Subgroups — #37548027

Order 23168.

1160 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26042024	C₂	1	2	yes	maximal, complemented
2	#26042016	C₂	1	2	yes	maximal, complemented
3	#26041993	C₂	1	1	yes	maximal, characteristic, complemented
4	#26041975	C₂	1	1	yes	maximal, characteristic, complemented
5	#26041970	C₂	1	1	yes	maximal, characteristic, complemented
6	#26041958	C₂	1	2	yes	maximal, complemented
7	#26041929	C₂	1	1	yes	maximal, characteristic, complemented
8	#26041918	C₂	1	2	yes	maximal, complemented
9	#26041917	C₂	1	1	yes	maximal, characteristic, complemented
10	#26041917	C₂	1	1	yes	maximal, characteristic, complemented
11	#26041914	C₂	1	1	yes	maximal, characteristic, complemented
12	#26041901	C₂	1	1	yes	maximal, characteristic, complemented
13	#26041883	C₂	1	1	yes	maximal, characteristic, complemented
14	#26041879	C₂	1	2	yes	maximal, complemented
15	#26041862	C₂	1	2	yes	maximal, complemented
16	#26041857	C₂	1	1	yes	maximal, characteristic, complemented
17	#26041845	C₂	1	1	yes	maximal, characteristic, complemented
18	#26041842	C₂	1	2	yes	maximal, complemented
19	#26041837	C₂	1	2	yes	maximal, complemented
20	#26041788	C₂	1	1	yes	maximal, characteristic, complemented
21	#26041786	C₂	1	1	yes	maximal, characteristic, complemented
22	#121×D₁₈₁	C₂	1	1	yes	maximal, characteristic, complemented
23	#550×C₁₈₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#15668449	C₂²	1	1	yes	characteristic, complemented
25	C₂×#15668448	C₂²	1	2	yes	complemented
26	C₂×D₄×D₁₈₁	C₂²	1	1	yes	characteristic
27	C₂×D₄×D₁₈₁	C₂²	1	2	yes	—
28	C₂×D₄×D₁₈₁	C₂²	1	1	yes	characteristic, complemented
29	C₂×D₄×D₁₈₁	C₂²	1	2	yes	complemented
30	C₂²×C₄×D₁₈₁	C₂²	1	1	yes	characteristic, complemented
31	#19153815	C₂²	1	1	yes	characteristic, complemented
32	#19153812	C₂²	1	2	yes	complemented
33	#19153811	C₂²	1	2	yes	complemented
34	#19153810	C₂²	1	2	yes	complemented
35	#19153810	C₂²	1	2	yes	complemented
36	#19153808	C₂²	1	1	yes	characteristic, complemented
37	#19153806	C₂²	1	2	yes	complemented
38	#19153805	C₂²	1	1	yes	characteristic, complemented
39	#19153804	C₂²	1	2	yes	complemented
40	#19153803	C₂²	1	2	yes	complemented
41	#19153802	C₂²	1	2	yes	complemented
42	#19153802	C₂²	1	2	yes	complemented
43	#19153801	C₂²	1	2	yes	—
44	#19153801	C₂²	1	1	yes	characteristic, complemented
45	#19153801	C₂²	1	2	yes	complemented
46	#19153799	C₂²	1	2	yes	complemented
47	#19153799	C₂²	1	2	yes	complemented
48	#19153798	C₂²	1	1	yes	characteristic, complemented
49	#19153798	C₂²	1	2	yes	complemented
50	#19153798	C₂²	1	2	yes	complemented
51	#19153797	C₂²	1	2	yes	complemented
52	#19153797	C₂²	1	2	yes	complemented
53	#19153797	C₂²	1	2	yes	complemented
54	#19153797	C₂²	1	2	yes	complemented
55	#19153795	C₂²	1	2	yes	complemented
56	#19153794	C₂²	1	2	yes	complemented
57	#19153794	C₂²	1	1	yes	characteristic, complemented
58	#19153793	C₂²	1	2	yes	complemented
59	#19153793	C₂²	1	1	yes	characteristic, complemented
60	#19153792	C₂²	1	1	yes	characteristic, complemented
61	#19153792	C₂²	1	1	yes	characteristic, complemented
62	#19153792	C₂²	1	1	yes	characteristic, complemented
63	#19153791	C₂²	1	1	yes	characteristic
64	#19153790	C₂²	1	1	yes	characteristic
