Subgroups — #14641439

Order 2816.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊(C₁₁⋊C₃₂)	C₂	1	2	yes	maximal
2	C₈×C₁₁×C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₁×C₁₆	C₄	1	1	yes	characteristic
4	C₄×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
5	C₈²×C₁₁	C₄	1	1	yes	characteristic
6	C₂×C₁₁⋊C₃₂	—	2	2	no	—
7	C₂×C₁₁×C₁₆	—	2	1	no	—
8	C₂×C₁₁×C₁₆	D₄	1	1	yes	characteristic
9	C₂×C₁₁×C₁₆	Q₈	1	1	yes	characteristic
10	C₄×C₈×C₁₁	C₈	1	1	yes	characteristic
11	C₄×C₈×C₁₁	C₈	1	1	yes	characteristic
12	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
13	C₁₁⋊C₃₂	—	4	2	no	—
14	#7455	—	11	1	no	maximal, Sylow
15	C₂×C₈×C₁₁	—	2	1	no	—
16	C₂×C₈×C₁₁	C₁₆	1	1	yes	characteristic
17	C₂×C₈×C₁₁	C₁₆	1	1	yes	characteristic
18	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
19	C₂×C₈×C₁₁	M₁₆	1	1	yes	characteristic
20	C₄²×C₁₁	C₂×C₈	1	1	yes	characteristic
21	C₁₁×C₁₆	—	2	2	no	—
22	C₁₁×C₁₆	—	2	1	no	—
23	C₁₁×C₁₆	SD₁₆	1	2	yes	—
24	C₄⋊C₃₂	—	11	2	no	—
25	C₈×C₁₆	D₁₁	1	1	yes	characteristic
26	C₂×C₄×C₁₁	C₄⋊C₈	1	1	yes	characteristic
27	C₂×C₄×C₁₁	C₂×C₁₆	1	1	yes	characteristic
28	C₂×C₄×C₁₁	M₃₂	1	1	yes	characteristic
29	C₈×C₁₁	—	2	2	no	—
30	C₈×C₁₁	—	2	1	no	—
31	C₈×C₁₁	—	2	1	no	—
32	C₈×C₁₁	C₃₂	1	2	yes	complemented
33	C₈×C₁₁	#106	1	1	yes	characteristic
34	C₈×C₁₁	#108	1	1	yes	characteristic
35	C₂×C₃₂	—	22	2	no	—
36	C₄×C₁₆	Dic₁₁	1	1	yes	characteristic
37	C₄×C₁₆	C₂×D₁₁	1	1	yes	characteristic
38	C₈²	Dic₁₁	1	1	yes	characteristic
39	C₂²×C₁₁	C₄⋊C₁₆	1	1	yes	characteristic
40	C₄×C₁₁	—	2	1	no	—
41	C₄×C₁₁	#334	1	1	yes	characteristic
42	C₄×C₁₁	#364	1	1	yes	characteristic
43	C₄×C₁₁	C₂×C₃₂	1	1	yes	characteristic
44	C₄×C₁₁	M₆₄	1	1	yes	characteristic
45	C₂×C₁₆	—	2	1	no	—
46	C₂×C₁₆	Dic₂₂	1	1	yes	characteristic
47	C₂×C₁₆	D₄₄	1	1	yes	characteristic
48	C₄×C₈	C₁₁⋊C₈	1	1	yes	characteristic
49	C₄×C₈	C₁₁⋊C₈	1	1	yes	characteristic
50	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
51	C₃₂	—	44	2	no	—
52	C₂×C₁₁	#1367	1	1	yes	characteristic
53	C₂×C₁₁	C₄⋊C₃₂	1	1	yes	characteristic
54	C₂×C₁₁	#1422	1	1	yes	characteristic
55	C₂×C₈	—	2	1	no	—
56	C₂×C₈	C₁₁⋊C₁₆	1	1	yes	characteristic
57	C₂×C₈	C₁₁⋊C₁₆	1	1	yes	characteristic
58	C₂×C₈	#4318	1	1	yes	characteristic
59	C₂×C₈	C₄⋊Dic₁₁	1	1	yes	characteristic
60	C₄²	C₂×C₁₁⋊C₈	1	1	yes	characteristic
61	C₁₆	—	2	2	no	—
62	C₁₆	—	2	1	no	—
63	C₁₆	#4314	1	2	yes	—
64	C₁₁	#7455	1	1	yes	characteristic, complemented, Sylow
65	C₂×C₄	C₄⋊(C₁₁⋊C₈)	1	1	yes	characteristic
66	C₂×C₄	C₂×C₁₁⋊C₁₆	1	1	yes	characteristic
67	C₂×C₄	#66876	1	1	yes	characteristic
68	C₈	—	2	2	no	—
69	C₈	—	2	1	no	—
70	C₈	—	2	1	no	—
71	C₈	C₁₁⋊C₃₂	1	2	yes	complemented
72	C₈	#66881	1	1	yes	characteristic
73	C₈	#66883	1	1	yes	characteristic
74	C₂²	C₄⋊(C₁₁⋊C₁₆)	1	1	yes	characteristic
75	C₄	—	2	1	no	—
76	C₄	#10622095	1	1	yes	characteristic
77	C₄	#10622101	1	1	yes	characteristic
78	C₄	C₂×C₁₁⋊C₃₂	1	1	yes	characteristic
79	C₄	#10622137	1	1	yes	characteristic
80	C₂	#13066680	1	1	yes	characteristic
81	C₂	C₄⋊(C₁₁⋊C₃₂)	1	1	yes	characteristic
82	C₂	#13066814	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₆	D₄₄
commutator	C₄×C₁₁	C₂×C₃₂
Frattini	C₄×C₁₆	C₂×D₁₁
Fitting	C₈×C₁₁×C₁₆	C₂
socle, prime radical	C₂²×C₁₁	C₄⋊C₁₆
cosocle	C₄×C₁₁×C₁₆	C₂²
hypercenter	C₈×C₁₆	D₁₁
hypocenter	C₁₁	#7455
LCS	G ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₁₆ ◁ C₄×C₁₆ ◁ C₈×C₁₆

Complements

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

N	H ≅ G/N	type
32. C₈×C₁₁	C₃₂	semidirect
64. C₁₁	#7455	semidirect
71. C₈	C₁₁⋊C₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊(C₁₁⋊C₃₂)	2
C₈×C₁₁×C₁₆	2
#7455	11