Subgroups — #1311×C₁₅₇ #34095669

Order 20096.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₆×C₁₅₇	C₂	1	2	yes	maximal
2	C₈²×C₁₅₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆×C₁₅₇	C₄	1	4	yes	—
4	C₄×C₈×C₁₅₇	C₄	1	2	yes	—
5	C₄×C₈×C₁₅₇	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₁₅₇	C₈	1	4	yes	—
7	C₂×C₈×C₁₅₇	C₂×C₄	1	2	yes	—
8	C₄²×C₁₅₇	C₂×C₄	1	1	yes	characteristic
9	C₁₆×C₁₅₇	C₈	1	8	yes	complemented
10	C₂×C₄×C₁₅₇	C₄²	1	1	yes	characteristic
11	C₂×C₄×C₁₅₇	C₂×C₈	1	2	yes	—
12	C₈×C₁₅₇	—	2	4	no	—
13	C₈×C₁₅₇	C₂×C₈	1	4	yes	—
14	C₂²×C₁₅₇	C₄×C₈	1	1	yes	characteristic
15	C₄×C₁₅₇	C₄×C₈	1	2	yes	—
16	C₄×C₁₅₇	M₃₂	1	4	yes	—
17	C₂×C₁₅₇	C₈²	1	1	yes	characteristic
18	C₂×C₁₅₇	#346	1	2	yes	—
19	C₁₅₇	#1311	1	1	yes	characteristic, direct product factor, Sylow
20	#1311	C₁₅₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₄×C₁₆	C₂×C₁₅₇	1	2	yes	—
22	C₈²	C₂×C₁₅₇	1	1	yes	characteristic
23	C₂×C₁₆	C₄×C₁₅₇	1	4	yes	—
24	C₄×C₈	C₄×C₁₅₇	1	2	yes	—
25	C₄×C₈	C₂²×C₁₅₇	1	1	yes	characteristic
26	C₂×C₈	C₈×C₁₅₇	1	4	yes	—
27	C₂×C₈	C₂×C₄×C₁₅₇	1	2	yes	—
28	C₄²	C₂×C₄×C₁₅₇	1	1	yes	characteristic
29	C₁₆	C₈×C₁₅₇	1	8	yes	complemented
30	C₂×C₄	C₄²×C₁₅₇	1	1	yes	characteristic
31	C₂×C₄	C₂×C₈×C₁₅₇	1	2	yes	—
32	C₈	—	2	4	no	—
33	C₈	C₂×C₈×C₁₅₇	1	4	yes	—
34	C₂²	C₄×C₈×C₁₅₇	1	1	yes	characteristic
35	C₄	C₄×C₈×C₁₅₇	1	2	yes	—
36	C₄	M₃₂×C₁₅₇	1	4	yes	—
37	C₂	C₈²×C₁₅₇	1	1	yes	characteristic
38	C₂	#346×C₁₅₇	1	2	yes	—

	subgroup	G/H
center	C₄×C₈×C₁₅₇	C₂²
commutator	C₂	C₈²×C₁₅₇
Frattini, cosocle	C₄×C₈	C₂²×C₁₅₇
socle, prime radical	C₂²×C₁₅₇	C₄×C₈
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₈×C₁₅₇ ◁ G

Complements

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

N	H ≅ G/N	type
9. C₁₆×C₁₅₇	C₈	semidirect
19. C₁₅₇	#1311	direct (N × H)
20. #1311	C₁₅₇	direct (N × H)
29. C₁₆	C₈×C₁₅₇	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₁₆×C₁₅₇	2
C₈²×C₁₅₇	2
#1311	157

Subgroups — #1311×C157 #34095669

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1311×C₁₅₇ #34095669