Subgroups — #14670251

Order 2816.

370 conjugacy classes of subgroups.

The subgroup lattice has 284 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13081718	C₂	1	1	yes	maximal, characteristic
2	#13070381	C₂	1	1	yes	maximal, characteristic, complemented
3	#13070231	C₂	1	1	yes	maximal, characteristic
4	#13068417	C₂	1	1	yes	maximal, characteristic
5	#13066706	C₂	1	1	yes	maximal, characteristic, complemented
6	#13066705	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#2153	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#66954	C₂²	1	1	yes	characteristic
9	C₂×C₁₁×M₃₂	C₂²	1	1	yes	characteristic
10	C₂×C₁₁×M₃₂	C₂²	1	1	yes	characteristic
11	C₁₁×#405	C₂²	1	1	yes	characteristic
12	#10622745	C₄	1	1	yes	characteristic
13	#10622714	C₂²	1	1	yes	characteristic
14	C₂×#66876	C₂²	1	1	yes	characteristic
15	C₂²×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
16	#10622619	C₄	1	1	yes	characteristic
17	#10622520	—	2	2	no	—
18	D₁₁×M₃₂	—	2	2	no	—
19	#10622514	—	2	2	no	—
20	C₁₁×#364	—	2	2	no	—
21	#10622197	C₄	1	1	yes	characteristic
22	#10622171	C₄	1	1	yes	characteristic
23	#10622149	—	2	2	no	—
24	(C₂×D₁₁)⋊C₁₆	—	2	2	no	—
25	C₂×#4339	C₂×C₄	1	1	yes	characteristic
26	C₂×C₁₁×M₁₆	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
28	C₁₁×#117	C₂×C₄	1	1	yes	characteristic
29	#66979	C₂×C₄	1	1	yes	characteristic
30	C₂×#4318	C₂×C₄	1	1	yes	characteristic
31	C₂×#4318	C₂×C₄	1	1	yes	characteristic
32	#66954	—	2	1	no	—
33	#66954	—	2	1	no	—
34	#66954	—	2	1	no	—
35	#66954	—	2	1	no	—
36	C₂×#4313	Q₈	1	2	yes	—
37	C₂×C₈×D₁₁	D₄	1	2	yes	—
38	C₁₁×M₃₂	—	2	1	no	—
39	C₁₁×M₃₂	—	2	1	no	—
40	C₁₁×M₃₂	—	2	1	no	—
41	C₁₁×M₃₂	D₄	1	2	yes	—
42	C₂×C₁₁×C₁₆	—	2	1	no	—
43	C₂×C₁₁×C₁₆	—	2	1	no	—
44	C₁₁×#97	—	2	1	no	—
45	C₄×C₈×C₁₁	—	2	1	no	—
46	#66888	C₈	1	2	yes	—
47	#66887	C₈	1	2	yes	—
48	#66879	—	2	1	no	—
49	C₈×Dic₁₁	—	2	1	no	—
50	#66876	—	2	1	no	—
51	#66876	D₄	1	2	yes	—
52	C₂×C₁₁⋊C₁₆	—	2	1	no	—
53	C₂×C₁₁⋊C₁₆	—	2	1	no	—
54	C₂×C₁₁⋊C₁₆	—	2	1	no	—
55	C₂×C₁₁⋊C₁₆	—	2	1	no	—
56	#66870	—	2	2	no	—
57	#66862	—	2	4	no	—
58	C₁₆×D₁₁	—	2	4	no	—
59	#12916	—	11	1	no	maximal, Sylow
60	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
61	C₂×C₂²⋊D₁₁	M₁₆	1	2	yes	—
62	#4339	—	2	1	no	—
63	#4339	—	2	1	no	—
64	#4339	—	2	1	no	—
65	#4339	—	2	1	no	—
66	C₂×D₄₄	C₂×C₈	1	1	yes	characteristic
