Subgroups — #14767652

Order 2816.

846 conjugacy classes of subgroups.

The subgroup lattice has 286 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13077328	C₂	1	2	yes	maximal, complemented
2	#13069445	C₂	1	2	yes	maximal, complemented
3	#13068945	C₂	1	8	yes	maximal, complemented
4	#13068754	C₂	1	1	yes	maximal, characteristic, complemented
5	#13068361	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#3147	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₁×#135	C₂²	1	4	yes	—
8	C₁₁×#532	C₂²	1	2	yes	—
9	C₂×#67001	C₂²	1	4	yes	—
10	C₁₁×#495	C₄	1	4	yes	complemented
11	C₁₁×#494	C₄	1	1	yes	characteristic, complemented
12	C₁₁×#493	C₄	1	1	yes	characteristic, complemented
13	C₁₁×#492	C₄	1	2	yes	complemented
14	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
15	C₂×#66901	C₂²	1	8	yes	—
16	#10622847	C₂²	1	4	yes	—
17	#10622625	—	2	2	no	—
18	#10622625	—	2	2	no	—
19	D₄×C₁₁⋊C₈	—	2	2	no	—
20	D₄×C₁₁⋊C₈	—	2	2	no	—
21	C₄²×Dic₁₁	C₂²	1	1	yes	characteristic
22	#10622537	C₂²	1	2	yes	—
23	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
24	#10622190	C₂²	1	4	yes	—
25	#10622188	C₂²	1	4	yes	—
26	C₂×C₁₁×#41	C₂³	1	4	yes	—
27	C₁₁×#135	—	4	8	no	—
28	C₂×C₁₁×Q₁₆	C₂×C₄	1	4	yes	—
29	C₂×C₁₁×SD₁₆	C₂×C₄	1	8	yes	—
30	C₂×C₁₁×D₈	C₂×C₄	1	4	yes	—
31	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
32	C₁₁×C₄⋊Q₈	C₂×C₄	1	2	yes	—
33	C₁₁×#127	C₂×C₄	1	2	yes	—
34	C₁₁×#124	C₂×C₄	1	4	yes	—
35	C₁₁×#121	—	2	2	no	—
36	C₁₁×#121	—	2	2	no	—
37	C₄×D₄×C₁₁	—	2	2	no	—
38	C₄×D₄×C₁₁	—	2	2	no	—
39	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
40	#67001	—	4	8	no	—
41	C₂×C₄×Dic₁₁	—	2	1	no	—
42	C₂×C₄×Dic₁₁	—	2	1	no	—
43	C₂×C₄×Dic₁₁	C₂³	1	2	yes	—
44	C₂×#4318	—	2	4	no	—
45	C₂×#4318	C₂³	1	4	yes	—
46	C₂²×C₁₁⋊C₈	—	2	4	no	—
47	C₂²×C₁₁⋊C₈	C₂³	1	2	yes	—
48	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
49	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
50	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
51	#66901	—	4	8	no	—
52	C₂²⋊(C₁₁⋊C₈)	—	2	4	no	—
53	C₂²⋊(C₁₁⋊C₈)	—	2	4	no	—
54	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
55	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
56	C₄×C₁₁⋊C₈	D₄	1	1	yes	characteristic
57	C₄×C₁₁⋊C₈	D₄	1	2	yes	—
58	C₄×C₁₁⋊C₈	D₄	1	1	yes	characteristic
59	#22280	—	11	1	no	maximal, Sylow
60	C₁₁×#41	—	2	8	no	—
61	C₁₁×#41	—	2	8	no	—
62	C₂×Q₈×C₁₁	C₂²×C₄	1	4	yes	—
63	C₂×D₄×C₁₁	—	2	4	no	—
64	C₂×D₄×C₁₁	—	2	2	no	—
65	C₂×D₄×C₁₁	—	2	2	no	—
