Subgroups — #14670269

Order 2816.

376 conjugacy classes of subgroups.

The subgroup lattice has 294 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	#13070382	C₂	1	1	yes	maximal, characteristic, complemented
3	#13070371	C₂	1	1	yes	maximal, characteristic, complemented
4	#13070243	C₂	1	1	yes	maximal, characteristic
5	#13068455	C₂	1	1	yes	maximal, characteristic
6	#13066697	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1378	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	C₂×#66889	C₄	1	1	yes	characteristic
13	C₂×C₈×Dic₁₁	C₂²	1	1	yes	characteristic
14	C₂×#66876	C₂²	1	1	yes	characteristic
15	C₂×#66876	C₂²	1	1	yes	characteristic
16	#10622615	C₄	1	1	yes	characteristic
17	#10622520	—	2	2	no	—
18	D₁₁×M₃₂	—	2	2	no	—
19	#10622514	—	2	2	no	—
20	#10622196	C₄	1	1	yes	characteristic
21	#10622170	C₄	1	1	yes	characteristic
22	#10622146	—	2	2	no	—
23	Dic₁₁⋊C₁₆	—	2	2	no	—
24	#10622101	—	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	C₂×C₄×Dic₁₁	C₂×C₄	1	1	yes	characteristic
30	C₂×#4318	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
32	#66954	—	2	1	no	—
33	#66954	—	2	1	no	—
34	#66954	D₄	1	2	yes	—
35	#66954	Q₈	1	2	yes	—
36	C₂×#4313	—	2	1	no	—
37	C₂×C₈×D₁₁	—	2	1	no	—
38	C₁₁×M₃₂	—	2	1	no	—
39	C₁₁×M₃₂	—	2	1	no	—
40	C₁₁×M₃₂	—	2	1	no	—
41	C₁₁×M₃₂	—	2	1	no	—
42	C₂×C₁₁×C₁₆	—	2	1	no	—
43	C₂×C₁₁×C₁₆	D₄	1	2	yes	—
44	C₁₁×#97	—	2	1	no	—
45	C₄×C₈×C₁₁	—	2	1	no	—
46	#66889	C₈	1	2	yes	—
47	#66889	C₈	1	2	yes	—
48	C₈×Dic₁₁	—	2	1	no	—
49	C₈×Dic₁₁	—	2	1	no	—
50	#66876	—	2	1	no	—
51	#66876	—	2	1	no	—
52	#66876	—	2	1	no	—
53	#66876	D₄	1	2	yes	—
54	C₂×C₁₁⋊C₁₆	—	2	1	no	—
55	C₂×C₁₁⋊C₁₆	—	2	1	no	—
56	#66874	—	2	1	no	—
57	#66873	—	2	1	no	—
58	#66862	—	2	4	no	—
59	C₁₆×D₁₁	—	2	4	no	—
60	#12918	—	11	1	no	maximal, Sylow
61	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
62	C₂×C₂²⋊D₁₁	—	2	1	no	—
63	C₂²×Dic₁₁	—	2	1	no	—
64	#4339	—	2	1	no	—
65	#4339	—	2	1	no	—
66	#4339	C₄⋊C₄	1	2	yes	—
67	#4339	C₂×C₈	1	2	yes	—
68	C₂×D₄₄	M₁₆	1	1	yes	characteristic
69	C₂×C₄×D₁₁	—	2	1	no	—
70	C₂×Dic₂₂	M₁₆	1	1	yes	characteristic
71	C₁₁×M₁₆	—	2	1	no	—
72	C₁₁×M₁₆	C₂×C₈	1	2	yes	—
73	C₂×C₈×C₁₁	—	2	1	no	—
74	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
75	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
