Group #11771424 — subgroups

Subgroups — #11771424

Order 1152.

168 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 54 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	C₉×#408	C₂	1	1	yes	maximal, characteristic
2	#10588230	C₂	1	2	yes	maximal, complemented
3	#67690	—	3	1	no	maximal
4	C₂×C₉×#41	C₄	1	1	yes	characteristic
5	C₂×C₉×M₁₆	C₂²	1	1	yes	characteristic
6	C₂²×C₈×C₉	C₄	1	1	yes	characteristic
7	C₉×C₂²⋊C₈	—	2	2	no	—
8	#63371	—	2	2	no	—
9	C₃×#408	D₃	1	1	yes	characteristic
10	#4553	—	3	2	no	—
11	C₉×#41	—	4	1	no	—
12	C₉×#41	—	4	1	no	—
13	C₂×Q₈×C₉	C₈	1	1	yes	characteristic
14	C₂×D₄×C₉	—	2	1	no	—
15	C₂×D₄×C₉	C₈	1	1	yes	characteristic
16	C₂²×C₄×C₉	—	2	1	no	—
17	C₂²×C₄×C₉	C₂×C₄	1	1	yes	characteristic
18	C₉×M₁₆	—	4	1	no	—
19	C₂×C₈×C₉	—	2	1	no	—
20	C₂×C₈×C₉	—	4	1	no	—
21	C₂×C₈×C₉	D₄	1	2	yes	—
22	C₉⋊C₁₆	—	4	2	no	—
23	#1321	—	9	1	no	Sylow
24	C₂×C₃×#41	Dic₃	1	1	yes	characteristic
25	C₂×C₃×M₁₆	C₂×D₃	1	1	yes	characteristic
26	C₂²×C₃×C₈	Dic₃	1	1	yes	characteristic
27	C₃×C₂²⋊C₈	—	2	2	no	—
28	#812	—	6	2	no	—
29	C₂³×C₉	—	2	1	no	—
30	C₂³×C₉	M₁₆	1	1	yes	characteristic
31	Q₈×C₉	—	4	1	no	—
32	D₄×C₉	—	4	1	no	—
33	D₄×C₉	—	4	2	no	—
34	C₂×C₄×C₉	—	2	1	no	—
35	C₂×C₄×C₉	—	2	1	no	—
36	C₂×C₄×C₉	—	2	1	no	—
37	C₂×C₄×C₉	—	4	1	no	—
38	C₂×C₄×C₉	—	4	1	no	—
39	C₂×C₄×C₉	C₂²⋊C₄	1	1	yes	characteristic
40	C₂×C₄×C₉	C₂×C₈	1	1	yes	characteristic
41	C₈×C₉	—	2	2	no	—
42	C₈×C₉	—	4	1	no	—
43	#408	D₉	1	1	yes	characteristic
44	#349	—	9	2	no	—
45	C₃×#41	—	4	1	no	—
46	C₃×#41	—	4	1	no	—
47	C₂×C₃×Q₈	C₃⋊C₈	1	1	yes	characteristic
48	C₂×C₃×D₄	—	2	1	no	—
49	C₂×C₃×D₄	C₃⋊C₈	1	1	yes	characteristic
50	C₂²×C₃×C₄	—	2	1	no	—
51	C₂²×C₃×C₄	C₂×Dic₃	1	1	yes	characteristic
52	C₃×M₁₆	—	4	1	no	—
53	C₂×C₃×C₈	—	2	1	no	—
54	C₂×C₃×C₈	—	4	1	no	—
55	C₂×C₃×C₈	#67	1	2	yes	—
56	C₃⋊C₁₆	—	12	2	no	—
57	C₂²×C₉	—	2	1	no	—
58	C₂²×C₉	—	4	1	no	—
59	C₂²×C₉	—	4	2	no	—
60	C₂²×C₉	—	4	1	no	—
61	C₂²×C₉	C₂²⋊C₈	1	1	yes	characteristic
62	C₄×C₉	—	2	1	no	—
63	C₄×C₉	—	4	1	no	—
64	C₄×C₉	#99	1	1	yes	characteristic
65	C₄×C₉	#100	1	1	yes	characteristic
66	C₂×#41	Dic₉	1	1	yes	characteristic
