Subgroups — #14641432

Order 2816.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13070898	C₂	1	1	yes	maximal, characteristic
2	#13066692	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1422	C₂	1	1	yes	maximal, characteristic
4	#10622295	—	2	1	no	—
5	C₁₁×M₆₄	—	2	1	no	—
6	C₄×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
7	#10622143	—	2	1	no	—
8	#10622143	C₄	1	2	yes	—
9	#10622101	—	2	1	no	—
10	#66922	—	4	1	no	—
11	C₂×C₁₁×C₁₆	C₂×C₄	1	1	yes	characteristic
12	C₂×C₁₁×C₁₆	D₄	1	1	yes	characteristic
13	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
14	#66882	—	2	2	no	—
15	#66882	—	4	1	no	—
16	#66876	—	4	1	no	—
17	C₁₁×C₃₂	—	4	1	no	—
18	#7453	—	11	1	no	maximal, Sylow
19	C₂×Dic₂₂	—	8	1	no	—
20	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
21	C₂×C₈×C₁₁	D₈	1	1	yes	characteristic
22	C₄²×C₁₁	SD₁₆	1	1	yes	characteristic
23	C₄⋊Dic₁₁	—	4	2	no	—
24	C₄⋊Dic₁₁	—	8	1	no	—
25	C₁₁×C₁₆	—	2	1	no	—
26	C₁₁×C₁₆	SD₁₆	1	1	yes	characteristic
27	C₁₁×C₁₆	Q₁₆	1	1	yes	characteristic
28	C₁₁⋊C₁₆	—	8	1	no	—
29	#2254	—	11	1	no	—
30	#1422	D₁₁	1	1	yes	characteristic
31	#1373	—	11	1	no	—
32	C₂×C₄×C₁₁	—	2	1	no	—
33	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
34	C₂×Dic₁₁	—	8	2	no	—
35	Dic₂₂	—	16	2	no	—
36	C₈×C₁₁	#101	1	1	yes	characteristic
37	C₈×C₁₁	#103	1	1	yes	characteristic
38	C₈×C₁₁	SD₃₂	1	1	yes	characteristic
39	C₈×C₁₁	Q₃₂	1	1	yes	characteristic
40	#500	—	22	1	no	—
41	M₆₄	—	2	1	no	—
42	#367	—	11	2	no	—
43	#367	—	22	1	no	—
44	#364	—	22	1	no	—
45	C₄×C₁₆	C₂×D₁₁	1	1	yes	characteristic
46	C₂²×C₁₁	#361	1	1	yes	characteristic
47	C₄×C₁₁	—	2	2	no	—
48	C₄×C₁₁	#332	1	1	yes	characteristic
49	C₄×C₁₁	#358	1	1	yes	characteristic
50	Dic₁₁	—	16	2	no	—
51	C₄⋊Q₈	—	44	1	no	—
52	M₃₂	—	44	1	no	—
53	C₂×C₁₆	C₄×D₁₁	1	1	yes	characteristic
54	C₂×C₁₆	C₂²⋊D₁₁	1	1	yes	characteristic
55	#107	—	22	2	no	—
56	#107	—	44	1	no	—
57	C₄×C₈	D₄₄	1	1	yes	characteristic
58	C₃₂	—	4	1	no	—
59	C₂×C₁₁	—	2	1	no	—
60	C₂×C₁₁	#1365	1	1	yes	characteristic
61	C₂×Q₈	—	88	1	no	—
62	C₂×C₈	D₈₈	1	1	yes	characteristic
63	C₂×C₈	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
64	C₄⋊C₄	—	44	2	no	—
65	C₄⋊C₄	—	88	1	no	—
66	C₄²	#4314	1	1	yes	characteristic
67	C₁₆	—	2	1	no	—
68	C₁₆	—	88	1	no	—
69	C₁₆	#4324	1	1	yes	characteristic
70	C₁₆	#4326	1	1	yes	characteristic
71	C₁₁	#7453	1	1	yes	characteristic, complemented, Sylow
72	Q₈	—	176	2	no	—
73	C₂×C₄	—	2	1	no	—
74	C₂×C₄	—	88	2	no	—
75	C₂×C₄	#66885	1	1	yes	characteristic
76	C₈	#66864	1	1	yes	characteristic
77	C₈	Dic₈₈	1	1	yes	characteristic
78	C₈	#66874	1	1	yes	characteristic
79	C₈	#66888	1	1	yes	characteristic
80	C₂²	#10622154	1	1	yes	characteristic
81	C₄	—	2	2	no	—
82	C₄	—	176	2	no	—
83	C₄	#10622124	1	1	yes	characteristic
84	C₄	#10622141	1	1	yes	characteristic
85	C₂	—	2	1	no	—
86	C₂	#13066673	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#13066673
commutator	C₂×C₁₁×C₁₆	C₂×C₄
Frattini	C₄×C₁₆	C₂×D₁₁
Fitting	C₁₁×#1422	C₂
socle	C₂×C₁₁	#1365
prime radical	C₂²×C₁₁	#361
cosocle	C₄×C₁₁×C₁₆	C₂²
hypercenter	#1422	D₁₁
hypocenter	C₁₁	#7453
LCS	G ▷ C₂×C₁₁×C₁₆ ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #1422

Complements

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

N	H ≅ G/N	type
71. C₁₁	#7453	semidirect

Maximal subgroups

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

subgroup	index
#13070898	2
#13066692	2
C₁₁×#1422	2
#7453	11