Subgroups — #14653152

Order 2816.

502 conjugacy classes of subgroups.

The subgroup lattice has 266 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13068780	C₂	1	1	yes	maximal, characteristic, complemented
2	#13067176	C₂	1	4	yes	maximal, complemented
3	#13066899	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#3147	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₁×#135	—	2	1	no	—
6	C₂×C₁₁×#135	—	2	1	no	—
7	C₁₁×#532	C₂²	1	2	yes	—
8	C₁₁×#495	—	2	1	no	—
9	C₁₁×#495	—	2	1	no	—
10	C₁₁×#494	C₄	1	1	yes	characteristic, complemented
11	C₁₁×#493	C₄	1	1	yes	characteristic, complemented
12	C₁₁×#492	C₄	1	2	yes	complemented
13	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
14	C₂×#66882	—	2	1	no	—
15	C₂×#66881	—	2	1	no	—
16	#10622549	C₂²	1	2	yes	—
17	#10622538	C₂²	1	2	yes	—
18	#10622175	—	2	8	no	—
19	#10622093	—	2	1	no	—
20	C₈×C₁₁⋊C₈	—	2	1	no	—
21	C₂×C₁₁×#41	—	2	2	no	—
22	C₁₁×#135	—	4	2	no	—
23	C₁₁×#135	—	4	2	no	—
24	C₁₁×#135	—	4	2	no	—
25	C₁₁×#135	—	4	2	no	—
26	C₂×C₁₁×Q₁₆	—	2	1	no	—
27	C₂×C₁₁×Q₁₆	—	2	1	no	—
28	C₂×C₁₁×SD₁₆	—	2	2	no	—
29	C₂×C₁₁×SD₁₆	—	2	2	no	—
30	C₂×C₁₁×D₈	—	2	1	no	—
31	C₂×C₁₁×D₈	—	2	1	no	—
32	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
33	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
34	C₁₁×C₄⋊Q₈	C₂×C₄	1	2	yes	—
35	C₁₁×#127	C₂×C₄	1	2	yes	—
36	C₁₁×#124	—	2	2	no	—
37	C₁₁×#121	—	2	4	no	—
38	C₄×D₄×C₁₁	—	2	4	no	—
39	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
40	C₂×C₄⋊Dic₁₁	—	2	2	no	—
41	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
42	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
43	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
44	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
45	C₁₁⋊#95	—	2	4	no	—
46	C₂²⋊(C₁₁⋊C₈)	D₄	1	4	yes	—
47	#66882	—	4	2	no	—
48	#66881	—	4	2	no	—
49	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
50	C₄×C₁₁⋊C₈	—	2	2	no	—
51	#9756	—	11	1	no	maximal, Sylow
52	C₁₁×#41	—	4	2	no	—
53	C₁₁×#41	—	4	2	no	—
54	C₁₁×#41	—	4	2	no	—
55	C₁₁×#41	—	4	2	no	—
56	C₂×Q₈×C₁₁	—	2	2	no	—
57	C₂×D₄×C₁₁	—	2	2	no	—
58	C₂×D₄×C₁₁	—	2	4	no	—
59	C₂×D₄×C₁₁	—	4	2	no	—
60	C₂²×C₄×C₁₁	—	4	2	no	—
61	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
62	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
63	C₂²×Dic₁₁	—	4	2	no	—
64	C₁₁×Q₁₆	—	4	2	no	—
65	C₁₁×Q₁₆	—	4	2	no	—
66	C₁₁×SD₁₆	—	4	4	no	—
67	C₁₁×SD₁₆	—	4	4	no	—
68	C₁₁×D₈	—	4	2	no	—
69	C₁₁×D₈	—	4	2	no	—
70	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
71	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
72	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
73	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
74	C₂×C₈×C₁₁	D₈	1	2	yes	—
75	C₂×C₈×C₁₁	D₈	1	2	yes	—
76	C₂×C₈×C₁₁	SD₁₆	1	2	yes	—
77	C₂×C₈×C₁₁	SD₁₆	1	2	yes	—
78	C₁₁×C₄⋊C₄	—	2	4	no	—
79	C₁₁×C₂²⋊C₄	—	4	4	no	—
80	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
81	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
82	C₄²×C₁₁	#41	1	2	yes	—
83	C₄⋊Dic₁₁	—	4	2	no	—
84	C₄⋊Dic₁₁	—	4	2	no	—
85	C₂×C₁₁⋊C₈	—	2	4	no	—
86	#3147	D₁₁	1	1	yes	characteristic
