₂²⋊C₄	—	181	1	no	—
561	C₂²⋊C₄	—	181	2	no	—
562	C₂²⋊C₄	—	181	1	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	1	no	—
570	C₂²⋊C₄	—	181	1	no	—
571	C₂²⋊C₄	—	181	2	no	—
572	C₂²⋊C₄	—	181	2	no	—
573	C₂²⋊C₄	—	181	2	no	—
574	C₂²⋊C₄	—	181	2	no	—
575	C₂²⋊C₄	—	181	2	no	—
576	C₂²⋊C₄	—	181	2	no	—
577	C₂²⋊C₄	—	181	1	no	—
578	C₂²⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
579	C₂²⋊C₄	C₂²×D₁₈₁	1	2	yes	—
580	C₂²⋊C₄	C₂²×D₁₈₁	1	2	yes	—
581	C₂²⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
582	C₂²⋊C₄	C₂²×D₁₈₁	1	2	yes	—
583	C₂²⋊C₄	C₂²×D₁₈₁	1	2	yes	—
584	C₄²	—	181	1	no	—
585	C₄²	—	181	1	no	—
586	C₄²	—	181	1	no	—
587	C₄²	—	181	2	no	—
588	C₄²	—	181	2	no	—
589	C₄²	C₂²×D₁₈₁	1	1	yes	characteristic
590	C₄²	C₂²×D₁₈₁	1	2	yes	—
591	C₂³	—	181	2	no	—
592	C₂³	—	181	1	no	—
593	C₂³	—	181	2	no	—
594	C₂³	—	181	1	no	—
595	C₂³	—	181	1	no	—
596	C₂³	—	724	2	no	—
597	C₂³	—	724	2	no	—
598	C₂³	—	724	2	no	—
599	C₂³	—	724	2	no	—
600	C₂³	—	724	2	no	—
601	C₂³	—	724	2	no	—
602	C₂³	C₂³×D₁₈₁	1	1	yes	characteristic
603	C₂³	C₂³×D₁₈₁	1	2	yes	—
604	C₂³	C₂³×D₁₈₁	1	1	yes	characteristic
605	Q₈	—	362	4	no	—
606	Q₈	—	362	2	no	—
607	Q₈	—	724	1	no	—
608	Q₈	—	724	1	no	—
609	D₄	—	2	2	no	—
610	D₄	—	4	2	no	—
611	D₄	—	4	1	no	—
612	D₄	—	4	2	no	—
613	D₄	—	362	2	no	—
614	D₄	—	362	4	no	—
615	D₄	—	362	2	no	—
616	D₄	—	362	2	no	—
617	D₄	—	362	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	1	no	—
623	D₄	—	724	1	no	—
624	D₄	—	724	1	no	—
625	D₄	—	724	2	no	—
626	D₄	—	724	2	no	—
627	D₄	—	724	2	no	—
628	D₄	—	724	2	no	—
629	D₄	—	724	2	no	—
630	D₄	—	724	1	no	—
631	D₄	—	724	1	no	—
632	D₄	—	724	1	no	—
633	D₄	—	724	1	no	—
634	D₄	—	724	2	no	—
635	D₄	—	724	2	no	—
636	D₄	—	724	2	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	4	2	no	—
640	C₂×C₄	—	4	2	no	—
641	C₂×C₄	—	362	4	no	—
642	C₂×C₄	—	362	2	no	—
643	C₂×C₄	—	362	2	no	—
644	C₂×C₄	—	362	2	no	—
645	C₂×C₄	—	362	2	no	—
646	C₂×C₄	—	181	1	no	—
647	C₂×C₄	—	181	1	no	—
648	C₂×C₄	—	181	1	no	—
649	C₂×C₄	—	181	2	no	—
650	C₂×C₄	—	181	2	no	—
651	C₂×C₄	—	181	1	no	—
652	C₂×C₄	—	181	1	no	—
653	C₂×C₄	—	724	2	no	—
654	C₂×C₄	—	724	2	no	—
655	C₂×C₄	—	724	2	no	—
656	C₂×C₄	—	724	1	no	—
657	C₂×C₄	—	724	2	no	—
658	C₂×C₄	C₂³×D₁₈₁	1	2	yes	—
659	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
660	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
661	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
662	C₂×C₄	C₂³×D₁₈₁	1	2	yes	—
663	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
664	C₂×C₄	C₂³×D₁₈₁	1	2	yes	—
665	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
666	C₂²	—	2	1	no	—
667	C₂²	—	2	2	no	—
