Group #22589953 — subgroups

Subgroups — #22589953

Order 9088.

228 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 93 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×#14556134	C₂	1	1	yes	maximal, characteristic
2	C₂×#14556068	C₂	1	1	yes	maximal, characteristic, complemented
3	(C₂×D₇₁)⋊C₁₆	C₂	1	4	yes	maximal, complemented
4	C₂²×C₁₆×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11765865	C₄	1	1	yes	characteristic
6	#14556134	—	2	2	no	—
7	#14556134	—	2	2	no	—
8	C₂×#11765849	C₄	1	1	yes	characteristic
9	C₂×#11765848	C₄	1	2	yes	—
10	C₂×C₈×D₇₁	C₂²	1	2	yes	—
11	#14556068	—	2	2	no	—
12	C₂×C₇₁⋊C₁₆	C₂²	1	2	yes	—
13	C₂²×C₈×C₇₁	C₂²	1	1	yes	characteristic
14	C₂×C₁₆×C₇₁	—	2	2	no	—
15	C₂×C₁₆×C₇₁	C₂²	1	2	yes	—
16	#11765865	—	2	2	no	—
17	#11765865	—	2	2	no	—
18	C₂×Dic₁₄₂	C₈	1	1	yes	characteristic
19	C₂×D₂₈₄	C₈	1	1	yes	characteristic
20	C₂×C₂²⋊D₇₁	C₈	1	2	yes	—
21	C₂×C₄×D₇₁	C₂×C₄	1	2	yes	—
22	#11765849	—	2	2	no	—
23	#11765848	—	2	4	no	—
24	C₂×C₇₁⋊C₈	C₂×C₄	1	2	yes	—
25	C₈×D₇₁	—	2	2	no	—
26	C₈×D₇₁	—	2	2	no	—
27	C₇₁⋊C₁₆	—	2	2	no	—
28	C₂²×C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
29	C₂×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
30	C₂×C₈×C₇₁	D₄	1	2	yes	—
31	C₂×C₈×C₇₁	D₄	1	2	yes	—
32	C₂×C₈×C₇₁	C₂³	1	1	yes	characteristic
33	C₁₆×C₇₁	—	2	2	no	—
34	C₂³×C₇₁	C₂×C₈	1	1	yes	characteristic
35	C₂²×D₇₁	C₂×C₈	1	2	yes	—
36	C₂×C₄×C₇₁	C₂²⋊C₄	1	2	yes	—
37	C₂×C₄×C₇₁	C₂×C₈	1	1	yes	characteristic
38	C₂×C₄×C₇₁	M₁₆	1	2	yes	—
39	C₂×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
40	C₂²⋊D₇₁	—	2	4	no	—
41	C₂×Dic₇₁	C₂×C₈	1	2	yes	—
42	D₂₈₄	—	2	2	no	—
43	C₄×D₇₁	—	2	2	no	—
44	C₄×D₇₁	—	2	2	no	—
45	Dic₁₄₂	—	2	2	no	—
46	C₈×C₇₁	C₂²⋊C₄	1	2	yes	—
47	C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
48	C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
49	C₇₁⋊C₈	—	2	2	no	—
50	C₂²×C₇₁	—	2	2	no	—
51	C₂²×C₇₁	C₂²⋊C₈	1	2	yes	—
52	C₂²×C₇₁	C₂²×C₈	1	1	yes	characteristic
53	C₂×D₇₁	—	2	2	no	—
54	C₂×D₇₁	—	2	4	no	—
55	C₄×C₇₁	C₂²⋊C₈	1	2	yes	—
56	C₄×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
