Subgroups — #14907306

Order 2816.

526 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13077587	C₂	1	1	yes	maximal, characteristic
2	#13070523	C₂	1	1	yes	maximal, characteristic, complemented
3	#13070518	C₂	1	1	yes	maximal, characteristic, complemented
4	#13070445	C₂	1	1	yes	maximal, characteristic, complemented
5	#13070444	C₂	1	1	yes	maximal, characteristic, complemented
6	#13070440	C₂	1	1	yes	maximal, characteristic, complemented
7	#13070435	C₂	1	1	yes	maximal, characteristic, complemented
8	(C₂²⋊D₁₁)⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
9	(C₂²⋊D₁₁)⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
10	#13070421	C₂	1	1	yes	maximal, characteristic, complemented
11	#13070417	C₂	1	1	yes	maximal, characteristic, complemented
12	#13070214	C₂	1	1	yes	maximal, characteristic, complemented
13	#13070213	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₁₆×D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₁×#2164	C₂	1	1	yes	maximal, characteristic, complemented
16	#10623059	C₄	1	1	yes	characteristic
17	C₁₁×#405	C₂²	1	1	yes	characteristic
18	#10622741	C₄	1	1	yes	characteristic
19	#10622740	C₄	1	1	yes	characteristic
20	C₈×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic
21	C₈×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic
22	C₂×#66876	C₂²	1	1	yes	characteristic
23	C₂²×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
24	#10622613	C₄	1	1	yes	characteristic
25	C₂×#66862	C₂²	1	1	yes	characteristic
26	C₂×C₁₆×D₁₁	C₂²	1	1	yes	characteristic
27	C₂×C₁₆×D₁₁	C₂²	1	1	yes	characteristic
28	C₂×C₁₆×D₁₁	C₂²	1	1	yes	characteristic
29	#10622322	C₄	1	1	yes	characteristic
30	#10622319	C₄	1	1	yes	characteristic
31	#10622318	C₄	1	1	yes	characteristic
32	#10622314	C₄	1	1	yes	characteristic
33	#10622302	C₂²	1	1	yes	characteristic
34	C₈×D₄₄	C₂²	1	1	yes	characteristic
35	C₄×C₈×D₁₁	C₂²	1	1	yes	characteristic
36	C₈×Dic₂₂	C₂²	1	1	yes	characteristic
37	C₁₁×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
38	C₁₁×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
39	C₁₁×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
40	C₁₁×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
41	C₁₁×#346	C₂²	1	1	yes	characteristic
42	C₄×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
43	(C₂×D₁₁)⋊C₁₆	C₂²	1	1	yes	characteristic
44	(C₂×D₁₁)⋊C₁₆	C₂²	1	1	yes	characteristic
45	(C₂×D₁₁)⋊C₁₆	C₂²	1	1	yes	characteristic
46	(C₂×D₁₁)⋊C₁₆	C₂²	1	1	yes	characteristic
47	#10622140	C₂²	1	1	yes	characteristic
48	Dic₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
49	Dic₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
50	Dic₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
51	Dic₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
52	C₁₆×Dic₁₁	C₂²	1	1	yes	characteristic
53	C₁₆×Dic₁₁	C₂²	1	1	yes	characteristic
54	C₁₆×Dic₁₁	C₂²	1	1	yes	characteristic
55	#10622099	C₂²	1	1	yes	characteristic
56	#10622099	C₂²	1	1	yes	characteristic
