Group #11792658 — subgroups

Subgroups — #11792658

Order 1152.

525 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 525 conjugacy classes of subgroups — too many to draw. Only its 98 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	#10589850	C₂	1	3	yes	maximal, complemented
2	#10588811	C₂	1	3	yes	maximal, complemented
3	C₉×#338	C₂	1	1	yes	maximal, characteristic, complemented
4	#68727	—	3	1	no	maximal
5	C₂×#3697	C₂²	1	3	yes	—
6	C₂×C₉×M₁₆	C₂²	1	3	yes	—
7	C₂²×C₉⋊C₈	C₂²	1	1	yes	characteristic
8	#63471	—	2	6	no	—
9	#63470	—	2	6	no	—
10	#63467	—	2	6	no	—
11	(C₂×D₉)⋊C₈	—	2	6	no	—
12	#5748	—	3	3	no	—
13	#5129	—	3	3	no	—
14	C₃×#338	D₃	1	1	yes	characteristic
15	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
16	C₂×#611	—	2	3	no	—
17	#3697	—	2	6	no	—
18	#3697	—	2	6	no	—
19	C₂×D₃₆	D₄	1	3	yes	—
20	C₂×C₄×D₉	—	2	3	no	—
21	C₂×Dic₁₈	D₄	1	3	yes	—
22	C₉×M₁₆	—	2	6	no	—
23	C₂×C₈×C₉	D₄	1	6	yes	—
24	C₂×C₉⋊C₈	—	2	3	no	—
25	D₇₂	—	2	6	no	—
26	#3664	—	2	12	no	—
27	Dic₃₆	—	2	6	no	—
28	#2017	—	9	1	no	Sylow
29	C₂×#235	—	3	3	no	—
30	C₂×C₃×M₁₆	C₂×D₃	1	3	yes	—
31	C₂²×C₃⋊C₈	—	3	1	no	—
32	#909	—	6	6	no	—
33	#908	—	6	6	no	—
34	#904	—	6	6	no	—
35	(C₂×D₃)⋊C₈	—	6	6	no	—
36	C₂³×C₉	#41	1	1	yes	characteristic
37	C₂²×D₉	—	2	3	no	—
38	C₂×C₄×C₉	C₂×D₄	1	3	yes	—
39	C₂×C₄×C₉	C₂×D₄	1	3	yes	—
40	#611	—	4	6	no	—
41	C₂×Dic₉	—	2	3	no	—
42	D₃₆	—	2	6	no	—
43	C₄×D₉	—	4	3	no	—
44	C₄×D₉	—	4	3	no	—
45	Dic₁₈	—	2	6	no	—
46	C₈×C₉	—	2	6	no	—
47	C₉⋊C₈	—	4	1	no	—
48	#575	—	9	3	no	—
49	#408	—	9	3	no	—
50	#338	D₉	1	1	yes	characteristic, complemented
51	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
52	C₂×#67	—	6	3	no	—
53	#235	—	6	6	no	—
54	#235	—	6	6	no	—
55	C₂×D₁₂	—	3	3	no	—
56	C₂×C₄×D₃	—	6	3	no	—
57	C₂×Dic₆	—	3	3	no	—
58	C₃×M₁₆	—	2	6	no	—
59	C₂×C₃×C₈	D₁₂	1	6	yes	—
60	C₂×C₃⋊C₈	—	6	3	no	—
61	Dic₁₂	—	6	6	no	—
62	D₂₄	—	6	6	no	—
63	#204	—	6	12	no	—
64	C₂²×C₉	—	4	1	no	—
