Group #11797014 — subgroups

Subgroups — #11797014

Order 1152.

240 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 126 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	C₂²×C₉×C₁₆	C₂	1	1	yes	maximal, characteristic
2	#10588782	C₂	1	1	yes	maximal, characteristic
3	C₂×#63371	C₂	1	1	yes	maximal, characteristic
4	Dic₉⋊C₁₆	C₂	1	4	yes	maximal, complemented
5	#71401	—	3	1	no	maximal
6	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
7	#63488	C₄	1	1	yes	characteristic
8	C₂×#3667	C₄	1	1	yes	characteristic
9	C₂×C₉×C₁₆	—	2	2	no	—
10	C₂×C₉×C₁₆	C₂²	1	2	yes	—
11	#63375	C₄	1	2	yes	—
12	C₈×Dic₉	C₂²	1	2	yes	—
13	#63371	—	2	2	no	—
14	C₂×C₉⋊C₁₆	C₂²	1	2	yes	—
15	C₂²×C₃×C₁₆	D₃	1	1	yes	characteristic
16	#5101	—	3	1	no	—
17	C₂×#812	—	3	1	no	—
18	Dic₃⋊C₁₆	—	3	4	no	—
19	C₂²×C₄×C₉	C₂×C₄	1	1	yes	characteristic
20	C₂×C₈×C₉	C₂×C₄	1	1	yes	characteristic
21	C₂×C₈×C₉	D₄	1	2	yes	—
22	C₂×C₈×C₉	Q₈	1	2	yes	—
23	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
24	#3676	C₈	1	2	yes	—
25	C₄⋊Dic₉	C₈	1	2	yes	—
26	C₄×Dic₉	C₂×C₄	1	2	yes	—
27	#3667	—	2	2	no	—
28	C₂×C₉⋊C₈	C₂×C₄	1	2	yes	—
29	C₉×C₁₆	—	2	2	no	—
30	C₉⋊C₁₆	—	2	2	no	—
31	#2151	—	9	1	no	Sylow
32	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
33	#926	—	3	1	no	—
34	C₂×#208	—	3	1	no	—
35	C₂×C₃×C₁₆	—	2	2	no	—
36	C₂×C₃×C₁₆	C₂×D₃	1	2	yes	—
37	#815	—	3	2	no	—
38	C₈×Dic₃	—	3	2	no	—
39	#812	—	6	2	no	—
40	C₂×C₃⋊C₁₆	—	3	2	no	—
41	C₂³×C₉	C₂×C₈	1	1	yes	characteristic
42	C₂×C₄×C₉	C₄⋊C₄	1	2	yes	—
43	C₂×C₄×C₉	C₂×C₈	1	1	yes	characteristic
44	C₂×C₄×C₉	M₁₆	1	2	yes	—
45	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
46	C₂×Dic₉	C₂×C₈	1	4	yes	—
47	C₈×C₉	C₄⋊C₄	1	2	yes	—
48	C₈×C₉	C₂×D₄	1	1	yes	characteristic
49	C₈×C₉	C₂×Q₈	1	1	yes	characteristic
50	C₉⋊C₈	—	2	2	no	—
51	C₂×M₃₂	—	9	1	no	—
52	C₂²×C₁₆	D₉	1	1	yes	characteristic
53	#405	—	9	1	no	—
54	C₄⋊C₁₆	—	9	4	no	—
55	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
56	C₂×C₃×C₈	Dic₆	1	2	yes	—
57	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
58	C₂×C₃×C₈	#67	1	2	yes	—
59	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
60	#217	—	3	2	no	—
61	C₄⋊Dic₃	—	3	2	no	—
62	C₄×Dic₃	—	3	2	no	—
63	#208	—	6	2	no	—
64	C₂×C₃⋊C₈	—	3	2	no	—
65	C₃×C₁₆	—	2	2	no	—
66	C₃⋊C₁₆	—	6	2	no	—
67	C₂²×C₉	—	2	2	no	—
