Group #23758241 — subgroups

Subgroups — D₁₅₇⋊(C₂²⋊C₈) #23758241

Order 10048.

202 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₅₇⋊C₈	C₂	1	2	yes	maximal, complemented
2	#19097828	C₂	1	2	yes	maximal, complemented
3	C₂²⋊#11929441	C₂	1	2	yes	maximal, complemented
4	C₂²×C₄×D₁₅₇	C₂	1	1	yes	maximal, characteristic
5	D₁₅₇⋊C₈	—	2	4	no	—
6	C₂×#11929441	C₂²	1	4	yes	complemented
7	C₂³×D₁₅₇	C₄	1	1	yes	characteristic
8	C₂²×Dic₁₅₇	C₂²	1	1	yes	characteristic
9	C₂×C₄×D₁₅₇	—	2	4	no	—
10	C₂×C₄×D₁₅₇	C₄	1	1	yes	characteristic
11	C₂×C₄×D₁₅₇	C₄	1	1	yes	characteristic
12	C₂×C₄×D₁₅₇	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₁₅₇	C₂²	1	1	yes	characteristic
14	C₂²×C₄×C₁₅₇	C₄	1	1	yes	characteristic
15	#11929441	—	2	4	no	—
16	C₂²×D₁₅₇	—	2	2	no	—
17	C₂²×D₁₅₇	—	2	2	no	—
18	C₂²×D₁₅₇	C₈	1	4	yes	complemented
19	C₂²×D₁₅₇	C₂×C₄	1	1	yes	characteristic
20	C₂²×D₁₅₇	C₂×C₄	1	1	yes	characteristic
21	C₂×Dic₁₅₇	—	2	2	no	—
22	C₂×Dic₁₅₇	C₂×C₄	1	1	yes	characteristic
23	C₂×Dic₁₅₇	C₂³	1	1	yes	characteristic
24	C₄×D₁₅₇	—	2	2	no	—
25	C₄×D₁₅₇	—	2	2	no	—
26	C₄×D₁₅₇	—	2	2	no	—
27	C₄×D₁₅₇	D₄	1	4	yes	—
28	C₂³×C₁₅₇	C₂×C₄	1	1	yes	characteristic
29	C₂×C₄×C₁₅₇	—	2	2	no	—
30	C₂×C₄×C₁₅₇	C₂×C₄	1	1	yes	characteristic
31	C₂×C₄×C₁₅₇	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₁₅₇	—	2	1	no	—
33	C₂²×C₁₅₇	—	2	1	no	—
34	C₂²×C₁₅₇	C₂×C₈	1	2	yes	complemented
35	C₂²×C₁₅₇	C₂²×C₄	1	1	yes	characteristic
36	C₂×D₁₅₇	—	2	1	no	—
37	C₂×D₁₅₇	—	2	1	no	—
38	C₂×D₁₅₇	—	2	8	no	—
39	C₂×D₁₅₇	C₂²⋊C₄	1	2	yes	—
40	C₂×D₁₅₇	C₂×C₈	1	2	yes	—
41	C₂×D₁₅₇	C₂×C₈	1	2	yes	complemented
42	C₂×D₁₅₇	M₁₆	1	2	yes	—
43	C₄×C₁₅₇	—	2	1	no	—
44	C₄×C₁₅₇	C₂²⋊C₄	1	2	yes	—
45	Dic₁₅₇	—	2	1	no	—
46	Dic₁₅₇	C₂×D₄	1	2	yes	—
47	C₂×C₁₅₇	—	2	2	no	—
48	C₂×C₁₅₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
49	C₂×C₁₅₇	C₂²×C₈	1	1	yes	characteristic
50	C₂×C₁₅₇	C₂×M₁₆	1	1	yes	characteristic
51	D₁₅₇	—	2	2	no	—
52	D₁₅₇	C₂²⋊C₈	1	4	yes	complemented
53	C₁₅₇	C₂×C₂²⋊C₈	1	1	yes	characteristic, complemented, Sylow
54	C₂×C₂²⋊C₈	—	157	1	no	maximal, Sylow
55	C₂³×C₄	—	157	1	no	—
56	C₂²×C₈	—	157	2	no	—
57	C₂²⋊C₈	—	157	2	no	—
58	C₂²⋊C₈	—	157	2	no	—
59	C₂⁴	—	157	1	no	—
60	C₂²×C₄	—	314	4	no	—
61	C₂²×C₄	—	157	1	no	—
62	C₂²×C₄	—	157	1	no	—
63	C₂²×C₄	—	157	1	no	—
64	C₂²×C₄	—	157	1	no	—
65	C₂²×C₄	—	157	1	no	—
66	C₂²×C₄	#10597845	1	1	yes	characteristic
67	C₂×C₈	—	314	4	no	—
68	C₂×C₈	—	157	4	no	—
69	C₂³	—	314	2	no	—
70	C₂³	—	314	2	no	—
71	C₂³	—	157	4	no	—
72	C₂³	—	157	1	no	—
73	C₂³	—	157	1	no	—
74	C₂³	C₂×#10597845	1	1	yes	characteristic
75	C₂×C₄	—	2	2	no	—
76	C₂×C₄	—	314	2	no	—
77	C₂×C₄	—	314	2	no	—
78	C₂×C₄	—	314	2	no	—
79	C₂×C₄	—	314	2	no	—
80	C₂×C₄	—	157	1	no	—
81	C₂×C₄	—	157	1	no	—
82	C₂×C₄	—	157	4	no	—
83	C₂×C₄	C₂×#10597845	1	1	yes	characteristic
84	C₂×C₄	C₂×#10597845	1	1	yes	characteristic
85	C₈	—	314	4	no	—
86	C₂²	—	2	1	no	—
87	C₂²	—	2	1	no	—
88	C₂²	—	314	8	no	—
89	C₂²	—	314	1	no	—
90	C₂²	—	314	1	no	—
91	C₂²	—	157	2	no	—
92	C₂²	—	157	2	no	—
93	C₂²	—	157	2	no	—
94	C₂²	—	157	2	no	—
95	C₂²	D₁₅₇⋊C₈	1	2	yes	complemented
96	C₂²	C₂²×#10597845	1	1	yes	characteristic
97	C₄	—	2	1	no	—
98	C₄	—	314	1	no	—
99	C₄	—	157	2	no	—
100	C₄	C₂²⋊#10597845	1	2	yes	—
101	C₂	—	2	2	no	—
102	C₂	—	314	2	no	—
103	C₂	—	157	4	no	—
104	C₂	C₂×C₂²⋊#10597845	1	1	yes	characteristic
105	C₂	C₂×D₁₅₇⋊C₈	1	1	yes	characteristic
106	C₂	D₁₅₇⋊M₁₆	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×D₁₅₇⋊C₈