57	C₄×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
58	C₄×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
59	C₂×C₁₁×M₁₆	C₂×C₄	1	1	yes	characteristic
60	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
61	C₁₁×#117	C₂×C₄	1	1	yes	characteristic
62	C₄×C₂²⋊D₁₁	C₂×C₄	1	1	yes	characteristic
63	C₄×C₂²⋊D₁₁	C₂×C₄	1	1	yes	characteristic
64	C₂×#4313	C₂×C₄	1	1	yes	characteristic
65	C₂×C₈×D₁₁	C₂×C₄	1	1	yes	characteristic
66	C₂×C₈×D₁₁	C₂³	1	1	yes	characteristic
67	C₂×C₈×D₁₁	C₂³	1	1	yes	characteristic
68	#66951	C₈	1	1	yes	characteristic
69	#66949	C₈	1	1	yes	characteristic
70	#66947	C₈	1	1	yes	characteristic
71	#66942	C₈	1	1	yes	characteristic
72	#66938	C₈	1	1	yes	characteristic
73	#66937	C₈	1	1	yes	characteristic
74	#66936	C₈	1	1	yes	characteristic
75	#66932	C₈	1	1	yes	characteristic
76	C₄×D₄₄	C₂×C₄	1	1	yes	characteristic
77	#66925	C₂×C₄	1	1	yes	characteristic
78	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
79	C₄×Dic₂₂	C₂×C₄	1	1	yes	characteristic
80	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
81	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
82	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
83	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
84	C₁₁×#97	C₂×C₄	1	1	yes	characteristic
85	C₁₁×#97	C₂×C₄	1	1	yes	characteristic
86	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
87	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
88	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
89	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
90	(C₂×D₁₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
91	(C₂×D₁₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
92	(C₂×D₁₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
93	(C₂×D₁₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
94	#66879	C₂×C₄	1	1	yes	characteristic
95	Dic₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
96	Dic₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
97	Dic₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
98	Dic₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
99	C₈×Dic₁₁	C₂×C₄	1	1	yes	characteristic
100	C₈×Dic₁₁	C₂³	1	1	yes	characteristic
101	C₈×Dic₁₁	C₂³	1	1	yes	characteristic
102	#66876	—	2	2	no	—
103	C₂×C₁₁⋊C₁₆	—	2	2	no	—
104	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
105	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
106	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
107	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
108	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
109	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
110	#66867	C₂×C₄	1	1	yes	characteristic
111	C₄×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
112	#66862	—	2	2	no	—
113	C₁₆×D₁₁	—	2	2	no	—
114	C₁₆×D₁₁	—	2	2	no	—
115	C₁₆×D₁₁	—	2	2	no	—
116	#33480	—	11	1	no	maximal, Sylow
117	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₂²⋊D₁₁	C₂×C₈	1	1	yes	characteristic
119	C₂×C₂²⋊D₁₁	C₂×C₈	1	1	yes	characteristic
