Subgroups — D₄×#15690200 #37566980

Order 24352.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#15690200	C₂	1	2	yes	maximal, complemented
2	C₄⋊#15690200	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²⋊#15690200	C₂	1	2	yes	maximal, complemented
4	C₄×#15690200	C₂	1	1	yes	maximal, characteristic, complemented
5	D₄×D₇₆₁	C₂	1	1	yes	maximal, characteristic
6	C₂×#15690200	—	2	4	no	—
7	C₂×#15690200	C₂²	1	1	yes	characteristic
8	C₂×#15690200	C₂²	1	2	yes	—
9	C₂×#15690200	C₂²	1	1	yes	characteristic
10	C₂²×D₇₆₁	C₂²	1	2	yes	—
11	D₃₀₄₄	C₄	1	1	yes	characteristic, complemented
12	C₂²⋊D₇₆₁	C₄	1	2	yes	complemented
13	C₄×D₇₆₁	C₂²	1	1	yes	characteristic
14	D₄×C₇₆₁	C₄	1	1	yes	characteristic, complemented
15	C₂²×C₇₆₁	C₂×C₄	1	2	yes	complemented
16	C₂×D₇₆₁	—	2	2	no	—
17	C₂×D₇₆₁	—	2	2	no	—
18	C₂×D₇₆₁	C₂×C₄	1	2	yes	complemented
19	C₂×D₇₆₁	C₂³	1	1	yes	characteristic
20	#15690200	—	2	2	no	—
21	#15690200	—	2	1	no	—
22	#15690200	D₄	1	2	yes	direct product factor
23	C₄×C₇₆₁	C₂×C₄	1	1	yes	characteristic, complemented
24	Dic₇₆₁	C₂×C₄	1	1	yes	characteristic, complemented
25	C₂×C₇₆₁	—	2	2	no	—
26	C₂×C₇₆₁	C₂²×C₄	1	1	yes	characteristic
27	D₇₆₁	—	2	2	no	—
28	D₇₆₁	C₂×D₄	1	1	yes	characteristic
29	D₇₆₁	#41	1	1	yes	characteristic
30	C₇₆₁	C₄×D₄	1	1	yes	characteristic, complemented, Sylow
31	C₄×D₄	—	761	1	no	maximal, Sylow
32	C₂×D₄	—	761	1	no	—
33	C₂²×C₄	—	761	2	no	—
34	C₄⋊C₄	—	761	1	no	—
35	C₂²⋊C₄	—	761	2	no	—
36	C₄²	—	761	1	no	—
37	C₂³	—	761	2	no	—
38	D₄	—	761	2	no	—
39	D₄	—	761	1	no	—
40	D₄	#15690200	1	1	yes	characteristic, direct product factor
41	C₂×C₄	—	1522	4	no	—
42	C₂×C₄	—	761	1	no	—
43	C₂×C₄	—	761	2	no	—
44	C₂×C₄	—	761	1	no	—
45	C₂×C₄	—	761	1	no	—
46	C₂²	—	1522	2	no	—
47	C₂²	—	1522	2	no	—
48	C₂²	—	761	2	no	—
49	C₂²	—	761	1	no	—
50	C₂²	C₂×#15690200	1	2	yes	complemented
51	C₄	—	1522	2	no	—
52	C₄	—	1522	1	no	—
53	C₄	—	761	2	no	—
54	C₄	—	761	1	no	—
55	C₄	C₂×#15690200	1	1	yes	characteristic, complemented
56	C₂	—	2	2	no	—
57	C₂	—	1522	2	no	—
58	C₂	—	761	1	no	—
59	C₂	—	761	1	no	—
60	C₂	C₂²×#15690200	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂²×#15690200
commutator, socle	C₂×C₇₆₁	C₂²×C₄
Fitting	D₄×C₇₆₁	C₄
prime radical	D₄×D₇₆₁	C₂
cosocle	C₂×D₇₆₁	C₂³
hypercenter	D₄	#15690200
hypocenter	C₇₆₁	C₄×D₄
LCS	G ▷ C₂×C₇₆₁ ▷ C₇₆₁
UCS	C₁ ◁ C₂ ◁ D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×#15690200	C₂	semidirect
2. C₄⋊#15690200	C₂	semidirect
3. C₂²⋊#15690200	C₂	semidirect
4. C₄×#15690200	C₂	semidirect
11. D₃₀₄₄	C₄	semidirect
12. C₂²⋊D₇₆₁	C₄	semidirect
14. D₄×C₇₆₁	C₄	semidirect
15. C₂²×C₇₆₁	C₂×C₄	semidirect
18. C₂×D₇₆₁	C₂×C₄	semidirect
22. #15690200	D₄	direct (N × H)
23. C₄×C₇₆₁	C₂×C₄	semidirect
24. Dic₇₆₁	C₂×C₄	semidirect
30. C₇₆₁	C₄×D₄	semidirect
40. D₄	#15690200	direct (N × H)
50. C₂²	C₂×#15690200	semidirect
55. C₄	C₂×#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
C₄⋊#15690200	2
C₂²⋊#15690200	2
C₄×#15690200	2
D₄×D₇₆₁	2
C₄×D₄	761

Subgroups — D4×#15690200 #37566980

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×#15690200 #37566980