C₂

yes

maximal, complemented

#19097828

C₂

yes

maximal, complemented

C₂²⋊#11929441

C₂

yes

maximal, complemented

C₂²×C₄×D₁₅₇

C₂

yes

maximal, characteristic

D₁₅₇⋊C₈

—

C₂×#11929441

C₂²

yes

complemented

C₂³×D₁₅₇

C₄

yes

characteristic

C₂²×Dic₁₅₇

C₂²

yes

characteristic

C₂×C₄×D₁₅₇

—

C₂×C₄×D₁₅₇

C₄

yes

characteristic

C₂×C₄×D₁₅₇

C₄

yes

characteristic

C₂×C₄×D₁₅₇

C₂²

yes

characteristic

C₂×C₄×D₁₅₇

C₂²

yes

characteristic

C₂²×C₄×C₁₅₇

C₄

yes

characteristic

#11929441

—

C₂²×D₁₅₇

—

C₂²×D₁₅₇

—

C₂²×D₁₅₇

C₈

yes

complemented

C₂²×D₁₅₇

C₂×C₄

yes

characteristic

C₂²×D₁₅₇

C₂×C₄

yes

characteristic

C₂×Dic₁₅₇

—

C₂×Dic₁₅₇

C₂×C₄

yes

characteristic

C₂×Dic₁₅₇

C₂³

yes

characteristic

C₄×D₁₅₇

—

C₄×D₁₅₇

—

C₄×D₁₅₇

—

C₄×D₁₅₇

D₄

yes

—

C₂³×C₁₅₇

C₂×C₄

yes

characteristic

C₂×C₄×C₁₅₇

—

C₂×C₄×C₁₅₇

C₂×C₄

yes

characteristic

C₂×C₄×C₁₅₇

C₂×C₄

yes

characteristic

C₂²×C₁₅₇

—

C₂²×C₁₅₇

—

C₂²×C₁₅₇

C₂×C₈

yes

complemented

C₂²×C₁₅₇

C₂²×C₄

yes

characteristic

C₂×D₁₅₇

—

C₂×D₁₅₇

—

C₂×D₁₅₇

—

C₂×D₁₅₇

C₂²⋊C₄

yes

—

C₂×D₁₅₇

C₂×C₈

yes

—

C₂×D₁₅₇

C₂×C₈

yes

complemented

C₂×D₁₅₇

M₁₆

yes

—

C₄×C₁₅₇

—

C₄×C₁₅₇

C₂²⋊C₄

yes

—

Dic₁₅₇

—

Dic₁₅₇

C₂×D₄

yes

—

C₂×C₁₅₇

—

C₂×C₁₅₇

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₁₅₇

C₂²×C₈

yes

characteristic

C₂×C₁₅₇

C₂×M₁₆

yes

characteristic

D₁₅₇

—

D₁₅₇

C₂²⋊C₈

yes

complemented

C₁₅₇

C₂×C₂²⋊C₈

yes

characteristic, complemented, Sylow

C₂×C₂²⋊C₈

—

157

maximal, Sylow

C₂³×C₄

—

157

—

C₂²×C₈

—

157

—

C₂²⋊C₈

—

157

—

C₂²⋊C₈

—

157

—

C₂⁴

—

157

—

C₂²×C₄

—

314

—

C₂²×C₄

—

157

—

C₂²×C₄

—

157

—

C₂²×C₄

—

157

—

C₂²×C₄

—

157

—

C₂²×C₄

—

157

—

C₂²×C₄

#10597845

yes

characteristic

C₂×C₈

—

314

—

C₂×C₈

—

157

—

C₂³

—

314

—

C₂³

—

314

—

C₂³

—

157

—

C₂³

—

157

—

C₂³

—

157

—

C₂³

C₂×#10597845

yes

characteristic

C₂×C₄

—

C₂×C₄

—

314

—

C₂×C₄

—

314

—

C₂×C₄

—

314

—

C₂×C₄

—

314

—

C₂×C₄

—

157

—

