Subgroups — #14911154

Order 2816.

470 conjugacy classes of subgroups.

The subgroup lattice has 314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13080987	C₂	1	2	yes	maximal
2	#13070893	C₂	1	1	yes	maximal, characteristic, complemented
3	#13070823	C₂	1	2	yes	maximal, complemented
4	#13070811	C₂	1	2	yes	maximal, complemented
5	#13070782	C₂	1	2	yes	maximal, complemented
6	#13070704	C₂	1	1	yes	maximal, characteristic, complemented
7	Q₃₂×Dic₁₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₆×C₂²⋊D₁₁	C₂	1	1	yes	maximal, characteristic
9	#13070397	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#10622142	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#2216	C₂	1	1	yes	maximal, characteristic, complemented
12	#10623173	—	2	2	no	—
13	C₂×C₁₁×Q₃₂	C₂²	1	1	yes	characteristic
14	C₂²×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
15	C₁₁×#467	C₂²	1	2	yes	—
16	#10622801	C₂²	1	2	yes	—
17	Q₁₆×Dic₁₁	C₂²	1	2	yes	—
18	C₈×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic
19	C₂×#66882	C₂²	1	2	yes	—
20	#10622656	—	2	2	no	—
21	C₂×C₁₆×D₁₁	C₂²	1	1	yes	characteristic
22	#10622493	C₂²	1	2	yes	—
23	#10622491	C₂²	1	2	yes	—
24	#10622427	—	2	2	no	—
25	#10622409	—	2	2	no	—
26	C₁₁×#366	C₂²	1	1	yes	characteristic
27	C₁₁×#358	C₂²	1	2	yes	—
28	#10622202	C₂²	1	2	yes	—
29	#10622202	C₂²	1	2	yes	—
30	C₂²⋊(C₁₁⋊C₁₆)	C₂²	1	1	yes	characteristic
31	(C₂×D₁₁)⋊C₁₆	C₂²	1	1	yes	characteristic
32	#10622142	C₂²	1	1	yes	characteristic
33	#10622142	C₂²	1	1	yes	characteristic
34	#10622142	C₂²	1	2	yes	—
35	Dic₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
36	C₁₆×Dic₁₁	C₂²	1	1	yes	characteristic
37	#10622128	C₂²	1	2	yes	—
38	#10622128	C₂²	1	2	yes	—
39	C₂×C₁₁×Q₁₆	C₂³	1	2	yes	—
40	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
41	C₁₁×C₂²⋊Q₈	—	2	2	no	—
42	#66999	—	2	2	no	—
43	Q₈×Dic₁₁	—	2	2	no	—
44	C₄×C₂²⋊D₁₁	D₄	1	1	yes	characteristic
45	C₂×C₄⋊Dic₁₁	—	2	2	no	—
46	C₂×C₈×D₁₁	C₂³	1	1	yes	characteristic
47	#66951	—	4	2	no	—
48	#66945	—	2	2	no	—
49	#66943	—	2	2	no	—
50	#66943	—	4	2	no	—
51	#66939	—	4	2	no	—
52	#66930	—	4	2	no	—
53	C₁₁×Q₃₂	—	2	2	no	—
54	C₂×C₁₁×C₁₆	—	2	2	no	—
55	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
56	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
57	C₁₁×#107	C₂³	1	2	yes	—
58	C₁₁×#103	—	2	2	no	—
59	#66899	—	2	2	no	—
60	#66899	—	2	2	no	—
61	C₂²⋊(C₁₁⋊C₈)	D₄	1	1	yes	characteristic
62	(C₂×D₁₁)⋊C₈	D₄	1	1	yes	characteristic
63	#66882	—	2	2	no	—
64	#66882	C₂³	1	2	yes	—
65	#66882	C₂³	1	2	yes	—
66	Dic₁₁⋊C₈	D₄	1	1	yes	characteristic
