Subgroups — #14907425

Order 2816.

452 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13077548	C₂	1	1	yes	maximal, characteristic
2	#13070524	C₂	1	1	yes	maximal, characteristic, complemented
3	#13070523	C₂	1	1	yes	maximal, characteristic, complemented
4	#13070523	C₂	1	1	yes	maximal, characteristic, complemented
5	#13070522	C₂	1	1	yes	maximal, characteristic, complemented
6	#13070522	C₂	1	1	yes	maximal, characteristic, complemented
7	#13070521	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₆×Dic₂₂	C₂	1	1	yes	maximal, characteristic, complemented
9	#13070518	C₂	1	1	yes	maximal, characteristic, complemented
10	#13070423	C₂	1	1	yes	maximal, characteristic
11	#13070420	C₂	1	1	yes	maximal, characteristic
12	#13070420	C₂	1	1	yes	maximal, characteristic
13	#13070416	C₂	1	1	yes	maximal, characteristic
14	#13070412	C₂	1	1	yes	maximal, characteristic
15	C₁₁×#2164	C₂	1	1	yes	maximal, characteristic
16	#10623048	C₄	1	1	yes	characteristic
17	C₁₁×#405	C₂²	1	1	yes	characteristic
18	#10622732	C₄	1	1	yes	characteristic
19	#10622731	C₄	1	1	yes	characteristic
20	#10622714	C₂²	1	1	yes	characteristic
21	C₂×C₈×Dic₁₁	C₂²	1	1	yes	characteristic
22	#10622612	C₄	1	1	yes	characteristic
23	#10622314	C₄	1	1	yes	characteristic
24	#10622314	C₄	1	1	yes	characteristic
25	#10622314	C₄	1	1	yes	characteristic
26	#10622314	C₄	1	1	yes	characteristic
27	C₈×Dic₂₂	C₂²	1	1	yes	characteristic
28	C₈×Dic₂₂	C₂²	1	1	yes	characteristic
29	C₈×Dic₂₂	C₂²	1	1	yes	characteristic
30	C₈×Dic₂₂	C₂²	1	1	yes	characteristic
31	C₁₁×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
32	C₁₁×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
33	C₁₁×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
34	C₁₁×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
35	C₁₁×#346	C₂²	1	1	yes	characteristic
36	C₄×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
37	C₂²⋊(C₁₁⋊C₁₆)	C₂²	1	1	yes	characteristic
38	C₂²⋊(C₁₁⋊C₁₆)	C₂²	1	1	yes	characteristic
39	#10622140	C₂²	1	1	yes	characteristic
40	#10622140	C₂²	1	1	yes	characteristic
41	#10622140	C₂²	1	1	yes	characteristic
42	#10622140	C₂²	1	1	yes	characteristic
43	Dic₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
44	Dic₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
45	Dic₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
46	Dic₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
47	Dic₁₁⋊C₁₆	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	C₁₆×Dic₁₁	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	C₄⋊(C₁₁⋊C₁₆)	C₂²	1	1	yes	characteristic
56	C₄⋊(C₁₁⋊C₁₆)	C₂²	1	1	yes	characteristic
57	#10622099	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	#66979	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄×Dic₁₁	C₂×C₄	1	1	yes	characteristic
64	C₂×#4318	C₂×C₄	1	1	yes	characteristic
65	C₂²×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
66	#66943	C₈	1	1	yes	characteristic
67	#66943	C₈	1	1	yes	characteristic
68	#66941	C₈	1	1	yes	characteristic
69	#66941	C₈	1	1	yes	characteristic
70	#66931	C₈	1	1	yes	characteristic
71	#66931	C₈	1	1	yes	characteristic
72	#66931	C₈	1	1	yes	characteristic
73	#66931	C₈	1	1	yes	characteristic