C₂×C₄

—

157

—

C₂×C₄

—

157

—

C₂×C₄

yes

C₂×C₄

yes

C₈

—

314

—

C₂²

—

C₂²

—

C₂²

—

314

—

C₂²

—

314

—

C₂²

—

314

—

C₂²

—

157

—

C₂²

—

157

—

C₂²

—

157

—

C₂²

—

157

—

C₂²

D₁₅₇⋊C₈

yes

complemented

C₂²

C₂²×#10597845

yes

characteristic

C₄

—

C₄

—

314

—

C₄

—

157

—

100

C₄

C₂²⋊#10597845

yes

—

101

C₂

—

102

C₂

—

314

—

103

C₂

—

157

—

104

C₂

C₂×C₂²⋊#10597845

yes

characteristic

105

C₂

C₂×D₁₅₇⋊C₈

yes

characteristic

106

C₂

D₁₅₇⋊M₁₆

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#10597845
commutator	C₂×C₁₅₇	C₂²×C₈
Frattini	C₂²	C₂²×#10597845
Fitting	C₂²×C₄×C₁₅₇	C₄
socle	C₂²×C₁₅₇	C₂²×C₄
prime radical	C₂³×D₁₅₇	C₄
cosocle	C₂×Dic₁₅₇	C₂³
hypercenter	C₂²×C₄	#10597845
hypocenter	C₁₅₇	C₂×C₂²⋊C₈
LCS	G ▷ C₂×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄

subgroup

G/H

center

C₂×C₄

C₂×#10597845

commutator

C₂×C₁₅₇

C₂²×C₈

Frattini

C₂²

C₂²×#10597845

Fitting

C₂²×C₄×C₁₅₇

C₄

socle

C₂²×C₁₅₇

C₂²×C₄

prime radical

C₂³×D₁₅₇

C₄

cosocle

C₂×Dic₁₅₇

C₂³

hypercenter

C₂²×C₄

#10597845

hypocenter

C₁₅₇

C₂×C₂²⋊C₈

LCS

G ▷ C₂×C₁₅₇ ▷ C₁₅₇

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄

N	H ≅ G/N	type
1. C₂×D₁₅₇⋊C₈	C₂	semidirect
2. #19097828	C₂	semidirect
3. C₂²⋊#11929441	C₂	semidirect
6. C₂×#11929441	C₂²	semidirect
18. C₂²×D₁₅₇	C₈	semidirect
34. C₂²×C₁₅₇	C₂×C₈	semidirect
41. C₂×D₁₅₇	C₂×C₈	semidirect
52. D₁₅₇	C₂²⋊C₈	semidirect
53. C₁₅₇	C₂×C₂²⋊C₈	semidirect
95. C₂²	D₁₅₇⋊C₈	semidirect

H ≅ G/N

type

1. C₂×D₁₅₇⋊C₈

C₂

semidirect

2. #19097828

C₂

semidirect

3. C₂²⋊#11929441

C₂

semidirect

6. C₂×#11929441

C₂²

semidirect

18. C₂²×D₁₅₇

C₈

semidirect

34. C₂²×C₁₅₇

C₂×C₈

semidirect

41. C₂×D₁₅₇

C₂×C₈

semidirect

52. D₁₅₇

C₂²⋊C₈

semidirect

53. C₁₅₇

C₂×C₂²⋊C₈

semidirect

95. C₂²

D₁₅₇⋊C₈

semidirect

Subgroups — D₁₅₇⋊(C₂²⋊C₈) #23758241

Conjugacy classes of subgroups

Complements

Subgroups — D157⋊(C22⋊C8) #23758241

Conjugacy classes of subgroups

Complements

Subgroups — D₁₅₇⋊(C₂²⋊C₈) #23758241