67	C₂×C₄×D₁₁	C₄⋊C₄	1	2	yes	—
68	C₂×Dic₂₂	C₂×C₈	1	1	yes	characteristic
69	C₁₁×M₁₆	—	2	1	no	—
70	C₁₁×M₁₆	C₂×C₈	1	2	yes	—
71	C₂×C₈×C₁₁	—	2	1	no	—
72	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
73	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
74	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
75	C₂×C₈×C₁₁	C₂×Q₈	1	1	yes	characteristic
76	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
77	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
78	C₁₁×C₄⋊C₄	—	2	1	no	—
79	C₁₁×C₂²⋊C₄	—	2	1	no	—
80	C₄²×C₁₁	—	2	1	no	—
81	C₂²⋊Dic₁₁	—	2	1	no	—
82	C₄⋊Dic₁₁	—	2	1	no	—
83	C₄×Dic₁₁	—	2	1	no	—
84	#4318	—	2	1	no	—
85	#4318	—	2	1	no	—
86	#4318	—	2	1	no	—
87	#4318	C₂×C₈	1	2	yes	—
88	C₂×C₁₁⋊C₈	—	2	1	no	—
89	C₂×C₁₁⋊C₈	C₄⋊C₄	1	2	yes	—
90	#4313	—	2	2	no	—
91	#4313	—	2	2	no	—
92	C₈×D₁₁	—	2	2	no	—
93	C₈×D₁₁	—	2	2	no	—
94	C₁₁×C₁₆	—	2	2	no	—
95	C₁₁×C₁₆	—	4	1	no	—
96	C₁₁⋊C₁₆	—	2	2	no	—
97	C₁₁⋊C₁₆	—	4	1	no	—
98	#3407	—	11	1	no	—
99	#2153	—	11	1	no	—
100	#2153	D₁₁	1	1	yes	characteristic, complemented
101	#2113	—	11	1	no	—
102	#1757	—	11	1	no	—
103	#1379	—	11	1	no	—
104	#1379	—	11	1	no	—
105	C₂³×C₁₁	C₂×M₁₆	1	1	yes	characteristic
106	C₂²×D₁₁	C₄⋊C₈	1	2	yes	—
107	C₂×C₄×C₁₁	—	4	1	no	—
108	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
109	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
110	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
111	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
112	C₂×C₄×C₁₁	#131	1	1	yes	characteristic
113	C₂×C₄×C₁₁	#131	1	1	yes	characteristic
114	C₂²⋊D₁₁	—	2	2	no	—
115	C₂²⋊D₁₁	—	2	2	no	—
116	C₂×Dic₁₁	—	4	1	no	—
117	C₂×Dic₁₁	C₄⋊C₈	1	2	yes	—
118	D₄₄	—	2	1	no	—
119	D₄₄	—	2	1	no	—
120	C₄×D₁₁	—	2	2	no	—
121	C₄×D₁₁	—	2	2	no	—
122	Dic₂₂	—	2	1	no	—
123	Dic₂₂	—	2	1	no	—
124	C₈×C₁₁	—	2	2	no	—
125	C₈×C₁₁	#120	1	1	yes	characteristic
126	C₈×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
127	C₈×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
128	C₈×C₁₁	#123	1	1	yes	characteristic
129	C₁₁⋊C₈	—	2	2	no	—
130	C₁₁⋊C₈	—	2	2	no	—
131	C₂×#131	—	11	1	no	—
132	#504	—	22	2	no	—
133	#504	—	22	2	no	—
134	C₂×M₃₂	—	11	1	no	—
135	C₂×M₃₂	—	22	2	no	—
136	C₂×M₃₂	C₂×D₁₁	1	1	yes	characteristic
137	C₂×M₃₂	C₂×D₁₁	1	1	yes	characteristic
138	C₂²×C₁₆	—	11	1	no	—
139	#413	—	11	1	no	—
140	#410	—	11	1	no	—