74	C₄×Dic₂₂	C₂×C₄	1	1	yes	characteristic
75	C₄×Dic₂₂	C₂×C₄	1	1	yes	characteristic
76	C₄×Dic₂₂	C₂×C₄	1	1	yes	characteristic
77	C₄×Dic₂₂	C₂×C₄	1	1	yes	characteristic
78	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
79	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
80	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
81	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
82	C₁₁×#97	C₂×C₄	1	1	yes	characteristic
83	C₁₁×#97	C₂×C₄	1	1	yes	characteristic
84	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
85	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
86	#66879	C₂×C₄	1	1	yes	characteristic
87	#66879	C₂×C₄	1	1	yes	characteristic
88	Dic₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
89	Dic₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
90	Dic₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
91	Dic₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
92	Dic₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
93	Dic₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
94	Dic₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
95	Dic₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
96	C₈×Dic₁₁	C₂×C₄	1	1	yes	characteristic
97	C₈×Dic₁₁	C₂×C₄	1	1	yes	characteristic
98	C₈×Dic₁₁	C₂³	1	1	yes	characteristic
99	C₈×Dic₁₁	C₂³	1	1	yes	characteristic
100	C₈×Dic₁₁	C₂³	1	1	yes	characteristic
101	C₈×Dic₁₁	C₂³	1	1	yes	characteristic
102	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
103	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
104	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
105	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
106	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
107	C₄⋊(C₁₁⋊C₈)	C₂×C₄	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	#33499	—	11	1	no	maximal, Sylow
111	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
112	C₂²×Dic₁₁	C₂×C₈	1	1	yes	characteristic
113	C₂²×Dic₁₁	C₂×C₈	1	1	yes	characteristic
114	C₂×Dic₂₂	C₂×C₈	1	1	yes	characteristic
115	C₂×Dic₂₂	C₂×C₈	1	1	yes	characteristic
116	C₂×Dic₂₂	C₂×C₈	1	1	yes	characteristic
117	C₂×Dic₂₂	C₂×C₈	1	1	yes	characteristic
118	C₁₁×M₁₆	—	4	1	no	—
119	C₂×C₈×C₁₁	—	2	1	no	—
120	C₂×C₈×C₁₁	—	2	1	no	—
121	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
125	C₁₁×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
126	C₁₁×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
127	C₁₁×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
128	C₁₁×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
129	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
130	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
131	C₂²⋊Dic₁₁	C₂×C₈	1	1	yes	characteristic
132	C₂²⋊Dic₁₁	C₂×C₈	1	1	yes	characteristic
133	C₄⋊Dic₁₁	C₂×C₈	1	1	yes	characteristic
134	C₄⋊Dic₁₁	C₂×C₈	1	1	yes	characteristic
135	C₄⋊Dic₁₁	C₂×C₈	1	1	yes	characteristic
136	C₄⋊Dic₁₁	C₂×C₈	1	1	yes	characteristic
137	C₄⋊Dic₁₁	C₂×C₈	1	1	yes	characteristic
138	C₄⋊Dic₁₁	C₂×C₈	1	1	yes	characteristic
139	Dic₁₁⋊C₄	C₂×C₈	1	1	yes	characteristic
140	Dic₁₁⋊C₄	C₂×C₈	1	1	yes	characteristic
141	Dic₁₁⋊C₄	C₂×C₈	1	1	yes	characteristic
142	Dic₁₁⋊C₄	C₂×C₈	1	1	yes	characteristic