120	C₂×D₄₄	C₂×C₈	1	1	yes	characteristic
121	C₂×C₄×D₁₁	C₂×C₈	1	1	yes	characteristic
122	C₂×C₄×D₁₁	C₂×C₈	1	1	yes	characteristic
123	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
125	C₂×Dic₂₂	C₂×C₈	1	1	yes	characteristic
126	C₁₁×M₁₆	—	2	2	no	—
127	C₂×C₈×C₁₁	—	2	1	no	—
128	C₂×C₈×C₁₁	—	2	1	no	—
129	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
133	C₁₁×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
134	C₁₁×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
135	C₁₁×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
136	C₁₁×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
137	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
138	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
139	C₂²⋊Dic₁₁	C₂×C₈	1	1	yes	characteristic
140	C₂²⋊Dic₁₁	C₂×C₈	1	1	yes	characteristic
141	(C₂×D₁₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
142	(C₂×D₁₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
143	(C₂×D₁₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
144	(C₂×D₁₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
145	(C₂×D₁₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
146	(C₂×D₁₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
147	C₄⋊Dic₁₁	C₂×C₈	1	1	yes	characteristic
148	C₄⋊Dic₁₁	C₂×C₈	1	1	yes	characteristic
149	Dic₁₁⋊C₄	C₂×C₈	1	1	yes	characteristic
150	Dic₁₁⋊C₄	C₂×C₈	1	1	yes	characteristic
151	Dic₁₁⋊C₄	C₂×C₈	1	1	yes	characteristic
152	Dic₁₁⋊C₄	C₂×C₈	1	1	yes	characteristic
153	Dic₁₁⋊C₄	C₂×C₈	1	1	yes	characteristic
154	Dic₁₁⋊C₄	C₂×C₈	1	1	yes	characteristic
155	C₄×Dic₁₁	C₂×C₈	1	1	yes	characteristic
156	C₄×Dic₁₁	C₂×C₈	1	1	yes	characteristic
157	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
158	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
163	#4313	—	2	2	no	—
164	C₈×D₁₁	—	2	2	no	—
165	C₈×D₁₁	—	2	1	no	—
166	C₈×D₁₁	—	2	1	no	—
167	C₈×D₁₁	—	2	1	no	—
168	C₈×D₁₁	—	2	1	no	—
169	C₁₁×C₁₆	—	2	1	no	—
170	C₁₁×C₁₆	—	2	1	no	—
171	C₁₁×C₁₆	—	2	1	no	—
172	C₁₁×C₁₆	—	2	1	no	—
173	C₁₁⋊C₁₆	—	2	1	no	—
174	C₁₁⋊C₁₆	—	2	1	no	—
175	C₁₁⋊C₁₆	#41	1	2	yes	—
176	C₁₁⋊C₁₆	#41	1	2	yes	—
177	#2966	—	11	1	no	—
178	#2183	—	11	1	no	—
179	Q₈×C₁₆	—	11	1	no	—
180	#2169	—	11	1	no	—
181	#2168	—	11	1	no	—
182	#2168	—	11	1	no	—
183	D₄×C₁₆	—	11	1	no	—
184	D₄×C₁₆	—	11	1	no	—
185	D₄×C₁₆	—	11	1	no	—
186	#2164	—	11	1	no	—
187	#2164	D₁₁	1	1	yes	characteristic, complemented
188	#2163	—	11	1	no	—
189	#2108	—	11	1	no	—
190	#2108	—	11	1	no	—
191	C₂×C₄×C₁₆	—	11	1	no	—
192	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
193	C₂²×D₁₁	C₂²×C₈	1	1	yes	characteristic
194	C₂²×D₁₁	C₂²×C₈	1	1	yes	characteristic
195	C₂×C₄×C₁₁	—	2	1	no	—
196	C₂×C₄×C₁₁	—	2	1	no	—
197	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
198	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
199	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
200	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
201	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
