Group #23752095 — subgroups

Subgroups — #23752095

Order 9664.

154 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 69 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×C₄⋊Dic₁₅₁	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₁₅₁⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×Dic₁₅₁	C₂	1	1	yes	maximal, characteristic
4	C₁₅₁⋊#95	C₂	1	1	yes	maximal, characteristic
5	C₁₅₁⋊#95	C₂	1	1	yes	maximal, characteristic
6	C₁₅₁⋊#95	C₂	1	1	yes	maximal, characteristic
7	#95×C₁₅₁	C₂	1	1	yes	maximal, characteristic
8	C₂²×Dic₁₅₁	C₂²	1	1	yes	characteristic
9	C₂²×Dic₁₅₁	C₂²	1	1	yes	characteristic
10	C₂²×Dic₁₅₁	C₂²	1	1	yes	characteristic
11	C₂²×Dic₁₅₁	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₁₅₁	C₄	1	4	yes	complemented
13	Dic₁₅₁⋊C₄	—	2	2	no	—
14	C₄×Dic₁₅₁	—	2	2	no	—
15	C₂²×C₄×C₁₅₁	C₂²	1	1	yes	characteristic
16	C₂²×C₄×C₁₅₁	C₂²	1	1	yes	characteristic
17	C₂²×C₄×C₁₅₁	C₂²	1	1	yes	characteristic
18	C₂×Dic₁₅₁	—	2	1	no	—
19	C₂×Dic₁₅₁	—	2	1	no	—
20	C₂×Dic₁₅₁	—	2	1	no	—
21	C₂×Dic₁₅₁	—	2	1	no	—
22	C₂×Dic₁₅₁	—	2	1	no	—
23	C₂×Dic₁₅₁	—	2	1	no	—
24	C₂×Dic₁₅₁	—	2	1	no	—
25	C₂×Dic₁₅₁	—	2	1	no	—
26	C₂×Dic₁₅₁	—	2	1	no	—
27	C₂×Dic₁₅₁	C₂×C₄	1	2	yes	—
28	C₂×Dic₁₅₁	C₂×C₄	1	2	yes	—
29	C₂×Dic₁₅₁	D₄	1	2	yes	—
30	C₂³×C₁₅₁	C₂³	1	1	yes	characteristic
31	C₂×C₄×C₁₅₁	—	2	1	no	—
32	C₂×C₄×C₁₅₁	—	2	1	no	—
33	C₂×C₄×C₁₅₁	—	2	1	no	—
34	C₂×C₄×C₁₅₁	—	2	1	no	—
35	C₂×C₄×C₁₅₁	—	2	1	no	—
36	C₂×C₄×C₁₅₁	—	2	1	no	—
37	C₂×C₄×C₁₅₁	—	2	1	no	—
38	C₂×C₄×C₁₅₁	C₂×C₄	1	2	yes	—
39	C₂×C₄×C₁₅₁	Q₈	1	2	yes	—
40	C₂²×C₁₅₁	C₂²×C₄	1	1	yes	characteristic
41	C₂²×C₁₅₁	C₂×D₄	1	1	yes	characteristic
42	C₂²×C₁₅₁	C₂×Q₈	1	1	yes	characteristic
43	C₂²×C₁₅₁	#41	1	1	yes	characteristic
44	C₂²×C₁₅₁	#41	1	1	yes	characteristic
45	C₂²×C₁₅₁	#41	1	1	yes	characteristic
46	C₂²×C₁₅₁	#41	1	1	yes	characteristic
47	C₄×C₁₅₁	—	2	2	no	—
48	C₄×C₁₅₁	—	2	2	no	—
49	C₄×C₁₅₁	—	4	1	no	—
50	Dic₁₅₁	—	2	2	no	—
51	Dic₁₅₁	—	2	2	no	—
52	Dic₁₅₁	—	2	2	no	—
53	Dic₁₅₁	—	4	1	no	—
54	C₂×C₁₅₁	#117	1	1	yes	characteristic
55	C₂×C₁₅₁	C₄×D₄	1	1	yes	characteristic
