Subgroups — #14907142

Order 2816.

682 conjugacy classes of subgroups.

The subgroup lattice has 302 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#66892	C₂	1	1	yes	maximal, characteristic
2	#13077469	C₂	1	1	yes	maximal, characteristic
3	#13070478	C₂	1	4	yes	maximal, complemented
4	C₄×#66892	C₂	1	4	yes	maximal, complemented
5	#13070398	C₂	1	1	yes	maximal, characteristic, complemented
6	#13070336	C₂	1	1	yes	maximal, characteristic, complemented
7	#13070331	C₂	1	1	yes	maximal, characteristic
8	#13070213	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#2950	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₁×Q₁₆	C₂²	1	1	yes	characteristic
11	C₁₁×#519	—	2	1	no	—
12	C₂²×D₈₈	C₂²	1	1	yes	characteristic
13	#10623052	—	2	1	no	—
14	C₁₁×#441	—	2	2	no	—
15	C₄×C₁₁×Q₁₆	C₂²	1	4	yes	complemented
16	C₁₁×#427	C₂²	1	1	yes	characteristic
17	C₁₁×#419	—	2	1	no	—
18	C₁₁×#405	C₂²	1	1	yes	characteristic
19	C₂×#66892	C₄	1	8	yes	complemented
20	C₂×#66892	C₂²	1	2	yes	—
21	C₂×#66892	C₂²	1	2	yes	—
22	#10622744	—	2	1	no	—
23	#10622719	C₂²	1	1	yes	characteristic
24	C₂×#66876	C₂²	1	1	yes	characteristic
25	C₂²×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
26	#10622324	—	2	2	no	—
27	C₄×D₈₈	C₂²	1	4	yes	—
28	#10622202	C₂²	1	4	yes	complemented
29	#10622129	C₂²	1	4	yes	—
30	#10622128	C₂²	1	2	yes	complemented
31	#10622127	C₂²	1	2	yes	complemented
32	#10622099	C₂²	1	2	yes	complemented
33	C₄×C₁₁⋊C₁₆	C₂²	1	2	yes	complemented
34	C₂²×Q₈×C₁₁	—	2	1	no	—
35	C₂²×D₄₄	—	2	1	no	—
36	C₂×C₁₁×Q₁₆	—	2	1	no	—
37	C₂×C₁₁×Q₁₆	—	2	2	no	—
38	C₂×C₁₁×Q₁₆	C₂×C₄	1	4	yes	complemented
39	C₂×C₁₁×Q₁₆	C₂³	1	2	yes	—
40	C₂×C₁₁×M₁₆	D₄	1	1	yes	characteristic
41	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
42	C₄×Q₈×C₁₁	—	2	4	no	—
43	C₄×Q₈×C₁₁	—	4	2	no	—
44	C₁₁×#117	—	2	1	no	—
45	C₁₁×#117	—	4	2	no	—
46	C₁₁×#117	D₄	1	1	yes	characteristic
47	#66979	—	2	1	no	—
48	C₂×D₈₈	—	2	1	no	—
49	C₂×D₈₈	—	2	2	no	—
50	C₂×D₈₈	C₂×C₄	1	4	yes	—
51	C₂×D₈₈	C₂³	1	2	yes	—
52	#66946	—	4	2	no	—
53	C₂²⋊C₄×D₁₁	—	4	2	no	—
54	C₄×D₄₄	—	2	4	no	—
55	C₁₁×#107	C₂³	1	2	yes	—
56	C₁₁×#106	—	2	1	no	—
57	C₁₁×#103	—	2	4	no	—
58	C₁₁×#97	D₄	1	2	yes	—
59	C₄×C₈×C₁₁	C₂³	1	2	yes	—
60	#66892	C₂×C₄	1	8	yes	complemented
61	#66892	C₂×C₄	1	8	yes	complemented
62	#66885	—	2	4	no	—
63	#66882	C₂³	1	2	yes	—
64	#66881	—	2	1	no	—
65	#66876	—	2	2	no	—
66	C₂×C₁₁⋊C₁₆	C₂×C₄	1	4	yes	complemented
67	C₂×C₁₁⋊C₁₆	C₂³	1	2	yes	—
68	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
69	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
