Subgroups — #1338×C₁₅₇ #34095696

Order 20096.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#446×C₁₅₇	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₁₆×C₁₅₇	C₂	1	1	yes	maximal, characteristic
3	#346×C₁₅₇	C₂	1	1	yes	maximal, characteristic
4	C₄×Q₈×C₁₅₇	C₄	1	1	yes	characteristic
5	C₂×C₁₆×C₁₅₇	—	2	1	no	—
6	C₂×C₁₆×C₁₅₇	—	2	1	no	—
7	C₄⋊C₈×C₁₅₇	—	2	1	no	—
8	C₄⋊C₈×C₁₅₇	C₄	1	1	yes	characteristic
9	#97×C₁₅₇	—	2	1	no	—
10	C₄×C₈×C₁₅₇	C₂²	1	1	yes	characteristic
11	C₂×Q₈×C₁₅₇	C₈	1	1	yes	characteristic
12	C₂×C₈×C₁₅₇	—	2	1	no	—
13	C₂×C₈×C₁₅₇	D₄	1	1	yes	characteristic
14	C₂×C₈×C₁₅₇	D₄	1	1	yes	characteristic
15	C₄⋊C₄×C₁₅₇	—	2	1	no	—
16	C₄⋊C₄×C₁₅₇	C₈	1	1	yes	characteristic
17	C₄²×C₁₅₇	—	2	1	no	—
18	C₄²×C₁₅₇	C₂×C₄	1	1	yes	characteristic
19	C₁₆×C₁₅₇	—	2	2	no	—
20	C₁₆×C₁₅₇	—	4	1	no	—
21	Q₈×C₁₅₇	—	4	1	no	—
22	C₂×C₄×C₁₅₇	—	2	1	no	—
23	C₂×C₄×C₁₅₇	—	2	1	no	—
24	C₂×C₄×C₁₅₇	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₁₅₇	C₂×C₈	1	1	yes	characteristic
26	C₂×C₄×C₁₅₇	M₁₆	1	1	yes	characteristic
27	C₈×C₁₅₇	—	2	1	no	—
28	C₈×C₁₅₇	—	4	1	no	—
29	C₈×C₁₅₇	SD₁₆	1	1	yes	characteristic
30	C₈×C₁₅₇	Q₁₆	1	1	yes	characteristic
31	C₂²×C₁₅₇	C₂²⋊C₈	1	1	yes	characteristic
32	C₄×C₁₅₇	—	2	1	no	—
33	C₄×C₁₅₇	—	2	1	no	—
34	C₄×C₁₅₇	—	4	1	no	—
35	C₄×C₁₅₇	—	4	1	no	—
36	C₄×C₁₅₇	#103	1	1	yes	characteristic
37	C₄×C₁₅₇	#104	1	1	yes	characteristic
38	C₂×C₁₅₇	Q₈⋊C₈	1	1	yes	characteristic
39	C₂×C₁₅₇	#349	1	1	yes	characteristic
40	C₂×C₁₅₇	#350	1	1	yes	characteristic
41	C₁₅₇	#1338	1	1	yes	characteristic, direct product factor, Sylow
42	#1338	C₁₅₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	#446	C₂×C₁₅₇	1	1	yes	characteristic
44	C₄⋊C₁₆	C₂×C₁₅₇	1	1	yes	characteristic
45	#346	C₂×C₁₅₇	1	1	yes	characteristic
46	C₄×Q₈	C₄×C₁₅₇	1	1	yes	characteristic
47	C₂×C₁₆	—	2	1	no	—
48	C₂×C₁₆	—	2	1	no	—
49	C₄⋊C₈	—	2	1	no	—
50	C₄⋊C₈	C₄×C₁₅₇	1	1	yes	characteristic
51	#97	—	2	1	no	—
52	C₄×C₈	C₂²×C₁₅₇	1	1	yes	characteristic
53	C₂×Q₈	C₈×C₁₅₇	1	1	yes	characteristic
54	C₂×C₈	—	2	1	no	—
55	C₂×C₈	D₄×C₁₅₇	1	1	yes	characteristic
56	C₂×C₈	D₄×C₁₅₇	1	1	yes	characteristic
57	C₄⋊C₄	—	2	1	no	—
58	C₄⋊C₄	C₈×C₁₅₇	1	1	yes	characteristic
59	C₄²	—	2	1	no	—
60	C₄²	C₂×C₄×C₁₅₇	1	1	yes	characteristic
61	C₁₆	—	2	2	no	—
62	C₁₆	—	4	1	no	—
63	Q₈	—	4	1	no	—
64	C₂×C₄	—	2	1	no	—
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	C₂²⋊C₄×C₁₅₇	1	1	yes	characteristic
67	C₂×C₄	C₂×C₈×C₁₅₇	1	1	yes	characteristic
68	C₂×C₄	M₁₆×C₁₅₇	1	1	yes	characteristic
69	C₈	—	2	1	no	—
70	C₈	—	4	1	no	—
71	C₈	SD₁₆×C₁₅₇	1	1	yes	characteristic
72	C₈	Q₁₆×C₁₅₇	1	1	yes	characteristic
73	C₂²	C₂²⋊C₈×C₁₅₇	1	1	yes	characteristic
74	C₄	—	2	1	no	—
75	C₄	—	2	1	no	—
76	C₄	—	4	1	no	—
77	C₄	—	4	1	no	—
78	C₄	#103×C₁₅₇	1	1	yes	characteristic
79	C₄	#104×C₁₅₇	1	1	yes	characteristic
80	C₂	Q₈⋊C₈×C₁₅₇	1	1	yes	characteristic
81	C₂	#349×C₁₅₇	1	1	yes	characteristic
82	C₂	#350×C₁₅₇	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
41. C₁₅₇	#1338	direct (N × H)
42. #1338	C₁₅₇	direct (N × H)

Maximal subgroups

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

subgroup	index
#446×C₁₅₇	2
C₄⋊C₁₆×C₁₅₇	2
#346×C₁₅₇	2
#1338	157

Subgroups — #1338×C157 #34095696

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1338×C₁₅₇ #34095696