Subgroups — #14909299

Order 2816.

482 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	#13079129	C₂	1	1	yes	maximal, characteristic
2	D₁₁×#499	C₂	1	1	yes	maximal, characteristic
3	#13070901	C₂	1	2	yes	maximal, complemented
4	#13070900	C₂	1	2	yes	maximal, complemented
5	#13070895	C₂	1	1	yes	maximal, characteristic, complemented
6	#13070892	C₂	1	1	yes	maximal, characteristic, complemented
7	#13070892	C₂	1	1	yes	maximal, characteristic, complemented
8	#13070403	C₂	1	2	yes	maximal
9	#13070401	C₂	1	2	yes	maximal
10	C₄×#66862	C₂	1	1	yes	maximal, characteristic
11	C₁₁×#2253	C₂	1	1	yes	maximal, characteristic, complemented
12	#10623219	—	2	1	no	—
13	D₁₁×#125	—	2	1	no	—
14	C₁₁×#499	C₂²	1	1	yes	characteristic
15	C₁₁×#499	C₂²	1	1	yes	characteristic
16	#10622677	—	2	1	no	—
17	#10622677	—	2	1	no	—
18	C₂×#66862	C₂²	1	1	yes	characteristic
19	C₂×#66862	C₂²	1	1	yes	characteristic
20	#10622493	C₂²	1	2	yes	—
21	D₁₁×#107	C₂²	1	2	yes	—
22	#10622491	C₂²	1	2	yes	—
23	#10622487	C₂²	1	2	yes	—
24	#10622473	—	2	1	no	—
25	D₁₁×#106	—	2	1	no	—
26	#10622471	—	2	1	no	—
27	#10622468	—	2	1	no	—
28	C₄×C₈×D₁₁	C₂²	1	1	yes	characteristic
29	#10622296	C₂²	1	1	yes	characteristic
30	#10622296	C₂²	1	1	yes	characteristic
31	C₁₁×#367	C₂²	1	2	yes	—
32	C₁₁×#366	C₂²	1	2	yes	—
33	C₄×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
34	#10622143	C₂²	1	2	yes	—
35	#10622142	C₂²	1	2	yes	—
36	#10622140	C₂²	1	1	yes	characteristic
37	#10622140	C₂²	1	1	yes	characteristic
38	#10622128	C₂²	1	2	yes	—
39	#10622128	C₂²	1	2	yes	—
40	#10622127	C₂²	1	2	yes	—
41	#10622127	C₂²	1	2	yes	—
42	C₄×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
43	C₁₁×#125	—	2	1	no	—
44	C₁₁×#125	—	2	1	no	—
45	C₂×C₈×D₁₁	D₄	1	1	yes	characteristic
46	C₂×C₈×D₁₁	C₂³	1	1	yes	characteristic
47	#66949	—	4	2	no	—
48	#66945	—	2	2	no	—
49	C₄⋊C₄×D₁₁	—	2	2	no	—
50	C₄⋊C₄×D₁₁	—	4	2	no	—
51	#66943	—	2	2	no	—
52	#66942	—	4	2	no	—
53	#66941	—	2	2	no	—
54	#66940	—	4	2	no	—
55	C₄²×D₁₁	D₄	1	1	yes	characteristic
56	#66923	—	2	1	no	—
57	#66923	—	2	1	no	—
58	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
59	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
60	C₁₁×#107	C₂³	1	2	yes	—
61	C₁₁×#107	C₂³	1	2	yes	—
62	C₁₁×#106	—	2	1	no	—
63	C₁₁×#106	—	2	1	no	—
64	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
65	#66882	C₂³	1	2	yes	—
66	#66882	C₂³	1	2	yes	—
