Subgroups — #108×D₁₅₇ #23757317

Order 10048.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	M₁₆×D₁₅₇	C₂	1	2	yes	maximal
2	C₂×C₈×D₁₅₇	C₂	1	1	yes	maximal, characteristic
3	#19097707	C₂	1	1	yes	maximal, characteristic, complemented
4	#19097706	C₂	1	2	yes	maximal, complemented
5	#108×C₁₅₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×D₁₅₇	C₂²	1	1	yes	characteristic
7	#14578938	C₂²	1	2	yes	—
8	#14578937	—	2	2	no	—
9	C₂×#11929434	C₂²	1	1	yes	characteristic
10	C₈×D₁₅₇	—	2	2	no	—
11	C₈×D₁₅₇	C₄	1	2	yes	—
12	C₈×D₁₅₇	C₄	1	2	yes	—
13	M₁₆×C₁₅₇	C₂²	1	2	yes	—
14	C₂×C₈×C₁₅₇	C₂²	1	1	yes	characteristic
15	C₂²×D₁₅₇	Q₈	1	1	yes	characteristic
16	C₂×Dic₁₅₇	Q₈	1	1	yes	characteristic
17	C₄×D₁₅₇	C₂×C₄	1	1	yes	characteristic
18	C₄×D₁₅₇	C₂×C₄	1	1	yes	characteristic
19	C₄×D₁₅₇	D₄	1	1	yes	characteristic
20	C₄×D₁₅₇	D₄	1	1	yes	characteristic
21	#11929434	—	2	2	no	—
22	#11929434	C₂×C₄	1	2	yes	—
23	C₂×C₄×C₁₅₇	C₂³	1	1	yes	characteristic
24	C₈×C₁₅₇	—	2	2	no	—
25	C₈×C₁₅₇	C₂×C₄	1	2	yes	—
26	C₂²×C₁₅₇	C₂×Q₈	1	1	yes	characteristic
27	C₂×D₁₅₇	—	2	2	no	—
28	C₂×D₁₅₇	C₄⋊C₄	1	1	yes	characteristic
29	C₂×D₁₅₇	C₄⋊C₄	1	1	yes	characteristic
30	C₄×C₁₅₇	C₂²×C₄	1	1	yes	characteristic
31	C₄×C₁₅₇	C₂×D₄	1	1	yes	characteristic
32	Dic₁₅₇	C₄⋊C₄	1	1	yes	characteristic
33	Dic₁₅₇	C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₁₅₇	—	2	1	no	—
35	C₂×C₁₅₇	C₂×C₄⋊C₄	1	1	yes	characteristic
36	D₁₅₇	—	2	1	no	—
37	D₁₅₇	#108	1	2	yes	direct product factor
38	C₁₅₇	C₂×#108	1	1	yes	characteristic, complemented, Sylow
39	C₂×#108	—	157	1	no	maximal, Sylow
40	C₂×M₁₆	—	157	2	no	—
41	C₂²×C₈	—	157	1	no	—
42	#108	—	157	2	no	—
43	#108	—	157	1	no	—
44	#108	D₁₅₇	1	1	yes	characteristic, direct product factor
45	C₂²×C₄	—	157	1	no	—
46	M₁₆	—	314	2	no	—
47	M₁₆	—	157	2	no	—
48	M₁₆	C₂×D₁₅₇	1	2	yes	—
49	C₂×C₈	—	314	2	no	—
50	C₂×C₈	—	157	1	no	—
51	C₂×C₈	—	157	2	no	—
52	C₂×C₈	—	157	2	no	—
53	C₂×C₈	C₂×D₁₅₇	1	1	yes	characteristic
54	C₂³	—	157	1	no	—
55	C₂×C₄	—	157	1	no	—
56	C₂×C₄	—	157	1	no	—
57	C₂×C₄	—	157	1	no	—
58	C₂×C₄	—	157	1	no	—
59	C₂×C₄	—	157	1	no	—
60	C₂×C₄	C₂²×D₁₅₇	1	1	yes	characteristic
61	C₈	—	2	2	no	—
62	C₈	—	314	2	no	—
63	C₈	—	157	2	no	—
64	C₈	C₄×D₁₅₇	1	2	yes	—
65	C₂²	—	314	2	no	—
66	C₂²	—	157	1	no	—
67	C₂²	—	157	1	no	—
68	C₂²	Q₈×D₁₅₇	1	1	yes	characteristic
69	C₄	—	157	1	no	—
70	C₄	—	157	1	no	—
71	C₄	C₂×C₄×D₁₅₇	1	1	yes	characteristic
72	C₄	D₄×D₁₅₇	1	1	yes	characteristic
73	C₂	—	2	1	no	—
74	C₂	—	314	1	no	—
75	C₂	—	157	2	no	—
76	C₂	C₄⋊C₄×D₁₅₇	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₄×D₁₅₇
commutator	C₄×C₁₅₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₁₅₇
Fitting	#108×C₁₅₇	C₂
socle	C₂×C₁₅₇	C₂×C₄⋊C₄
prime radical	C₂²×D₁₅₇	Q₈
cosocle	C₂×C₄×C₁₅₇	C₂³
hypercenter	#108	D₁₅₇
hypocenter	C₁₅₇	C₂×#108
LCS	G ▷ C₄×C₁₅₇ ▷ C₂×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #108

Complements

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

N	H ≅ G/N	type
3. #19097707	C₂	semidirect
4. #19097706	C₂	semidirect
5. #108×C₁₅₇	C₂	semidirect
37. D₁₅₇	#108	direct (N × H)
38. C₁₅₇	C₂×#108	semidirect
44. #108	D₁₅₇	direct (N × H)

Subgroups — #108×D157 #23757317

Conjugacy classes of subgroups

Complements

Subgroups — #108×D₁₅₇ #23757317