57	C₄×C₇₁	C₂×M₁₆	1	1	yes	characteristic
58	Dic₇₁	—	2	2	no	—
59	C₂×C₇₁	—	2	2	no	—
60	C₂×C₇₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
61	C₂×C₇₁	#504	1	2	yes	—
62	D₇₁	—	4	2	no	—
63	#2113	—	71	1	no	maximal, Sylow
64	C₇₁	#2113	1	1	yes	characteristic, complemented, Sylow
65	C₂×#131	—	71	1	no	—
66	C₂×M₃₂	—	71	1	no	—
67	C₂²×C₁₆	D₇₁	1	1	yes	characteristic, complemented
68	C₂²⋊C₁₆	—	71	4	no	—
69	C₂×#41	—	71	1	no	—
70	#131	—	142	2	no	—
71	#131	—	142	2	no	—
72	C₂×M₁₆	—	71	1	no	—
73	C₂×M₁₆	—	71	2	no	—
74	C₂²×C₈	—	71	2	no	—
75	C₂²×C₈	C₂×D₇₁	1	1	yes	characteristic
76	M₃₂	—	142	2	no	—
77	C₂×C₁₆	—	2	2	no	—
78	C₂×C₁₆	—	71	2	no	—
79	C₂×C₁₆	C₂×D₇₁	1	2	yes	—
80	#41	—	142	2	no	—
81	#41	—	142	2	no	—
82	C₂×Q₈	—	71	1	no	—
83	C₂×D₄	—	71	2	no	—
84	C₂×D₄	—	71	1	no	—
85	C₂²×C₄	—	71	2	no	—
86	C₂²×C₄	C₄×D₇₁	1	1	yes	characteristic
87	M₁₆	—	142	2	no	—
88	M₁₆	—	142	4	no	—
89	C₂×C₈	—	71	2	no	—
90	C₂×C₈	—	142	2	no	—
91	C₂×C₈	—	142	2	no	—
92	C₂×C₈	C₄×D₇₁	1	1	yes	characteristic
93	C₂×C₈	D₂₈₄	1	2	yes	—
94	C₂×C₈	C₂²⋊D₇₁	1	2	yes	—
95	C₂×C₈	C₂²×D₇₁	1	1	yes	characteristic
96	C₁₆	—	2	2	no	—
97	C₁₆	—	142	2	no	—
98	C₂³	—	71	2	no	—
99	C₂³	C₈×D₇₁	1	1	yes	characteristic
100	Q₈	—	142	2	no	—
101	D₄	—	142	4	no	—
102	D₄	—	142	2	no	—
103	C₂×C₄	—	71	2	no	—
104	C₂×C₄	—	142	2	no	—
105	C₂×C₄	—	142	2	no	—
106	C₂×C₄	(C₂×D₇₁)⋊C₄	1	2	yes	—
107	C₂×C₄	C₈×D₇₁	1	1	yes	characteristic
108	C₂×C₄	#11765848	1	2	yes	—
109	C₂×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
110	C₈	—	142	2	no	—
111	C₈	(C₂×D₇₁)⋊C₄	1	2	yes	—
112	C₈	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
113	C₈	C₂×D₂₈₄	1	1	yes	characteristic
114	C₂²	—	2	2	no	—
115	C₂²	—	142	4	no	—
116	C₂²	—	142	2	no	—
117	C₂²	(C₂×D₇₁)⋊C₈	1	2	yes	—
118	C₂²	C₂×C₈×D₇₁	1	1	yes	characteristic
119	C₄	—	142	2	no	—
120	C₄	(C₂×D₇₁)⋊C₈	1	2	yes	—
121	C₄	C₂×(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
122	C₄	C₂×#11765848	1	1	yes	characteristic
123	C₂	—	2	2	no	—
124	C₂	—	284	2	no	—
125	C₂	C₂×(C₂×D₇₁)⋊C₈	1	1	yes	characteristic
126	C₂	#17986415	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556134