143	Dic₁₁⋊C₄	C₂×C₈	1	1	yes	characteristic
144	Dic₁₁⋊C₄	C₂×C₈	1	1	yes	characteristic
145	Dic₁₁⋊C₄	C₂×C₈	1	1	yes	characteristic
146	Dic₁₁⋊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	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
150	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
151	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
152	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
153	#4318	—	4	1	no	—
154	C₂×C₁₁⋊C₈	—	4	1	no	—
155	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
156	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
157	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
159	C₁₁×C₁₆	—	2	1	no	—
160	C₁₁×C₁₆	—	2	1	no	—
161	C₁₁×C₁₆	—	2	1	no	—
162	C₁₁×C₁₆	—	2	1	no	—
163	C₁₁⋊C₁₆	—	2	1	no	—
164	C₁₁⋊C₁₆	—	2	1	no	—
165	C₁₁⋊C₁₆	—	2	1	no	—
166	C₁₁⋊C₁₆	—	2	1	no	—
167	#2960	—	11	1	no	—
168	#2183	—	11	1	no	—
169	#2183	—	11	1	no	—
170	#2183	—	11	1	no	—
171	#2183	—	11	1	no	—
172	#2183	—	11	1	no	—
173	#2183	—	11	1	no	—
174	Q₈×C₁₆	—	11	1	no	—
175	Q₈×C₁₆	—	11	1	no	—
176	#2164	—	11	1	no	—
177	#2164	—	11	1	no	—
178	#2164	—	11	1	no	—
179	#2164	D₁₁	1	1	yes	characteristic
180	#2163	—	11	1	no	—
181	#2162	—	11	1	no	—
182	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
183	C₂×C₄×C₁₁	—	2	1	no	—
184	C₂×C₄×C₁₁	—	2	1	no	—
185	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
186	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
187	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
188	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
189	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
190	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
191	C₂×Dic₁₁	—	2	2	no	—
192	C₂×Dic₁₁	—	4	1	no	—
193	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
194	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
195	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
196	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
197	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
198	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
199	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
200	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
201	Dic₂₂	—	2	2	no	—
202	Dic₂₂	—	2	2	no	—
203	Dic₂₂	—	4	1	no	—
204	Dic₂₂	—	4	1	no	—
205	C₈×C₁₁	—	2	1	no	—
206	C₈×C₁₁	—	2	1	no	—
207	C₈×C₁₁	—	2	1	no	—
208	C₈×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
209	C₈×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
210	C₁₁⋊C₈	—	2	1	no	—
211	C₁₁⋊C₈	—	2	1	no	—
212	C₁₁⋊C₈	—	2	1	no	—
213	C₁₁⋊C₈	—	2	1	no	—
214	#533	—	11	1	no	—
215	#446	—	11	1	no	—
216	#446	—	11	1	no	—
217	#446	—	11	1	no	—
218	#446	—	11	1	no	—
219	C₈×Q₈	—	11	1	no	—
220	C₈×Q₈	—	11	1	no	—
221	C₈×Q₈	—	11	1	no	—
222	C₈×Q₈	—	11	1	no	—
223	#424	—	11	1	no	—
224	#424	—	11	1	no	—
225	#423	—	11	1	no	—
226	#405	—	11	1	no	—
227	#405	C₂×D₁₁	1	1	yes	characteristic
228	C₂×C₄×C₈	—	11	1	no	—
229	C₄⋊C₁₆	—	11	1	no	—
230	C₄⋊C₁₆	—	11	1	no	—
231	C₄⋊C₁₆	—	11	1	no	—
232	C₄⋊C₁₆	—	11	1	no	—
233	C₄⋊C₁₆	—	11	1	no	—
234	C₄⋊C₁₆	—	11	1	no	—
235	C₄⋊C₁₆	—	11	1	no	—
236	C₄⋊C₁₆	—	11	1	no	—
237	C₄⋊C₁₆	—	11	1	no	—
238	C₄⋊C₁₆	—	11	1	no	—
