Subgroups — C₂×#27131076 #37564401

Order 24224.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₅₁₄	C₂	1	1	yes	maximal, characteristic, complemented
2	#27131076	C₂	1	4	yes	maximal, direct product factor
3	C₂×#20258493	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄×C₇₅₇	C₂	1	1	yes	maximal, characteristic
5	Dic₁₅₁₄	—	2	1	no	—
6	Dic₁₅₁₄	C₂²	1	2	yes	complemented
7	C₂×Dic₇₅₇	—	2	1	no	—
8	#20258493	C₂²	1	2	yes	complemented
9	C₂³×C₇₅₇	—	2	1	no	—
10	D₄×C₇₅₇	—	2	1	no	—
11	D₄×C₇₅₇	C₂²	1	2	yes	—
12	C₂×C₄×C₇₅₇	C₂²	1	1	yes	characteristic
13	C₂²×C₇₅₇	—	2	2	no	—
14	C₂²×C₇₅₇	—	4	2	no	—
15	C₂²×C₇₅₇	D₄	1	1	yes	characteristic
16	C₄×C₇₅₇	D₄	1	1	yes	characteristic
17	C₄×C₇₅₇	C₂³	1	1	yes	characteristic
18	Dic₇₅₇	—	2	2	no	—
19	C₂×C₇₅₇	—	4	2	no	—
20	C₂×C₇₅₇	SD₁₆	1	2	yes	complemented
21	C₂×C₇₅₇	C₂×D₄	1	1	yes	characteristic
22	C₇₅₇	C₂×SD₁₆	1	1	yes	characteristic, complemented, Sylow
23	C₂×SD₁₆	—	757	1	no	maximal, Sylow
24	C₂×Q₈	—	757	1	no	—
25	C₂×D₄	D₇₅₇	1	1	yes	characteristic
26	SD₁₆	—	757	4	no	—
27	C₂×C₈	—	757	1	no	—
28	C₂³	—	2	1	no	—
29	Q₈	—	1514	1	no	—
30	Q₈	—	757	2	no	—
31	D₄	—	2	1	no	—
32	D₄	C₂×D₇₅₇	1	2	yes	—
33	C₂×C₄	—	1514	1	no	—
34	C₂×C₄	C₂×D₇₅₇	1	1	yes	characteristic
35	C₈	—	757	2	no	—
36	C₂²	—	2	2	no	—
37	C₂²	—	4	2	no	—
38	C₂²	C₂²⋊D₇₅₇	1	1	yes	characteristic
39	C₄	—	1514	2	no	—
40	C₄	C₂²⋊D₇₅₇	1	1	yes	characteristic
41	C₄	C₂²×D₇₅₇	1	1	yes	characteristic
42	C₂	—	4	2	no	—
43	C₂	#27131076	1	2	yes	direct product factor
44	C₂	C₂×C₂²⋊D₇₅₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊D₇₅₇
commutator, cosocle	C₄×C₇₅₇	C₂³
Frattini	C₄	C₂²×D₇₅₇
Fitting, prime radical	C₂×D₄×C₇₅₇	C₂
socle	C₂²×C₇₅₇	D₄
hypercenter	C₂×D₄	D₇₅₇
hypocenter	C₇₅₇	C₂×SD₁₆
LCS	G ▷ C₄×C₇₅₇ ▷ C₂×C₇₅₇ ▷ C₇₅₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×Dic₁₅₁₄	C₂	semidirect
2. #27131076	C₂	direct (N × H)
3. C₂×#20258493	C₂	semidirect
6. Dic₁₅₁₄	C₂²	semidirect
8. #20258493	C₂²	semidirect
20. C₂×C₇₅₇	SD₁₆	semidirect
22. C₇₅₇	C₂×SD₁₆	semidirect
43. C₂	#27131076	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×Dic₁₅₁₄	2
#27131076	2
C₂×#20258493	2
C₂×D₄×C₇₅₇	2
C₂×SD₁₆	757

Subgroups — C2×#27131076 #37564401

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#27131076 #37564401