Subgroups — C₂×C₄⋊Dic₇₅₇ #37564342

Order 24224.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₇₅₇	C₂	1	2	yes	maximal
2	C₄⋊Dic₇₅₇	C₂	1	4	yes	maximal, direct product factor
3	C₂²×C₄×C₇₅₇	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₇₅₇	—	2	4	no	—
5	C₂×Dic₇₅₇	C₂²	1	4	yes	—
6	C₂³×C₇₅₇	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₇₅₇	C₄	1	4	yes	complemented
8	C₂×C₄×C₇₅₇	C₂²	1	2	yes	—
9	C₂²×C₇₅₇	C₂×C₄	1	2	yes	—
10	C₂²×C₇₅₇	D₄	1	2	yes	—
11	C₂²×C₇₅₇	Q₈	1	2	yes	—
12	C₂²×C₇₅₇	C₂³	1	1	yes	characteristic
13	C₄×C₇₅₇	C₂×C₄	1	4	yes	complemented
14	Dic₇₅₇	—	2	4	no	—
15	C₂×C₇₅₇	C₄⋊C₄	1	4	yes	complemented
16	C₂×C₇₅₇	C₂²×C₄	1	1	yes	characteristic
17	C₂×C₇₅₇	C₂×D₄	1	1	yes	characteristic
18	C₂×C₇₅₇	C₂×Q₈	1	1	yes	characteristic
19	C₇₅₇	C₂×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₄⋊C₄	—	757	1	no	maximal, Sylow
21	C₂²×C₄	—	757	2	no	—
22	C₂²×C₄	D₇₅₇	1	1	yes	characteristic
23	C₄⋊C₄	—	757	4	no	—
24	C₂³	C₂×D₇₅₇	1	1	yes	characteristic
25	C₂×C₄	—	1514	4	no	—
26	C₂×C₄	—	757	4	no	—
27	C₂×C₄	Dic₇₅₇	1	4	yes	complemented
28	C₂×C₄	C₂×D₇₅₇	1	2	yes	—
29	C₂²	C₂×Dic₇₅₇	1	2	yes	—
30	C₂²	D₃₀₂₈	1	2	yes	—
31	C₂²	Dic₁₅₁₄	1	2	yes	—
32	C₂²	C₂²×D₇₅₇	1	1	yes	characteristic
33	C₄	—	1514	4	no	—
34	C₄	C₂×Dic₇₅₇	1	4	yes	complemented
35	C₂	C₄⋊Dic₇₅₇	1	4	yes	direct product factor
36	C₂	C₂²×Dic₇₅₇	1	1	yes	characteristic
37	C₂	C₂×D₃₀₂₈	1	1	yes	characteristic
38	C₂	C₂×Dic₁₅₁₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₇₅₇
commutator	C₂×C₇₅₇	C₂²×C₄
Frattini	C₂²	C₂²×D₇₅₇
Fitting	C₂²×C₄×C₇₅₇	C₂
socle, prime radical	C₂³×C₇₅₇	C₂²
cosocle	C₂²×C₇₅₇	C₂³
hypercenter	C₂²×C₄	D₇₅₇
hypocenter	C₇₅₇	C₂×C₄⋊C₄
LCS	G ▷ C₂×C₇₅₇ ▷ C₇₅₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
2. C₄⋊Dic₇₅₇	C₂	direct (N × H)
7. C₂×C₄×C₇₅₇	C₄	semidirect
13. C₄×C₇₅₇	C₂×C₄	semidirect
15. C₂×C₇₅₇	C₄⋊C₄	semidirect
19. C₇₅₇	C₂×C₄⋊C₄	semidirect
27. C₂×C₄	Dic₇₅₇	semidirect
34. C₄	C₂×Dic₇₅₇	semidirect
35. C₂	C₄⋊Dic₇₅₇	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×Dic₇₅₇	2
C₄⋊Dic₇₅₇	2
C₂²×C₄×C₇₅₇	2
C₂×C₄⋊C₄	757

Subgroups — C2×C4⋊Dic757 #37564342

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄⋊Dic₇₅₇ #37564342