68	C₂²×C₉	C₄⋊C₈	1	2	yes	—
69	C₂²×C₉	C₂²×C₈	1	1	yes	characteristic
70	C₄×C₉	C₄⋊C₈	1	2	yes	—
71	C₄×C₉	C₂×C₄⋊C₄	1	1	yes	characteristic
72	C₄×C₉	C₂×M₁₆	1	1	yes	characteristic
73	Dic₉	—	2	4	no	—
74	C₂×M₁₆	—	9	1	no	—
75	C₂²×C₈	C₂×D₉	1	1	yes	characteristic
76	#117	—	9	1	no	—
77	M₃₂	—	18	2	no	—
78	C₂×C₁₆	—	2	2	no	—
79	C₂×C₁₆	—	9	2	no	—
80	C₂×C₁₆	C₂×D₉	1	2	yes	—
81	#97	—	9	2	no	—
82	C₄×C₈	—	9	2	no	—
83	C₂³×C₃	D₃×C₈	1	1	yes	characteristic
84	C₂×C₃×C₄	D₃×C₈	1	1	yes	characteristic
85	C₂×C₃×C₄	ΓL(1,𝔽₂₅)	1	2	yes	—
86	C₂×C₃×C₄	Dic₃⋊C₄	1	2	yes	—
87	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
88	C₂×Dic₃	—	3	4	no	—
89	C₃×C₈	Dic₃⋊C₄	1	2	yes	—
90	C₃×C₈	C₂×Dic₆	1	1	yes	characteristic
91	C₃×C₈	C₂×#67	1	1	yes	characteristic
92	C₃⋊C₈	—	6	2	no	—
93	C₂×C₉	—	2	2	no	—
94	C₂×C₉	C₂×C₄⋊C₈	1	1	yes	characteristic
95	C₂×C₉	#504	1	2	yes	—
96	C₂²×C₄	C₄×D₉	1	1	yes	characteristic
97	M₁₆	—	18	2	no	—
98	C₂×C₈	—	9	2	no	—
99	C₂×C₈	Dic₁₈	1	2	yes	—
100	C₂×C₈	C₄×D₉	1	1	yes	characteristic
101	C₂×C₈	#611	1	2	yes	—
102	C₂×C₈	C₂²×D₉	1	1	yes	characteristic
103	C₄⋊C₄	—	9	2	no	—
104	C₂²⋊C₄	—	9	2	no	—
105	C₄²	—	9	2	no	—
106	C₁₆	—	2	2	no	—
107	C₁₆	—	18	2	no	—
108	C₂²×C₃	—	2	2	no	—
109	C₂²×C₃	Dic₃⋊C₈	1	2	yes	—
110	C₂²×C₃	C₂×D₃×C₈	1	1	yes	characteristic
111	C₃×C₄	Dic₃⋊C₈	1	2	yes	—
112	C₃×C₄	C₂×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
113	C₃×C₄	C₂×Dic₃⋊C₄	1	1	yes	characteristic
114	Dic₃	—	6	4	no	—
115	C₉	#2151	1	1	yes	characteristic, complemented, Sylow
116	C₂³	C₈×D₉	1	1	yes	characteristic
117	C₂×C₄	—	9	4	no	—
118	C₂×C₄	C₈×D₉	1	1	yes	characteristic
119	C₂×C₄	#3663	1	2	yes	—
120	C₂×C₄	Dic₉⋊C₄	1	2	yes	—
121	C₂×C₄	C₂×C₄×D₉	1	1	yes	characteristic
122	C₈	—	18	2	no	—
123	C₈	Dic₉⋊C₄	1	2	yes	—
124	C₈	C₂×Dic₁₈	1	1	yes	characteristic
125	C₈	C₂×#611	1	1	yes	characteristic
126	C₂×C₃	—	2	2	no	—
127	C₂×C₃	#4901	1	2	yes	—
128	C₂×C₃	C₂×Dic₃⋊C₈	1	1	yes	characteristic
129	C₂²	—	2	2	no	—
130	C₂²	Dic₉⋊C₈	1	2	yes	—
131	C₂²	C₂×C₈×D₉	1	1	yes	characteristic
132	C₄	—	18	4	no	—
133	C₄	Dic₉⋊C₈	1	2	yes	—
134	C₄	C₂×#3663	1	1	yes	characteristic
135	C₄	C₂×Dic₉⋊C₄	1	1	yes	characteristic
136	C₃	#71401	1	1	yes	characteristic
137	C₂	—	2	2	no	—
138	C₂	#10588581	1	2	yes	—
139	C₂	C₂×Dic₉⋊C₈	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₉×C₁₆