65	C₂²×C₉	#121	1	3	yes	—
66	C₂×D₉	—	4	6	no	—
67	C₂×D₉	—	4	3	no	—
68	C₄×C₉	#120	1	3	yes	—
69	C₄×C₉	#127	1	1	yes	characteristic
70	Dic₉	—	4	3	no	—
71	C₂×#41	—	9	3	no	—
72	#137	—	18	6	no	—
73	AGL(1,ℤ/8)	—	18	6	no	—
74	#135	—	18	6	no	—
75	C₂×M₁₆	C₂×D₉	1	3	yes	—
76	C₂²×C₈	—	9	1	no	—
77	C₂²⋊C₈	—	18	6	no	—
78	C₂³×C₃	#239	1	1	yes	characteristic
79	C₂²×D₃	—	6	3	no	—
80	C₂×C₃×C₄	C₂×D₁₂	1	3	yes	—
81	C₂×C₃×C₄	D₃×D₄	1	3	yes	—
82	#67	—	12	6	no	—
83	C₂×Dic₃	—	6	3	no	—
84	D₁₂	—	6	6	no	—
85	C₄×D₃	—	12	3	no	—
86	C₄×D₃	—	12	3	no	—
87	Dic₆	—	6	6	no	—
88	C₃×C₈	—	2	6	no	—
89	C₃⋊C₈	—	12	1	no	—
90	C₂×C₉	—	2	3	no	—
91	C₂×C₉	#392	1	1	yes	characteristic
92	D₉	—	8	3	no	—
93	#41	—	18	6	no	—
94	#41	—	18	6	no	—
95	C₂×Q₈	—	9	3	no	—
96	C₂×D₄	—	9	3	no	—
97	C₂×D₄	—	18	3	no	—
98	C₂²×C₄	—	18	3	no	—
99	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
100	Q₁₆	—	18	6	no	—
101	SD₁₆	—	18	12	no	—
102	D₈	—	18	6	no	—
103	M₁₆	—	2	6	no	—
104	C₂×C₈	—	18	3	no	—
105	C₂×C₈	D₃₆	1	6	yes	—
106	C₂²×C₃	—	4	1	no	—
107	C₂²×C₃	#895	1	3	yes	—
108	C₂×D₃	—	12	6	no	—
109	C₂×D₃	—	12	3	no	—
110	C₃×C₄	#874	1	1	yes	characteristic
111	C₃×C₄	#882	1	3	yes	—
112	Dic₃	—	12	3	no	—
113	C₉	#2017	1	1	yes	characteristic, complemented, Sylow
114	C₂³	—	18	3	no	—
115	C₂³	#3701	1	1	yes	characteristic
116	Q₈	—	18	6	no	—
117	D₄	—	18	6	no	—
118	D₄	—	36	6	no	—
119	C₂×C₄	—	18	3	no	—
120	C₂×C₄	—	36	3	no	—
121	C₂×C₄	—	36	3	no	—
122	C₂×C₄	C₂×D₃₆	1	3	yes	—
123	C₂×C₄	D₄×D₉	1	3	yes	—
124	C₈	—	2	6	no	—
125	C₈	—	36	1	no	—
126	C₂×C₃	—	2	3	no	—
127	C₂×C₃	#4671	1	1	yes	characteristic
128	D₃	—	24	3	no	—
129	C₂²	—	4	1	no	—
130	C₂²	—	36	6	no	—
131	C₂²	—	36	3	no	—
132	C₂²	#63457	1	3	yes	—
133	C₄	—	36	3	no	—
134	C₄	#63436	1	1	yes	characteristic
135	C₄	#63444	1	3	yes	—
136	C₃	#68727	1	1	yes	characteristic
137	C₂	—	2	3	no	—
138	C₂	—	72	3	no	—
139	C₂	#10588351	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#10589850

