Group #11775757 — subgroups

Subgroups — #11775757

Order 1152.

339 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 339 conjugacy classes of subgroups — too many to draw. Only its 122 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×#533	C₂	1	1	yes	maximal, characteristic
2	C₄×#3667	C₂	1	2	yes	maximal
3	#10588220	C₂	1	4	yes	maximal, complemented
4	#71821	—	3	1	no	maximal
5	C₉×C₄⋊Q₈	C₄	1	2	yes	—
6	C₉×#125	C₂²	1	2	yes	—
7	C₉×C₂²⋊Q₈	—	2	2	no	—
8	C₄×Q₈×C₉	—	2	2	no	—
9	C₉×#117	C₄	1	2	yes	—
10	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
11	C₂×#3667	—	2	2	no	—
12	#63362	C₂²	1	4	yes	—
13	C₄×C₉⋊C₈	—	2	2	no	—
14	C₃×#533	D₃	1	1	yes	characteristic
15	C₄×#208	—	3	2	no	—
16	#4543	—	3	4	no	—
17	C₂×Q₈×C₉	—	2	2	no	—
18	C₂²×C₄×C₉	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₄×C₉	D₄	1	2	yes	—
20	C₉×C₄⋊C₄	—	2	2	no	—
21	C₉×C₄⋊C₄	—	2	4	no	—
22	C₉×C₄⋊C₄	C₂×C₄	1	4	yes	—
23	C₉×C₂²⋊C₄	—	2	2	no	—
24	C₄²×C₉	—	2	2	no	—
25	C₄²×C₉	C₂×C₄	1	1	yes	characteristic
26	C₄²×C₉	D₄	1	2	yes	—
27	C₄²×C₉	C₂³	1	1	yes	characteristic
28	#3667	—	2	8	no	—
29	C₂×C₉⋊C₈	—	2	4	no	—
30	#1526	—	9	1	no	Sylow
31	C₃×C₄⋊Q₈	Dic₃	1	2	yes	—
32	C₃×#125	C₂×D₃	1	2	yes	—
33	C₃×C₂²⋊Q₈	—	2	2	no	—
34	C₃×C₄×Q₈	—	2	2	no	—
35	C₃×#117	Dic₃	1	2	yes	—
36	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
37	C₂×#208	—	6	2	no	—
38	#803	—	3	4	no	—
39	C₄×C₃⋊C₈	—	6	2	no	—
40	C₂³×C₉	C₂²⋊C₄	1	1	yes	characteristic
41	Q₈×C₉	—	4	4	no	—
42	C₂×C₄×C₉	—	2	2	no	—
43	C₂×C₄×C₉	—	2	4	no	—
44	C₂×C₄×C₉	—	2	4	no	—
45	C₂×C₄×C₉	C₂²⋊C₄	1	1	yes	characteristic
46	C₂×C₄×C₉	C₂²⋊C₄	1	2	yes	—
47	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
48	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
49	C₉⋊C₈	—	2	8	no	—
50	#533	D₉	1	1	yes	characteristic
51	C₄×M₁₆	—	9	2	no	—
52	#330	—	9	4	no	—
53	C₂×C₃×Q₈	—	2	2	no	—
54	C₂²×C₃×C₄	C₂×Dic₃	1	1	yes	characteristic
55	C₂²×C₃×C₄	#67	1	2	yes	—
56	C₃×C₄⋊C₄	—	2	2	no	—
57	C₃×C₄⋊C₄	—	2	4	no	—
58	C₃×C₄⋊C₄	C₂×Dic₃	1	4	yes	—
59	C₃×C₂²⋊C₄	—	2	2	no	—
60	C₃×C₄²	—	2	2	no	—
61	C₃×C₄²	C₂×Dic₃	1	1	yes	characteristic
62	C₃×C₄²	#67	1	2	yes	—
63	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
64	#208	—	6	8	no	—
65	C₂×C₃⋊C₈	—	6	4	no	—
