Subgroups — C₁₆×#10597845 #23758157

Order 10048.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₅₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₈×#10597845	C₂	1	1	yes	maximal, characteristic
3	C₁₆×D₁₅₇	C₂	1	1	yes	maximal, characteristic
4	D₁₅₇⋊C₈	C₄	1	1	yes	characteristic
5	C₄×#10597845	C₄	1	1	yes	characteristic
6	#14578957	C₄	1	2	yes	complemented
7	C₈×D₁₅₇	C₂²	1	1	yes	characteristic
8	#14578929	C₄	1	1	yes	characteristic, complemented
9	C₁₆×C₁₅₇	C₄	1	1	yes	characteristic, complemented
10	C₂×#10597845	C₈	1	2	yes	—
11	#11929441	C₈	1	2	yes	—
12	C₄×D₁₅₇	C₂×C₄	1	1	yes	characteristic
13	#11929434	C₂×C₄	1	1	yes	characteristic
14	C₈×C₁₅₇	C₂×C₄	1	1	yes	characteristic
15	C₂×D₁₅₇	C₂×C₈	1	1	yes	characteristic
16	#10597845	C₁₆	1	4	yes	direct product factor
17	C₄×C₁₅₇	C₄²	1	1	yes	characteristic
18	Dic₁₅₇	C₂×C₈	1	1	yes	characteristic
19	C₂×C₁₅₇	C₄×C₈	1	1	yes	characteristic
20	D₁₅₇	C₂×C₁₆	1	2	yes	—
21	C₁₅₇	C₄×C₁₆	1	1	yes	characteristic, complemented, Sylow
22	C₄×C₁₆	—	157	1	no	maximal, Sylow
23	C₂×C₁₆	—	157	1	no	—
24	C₂×C₁₆	—	157	1	no	—
25	C₄×C₈	—	157	1	no	—
26	C₂×C₈	—	157	1	no	—
27	C₂×C₈	—	157	1	no	—
28	C₄²	—	157	1	no	—
29	C₁₆	—	157	2	no	—
30	C₁₆	—	157	1	no	—
31	C₁₆	#10597845	1	1	yes	characteristic, direct product factor
32	C₂×C₄	—	157	2	no	—
33	C₂×C₄	—	157	1	no	—
34	C₈	—	157	2	no	—
35	C₈	—	157	1	no	—
36	C₈	C₂×#10597845	1	1	yes	characteristic
37	C₂²	—	157	1	no	—
38	C₄	—	157	4	no	—
39	C₄	—	157	1	no	—
40	C₄	C₄×#10597845	1	1	yes	characteristic
41	C₂	—	157	2	no	—
42	C₂	C₈×#10597845	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₁₆	#10597845
commutator, hypocenter	C₁₅₇	C₄×C₁₆
Frattini	C₈	C₂×#10597845
Fitting	C₁₆×C₁₅₇	C₄
socle	C₂×C₁₅₇	C₄×C₈
prime radical	C₂×D₁₅₇	C₂×C₈
cosocle	C₈×D₁₅₇	C₂²
LCS	G ▷ C₁₅₇
UCS	C₁ ◁ C₁₆

Complements

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

N	H ≅ G/N	type
6. #14578957	C₄	semidirect
8. #14578929	C₄	semidirect
9. C₁₆×C₁₅₇	C₄	semidirect
16. #10597845	C₁₆	direct (N × H)
21. C₁₅₇	C₄×C₁₆	semidirect
31. C₁₆	#10597845	direct (N × H)

Subgroups — C16×#10597845 #23758157

Conjugacy classes of subgroups

Complements

Subgroups — C₁₆×#10597845 #23758157