65	#19153790	C₂²	1	2	yes	complemented
66	#19153790	C₂²	1	1	yes	characteristic, complemented
67	#19153789	C₂²	1	1	yes	characteristic
68	#19153789	C₂²	1	2	yes	complemented
69	#19153788	C₂²	1	2	yes	complemented
70	#19153788	C₂²	1	2	yes	complemented
71	#19153788	C₂²	1	2	yes	complemented
72	#19153788	C₂²	1	2	yes	complemented
73	#19153788	C₂²	1	2	yes	complemented
74	#19153788	C₂²	1	2	yes	complemented
75	#19153788	C₂²	1	2	yes	complemented
76	#19153788	C₂²	1	2	yes	complemented
77	#19153788	C₂²	1	1	yes	characteristic, complemented
78	#19153788	C₂²	1	2	yes	complemented
79	#19153787	C₂²	1	1	yes	characteristic
80	#19153787	C₂²	1	1	yes	characteristic, complemented
81	#19153787	C₂²	1	1	yes	characteristic, complemented
82	#19153787	C₂²	1	2	yes	complemented
83	#19153787	C₂²	1	1	yes	characteristic, complemented
84	#19153786	C₂²	1	1	yes	characteristic
85	#19153786	C₂²	1	2	yes	complemented
86	#19153784	C₂²	1	2	yes	—
87	#19153784	C₂²	1	2	yes	complemented
88	#19153784	C₂²	1	2	yes	complemented
89	#19153784	C₂²	1	2	yes	complemented
90	#19153784	C₂²	1	2	yes	complemented
91	#19153784	C₂²	1	2	yes	complemented
92	#19153784	C₂²	1	1	yes	characteristic, complemented
93	C₄×D₇₂₄	C₂²	1	1	yes	characteristic
94	C₄×D₇₂₄	C₂²	1	1	yes	characteristic, complemented
95	D₄×Dic₁₈₁	C₂²	1	1	yes	characteristic, complemented
96	D₄×Dic₁₈₁	C₂²	1	1	yes	characteristic, complemented
97	C₄×C₂²⋊D₁₈₁	C₂²	1	2	yes	complemented
98	C₄×C₂²⋊D₁₈₁	C₂²	1	1	yes	characteristic, complemented
99	C₄×C₂²⋊D₁₈₁	C₂²	1	1	yes	characteristic, complemented
100	C₄×C₂²⋊D₁₈₁	C₂²	1	2	yes	complemented
101	#19153776	C₂²	1	2	yes	complemented
102	#19153775	C₂²	1	1	yes	characteristic, complemented
103	#19153774	C₂²	1	1	yes	characteristic, complemented
104	#19153773	C₂²	1	1	yes	characteristic, complemented
105	#19153773	C₂²	1	2	yes	complemented
106	#19153772	C₂²	1	2	yes	complemented
107	C₂×C₄⋊Dic₁₈₁	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	C₂×#15668426	C₂²	1	2	yes	complemented
111	C₂²⋊C₄×D₁₈₁	C₂²	1	2	yes	complemented
112	C₂×#41×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
113	C₂×#41×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
114	#127×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
115	#127×C₁₈₁	C₂²	1	2	yes	complemented
116	#121×C₁₈₁	C₂²	1	2	yes	complemented
117	#121×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
118	#121×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
119	#121×C₁₈₁	C₂²	1	2	yes	complemented
120	C₄×Q₈×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₄×C₁₈₁	C₂²	1	2	yes	complemented
122	C₄×D₄×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	2	yes	—
126	#15668449	—	4	2	no	—
127	#15668448	—	4	4	no	—
128	C₂×Dic₃₆₂	C₂³	1	1	yes	characteristic
129	C₂×Dic₃₆₂	C₂³	1	2	yes	—
130	C₂×D₇₂₄	C₂³	1	1	yes	characteristic
131	C₂×D₇₂₄	C₂³	1	1	yes	characteristic
132	C₂×D₇₂₄	C₂³	1	1	yes	characteristic
133	C₂×D₇₂₄	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₁₈₁	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₁₈₁	C₂³	1	1	yes	characteristic
136	C₂×C₂²⋊D₁₈₁	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₁₈₁	C₂³	1	1	yes	characteristic
