Subgroups — #23757078

Order 10048.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₆₂₈	C₂	1	1	yes	maximal, characteristic
2	#19097705	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆×C₁₅₇	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₃₁₄	—	2	1	no	—
5	Dic₆₂₈	—	2	1	no	—
6	Dic₆₂₈	C₄	1	2	yes	complemented
7	C₄⋊Dic₁₅₇	—	2	1	no	—
8	C₂×C₈×C₁₅₇	C₂²	1	1	yes	characteristic
9	C₁₆×C₁₅₇	—	2	1	no	—
10	Dic₃₁₄	—	2	2	no	—
11	Dic₃₁₄	—	4	1	no	—
12	C₂×Dic₁₅₇	—	4	1	no	—
13	C₂×Dic₁₅₇	—	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	D₈	1	1	yes	characteristic
18	C₄×C₁₅₇	C₂²⋊C₄	1	1	yes	characteristic
19	C₄×C₁₅₇	SD₁₆	1	1	yes	characteristic
20	Dic₁₅₇	—	4	2	no	—
21	Dic₁₅₇	—	8	1	no	—
22	C₂×C₁₅₇	#102	1	1	yes	characteristic
23	C₂×C₁₅₇	SD₃₂	1	1	yes	characteristic
24	C₂×C₁₅₇	Q₃₂	1	1	yes	characteristic
25	C₁₅₇	#358	1	1	yes	characteristic, complemented, Sylow
26	#358	—	157	1	no	maximal, Sylow
27	C₂×Q₁₆	—	157	1	no	—
28	C₂×C₁₆	D₁₅₇	1	1	yes	characteristic
29	#107	—	157	1	no	—
30	C₂×Q₈	—	314	1	no	—
31	Q₁₆	—	314	1	no	—
32	Q₁₆	—	157	2	no	—
33	C₂×C₈	C₂×D₁₅₇	1	1	yes	characteristic
34	C₄⋊C₄	—	314	1	no	—
35	C₁₆	—	2	1	no	—
36	Q₈	—	314	2	no	—
37	Q₈	—	628	1	no	—
38	C₂×C₄	—	628	1	no	—
39	C₂×C₄	—	628	1	no	—
40	C₂×C₄	D₆₂₈	1	1	yes	characteristic
41	C₈	C₄×D₁₅₇	1	1	yes	characteristic
42	C₈	C₂²⋊D₁₅₇	1	1	yes	characteristic
43	C₂²	D₁₂₅₆	1	1	yes	characteristic
44	C₄	—	628	2	no	—
45	C₄	—	1256	1	no	—
46	C₄	#14578931	1	1	yes	characteristic
47	C₄	#14578943	1	1	yes	characteristic
48	C₂	#19097693	1	1	yes	characteristic
49	C₂	#19097716	1	1	yes	characteristic
50	C₂	Dic₁₂₅₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₁₂₅₆
commutator	C₈×C₁₅₇	C₂×C₄
Frattini	C₂×C₈	C₂×D₁₅₇
Fitting	C₂×C₁₆×C₁₅₇	C₂
socle, prime radical	C₂²×C₁₅₇	D₈
cosocle	C₂×C₈×C₁₅₇	C₂²
hypercenter	C₂×C₁₆	D₁₅₇
hypocenter	C₁₅₇	#358
LCS	G ▷ C₈×C₁₅₇ ▷ C₄×C₁₅₇ ▷ C₂×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
6. Dic₆₂₈	C₄	semidirect
25. C₁₅₇	#358	semidirect