76	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
77	C₂×C₈×C₁₁	C₂×Q₈	1	1	yes	characteristic
78	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
79	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
80	C₁₁×C₄⋊C₄	—	2	1	no	—
81	C₁₁×C₂²⋊C₄	—	2	1	no	—
82	C₄²×C₁₁	—	2	1	no	—
83	C₄×Dic₁₁	—	2	1	no	—
84	C₄×Dic₁₁	C₂×C₈	1	1	yes	characteristic
85	C₄×Dic₁₁	C₂×C₈	1	1	yes	characteristic
86	#4318	—	2	1	no	—
87	#4318	C₄⋊C₄	1	2	yes	—
88	C₂×C₁₁⋊C₈	—	2	1	no	—
89	C₂×C₁₁⋊C₈	—	2	1	no	—
90	C₂×C₁₁⋊C₈	—	2	1	no	—
91	C₂×C₁₁⋊C₈	—	2	1	no	—
92	#4313	—	2	2	no	—
93	#4313	—	2	2	no	—
94	C₈×D₁₁	—	2	2	no	—
95	C₈×D₁₁	—	2	2	no	—
96	C₁₁×C₁₆	—	2	2	no	—
97	C₁₁×C₁₆	—	4	1	no	—
98	C₁₁⋊C₁₆	—	2	2	no	—
99	C₁₁⋊C₁₆	—	4	1	no	—
100	#3407	—	11	1	no	—
101	#2153	—	11	1	no	—
102	#2150	—	11	1	no	—
103	#2117	—	11	1	no	—
104	#1764	—	11	1	no	—
105	#1378	D₁₁	1	1	yes	characteristic, complemented
106	#1376	—	11	1	no	—
107	C₂³×C₁₁	#131	1	1	yes	characteristic
108	C₂²×D₁₁	—	2	1	no	—
109	C₂×C₄×C₁₁	—	4	1	no	—
110	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
111	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
112	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
113	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
114	C₂×C₄×C₁₁	C₂×M₁₆	1	1	yes	characteristic
115	C₂×C₄×C₁₁	#131	1	1	yes	characteristic
116	C₂²⋊D₁₁	—	2	2	no	—
117	C₂²⋊D₁₁	—	2	2	no	—
118	C₂×Dic₁₁	—	2	1	no	—
119	C₂×Dic₁₁	—	2	1	no	—
120	C₂×Dic₁₁	—	2	1	no	—
121	C₂×Dic₁₁	—	4	2	no	—
122	D₄₄	—	2	1	no	—
123	D₄₄	C₄⋊C₈	1	2	yes	—
124	C₄×D₁₁	—	2	2	no	—
125	C₄×D₁₁	—	2	2	no	—
126	Dic₂₂	—	2	1	no	—
127	Dic₂₂	C₄⋊C₈	1	2	yes	—
128	C₈×C₁₁	—	2	2	no	—
129	C₈×C₁₁	#120	1	1	yes	characteristic
130	C₈×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
131	C₈×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
132	C₈×C₁₁	#123	1	1	yes	characteristic
133	C₁₁⋊C₈	—	2	2	no	—
134	C₁₁⋊C₈	—	4	1	no	—
135	C₂×#131	—	11	1	no	—
136	#504	—	22	2	no	—
137	#504	—	22	2	no	—
138	C₂×M₃₂	—	11	1	no	—
139	C₂×M₃₂	—	11	1	no	—
140	C₂×M₃₂	—	22	2	no	—
141	C₂×M₃₂	C₂×D₁₁	1	1	yes	characteristic
142	C₂×M₃₂	C₂×D₁₁	1	1	yes	characteristic
143	C₂×#104	—	11	1	no	—
144	#416	—	11	1	no	—
145	#405	C₂×D₁₁	1	1	yes	characteristic
146	C₂×C₄×C₈	—	11	1	no	—
147	#364	—	22	2	no	—
148	C₄⋊C₁₆	—	22	2	no	—
149	#350	—	22	2	no	—
150	#341	—	11	1	no	—
151	#339	—	11	1	no	—
