Subgroups — #11929441⋊C₈ #23758115

Order 10048.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#11929441	C₂	1	1	yes	maximal, characteristic
2	C₄×#11929441	C₂	1	1	yes	maximal, characteristic
3	C₈×Dic₁₅₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#11929441	C₄	1	2	yes	—
5	C₂×#11929441	C₄	1	2	yes	—
6	C₂×#11929434	C₄	1	1	yes	characteristic
7	C₄×Dic₁₅₇	C₂²	1	1	yes	characteristic
8	C₂×C₈×C₁₅₇	C₄	1	1	yes	characteristic
9	#11929441	—	2	2	no	—
10	#11929441	C₈	1	4	yes	complemented
11	C₂×Dic₁₅₇	C₂×C₄	1	1	yes	characteristic
12	C₂×Dic₁₅₇	C₂×C₄	1	1	yes	characteristic
13	#11929434	—	2	1	no	—
14	C₂×C₄×C₁₅₇	C₂×C₄	1	1	yes	characteristic
15	C₈×C₁₅₇	—	2	1	no	—
16	C₂²×C₁₅₇	C₄²	1	1	yes	characteristic
17	C₄×C₁₅₇	M₁₆	1	1	yes	characteristic
18	C₄×C₁₅₇	M₁₆	1	1	yes	characteristic
19	Dic₁₅₇	C₂×C₈	1	2	yes	—
20	Dic₁₅₇	M₁₆	1	2	yes	—
21	C₂×C₁₅₇	C₄×C₈	1	1	yes	characteristic
22	C₂×C₁₅₇	#97	1	1	yes	characteristic
23	C₂×C₁₅₇	#97	1	1	yes	characteristic
24	C₁₅₇	#322	1	1	yes	characteristic, complemented, Sylow
25	#322	—	157	1	no	maximal, Sylow
26	C₄×C₈	—	157	1	no	—
27	C₄×C₈	—	157	1	no	—
28	C₄×C₈	—	157	1	no	—
29	C₂×C₈	—	157	2	no	—
30	C₂×C₈	—	157	1	no	—
31	C₂×C₈	—	157	2	no	—
32	C₂×C₈	#10597845	1	1	yes	characteristic
33	C₄²	—	157	1	no	—
34	C₂×C₄	—	157	1	no	—
35	C₂×C₄	—	157	1	no	—
36	C₂×C₄	C₂×#10597845	1	1	yes	characteristic
37	C₈	—	2	1	no	—
38	C₈	—	314	2	no	—
39	C₈	—	314	1	no	—
40	C₈	—	157	4	no	—
41	C₂²	C₄×#10597845	1	1	yes	characteristic
42	C₄	—	157	2	no	—
43	C₄	—	157	2	no	—
44	C₄	#14578963	1	1	yes	characteristic
45	C₄	#14578964	1	1	yes	characteristic
46	C₂	C₈×#10597845	1	1	yes	characteristic
47	C₂	#19097825	1	1	yes	characteristic
48	C₂	#19097826	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×#10597845
commutator	C₂×C₁₅₇	C₄×C₈
Fitting	C₂×C₈×C₁₅₇	C₄
socle, prime radical	C₂²×C₁₅₇	C₄²
cosocle	C₄×Dic₁₅₇	C₂²
hypercenter	C₂×C₈	#10597845
hypocenter	C₁₅₇	#322
LCS	G ▷ C₂×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
10. #11929441	C₈	semidirect
24. C₁₅₇	#322	semidirect

Subgroups — #11929441⋊C8 #23758115

Conjugacy classes of subgroups

Complements

Subgroups — #11929441⋊C₈ #23758115