67	C₈×Dic₁₁	C₂³	1	1	yes	characteristic
68	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
69	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
70	#66872	—	2	2	no	—
71	#66872	—	2	2	no	—
72	C₁₆×D₁₁	—	2	2	no	—
73	#33903	—	11	1	no	maximal, Sylow
74	C₂×Q₈×C₁₁	—	2	2	no	—
75	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
76	C₂×C₂²⋊D₁₁	D₈	1	1	yes	characteristic
77	C₂²×Dic₁₁	—	4	2	no	—
78	C₂×C₄×D₁₁	C₂×D₄	1	1	yes	characteristic
79	C₁₁×Q₁₆	—	2	2	no	—
80	C₁₁×Q₁₆	—	2	2	no	—
81	C₂×C₈×C₁₁	—	2	1	no	—
82	C₂×C₈×C₁₁	—	2	1	no	—
83	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
84	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
85	C₁₁×C₄⋊C₄	—	2	2	no	—
86	C₁₁×C₄⋊C₄	—	4	2	no	—
87	C₁₁×C₂²⋊C₄	—	4	2	no	—
88	C₂²⋊Dic₁₁	D₈	1	1	yes	characteristic
89	(C₂×D₁₁)⋊C₄	—	4	2	no	—
90	(C₂×D₁₁)⋊C₄	—	4	2	no	—
91	(C₂×D₁₁)⋊C₄	D₈	1	1	yes	characteristic
92	C₄⋊Dic₁₁	—	2	2	no	—
93	C₄⋊Dic₁₁	—	2	2	no	—
94	C₄⋊Dic₁₁	—	4	2	no	—
95	C₄⋊Dic₁₁	—	4	2	no	—
96	C₄⋊Dic₁₁	—	4	2	no	—
97	Dic₁₁⋊C₄	—	4	2	no	—
98	Dic₁₁⋊C₄	—	4	2	no	—
99	Dic₁₁⋊C₄	D₈	1	1	yes	characteristic
100	C₄×Dic₁₁	—	4	2	no	—
101	C₄×Dic₁₁	—	4	2	no	—
102	C₄×Dic₁₁	C₂×D₄	1	1	yes	characteristic
103	C₂×C₁₁⋊C₈	C₂×D₄	1	1	yes	characteristic
104	C₂×C₁₁⋊C₈	C₂×D₄	1	1	yes	characteristic
105	C₈×D₁₁	—	2	1	no	—
106	C₈×D₁₁	—	2	1	no	—
107	C₁₁×C₁₆	—	2	1	no	—
108	C₁₁×C₁₆	#41	1	2	yes	—
109	C₁₁⋊C₁₆	—	2	1	no	—
110	C₁₁⋊C₁₆	—	2	1	no	—
111	#3336	—	11	2	no	—
112	#2253	—	11	1	no	—
113	#2237	—	11	2	no	—
114	#2235	—	11	2	no	—
115	#2229	—	11	2	no	—
116	#2216	—	11	1	no	—
117	#2216	D₁₁	1	1	yes	characteristic, complemented
118	C₄×Q₃₂	—	11	1	no	—
119	D₄×C₁₆	—	11	1	no	—
120	#2158	—	11	1	no	—
121	C₂×#366	—	11	1	no	—
122	C₂³×C₁₁	C₂×D₈	1	1	yes	characteristic
123	C₂²×D₁₁	C₂×D₈	1	1	yes	characteristic
124	Q₈×C₁₁	—	4	2	no	—
125	Q₈×C₁₁	—	4	2	no	—
126	C₂×C₄×C₁₁	—	2	1	no	—
127	C₂×C₄×C₁₁	—	2	1	no	—
128	C₂×C₄×C₁₁	—	4	2	no	—
129	C₂×C₄×C₁₁	—	4	2	no	—
130	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
131	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
132	C₂²⋊D₁₁	—	2	2	no	—
133	C₂×Dic₁₁	—	4	2	no	—
134	C₂×Dic₁₁	—	4	2	no	—
135	C₂×Dic₁₁	—	8	4	no	—
136	C₂×Dic₁₁	C₂×D₈	1	1	yes	characteristic
137	C₂×Dic₁₁	C₂×D₈	1	1	yes	characteristic
138	C₂×Dic₁₁	C₂×D₈	1	1	yes	characteristic
139	C₄×D₁₁	—	2	1	no	—
140	C₄×D₁₁	—	2	1	no	—
141	C₈×C₁₁	—	2	1	no	—
142	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
143	C₈×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
144	C₁₁⋊C₈	—	2	1	no	—
145	C₁₁⋊C₈	—	2	1	no	—
146	#552	—	22	2	no	—
147	C₂×Q₃₂	C₂×D₁₁	1	1	yes	characteristic
148	C₂²×C₁₆	—	11	1	no	—