67	#66881	—	2	1	no	—
68	#66881	—	2	1	no	—
69	C₈×Dic₁₁	D₄	1	1	yes	characteristic
70	C₈×Dic₁₁	C₂³	1	1	yes	characteristic
71	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
72	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
73	#66872	—	2	2	no	—
74	#66872	—	2	2	no	—
75	#66871	—	2	2	no	—
76	#66871	—	2	2	no	—
77	C₄×C₁₁⋊C₈	D₄	1	1	yes	characteristic
78	#66862	Q₈	1	4	yes	complemented
79	#66862	Q₈	1	4	yes	complemented
80	#33732	—	11	1	no	maximal, Sylow
81	C₂×C₄×D₁₁	—	4	2	no	—
82	C₂×C₄×D₁₁	D₈	1	2	yes	—
83	C₂×C₄×D₁₁	C₂×D₄	1	1	yes	characteristic
84	C₂×Dic₂₂	—	4	2	no	—
85	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
86	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
87	C₁₁×C₄⋊C₄	—	2	2	no	—
88	C₁₁×C₄⋊C₄	—	2	2	no	—
89	C₁₁×C₄⋊C₄	—	4	2	no	—
90	C₁₁×C₄⋊C₄	—	4	2	no	—
91	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
92	(C₂×D₁₁)⋊C₄	—	4	2	no	—
93	C₄⋊Dic₁₁	—	2	2	no	—
94	C₄⋊Dic₁₁	—	2	2	no	—
95	C₄⋊Dic₁₁	—	4	2	no	—
96	Dic₁₁⋊C₄	—	4	2	no	—
97	Dic₁₁⋊C₄	—	4	2	no	—
98	Dic₁₁⋊C₄	—	4	2	no	—
99	Dic₁₁⋊C₄	—	4	2	no	—
100	Dic₁₁⋊C₄	—	4	2	no	—
101	C₄×Dic₁₁	—	4	2	no	—
102	C₄×Dic₁₁	D₈	1	2	yes	—
103	C₄×Dic₁₁	C₂×D₄	1	1	yes	characteristic
104	C₂×C₁₁⋊C₈	C₂×D₄	1	1	yes	characteristic
105	C₂×C₁₁⋊C₈	C₂×D₄	1	1	yes	characteristic
106	C₈×D₁₁	Q₁₆	1	4	yes	—
107	C₈×D₁₁	C₂×Q₈	1	2	yes	—
108	C₈×D₁₁	C₂×Q₈	1	2	yes	—
109	C₁₁×C₁₆	C₂×Q₈	1	2	yes	—
110	C₁₁×C₁₆	C₂×Q₈	1	2	yes	—
111	C₁₁⋊C₁₆	C₂×Q₈	1	2	yes	—
112	C₁₁⋊C₁₆	C₂×Q₈	1	2	yes	—
113	#3160	—	11	1	no	—
114	C₂×#499	—	11	1	no	—
115	#2255	—	11	2	no	—
116	#2255	—	11	2	no	—
117	#2253	—	11	1	no	—
118	#2253	—	11	1	no	—
119	#2253	—	11	1	no	—
120	#2253	D₁₁	1	1	yes	characteristic, complemented
121	#2159	—	11	2	no	—
122	#2159	—	11	2	no	—
123	C₄×M₃₂	—	11	1	no	—
124	C₂²×D₁₁	C₂×D₈	1	1	yes	characteristic
125	C₂×C₄×C₁₁	—	4	2	no	—
126	C₂×C₄×C₁₁	—	4	2	no	—
127	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
128	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
129	C₂×Dic₁₁	—	4	2	no	—
130	C₂×Dic₁₁	—	4	2	no	—
131	C₂×Dic₁₁	C₂×D₈	1	2	yes	—
132	C₂×Dic₁₁	C₂×D₈	1	1	yes	characteristic
133	C₄×D₁₁	—	4	2	no	—
134	C₄×D₁₁	—	8	4	no	—
135	C₄×D₁₁	C₄⋊Q₈	1	2	yes	—
136	C₄×D₁₁	C₂×Q₁₆	1	2	yes	—
137	Dic₂₂	—	8	4	no	—
138	C₈×C₁₁	C₂×Q₁₆	1	2	yes	—
139	C₈×C₁₁	C₂²×Q₈	1	1	yes	characteristic
140	C₈×C₁₁	C₂²×Q₈	1	1	yes	characteristic
141	C₁₁⋊C₈	C₄⋊Q₈	1	2	yes	—
142	C₁₁⋊C₈	C₂×Q₁₆	1	2	yes	—