668	C₂²	—	2	1	no	—
669	C₂²	—	2	1	no	—
670	C₂²	—	2	2	no	—
671	C₂²	—	2	1	no	—
672	C₂²	—	2	1	no	—
673	C₂²	—	2	1	no	—
674	C₂²	—	2	2	no	—
675	C₂²	—	362	1	no	—
676	C₂²	—	362	1	no	—
677	C₂²	—	362	2	no	—
678	C₂²	—	362	2	no	—
679	C₂²	—	362	1	no	—
680	C₂²	—	362	1	no	—
681	C₂²	—	362	2	no	—
682	C₂²	—	362	1	no	—
683	C₂²	—	362	2	no	—
684	C₂²	—	362	1	no	—
685	C₂²	—	362	1	no	—
686	C₂²	—	362	1	no	—
687	C₂²	—	362	1	no	—
688	C₂²	—	362	2	no	—
689	C₂²	—	362	2	no	—
690	C₂²	—	1448	4	no	—
691	C₂²	—	1448	4	no	—
692	C₂²	C₂⁴×D₁₈₁	1	1	yes	characteristic
693	C₄	—	2	1	no	—
694	C₄	—	2	2	no	—
695	C₄	—	2	1	no	—
696	C₄	—	2	2	no	—
697	C₄	—	2	2	no	—
698	C₄	—	2	1	no	—
699	C₄	—	2	1	no	—
700	C₄	—	362	1	no	—
701	C₄	—	362	2	no	—
702	C₄	—	362	1	no	—
703	C₄	—	362	1	no	—
704	C₄	—	362	1	no	—
705	C₄	—	362	2	no	—
706	C₄	—	181	2	no	—
707	C₄	#19153862	1	2	yes	—
708	C₂	—	4	1	no	—
709	C₂	—	4	2	no	—
710	C₂	—	4	1	no	—
711	C₂	—	724	2	no	—
712	C₂	—	724	1	no	—
713	C₂	—	724	2	no	—
714	C₂	—	724	1	no	—
715	C₂	—	724	1	no	—
716	C₂	H(5,𝔽₂)×D₁₈₁	1	1	yes	characteristic
717	C₂	C₂×#19153862	1	1	yes	characteristic
718	C₂	#26042115	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₈₁
commutator, socle, cosocle	C₂²×C₁₈₁	C₂⁵
Fitting	#553×C₁₈₁	C₂
hypercenter	#553	D₁₈₁
hypocenter	C₁₈₁	#3546
LCS	G ▷ C₂²×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂² ◁ #553

Complements

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

N	H ≅ G/N	type
1. #26042020	C₂	semidirect
2. #26042017	C₂	semidirect
3. #26041997	C₂	semidirect
4. #26041982	C₂	semidirect
5. #26041950	C₂	semidirect
6. #26041947	C₂	semidirect
7. #26041930	C₂	semidirect
8. #26041925	C₂	semidirect
9. #26041924	C₂	semidirect
10. #26041921	C₂	semidirect
11. #26041913	C₂	semidirect
12. #26041895	C₂	semidirect
13. #26041865	C₂	semidirect
14. #26041862	C₂	semidirect
15. #26041860	C₂	semidirect
16. #26041858	C₂	semidirect
17. #26041848	C₂	semidirect
18. #26041845	C₂	semidirect
19. #26041845	C₂	semidirect
20. #26041826	C₂	semidirect
21. #26041826	C₂	semidirect
22. #26041814	C₂	semidirect
23. #553×C₁₈₁	C₂	semidirect
24. C₂×#15668449	C₂²	semidirect
25. C₂×#15668449	C₂²	semidirect
26. C₂×#15668449	C₂²	semidirect
27. C₂×#15668449	C₂²	semidirect
28. C₂×#15668449	C₂²	semidirect
29. C₂×#15668448	C₂²	semidirect
33. #19153815	C₂²	semidirect
34. #19153815	C₂²	semidirect
35. #19153813	C₂²	semidirect
38. #19153812	C₂²	semidirect
39. #19153812	C₂²	semidirect
40. #19153811	C₂²	semidirect
41. #19153811	C₂²	semidirect
42. #19153810	C₂²	semidirect
43. #19153809	C₂²	semidirect
45. #19153804	C₂²	semidirect
47. #19153802	C₂²	semidirect