149	C₂²×C₁₆	C₂×D₁₁	1	1	yes	characteristic
150	#499	—	11	2	no	—
151	#485	—	22	2	no	—
152	#483	—	22	2	no	—
153	#479	—	22	2	no	—
154	#467	—	11	2	no	—
155	#467	C₂×D₁₁	1	2	yes	—
156	C₄×Q₁₆	—	11	2	no	—
157	C₈×D₄	—	11	1	no	—
158	#427	—	11	2	no	—
159	C₂×#107	—	11	2	no	—
160	#367	—	11	2	no	—
161	#367	—	11	2	no	—
162	#366	—	11	1	no	—
163	#366	—	11	1	no	—
164	#366	—	11	2	no	—
165	#366	C₂×D₁₁	1	1	yes	characteristic
166	C₄⋊C₁₆	—	11	1	no	—
167	#358	—	11	2	no	—
168	#358	—	11	2	no	—
169	#358	C₂×D₁₁	1	2	yes	—
170	C₂²⋊C₁₆	—	11	1	no	—
171	C₂²⋊C₁₆	—	11	1	no	—
172	C₄×C₁₆	—	11	1	no	—
173	C₂²×C₁₁	—	2	1	no	—
174	C₂²×C₁₁	—	2	1	no	—
175	C₂²×C₁₁	#508	1	2	yes	—
176	C₂²×C₁₁	C₂²×D₈	1	1	yes	characteristic
177	C₂×D₁₁	—	2	1	no	—
178	C₂×D₁₁	—	2	1	no	—
179	C₂×D₁₁	—	2	1	no	—
180	C₄×C₁₁	—	2	1	no	—
181	C₄×C₁₁	—	8	2	no	—
182	C₄×C₁₁	—	8	2	no	—
183	C₄×C₁₁	#547	1	1	yes	characteristic
184	C₄×C₁₁	#578	1	1	yes	characteristic
185	Dic₁₁	—	2	1	no	—
186	Dic₁₁	—	2	1	no	—
187	Dic₁₁	—	2	1	no	—
188	Dic₁₁	—	8	2	no	—
189	Dic₁₁	—	8	2	no	—
190	C₂×Q₁₆	C₂²×D₁₁	1	2	yes	—
191	C₂²×C₈	—	11	1	no	—
192	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
193	#126	—	44	2	no	—
194	#125	—	22	2	no	—
195	#125	—	44	2	no	—
196	#123	—	44	2	no	—
197	C₂²⋊Q₈	—	2	2	no	—
198	C₂²⋊Q₈	—	22	2	no	—
199	C₄×Q₈	—	22	2	no	—
200	C₄×D₄	—	11	1	no	—
201	#117	—	22	2	no	—
202	#117	—	44	2	no	—
203	C₂×C₄⋊C₄	—	22	2	no	—
204	Q₃₂	—	2	2	no	—
205	C₂×C₁₆	—	2	2	no	—
206	C₂×C₁₆	—	11	1	no	—
207	C₂×C₁₆	—	11	1	no	—
208	C₂×C₁₆	—	22	2	no	—
209	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
210	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
211	#107	—	11	2	no	—
212	#107	—	11	2	no	—
213	#107	—	22	2	no	—
214	#107	C₂²×D₁₁	1	2	yes	—
215	#106	—	22	2	no	—
216	#106	—	22	2	no	—
217	C₄⋊C₈	—	11	1	no	—
218	#103	—	2	2	no	—
219	#103	—	22	2	no	—
220	#103	—	22	2	no	—
221	C₂²⋊C₈	—	11	1	no	—
222	C₂²⋊C₈	—	11	1	no	—
223	C₄×C₈	—	11	1	no	—
224	C₂×C₁₁	—	2	2	no	—
225	C₂×C₁₁	#3334	1	1	yes	characteristic
226	C₂×C₁₁	C₂×#508	1	1	yes	characteristic
227	C₂×C₁₁	#3417	1	1	yes	characteristic
228	D₁₁	—	4	1	no	—
229	C₂×Q₈	—	2	2	no	—
230	C₂×D₄	—	11	1	no	—
231	C₂²×C₄	—	11	1	no	—
232	C₂²×C₄	—	44	2	no	—
233	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
234	Q₁₆	—	2	2	no	—
235	Q₁₆	—	2	2	no	—
236	C₂×C₈	—	2	1	no	—
237	C₂×C₈	—	2	1	no	—
238	C₂×C₈	—	11	1	no	—
239	C₂×C₈	—	11	1	no	—
240	C₂×C₈	—	22	1	no	—
241	C₂×C₈	—	22	1	no	—
242	C₂×C₈	D₄×D₁₁	1	1	yes	characteristic
243	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
244	C₄⋊C₄	—	2	2	no	—
245	C₄⋊C₄	—	4	2	no	—
246	C₄⋊C₄	—	11	1	no	—