138	C₂×C₂²⋊D₁₈₁	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₁₈₁	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₁₈₁	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊D₁₈₁	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₁₈₁	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₁₈₁	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₁₈₁	C₂³	1	1	yes	characteristic
145	C₂×C₂²⋊D₁₈₁	C₂³	1	2	yes	—
146	D₄×D₁₈₁	—	4	2	no	—
147	D₄×D₁₈₁	—	4	2	no	—
148	D₄×D₁₈₁	—	4	4	no	—
149	D₄×D₁₈₁	—	4	4	no	—
150	C₂²×Dic₁₈₁	C₂³	1	2	yes	—
151	C₂²×Dic₁₈₁	C₂³	1	2	yes	—
152	C₂²×Dic₁₈₁	C₂³	1	2	yes	—
153	C₂²×Dic₁₈₁	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₁₈₁	—	4	2	no	—
155	C₂×C₄×D₁₈₁	C₂³	1	2	yes	—
156	C₂×C₄×D₁₈₁	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₁₈₁	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₁₈₁	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₁₈₁	C₂³	1	1	yes	characteristic
160	C₂×C₄×D₁₈₁	C₂³	1	2	yes	—
161	C₂×C₄×D₁₈₁	C₂³	1	1	yes	characteristic
162	C₄⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
163	C₄⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
164	C₄⋊Dic₁₈₁	C₂³	1	2	yes	—
165	C₄⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
166	C₄⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
167	#15668428	C₂³	1	2	yes	—
168	#15668428	C₂³	1	1	yes	characteristic
169	#15668428	C₂³	1	2	yes	—
170	#15668428	C₂³	1	2	yes	—
171	#15668428	C₂³	1	2	yes	—
172	#15668428	C₂³	1	1	yes	characteristic
173	#15668428	C₂³	1	1	yes	characteristic
174	#15668428	C₂³	1	2	yes	—
175	#15668428	C₂³	1	2	yes	—
176	#15668428	C₂³	1	2	yes	—
177	#15668428	C₂³	1	1	yes	characteristic
178	C₂²⋊Dic₁₈₁	C₂³	1	2	yes	—
179	C₂²⋊Dic₁₈₁	C₂³	1	2	yes	—
180	C₂²⋊Dic₁₈₁	C₂³	1	2	yes	—
181	C₂²⋊Dic₁₈₁	C₂³	1	2	yes	—
182	C₂²⋊Dic₁₈₁	C₂³	1	2	yes	—
183	C₂²⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
184	C₂²⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
185	C₂²⋊Dic₁₈₁	C₂³	1	2	yes	—
186	C₂²⋊Dic₁₈₁	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	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	1	yes	characteristic
197	#15668426	C₂³	1	1	yes	characteristic
198	#15668426	C₂³	1	1	yes	characteristic
199	#15668426	C₂³	1	2	yes	—
200	#15668426	C₂³	1	2	yes	—
201	#15668426	C₂³	1	1	yes	characteristic
202	#15668426	C₂³	1	2	yes	—
203	C₄×Dic₁₈₁	C₂³	1	2	yes	—
204	C₄×Dic₁₈₁	C₂³	1	2	yes	—
205	C₄×Dic₁₈₁	C₂³	1	1	yes	characteristic
206	#41×C₁₈₁	—	4	2	no	—
207	#41×C₁₈₁	—	4	2	no	—
208	C₂×Q₈×C₁₈₁	C₂³	1	1	yes	characteristic
209	C₂×D₄×C₁₈₁	C₂³	1	1	yes	characteristic
210	C₂×D₄×C₁₈₁	C₂³	1	1	yes	characteristic
211	C₂×D₄×C₁₈₁	C₂³	1	2	yes	—
212	C₂×D₄×C₁₈₁	C₂³	1	1	yes	characteristic
213	C₂×D₄×C₁₈₁	C₂³	1	2	yes	—
214	C₂×D₄×C₁₈₁	C₂³	1	2	yes	—
215	C₂×D₄×C₁₈₁	C₂³	1	2	yes	—
216	C₂×D₄×C₁₈₁	C₂³	1	2	yes	—
217	C₂×D₄×C₁₈₁	C₂³	1	2	yes	—
218	C₂²×C₄×C₁₈₁	C₂³	1	1	yes	characteristic
219	C₂²×C₄×C₁₈₁	C₂³	1	1	yes	characteristic
220	C₂²×C₄×C₁₈₁	C₂³	1	2	yes	—
221	C₂²×C₄×C₁₈₁	C₂³	1	2	yes	—
222	C₄⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
223	C₄⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
224	C₄⋊C₄×C₁₈₁	C₂³	1	2	yes	—
225	C₂²⋊C₄×C₁₈₁	C₂³	1	2	yes	—
226	C₂²⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
227	C₂²⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
