Subgroups — #23757087

Order 10048.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₂₅₆	C₂	1	1	yes	maximal, characteristic
2	#19097707	C₂	1	1	yes	maximal, characteristic, complemented
3	M₃₂×C₁₅₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₆₂₈	—	2	1	no	—
5	D₁₂₅₆	—	2	1	no	—
6	D₁₂₅₆	C₄	1	2	yes	—
7	#14578938	—	2	1	no	—
8	C₂×C₈×C₁₅₇	C₂²	1	1	yes	characteristic
9	C₁₆×C₁₅₇	—	2	1	no	—
10	C₂²×D₁₅₇	—	4	1	no	—
11	D₆₂₈	—	2	2	no	—
12	D₆₂₈	—	4	1	no	—
13	#11929434	—	4	1	no	—
14	C₂×C₄×C₁₅₇	D₄	1	1	yes	characteristic
15	C₈×C₁₅₇	C₂×C₄	1	1	yes	characteristic
16	C₈×C₁₅₇	D₄	1	1	yes	characteristic
17	C₂²×C₁₅₇	SD₁₆	1	1	yes	characteristic
18	C₂×D₁₅₇	—	4	2	no	—
19	C₂×D₁₅₇	—	8	2	no	—
20	C₄×C₁₅₇	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₁₅₇	D₈	1	1	yes	characteristic
22	C₂×C₁₅₇	—	2	1	no	—
23	C₂×C₁₅₇	#102	1	1	yes	characteristic
24	D₁₅₇	—	8	2	no	—
25	C₁₅₇	#361	1	1	yes	characteristic, complemented, Sylow
26	#361	—	157	1	no	maximal, Sylow
27	C₂×D₈	—	157	1	no	—
28	M₃₂	D₁₅₇	1	1	yes	characteristic, complemented
29	#108	—	157	1	no	—
30	C₂×D₄	—	314	1	no	—
31	D₈	—	314	1	no	—
32	D₈	—	157	2	no	—
33	M₁₆	—	314	1	no	—
34	C₂×C₈	C₂×D₁₅₇	1	1	yes	characteristic
35	C₁₆	—	2	1	no	—
36	C₂³	—	628	1	no	—
37	D₄	—	314	2	no	—
38	D₄	—	628	1	no	—
39	C₂×C₄	D₆₂₈	1	1	yes	characteristic
40	C₈	—	628	1	no	—
41	C₈	C₄×D₁₅₇	1	1	yes	characteristic
42	C₈	C₂²⋊D₁₅₇	1	1	yes	characteristic
43	C₂²	—	628	2	no	—
44	C₂²	—	1256	2	no	—
45	C₂²	#14578943	1	1	yes	characteristic
46	C₄	#14578931	1	1	yes	characteristic
47	C₄	D₁₂₅₆	1	1	yes	characteristic
48	C₂	—	2	1	no	—
49	C₂	—	1256	2	no	—
50	C₂	#19097693	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#19097693
commutator	C₈×C₁₅₇	C₂×C₄
Frattini	C₂×C₈	C₂×D₁₅₇
Fitting	M₃₂×C₁₅₇	C₂
socle	C₂×C₁₅₇	#102
prime radical	C₂×D₁₂₅₆	C₂
cosocle	C₂×C₈×C₁₅₇	C₂²
hypercenter	M₃₂	D₁₅₇
hypocenter	C₁₅₇	#361
LCS	G ▷ C₈×C₁₅₇ ▷ C₄×C₁₅₇ ▷ C₂×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ M₃₂

Complements

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

N	H ≅ G/N	type
2. #19097707	C₂	semidirect
3. M₃₂×C₁₅₇	C₂	semidirect
25. C₁₅₇	#361	semidirect
28. M₃₂	D₁₅₇	semidirect