239	C₄⋊C₁₆	C₂×D₁₁	1	1	yes	characteristic
240	C₄⋊C₁₆	C₂×D₁₁	1	1	yes	characteristic
241	C₂²⋊C₁₆	—	11	1	no	—
242	C₂²⋊C₁₆	—	11	1	no	—
243	C₂²⋊C₁₆	C₂×D₁₁	1	1	yes	characteristic
244	C₂²⋊C₁₆	C₂×D₁₁	1	1	yes	characteristic
245	#346	—	11	1	no	—
246	#346	—	11	1	no	—
247	#346	—	11	1	no	—
248	#346	—	11	1	no	—
249	#346	—	11	1	no	—
250	#346	C₂×D₁₁	1	1	yes	characteristic
251	C₄×C₁₆	—	11	1	no	—
252	C₄×C₁₆	—	11	1	no	—
253	C₄×C₁₆	—	11	1	no	—
254	C₄×C₁₆	—	11	1	no	—
255	C₄×C₁₆	—	11	1	no	—
256	C₄×C₁₆	C₂×D₁₁	1	1	yes	characteristic
257	C₂²×C₁₁	—	2	1	no	—
258	C₂²×C₁₁	—	2	1	no	—
259	C₂²×C₁₁	—	2	1	no	—
260	C₂²×C₁₁	C₂³×C₈	1	1	yes	characteristic
261	C₄×C₁₁	—	2	1	no	—
262	C₄×C₁₁	—	2	1	no	—
263	C₄×C₁₁	—	2	1	no	—
264	C₄×C₁₁	—	2	1	no	—
265	C₄×C₁₁	—	2	1	no	—
266	C₄×C₁₁	#519	1	1	yes	characteristic
267	C₄×C₁₁	#568	1	1	yes	characteristic
268	Dic₁₁	—	2	1	no	—
269	Dic₁₁	—	2	1	no	—
270	Dic₁₁	—	2	1	no	—
271	Dic₁₁	—	2	1	no	—
272	Dic₁₁	—	2	1	no	—
273	Dic₁₁	—	2	1	no	—
274	Dic₁₁	—	2	1	no	—
275	Dic₁₁	#504	1	2	yes	—
276	C₂×M₁₆	—	11	1	no	—
277	C₂×M₁₆	C₄×D₁₁	1	1	yes	characteristic
278	C₂²×C₈	—	11	1	no	—
279	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
280	C₄⋊Q₈	—	11	1	no	—
281	C₄⋊Q₈	—	11	1	no	—
282	#125	—	11	1	no	—
283	#125	—	11	1	no	—
284	C₂²⋊Q₈	—	11	1	no	—
285	C₂²⋊Q₈	—	11	1	no	—
286	C₂²⋊Q₈	—	11	1	no	—
287	C₂²⋊Q₈	—	11	1	no	—
288	C₄×Q₈	—	11	1	no	—
289	C₄×Q₈	—	11	1	no	—
290	C₄×Q₈	—	11	1	no	—
291	C₄×Q₈	—	11	1	no	—
292	#117	—	11	1	no	—
293	#117	C₄×D₁₁	1	1	yes	characteristic
294	C₂×C₄²	—	11	1	no	—
295	C₂×C₁₆	—	11	1	no	—
296	C₂×C₁₆	—	11	1	no	—
297	C₂×C₁₆	—	11	1	no	—
298	C₂×C₁₆	—	11	1	no	—
299	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
300	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
301	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
302	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
303	C₄⋊C₈	—	11	1	no	—
304	C₄⋊C₈	—	11	1	no	—
305	C₄⋊C₈	—	11	1	no	—
306	C₄⋊C₈	—	11	1	no	—
307	C₄⋊C₈	—	11	1	no	—
308	C₄⋊C₈	—	11	1	no	—
309	C₄⋊C₈	—	11	1	no	—
310	C₄⋊C₈	—	11	1	no	—
311	C₄⋊C₈	—	11	1	no	—
312	C₄⋊C₈	—	11	1	no	—
313	C₄⋊C₈	—	11	1	no	—
314	C₄⋊C₈	—	11	1	no	—
315	#97	—	11	1	no	—
316	#97	—	11	1	no	—
317	#97	C₄×D₁₁	1	1	yes	characteristic
318	#97	C₄×D₁₁	1	1	yes	characteristic
319	C₄×C₈	—	11	1	no	—
320	C₄×C₈	—	11	1	no	—
321	C₄×C₈	—	11	1	no	—
322	C₄×C₈	—	11	1	no	—
323	C₄×C₈	—	11	1	no	—
324	C₄×C₈	—	11	1	no	—
325	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
326	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
327	C₂×C₁₁	—	4	1	no	—
328	C₂×C₁₁	#2982	1	1	yes	characteristic
329	C₂×C₁₁	C₂×#504	1	1	yes	characteristic
330	C₂×C₁₁	#3407	1	1	yes	characteristic
331	C₂×Q₈	—	11	1	no	—
332	C₂×Q₈	—	11	1	no	—
333	C₂×Q₈	—	11	1	no	—
334	C₂×Q₈	—	11	1	no	—
335	C₂²×C₄	—	11	1	no	—
336	C₂²×C₄	—	11	1	no	—
337	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
338	M₁₆	—	4	1	no	—
339	M₁₆	—	44	1	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	11	1	no	—
343	C₂×C₈	—	11	1	no	—
344	C₂×C₈	—	11	1	no	—
345	C₂×C₈	—	11	1	no	—
346	C₂×C₈	—	44	1	no	—
347	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
348	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
349	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