228	C₂²⋊C₄×C₁₈₁	C₂³	1	2	yes	—
229	C₄²×C₁₈₁	C₂³	1	1	yes	characteristic
230	C₄²×C₁₈₁	C₂³	1	2	yes	—
231	C₂²×D₁₈₁	—	2	2	no	—
232	C₂²×D₁₈₁	—	2	4	no	—
233	C₂²×D₁₈₁	—	4	1	no	—
234	C₂²×D₁₈₁	—	4	1	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	1	yes	characteristic
243	C₂²×D₁₈₁	C₂⁴	1	1	yes	characteristic
244	Dic₃₆₂	—	4	2	no	—
245	Dic₃₆₂	—	4	1	no	—
246	D₇₂₄	—	2	2	no	—
247	D₇₂₄	—	2	2	no	—
248	D₇₂₄	—	4	2	no	—
249	D₇₂₄	—	4	1	no	—
250	C₂²⋊D₁₈₁	—	2	4	no	—
251	C₂²⋊D₁₈₁	—	2	2	no	—
252	C₂²⋊D₁₈₁	—	4	2	no	—
253	C₂²⋊D₁₈₁	—	4	2	no	—
254	C₂²⋊D₁₈₁	—	4	2	no	—
255	C₂²⋊D₁₈₁	—	4	2	no	—
256	C₂²⋊D₁₈₁	—	4	2	no	—
257	C₂²⋊D₁₈₁	—	4	1	no	—
258	C₂²⋊D₁₈₁	—	4	2	no	—
259	C₂²⋊D₁₈₁	—	4	2	no	—
260	C₂²⋊D₁₈₁	—	4	1	no	—
261	C₂²⋊D₁₈₁	—	4	1	no	—
262	C₂×Dic₁₈₁	—	4	1	no	—
263	C₂×Dic₁₈₁	—	4	2	no	—
264	C₂×Dic₁₈₁	—	4	2	no	—
265	C₂×Dic₁₈₁	—	4	2	no	—
266	C₂×Dic₁₈₁	C₂⁴	1	2	yes	—
267	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
268	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
269	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
270	C₂×Dic₁₈₁	C₂⁴	1	2	yes	—
271	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
272	C₂×Dic₁₈₁	C₂⁴	1	2	yes	—
273	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
274	C₄×D₁₈₁	—	2	4	no	—
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	1	no	—
280	C₄×D₁₈₁	—	4	2	no	—
281	C₂³×C₁₈₁	C₂⁴	1	1	yes	characteristic
282	C₂³×C₁₈₁	C₂⁴	1	2	yes	—
283	C₂³×C₁₈₁	C₂⁴	1	2	yes	—
284	C₂³×C₁₈₁	C₂⁴	1	1	yes	characteristic
285	Q₈×C₁₈₁	—	2	2	no	—
286	D₄×C₁₈₁	—	2	2	no	—
287	D₄×C₁₈₁	—	2	2	no	—
288	D₄×C₁₈₁	—	4	2	no	—
289	D₄×C₁₈₁	—	4	1	no	—
290	D₄×C₁₈₁	—	4	2	no	—
291	D₄×C₁₈₁	—	4	2	no	—
292	D₄×C₁₈₁	—	4	2	no	—
293	D₄×C₁₈₁	—	4	2	no	—
294	D₄×C₁₈₁	—	4	2	no	—
295	C₂×C₄×C₁₈₁	—	2	2	no	—
296	C₂×C₄×C₁₈₁	—	2	2	no	—
297	C₂×C₄×C₁₈₁	—	4	2	no	—
298	C₂×C₄×C₁₈₁	—	4	2	no	—
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	C₂×C₄×C₁₈₁	C₂⁴	1	2	yes	—
303	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
304	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
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	2	no	—
309	C₂²×C₁₈₁	—	2	2	no	—
310	C₂²×C₁₈₁	—	2	1	no	—
311	C₂²×C₁₈₁	—	2	2	no	—
312	C₂²×C₁₈₁	—	2	1	no	—
313	C₂²×C₁₈₁	—	2	2	no	—
314	C₂²×C₁₈₁	—	2	2	no	—
315	C₂²×C₁₈₁	—	2	1	no	—
316	C₂²×C₁₈₁	—	2	1	no	—
317	C₂²×C₁₈₁	—	2	2	no	—
318	C₂²×C₁₈₁	C₂⁵	1	1	yes	characteristic
319	C₂×D₁₈₁	—	2	1	no	—
320	C₂×D₁₈₁	—	2	1	no	—
321	C₂×D₁₈₁	—	2	1	no	—
322	C₂×D₁₈₁	—	2	1	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	1	no	—
328	C₂×D₁₈₁	—	2	1	no	—
329	C₂×D₁₈₁	—	2	2	no	—
330	C₂×D₁₈₁	—	4	4	no	—
331	C₂×D₁₈₁	—	8	4	no	—
332	C₂×D₁₈₁	—	8	4	no	—
333	C₂×D₁₈₁	H(5,𝔽₂)	1	2	yes	—
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	1	no	—
340	C₄×C₁₈₁	H(5,𝔽₂)	1	2	yes	—
341	Dic₁₈₁	—	2	1	no	—
342	Dic₁₈₁	—	2	1	no	—
343	Dic₁₈₁	—	2	2	no	—
344	Dic₁₈₁	—	2	1	no	—
345	Dic₁₈₁	—	2	2	no	—
346	Dic₁₈₁	—	2	1	no	—
347	Dic₁₈₁	—	2	1	no	—
348	Dic₁₈₁	—	2	2	no	—
349	C₂×C₁₈₁	—	4	1	no	—
350	C₂×C₁₈₁	—	4	2	no	—
351	C₂×C₁₈₁	—	4	2	no	—
352	C₂×C₁₈₁	—	4	1	no	—
353	C₂×C₁₈₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
354	C₂×C₁₈₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
355	C₂×C₁₈₁	#585	1	1	yes	characteristic
356	D₁₈₁	—	2	2	no	—
357	D₁₈₁	—	4	1	no	—
358	D₁₈₁	—	4	1	no	—