66	C₂²×C₉	—	2	1	no	—
67	C₂²×C₉	—	2	2	no	—
68	C₂²×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
69	C₄×C₉	—	2	1	no	—
70	C₄×C₉	—	2	2	no	—
71	C₄×C₉	—	4	4	no	—
72	C₄×C₉	#101	1	2	yes	—
73	C₄×C₉	#104	1	4	yes	—
74	C₂×M₁₆	—	18	2	no	—
75	C₄⋊Q₈	Dic₉	1	2	yes	—
76	#125	C₂×D₉	1	2	yes	—
77	C₂²⋊Q₈	—	2	2	no	—
78	C₄×Q₈	—	2	2	no	—
79	#117	Dic₉	1	2	yes	—
80	C₂×C₄²	C₂×D₉	1	1	yes	characteristic
81	#97	—	9	4	no	—
82	C₄×C₈	—	18	2	no	—
83	C₂³×C₃	#217	1	1	yes	characteristic
84	C₃×Q₈	—	4	4	no	—
85	C₂×C₃×C₄	—	2	2	no	—
86	C₂×C₃×C₄	—	2	4	no	—
87	C₂×C₃×C₄	—	2	4	no	—
88	C₂×C₃×C₄	#217	1	2	yes	—
89	C₂×C₃×C₄	#217	1	1	yes	characteristic
90	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
91	C₂×C₃×C₄	C₂×#67	1	2	yes	—
92	C₃⋊C₈	—	6	8	no	—
93	C₂×C₉	—	4	1	no	—
94	C₂×C₉	C₂×#101	1	1	yes	characteristic
95	C₂×C₉	C₂×#104	1	2	yes	—
96	C₂×Q₈	—	2	2	no	—
97	C₂²×C₄	C₂×Dic₉	1	1	yes	characteristic
98	C₂²×C₄	#611	1	2	yes	—
99	M₁₆	—	18	8	no	—
100	C₂×C₈	—	18	4	no	—
101	C₄⋊C₄	—	2	2	no	—
102	C₄⋊C₄	—	2	4	no	—
103	C₄⋊C₄	C₂×Dic₉	1	4	yes	—
104	C₂²⋊C₄	—	2	2	no	—
105	C₄²	—	2	2	no	—
106	C₄²	C₂×Dic₉	1	1	yes	characteristic
107	C₄²	#611	1	2	yes	—
108	C₄²	C₂²×D₉	1	1	yes	characteristic
109	C₂²×C₃	—	2	1	no	—
110	C₂²×C₃	—	2	2	no	—
111	C₂²×C₃	C₂×#217	1	1	yes	characteristic
112	C₃×C₄	—	2	1	no	—
113	C₃×C₄	—	2	2	no	—
114	C₃×C₄	—	4	4	no	—
115	C₃×C₄	#836	1	2	yes	—
116	C₃×C₄	#837	1	4	yes	—
117	C₉	#1526	1	1	yes	characteristic, complemented, Sylow
118	C₂³	#3676	1	1	yes	characteristic
119	Q₈	—	4	4	no	—
120	C₂×C₄	—	2	2	no	—
121	C₂×C₄	—	2	4	no	—
122	C₂×C₄	—	2	4	no	—
123	C₂×C₄	#3676	1	2	yes	—
124	C₂×C₄	#3676	1	1	yes	characteristic
125	C₂×C₄	C₂²×Dic₉	1	1	yes	characteristic
126	C₂×C₄	C₂×#611	1	2	yes	—
127	C₈	—	18	8	no	—
128	C₂×C₃	—	4	1	no	—
129	C₂×C₃	C₂×#836	1	1	yes	characteristic
130	C₂×C₃	C₂×#837	1	2	yes	—
131	C₂²	—	2	1	no	—
132	C₂²	—	2	2	no	—
133	C₂²	C₂×#3676	1	1	yes	characteristic
134	C₄	—	2	1	no	—
135	C₄	—	2	2	no	—
136	C₄	—	4	4	no	—
137	C₄	#63394	1	2	yes	—
138	C₄	#63396	1	4	yes	—
139	C₃	#71821	1	1	yes	characteristic
140	C₂	—	4	1	no	—
141	C₂	C₂×#63394	1	1	yes	characteristic
142	C₂	C₂×#63396	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₉×#533