202	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
203	C₂²⋊D₁₁	—	2	2	no	—
204	C₂²⋊D₁₁	—	2	2	no	—
205	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
206	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
207	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
208	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
209	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
210	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
211	D₄₄	—	2	2	no	—
212	C₄×D₁₁	—	2	2	no	—
213	C₄×D₁₁	—	2	1	no	—
214	C₄×D₁₁	—	2	1	no	—
215	C₄×D₁₁	—	2	1	no	—
216	C₄×D₁₁	—	2	1	no	—
217	C₄×D₁₁	—	2	2	no	—
218	Dic₂₂	—	2	2	no	—
219	C₈×C₁₁	—	2	1	no	—
220	C₈×C₁₁	—	2	1	no	—
221	C₈×C₁₁	#131	1	2	yes	—
222	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
223	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
224	C₁₁⋊C₈	—	2	1	no	—
225	C₁₁⋊C₈	—	2	1	no	—
226	C₁₁⋊C₈	—	2	1	no	—
227	C₁₁⋊C₈	—	2	1	no	—
228	#529	—	11	1	no	—
229	C₂×M₃₂	—	11	1	no	—
230	C₂×M₃₂	—	11	1	no	—
231	C₂²×C₁₆	—	11	1	no	—
232	C₂²×C₁₆	—	11	1	no	—
233	C₂²×C₁₆	—	11	1	no	—
234	C₂²×C₁₆	—	11	1	no	—
235	#446	—	11	1	no	—
236	C₈×Q₈	—	11	1	no	—
237	#436	—	11	1	no	—
238	#435	—	11	1	no	—
239	#435	—	11	1	no	—
240	C₈×D₄	—	11	1	no	—
241	C₈×D₄	—	11	1	no	—
242	C₈×D₄	—	11	1	no	—
243	#433	—	11	1	no	—
244	#433	—	11	1	no	—
245	#432	—	11	1	no	—
246	#405	—	11	1	no	—
247	#405	C₂×D₁₁	1	1	yes	characteristic
248	C₂×C₄×C₈	—	11	1	no	—
249	C₄⋊C₁₆	—	11	1	no	—
250	C₄⋊C₁₆	—	11	1	no	—
251	C₄⋊C₁₆	—	11	1	no	—
252	C₄⋊C₁₆	—	11	1	no	—
253	C₄⋊C₁₆	C₂×D₁₁	1	1	yes	characteristic
254	C₄⋊C₁₆	C₂×D₁₁	1	1	yes	characteristic
255	C₂²⋊C₁₆	—	11	1	no	—
256	C₂²⋊C₁₆	—	11	1	no	—
257	C₂²⋊C₁₆	—	11	1	no	—
258	C₂²⋊C₁₆	—	11	1	no	—
259	C₂²⋊C₁₆	C₂×D₁₁	1	1	yes	characteristic
260	C₂²⋊C₁₆	C₂×D₁₁	1	1	yes	characteristic
261	#346	—	11	1	no	—
262	#346	—	11	1	no	—
263	#346	—	11	1	no	—
264	#346	C₂×D₁₁	1	1	yes	characteristic
265	C₄×C₁₆	—	11	1	no	—
266	C₄×C₁₆	—	11	1	no	—
267	C₄×C₁₆	—	11	1	no	—
268	C₄×C₁₆	—	11	1	no	—
269	C₄×C₁₆	—	11	1	no	—
270	C₄×C₁₆	C₂×D₁₁	1	1	yes	characteristic
271	C₂²×C₁₁	—	2	1	no	—
272	C₂²×C₁₁	—	2	1	no	—
273	C₂²×C₁₁	—	2	1	no	—
274	C₂²×C₁₁	C₂³×C₈	1	1	yes	characteristic
275	C₂×D₁₁	—	2	1	no	—
276	C₂×D₁₁	—	2	1	no	—
277	C₂×D₁₁	—	2	1	no	—
278	C₂×D₁₁	—	2	1	no	—
279	C₂×D₁₁	—	2	1	no	—
280	C₂×D₁₁	#504	1	2	yes	—
281	C₄×C₁₁	—	2	1	no	—
282	C₄×C₁₁	—	2	1	no	—
283	C₄×C₁₁	—	2	1	no	—
284	C₄×C₁₁	—	2	1	no	—
285	C₄×C₁₁	—	2	1	no	—
286	C₄×C₁₁	C₄×#41	1	1	yes	characteristic
287	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
288	Dic₁₁	—	2	1	no	—
289	Dic₁₁	—	2	1	no	—
290	Dic₁₁	—	2	1	no	—
291	Dic₁₁	—	2	1	no	—
292	Dic₁₁	—	2	1	no	—
293	Dic₁₁	#504	1	2	yes	—
294	C₂×M₁₆	—	11	1	no	—
295	C₂×M₁₆	C₄×D₁₁	1	1	yes	characteristic
296	C₂²×C₈	—	11	1	no	—
297	C₂²×C₈	—	11	1	no	—
298	C₂²×C₈	—	11	1	no	—
299	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
300	#126	—	11	1	no	—
301	#126	—	11	1	no	—
302	#125	—	11	1	no	—
303	#124	—	11	1	no	—
304	#123	—	11	1	no	—
305	#123	—	11	1	no	—
306	C₂²⋊Q₈	—	11	1	no	—