56	C₂×C₁₅₁	C₄×Q₈	1	1	yes	characteristic
57	C₂×C₁₅₁	C₂²⋊Q₈	1	1	yes	characteristic
58	C₂×C₁₅₁	#123	1	1	yes	characteristic
59	C₂×C₁₅₁	#125	1	1	yes	characteristic
60	C₂×C₁₅₁	#126	1	1	yes	characteristic
61	C₁₅₁	#387	1	1	yes	characteristic, complemented, Sylow
62	#387	—	151	1	no	maximal, Sylow
63	C₂×C₄⋊C₄	—	151	1	no	—
64	C₂×C₄⋊C₄	—	151	1	no	—
65	C₂×C₄²	—	151	1	no	—
66	#95	—	151	1	no	—
67	#95	—	151	1	no	—
68	#95	—	151	1	no	—
69	#95	D₁₅₁	1	1	yes	characteristic
70	C₂²×C₄	—	151	1	no	—
71	C₂²×C₄	—	151	1	no	—
72	C₂²×C₄	—	151	1	no	—
73	C₂²×C₄	—	151	1	no	—
74	C₂²×C₄	C₂×D₁₅₁	1	1	yes	characteristic
75	C₂²×C₄	C₂×D₁₅₁	1	1	yes	characteristic
76	C₂²×C₄	C₂×D₁₅₁	1	1	yes	characteristic
77	C₄⋊C₄	—	302	2	no	—
78	C₄⋊C₄	—	151	4	no	—
79	C₄²	—	302	2	no	—
80	C₂³	C₂²×D₁₅₁	1	1	yes	characteristic
81	C₂×C₄	—	2	1	no	—
82	C₂×C₄	—	2	1	no	—
83	C₂×C₄	—	2	1	no	—
84	C₂×C₄	—	2	1	no	—
85	C₂×C₄	—	2	1	no	—
86	C₂×C₄	—	2	1	no	—
87	C₂×C₄	—	2	1	no	—
88	C₂×C₄	—	302	1	no	—
89	C₂×C₄	—	302	1	no	—
90	C₂×C₄	—	302	1	no	—
91	C₂×C₄	—	302	1	no	—
92	C₂×C₄	—	302	1	no	—
93	C₂×C₄	—	302	1	no	—
94	C₂×C₄	—	302	1	no	—
95	C₂×C₄	—	302	1	no	—
96	C₂×C₄	—	302	1	no	—
97	C₂×C₄	—	151	2	no	—
98	C₂×C₄	—	151	2	no	—
99	C₂×C₄	—	151	2	no	—
100	C₂×C₄	C₄×D₁₅₁	1	2	yes	—
101	C₂×C₄	Dic₃₀₂	1	2	yes	—
102	C₂²	C₂×C₄×D₁₅₁	1	1	yes	characteristic
103	C₂²	D₄×D₁₅₁	1	1	yes	characteristic
104	C₂²	C₂×Dic₃₀₂	1	1	yes	characteristic
105	C₂²	#14559003	1	1	yes	characteristic
106	C₂²	#14559003	1	1	yes	characteristic
107	C₂²	#14559004	1	1	yes	characteristic
108	C₂²	#14559005	1	1	yes	characteristic
109	C₄	—	2	2	no	—
110	C₄	—	2	2	no	—
111	C₄	—	4	1	no	—
112	C₄	—	302	2	no	—
113	C₄	—	302	2	no	—
114	C₄	—	302	2	no	—
115	C₄	—	604	1	no	—
116	C₂	#18012695	1	1	yes	characteristic
117	C₂	#18012701	1	1	yes	characteristic
118	C₂	C₄×Dic₃₀₂	1	1	yes	characteristic
119	C₂	#18012716	1	1	yes	characteristic
120	C₂	#18012721	1	1	yes	characteristic
121	C₂	#18012730	1	1	yes	characteristic
122	C₂	#18012734	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊Dic₁₅₁

C₂

yes

maximal, characteristic

C₂×Dic₁₅₁⋊C₄

C₂

yes

maximal, characteristic

C₂×C₄×Dic₁₅₁

C₂

yes

maximal, characteristic

C₁₅₁⋊#95

C₂

yes

maximal, characteristic

C₁₅₁⋊#95

C₂

yes

maximal, characteristic

C₁₅₁⋊#95

C₂

yes

maximal, characteristic

#95×C₁₅₁

C₂

yes

maximal, characteristic

C₂²×Dic₁₅₁

C₂²

yes

characteristic

C₂²×Dic₁₅₁

C₂²

yes

characteristic

C₂²×Dic₁₅₁

C₂²

yes

characteristic

C₂²×Dic₁₅₁

C₂²

yes

characteristic

C₄⋊Dic₁₅₁

C₄

yes

complemented

Dic₁₅₁⋊C₄

—

C₄×Dic₁₅₁

—

C₂²×C₄×C₁₅₁

C₂²

yes

characteristic

C₂²×C₄×C₁₅₁

C₂²

yes

characteristic

C₂²×C₄×C₁₅₁

C₂²

yes

characteristic

C₂×Dic₁₅₁

—

C₂×Dic₁₅₁

—

C₂×Dic₁₅₁

—

C₂×Dic₁₅₁

—

C₂×Dic₁₅₁

—

C₂×Dic₁₅₁

—

C₂×Dic₁₅₁

—

C₂×Dic₁₅₁

—

C₂×Dic₁₅₁

—

C₂×Dic₁₅₁

C₂×C₄

yes

—

C₂×Dic₁₅₁

C₂×C₄

yes

—

C₂×Dic₁₅₁

D₄

yes

—

C₂³×C₁₅₁

C₂³

yes

characteristic

C₂×C₄×C₁₅₁

—

C₂×C₄×C₁₅₁

—

C₂×C₄×C₁₅₁

—

C₂×C₄×C₁₅₁

—

C₂×C₄×C₁₅₁

—

C₂×C₄×C₁₅₁

—

C₂×C₄×C₁₅₁

—

C₂×C₄×C₁₅₁

C₂×C₄

yes

—

C₂×C₄×C₁₅₁

Q₈

yes

—

C₂²×C₁₅₁

C₂²×C₄

yes

characteristic

C₂²×C₁₅₁

C₂×D₄

yes

characteristic

C₂²×C₁₅₁

C₂×Q₈

yes

C₂²×C₁₅₁

yes

C₂²×C₁₅₁

yes

C₂²×C₁₅₁

yes

C₂²×C₁₅₁

yes

C₄×C₁₅₁

—

C₄×C₁₅₁

—

C₄×C₁₅₁

—

Dic₁₅₁

—

Dic₁₅₁

—

Dic₁₅₁

—

Dic₁₅₁

—

C₂×C₁₅₁

#117

yes

characteristic

C₂×C₁₅₁

C₄×D₄

yes

characteristic

C₂×C₁₅₁

C₄×Q₈

yes

characteristic

C₂×C₁₅₁

C₂²⋊Q₈

yes

C₂×C₁₅₁

yes

C₂×C₁₅₁

yes

C₂×C₁₅₁

yes

C₁₅₁

yes

characteristic, complemented, Sylow

#387

—

151

maximal, Sylow

C₂×C₄⋊C₄

—

151

—

C₂×C₄⋊C₄

—

151

—

C₂×C₄²

—

151

—

#95

—

151

—

#95

—

151

—

#95

—

151

—

#95

D₁₅₁

yes

characteristic

C₂²×C₄

—

151

—

C₂²×C₄

—

151

—

C₂²×C₄

—

151

—

C₂²×C₄

—

151

—

C₂²×C₄

C₂×D₁₅₁

yes

characteristic

C₂²×C₄

C₂×D₁₅₁

yes

characteristic

C₂²×C₄

C₂×D₁₅₁

yes

characteristic

C₄⋊C₄

—

302

—

C₄⋊C₄

—

151

—

C₄²

—

302

—

C₂³

C₂²×D₁₅₁

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

302

—

C₂×C₄

—

302

—

C₂×C₄

—

302

—

C₂×C₄

—

302

—

C₂×C₄

—

302

—

C₂×C₄

—

302

—

C₂×C₄

—

302

—

C₂×C₄

—

302

—

C₂×C₄

—

302

—

C₂×C₄

—

151

—

C₂×C₄

—

151

—

C₂×C₄

—

151

—

100

C₂×C₄

C₄×D₁₅₁

yes

—

101

C₂×C₄

Dic₃₀₂

yes

—

102

C₂²

C₂×C₄×D₁₅₁

yes

characteristic

103

C₂²

D₄×D₁₅₁

yes

characteristic

104

C₂²

C₂×Dic₃₀₂

yes

characteristic

105

C₂²

#14559003

yes

characteristic

106

C₂²

#14559003

yes

characteristic

107

C₂²

#14559004

yes

characteristic

108

C₂²

#14559005

yes

characteristic

109

C₄

—

110

C₄

—

111

C₄

—

112

C₄

—

302

—

113

C₄

—

302

—

114

C₄

—

302

—

115

C₄

—

604

—

116

C₂

#18012695

yes

characteristic

117

C₂

#18012701

yes

characteristic

118

C₂

C₄×Dic₃₀₂

yes

characteristic

119

C₂

#18012716

yes

characteristic

120

C₂

#18012721

yes

characteristic

121

C₂

#18012730

yes

characteristic

122

C₂

#18012734

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₁₅₁
commutator	C₂²×C₁₅₁	C₂²×C₄
Fitting	#95×C₁₅₁	C₂
socle, prime radical, cosocle	C₂³×C₁₅₁	C₂³
hypercenter	#95	D₁₅₁
hypocenter	C₁₅₁	#387
LCS	G ▷ C₂²×C₁₅₁ ▷ C₁₅₁
UCS	C₁ ◁ C₂³ ◁ #95

subgroup

G/H

center, Frattini

C₂³

C₂²×D₁₅₁

commutator

C₂²×C₁₅₁

C₂²×C₄

Fitting

#95×C₁₅₁

C₂

socle, prime radical, cosocle

C₂³×C₁₅₁

C₂³

D₁₅₁

C₁₅₁

G ▷ C₂²×C₁₅₁ ▷ C₁₅₁

C₁ ◁ C₂³ ◁ #95

N	H ≅ G/N	type
12. C₄⋊Dic₁₅₁	C₄	semidirect
61. C₁₅₁	#387	semidirect

H ≅ G/N

type

12. C₄⋊Dic₁₅₁

C₄

semidirect

61. C₁₅₁

#387

semidirect

Subgroups — #23752095

Conjugacy classes of subgroups

Complements