Subgroups — #11718751

Order 832.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#6107	C₂	1	2	yes	maximal
3	C₄×Dic₂₆	C₂	1	1	yes	maximal, characteristic
4	#88075	C₂	1	2	yes	maximal
5	C₄⋊#1055	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₈×C₁₃	C₂²	1	2	yes	—
7	C₂×Dic₂₆	C₂²	1	1	yes	characteristic
8	C₁₃×C₄⋊C₄	—	2	1	no	—
9	C₁₃×C₄⋊C₄	—	2	1	no	—
10	C₄²×C₁₃	C₂²	1	1	yes	characteristic
11	#6107	—	2	4	no	—
12	C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
13	#6101	—	2	1	no	—
14	C₄×Dic₁₃	—	2	1	no	—
15	C₂×#1055	C₂²	1	2	yes	—
16	Q₈×C₁₃	—	2	2	no	—
17	Q₈×C₁₃	—	2	2	no	—
18	C₂×C₄×C₁₃	—	2	2	no	—
19	C₂×C₄×C₁₃	D₄	1	1	yes	characteristic
20	C₂×C₄×C₁₃	D₄	1	1	yes	characteristic
21	C₂×C₄×C₁₃	C₂³	1	1	yes	characteristic
22	C₂×Dic₁₃	—	2	1	no	—
23	C₂×Dic₁₃	—	2	1	no	—
24	Dic₂₆	—	2	1	no	—
25	Dic₂₆	D₄	1	2	yes	—
26	#1055	—	2	2	no	—
27	#462	—	13	1	no	maximal, Sylow
28	C₂²×C₁₃	C₂×D₄	1	1	yes	characteristic
29	C₄×C₁₃	—	2	1	no	—
30	C₄×C₁₃	—	4	2	no	—
31	C₄×C₁₃	Q₁₆	1	2	yes	complemented
32	C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
33	C₄×C₁₃	#41	1	1	yes	characteristic
34	Dic₁₃	—	2	2	no	—
35	Dic₁₃	—	4	1	no	—
36	C₂×Q₁₆	—	13	2	no	—
37	C₄⋊Q₈	D₁₃	1	1	yes	characteristic
38	C₄×Q₈	—	13	1	no	—
39	C₄⋊C₈	—	13	1	no	—
40	#103	—	13	2	no	—
41	C₂×C₁₃	#121	1	1	yes	characteristic
42	C₂×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
43	C₂×C₁₃	#137	1	1	yes	characteristic
44	C₂×Q₈	—	13	1	no	—
45	C₂×Q₈	C₂×D₁₃	1	2	yes	—
46	Q₁₆	—	26	4	no	—
47	C₂×C₈	—	13	2	no	—
48	C₄⋊C₄	—	2	1	no	—
49	C₄⋊C₄	—	2	1	no	—
50	C₄⋊C₄	—	13	1	no	—
51	C₄⋊C₄	—	26	1	no	—
52	C₄²	—	26	1	no	—
53	C₄²	C₂×D₁₃	1	1	yes	characteristic
54	C₁₃	#462	1	1	yes	characteristic, complemented, Sylow
55	Q₈	—	2	2	no	—
56	Q₈	—	2	2	no	—
57	Q₈	—	13	2	no	—
58	Q₈	—	26	1	no	—
59	C₂×C₄	—	2	2	no	—
60	C₂×C₄	—	26	1	no	—
61	C₂×C₄	—	26	1	no	—
62	C₂×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
63	C₂×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
64	C₂×C₄	C₂²×D₁₃	1	1	yes	characteristic
65	C₈	—	26	2	no	—
66	C₂²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
67	C₄	—	2	1	no	—
68	C₄	—	4	2	no	—
69	C₄	—	26	2	no	—
70	C₄	—	52	1	no	—
71	C₄	#6107	1	2	yes	complemented
72	C₄	D₄×D₁₃	1	1	yes	characteristic
73	C₄	#6129	1	1	yes	characteristic
74	C₂	#88192	1	1	yes	characteristic
75	C₂	#88196	1	1	yes	characteristic
76	C₂	C₂×#6107	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₁₃
commutator, cosocle	C₂×C₄×C₁₃	C₂³
Frattini	C₂×C₄	C₂²×D₁₃
Fitting	C₁₃×C₄⋊Q₈	C₂
socle, prime radical	C₂²×C₁₃	C₂×D₄
hypercenter	C₄⋊Q₈	D₁₃
hypocenter	C₁₃	#462
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
31. C₄×C₁₃	Q₁₆	semidirect
54. C₁₃	#462	semidirect
71. C₄	#6107	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×C₄⋊Q₈	2
C₂×#6107	2
C₄×Dic₂₆	2
#88075	2
C₄⋊#1055	2
#462	13