Subgroups — #34115171

Order 20096.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23758195	C₂	1	2	yes	maximal
2	C₁₆×Dic₁₅₇	C₂	1	1	yes	maximal, characteristic
3	#19097845	—	2	2	no	—
4	C₂×#14578929	C₄	1	1	yes	characteristic
5	C₈×Dic₁₅₇	C₂²	1	1	yes	characteristic
6	C₂×C₁₆×C₁₅₇	C₄	1	1	yes	characteristic
7	#14578957	—	4	2	no	—
8	C₂×#11929434	D₄	1	1	yes	characteristic
9	C₄×Dic₁₅₇	Q₈	1	1	yes	characteristic
10	#14578929	—	2	1	no	—
11	C₂×C₈×C₁₅₇	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₁₅₇	C₈	1	2	yes	—
13	C₂×Dic₁₅₇	—	2	1	no	—
14	#11929434	D₈	1	1	yes	characteristic
15	#11929434	Q₁₆	1	1	yes	characteristic
16	C₂×C₄×C₁₅₇	C₄⋊C₄	1	1	yes	characteristic
17	C₈×C₁₅₇	C₂×C₈	1	1	yes	characteristic
18	C₈×C₁₅₇	M₁₆	1	1	yes	characteristic
19	C₂²×C₁₅₇	#108	1	1	yes	characteristic
20	C₄×C₁₅₇	C₄⋊C₈	1	1	yes	characteristic
21	C₄×C₁₅₇	#107	1	1	yes	characteristic
22	Dic₁₅₇	—	2	2	no	—
23	C₂×C₁₅₇	—	2	1	no	—
24	C₂×C₁₅₇	#335	1	1	yes	characteristic
25	C₁₅₇	#1373	1	1	yes	characteristic, complemented, Sylow
26	#1373	—	157	1	no	maximal, Sylow
27	#364	—	157	2	no	—
28	C₄×C₁₆	—	157	1	no	—
29	M₃₂	—	314	2	no	—
30	C₂×C₁₆	—	157	1	no	—
31	C₂×C₁₆	#10597845	1	1	yes	characteristic
32	C₄×C₈	—	157	1	no	—
33	C₂×C₈	—	157	1	no	—
34	C₂×C₈	C₂×#10597845	1	1	yes	characteristic
35	C₄²	—	157	1	no	—
36	C₁₆	—	314	1	no	—
37	C₁₆	—	628	2	no	—
38	C₁₆	#11929441	1	2	yes	—
39	C₂×C₄	—	314	1	no	—
40	C₂×C₄	C₄⋊#10597845	1	1	yes	characteristic
41	C₈	—	157	1	no	—
42	C₈	—	157	1	no	—
43	C₈	C₂×#11929441	1	1	yes	characteristic
44	C₈	#14578964	1	1	yes	characteristic
45	C₂²	#19097842	1	1	yes	characteristic
46	C₄	—	314	2	no	—
47	C₄	C₄⋊#11929441	1	1	yes	characteristic
48	C₄	#19097840	1	1	yes	characteristic
49	C₂	—	2	1	no	—
50	C₂	#23758136	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#19097840
commutator	C₈×C₁₅₇	C₂×C₈
Frattini	C₂×C₈	C₂×#10597845
Fitting	C₂×C₁₆×C₁₅₇	C₄
socle	C₂×C₁₅₇	#335
prime radical	C₂²×C₁₅₇	#108
cosocle	C₈×Dic₁₅₇	C₂²
hypercenter	C₂×C₁₆	#10597845
hypocenter	C₁₅₇	#1373
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
25. C₁₅₇	#1373	semidirect

Maximal subgroups

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

subgroup	index
#23758195	2
C₁₆×Dic₁₅₇	2
#1373	157