66	C₂×D₄×C₁₁	C₂²×C₄	1	4	yes	—
67	C₂²×C₄×C₁₁	—	2	4	no	—
68	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
69	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
70	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
71	C₂²×Dic₁₁	—	2	2	no	—
72	C₁₁×Q₁₆	—	4	4	no	—
73	C₁₁×SD₁₆	—	4	8	no	—
74	C₁₁×D₈	—	4	4	no	—
75	C₂×C₈×C₁₁	—	2	4	no	—
76	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
77	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
78	C₁₁×C₄⋊C₄	—	2	2	no	—
79	C₁₁×C₄⋊C₄	—	2	2	no	—
80	C₁₁×C₂²⋊C₄	—	2	4	no	—
81	C₁₁×C₂²⋊C₄	—	2	4	no	—
82	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
83	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
84	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
85	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
86	C₄×Dic₁₁	—	2	4	no	—
87	C₄×Dic₁₁	—	2	4	no	—
88	C₄×Dic₁₁	—	4	2	no	—
89	#4318	—	2	8	no	—
90	#4318	—	4	8	no	—
91	C₂×C₁₁⋊C₈	—	2	4	no	—
92	C₂×C₁₁⋊C₈	—	2	4	no	—
93	C₂×C₁₁⋊C₈	—	4	8	no	—
94	C₂×C₁₁⋊C₈	C₂×D₄	1	2	yes	—
95	C₂×C₁₁⋊C₈	C₂×D₄	1	2	yes	—
96	#3147	D₁₁	1	1	yes	characteristic
97	#2931	—	11	2	no	—
98	#1962	—	11	2	no	—
99	#1876	—	11	8	no	—
100	#1837	—	11	1	no	—
101	#1744	—	11	1	no	—
102	C₂³×C₁₁	—	2	4	no	—
103	C₂³×C₁₁	C₂×#41	1	1	yes	characteristic
104	Q₈×C₁₁	—	2	8	no	—
105	D₄×C₁₁	—	2	8	no	—
106	D₄×C₁₁	—	4	8	no	—
107	D₄×C₁₁	—	4	4	no	—
108	D₄×C₁₁	—	4	4	no	—
109	C₂×C₄×C₁₁	—	2	2	no	—
110	C₂×C₄×C₁₁	—	2	2	no	—
111	C₂×C₄×C₁₁	—	2	4	no	—
112	C₂×C₄×C₁₁	—	4	4	no	—
113	C₂×C₄×C₁₁	—	4	4	no	—
114	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
115	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
116	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
117	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
118	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
119	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
120	C₂×C₄×C₁₁	H(5,𝔽₂)	1	4	yes	—
121	C₂×Dic₁₁	—	2	4	no	—
122	C₂×Dic₁₁	—	4	2	no	—
123	C₂×Dic₁₁	—	4	2	no	—
124	C₈×C₁₁	—	2	2	no	—
125	C₈×C₁₁	—	2	2	no	—
126	C₁₁⋊C₈	—	2	2	no	—
127	C₁₁⋊C₈	—	2	2	no	—
128	C₁₁⋊C₈	—	4	4	no	—
129	C₂×#135	C₂×D₁₁	1	4	yes	—
130	C₂×#131	—	11	4	no	—
131	#532	C₂×D₁₁	1	2	yes	—
132	#495	Dic₁₁	1	4	yes	complemented
133	#494	Dic₁₁	1	1	yes	characteristic, complemented
134	#493	Dic₁₁	1	1	yes	characteristic, complemented
135	#492	Dic₁₁	1	2	yes	complemented
136	#436	—	22	2	no	—
137	#436	—	22	2	no	—
138	C₈×D₄	—	22	2	no	—
139	C₈×D₄	—	22	2	no	—
140	#423	—	11	2	no	—
