Subgroups — C₂×(C₂×D₇₅₁)⋊C₄ #37562389

Order 24032.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₇₅₁	C₂	1	1	yes	maximal, characteristic
2	C₂²×Dic₇₅₁	C₂	1	1	yes	maximal, characteristic, complemented
3	(C₂×D₇₅₁)⋊C₄	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₄×C₇₅₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₇₅₁	—	2	2	no	—
6	C₂²×D₇₅₁	—	2	2	no	—
7	C₂²×D₇₅₁	C₄	1	4	yes	complemented
8	C₂²×D₇₅₁	C₂²	1	2	yes	—
9	C₂×Dic₇₅₁	—	2	2	no	—
10	C₂×Dic₇₅₁	C₂²	1	2	yes	complemented
11	C₂³×C₇₅₁	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₇₅₁	—	2	2	no	—
13	C₂×C₄×C₇₅₁	C₂²	1	2	yes	complemented
14	C₂²×C₇₅₁	C₂×C₄	1	2	yes	—
15	C₂²×C₇₅₁	D₄	1	2	yes	—
16	C₂²×C₇₅₁	D₄	1	2	yes	—
17	C₂²×C₇₅₁	C₂³	1	1	yes	characteristic
18	C₂×D₇₅₁	—	2	8	no	—
19	C₂×D₇₅₁	—	2	2	no	—
20	C₂×D₇₅₁	—	2	2	no	—
21	C₂×D₇₅₁	C₂×C₄	1	4	yes	complemented
22	C₄×C₇₅₁	—	2	2	no	—
23	Dic₇₅₁	—	2	2	no	—
24	C₂×C₇₅₁	C₂²⋊C₄	1	4	yes	complemented
25	C₂×C₇₅₁	C₂²×C₄	1	1	yes	characteristic
26	C₂×C₇₅₁	C₂×D₄	1	1	yes	characteristic
27	C₂×C₇₅₁	C₂×D₄	1	1	yes	characteristic
28	D₇₅₁	—	2	4	no	—
29	C₇₅₁	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₂²⋊C₄	—	751	1	no	maximal, Sylow
31	C₂⁴	—	751	1	no	—
32	C₂²×C₄	—	751	1	no	—
33	C₂²×C₄	D₇₅₁	1	1	yes	characteristic, complemented
34	C₂²⋊C₄	—	751	4	no	—
35	C₂³	—	1502	2	no	—
36	C₂³	—	1502	2	no	—
37	C₂³	—	751	4	no	—
38	C₂³	—	751	2	no	—
39	C₂³	C₂×D₇₅₁	1	1	yes	characteristic
40	C₂×C₄	—	2	2	no	—
41	C₂×C₄	—	1502	2	no	—
42	C₂×C₄	—	751	2	no	—
43	C₂×C₄	C₂×D₇₅₁	1	2	yes	complemented
44	C₂²	—	1502	8	no	—
45	C₂²	—	1502	2	no	—
46	C₂²	—	1502	2	no	—
47	C₂²	—	751	4	no	—
48	C₂²	C₄×D₇₅₁	1	2	yes	—
49	C₂²	C₂²⋊D₇₅₁	1	2	yes	—
50	C₂²	D₃₀₀₄	1	2	yes	—
51	C₂²	C₂²×D₇₅₁	1	1	yes	characteristic
52	C₄	—	2	2	no	—
53	C₄	—	1502	2	no	—
54	C₂	—	1502	4	no	—
55	C₂	(C₂×D₇₅₁)⋊C₄	1	4	yes	direct product factor
56	C₂	C₂×C₄×D₇₅₁	1	1	yes	characteristic
57	C₂	C₂×C₂²⋊D₇₅₁	1	1	yes	characteristic
58	C₂	C₂×D₃₀₀₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₇₅₁
commutator	C₂×C₇₅₁	C₂²×C₄
Frattini	C₂²	C₂²×D₇₅₁
Fitting	C₂²×C₄×C₇₅₁	C₂
socle	C₂³×C₇₅₁	C₂²
prime radical	C₂³×D₇₅₁	C₂
cosocle	C₂²×C₇₅₁	C₂³
hypercenter	C₂²×C₄	D₇₅₁
hypocenter	C₇₅₁	C₂×C₂²⋊C₄
LCS	G ▷ C₂×C₇₅₁ ▷ C₇₅₁
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
2. C₂²×Dic₇₅₁	C₂	semidirect
3. (C₂×D₇₅₁)⋊C₄	C₂	direct (N × H)
4. C₂²×C₄×C₇₅₁	C₂	semidirect
7. C₂²×D₇₅₁	C₄	semidirect
10. C₂×Dic₇₅₁	C₂²	semidirect
13. C₂×C₄×C₇₅₁	C₂²	semidirect
21. C₂×D₇₅₁	C₂×C₄	semidirect
24. C₂×C₇₅₁	C₂²⋊C₄	semidirect
29. C₇₅₁	C₂×C₂²⋊C₄	semidirect
33. C₂²×C₄	D₇₅₁	semidirect
43. C₂×C₄	C₂×D₇₅₁	semidirect
55. C₂	(C₂×D₇₅₁)⋊C₄	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×D₇₅₁	2
C₂²×Dic₇₅₁	2
(C₂×D₇₅₁)⋊C₄	2
C₂²×C₄×C₇₅₁	2
C₂×C₂²⋊C₄	751

Subgroups — C2×(C2×D751)⋊C4 #37562389

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×(C₂×D₇₅₁)⋊C₄ #37562389