359	D₁₈₁	—	4	2	no	—
360	C₁₈₁	#3542	1	1	yes	characteristic, complemented, Sylow
361	#3542	—	181	1	no	maximal, Sylow
362	#562	—	181	2	no	—
363	#560	—	181	2	no	—
364	#555	—	181	1	no	—
365	#553	—	181	1	no	—
366	#552	—	181	1	no	—
367	#551	—	181	2	no	—
368	#550	D₁₈₁	1	1	yes	characteristic, complemented
369	#547	—	181	1	no	—
370	#546	—	181	1	no	—
371	#546	—	181	1	no	—
372	#546	—	181	2	no	—
373	D₄²	—	181	1	no	—
374	#542	—	181	1	no	—
375	#540	—	181	1	no	—
376	#540	—	181	2	no	—
377	#538	—	181	2	no	—
378	#537	—	181	1	no	—
379	#535	—	181	2	no	—
380	#535	—	181	1	no	—
381	#534	—	181	2	no	—
382	#525	—	181	1	no	—
383	#525	—	181	1	no	—
384	C₂×#121	—	181	1	no	—
385	C₂×#41	—	181	2	no	—
386	C₂×#41	—	181	1	no	—
387	C₂×#41	C₂×D₁₈₁	1	1	yes	characteristic, complemented
388	C₂×#41	C₂×D₁₈₁	1	1	yes	characteristic, complemented
389	C₂²×D₄	—	181	2	no	—
390	C₂²×D₄	—	181	1	no	—
391	C₂²×D₄	—	181	2	no	—
392	C₂²×D₄	—	181	1	no	—
393	C₂³×C₄	—	181	1	no	—
394	C₄⋊Q₈	—	181	1	no	—
395	#127	—	181	2	no	—
396	#127	C₂×D₁₈₁	1	2	yes	complemented
397	#127	C₂×D₁₈₁	1	1	yes	characteristic, complemented
398	#126	—	181	2	no	—
399	#126	—	181	2	no	—
400	#126	—	181	2	no	—
401	#125	—	181	2	no	—
402	#125	—	181	1	no	—
403	#124	—	181	1	no	—
404	#124	—	181	2	no	—
405	#124	—	181	2	no	—
406	#124	—	181	2	no	—
407	#124	—	181	2	no	—
408	#123	—	181	2	no	—
409	#123	—	181	2	no	—
410	#123	—	181	2	no	—
411	#123	—	181	2	no	—
412	#123	—	181	2	no	—
413	#123	—	181	2	no	—
414	#123	—	181	1	no	—
415	#123	—	181	2	no	—
416	#123	—	181	2	no	—
417	#123	—	181	1	no	—
418	#123	—	181	2	no	—
419	#123	—	181	2	no	—
420	C₂²⋊Q₈	—	181	1	no	—
421	C₂²⋊Q₈	—	181	1	no	—
422	C₂²⋊Q₈	—	181	1	no	—
423	C₂²⋊Q₈	—	181	2	no	—
424	C₂²⋊Q₈	—	181	1	no	—
425	C₂²⋊Q₈	—	181	2	no	—
426	C₂²⋊Q₈	—	181	1	no	—
427	C₂²⋊Q₈	—	181	2	no	—
428	#121	—	181	1	no	—
429	#121	—	181	2	no	—
430	#121	—	181	1	no	—
431	#121	—	181	1	no	—
432	#121	—	181	1	no	—
433	#121	—	181	2	no	—
434	#121	—	181	2	no	—
435	#121	—	181	2	no	—
436	#121	—	181	2	no	—
437	#121	—	181	2	no	—
438	#121	—	181	2	no	—
439	#121	—	181	1	no	—
440	#121	—	181	2	no	—
441	#121	—	181	2	no	—
442	#121	—	181	2	no	—
443	#121	—	181	1	no	—
444	#121	—	181	2	no	—
445	#121	—	181	1	no	—
446	#121	—	181	1	no	—
447	#121	—	181	2	no	—
448	#121	—	181	1	no	—
449	#121	C₂×D₁₈₁	1	1	yes	characteristic, complemented
450	#121	C₂×D₁₈₁	1	2	yes	complemented
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	1	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	1	no	—
461	#120	—	181	2	no	—
462	C₄×Q₈	C₂×D₁₈₁	1	1	yes	characteristic, complemented
463	C₄×D₄	—	181	1	no	—
464	C₄×D₄	—	181	1	no	—
465	C₄×D₄	—	181	2	no	—
466	C₄×D₄	—	181	1	no	—
467	C₄×D₄	—	181	2	no	—
468	C₄×D₄	—	181	1	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	2	yes	complemented
474	#117	—	181	1	no	—
475	#117	—	181	1	no	—
476	#117	—	181	2	no	—
477	#117	—	181	1	no	—
478	#117	—	181	2	no	—
479	C₂×C₄⋊C₄	—	181	1	no	—
480	C₂×C₄⋊C₄	—	181	1	no	—
481	C₂×C₂²⋊C₄	—	181	2	no	—
482	C₂×C₂²⋊C₄	—	181	2	no	—
483	C₂×C₂²⋊C₄	—	181	2	no	—
484	C₂⁴	—	181	2	no	—
485	C₂⁴	—	181	1	no	—
486	C₂⁴	—	181	2	no	—
487	#41	—	4	2	no	—
488	#41	—	4	2	no	—
489	#41	—	724	2	no	—
490	#41	—	724	4	no	—
491	C₂×Q₈	—	181	1	no	—
492	C₂×Q₈	—	181	2	no	—