141	C₂×#104	—	11	8	no	—
142	#408	—	11	4	no	—
143	C₂×C₄×C₈	—	11	1	no	—
144	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
145	C₄³	—	11	1	no	—
146	#341	—	11	4	no	—
147	#336	—	11	4	no	—
148	C₂²×C₁₁	—	2	1	no	—
149	C₂²×C₁₁	—	2	1	no	—
150	C₂²×C₁₁	—	4	4	no	—
151	C₂²×C₁₁	—	4	4	no	—
152	C₂²×C₁₁	—	4	4	no	—
153	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
154	C₂²×C₁₁	#540	1	2	yes	—
155	C₄×C₁₁	—	2	1	no	—
156	C₄×C₁₁	—	2	1	no	—
157	C₄×C₁₁	—	4	4	no	—
158	C₄×C₁₁	#443	1	2	yes	—
159	C₄×C₁₁	#444	1	2	yes	—
160	C₄×C₁₁	#518	1	2	yes	—
161	C₄×C₁₁	#535	1	2	yes	—
162	Dic₁₁	—	4	4	no	—
163	C₂×#41	C₂²×D₁₁	1	4	yes	—
164	#135	—	4	8	no	—
165	C₂×Q₁₆	C₂×Dic₁₁	1	4	yes	—
166	C₂×SD₁₆	C₂×Dic₁₁	1	8	yes	—
167	C₂×D₈	C₂×Dic₁₁	1	4	yes	—
168	#131	—	44	8	no	—
169	C₂×M₁₆	—	11	4	no	—
170	C₂×M₁₆	—	22	4	no	—
171	C₂²×C₈	—	11	2	no	—
172	C₂²×C₈	—	22	4	no	—
173	C₂²×C₈	C₂²×D₁₁	1	2	yes	—
174	C₄⋊Q₈	C₂×Dic₁₁	1	2	yes	—
175	#127	C₂×Dic₁₁	1	2	yes	—
176	#124	C₂×Dic₁₁	1	4	yes	—
177	#121	—	2	2	no	—
178	#121	—	2	2	no	—
179	C₄×D₄	—	2	2	no	—
180	C₄×D₄	—	2	2	no	—
181	C₂×C₄²	—	11	2	no	—
182	C₂×C₄²	—	22	1	no	—
183	C₂×C₄²	—	22	1	no	—
184	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
185	C₄⋊C₈	—	22	2	no	—
186	C₄⋊C₈	—	22	2	no	—
187	#104	—	44	8	no	—
188	C₂²⋊C₈	—	22	4	no	—
189	C₂²⋊C₈	—	22	4	no	—
190	C₄×C₈	—	11	1	no	—
191	C₄×C₈	—	11	2	no	—
192	C₄×C₈	—	11	1	no	—
193	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
194	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
195	C₄×C₈	C₂×Dic₁₁	1	2	yes	—
196	C₂×C₁₁	—	2	2	no	—
197	C₂×C₁₁	—	8	4	no	—
198	C₂×C₁₁	#2328	1	1	yes	characteristic
199	C₂×C₁₁	C₂×#443	1	1	yes	characteristic
200	C₂×C₁₁	C₂×#444	1	1	yes	characteristic
201	#41	—	2	8	no	—
202	#41	—	2	8	no	—
203	C₂×Q₈	C₂²×Dic₁₁	1	4	yes	—
204	C₂×D₄	—	2	4	no	—
205	C₂×D₄	—	2	2	no	—
206	C₂×D₄	—	2	2	no	—
207	C₂×D₄	C₂²×Dic₁₁	1	4	yes	—
208	C₂²×C₄	—	2	4	no	—
209	C₂²×C₄	—	22	2	no	—
210	C₂²×C₄	#4341	1	1	yes	characteristic
211	C₂²×C₄	#4341	1	1	yes	characteristic
212	C₂²×C₄	C₂³×D₁₁	1	1	yes	characteristic
213	Q₁₆	—	4	4	no	—
214	SD₁₆	—	4	8	no	—
215	D₈	—	4	4	no	—
216	M₁₆	—	22	8	no	—
217	M₁₆	—	44	8	no	—
218	C₂×C₈	—	2	4	no	—
219	C₂×C₈	—	11	2	no	—
220	C₂×C₈	—	11	2	no	—
221	C₂×C₈	—	22	4	no	—
222	C₂×C₈	—	22	4	no	—
223	C₂×C₈	—	44	8	no	—
224	C₂×C₈	C₂²×Dic₁₁	1	2	yes	—
225	C₂×C₈	C₂²×Dic₁₁	1	2	yes	—
226	C₄⋊C₄	—	2	2	no	—
227	C₄⋊C₄	—	2	2	no	—
228	C₂²⋊C₄	—	2	4	no	—
229	C₂²⋊C₄	—	2	4	no	—
230	C₄²	—	22	4	no	—
231	C₄²	—	22	4	no	—