C₂

yes

maximal, characteristic

#10588782

C₂

yes

maximal, characteristic

C₂×#63371

C₂

yes

maximal, characteristic

Dic₉⋊C₁₆

C₂

yes

maximal, complemented

#71401

—

maximal

C₂²×C₈×C₉

C₂²

yes

characteristic

#63488

C₄

yes

characteristic

C₂×#3667

C₄

yes

characteristic

C₂×C₉×C₁₆

—

C₂×C₉×C₁₆

C₂²

yes

—

#63375

C₄

yes

—

C₈×Dic₉

C₂²

yes

—

#63371

—

C₂×C₉⋊C₁₆

C₂²

yes

—

C₂²×C₃×C₁₆

D₃

yes

characteristic

#5101

—

C₂×#812

—

Dic₃⋊C₁₆

—

C₂²×C₄×C₉

C₂×C₄

yes

characteristic

C₂×C₈×C₉

C₂×C₄

yes

characteristic

C₂×C₈×C₉

D₄

yes

—

C₂×C₈×C₉

Q₈

yes

—

C₂×C₈×C₉

C₂³

yes

characteristic

#3676

C₈

yes

—

C₄⋊Dic₉

C₈

yes

—

C₄×Dic₉

C₂×C₄

yes

—

#3667

—

C₂×C₉⋊C₈

C₂×C₄

yes

—

C₉×C₁₆

—

C₉⋊C₁₆

—

#2151

—

Sylow

C₂²×C₃×C₈

C₂×D₃

yes

characteristic

#926

—

C₂×#208

—

C₂×C₃×C₁₆

—

C₂×C₃×C₁₆

C₂×D₃

yes

—

#815

—

C₈×Dic₃

—

#812

—

C₂×C₃⋊C₁₆

—

C₂³×C₉

C₂×C₈

yes

characteristic

C₂×C₄×C₉

C₄⋊C₄

yes

—

C₂×C₄×C₉

C₂×C₈

yes

characteristic

C₂×C₄×C₉

M₁₆

yes

—

C₂×C₄×C₉

C₂²×C₄

yes

characteristic

C₂×Dic₉

C₂×C₈

yes

—

C₈×C₉

C₄⋊C₄

yes

—

C₈×C₉

C₂×D₄

yes

characteristic

C₈×C₉

C₂×Q₈

yes

characteristic

C₉⋊C₈

—

C₂×M₃₂

—

C₂²×C₁₆

D₉

yes

characteristic

#405

—

C₄⋊C₁₆

—

C₂²×C₃×C₄

C₄×D₃

yes

characteristic

C₂×C₃×C₈

Dic₆

yes

—

C₂×C₃×C₈

C₄×D₃

yes

characteristic

C₂×C₃×C₈

#67

yes

—

C₂×C₃×C₈

C₂²×D₃

yes

characteristic

#217

—

C₄⋊Dic₃

—

C₄×Dic₃

—

#208

—

C₂×C₃⋊C₈

—

C₃×C₁₆

—

C₃⋊C₁₆

—

C₂²×C₉

—

C₂²×C₉

C₄⋊C₈

yes

—

C₂²×C₉

C₂²×C₈

yes

characteristic

C₄×C₉

C₄⋊C₈

yes

—

C₄×C₉

C₂×C₄⋊C₄

yes

characteristic

C₄×C₉

C₂×M₁₆

yes

characteristic

Dic₉

—

C₂×M₁₆

—

C₂²×C₈

C₂×D₉

yes

characteristic

#117

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₉

yes

—

#97

—

C₄×C₈

—

C₂³×C₃

D₃×C₈

yes

characteristic

C₂×C₃×C₄

D₃×C₈

yes

characteristic

C₂×C₃×C₄

ΓL(1,𝔽₂₅)