70	#33457	—	11	1	no	maximal, Sylow
71	C₂³×D₁₁	—	4	1	no	—
72	C₂×Q₈×C₁₁	—	2	4	no	—
73	C₂×Q₈×C₁₁	—	2	2	no	—
74	C₂×Q₈×C₁₁	—	4	1	no	—
75	C₂×Q₈×C₁₁	—	4	2	no	—
76	C₂²×C₄×C₁₁	—	4	1	no	—
77	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
78	C₂×D₄₄	—	2	4	no	—
79	C₂×D₄₄	—	2	2	no	—
80	C₂×D₄₄	—	4	1	no	—
81	C₂×D₄₄	—	4	2	no	—
82	C₂×C₄×D₁₁	—	4	4	no	—
83	C₁₁×Q₁₆	—	2	4	no	—
84	C₁₁×Q₁₆	—	2	2	no	—
85	C₁₁×Q₁₆	C₂²×C₄	1	4	yes	—
86	C₁₁×M₁₆	—	2	2	no	—
87	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
88	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
89	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
90	C₂×C₈×C₁₁	#41	1	2	yes	—
91	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
92	C₁₁×C₄⋊C₄	—	2	2	no	—
93	C₁₁×C₄⋊C₄	—	4	4	no	—
94	C₁₁×C₄⋊C₄	D₈	1	2	yes	—
95	C₁₁×C₂²⋊C₄	—	4	1	no	—
96	C₁₁×C₂²⋊C₄	D₈	1	2	yes	—
97	C₄²×C₁₁	—	4	1	no	—
98	C₄²×C₁₁	—	4	4	no	—
99	C₄²×C₁₁	C₂×D₄	1	2	yes	—
100	C₂²⋊Dic₁₁	—	4	1	no	—
101	(C₂×D₁₁)⋊C₄	—	4	4	no	—
102	C₄⋊Dic₁₁	—	2	2	no	—
103	C₄×Dic₁₁	—	4	1	no	—
104	D₈₈	—	2	4	no	—
105	D₈₈	—	2	2	no	—
106	D₈₈	C₂²×C₄	1	4	yes	—
107	C₁₁⋊C₁₆	—	2	2	no	—
108	C₁₁⋊C₁₆	C₂²×C₄	1	2	yes	—
109	C₁₁⋊C₁₆	C₂²×C₄	1	2	yes	—
110	C₂²×SD₃₂	—	11	1	no	—
111	#2950	D₁₁	1	1	yes	characteristic, complemented
112	#2948	—	11	1	no	—
113	#2175	—	11	4	no	—
114	C₄×SD₃₂	—	11	4	no	—
115	#2158	—	11	1	no	—
116	#2141	—	11	1	no	—
117	#2140	—	11	1	no	—
118	#2108	—	11	1	no	—
119	C₂³×C₁₁	C₂×D₈	1	1	yes	characteristic
120	C₂²×D₁₁	—	4	2	no	—
121	C₂²×D₁₁	—	4	4	no	—
122	C₂²×D₁₁	—	16	2	no	—
123	Q₈×C₁₁	—	2	4	no	—
124	Q₈×C₁₁	—	4	2	no	—
125	Q₈×C₁₁	—	4	4	no	—
126	C₂×C₄×C₁₁	—	4	2	no	—
127	C₂×C₄×C₁₁	—	4	4	no	—
128	C₂×C₄×C₁₁	—	4	2	no	—
129	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
130	C₂×C₄×C₁₁	C₂×D₈	1	4	yes	—
131	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
132	C₂×C₄×C₁₁	#135	1	2	yes	—
133	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
134	C₂×Dic₁₁	—	4	2	no	—
135	D₄₄	—	2	4	no	—
136	D₄₄	—	4	2	no	—
137	D₄₄	—	4	4	no	—
138	C₄×D₁₁	—	16	4	no	—
139	C₈×C₁₁	—	2	2	no	—
140	C₈×C₁₁	C₄×D₄	1	2	yes	—
141	C₈×C₁₁	C₂³×C₄	1	1	yes	characteristic
142	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
143	C₂²×Q₁₆	C₂×D₁₁	1	1	yes	characteristic
144	C₂²×D₈	—	11	1	no	—
145	#519	—	2	1	no	—
146	#518	—	22	1	no	—
147	C₂×SD₃₂	—	11	2	no	—
148	C₂×SD₃₂	—	11	2	no	—
149	C₂×SD₃₂	—	11	8	no	—
150	C₂×M₃₂	—	11	1	no	—
151	C₂²×C₁₆	—	11	1	no	—
152	#442	—	22	2	no	—
153	#441	—	2	2	no	—
154	C₄×Q₁₆	C₂×D₁₁	1	4	yes	complemented
155	C₄×D₈	—	11	4	no	—
156	#427	—	11	1	no	—