C₂

yes

maximal, characteristic

C₄×#3667

C₂

yes

maximal

#10588220

C₂

yes

maximal, complemented

#71821

—

maximal

C₉×C₄⋊Q₈

C₄

yes

—

C₉×#125

C₂²

yes

—

C₉×C₂²⋊Q₈

—

C₄×Q₈×C₉

—

C₉×#117

C₄

yes

—

C₂×C₄²×C₉

C₂²

yes

characteristic

C₂×#3667

—

#63362

C₂²

yes

—

C₄×C₉⋊C₈

—

C₃×#533

D₃

yes

characteristic

C₄×#208

—

#4543

—

C₂×Q₈×C₉

—

C₂²×C₄×C₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₉

D₄

yes

—

C₉×C₄⋊C₄

—

C₉×C₄⋊C₄

—

C₉×C₄⋊C₄

C₂×C₄

yes

—

C₉×C₂²⋊C₄

—

C₄²×C₉

—

C₄²×C₉

C₂×C₄

yes

characteristic

C₄²×C₉

D₄

yes

—

C₄²×C₉

C₂³

yes

characteristic

#3667

—

C₂×C₉⋊C₈

—

#1526

—

Sylow

C₃×C₄⋊Q₈

Dic₃

yes

—

C₃×#125

C₂×D₃

yes

—

C₃×C₂²⋊Q₈

—

C₃×C₄×Q₈

—

C₃×#117

Dic₃

yes

—

C₂×C₃×C₄²

C₂×D₃

yes

characteristic

C₂×#208

—

#803

—

C₄×C₃⋊C₈

—

C₂³×C₉

C₂²⋊C₄

yes

characteristic

Q₈×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₉

C₂²⋊C₄

yes

—

C₂×C₄×C₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₉

C₂×D₄

yes

—

C₉⋊C₈

—

#533

D₉

yes

characteristic

C₄×M₁₆

—

#330

—

C₂×C₃×Q₈

—

C₂²×C₃×C₄

C₂×Dic₃

yes

characteristic

C₂²×C₃×C₄

#67

yes

—

C₃×C₄⋊C₄

—

C₃×C₄⋊C₄

—

C₃×C₄⋊C₄

C₂×Dic₃

yes

—

C₃×C₂²⋊C₄

—

C₃×C₄²

—

C₃×C₄²

C₂×Dic₃

yes

characteristic

C₃×C₄²

#67

yes

—

C₃×C₄²

C₂²×D₃

yes

characteristic

#208

—

C₂×C₃⋊C₈

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₉

—

C₄×C₉

—

C₄×C₉

—

C₄×C₉

#101

yes

—

C₄×C₉

#104

yes

—

C₂×M₁₆

—

C₄⋊Q₈

Dic₉

yes

—

#125

C₂×D₉

yes

—

C₂²⋊Q₈

—

C₄×Q₈

—

#117

Dic₉

yes

—

C₂×C₄²

C₂×D₉

yes

characteristic

#97

—

C₄×C₈

—

C₂³×C₃

#217

yes

characteristic

C₃×Q₈

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

#217

yes

—

C₂×C₃×C₄

#217

yes

characteristic

C₂×C₃×C₄

C₂²×Dic₃

yes

characteristic

C₂×C₃×C₄

C₂×#67

yes

—

C₃⋊C₈

—

C₂×C₉

—

C₂×C₉

C₂×#101

yes

characteristic

C₂×C₉

C₂×#104

yes

—

C₂×Q₈

—

C₂²×C₄

C₂×Dic₉

yes

characteristic

C₂²×C₄

#611

yes

—

M₁₆

—

100

C₂×C₈

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄⋊C₄

C₂×Dic₉

yes

—

104

C₂²⋊C₄

—

105

C₄²

—

106

C₄²

C₂×Dic₉

yes

characteristic

107

C₄²

#611

yes

—

108

C₄²

C₂²×D₉

yes

characteristic

109

C₂²×C₃

—

110

C₂²×C₃

—

111

C₂²×C₃

C₂×#217

yes

characteristic

112

C₃×C₄

—

113

C₃×C₄

—

114

C₃×C₄

—

115

C₃×C₄

#836

yes

—

116

C₃×C₄

#837

yes

—

117

C₉

#1526

yes

characteristic, complemented, Sylow

118

C₂³

#3676

yes

characteristic

119

Q₈

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

#3676

yes

—

124

C₂×C₄

#3676

yes

characteristic

125

C₂×C₄

C₂²×Dic₉

yes

characteristic

126

C₂×C₄

C₂×#611

yes

—

127

C₈

—

128

C₂×C₃

—

129

C₂×C₃

C₂×#836

yes

characteristic

130

C₂×C₃

C₂×#837

yes

—

131

C₂²

—

132

C₂²

—

133

C₂²

C₂×#3676

yes

characteristic

134

C₄

—

135

C₄

—

136

C₄

—

137

C₄

#63394

yes

—

138

C₄

#63396

yes

—

139

C₃

#71821

yes

characteristic

140

C₂

—

141

C₂

C₂×#63394

yes

characteristic

142

C₂

C₂×#63396

yes

—

	subgroup	G/H
center	C₂×C₄	#3676
commutator	C₂×C₄×C₉	C₂²×C₄
Frattini	C₃×C₄²	C₂²×D₃
Fitting	C₉×#533	C₂
socle	C₂²×C₃	C₂×#217
prime radical	C₂³×C₃	#217
cosocle	C₄²×C₉	C₂³
hypercenter	#533	D₉
hypocenter	C₉	#1526
LCS	G ▷ C₂×C₄×C₉ ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #533

subgroup

G/H

center

C₂×C₄

#3676

commutator

C₂×C₄×C₉

C₂²×C₄

Frattini

C₃×C₄²

C₂²×D₃

C₂

C₂²×C₃

C₂³×C₃

C₄²×C₉

C₂³

D₉

C₉

G ▷ C₂×C₄×C₉ ▷ C₂²×C₉ ▷ C₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #533

N	H ≅ G/N	type
3. #10588220	C₂	semidirect
117. C₉	#1526	semidirect

H ≅ G/N

type

3. #10588220

C₂

semidirect

117. C₉

#1526

semidirect

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

subgroup	index
C₉×#533	2
C₄×#3667	2
#10588220	2
#71821	3

subgroup

index

Subgroups — #11775757

Conjugacy classes of subgroups

Complements

Maximal subgroups