141	#405	—	11	1	no	—
142	#405	C₂×D₁₁	1	1	yes	characteristic
143	#364	—	2	2	no	—
144	#364	—	22	2	no	—
145	C₂²⋊C₁₆	—	22	2	no	—
146	#344	—	11	1	no	—
147	#344	—	11	1	no	—
148	C₂²×C₁₁	—	4	1	no	—
149	C₂²×C₁₁	C₂×C₄⋊C₈	1	1	yes	characteristic
150	C₂²×C₁₁	#435	1	1	yes	characteristic
151	C₂²×C₁₁	#435	1	1	yes	characteristic
152	C₂×D₁₁	—	2	2	no	—
153	C₂×D₁₁	—	4	2	no	—
154	C₄×C₁₁	—	8	1	no	—
155	C₄×C₁₁	#385	1	1	yes	characteristic
156	C₄×C₁₁	#424	1	1	yes	characteristic
157	C₄×C₁₁	C₈×D₄	1	1	yes	characteristic
158	C₄×C₁₁	C₈×D₄	1	1	yes	characteristic
159	Dic₁₁	—	2	2	no	—
160	Dic₁₁	—	8	1	no	—
161	C₂×#41	—	11	1	no	—
162	#131	—	22	1	no	—
163	#131	—	22	1	no	—
164	#131	—	22	1	no	—
165	#131	—	22	1	no	—
166	C₂×M₁₆	—	11	1	no	—
167	C₂×M₁₆	—	11	2	no	—
168	C₂×M₁₆	—	11	1	no	—
169	C₂×M₁₆	C₄×D₁₁	1	1	yes	characteristic
170	C₂²×C₈	—	11	2	no	—
171	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
172	#117	—	11	1	no	—
173	#117	C₄×D₁₁	1	1	yes	characteristic
174	M₃₂	—	2	1	no	—
175	M₃₂	—	2	1	no	—
176	M₃₂	—	2	1	no	—
177	M₃₂	—	11	2	no	—
178	M₃₂	—	22	4	no	—
179	M₃₂	—	22	1	no	—
180	M₃₂	C₂²⋊D₁₁	1	2	yes	—
181	C₂×C₁₆	—	2	1	no	—
182	C₂×C₁₆	—	2	1	no	—
183	C₂×C₁₆	—	22	4	no	—
184	C₂×C₁₆	—	22	1	no	—
185	C₂×C₁₆	—	22	1	no	—
186	C₂×C₁₆	—	22	1	no	—
187	C₂×C₁₆	—	22	1	no	—
188	#101	—	11	2	no	—
189	#100	—	11	2	no	—
190	#99	—	22	2	no	—
191	#97	—	2	1	no	—
192	#97	—	22	1	no	—
193	C₄×C₈	—	2	1	no	—
194	C₄×C₈	—	22	1	no	—
195	C₂×C₁₁	—	2	1	no	—
196	C₂×C₁₁	—	2	1	no	—
197	C₂×C₁₁	—	2	1	no	—
198	C₂×C₁₁	#1850	1	1	yes	characteristic
199	D₁₁	—	4	2	no	—
200	#41	—	22	1	no	—
201	#41	—	22	1	no	—
202	#41	—	22	1	no	—
203	#41	—	22	1	no	—
204	C₂×Q₈	—	11	1	no	—
205	C₂×D₄	—	11	2	no	—
206	C₂×D₄	—	11	1	no	—
207	C₂²×C₄	—	11	2	no	—
208	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
209	M₁₆	—	2	1	no	—
210	M₁₆	—	11	2	no	—
211	M₁₆	—	22	1	no	—
212	M₁₆	—	22	1	no	—
213	M₁₆	—	22	1	no	—
214	M₁₆	—	22	2	no	—
215	M₁₆	—	22	2	no	—
216	M₁₆	C₈×D₁₁	1	2	yes	—
217	C₂×C₈	—	2	1	no	—
218	C₂×C₈	—	11	2	no	—
219	C₂×C₈	—	22	1	no	—
220	C₂×C₈	—	22	2	no	—
221	C₂×C₈	—	22	2	no	—
222	C₂×C₈	#4339	1	1	yes	characteristic
223	C₂×C₈	D₄×D₁₁	1	1	yes	characteristic
224	C₂×C₈	D₄×D₁₁	1	1	yes	characteristic
225	C₂×C₈	Q₈×D₁₁	1	1	yes	characteristic
226	C₂×C₈	#4343	1	1	yes	characteristic
227	C₂×C₈	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