143	#533	—	22	1	no	—
144	C₂×#125	—	22	1	no	—
145	C₂×M₃₂	—	11	1	no	—
146	C₂×M₃₂	—	11	1	no	—
147	#500	—	11	2	no	—
148	#499	—	11	2	no	—
149	#499	—	11	1	no	—
150	#499	—	11	1	no	—
151	#499	—	22	1	no	—
152	#499	—	22	1	no	—
153	#499	—	22	1	no	—
154	#499	C₂×D₁₁	1	1	yes	characteristic
155	#499	C₂×D₁₁	1	1	yes	characteristic
156	#498	—	22	1	no	—
157	#427	—	11	2	no	—
158	#427	—	22	1	no	—
159	C₂×#107	—	11	2	no	—
160	C₂×#106	—	22	1	no	—
161	C₂×C₄×C₈	—	11	1	no	—
162	#367	—	11	2	no	—
163	#367	—	11	2	no	—
164	#367	—	11	2	no	—
165	#367	C₂×D₁₁	1	2	yes	—
166	#366	—	11	2	no	—
167	#366	—	11	2	no	—
168	#366	—	11	2	no	—
169	#366	C₂×D₁₁	1	2	yes	—
170	#346	—	11	1	no	—
171	#346	—	11	1	no	—
172	C₄×C₁₆	—	11	1	no	—
173	C₄×C₁₆	C₂×D₁₁	1	1	yes	characteristic
174	C₂²×C₁₁	C₂²×D₈	1	1	yes	characteristic
175	C₂×D₁₁	—	2	2	no	—
176	C₂×D₁₁	#500	1	2	yes	—
177	C₄×C₁₁	—	2	2	no	—
178	C₄×C₁₁	—	8	2	no	—
179	C₄×C₁₁	—	8	2	no	—
180	C₄×C₁₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
181	C₄×C₁₁	C₂²×Q₁₆	1	1	yes	characteristic
182	Dic₁₁	—	2	2	no	—
183	Dic₁₁	—	8	2	no	—
184	Dic₁₁	—	8	2	no	—
185	Dic₁₁	#500	1	2	yes	—
186	C₂²×C₈	—	11	1	no	—
187	C₂²×C₈	—	11	1	no	—
188	C₄⋊Q₈	—	22	2	no	—
189	#125	—	2	1	no	—
190	#125	—	2	1	no	—
191	#125	—	22	2	no	—
192	#125	—	22	1	no	—
193	#125	—	22	1	no	—
194	#125	—	44	2	no	—
195	C₂²⋊Q₈	—	44	2	no	—
196	C₄×Q₈	—	44	2	no	—
197	#117	—	22	2	no	—
198	C₂×C₄⋊C₄	—	22	2	no	—
199	C₂×C₄⋊C₄	—	44	2	no	—
200	C₂×C₄²	—	11	1	no	—
201	M₃₂	—	11	4	no	—
202	M₃₂	—	11	4	no	—
203	C₂×C₁₆	—	11	1	no	—
204	C₂×C₁₆	—	11	1	no	—
205	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
206	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
207	#107	—	11	2	no	—
208	#107	—	11	2	no	—
209	#107	—	22	2	no	—
210	#107	—	22	2	no	—
211	#107	C₂²×D₁₁	1	2	yes	—
212	#107	C₂²×D₁₁	1	2	yes	—
213	#106	—	2	1	no	—
214	#106	—	2	1	no	—
215	#106	—	22	2	no	—
216	#106	—	22	2	no	—
217	#106	—	22	1	no	—
218	#106	—	22	1	no	—
219	C₄×C₈	—	11	1	no	—
220	C₄×C₈	—	11	1	no	—
221	C₄×C₈	—	11	1	no	—
222	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
223	C₂×C₁₁	C₂×#500	1	1	yes	characteristic
224	C₂×C₁₁	#3414	1	2	yes	—
225	D₁₁	—	2	2	no	—
226	C₂×Q₈	—	44	2	no	—
227	C₂²×C₄	—	11	1	no	—
228	C₂²×C₄	—	11	2	no	—
229	C₂²×C₄	—	44	2	no	—
230	C₂×C₈	—	11	1	no	—
231	C₂×C₈	—	11	1	no	—
232	C₂×C₈	—	11	4	no	—
233	C₂×C₈	—	11	2	no	—
234	C₂×C₈	—	11	2	no	—
235	C₂×C₈	D₄×D₁₁	1	1	yes	characteristic