48. #19153802	C₂²	semidirect
49. #19153802	C₂²	semidirect
50. #19153802	C₂²	semidirect
51. #19153801	C₂²	semidirect
52. #19153801	C₂²	semidirect
53. #19153801	C₂²	semidirect
54. #19153801	C₂²	semidirect
55. #19153800	C₂²	semidirect
56. #19153799	C₂²	semidirect
57. #19153796	C₂²	semidirect
58. #19153796	C₂²	semidirect
59. #19153796	C₂²	semidirect
60. #19153795	C₂²	semidirect
61. #19153794	C₂²	semidirect
62. #19153793	C₂²	semidirect
66. #19153791	C₂²	semidirect
67. #19153791	C₂²	semidirect
68. #19153791	C₂²	semidirect
69. #19153791	C₂²	semidirect
70. #19153791	C₂²	semidirect
72. #19153790	C₂²	semidirect
73. #19153790	C₂²	semidirect
74. #19153790	C₂²	semidirect
77. #19153789	C₂²	semidirect
78. #19153789	C₂²	semidirect
79. #19153789	C₂²	semidirect
80. #19153789	C₂²	semidirect
81. #19153789	C₂²	semidirect
82. #19153788	C₂²	semidirect
83. #19153788	C₂²	semidirect
84. #19153787	C₂²	semidirect
85. #19153787	C₂²	semidirect
86. #19153787	C₂²	semidirect
88. #19153786	C₂²	semidirect
89. #19153786	C₂²	semidirect
90. #19153786	C₂²	semidirect
91. #19153786	C₂²	semidirect
93. #19153784	C₂²	semidirect
94. #19153784	C₂²	semidirect
95. C₄×Dic₃₆₂	C₂²	semidirect
96. #19153781	C₂²	semidirect
97. C₄×D₇₂₄	C₂²	semidirect
98. C₄×D₇₂₄	C₂²	semidirect
100. #19153778	C₂²	semidirect
101. #19153778	C₂²	semidirect
103. C₄×C₂²⋊D₁₈₁	C₂²	semidirect
104. C₄×C₂²⋊D₁₈₁	C₂²	semidirect
105. #19153776	C₂²	semidirect
106. #19153774	C₂²	semidirect
107. #19153774	C₂²	semidirect
108. C₄⋊C₄×D₁₈₁	C₂²	semidirect
109. C₂×#15668426	C₂²	semidirect
110. C₂²⋊C₄×D₁₈₁	C₂²	semidirect
111. C₄²×D₁₈₁	C₂²	semidirect
112. #126×C₁₈₁	C₂²	semidirect
113. #125×C₁₈₁	C₂²	semidirect
114. #123×C₁₈₁	C₂²	semidirect
116. #121×C₁₈₁	C₂²	semidirect
117. #121×C₁₈₁	C₂²	semidirect
118. C₄×D₄×C₁₈₁	C₂²	semidirect
119. C₄×D₄×C₁₈₁	C₂²	semidirect
120. C₄×D₄×C₁₈₁	C₂²	semidirect
121. #117×C₁₈₁	C₂²	semidirect
122. C₂×C₄⋊C₄×C₁₈₁	C₂²	semidirect
359. C₁₈₁	#3546	semidirect
365. #553	D₁₈₁	semidirect
404. #126	C₂×D₁₈₁	semidirect
405. #125	C₂×D₁₈₁	semidirect
419. #123	C₂×D₁₈₁	semidirect
451. #121	C₂×D₁₈₁	semidirect
452. #121	C₂×D₁₈₁	semidirect
472. C₄×D₄	C₂×D₁₈₁	semidirect
473. C₄×D₄	C₂×D₁₈₁	semidirect
474. C₄×D₄	C₂×D₁₈₁	semidirect
477. #117	C₂×D₁₈₁	semidirect
479. 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
#26042020	2
#26042017	2
#26041997	2
#26041982	2
#26041950	2
#26041947	2
#26041930	2
#26041925	2
#26041924	2
#26041921	2
#26041913	2
#26041895	2
#26041865	2
#26041862	2
#26041860	2
#26041858	2
#26041848	2
#26041845	2
#26041826	2
#26041814	2
#553×C₁₈₁	2
#3546	181