67	C₂×M₁₆	C₂×D₉	1	1	yes	characteristic
68	C₂²×C₈	Dic₉	1	1	yes	characteristic
69	M₃₂	—	18	2	no	—
70	C₂²⋊C₈	—	2	2	no	—
71	C₂³×C₃	—	2	1	no	—
72	C₂³×C₃	#208	1	1	yes	characteristic
73	C₃×Q₈	—	4	1	no	—
74	C₃×D₄	—	4	1	no	—
75	C₃×D₄	—	4	2	no	—
76	C₂×C₃×C₄	—	2	1	no	—
77	C₂×C₃×C₄	—	2	1	no	—
78	C₂×C₃×C₄	—	2	1	no	—
79	C₂×C₃×C₄	—	4	1	no	—
80	C₂×C₃×C₄	—	4	1	no	—
81	C₂×C₃×C₄	C₂×C₃⋊C₈	1	1	yes	characteristic
82	C₂×C₃×C₄	#217	1	1	yes	characteristic
83	C₃×C₈	—	2	2	no	—
84	C₃×C₈	—	4	1	no	—
85	C₂×C₉	—	2	1	no	—
86	C₂×C₉	—	4	1	no	—
87	C₂×C₉	—	8	1	no	—
88	C₂×C₉	#323	1	1	yes	characteristic
89	#41	—	4	1	no	—
90	#41	—	4	1	no	—
91	C₂×Q₈	C₉⋊C₈	1	1	yes	characteristic
92	C₂×D₄	—	2	1	no	—
93	C₂×D₄	C₉⋊C₈	1	1	yes	characteristic
94	C₂²×C₄	—	2	1	no	—
95	C₂²×C₄	C₂×Dic₉	1	1	yes	characteristic
96	M₁₆	—	4	1	no	—
97	C₂×C₈	—	2	1	no	—
98	C₂×C₈	—	4	1	no	—
99	C₂×C₈	#611	1	2	yes	—
100	C₁₆	—	36	2	no	—
101	C₂²×C₃	—	2	1	no	—
102	C₂²×C₃	—	4	1	no	—
103	C₂²×C₃	—	4	2	no	—
104	C₂²×C₃	—	4	1	no	—
105	C₂²×C₃	#830	1	1	yes	characteristic
106	C₃×C₄	—	2	1	no	—
107	C₃×C₄	—	4	1	no	—
108	C₃×C₄	#833	1	1	yes	characteristic
109	C₃×C₄	#834	1	1	yes	characteristic
110	C₉	#1321	1	1	yes	characteristic, complemented, Sylow
111	C₂³	—	2	1	no	—
112	C₂³	#3667	1	1	yes	characteristic
113	Q₈	—	4	1	no	—
114	D₄	—	4	1	no	—
115	D₄	—	4	2	no	—
116	C₂×C₄	—	2	1	no	—
117	C₂×C₄	—	2	1	no	—
118	C₂×C₄	—	2	1	no	—
119	C₂×C₄	—	4	1	no	—
120	C₂×C₄	—	4	1	no	—
121	C₂×C₄	C₂×C₉⋊C₈	1	1	yes	characteristic
122	C₂×C₄	#3676	1	1	yes	characteristic
123	C₈	—	2	2	no	—
124	C₈	—	4	1	no	—
125	C₂×C₃	—	2	1	no	—
126	C₂×C₃	—	4	1	no	—
127	C₂×C₃	—	8	1	no	—
128	C₂×C₃	#4525	1	1	yes	characteristic
129	C₂²	—	2	1	no	—
130	C₂²	—	4	1	no	—
131	C₂²	—	4	2	no	—
132	C₂²	—	4	1	no	—
133	C₂²	#63389	1	1	yes	characteristic
134	C₄	—	2	1	no	—
135	C₄	—	4	1	no	—
136	C₄	#63391	1	1	yes	characteristic
137	C₄	#63393	1	1	yes	characteristic
138	C₃	#67690	1	1	yes	characteristic
139	C₂	—	2	1	no	—
140	C₂	—	4	1	no	—
141	C₂	—	8	1	no	—
142	C₂	#10588202	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₉×#408