350	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
351	C₄⋊C₄	—	11	1	no	—
352	C₄⋊C₄	—	11	1	no	—
353	C₄⋊C₄	—	11	1	no	—
354	C₄⋊C₄	—	11	1	no	—
355	C₄⋊C₄	—	11	1	no	—
356	C₄⋊C₄	—	11	1	no	—
357	C₄⋊C₄	—	11	1	no	—
358	C₄⋊C₄	—	11	1	no	—
359	C₄⋊C₄	—	11	1	no	—
360	C₄⋊C₄	—	11	1	no	—
361	C₄⋊C₄	—	11	1	no	—
362	C₄⋊C₄	—	11	1	no	—
363	C₄⋊C₄	—	11	1	no	—
364	C₄⋊C₄	—	11	1	no	—
365	C₄⋊C₄	C₈×D₁₁	1	1	yes	characteristic
366	C₄⋊C₄	C₈×D₁₁	1	1	yes	characteristic
367	C₂²⋊C₄	—	11	1	no	—
368	C₂²⋊C₄	—	11	1	no	—
369	C₂²⋊C₄	C₈×D₁₁	1	1	yes	characteristic
370	C₂²⋊C₄	C₈×D₁₁	1	1	yes	characteristic
371	C₄²	—	11	1	no	—
372	C₄²	—	11	1	no	—
373	C₄²	—	11	1	no	—
374	C₄²	—	11	1	no	—
375	C₄²	—	11	1	no	—
376	C₄²	—	11	1	no	—
377	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
378	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
379	C₁₆	—	2	1	no	—
380	C₁₆	—	2	1	no	—
381	C₁₆	—	2	1	no	—
382	C₁₆	—	2	1	no	—
383	C₁₆	—	22	1	no	—
384	C₁₆	—	22	1	no	—
385	C₁₆	—	22	1	no	—
386	C₁₆	—	22	1	no	—
387	C₁₁	#33499	1	1	yes	characteristic, complemented, Sylow
388	C₂³	C₂×C₈×D₁₁	1	1	yes	characteristic
389	Q₈	—	22	2	no	—
390	Q₈	—	22	2	no	—
391	Q₈	—	44	1	no	—
392	Q₈	—	44	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	11	1	no	—
396	C₂×C₄	—	11	1	no	—
397	C₂×C₄	—	11	1	no	—
398	C₂×C₄	—	11	1	no	—
399	C₂×C₄	—	11	1	no	—
400	C₂×C₄	—	11	1	no	—
401	C₂×C₄	—	11	1	no	—
402	C₂×C₄	—	11	1	no	—
403	C₂×C₄	—	22	2	no	—
404	C₂×C₄	—	44	1	no	—
405	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
406	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
407	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
408	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
409	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
410	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
411	C₈	—	2	1	no	—
412	C₈	—	2	1	no	—
413	C₈	—	2	1	no	—
414	C₈	—	22	1	no	—
415	C₈	—	22	1	no	—
416	C₈	—	22	1	no	—
417	C₈	—	22	1	no	—
418	C₈	#67043	1	1	yes	characteristic
419	C₈	#67043	1	1	yes	characteristic
420	C₂²	—	2	1	no	—
421	C₂²	—	2	1	no	—
422	C₂²	—	2	1	no	—
423	C₂²	C₂²×C₈×D₁₁	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	11	2	no	—
430	C₄	—	22	1	no	—
431	C₄	—	22	1	no	—
432	C₄	—	22	1	no	—
433	C₄	—	22	1	no	—
434	C₄	—	22	1	no	—
435	C₄	—	22	1	no	—
436	C₄	—	22	1	no	—
437	C₄	#10623047	1	1	yes	characteristic
438	C₄	#10623276	1	1	yes	characteristic
439	C₂	—	4	1	no	—
440	C₂	#13077696	1	1	yes	characteristic
441	C₂	D₁₁×#504	1	1	yes	characteristic
442	C₂	#13081717	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	C₂³×C₁₁	C₂²×C₈
cosocle	C₂×C₈×C₁₁	C₂⁴
hypercenter	#2164	D₁₁
hypocenter	C₁₁	#33499
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. #13070524	C₂	semidirect
3. #13070523	C₂	semidirect
4. #13070523	C₂	semidirect
5. #13070522	C₂	semidirect
6. #13070522	C₂	semidirect
7. #13070521	C₂	semidirect
8. C₁₆×Dic₂₂	C₂	semidirect
9. #13070518	C₂	semidirect
387. C₁₁	#33499	semidirect

Maximal subgroups

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

subgroup	index
#13077548	2
#13070524	2
#13070523	2
#13070522	2
#13070521	2
C₁₆×Dic₂₂	2
#13070518	2
#13070423	2
#13070420	2
#13070416	2
#13070412	2
C₁₁×#2164	2
#33499	11