Subgroups — #11718239

Order 832.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#6122	C₂	1	1	yes	maximal, characteristic
2	C₂×#6122	C₂	1	1	yes	maximal, characteristic
3	#88131	C₂	1	1	yes	maximal, characteristic
4	C₂²×Dic₁₃	C₂²	1	1	yes	characteristic
5	#6122	—	2	1	no	—
6	#6122	—	2	1	no	—
7	#6122	—	2	1	no	—
8	#6122	C₄	1	2	yes	complemented
9	C₂×#1057	—	2	1	no	—
10	C₂×#1057	C₄	1	2	yes	complemented
11	C₁₃×C₂²⋊C₄	C₄	1	1	yes	characteristic
12	C₂²⋊Dic₁₃	C₄	1	1	yes	characteristic
13	#6101	—	2	1	no	—
14	C₄×Dic₁₃	—	2	1	no	—
15	C₂³×C₁₃	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₁₃	—	2	1	no	—
17	C₂×Dic₁₃	—	2	1	no	—
18	C₂×Dic₁₃	C₂×C₄	1	1	yes	characteristic
19	C₂×Dic₁₃	C₂×C₄	1	1	yes	characteristic
20	C₂×Dic₁₃	D₄	1	1	yes	characteristic
21	C₂×Dic₁₃	D₄	1	1	yes	characteristic
22	C₂×Dic₁₃	D₄	1	1	yes	characteristic
23	C₂×Dic₁₃	Q₈	1	1	yes	characteristic
24	#1057	—	2	2	no	—
25	#1057	—	2	2	no	—
26	#344	—	13	1	no	maximal, Sylow
27	C₂²×C₁₃	—	4	1	no	—
28	C₂²×C₁₃	C₄²	1	1	yes	characteristic
29	C₂²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
30	C₂²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
31	C₄×C₁₃	—	4	1	no	—
32	Dic₁₃	—	4	1	no	—
33	Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
34	Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
35	Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
36	Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
37	C₂×M₁₆	—	13	1	no	—
38	C₂×M₁₆	—	13	1	no	—
39	#117	—	13	1	no	—
40	C₂×C₁₃	—	2	1	no	—
41	C₂×C₁₃	—	2	1	no	—
42	C₂×C₁₃	—	2	1	no	—
43	C₂×C₁₃	#95	1	1	yes	characteristic
44	C₂²×C₄	—	13	1	no	—
45	M₁₆	—	13	2	no	—
46	M₁₆	—	26	1	no	—
47	M₁₆	—	26	1	no	—
48	M₁₆	—	26	1	no	—
49	C₂×C₈	—	13	2	no	—
50	C₂×C₈	—	26	1	no	—
51	C₄⋊C₄	—	26	1	no	—
52	C₂²⋊C₄	—	13	1	no	—
53	C₂²⋊C₄	#261	1	1	yes	characteristic
54	C₄²	—	26	1	no	—
55	C₁₃	#344	1	1	yes	characteristic, complemented, Sylow
56	C₂³	C₂×#261	1	1	yes	characteristic
57	C₂×C₄	—	2	1	no	—
58	C₂×C₄	—	13	1	no	—
59	C₂×C₄	—	13	1	no	—
60	C₂×C₄	—	13	1	no	—
61	C₂×C₄	—	13	1	no	—
62	C₂×C₄	—	13	1	no	—
63	C₂×C₄	—	13	1	no	—
64	C₂×C₄	—	26	1	no	—
65	C₈	—	26	2	no	—
66	C₈	—	26	2	no	—
67	C₂²	—	4	1	no	—
68	C₂²	C₄×#261	1	1	yes	characteristic
69	C₂²	C₄⋊#261	1	1	yes	characteristic
70	C₂²	C₂²⋊#261	1	1	yes	characteristic
71	C₄	—	4	1	no	—
72	C₄	—	13	1	no	—
73	C₄	—	13	1	no	—
74	C₄	—	13	1	no	—
75	C₄	—	13	1	no	—
76	C₄	—	52	1	no	—
77	C₂	—	2	1	no	—
78	C₂	—	2	1	no	—
79	C₂	—	2	1	no	—
80	C₂	(C₂×#261)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂	(C₂×#261)⋊C₄
commutator	C₂²×C₁₃	C₄²
Frattini	C₂³	C₂×#261
Fitting	C₁₃×C₂²⋊C₄	C₄
socle	C₂×C₁₃	#95
prime radical	C₂³×C₁₃	C₂×C₄
cosocle	C₂²×Dic₁₃	C₂²
hypercenter	C₂²⋊C₄	#261
hypocenter	C₁₃	#344
LCS	G ▷ C₂²×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₂³ ◁ C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
8. #6122	C₄	semidirect
10. C₂×#1057	C₄	semidirect
55. C₁₃	#344	semidirect

Maximal subgroups

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

subgroup	index
C₂×#6122	2
#88131	2
#344	13