236	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
237	C₄⋊C₄	—	2	2	no	—
238	C₄⋊C₄	—	2	2	no	—
239	C₄⋊C₄	—	4	2	no	—
240	C₄⋊C₄	—	4	2	no	—
241	C₄⋊C₄	—	22	2	no	—
242	C₄⋊C₄	—	22	2	no	—
243	C₄⋊C₄	—	44	2	no	—
244	C₄⋊C₄	—	44	2	no	—
245	C₄⋊C₄	—	44	2	no	—
246	C₄⋊C₄	—	44	2	no	—
247	C₄⋊C₄	—	44	2	no	—
248	C₄⋊C₄	—	44	2	no	—
249	C₂²⋊C₄	—	44	2	no	—
250	C₄²	—	11	2	no	—
251	C₄²	—	11	1	no	—
252	C₄²	—	44	2	no	—
253	C₄²	D₄×D₁₁	1	1	yes	characteristic
254	C₁₆	—	11	2	no	—
255	C₁₆	—	11	2	no	—
256	C₁₆	Q₈×D₁₁	1	2	yes	—
257	C₁₆	Q₈×D₁₁	1	2	yes	—
258	C₁₁	#33732	1	1	yes	characteristic, complemented, Sylow
259	C₂³	—	11	1	no	—
260	Q₈	—	88	4	no	—
261	C₂×C₄	—	4	2	no	—
262	C₂×C₄	—	4	2	no	—
263	C₂×C₄	—	11	1	no	—
264	C₂×C₄	—	11	2	no	—
265	C₂×C₄	—	11	2	no	—
266	C₂×C₄	—	11	2	no	—
267	C₂×C₄	—	44	2	no	—
268	C₂×C₄	—	44	2	no	—
269	C₂×C₄	—	44	2	no	—
270	C₂×C₄	—	88	4	no	—
271	C₂×C₄	D₈×D₁₁	1	2	yes	—
272	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
273	C₈	—	11	2	no	—
274	C₈	—	11	2	no	—
275	C₈	Q₁₆×D₁₁	1	2	yes	—
276	C₈	C₂×Q₈×D₁₁	1	1	yes	characteristic
277	C₈	C₂×Q₈×D₁₁	1	1	yes	characteristic
278	C₂²	—	11	2	no	—
279	C₂²	—	22	2	no	—
280	C₂²	C₂×D₈×D₁₁	1	1	yes	characteristic
281	C₄	—	2	2	no	—
282	C₄	—	8	2	no	—
283	C₄	—	8	2	no	—
284	C₄	—	11	2	no	—
285	C₄	—	22	2	no	—
286	C₄	—	88	2	no	—
287	C₄	—	88	2	no	—
288	C₄	D₁₁×C₄⋊Q₈	1	1	yes	characteristic
289	C₄	C₂×Q₁₆×D₁₁	1	1	yes	characteristic
290	C₂	—	22	2	no	—
291	C₂	D₁₁×#500	1	1	yes	characteristic
292	C₂	#13081749	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₈×D₁₁
commutator, cosocle	C₂×C₈×C₁₁	C₂⁴
Frattini	C₂×C₈	C₂³×D₁₁
Fitting	C₁₁×#2253	C₂
socle	C₂²×C₁₁	C₂²×D₈
prime radical	C₂²×D₁₁	C₂×D₈
hypercenter	#2253	D₁₁
hypocenter	C₁₁	#33732
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #2253

Complements

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

N	H ≅ G/N	type
3. #13070901	C₂	semidirect
4. #13070900	C₂	semidirect
5. #13070895	C₂	semidirect
6. #13070892	C₂	semidirect
7. #13070892	C₂	semidirect
11. C₁₁×#2253	C₂	semidirect
78. #66862	Q₈	semidirect
79. #66862	Q₈	semidirect
120. #2253	D₁₁	semidirect
258. C₁₁	#33732	semidirect

Maximal subgroups

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

subgroup	index
#13079129	2
D₁₁×#499	2
#13070901	2
#13070900	2
#13070895	2
#13070892	2
#13070403	2
#13070401	2
C₄×#66862	2
C₁₁×#2253	2
#33732	11