493	C₂×Q₈	C₂²×D₁₈₁	1	1	yes	characteristic
494	C₂×D₄	—	181	1	no	—
495	C₂×D₄	—	181	2	no	—
496	C₂×D₄	—	181	1	no	—
497	C₂×D₄	—	181	2	no	—
498	C₂×D₄	—	181	2	no	—
499	C₂×D₄	—	181	1	no	—
500	C₂×D₄	—	181	2	no	—
501	C₂×D₄	—	181	2	no	—
502	C₂×D₄	—	181	2	no	—
503	C₂×D₄	—	181	2	no	—
504	C₂×D₄	—	181	1	no	—
505	C₂×D₄	—	181	2	no	—
506	C₂×D₄	—	181	1	no	—
507	C₂×D₄	—	181	1	no	—
508	C₂×D₄	—	181	1	no	—
509	C₂×D₄	—	181	2	no	—
510	C₂×D₄	—	724	2	no	—
511	C₂×D₄	—	724	2	no	—
512	C₂×D₄	—	724	4	no	—
513	C₂×D₄	—	724	4	no	—
514	C₂×D₄	C₂²×D₁₈₁	1	1	yes	characteristic
515	C₂×D₄	C₂²×D₁₈₁	1	1	yes	characteristic
516	C₂×D₄	C₂²×D₁₈₁	1	2	yes	—
517	C₂×D₄	C₂²×D₁₈₁	1	1	yes	characteristic
518	C₂×D₄	C₂²×D₁₈₁	1	2	yes	—
519	C₂×D₄	C₂²×D₁₈₁	1	2	yes	—
520	C₂×D₄	C₂²×D₁₈₁	1	2	yes	—
521	C₂×D₄	C₂²×D₁₈₁	1	2	yes	—
522	C₂×D₄	C₂²×D₁₈₁	1	2	yes	—
523	C₂²×C₄	—	181	2	no	—
524	C₂²×C₄	—	181	1	no	—
525	C₂²×C₄	—	181	1	no	—
526	C₂²×C₄	—	181	1	no	—
527	C₂²×C₄	—	181	2	no	—
528	C₂²×C₄	—	181	2	no	—
529	C₂²×C₄	—	181	2	no	—
530	C₂²×C₄	—	181	1	no	—
531	C₂²×C₄	—	181	1	no	—
532	C₂²×C₄	—	181	1	no	—
533	C₂²×C₄	—	181	2	no	—
534	C₂²×C₄	—	724	2	no	—
535	C₂²×C₄	C₂²×D₁₈₁	1	1	yes	characteristic
536	C₂²×C₄	C₂²×D₁₈₁	1	1	yes	characteristic
537	C₂²×C₄	C₂²×D₁₈₁	1	2	yes	—
538	C₂²×C₄	C₂²×D₁₈₁	1	2	yes	—
539	C₄⋊C₄	—	181	1	no	—
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	2	no	—
547	C₄⋊C₄	—	181	1	no	—
548	C₄⋊C₄	—	181	1	no	—
549	C₄⋊C₄	—	181	2	no	—
550	C₄⋊C₄	—	181	1	no	—
551	C₄⋊C₄	—	181	2	no	—
552	C₄⋊C₄	—	181	2	no	—
553	C₄⋊C₄	—	181	2	no	—
554	C₄⋊C₄	—	181	1	no	—
555	C₄⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
556	C₄⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
557	C₄⋊C₄	C₂²×D₁₈₁	1	2	yes	—
558	C₂²⋊C₄	—	181	2	no	—
559	C₂²⋊C₄	—	181	2	no	—
560	C₂²⋊C₄	—	181	2	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	1	no	—
567	C₂²⋊C₄	—	181	1	no	—
568	C₂²⋊C₄	—	181	2	no	—
569	C₂²⋊C₄	—	181	1	no	—
570	C₂²⋊C₄	—	181	2	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	1	no	—
577	C₂²⋊C₄	—	181	2	no	—
578	C₂²⋊C₄	—	181	1	no	—
579	C₂²⋊C₄	—	181	1	no	—
580	C₂²⋊C₄	—	181	1	no	—
581	C₂²⋊C₄	—	181	2	no	—
582	C₂²⋊C₄	—	181	2	no	—
583	C₂²⋊C₄	C₂²×D₁₈₁	1	2	yes	—
584	C₂²⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
585	C₂²⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
586	C₂²⋊C₄	C₂²×D₁₈₁	1	2	yes	—
587	C₄²	—	181	2	no	—
588	C₄²	—	181	2	no	—
589	C₄²	—	181	1	no	—
590	C₄²	C₂²×D₁₈₁	1	1	yes	characteristic
591	C₄²	C₂²×D₁₈₁	1	2	yes	—
592	C₂³	—	362	4	no	—
593	C₂³	—	362	2	no	—
594	C₂³	—	181	2	no	—
595	C₂³	—	181	1	no	—
596	C₂³	—	181	1	no	—
597	C₂³	—	181	1	no	—
598	C₂³	—	724	2	no	—
599	C₂³	—	724	2	no	—
600	C₂³	—	724	2	no	—
601	C₂³	—	724	2	no	—
602	C₂³	—	724	2	no	—
603	C₂³	—	724	1	no	—
604	C₂³	—	724	1	no	—
605	C₂³	C₂³×D₁₈₁	1	2	yes	—
606	C₂³	C₂³×D₁₈₁	1	2	yes	—
607	C₂³	C₂³×D₁₈₁	1	1	yes	characteristic
608	C₂³	C₂³×D₁₈₁	1	1	yes	characteristic
609	Q₈	—	2	2	no	—
610	Q₈	—	724	2	no	—
611	Q₈	—	724	1	no	—
612	D₄	—	2	2	no	—
613	D₄	—	2	2	no	—
614	D₄	—	4	2	no	—
615	D₄	—	4	2	no	—
616	D₄	—	4	2	no	—
617	D₄	—	4	2	no	—
618	D₄	—	4	2	no	—
619	D₄	—	4	2	no	—
620	D₄	—	4	1	no	—
621	D₄	—	362	2	no	—
622	D₄	—	362	4	no	—
623	D₄	—	362	2	no	—
624	D₄	—	362	2	no	—
625	D₄	—	724	2	no	—
626	D₄	—	724	1	no	—
627	D₄	—	724	2	no	—