228	C₄⋊C₄	—	2	1	no	—
229	C₄⋊C₄	—	22	1	no	—
230	C₂²⋊C₄	—	2	1	no	—
231	C₂²⋊C₄	—	22	1	no	—
232	C₄²	—	2	1	no	—
233	C₄²	—	22	1	no	—
234	C₁₆	—	2	2	no	—
235	C₁₆	—	4	1	no	—
236	C₁₆	—	22	2	no	—
237	C₁₆	—	44	1	no	—
238	C₁₁	#12916	1	1	yes	characteristic, complemented, Sylow
239	C₂³	—	11	2	no	—
240	C₂³	M₁₆×D₁₁	1	1	yes	characteristic
241	Q₈	—	22	1	no	—
242	Q₈	—	22	1	no	—
243	D₄	—	22	2	no	—
244	D₄	—	22	2	no	—
245	D₄	—	22	1	no	—
246	D₄	—	22	1	no	—
247	C₂×C₄	—	4	1	no	—
248	C₂×C₄	—	11	2	no	—
249	C₂×C₄	—	22	2	no	—
250	C₂×C₄	—	22	2	no	—
251	C₂×C₄	—	44	1	no	—
252	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
253	C₂×C₄	#66946	1	1	yes	characteristic
254	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
255	C₂×C₄	#66954	1	1	yes	characteristic
256	C₂×C₄	#66960	1	1	yes	characteristic
257	C₂×C₄	C₄×C₂²⋊D₁₁	1	1	yes	characteristic
258	C₈	—	2	2	no	—
259	C₈	—	22	2	no	—
260	C₈	—	22	2	no	—
261	C₈	#66947	1	1	yes	characteristic
262	C₈	#66949	1	1	yes	characteristic
263	C₈	#66990	1	1	yes	characteristic
264	C₈	#66999	1	1	yes	characteristic
265	C₂²	—	4	1	no	—
266	C₂²	—	22	2	no	—
267	C₂²	—	44	2	no	—
268	C₂²	D₁₁×C₄⋊C₈	1	1	yes	characteristic
269	C₂²	#10622449	1	1	yes	characteristic
270	C₂²	#10622740	1	1	yes	characteristic
271	C₄	—	8	1	no	—
272	C₄	—	22	2	no	—
273	C₄	—	88	1	no	—
274	C₄	#10622447	1	1	yes	characteristic
275	C₄	#10622452	1	1	yes	characteristic
276	C₄	#10622602	1	1	yes	characteristic
277	C₄	C₈×C₂²⋊D₁₁	1	1	yes	characteristic
278	C₂	—	2	1	no	—
279	C₂	—	2	1	no	—
280	C₂	—	2	1	no	—
281	C₂	—	44	2	no	—
282	C₂	#13068792	1	1	yes	characteristic

	subgroup	G/H
center	C₈	#66990
commutator	C₂×C₄×C₁₁	C₂²×C₈
Frattini	C₂²×C₈	C₂²×D₁₁
Fitting	C₁₁×#2153	C₂
socle	C₂×C₁₁	#1850
prime radical	C₂×#4339	C₂×C₄
cosocle	C₂²×C₈×C₁₁	C₂³
hypercenter	#2153	D₁₁
hypocenter	C₁₁	#12916
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ #2153

Complements

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

N	H ≅ G/N	type
2. #13070381	C₂	semidirect
5. #13066706	C₂	semidirect
6. #13066705	C₂	semidirect
7. C₁₁×#2153	C₂	semidirect
100. #2153	D₁₁	semidirect
238. C₁₁	#12916	semidirect

Maximal subgroups

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

subgroup	index
#13081718	2
#13070381	2
#13070231	2
#13068417	2
#13066706	2
#13066705	2
C₁₁×#2153	2
#12916	11