247	C₄⋊C₄	—	22	2	no	—
248	C₄⋊C₄	—	22	2	no	—
249	C₄⋊C₄	—	44	2	no	—
250	C₄⋊C₄	—	44	2	no	—
251	C₄⋊C₄	—	44	2	no	—
252	C₄⋊C₄	—	44	2	no	—
253	C₄⋊C₄	—	44	2	no	—
254	C₂²⋊C₄	—	4	2	no	—
255	C₂²⋊C₄	—	11	1	no	—
256	C₂²⋊C₄	—	11	1	no	—
257	C₂²⋊C₄	—	44	2	no	—
258	C₂²⋊C₄	—	44	2	no	—
259	C₄²	—	11	1	no	—
260	C₄²	—	44	2	no	—
261	C₄²	—	44	2	no	—
262	C₁₆	—	2	1	no	—
263	C₁₆	—	22	1	no	—
264	C₁₆	—	22	1	no	—
265	C₁₆	#4341	1	2	yes	—
266	C₁₁	#33903	1	1	yes	characteristic, complemented, Sylow
267	C₂³	—	11	1	no	—
268	C₂³	D₈×D₁₁	1	1	yes	characteristic
269	Q₈	—	4	2	no	—
270	Q₈	—	4	2	no	—
271	D₄	—	22	2	no	—
272	C₂×C₄	—	2	1	no	—
273	C₂×C₄	—	2	1	no	—
274	C₂×C₄	—	4	2	no	—
275	C₂×C₄	—	4	2	no	—
276	C₂×C₄	—	11	1	no	—
277	C₂×C₄	—	11	1	no	—
278	C₂×C₄	—	11	1	no	—
279	C₂×C₄	—	22	1	no	—
280	C₂×C₄	—	22	1	no	—
281	C₂×C₄	—	44	2	no	—
282	C₂×C₄	—	44	2	no	—
283	C₂×C₄	—	88	4	no	—
284	C₂×C₄	D₈×D₁₁	1	1	yes	characteristic
285	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
286	C₈	—	2	1	no	—
287	C₈	—	22	1	no	—
288	C₈	—	22	1	no	—
289	C₈	C₂×#4341	1	1	yes	characteristic
290	C₈	#67043	1	1	yes	characteristic
291	C₂²	—	2	1	no	—
292	C₂²	—	2	1	no	—
293	C₂²	—	22	1	no	—
294	C₂²	—	22	1	no	—
295	C₂²	—	22	1	no	—
296	C₂²	#10622532	1	2	yes	—
297	C₂²	C₂×D₈×D₁₁	1	1	yes	characteristic
298	C₄	—	2	1	no	—
299	C₄	—	8	2	no	—
300	C₄	—	8	2	no	—
301	C₄	—	22	1	no	—
302	C₄	—	22	1	no	—
303	C₄	—	22	1	no	—
304	C₄	—	88	2	no	—
305	C₄	—	88	2	no	—
306	C₄	#10623142	1	1	yes	characteristic
307	C₄	#10623302	1	1	yes	characteristic
308	C₂	—	2	2	no	—
309	C₂	—	44	1	no	—
310	C₂	#13080960	1	1	yes	characteristic
311	C₂	C₂×#10622532	1	1	yes	characteristic
312	C₂	#13081766	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₈×D₁₁
commutator, cosocle	C₂×C₈×C₁₁	C₂⁴
Frattini	C₂×C₈	C₂³×D₁₁
Fitting	C₁₁×#2216	C₂
socle	C₂²×C₁₁	C₂²×D₈
prime radical	C₂×C₂²⋊D₁₁	D₈
hypercenter	#2216	D₁₁
hypocenter	C₁₁	#33903
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #2216

Complements

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

N	H ≅ G/N	type
2. #13070893	C₂	semidirect
3. #13070823	C₂	semidirect
4. #13070811	C₂	semidirect
5. #13070782	C₂	semidirect
6. #13070704	C₂	semidirect
7. Q₃₂×Dic₁₁	C₂	semidirect
9. #13070397	C₂	semidirect
10. C₂×#10622142	C₂	semidirect
11. C₁₁×#2216	C₂	semidirect
117. #2216	D₁₁	semidirect
266. C₁₁	#33903	semidirect

Maximal subgroups

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

subgroup	index
#13080987	2
#13070893	2
#13070823	2
#13070811	2
#13070782	2
#13070704	2
Q₃₂×Dic₁₁	2
C₁₆×C₂²⋊D₁₁	2
#13070397	2
C₂×#10622142	2
C₁₁×#2216	2
#33903	11