157	#427	C₂×D₁₁	1	1	yes	characteristic
158	#419	—	2	1	no	—
159	#418	—	22	1	no	—
160	#405	C₂×D₁₁	1	1	yes	characteristic
161	#367	—	11	2	no	—
162	#366	—	11	2	no	—
163	#358	—	11	4	no	—
164	#357	—	11	4	no	—
165	#346	—	11	2	no	—
166	C₄×C₁₆	—	11	2	no	—
167	C₂²×C₁₁	—	2	2	no	—
168	C₂²×C₁₁	C₄×D₈	1	2	yes	—
169	C₂²×C₁₁	C₂²×D₈	1	1	yes	characteristic
170	C₂×D₁₁	—	4	4	no	—
171	C₂×D₁₁	—	8	4	no	—
172	C₂×D₁₁	—	16	4	no	—
173	C₄×C₁₁	—	2	4	no	—
174	C₄×C₁₁	—	4	4	no	—
175	C₄×C₁₁	—	8	2	no	—
176	C₄×C₁₁	C₄×D₈	1	2	yes	—
177	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
178	C₄×C₁₁	C₂×#135	1	1	yes	characteristic
179	Dic₁₁	—	8	2	no	—
180	C₂²×Q₈	—	2	1	no	—
181	C₂²×D₄	—	22	1	no	—
182	C₂×Q₁₆	—	2	2	no	—
183	C₂×Q₁₆	—	2	1	no	—
184	C₂×Q₁₆	C₄×D₁₁	1	4	yes	complemented
185	C₂×Q₁₆	C₂²×D₁₁	1	2	yes	—
186	C₂×D₈	—	11	4	no	—
187	C₂×D₈	—	11	2	no	—
188	C₂×D₈	—	22	2	no	—
189	C₂×D₈	—	22	1	no	—
190	C₂×M₁₆	C₂²⋊D₁₁	1	1	yes	characteristic
191	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
192	C₄×Q₈	—	2	4	no	—
193	C₄×Q₈	—	4	2	no	—
194	C₄×D₄	—	22	4	no	—
195	C₄×D₄	—	44	2	no	—
196	#117	—	2	1	no	—
197	#117	—	4	2	no	—
198	#117	—	22	1	no	—
199	#117	C₂²⋊D₁₁	1	1	yes	characteristic
200	C₂×C₂²⋊C₄	—	44	2	no	—
201	SD₃₂	—	11	8	no	—
202	SD₃₂	—	11	8	no	—
203	M₃₂	—	22	2	no	—
204	C₂×C₁₆	—	11	4	no	—
205	C₂×C₁₆	—	11	1	no	—
206	C₂×C₁₆	—	11	1	no	—
207	C₂×C₁₆	—	11	2	no	—
208	#107	—	11	2	no	—
209	#107	C₂²×D₁₁	1	2	yes	—
210	#106	—	2	1	no	—
211	#106	—	22	1	no	—
212	#103	—	2	4	no	—
213	#102	—	22	4	no	—
214	#97	C₂²⋊D₁₁	1	2	yes	—
215	C₄×C₈	C₂²×D₁₁	1	2	yes	—
216	C₂×C₁₁	—	2	2	no	—
217	C₂×C₁₁	C₂×C₄×D₈	1	1	yes	characteristic
218	C₂×C₁₁	#3416	1	2	yes	—
219	D₁₁	—	8	4	no	—
220	C₂⁴	—	44	1	no	—
221	C₂×Q₈	—	2	4	no	—
222	C₂×Q₈	—	2	2	no	—
223	C₂×Q₈	—	4	1	no	—
224	C₂×Q₈	—	4	2	no	—
225	C₂×D₄	—	22	4	no	—
226	C₂×D₄	—	22	2	no	—
227	C₂×D₄	—	44	1	no	—
228	C₂×D₄	—	44	2	no	—
229	C₂²×C₄	—	4	1	no	—
230	C₂²×C₄	—	44	4	no	—
231	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
232	Q₁₆	—	2	4	no	—
233	Q₁₆	—	2	2	no	—
234	Q₁₆	C₂×C₄×D₁₁	1	4	yes	—
235	D₈	—	11	4	no	—
236	D₈	—	22	4	no	—
237	D₈	—	22	2	no	—
238	M₁₆	—	2	2	no	—
239	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
240	C₂×C₈	#4339	1	2	yes	—
241	C₂×C₈	C₂×C₂²⋊D₁₁	1	2	yes	—
242	C₂×C₈	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
243	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
244	C₄⋊C₄	—	2	2	no	—
245	C₄⋊C₄	—	4	4	no	—
246	C₄⋊C₄	—	22	2	no	—
247	C₄⋊C₄	#4323	1	2	yes	—
248	C₂²⋊C₄	—	4	1	no	—
249	C₂²⋊C₄	—	44	1	no	—
250	C₂²⋊C₄	—	44	4	no	—
