Subgroups — D₇₅₇⋊M₁₆ #37564472

Order 24224.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27131098	C₂	1	2	yes	maximal, complemented
2	#27131097	C₂	1	2	yes	maximal, complemented
3	D₇₅₇⋊C₈	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×D₇₅₇	C₂	1	1	yes	maximal, characteristic
5	#20258500	C₂²	1	4	yes	complemented
6	C₂²×D₇₅₇	C₄	1	1	yes	characteristic
7	C₂×Dic₇₅₇	C₂²	1	1	yes	characteristic
8	C₄×D₇₅₇	C₄	1	1	yes	characteristic
9	C₄×D₇₅₇	C₄	1	1	yes	characteristic
10	C₄×D₇₅₇	C₂²	1	1	yes	characteristic
11	C₄×D₇₅₇	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₇₅₇	C₄	1	1	yes	characteristic
13	C₂²×C₇₅₇	C₂×C₄	1	1	yes	characteristic
14	C₂×D₇₅₇	—	2	2	no	—
15	C₂×D₇₅₇	C₂×C₄	1	1	yes	characteristic
16	C₂×D₇₅₇	C₂×C₄	1	1	yes	characteristic
17	C₄×C₇₅₇	C₂×C₄	1	1	yes	characteristic
18	C₄×C₇₅₇	C₂×C₄	1	1	yes	characteristic
19	Dic₇₅₇	C₂×C₄	1	1	yes	characteristic
20	Dic₇₅₇	C₂³	1	1	yes	characteristic
21	C₂×C₇₅₇	—	2	1	no	—
22	C₂×C₇₅₇	C₂²×C₄	1	1	yes	characteristic
23	D₇₅₇	—	2	1	no	—
24	D₇₅₇	M₁₆	1	2	yes	complemented
25	C₇₅₇	C₂×M₁₆	1	1	yes	characteristic, complemented, Sylow
26	C₂×M₁₆	—	757	1	no	maximal, Sylow
27	C₂²×C₄	—	757	1	no	—
28	M₁₆	—	757	2	no	—
29	M₁₆	—	757	2	no	—
30	C₂×C₈	—	757	2	no	—
31	C₂³	—	757	1	no	—
32	C₂×C₄	—	757	1	no	—
33	C₂×C₄	—	757	1	no	—
34	C₂×C₄	—	757	1	no	—
35	C₂×C₄	—	757	1	no	—
36	C₂×C₄	—	757	1	no	—
37	C₂×C₄	#15690044	1	1	yes	characteristic
38	C₈	—	757	4	no	—
39	C₂²	—	1514	2	no	—
40	C₂²	—	757	1	no	—
41	C₂²	—	757	1	no	—
42	C₂²	C₂×#15690044	1	1	yes	characteristic
43	C₄	—	757	1	no	—
44	C₄	—	757	1	no	—
45	C₄	C₂×#15690044	1	1	yes	characteristic
46	C₄	C₂×#15690044	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	—	1514	1	no	—
49	C₂	—	757	2	no	—
50	C₂	C₂²×#15690044	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×#15690044
commutator, socle	C₂×C₇₅₇	C₂²×C₄
Frattini	C₂	C₂²×#15690044
Fitting	C₂×C₄×C₇₅₇	C₄
prime radical	C₂²×D₇₅₇	C₄
cosocle	Dic₇₅₇	C₂³
hypercenter	C₂×C₄	#15690044
hypocenter	C₇₅₇	C₂×M₁₆
LCS	G ▷ C₂×C₇₅₇ ▷ C₇₅₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
1. #27131098	C₂	semidirect
2. #27131097	C₂	semidirect
3. D₇₅₇⋊C₈	C₂	semidirect
5. #20258500	C₂²	semidirect
24. D₇₅₇	M₁₆	semidirect
25. C₇₅₇	C₂×M₁₆	semidirect

Maximal subgroups

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

subgroup	index
#27131098	2
#27131097	2
D₇₅₇⋊C₈	2
C₂×C₄×D₇₅₇	2
C₂×M₁₆	757

Subgroups — D757⋊M16 #37564472

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇₅₇⋊M₁₆ #37564472