628	D₄	—	724	2	no	—
629	D₄	—	724	2	no	—
630	D₄	—	724	2	no	—
631	D₄	—	724	2	no	—
632	D₄	—	724	1	no	—
633	D₄	—	724	1	no	—
634	D₄	—	724	1	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	—	181	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	1	no	—
651	C₂×C₄	—	181	2	no	—
652	C₂×C₄	—	181	1	no	—
653	C₂×C₄	—	724	1	no	—
654	C₂×C₄	—	724	1	no	—
655	C₂×C₄	—	724	2	no	—
656	C₂×C₄	—	724	1	no	—
657	C₂×C₄	—	724	2	no	—
658	C₂×C₄	—	724	2	no	—
659	C₂×C₄	—	724	2	no	—
660	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
661	C₂×C₄	C₂³×D₁₈₁	1	2	yes	—
662	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
663	C₂×C₄	C₂³×D₁₈₁	1	2	yes	—
664	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
665	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
666	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
667	C₂²	—	2	2	no	—
668	C₂²	—	2	1	no	—
669	C₂²	—	2	2	no	—
670	C₂²	—	2	1	no	—
671	C₂²	—	2	1	no	—
672	C₂²	—	2	2	no	—
673	C₂²	—	2	2	no	—
674	C₂²	—	2	1	no	—
675	C₂²	—	2	1	no	—
676	C₂²	—	2	1	no	—
677	C₂²	—	2	2	no	—
678	C₂²	—	2	2	no	—
679	C₂²	—	362	1	no	—
680	C₂²	—	362	1	no	—
681	C₂²	—	362	1	no	—
682	C₂²	—	362	2	no	—
683	C₂²	—	362	1	no	—
684	C₂²	—	362	2	no	—
685	C₂²	—	362	1	no	—
686	C₂²	—	362	1	no	—
687	C₂²	—	362	1	no	—
688	C₂²	—	362	1	no	—
689	C₂²	—	362	2	no	—
690	C₂²	—	1448	4	no	—
691	C₂²	—	1448	4	no	—
692	C₂²	—	181	2	no	—
693	C₂²	—	724	4	no	—
694	C₂²	C₂⁴×D₁₈₁	1	1	yes	characteristic
695	C₄	—	2	1	no	—
696	C₄	—	2	2	no	—
697	C₄	—	2	1	no	—
698	C₄	—	2	1	no	—
699	C₄	—	2	1	no	—
700	C₄	—	2	2	no	—
701	C₄	—	362	1	no	—
702	C₄	—	362	2	no	—
703	C₄	—	362	2	no	—
704	C₄	—	362	2	no	—
705	C₄	—	362	1	no	—
706	C₄	—	362	1	no	—
707	C₄	—	362	1	no	—
708	C₄	—	362	1	no	—
709	C₄	#19153861	1	2	yes	—
710	C₂	—	4	2	no	—
711	C₂	—	4	2	no	—
712	C₂	—	4	1	no	—
713	C₂	—	4	1	no	—
714	C₂	—	362	2	no	—
715	C₂	—	724	2	no	—
716	C₂	—	724	1	no	—
717	C₂	—	724	1	no	—
718	C₂	H(5,𝔽₂)×D₁₈₁	1	1	yes	characteristic
719	C₂	C₂×#19153861	1	1	yes	characteristic
720	C₂	#26042115	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₈₁
commutator, socle, cosocle	C₂²×C₁₈₁	C₂⁵
Fitting	#550×C₁₈₁	C₂
hypercenter	#550	D₁₈₁
hypocenter	C₁₈₁	#3542
LCS	G ▷ C₂²×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂² ◁ #550

Complements

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

N	H ≅ G/N	type
1. #26042024	C₂	semidirect
2. #26042016	C₂	semidirect
3. #26041993	C₂	semidirect
4. #26041975	C₂	semidirect
5. #26041970	C₂	semidirect
6. #26041958	C₂	semidirect
7. #26041929	C₂	semidirect
8. #26041918	C₂	semidirect
9. #26041917	C₂	semidirect
10. #26041917	C₂	semidirect
11. #26041914	C₂	semidirect
12. #26041901	C₂	semidirect
13. #26041883	C₂	semidirect
14. #26041879	C₂	semidirect
15. #26041862	C₂	semidirect
16. #26041857	C₂	semidirect
17. #26041845	C₂	semidirect
18. #26041842	C₂	semidirect
19. #26041837	C₂	semidirect
20. #26041788	C₂	semidirect
21. #26041786	C₂	semidirect
22. #121×D₁₈₁	C₂	semidirect
23. #550×C₁₈₁	C₂	semidirect
24. C₂×#15668449	C₂²	semidirect
25. C₂×#15668448	C₂²	semidirect
28. C₂×D₄×D₁₈₁	C₂²	semidirect
29. C₂×D₄×D₁₈₁	C₂²	semidirect
30. C₂²×C₄×D₁₈₁	C₂²	semidirect
31. #19153815	C₂²	semidirect
32. #19153812	C₂²	semidirect
33. #19153811	C₂²	semidirect