251	C₂²⋊C₄	#4323	1	2	yes	—
252	C₄²	—	4	1	no	—
253	C₄²	—	4	4	no	—
254	C₄²	—	44	1	no	—
255	C₄²	C₂×C₂²⋊D₁₁	1	2	yes	—
256	C₁₆	—	11	2	no	—
257	C₁₆	—	11	2	no	—
258	C₁₆	—	22	2	no	—
259	C₁₁	#33457	1	1	yes	characteristic, complemented, Sylow
260	C₂³	—	44	2	no	—
261	C₂³	—	44	4	no	—
262	C₂³	—	176	2	no	—
263	C₂³	C₂×#4323	1	1	yes	characteristic
264	Q₈	—	2	4	no	—
265	Q₈	—	4	2	no	—
266	Q₈	—	4	4	no	—
267	D₄	—	22	4	no	—
268	D₄	—	44	2	no	—
269	D₄	—	44	4	no	—
270	C₂×C₄	—	4	2	no	—
271	C₂×C₄	—	4	4	no	—
272	C₂×C₄	—	4	2	no	—
273	C₂×C₄	—	44	2	no	—
274	C₂×C₄	—	176	4	no	—
275	C₂×C₄	C₄×C₂²⋊D₁₁	1	2	yes	—
276	C₂×C₄	C₂×#4323	1	4	yes	—
277	C₂×C₄	C₂×#4323	1	1	yes	characteristic
278	C₂×C₄	#67003	1	2	yes	—
279	C₂×C₄	C₂²×C₂²⋊D₁₁	1	1	yes	characteristic
280	C₈	—	2	2	no	—
281	C₈	C₄×C₂²⋊D₁₁	1	2	yes	—
282	C₈	C₂²×C₄×D₁₁	1	1	yes	characteristic
283	C₈	C₂×#4339	1	1	yes	characteristic
284	C₂²	—	2	2	no	—
285	C₂²	—	44	4	no	—
286	C₂²	—	88	4	no	—
287	C₂²	—	176	4	no	—
288	C₂²	C₄×#4323	1	2	yes	—
289	C₂²	C₂²×#4323	1	1	yes	characteristic
290	C₄	—	2	4	no	—
291	C₄	—	4	4	no	—
292	C₄	—	8	2	no	—
293	C₄	—	88	2	no	—
294	C₄	C₄×#4323	1	2	yes	—
295	C₄	C₂×C₄×C₂²⋊D₁₁	1	1	yes	characteristic
296	C₄	C₂×#67003	1	1	yes	characteristic
297	C₂	—	2	2	no	—
298	C₂	—	88	4	no	—
299	C₂	C₂×C₄×#4323	1	1	yes	characteristic
300	C₂	#13081760	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂²×#4323
commutator	C₈×C₁₁	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₁₁
Fitting	C₁₁×#2950	C₂
socle	C₂²×C₁₁	C₂²×D₈
prime radical	C₂²×D₈₈	C₂²
cosocle	C₂×C₈×C₁₁	C₂⁴
hypercenter	#2950	D₁₁
hypocenter	C₁₁	#33457
LCS	G ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ #117 ◁ #405 ◁ #2950

Complements

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

N	H ≅ G/N	type
3. #13070478	C₂	semidirect
4. C₄×#66892	C₂	semidirect
5. #13070398	C₂	semidirect
6. #13070336	C₂	semidirect
8. #13070213	C₂	semidirect
9. C₁₁×#2950	C₂	semidirect
15. C₄×C₁₁×Q₁₆	C₂²	semidirect
19. C₂×#66892	C₄	semidirect
28. #10622202	C₂²	semidirect
30. #10622128	C₂²	semidirect
31. #10622127	C₂²	semidirect
32. #10622099	C₂²	semidirect
33. C₄×C₁₁⋊C₁₆	C₂²	semidirect
38. C₂×C₁₁×Q₁₆	C₂×C₄	semidirect
60. #66892	C₂×C₄	semidirect
61. #66892	C₂×C₄	semidirect
66. C₂×C₁₁⋊C₁₆	C₂×C₄	semidirect
111. #2950	D₁₁	semidirect
154. C₄×Q₁₆	C₂×D₁₁	semidirect
184. C₂×Q₁₆	C₄×D₁₁	semidirect
259. C₁₁	#33457	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#66892	2
#13077469	2
#13070478	2
C₄×#66892	2
#13070398	2
#13070336	2
#13070331	2
#13070213	2
C₁₁×#2950	2
#33457	11