Subgroups — #34115206

Order 20096.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₅₇⋊#108	C₂	1	2	yes	maximal
2	C₂×#19097710	C₂	1	1	yes	maximal, characteristic
3	D₁₅₇⋊M₁₆	—	2	2	no	—
4	#19097842	—	2	2	no	—
5	#19097841	C₄	1	4	yes	—
6	C₂×C₈×D₁₅₇	C₂²	1	1	yes	characteristic
7	#19097710	—	2	2	no	—
8	C₂×#14578929	C₄	1	1	yes	characteristic
9	C₂×C₁₆×C₁₅₇	C₄	1	1	yes	characteristic
10	#14578964	—	2	4	no	—
11	#14578963	—	4	2	no	—
12	D₁₅₇⋊C₈	—	4	2	no	—
13	C₂×C₄×D₁₅₇	D₄	1	1	yes	characteristic
14	C₂×#11929434	Q₈	1	1	yes	characteristic
15	C₈×D₁₅₇	C₂×C₄	1	2	yes	—
16	C₈×D₁₅₇	D₄	1	2	yes	—
17	#14578929	—	2	1	no	—
18	C₂×C₈×C₁₅₇	C₂×C₄	1	1	yes	characteristic
19	C₁₆×C₁₅₇	—	2	1	no	—
20	#11929441	—	4	4	no	—
21	C₂²×D₁₅₇	Q₁₆	1	1	yes	characteristic
22	C₂×Dic₁₅₇	D₈	1	1	yes	characteristic
23	C₄×D₁₅₇	C₂²⋊C₄	1	2	yes	—
24	C₄×D₁₅₇	SD₁₆	1	2	yes	—
25	#11929434	C₄⋊C₄	1	2	yes	—
26	C₂×C₄×C₁₅₇	C₄⋊C₄	1	1	yes	characteristic
27	C₈×C₁₅₇	C₄²	1	1	yes	characteristic
28	C₈×C₁₅₇	C₂²⋊C₄	1	1	yes	characteristic
29	C₂²×C₁₅₇	#107	1	1	yes	characteristic
30	C₂×D₁₅₇	—	4	1	no	—
31	C₂×D₁₅₇	#103	1	2	yes	—
32	C₄×C₁₅₇	#95	1	1	yes	characteristic
33	C₄×C₁₅₇	#106	1	1	yes	characteristic
34	Dic₁₅₇	#102	1	2	yes	—
35	C₂×C₁₅₇	—	2	1	no	—
36	C₂×C₁₅₇	#340	1	1	yes	characteristic
37	D₁₅₇	—	2	2	no	—
38	C₁₅₇	#1385	1	1	yes	characteristic, complemented, Sylow
39	#1385	—	157	1	no	maximal, Sylow
40	C₂×M₃₂	—	157	1	no	—
41	C₂×#108	—	157	2	no	—
42	C₂×M₁₆	—	314	2	no	—
43	C₂²×C₈	—	157	1	no	—
44	M₃₂	—	314	2	no	—
45	C₂×C₁₆	—	157	1	no	—
46	C₂×C₁₆	#10597845	1	1	yes	characteristic
47	#108	—	314	2	no	—
48	#108	—	157	4	no	—
49	C₂²×C₄	—	157	1	no	—
50	M₁₆	—	314	4	no	—
51	M₁₆	—	628	2	no	—
52	C₂×C₈	—	628	2	no	—
53	C₂×C₈	—	157	1	no	—
54	C₂×C₈	—	157	2	no	—
55	C₂×C₈	—	157	2	no	—
56	C₂×C₈	C₂×#10597845	1	1	yes	characteristic
57	C₁₆	—	2	1	no	—
58	C₁₆	—	314	1	no	—
59	C₂³	—	157	1	no	—
60	C₂×C₄	—	157	1	no	—
61	C₂×C₄	—	157	2	no	—
62	C₂×C₄	—	157	2	no	—
63	C₂×C₄	C₄⋊#10597845	1	1	yes	characteristic
64	C₈	—	628	4	no	—
65	C₈	—	157	2	no	—
66	C₈	C₄×#10597845	1	1	yes	characteristic
67	C₈	C₂²⋊#10597845	1	1	yes	characteristic
68	C₂²	—	628	1	no	—
69	C₂²	—	157	2	no	—
70	C₂²	#19097840	1	1	yes	characteristic
71	C₄	—	157	2	no	—
72	C₄	(C₂×#10597845)⋊C₄	1	1	yes	characteristic
73	C₄	#19097839	1	1	yes	characteristic
74	C₂	—	2	1	no	—
75	C₂	—	314	2	no	—
76	C₂	#23758147	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#19097839
commutator	C₈×C₁₅₇	C₄²
Frattini	C₂×C₈	C₂×#10597845
Fitting	C₂×C₁₆×C₁₅₇	C₄
socle	C₂×C₁₅₇	#340
prime radical	C₂²×D₁₅₇	Q₁₆
cosocle	C₂×C₈×D₁₅₇	C₂²
hypercenter	C₂×C₁₆	#10597845
hypocenter	C₁₅₇	#1385
LCS	G ▷ C₈×C₁₅₇ ▷ C₄×C₁₅₇ ▷ C₂×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
38. C₁₅₇	#1385	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
D₁₅₇⋊#108	2
C₂×#19097710	2
#1385	157