34. #19153810	C₂²	semidirect
35. #19153810	C₂²	semidirect
36. #19153808	C₂²	semidirect
37. #19153806	C₂²	semidirect
38. #19153805	C₂²	semidirect
39. #19153804	C₂²	semidirect
40. #19153803	C₂²	semidirect
41. #19153802	C₂²	semidirect
42. #19153802	C₂²	semidirect
44. #19153801	C₂²	semidirect
45. #19153801	C₂²	semidirect
46. #19153799	C₂²	semidirect
47. #19153799	C₂²	semidirect
48. #19153798	C₂²	semidirect
49. #19153798	C₂²	semidirect
50. #19153798	C₂²	semidirect
51. #19153797	C₂²	semidirect
52. #19153797	C₂²	semidirect
53. #19153797	C₂²	semidirect
54. #19153797	C₂²	semidirect
55. #19153795	C₂²	semidirect
56. #19153794	C₂²	semidirect
57. #19153794	C₂²	semidirect
58. #19153793	C₂²	semidirect
59. #19153793	C₂²	semidirect
60. #19153792	C₂²	semidirect
61. #19153792	C₂²	semidirect
62. #19153792	C₂²	semidirect
65. #19153790	C₂²	semidirect
66. #19153790	C₂²	semidirect
68. #19153789	C₂²	semidirect
69. #19153788	C₂²	semidirect
70. #19153788	C₂²	semidirect
71. #19153788	C₂²	semidirect
72. #19153788	C₂²	semidirect
73. #19153788	C₂²	semidirect
74. #19153788	C₂²	semidirect
75. #19153788	C₂²	semidirect
76. #19153788	C₂²	semidirect
77. #19153788	C₂²	semidirect
78. #19153788	C₂²	semidirect
80. #19153787	C₂²	semidirect
81. #19153787	C₂²	semidirect
82. #19153787	C₂²	semidirect
83. #19153787	C₂²	semidirect
85. #19153786	C₂²	semidirect
87. #19153784	C₂²	semidirect
88. #19153784	C₂²	semidirect
89. #19153784	C₂²	semidirect
90. #19153784	C₂²	semidirect
91. #19153784	C₂²	semidirect
92. #19153784	C₂²	semidirect
94. C₄×D₇₂₄	C₂²	semidirect
95. D₄×Dic₁₈₁	C₂²	semidirect
96. D₄×Dic₁₈₁	C₂²	semidirect
97. C₄×C₂²⋊D₁₈₁	C₂²	semidirect
98. C₄×C₂²⋊D₁₈₁	C₂²	semidirect
99. C₄×C₂²⋊D₁₈₁	C₂²	semidirect
100. C₄×C₂²⋊D₁₈₁	C₂²	semidirect
101. #19153776	C₂²	semidirect
102. #19153775	C₂²	semidirect
103. #19153774	C₂²	semidirect
104. #19153773	C₂²	semidirect
105. #19153773	C₂²	semidirect
106. #19153772	C₂²	semidirect
107. C₂×C₄⋊Dic₁₈₁	C₂²	semidirect
108. C₄⋊C₄×D₁₈₁	C₂²	semidirect
109. C₂×#15668426	C₂²	semidirect
110. C₂×#15668426	C₂²	semidirect
111. C₂²⋊C₄×D₁₈₁	C₂²	semidirect
112. C₂×#41×C₁₈₁	C₂²	semidirect
113. C₂×#41×C₁₈₁	C₂²	semidirect
114. #127×C₁₈₁	C₂²	semidirect
115. #127×C₁₈₁	C₂²	semidirect
116. #121×C₁₈₁	C₂²	semidirect
117. #121×C₁₈₁	C₂²	semidirect
118. #121×C₁₈₁	C₂²	semidirect
119. #121×C₁₈₁	C₂²	semidirect
120. C₄×Q₈×C₁₈₁	C₂²	semidirect
121. C₄×D₄×C₁₈₁	C₂²	semidirect
122. C₄×D₄×C₁₈₁	C₂²	semidirect
360. C₁₈₁	#3542	semidirect
368. #550	D₁₈₁	semidirect
387. C₂×#41	C₂×D₁₈₁	semidirect
388. C₂×#41	C₂×D₁₈₁	semidirect
396. #127	C₂×D₁₈₁	semidirect
397. #127	C₂×D₁₈₁	semidirect
449. #121	C₂×D₁₈₁	semidirect
450. #121	C₂×D₁₈₁	semidirect
451. #121	C₂×D₁₈₁	semidirect
452. #121	C₂×D₁₈₁	semidirect
462. C₄×Q₈	C₂×D₁₈₁	semidirect
472. C₄×D₄	C₂×D₁₈₁	semidirect
473. C₄×D₄	C₂×D₁₈₁	semidirect

Maximal subgroups

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

subgroup	index
#26042024	2
#26042016	2
#26041993	2
#26041975	2
#26041970	2
#26041958	2
#26041929	2
#26041918	2
#26041917	2
#26041914	2
#26041901	2
#26041883	2
#26041879	2
#26041862	2
#26041857	2
#26041845	2
#26041842	2
#26041837	2
#26041788	2
#26041786	2
#121×D₁₈₁	2
#550×C₁₈₁	2
#3542	181