Subgroups — (C₂×#15690200)⋊C₄ #37566951

Order 24352.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#15690200	C₂	1	2	yes	maximal
2	C₂×C₄×D₇₆₁	C₂	1	1	yes	maximal, characteristic
3	C₂×#15690200	—	2	2	no	—
4	C₂×#15690200	—	2	2	no	—
5	C₂×#15690200	C₄	1	4	yes	complemented
6	C₂²×D₇₆₁	C₂²	1	1	yes	characteristic
7	C₂×Dic₇₆₁	C₄	1	1	yes	characteristic, complemented
8	C₄×D₇₆₁	—	2	2	no	—
9	C₂×C₄×C₇₆₁	C₄	1	1	yes	characteristic, complemented
10	C₂²×C₇₆₁	C₂×C₄	1	1	yes	characteristic
11	C₂×D₇₆₁	C₂×C₄	1	2	yes	—
12	C₂×D₇₆₁	D₄	1	1	yes	characteristic
13	C₂×D₇₆₁	D₄	1	2	yes	—
14	C₂×D₇₆₁	Q₈	1	1	yes	characteristic
15	#15690200	—	2	4	no	—
16	C₄×C₇₆₁	—	2	1	no	—
17	Dic₇₆₁	—	2	1	no	—
18	C₂×C₇₆₁	C₄²	1	1	yes	characteristic
19	C₂×C₇₆₁	C₂²⋊C₄	1	1	yes	characteristic
20	C₂×C₇₆₁	C₄⋊C₄	1	1	yes	characteristic
21	D₇₆₁	C₂²⋊C₄	1	2	yes	—
22	D₇₆₁	C₄⋊C₄	1	2	yes	—
23	C₇₆₁	#95	1	1	yes	characteristic, complemented, Sylow
24	#95	—	761	1	no	maximal, Sylow
25	C₂²×C₄	—	761	2	no	—
26	C₂²×C₄	—	761	1	no	—
27	C₂³	—	761	1	no	—
28	C₂×C₄	—	1522	2	no	—
29	C₂×C₄	—	1522	2	no	—
30	C₂×C₄	—	1522	2	no	—
31	C₂×C₄	—	761	4	no	—
32	C₂×C₄	—	761	1	no	—
33	C₂×C₄	#15690200	1	1	yes	characteristic, complemented
34	C₂²	—	761	2	no	—
35	C₂²	—	761	2	no	—
36	C₂²	—	761	1	no	—
37	C₂²	—	761	1	no	—
38	C₂²	C₂×#15690200	1	1	yes	characteristic
39	C₄	—	2	1	no	—
40	C₄	—	1522	4	no	—
41	C₄	—	1522	1	no	—
42	C₂	—	761	2	no	—
43	C₂	—	761	2	no	—
44	C₂	C₄×#15690200	1	1	yes	characteristic
45	C₂	C₂²⋊#15690200	1	1	yes	characteristic
46	C₂	C₄⋊#15690200	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂×#15690200
commutator	C₂×C₇₆₁	C₄²
Fitting	C₂×C₄×C₇₆₁	C₄
socle	C₂²×C₇₆₁	C₂×C₄
prime radical, cosocle	C₂²×D₇₆₁	C₂²
hypercenter	C₂×C₄	#15690200
hypocenter	C₇₆₁	#95
LCS	G ▷ C₂×C₇₆₁ ▷ C₇₆₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
5. C₂×#15690200	C₄	semidirect
7. C₂×Dic₇₆₁	C₄	semidirect
9. C₂×C₄×C₇₆₁	C₄	semidirect
23. C₇₆₁	#95	semidirect
33. C₂×C₄	#15690200	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#15690200	2
C₂×C₄×D₇₆₁	2
#95	761

Subgroups — (C2×#15690200)⋊C4 #37566951

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₂×#15690200)⋊C₄ #37566951