Subgroups — #11718656

Order 832.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#117	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊Dic₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#6099	C₂	1	1	yes	maximal, characteristic
4	#88048	C₂	1	2	yes	maximal, complemented
5	#88047	C₂	1	2	yes	maximal, complemented
6	C₂²×C₄×C₁₃	C₂²	1	1	yes	characteristic
7	C₂²×Dic₁₃	—	2	1	no	—
8	C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
9	C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
10	C₁₃×C₂²⋊C₄	—	2	1	no	—
11	C₄²×C₁₃	—	2	1	no	—
12	C₄⋊Dic₁₃	—	2	1	no	—
13	C₄⋊Dic₁₃	C₂²	1	2	yes	—
14	#6099	C₄	1	4	yes	complemented
15	C₂×#1055	C₂²	1	2	yes	—
16	C₂³×C₁₃	D₄	1	1	yes	characteristic
17	C₂×C₄×C₁₃	—	2	1	no	—
18	C₂×C₄×C₁₃	—	2	1	no	—
19	C₂×C₄×C₁₃	C₂×C₄	1	2	yes	—
20	C₂×C₄×C₁₃	D₄	1	1	yes	characteristic
21	C₂×C₄×C₁₃	Q₈	1	2	yes	—
22	C₂×C₄×C₁₃	C₂³	1	1	yes	characteristic
23	C₂×Dic₁₃	—	2	2	no	—
24	C₂×Dic₁₃	—	4	2	no	—
25	#1055	C₂×C₄	1	4	yes	complemented
26	#428	—	13	1	no	maximal, Sylow
27	C₂²×C₁₃	—	2	1	no	—
28	C₂²×C₁₃	—	2	1	no	—
29	C₂²×C₁₃	C₄⋊C₄	1	2	yes	—
30	C₂²×C₁₃	C₂×D₄	1	1	yes	characteristic
31	C₄×C₁₃	—	4	1	no	—
32	C₄×C₁₃	—	4	1	no	—
33	C₄×C₁₃	C₄⋊C₄	1	2	yes	—
34	C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
35	C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
36	Dic₁₃	—	4	2	no	—
37	C₂×M₁₆	—	13	1	no	—
38	#117	D₁₃	1	1	yes	characteristic
39	C₂×C₄⋊C₄	—	13	1	no	—
40	#107	—	13	2	no	—
41	#106	—	13	2	no	—
42	C₂×C₁₃	—	2	2	no	—
43	C₂×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
44	C₂×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
45	C₂×C₁₃	#137	1	1	yes	characteristic
46	C₂²×C₄	—	26	1	no	—
47	C₂²×C₄	C₂×D₁₃	1	1	yes	characteristic
48	M₁₆	—	13	4	no	—
49	C₂×C₈	—	13	2	no	—
50	C₄⋊C₄	—	13	2	no	—
51	C₄⋊C₄	—	26	1	no	—
52	C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
53	C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
54	C₂²⋊C₄	—	2	1	no	—
55	C₄²	—	2	1	no	—
56	C₁₃	#428	1	1	yes	characteristic, complemented, Sylow
57	C₂³	C₂²⋊D₁₃	1	1	yes	characteristic
58	C₂×C₄	—	2	1	no	—
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	26	2	no	—
61	C₂×C₄	—	52	2	no	—
62	C₂×C₄	Dic₂₆	1	2	yes	—
63	C₂×C₄	C₄×D₁₃	1	2	yes	—
64	C₂×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
65	C₂×C₄	C₂²×D₁₃	1	1	yes	characteristic
66	C₈	—	13	4	no	—
67	C₂²	—	2	1	no	—
68	C₂²	—	2	1	no	—
69	C₂²	#6101	1	2	yes	—
70	C₂²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
71	C₄	—	4	1	no	—
72	C₄	—	4	1	no	—
73	C₄	—	52	2	no	—
74	C₄	#6101	1	2	yes	—
75	C₄	C₂×Dic₂₆	1	1	yes	characteristic
76	C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
77	C₂	—	2	2	no	—
78	C₂	C₂×#6101	1	1	yes	characteristic
79	C₂	#88203	1	1	yes	characteristic
80	C₂	#88205	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₁₃
commutator	C₄×C₁₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₁₃
Fitting	C₁₃×#117	C₂
socle	C₂²×C₁₃	C₂×D₄
prime radical	C₂³×C₁₃	D₄
cosocle	C₂×C₄×C₁₃	C₂³
hypercenter	#117	D₁₃
hypocenter	C₁₃	#428
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #117

Complements

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

N	H ≅ G/N	type
4. #88048	C₂	semidirect
5. #88047	C₂	semidirect
14. #6099	C₄	semidirect
25. #1055	C₂×C₄	semidirect
56. C₁₃	#428	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#117	2
C₂×C₄⋊Dic₁₃	2
C₂×#6099	2
#88048	2
#88047	2
#428	13