152	C₂²×C₁₁	—	4	1	no	—
153	C₂²×C₁₁	#424	1	1	yes	characteristic
154	C₂²×C₁₁	C₈×D₄	1	1	yes	characteristic
155	C₂²×C₁₁	#435	1	1	yes	characteristic
156	C₂×D₁₁	—	2	2	no	—
157	C₂×D₁₁	—	8	1	no	—
158	C₄×C₁₁	—	8	1	no	—
159	C₄×C₁₁	#385	1	1	yes	characteristic
160	C₄×C₁₁	C₂×C₄⋊C₈	1	1	yes	characteristic
161	C₄×C₁₁	C₈×D₄	1	1	yes	characteristic
162	C₄×C₁₁	#435	1	1	yes	characteristic
163	Dic₁₁	—	2	2	no	—
164	Dic₁₁	—	2	2	no	—
165	Dic₁₁	—	4	1	no	—
166	C₂×#41	—	11	1	no	—
167	#131	—	11	2	no	—
168	#131	—	11	2	no	—
169	#131	—	22	1	no	—
170	#131	—	22	1	no	—
171	C₂×M₁₆	—	11	1	no	—
172	C₂×M₁₆	—	22	1	no	—
173	C₂×M₁₆	C₄×D₁₁	1	1	yes	characteristic
174	C₂²×C₈	—	11	1	no	—
175	C₂²×C₈	—	22	1	no	—
176	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
177	#117	C₄×D₁₁	1	1	yes	characteristic
178	C₂×C₄²	—	11	1	no	—
179	M₃₂	—	2	1	no	—
180	M₃₂	—	2	1	no	—
181	M₃₂	—	2	1	no	—
182	M₃₂	—	2	1	no	—
183	M₃₂	—	11	2	no	—
184	M₃₂	—	22	4	no	—
185	M₃₂	—	22	1	no	—
186	M₃₂	—	22	1	no	—
187	M₃₂	—	22	1	no	—
188	C₂×C₁₆	—	2	1	no	—
189	C₂×C₁₆	—	22	4	no	—
190	C₂×C₁₆	—	22	1	no	—
191	C₂×C₁₆	—	22	1	no	—
192	C₂×C₁₆	D₄₄	1	2	yes	—
193	#104	—	11	2	no	—
194	#104	—	11	2	no	—
195	#103	—	22	1	no	—
196	#102	—	22	1	no	—
197	#97	—	2	1	no	—
198	C₄×C₈	—	2	1	no	—
199	C₄×C₈	—	22	1	no	—
200	C₄×C₈	—	22	1	no	—
201	C₂×C₁₁	—	2	1	no	—
202	C₂×C₁₁	—	2	1	no	—
203	C₂×C₁₁	—	2	1	no	—
204	C₂×C₁₁	#1850	1	1	yes	characteristic
205	D₁₁	—	4	2	no	—
206	#41	—	11	2	no	—
207	#41	—	11	2	no	—
208	#41	—	22	1	no	—
209	#41	—	22	1	no	—
210	C₂×Q₈	—	11	1	no	—
211	C₂×D₄	—	11	1	no	—
212	C₂×D₄	—	22	1	no	—
213	C₂²×C₄	—	22	1	no	—
214	C₂²×C₄	—	22	1	no	—
215	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
216	M₁₆	—	2	1	no	—
217	M₁₆	—	11	2	no	—
218	M₁₆	—	22	1	no	—
219	M₁₆	—	22	2	no	—
220	M₁₆	—	22	2	no	—
221	M₁₆	C₈×D₁₁	1	2	yes	—
222	C₂×C₈	—	2	1	no	—
223	C₂×C₈	—	22	1	no	—
224	C₂×C₈	—	22	2	no	—
225	C₂×C₈	—	22	2	no	—
226	C₂×C₈	—	22	1	no	—
227	C₂×C₈	—	22	1	no	—
228	C₂×C₈	—	22	1	no	—
229	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
230	C₂×C₈	#4339	1	1	yes	characteristic
231	C₂×C₈	D₄×D₁₁	1	1	yes	characteristic
232	C₂×C₈	D₄×D₁₁	1	1	yes	characteristic
233	C₂×C₈	#4341	1	1	yes	characteristic
234	C₂×C₈	Q₈×D₁₁	1	1	yes	characteristic
235	C₄⋊C₄	—	2	1	no	—
236	C₂²⋊C₄	—	2	1	no	—
237	C₄²	—	2	1	no	—