232	C₄²	—	44	2	no	—
233	C₄²	D₄×D₁₁	1	1	yes	characteristic
234	C₄²	D₄×D₁₁	1	1	yes	characteristic
235	C₄²	C₂²×Dic₁₁	1	1	yes	characteristic
236	C₄²	C₂²×Dic₁₁	1	1	yes	characteristic
237	C₁₁	#22280	1	1	yes	characteristic, complemented, Sylow
238	C₂³	—	2	4	no	—
239	C₂³	C₂×#4341	1	1	yes	characteristic
240	Q₈	—	2	8	no	—
241	D₄	—	2	8	no	—
242	D₄	—	4	8	no	—
243	D₄	—	4	4	no	—
244	D₄	—	4	4	no	—
245	C₂×C₄	—	2	2	no	—
246	C₂×C₄	—	2	2	no	—
247	C₂×C₄	—	2	4	no	—
248	C₂×C₄	—	4	4	no	—
249	C₂×C₄	—	4	4	no	—
250	C₂×C₄	—	22	4	no	—
251	C₂×C₄	—	44	2	no	—
252	C₂×C₄	—	44	2	no	—
253	C₂×C₄	D₄×Dic₁₁	1	1	yes	characteristic
254	C₂×C₄	D₄×Dic₁₁	1	1	yes	characteristic
255	C₂×C₄	D₄×Dic₁₁	1	1	yes	characteristic
256	C₂×C₄	D₄×Dic₁₁	1	1	yes	characteristic
257	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
258	C₂×C₄	#67037	1	4	yes	—
259	C₂×C₄	C₂³×Dic₁₁	1	1	yes	characteristic
260	C₈	—	2	2	no	—
261	C₈	—	2	2	no	—
262	C₈	—	22	2	no	—
263	C₈	—	22	2	no	—
264	C₈	—	44	4	no	—
265	C₂²	—	2	1	no	—
266	C₂²	—	2	1	no	—
267	C₂²	—	4	4	no	—
268	C₂²	—	4	4	no	—
269	C₂²	—	4	4	no	—
270	C₂²	#10623250	1	2	yes	—
271	C₂²	C₂×D₄×Dic₁₁	1	1	yes	characteristic
272	C₄	—	2	1	no	—
273	C₄	—	2	1	no	—
274	C₄	—	4	4	no	—
275	C₄	—	44	4	no	—
276	C₄	#10622809	1	2	yes	—
277	C₄	#10622810	1	2	yes	—
278	C₄	#10623246	1	2	yes	—
279	C₄	#10623329	1	2	yes	—
280	C₂	—	2	2	no	—
281	C₂	—	8	4	no	—
282	C₂	#13071342	1	1	yes	characteristic
283	C₂	C₂×#10622809	1	1	yes	characteristic
284	C₂	C₂×#10622810	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₁
commutator	C₂×C₄×C₁₁	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₁
Fitting, prime radical	C₁₁×#3147	C₂
socle	C₂²×C₁₁	C₂×C₄×D₄
cosocle	C₂²×C₄×C₁₁	C₂⁴
hypercenter	#3147	D₁₁
hypocenter	C₁₁	#22280
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3147

Complements

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

N	H ≅ G/N	type
1. #13077328	C₂	semidirect
2. #13069445	C₂	semidirect
3. #13068945	C₂	semidirect
4. #13068754	C₂	semidirect
5. #13068361	C₂	semidirect
10. C₁₁×#495	C₄	semidirect
11. C₁₁×#494	C₄	semidirect
12. C₁₁×#493	C₄	semidirect
13. C₁₁×#492	C₄	semidirect
132. #495	Dic₁₁	semidirect
133. #494	Dic₁₁	semidirect
134. #493	Dic₁₁	semidirect
135. #492	Dic₁₁	semidirect
237. C₁₁	#22280	semidirect

Maximal subgroups

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

subgroup	index
#13077328	2
#13069445	2
#13068945	2
#13068754	2
#13068361	2
C₁₁×#3147	2
#22280	11