Subgroups — C₂×#27131071 #37564391

Order 24224.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₇₅₇	C₂	1	1	yes	maximal, characteristic
2	#27131071	C₂	1	4	yes	maximal, direct product factor
3	C₂×#20258493	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₈×C₇₅₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₇₅₇	C₄	1	1	yes	characteristic
6	C₂×Dic₇₅₇	C₄	1	1	yes	characteristic
7	C₄×D₇₅₇	C₄	1	2	yes	—
8	C₄×D₇₅₇	C₂²	1	2	yes	—
9	#20258493	C₂²	1	2	yes	complemented
10	C₂×C₄×C₇₅₇	C₂²	1	1	yes	characteristic
11	C₈×C₇₅₇	C₂²	1	2	yes	complemented
12	C₂²×C₇₅₇	C₂×C₄	1	1	yes	characteristic
13	C₂×D₇₅₇	—	2	2	no	—
14	C₂×D₇₅₇	C₂×C₄	1	2	yes	—
15	C₄×C₇₅₇	C₂×C₄	1	1	yes	characteristic
16	C₄×C₇₅₇	C₂³	1	1	yes	characteristic
17	Dic₇₅₇	C₂×C₄	1	2	yes	—
18	C₂×C₇₅₇	M₁₆	1	2	yes	complemented
19	C₂×C₇₅₇	C₂²×C₄	1	1	yes	characteristic
20	D₇₅₇	—	2	2	no	—
21	C₇₅₇	C₂×M₁₆	1	1	yes	characteristic, complemented, Sylow
22	C₂×M₁₆	—	757	1	no	maximal, Sylow
23	C₂²×C₄	—	757	1	no	—
24	M₁₆	—	757	4	no	—
25	C₂×C₈	—	757	1	no	—
26	C₂×C₈	D₇₅₇	1	1	yes	characteristic, complemented
27	C₂³	—	757	1	no	—
28	C₂×C₄	—	757	1	no	—
29	C₂×C₄	—	757	2	no	—
30	C₂×C₄	—	757	2	no	—
31	C₂×C₄	C₂×D₇₅₇	1	1	yes	characteristic
32	C₈	—	757	2	no	—
33	C₈	C₂×D₇₅₇	1	2	yes	complemented
34	C₂²	—	1514	2	no	—
35	C₂²	—	757	2	no	—
36	C₂²	C₄×D₇₅₇	1	1	yes	characteristic
37	C₄	—	757	2	no	—
38	C₄	C₄×D₇₅₇	1	1	yes	characteristic
39	C₄	C₂²×D₇₅₇	1	1	yes	characteristic
40	C₂	—	1514	2	no	—
41	C₂	#27131071	1	2	yes	direct product factor
42	C₂	C₂×C₄×D₇₅₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₇₅₇
commutator	C₂×C₇₅₇	C₂²×C₄
Frattini	C₄	C₂²×D₇₅₇
Fitting	C₂×C₈×C₇₅₇	C₂
socle	C₂²×C₇₅₇	C₂×C₄
prime radical	C₂²×D₇₅₇	C₄
cosocle	C₄×C₇₅₇	C₂³
hypercenter	C₂×C₈	D₇₅₇
hypocenter	C₇₅₇	C₂×M₁₆
LCS	G ▷ C₂×C₇₅₇ ▷ C₇₅₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. #27131071	C₂	direct (N × H)
3. C₂×#20258493	C₂	semidirect
4. C₂×C₈×C₇₅₇	C₂	semidirect
9. #20258493	C₂²	semidirect
11. C₈×C₇₅₇	C₂²	semidirect
18. C₂×C₇₅₇	M₁₆	semidirect
21. C₇₅₇	C₂×M₁₆	semidirect
26. C₂×C₈	D₇₅₇	semidirect
33. C₈	C₂×D₇₅₇	semidirect
41. C₂	#27131071	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×C₄×D₇₅₇	2
#27131071	2
C₂×#20258493	2
C₂×C₈×C₇₅₇	2
C₂×M₁₆	757

Subgroups — C2×#27131071 #37564391

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#27131071 #37564391