238	C₄²	—	11	1	no	—
239	C₄²	—	11	1	no	—
240	C₄²	—	22	1	no	—
241	C₁₆	—	2	2	no	—
242	C₁₆	—	4	1	no	—
243	C₁₆	—	22	2	no	—
244	C₁₆	—	44	1	no	—
245	C₁₁	#12918	1	1	yes	characteristic, complemented, Sylow
246	C₂³	—	22	1	no	—
247	C₂³	#66954	1	1	yes	characteristic
248	Q₈	—	11	2	no	—
249	Q₈	—	22	1	no	—
250	D₄	—	11	2	no	—
251	D₄	—	22	2	no	—
252	D₄	—	22	2	no	—
253	D₄	—	22	1	no	—
254	C₂×C₄	—	4	1	no	—
255	C₂×C₄	—	22	1	no	—
256	C₂×C₄	—	22	1	no	—
257	C₂×C₄	—	22	2	no	—
258	C₂×C₄	—	22	2	no	—
259	C₂×C₄	—	22	1	no	—
260	C₂×C₄	—	44	2	no	—
261	C₂×C₄	C₄×D₄₄	1	1	yes	characteristic
262	C₂×C₄	(C₂²⋊D₁₁)⋊C₄	1	1	yes	characteristic
263	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
264	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
265	C₂×C₄	M₁₆×D₁₁	1	1	yes	characteristic
266	C₂×C₄	#66960	1	1	yes	characteristic
267	C₈	—	2	2	no	—
268	C₈	—	22	2	no	—
269	C₈	—	44	1	no	—
270	C₈	#66935	1	1	yes	characteristic
271	C₈	#66936	1	1	yes	characteristic
272	C₈	#66949	1	1	yes	characteristic
273	C₈	#66950	1	1	yes	characteristic
274	C₂²	—	4	1	no	—
275	C₂²	—	22	2	no	—
276	C₂²	—	88	1	no	—
277	C₂²	C₈×D₄₄	1	1	yes	characteristic
278	C₂²	#10622341	1	1	yes	characteristic
279	C₂²	#10622452	1	1	yes	characteristic
280	C₄	—	8	1	no	—
281	C₄	—	22	2	no	—
282	C₄	—	22	2	no	—
283	C₄	—	44	1	no	—
284	C₄	#10622281	1	1	yes	characteristic
285	C₄	#10622319	1	1	yes	characteristic
286	C₄	(C₂²⋊D₁₁)⋊C₈	1	1	yes	characteristic
287	C₄	D₁₁×C₄⋊C₈	1	1	yes	characteristic
288	C₂	—	2	1	no	—
289	C₂	—	2	1	no	—
290	C₂	—	2	1	no	—
291	C₂	—	44	2	no	—
292	C₂	#13068795	1	1	yes	characteristic

	subgroup	G/H
center	C₈	#66935
commutator	C₂×C₄×C₁₁	C₂²×C₈
Frattini	C₂²×C₈	C₂²×D₁₁
Fitting	C₁₁×#1378	C₂
socle	C₂×C₁₁	#1850
prime radical	C₂×#4339	C₂×C₄
cosocle	C₂²×C₈×C₁₁	C₂³
hypercenter	#1378	D₁₁
hypocenter	C₁₁	#12918
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ #1378

Complements

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

N	H ≅ G/N	type
2. #13070382	C₂	semidirect
3. #13070371	C₂	semidirect
6. #13066697	C₂	semidirect
7. C₁₁×#1378	C₂	semidirect
105. #1378	D₁₁	semidirect
245. C₁₁	#12918	semidirect

Maximal subgroups

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

subgroup	index
#13081718	2
#13070382	2
#13070371	2
#13070243	2
#13068455	2
#13066697	2
C₁₁×#1378	2
#12918	11