307	#121	—	11	1	no	—
308	C₄×Q₈	—	11	1	no	—
309	C₄×D₄	—	11	1	no	—
310	C₄×D₄	—	11	1	no	—
311	C₄×D₄	—	11	1	no	—
312	#117	—	11	1	no	—
313	#117	C₄×D₁₁	1	1	yes	characteristic
314	C₂×C₄²	—	11	1	no	—
315	M₃₂	—	22	2	no	—
316	M₃₂	—	22	2	no	—
317	C₂×C₁₆	—	11	1	no	—
318	C₂×C₁₆	—	11	1	no	—
319	C₂×C₁₆	—	11	1	no	—
320	C₂×C₁₆	—	11	1	no	—
321	C₂×C₁₆	—	22	2	no	—
322	C₂×C₁₆	—	22	2	no	—
323	C₂×C₁₆	—	22	2	no	—
324	C₂×C₁₆	—	22	2	no	—
325	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
326	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
327	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
328	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
329	C₄⋊C₈	—	11	1	no	—
330	C₄⋊C₈	—	11	1	no	—
331	C₄⋊C₈	—	11	1	no	—
332	C₄⋊C₈	—	11	1	no	—
333	C₄⋊C₈	—	11	1	no	—
334	C₄⋊C₈	—	11	1	no	—
335	C₂²⋊C₈	—	11	1	no	—
336	C₂²⋊C₈	—	11	1	no	—
337	C₂²⋊C₈	—	11	1	no	—
338	C₂²⋊C₈	—	11	1	no	—
339	C₂²⋊C₈	—	11	1	no	—
340	C₂²⋊C₈	—	11	1	no	—
341	#97	—	11	1	no	—
342	#97	—	11	1	no	—
343	#97	C₄×D₁₁	1	1	yes	characteristic
344	#97	C₄×D₁₁	1	1	yes	characteristic
345	C₄×C₈	—	11	1	no	—
346	C₄×C₈	—	11	1	no	—
347	C₄×C₈	—	11	1	no	—
348	C₄×C₈	—	11	1	no	—
349	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
350	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
351	C₂×C₁₁	—	4	1	no	—
352	C₂×C₁₁	C₈×#41	1	1	yes	characteristic
353	C₂×C₁₁	C₂×#504	1	1	yes	characteristic
354	C₂×C₁₁	C₂×#504	1	1	yes	characteristic
355	D₁₁	—	2	2	no	—
356	D₁₁	—	4	1	no	—
357	C₂×Q₈	—	11	1	no	—
358	C₂×D₄	—	11	1	no	—
359	C₂×D₄	—	11	1	no	—
360	C₂×D₄	—	11	1	no	—
361	C₂²×C₄	—	11	1	no	—
362	C₂²×C₄	—	11	1	no	—
363	C₂²×C₄	—	11	1	no	—
364	C₂²×C₄	—	11	1	no	—
365	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
366	M₁₆	—	2	2	no	—
367	M₁₆	—	22	2	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	11	1	no	—
371	C₂×C₈	—	11	1	no	—
372	C₂×C₈	—	11	1	no	—
373	C₂×C₈	—	11	1	no	—
374	C₂×C₈	—	22	2	no	—
375	C₂×C₈	—	22	1	no	—
376	C₂×C₈	—	22	1	no	—
377	C₂×C₈	—	22	1	no	—
378	C₂×C₈	—	22	1	no	—
379	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
380	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
381	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
382	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
383	C₄⋊C₄	—	11	1	no	—
384	C₄⋊C₄	—	11	1	no	—
385	C₄⋊C₄	—	11	1	no	—
386	C₄⋊C₄	—	11	1	no	—
387	C₄⋊C₄	—	11	1	no	—
388	C₄⋊C₄	—	11	1	no	—
389	C₄⋊C₄	—	11	1	no	—
390	C₄⋊C₄	—	11	1	no	—
391	C₄⋊C₄	C₈×D₁₁	1	1	yes	characteristic
392	C₄⋊C₄	C₈×D₁₁	1	1	yes	characteristic
393	C₂²⋊C₄	—	11	1	no	—
394	C₂²⋊C₄	—	11	1	no	—
395	C₂²⋊C₄	—	11	1	no	—
396	C₂²⋊C₄	—	11	1	no	—
397	C₂²⋊C₄	—	11	1	no	—
398	C₂²⋊C₄	—	11	1	no	—
399	C₂²⋊C₄	—	11	1	no	—
400	C₂²⋊C₄	—	11	1	no	—
401	C₂²⋊C₄	C₈×D₁₁	1	1	yes	characteristic
402	C₂²⋊C₄	C₈×D₁₁	1	1	yes	characteristic
403	C₄²	—	11	1	no	—
404	C₄²	—	11	1	no	—
405	C₄²	—	11	1	no	—
406	C₄²	—	11	1	no	—
407	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
408	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
409	C₁₆	—	2	1	no	—
410	C₁₆	—	2	1	no	—