yes

—

C₂×C₃×C₄

Dic₃⋊C₄

yes

—

C₂×C₃×C₄

C₂×C₄×D₃

yes

characteristic

C₂×Dic₃

—

C₃×C₈

Dic₃⋊C₄

yes

—

C₃×C₈

C₂×Dic₆

yes

characteristic

C₃×C₈

C₂×#67

yes

characteristic

C₃⋊C₈

—

C₂×C₉

—

C₂×C₉

C₂×C₄⋊C₈

yes

characteristic

C₂×C₉

#504

yes

—

C₂²×C₄

C₄×D₉

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

Dic₁₈

yes

—

100

C₂×C₈

C₄×D₉

yes

characteristic

101

C₂×C₈

#611

yes

—

102

C₂×C₈

C₂²×D₉

yes

characteristic

103

C₄⋊C₄

—

104

C₂²⋊C₄

—

105

C₄²

—

106

C₁₆

—

107

C₁₆

—

108

C₂²×C₃

—

109

C₂²×C₃

Dic₃⋊C₈

yes

—

110

C₂²×C₃

C₂×D₃×C₈

yes

characteristic

111

C₃×C₄

Dic₃⋊C₈

yes

—

112

C₃×C₄

C₂×ΓL(1,𝔽₂₅)

yes

characteristic

113

C₃×C₄

C₂×Dic₃⋊C₄

yes

characteristic

114

Dic₃

—

115

C₉

#2151

yes

characteristic, complemented, Sylow

116

C₂³

C₈×D₉

yes

characteristic

117

C₂×C₄

—

118

C₂×C₄

C₈×D₉

yes

characteristic

119

C₂×C₄

#3663

yes

—

120

C₂×C₄

Dic₉⋊C₄

yes

—

121

C₂×C₄

C₂×C₄×D₉

yes

characteristic

122

C₈

—

123

C₈

Dic₉⋊C₄

yes

—

124

C₈

C₂×Dic₁₈

yes

characteristic

125

C₈

C₂×#611

yes

characteristic

126

C₂×C₃

—

127

C₂×C₃

#4901

yes

—

128

C₂×C₃

C₂×Dic₃⋊C₈

yes

characteristic

129

C₂²

—

130

C₂²

Dic₉⋊C₈

yes

—

131

C₂²

C₂×C₈×D₉

yes

characteristic

132

C₄

—

133

C₄

Dic₉⋊C₈

yes

—

134

C₄

C₂×#3663

yes

characteristic

135

C₄

C₂×Dic₉⋊C₄

yes

characteristic

136

C₃

#71401

yes

characteristic

137

C₂

—

138

C₂

#10588581

yes

—

139

C₂

C₂×Dic₉⋊C₈

yes

characteristic

	subgroup	G/H
center	C₂×C₈	C₂²×D₉
commutator	C₂²×C₉	C₂²×C₈
Frattini	C₂×C₃×C₈	C₂²×D₃
Fitting	C₂²×C₉×C₁₆	C₂
socle	C₂²×C₃	C₂×D₃×C₈
prime radical	C₂³×C₃	D₃×C₈
cosocle	C₂×C₈×C₉	C₂³
hypercenter	C₂²×C₁₆	D₉
hypocenter	C₉	#2151
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₁₆

subgroup

G/H

center

C₂×C₈

C₂²×D₉

commutator

C₂²×C₉

C₂²×C₈

Frattini

C₂×C₃×C₈

C₂²×D₃

Fitting

C₂²×C₉×C₁₆

C₂

socle

C₂²×C₃

C₂×D₃×C₈

prime radical

C₂³×C₃

D₃×C₈

cosocle

C₂×C₈×C₉

C₂³

hypercenter

C₂²×C₁₆

D₉

C₉

G ▷ C₂²×C₉ ▷ C₉

C₁ ◁ C₂×C₈ ◁ C₂²×C₁₆

N	H ≅ G/N	type
4. Dic₉⋊C₁₆	C₂	semidirect
115. C₉	#2151	semidirect

H ≅ G/N

type

4. Dic₉⋊C₁₆

C₂

semidirect

115. C₉

#2151

semidirect

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

subgroup	index
C₂²×C₉×C₁₆	2
#10588782	2
C₂×#63371	2
Dic₉⋊C₁₆	2
#71401	3

subgroup

index

C₂²×C₉×C₁₆

#10588782

C₂×#63371

Dic₉⋊C₁₆

#71401

Subgroups — #11797014

Conjugacy classes of subgroups

Complements

Maximal subgroups