C₂

yes

maximal, characteristic

C₂×#14556068

C₂

yes

maximal, characteristic, complemented

(C₂×D₇₁)⋊C₁₆

C₂

yes

maximal, complemented

C₂²×C₁₆×C₇₁

C₂

yes

maximal, characteristic, complemented

C₂×#11765865

C₄

yes

—

—

C₄

yes

characteristic

C₂×#11765848

C₄

yes

—

C₂×C₈×D₇₁

C₂²

yes

—

#14556068

—

C₂×C₇₁⋊C₁₆

C₂²

yes

—

C₂²×C₈×C₇₁

C₂²

yes

characteristic

C₂×C₁₆×C₇₁

—

C₂×C₁₆×C₇₁

C₂²

yes

—

#11765865

—

#11765865

—

C₂×Dic₁₄₂

C₈

yes

characteristic

C₂×D₂₈₄

C₈

yes

characteristic

C₂×C₂²⋊D₇₁

C₈

yes

—

C₂×C₄×D₇₁

C₂×C₄

yes

—

#11765849

—

#11765848

—

C₂×C₇₁⋊C₈

C₂×C₄

yes

—

C₈×D₇₁

—

C₈×D₇₁

—

C₇₁⋊C₁₆

—

C₂²×C₄×C₇₁

C₂×C₄

yes

characteristic

C₂×C₈×C₇₁

C₂×C₄

yes

characteristic

C₂×C₈×C₇₁

D₄

yes

—

C₂×C₈×C₇₁

D₄

yes

—

C₂×C₈×C₇₁

C₂³

yes

characteristic

C₁₆×C₇₁

—

C₂³×C₇₁

C₂×C₈

yes

characteristic

C₂²×D₇₁

C₂×C₈

yes

—

C₂×C₄×C₇₁

C₂²⋊C₄

yes

—

C₂×C₄×C₇₁

C₂×C₈

yes

characteristic

C₂×C₄×C₇₁

M₁₆

yes

—

C₂×C₄×C₇₁

C₂²×C₄

yes

characteristic

C₂²⋊D₇₁

—

C₂×Dic₇₁

C₂×C₈

yes

—

D₂₈₄

—

C₄×D₇₁

—

C₄×D₇₁

—

Dic₁₄₂

—

C₈×C₇₁

C₂²⋊C₄

yes

—

C₈×C₇₁

C₂×D₄

yes

characteristic

C₈×C₇₁

C₂×D₄

yes

characteristic

C₇₁⋊C₈

—

C₂²×C₇₁

—

C₂²×C₇₁

C₂²⋊C₈

yes

—

C₂²×C₇₁

C₂²×C₈

yes

characteristic

C₂×D₇₁

—

C₂×D₇₁

—

C₄×C₇₁

C₂²⋊C₈

yes

—

C₄×C₇₁

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₇₁

C₂×M₁₆

yes

characteristic

Dic₇₁

—

C₂×C₇₁

—

C₂×C₇₁

C₂×C₂²⋊C₈

yes

characteristic

C₂×C₇₁

#504

yes

—

D₇₁

—

#2113

—

maximal, Sylow

C₇₁

#2113

yes

characteristic, complemented, Sylow

C₂×#131

—

C₂×M₃₂

—

C₂²×C₁₆

D₇₁

yes

characteristic, complemented

C₂²⋊C₁₆

—

C₂×#41

—

#131

—

142

—

#131

—

142

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

C₂×D₇₁

yes

characteristic

M₃₂

—

142

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₇₁

yes

—

#41

—

142

—

#41

—

142

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₇₁

yes

characteristic

M₁₆

—

142

—

M₁₆

—

142

—

C₂×C₈

—

C₂×C₈

—

142

—

C₂×C₈

—

142

—

C₂×C₈

C₄×D₇₁

yes

characteristic

C₂×C₈

D₂₈₄

yes

—

C₂×C₈

C₂²⋊D₇₁

yes

—

C₂×C₈

C₂²×D₇₁

yes

characteristic

C₁₆

—

C₁₆

—

142

—

C₂³

—

C₂³

C₈×D₇₁

yes

characteristic

100

Q₈

—

142

—

101

D₄

—

142

—

102

D₄

—

142

—

103

C₂×C₄

—

104

C₂×C₄

—

142

—

105

C₂×C₄

—

142

—

106

C₂×C₄

(C₂×D₇₁)⋊C₄

yes

—

107

C₂×C₄

C₈×D₇₁

yes

characteristic

108

C₂×C₄

#11765848

yes

—

109

C₂×C₄

C₂×C₄×D₇₁

yes

characteristic

110

C₈

—

142

—

111

C₈

(C₂×D₇₁)⋊C₄

yes

—

112

C₈

C₂×C₂²⋊D₇₁

yes

characteristic

113

C₈

C₂×D₂₈₄

yes

characteristic

114

C₂²

—

115

C₂²

—

142

—

116

C₂²

—

142

—

117

C₂²

(C₂×D₇₁)⋊C₈

yes

—

118

C₂²

C₂×C₈×D₇₁

yes

characteristic

119

C₄

—

142

—

120

C₄

(C₂×D₇₁)⋊C₈

yes

—

121

C₄

C₂×(C₂×D₇₁)⋊C₄

yes

characteristic

122

C₄

C₂×#11765848

yes

characteristic

123

C₂

—

124

C₂

—

284

—

125

C₂

C₂×(C₂×D₇₁)⋊C₈

yes

characteristic

126

C₂

#17986415

yes

—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₇₁
commutator, socle	C₂²×C₇₁	C₂²×C₈
Fitting	C₂²×C₁₆×C₇₁	C₂
hypercenter	C₂²×C₁₆	D₇₁
hypocenter	C₇₁	#2113
LCS	G ▷ C₂²×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₁₆

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×D₇₁

commutator, socle

C₂²×C₇₁

C₂²×C₈

Fitting

C₂²×C₁₆×C₇₁

C₂

hypercenter

C₂²×C₁₆

D₇₁

C₇₁

G ▷ C₂²×C₇₁ ▷ C₇₁

C₁ ◁ C₂×C₈ ◁ C₂²×C₁₆

N	H ≅ G/N	type
2. C₂×#14556068	C₂	semidirect
3. (C₂×D₇₁)⋊C₁₆	C₂	semidirect
4. C₂²×C₁₆×C₇₁	C₂	semidirect
64. C₇₁	#2113	semidirect
67. C₂²×C₁₆	D₇₁	semidirect

H ≅ G/N

type

2. C₂×#14556068

C₂

semidirect

3. (C₂×D₇₁)⋊C₁₆

C₂

semidirect

4. C₂²×C₁₆×C₇₁

C₂

semidirect

64. C₇₁

#2113

semidirect

67. C₂²×C₁₆

D₇₁

semidirect

Subgroups — #22589953

Conjugacy classes of subgroups

Complements