411	C₁₆	—	2	1	no	—
412	C₁₆	—	2	1	no	—
413	C₁₆	—	11	2	no	—
414	C₁₆	—	11	2	no	—
415	C₁₆	—	22	1	no	—
416	C₁₆	—	22	1	no	—
417	C₁₁	#33480	1	1	yes	characteristic, complemented, Sylow
418	C₂³	—	11	1	no	—
419	C₂³	—	11	1	no	—
420	C₂³	C₂×C₈×D₁₁	1	1	yes	characteristic
421	Q₈	—	22	2	no	—
422	D₄	—	22	2	no	—
423	D₄	—	22	2	no	—
424	D₄	—	22	2	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	11	1	no	—
428	C₂×C₄	—	11	1	no	—
429	C₂×C₄	—	11	1	no	—
430	C₂×C₄	—	11	1	no	—
431	C₂×C₄	—	11	1	no	—
432	C₂×C₄	—	11	1	no	—
433	C₂×C₄	—	22	2	no	—
434	C₂×C₄	—	22	2	no	—
435	C₂×C₄	—	22	1	no	—
436	C₂×C₄	—	22	1	no	—
437	C₂×C₄	—	22	1	no	—
438	C₂×C₄	—	22	1	no	—
439	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
440	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
441	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
442	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
443	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
444	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
445	C₈	—	2	1	no	—
446	C₈	—	2	1	no	—
447	C₈	—	22	1	no	—
448	C₈	—	22	1	no	—
449	C₈	—	22	1	no	—
450	C₈	—	22	1	no	—
451	C₈	#66960	1	2	yes	—
452	C₈	#41×D₁₁	1	1	yes	characteristic
453	C₈	#41×D₁₁	1	1	yes	characteristic
454	C₂²	—	2	1	no	—
455	C₂²	—	2	1	no	—
456	C₂²	—	2	1	no	—
457	C₂²	—	11	2	no	—
458	C₂²	—	22	1	no	—
459	C₂²	—	22	1	no	—
460	C₂²	—	22	1	no	—
461	C₂²	—	22	1	no	—
462	C₂²	—	22	1	no	—
463	C₂²	C₂²×C₈×D₁₁	1	1	yes	characteristic
464	C₄	—	2	1	no	—
465	C₄	—	2	1	no	—
466	C₄	—	2	1	no	—
467	C₄	—	2	1	no	—
468	C₄	—	2	1	no	—
469	C₄	—	11	2	no	—
470	C₄	—	22	1	no	—
471	C₄	—	22	1	no	—
472	C₄	—	22	1	no	—
473	C₄	—	22	1	no	—
474	C₄	—	22	1	no	—
475	C₄	#10623053	1	1	yes	characteristic
476	C₄	C₂×#66960	1	1	yes	characteristic
477	C₂	—	4	1	no	—
478	C₂	—	22	2	no	—
479	C₂	—	44	1	no	—
480	C₂	#13077572	1	1	yes	characteristic
481	C₂	D₁₁×#504	1	1	yes	characteristic
482	C₂	D₁₁×#504	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₁₁
commutator, socle	C₂²×C₁₁	C₂³×C₈
Fitting	C₁₁×#2164	C₂
prime radical	#66937	C₈
cosocle	C₂×C₈×C₁₁	C₂⁴
hypercenter	#2164	D₁₁
hypocenter	C₁₁	#33480
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₈ ◁ #2164

Complements

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

N	H ≅ G/N	type
2. #13070523	C₂	semidirect
3. #13070518	C₂	semidirect
4. #13070445	C₂	semidirect
5. #13070444	C₂	semidirect
6. #13070440	C₂	semidirect
7. #13070435	C₂	semidirect
8. (C₂²⋊D₁₁)⋊C₁₆	C₂	semidirect
9. (C₂²⋊D₁₁)⋊C₁₆	C₂	semidirect
10. #13070421	C₂	semidirect
11. #13070417	C₂	semidirect
12. #13070214	C₂	semidirect
13. #13070213	C₂	semidirect
14. C₄×C₁₆×D₁₁	C₂	semidirect
15. C₁₁×#2164	C₂	semidirect
187. #2164	D₁₁	semidirect
417. C₁₁	#33480	semidirect

Maximal subgroups

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

subgroup	index
#13077587	2
#13070523	2
#13070518	2
#13070445	2
#13070444	2
#13070440	2
#13070435	2
(C₂²⋊D₁₁)⋊C₁₆	2
#13070421	2
#13070417	2
#13070214	2
#13070213	2
C₄×C₁₆×D₁₁	2
C₁₁×#2164	2
#33480	11