C₂

yes

maximal, characteristic

#10588230

C₂

yes

maximal, complemented

#67690

—

maximal

C₂×C₉×#41

C₄

yes

characteristic

C₂×C₉×M₁₆

C₂²

yes

characteristic

C₂²×C₈×C₉

C₄

yes

characteristic

C₉×C₂²⋊C₈

—

#63371

—

C₃×#408

D₃

yes

characteristic

#4553

—

C₉×#41

—

C₉×#41

—

C₂×Q₈×C₉

C₈

yes

characteristic

C₂×D₄×C₉

—

C₂×D₄×C₉

C₈

yes

characteristic

C₂²×C₄×C₉

—

C₂²×C₄×C₉

C₂×C₄

yes

characteristic

C₉×M₁₆

—

C₂×C₈×C₉

—

C₂×C₈×C₉

—

C₂×C₈×C₉

D₄

yes

—

C₉⋊C₁₆

—

#1321

—

Sylow

C₂×C₃×#41

Dic₃

yes

characteristic

C₂×C₃×M₁₆

C₂×D₃

yes

characteristic

C₂²×C₃×C₈

Dic₃

yes

characteristic

C₃×C₂²⋊C₈

—

#812

—

C₂³×C₉

—

C₂³×C₉

M₁₆

yes

characteristic

Q₈×C₉

—

D₄×C₉

—

D₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₉

C₂×C₈

yes

characteristic

C₈×C₉

—

C₈×C₉

—

#408

D₉

yes

characteristic

#349

—

C₃×#41

—

C₃×#41

—

C₂×C₃×Q₈

C₃⋊C₈

yes

characteristic

C₂×C₃×D₄

—

C₂×C₃×D₄

C₃⋊C₈

yes

characteristic

C₂²×C₃×C₄

—

C₂²×C₃×C₄

C₂×Dic₃

yes

characteristic

C₃×M₁₆

—

C₂×C₃×C₈

—

C₂×C₃×C₈

—

C₂×C₃×C₈

#67

yes

—

C₃⋊C₁₆

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

C₂²⋊C₈

yes

characteristic

C₄×C₉

—

C₄×C₉

—

C₄×C₉

yes

C₄×C₉

yes

C₂×#41

Dic₉

yes

characteristic

C₂×M₁₆

C₂×D₉

yes

characteristic

C₂²×C₈

Dic₉

yes

characteristic

M₃₂

—

C₂²⋊C₈

—

C₂³×C₃

—

C₂³×C₃

#208

yes

characteristic

C₃×Q₈

—

C₃×D₄

—

C₃×D₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

C₂×C₃⋊C₈

yes

characteristic

C₂×C₃×C₄

#217

yes

characteristic

C₃×C₈

—

C₃×C₈

—

C₂×C₉

—

C₂×C₉

—

C₂×C₉

—

C₂×C₉

yes

—

—

C₂×Q₈

C₉⋊C₈

yes

characteristic

C₂×D₄

—

C₂×D₄

C₉⋊C₈

yes

characteristic

C₂²×C₄

—

C₂²×C₄

C₂×Dic₉

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

#611

yes

—

100

C₁₆

—

101

C₂²×C₃

—

102

C₂²×C₃

—

103

C₂²×C₃

—

104

C₂²×C₃

—

105

C₂²×C₃

#830

yes

characteristic

106

C₃×C₄

—

107

C₃×C₄

—

108

C₃×C₄

#833

yes

characteristic

109

C₃×C₄

#834

yes

characteristic

110

C₉

#1321

yes

characteristic, complemented, Sylow

111

C₂³

—

112

C₂³

#3667

yes

characteristic

113

Q₈

—

114

D₄

—

115

D₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

C₂×C₉⋊C₈

yes

characteristic

122

C₂×C₄

#3676

yes

characteristic

123

C₈

—

124

C₈

—

125

C₂×C₃

—

126

C₂×C₃

—

127

C₂×C₃

—

128

C₂×C₃

#4525

yes

characteristic

129

C₂²

—

130

C₂²

—

131

C₂²

—

132

C₂²

—

133

C₂²

#63389

yes

characteristic

134

C₄

—

135

C₄

—

136

C₄

#63391

yes

characteristic

137

C₄

#63393

yes

characteristic

138

C₃

#67690

yes

characteristic

139

C₂

—

140

C₂

—

141

C₂

—

142

C₂

#10588202

yes

characteristic

	subgroup	G/H
center	C₄	#63393
commutator	C₂×C₄×C₉	C₂×C₈
Frattini	C₂×C₃×M₁₆	C₂×D₃
Fitting	C₉×#408	C₂
socle	C₂×C₃	#4525
prime radical	C₂×C₃×#41	Dic₃
cosocle	C₂×C₉×M₁₆	C₂²
hypercenter	#408	D₉
hypocenter	C₉	#1321
LCS	G ▷ C₂×C₄×C₉ ▷ C₂²×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #408

subgroup

G/H

center

C₄

#63393

commutator

C₂×C₄×C₉

C₂×C₈

Frattini

C₂×C₃×M₁₆

C₂×D₃

C₂

C₂×C₃

C₂×C₃×#41

Dic₃

cosocle

C₂×C₉×M₁₆

C₂²

D₉

C₉

G ▷ C₂×C₄×C₉ ▷ C₂²×C₉ ▷ C₂×C₉ ▷ C₉

UCS

C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #408

N	H ≅ G/N	type
2. #10588230	C₂	semidirect
110. C₉	#1321	semidirect

H ≅ G/N

type

2. #10588230

C₂

semidirect

110. C₉

#1321

semidirect

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

subgroup	index
C₉×#408	2
#10588230	2
#67690	3

subgroup

index

C₉×#408

#10588230

#67690

Subgroups — #11771424

Conjugacy classes of subgroups

Complements

Maximal subgroups