C₂

yes

maximal, complemented

#10588811

C₂

yes

maximal, complemented

C₉×#338

C₂

yes

maximal, characteristic, complemented

#68727

—

maximal

C₂×#3697

C₂²

yes

—

C₂×C₉×M₁₆

C₂²

yes

—

C₂²×C₉⋊C₈

C₂²

yes

—

—

—

(C₂×D₉)⋊C₈

—

#5748

—

#5129

—

C₃×#338

D₃

yes

characteristic

C₂²×C₄×C₉

C₂³

yes

—

—

—

C₂×D₃₆

D₄

yes

—

C₂×C₄×D₉

—

C₂×Dic₁₈

D₄

yes

—

C₉×M₁₆

—

C₂×C₈×C₉

D₄

yes

—

C₂×C₉⋊C₈

—

D₇₂

—

#3664

—

Dic₃₆

—

#2017

—

Sylow

C₂×#235

—

C₂×C₃×M₁₆

C₂×D₃

yes

—

C₂²×C₃⋊C₈

—

#909

—

#908

—

#904

—

(C₂×D₃)⋊C₈

—

C₂³×C₉

#41

yes

characteristic

C₂²×D₉

—

C₂×C₄×C₉

C₂×D₄

yes

—

C₂×C₄×C₉

C₂×D₄

yes

—

#611

—

C₂×Dic₉

—

D₃₆

—

C₄×D₉

—

C₄×D₉

—

Dic₁₈

—

C₈×C₉

—

C₉⋊C₈

—

#575

—

#408

—

#338

D₉

yes

characteristic, complemented

C₂²×C₃×C₄

C₂²×D₃

yes

characteristic

C₂×#67

—

#235

—

#235

—

C₂×D₁₂

—

C₂×C₄×D₃

—

C₂×Dic₆

—

C₃×M₁₆

—

C₂×C₃×C₈

D₁₂

yes

—

C₂×C₃⋊C₈

—

Dic₁₂

—

D₂₄

—

#204

—

C₂²×C₉

—

C₂²×C₉

#121

yes

—

C₂×D₉

—

C₂×D₉

—

C₄×C₉

#120

yes

—

C₄×C₉

#127

yes

characteristic

Dic₉

—

C₂×#41

—

#137

—

AGL(1,ℤ/8)

—

#135

—

C₂×M₁₆

C₂×D₉

yes

—

C₂²×C₈

—

C₂²⋊C₈

—

C₂³×C₃

#239

yes

characteristic

C₂²×D₃

—

C₂×C₃×C₄

C₂×D₁₂

yes

—

C₂×C₃×C₄

D₃×D₄

yes

—

#67

—

C₂×Dic₃

—

D₁₂

—

C₄×D₃

—

C₄×D₃

—

Dic₆

—

C₃×C₈

—

C₃⋊C₈

—

C₂×C₉

—

C₂×C₉

#392

yes

characteristic

D₉

—

#41

—

#41

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₉

yes

characteristic

100

Q₁₆

—

101

SD₁₆

—

102

D₈

—

103

M₁₆

—

104

C₂×C₈

—

105

C₂×C₈

D₃₆

yes

—

106

C₂²×C₃

—

107

C₂²×C₃

#895

yes

—

108

C₂×D₃

—

109

C₂×D₃

—

110

C₃×C₄

#874

yes

characteristic

111

C₃×C₄

#882

yes

—

112

Dic₃

—

113

C₉

#2017

yes

characteristic, complemented, Sylow

114

C₂³

—

115

C₂³

#3701

yes

characteristic

116

Q₈

—

117

D₄

—

118

D₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

C₂×D₃₆

yes

—

123

C₂×C₄

D₄×D₉

yes

—

124

C₈

—

125

C₈

—

126

C₂×C₃

—

127

C₂×C₃

#4671

yes

characteristic

128

D₃

—

129

C₂²

—

130

C₂²

—

131

C₂²

—

132

C₂²

#63457

yes

—

133

C₄

—

134

C₄

#63436

yes

characteristic

135

C₄

#63444

yes

—

136

C₃

#68727

yes

characteristic

137

C₂

—

138

C₂

—

139

C₂

#10588351

yes

characteristic

	subgroup	G/H
center	C₄	#63436
commutator, cosocle	C₂²×C₄×C₉	C₂³
Frattini	C₂²×C₃×C₄	C₂²×D₃
Fitting	C₉×#338	C₂
socle	C₂×C₃	#4671
hypercenter	#338	D₉
hypocenter	C₉	#2017
LCS	G ▷ C₂²×C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #338

subgroup

G/H

center

C₄

#63436

commutator, cosocle

C₂²×C₄×C₉

C₂³

Frattini

C₂²×C₃×C₄

C₂²×D₃

C₂

C₂×C₃

D₉

C₉

G ▷ C₂²×C₄×C₉ ▷ C₂×C₉ ▷ C₉

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #338

N	H ≅ G/N	type
1. #10589850	C₂	semidirect
2. #10588811	C₂	semidirect
3. C₉×#338	C₂	semidirect
50. #338	D₉	semidirect
113. C₉	#2017	semidirect

H ≅ G/N

type

1. #10589850

C₂

semidirect

2. #10588811

C₂

semidirect

3. C₉×#338

C₂

semidirect

50. #338

D₉

semidirect

113. C₉

#2017

semidirect

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

subgroup	index
#10589850	2
#10588811	2
C₉×#338	2
#68727	3

subgroup

index

Subgroups — #11792658

Conjugacy classes of subgroups

Complements

Maximal subgroups