87	#1846	—	11	1	no	—
88	#1517	—	11	4	no	—
89	#1450	—	11	1	no	—
90	C₂³×C₁₁	—	4	2	no	—
91	C₂³×C₁₁	#127	1	1	yes	characteristic
92	Q₈×C₁₁	—	4	2	no	—
93	Q₈×C₁₁	—	4	2	no	—
94	D₄×C₁₁	—	4	2	no	—
95	D₄×C₁₁	—	4	2	no	—
96	D₄×C₁₁	—	8	4	no	—
97	D₄×C₁₁	—	8	2	no	—
98	D₄×C₁₁	—	8	2	no	—
99	C₂×C₄×C₁₁	—	4	2	no	—
100	C₂×C₄×C₁₁	—	4	2	no	—
101	C₂×C₄×C₁₁	—	8	2	no	—
102	C₂×C₄×C₁₁	—	8	2	no	—
103	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
104	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
105	C₂×C₄×C₁₁	#121	1	2	yes	—
106	C₂×C₄×C₁₁	#124	1	1	yes	characteristic
107	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
108	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
109	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
110	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
111	C₂×Dic₁₁	—	8	4	no	—
112	C₂×Dic₁₁	—	8	2	no	—
113	C₈×C₁₁	#102	1	2	yes	—
114	C₈×C₁₁	#102	1	2	yes	—
115	C₈×C₁₁	#102	1	2	yes	—
116	C₈×C₁₁	#102	1	2	yes	—
117	C₁₁⋊C₈	—	4	4	no	—
118	C₂×#135	—	2	1	no	—
119	C₂×#135	—	2	1	no	—
120	#532	C₂×D₁₁	1	2	yes	—
121	#495	—	2	1	no	—
122	#495	—	2	1	no	—
123	#494	Dic₁₁	1	1	yes	characteristic, complemented
124	#493	Dic₁₁	1	1	yes	characteristic, complemented
125	#492	Dic₁₁	1	2	yes	complemented
126	#431	—	11	2	no	—
127	C₂×#107	—	22	1	no	—
128	C₂×#106	—	22	1	no	—
129	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
130	#382	—	11	2	no	—
131	#327	—	22	8	no	—
132	#322	—	22	1	no	—
133	C₈²	—	22	1	no	—
134	C₂²×C₁₁	—	2	2	no	—
135	C₂²×C₁₁	—	8	2	no	—
136	C₂²×C₁₁	—	8	4	no	—
137	C₂²×C₁₁	#390	1	1	yes	characteristic
138	C₂²×C₁₁	#492	1	1	yes	characteristic
139	C₂²×C₁₁	#493	1	1	yes	characteristic
140	C₄×C₁₁	—	2	2	no	—
141	C₄×C₁₁	—	2	2	no	—
142	C₄×C₁₁	—	8	2	no	—
143	C₄×C₁₁	C₂×#102	1	1	yes	characteristic
144	C₄×C₁₁	C₂×#102	1	1	yes	characteristic
145	C₄×C₁₁	#486	1	1	yes	characteristic
146	C₄×C₁₁	#486	1	1	yes	characteristic
147	Dic₁₁	—	16	2	no	—
148	C₂×#41	—	2	2	no	—
149	#135	—	4	2	no	—
150	#135	—	4	2	no	—
151	#135	—	4	2	no	—
152	#135	—	4	2	no	—
153	C₂×Q₁₆	—	2	1	no	—
154	C₂×Q₁₆	—	2	1	no	—
155	C₂×SD₁₆	—	2	2	no	—
156	C₂×SD₁₆	—	2	2	no	—
157	C₂×D₈	—	2	1	no	—
158	C₂×D₈	—	2	1	no	—
159	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
160	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
161	C₄⋊Q₈	C₂×Dic₁₁	1	2	yes	—
162	#127	C₂×Dic₁₁	1	2	yes	—
163	#124	—	2	2	no	—
164	#121	—	2	4	no	—
165	C₄×D₄	—	2	4	no	—
166	C₂×C₄⋊C₄	—	22	2	no	—
167	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
168	#107	—	44	2	no	—
169	#106	—	44	2	no	—
170	C₄⋊C₈	—	22	2	no	—
171	C₂²⋊C₈	—	11	4	no	—
172	C₄×C₈	—	22	2	no	—
173	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
174	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
175	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
176	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
177	#95	—	22	4	no	—
178	C₂×C₁₁	—	2	1	no	—
179	C₂×C₁₁	—	2	1	no	—
180	C₂×C₁₁	—	16	2	no	—
181	C₂×C₁₁	#1957	1	1	yes	characteristic
182	C₂×C₁₁	#1976	1	2	yes	—
183	#41	—	4	2	no	—
184	#41	—	4	2	no	—
185	#41	—	4	2	no	—
