Subgroups — C₂×C₄×#15690200 #37566976

Order 24352.

108 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	C₄×#15690200	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄×D₇₆₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#15690200	C₄	1	8	yes	direct product factor
5	C₂×#15690200	C₂²	1	4	yes	—
6	C₂²×D₇₆₁	C₂²	1	1	yes	characteristic
7	C₂×Dic₇₆₁	C₄	1	1	yes	characteristic, complemented
8	C₄×D₇₆₁	C₄	1	2	yes	complemented
9	C₄×D₇₆₁	C₂²	1	2	yes	—
10	C₂×C₄×C₇₆₁	C₄	1	1	yes	characteristic, complemented
11	C₂²×C₇₆₁	C₂×C₄	1	1	yes	characteristic
12	C₂×D₇₆₁	C₂×C₄	1	1	yes	characteristic
13	C₂×D₇₆₁	C₂×C₄	1	4	yes	—
14	C₂×D₇₆₁	C₂³	1	1	yes	characteristic
15	#15690200	C₂×C₄	1	8	yes	direct product factor
16	C₄×C₇₆₁	C₂×C₄	1	2	yes	complemented
17	Dic₇₆₁	C₂×C₄	1	2	yes	complemented
18	C₂×C₇₆₁	C₄²	1	2	yes	complemented
19	C₂×C₇₆₁	C₂²×C₄	1	1	yes	characteristic
20	D₇₆₁	C₄²	1	2	yes	complemented
21	D₇₆₁	C₂²×C₄	1	2	yes	—
22	C₇₆₁	C₂×C₄²	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₄²	—	761	1	no	maximal, Sylow
24	C₂²×C₄	—	761	2	no	—
25	C₂²×C₄	—	761	1	no	—
26	C₄²	—	761	4	no	—
27	C₂³	—	761	1	no	—
28	C₂×C₄	—	761	4	no	—
29	C₂×C₄	—	761	8	no	—
30	C₂×C₄	—	761	1	no	—
31	C₂×C₄	—	761	2	no	—
32	C₂×C₄	—	761	2	no	—
33	C₂×C₄	#15690200	1	1	yes	characteristic, direct product factor
34	C₂²	—	761	4	no	—
35	C₂²	—	761	1	no	—
36	C₂²	—	761	1	no	—
37	C₂²	C₂×#15690200	1	1	yes	characteristic
38	C₄	—	761	8	no	—
39	C₄	—	761	2	no	—
40	C₄	C₂×#15690200	1	2	yes	direct product factor
41	C₂	—	761	2	no	—
42	C₂	—	761	2	no	—
43	C₂	C₄×#15690200	1	2	yes	direct product factor
44	C₂	C₂²×#15690200	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄	#15690200
commutator, hypocenter	C₇₆₁	C₂×C₄²
Frattini	C₂	C₂²×#15690200
Fitting	C₂×C₄×C₇₆₁	C₄
socle	C₂²×C₇₆₁	C₂×C₄
prime radical	C₂²×D₇₆₁	C₂²
cosocle	C₂×D₇₆₁	C₂³
LCS	G ▷ C₇₆₁
UCS	C₁ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
2. C₄×#15690200	C₂	direct (N × H)
4. C₂×#15690200	C₄	direct (N × H)
7. C₂×Dic₇₆₁	C₄	semidirect
8. C₄×D₇₆₁	C₄	semidirect
10. C₂×C₄×C₇₆₁	C₄	semidirect
15. #15690200	C₂×C₄	direct (N × H)
16. C₄×C₇₆₁	C₂×C₄	semidirect
17. Dic₇₆₁	C₂×C₄	semidirect
18. C₂×C₇₆₁	C₄²	semidirect
20. D₇₆₁	C₄²	semidirect
22. C₇₆₁	C₂×C₄²	semidirect
33. C₂×C₄	#15690200	direct (N × H)
40. C₄	C₂×#15690200	direct (N × H)
43. C₂	C₄×#15690200	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#15690200	2
C₄×#15690200	2
C₂×C₄×D₇₆₁	2
C₂×C₄²	761

Subgroups — C2×C4×#15690200 #37566976

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×#15690200 #37566976