186	#41	—	4	2	no	—
187	C₂×Q₈	—	2	2	no	—
188	C₂×D₄	—	2	4	no	—
189	C₂×D₄	—	2	2	no	—
190	C₂×D₄	—	4	2	no	—
191	C₂²×C₄	—	4	2	no	—
192	C₂²×C₄	—	44	2	no	—
193	C₂²×C₄	D₄×D₁₁	1	2	yes	—
194	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
195	Q₁₆	—	4	2	no	—
196	Q₁₆	—	4	2	no	—
197	SD₁₆	—	4	4	no	—
198	SD₁₆	—	4	4	no	—
199	D₈	—	4	2	no	—
200	D₈	—	4	2	no	—
201	C₂×C₈	—	22	4	no	—
202	C₂×C₈	#4323	1	2	yes	—
203	C₂×C₈	#4323	1	2	yes	—
204	C₂×C₈	#4324	1	2	yes	—
205	C₂×C₈	#4324	1	2	yes	—
206	C₂×C₈	C₂²⋊Dic₁₁	1	1	yes	characteristic
207	C₂×C₈	C₂²⋊Dic₁₁	1	1	yes	characteristic
208	C₂×C₈	C₂²⋊Dic₁₁	1	1	yes	characteristic
209	C₂×C₈	C₂²⋊Dic₁₁	1	1	yes	characteristic
210	C₄⋊C₄	—	2	4	no	—
211	C₄⋊C₄	—	44	2	no	—
212	C₄⋊C₄	—	44	2	no	—
213	C₂²⋊C₄	—	4	4	no	—
214	C₄²	#4341	1	2	yes	—
215	C₄²	C₂²×Dic₁₁	1	1	yes	characteristic
216	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
217	C₁₁	#9756	1	1	yes	characteristic, complemented, Sylow
218	C₂³	—	4	2	no	—
219	C₂³	#66993	1	1	yes	characteristic
220	Q₈	—	4	2	no	—
221	Q₈	—	4	2	no	—
222	D₄	—	4	2	no	—
223	D₄	—	4	2	no	—
224	D₄	—	8	4	no	—
225	D₄	—	8	2	no	—
226	D₄	—	8	2	no	—
227	C₂×C₄	—	4	2	no	—
228	C₂×C₄	—	4	2	no	—
229	C₂×C₄	—	8	2	no	—
230	C₂×C₄	—	8	2	no	—
231	C₂×C₄	—	88	4	no	—
232	C₂×C₄	—	88	2	no	—
233	C₂×C₄	C₂×#4323	1	1	yes	characteristic
234	C₂×C₄	C₂×#4323	1	1	yes	characteristic
235	C₂×C₄	C₂×#4324	1	1	yes	characteristic
236	C₂×C₄	C₂×#4324	1	1	yes	characteristic
237	C₂×C₄	D₄×Dic₁₁	1	2	yes	—
238	C₂×C₄	#66989	1	1	yes	characteristic
239	C₂×C₄	#66991	1	2	yes	—
240	C₂×C₄	C₂×C₂²⋊Dic₁₁	1	1	yes	characteristic
241	C₈	—	44	4	no	—
242	C₈	#66896	1	2	yes	—
243	C₈	#66896	1	2	yes	—
244	C₈	#66896	1	2	yes	—
245	C₈	#66896	1	2	yes	—
246	C₂²	—	2	2	no	—
247	C₂²	—	8	2	no	—
248	C₂²	—	8	4	no	—
249	C₂²	#10622686	1	1	yes	characteristic
250	C₂²	#10622689	1	1	yes	characteristic
251	C₂²	#10622834	1	1	yes	characteristic
252	C₄	—	2	2	no	—
253	C₄	—	2	2	no	—
254	C₄	—	8	2	no	—
255	C₄	—	176	2	no	—
256	C₄	#10622683	1	1	yes	characteristic
257	C₄	#10622683	1	1	yes	characteristic
258	C₄	C₂×#66896	1	1	yes	characteristic
259	C₄	C₂×#66896	1	1	yes	characteristic
260	C₂	—	2	1	no	—
261	C₂	—	2	1	no	—
262	C₂	—	16	2	no	—
263	C₂	#13069423	1	1	yes	characteristic
264	C₂	#13069515	1	2	yes	—

	subgroup	G/H
center	C₂²	#10622834
commutator	C₄²×C₁₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting, prime radical	C₁₁×#3147	C₂
socle	C₂²×C₁₁	#390
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	#3147	D₁₁
hypocenter	C₁₁	#9756
LCS	G ▷ C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3147

Complements

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

N	H ≅ G/N	type
1. #13068780	C₂	semidirect
2. #13067176	C₂	semidirect
3. #13066899	C₂	semidirect
10. C₁₁×#494	C₄	semidirect
11. C₁₁×#493	C₄	semidirect
12. C₁₁×#492	C₄	semidirect
123. #494	Dic₁₁	semidirect
124. #493	Dic₁₁	semidirect
125. #492	Dic₁₁	semidirect
217. C₁₁	#9756	semidirect

Maximal subgroups

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

subgroup	index
#13068780	2
#13067176	2
#13066899	2
C₁₁×#3147	2
#9756	11