Group #11767102 — subgroups

Subgroups — C₉×#2381 #11767102

Order 1152.

636 conjugacy classes of subgroups; only the 396 normal subgroups are shown.

normal subgroups only

This group has 636 conjugacy classes of subgroups — too many to draw. Only its 396 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×C₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₉×#391	C₂	1	4	yes	maximal
3	C₉×#387	C₂	1	8	yes	maximal
4	C₉×#383	C₂	1	2	yes	maximal
5	C₃×#2381	C₃	1	1	yes	maximal, characteristic
6	C₂²×Q₈×C₉	C₂²	1	2	yes	—
7	C₉×C₄⋊Q₈	C₄	1	8	yes	complemented
8	C₂×C₉×C₄⋊C₄	C₂²	1	4	yes	—
9	C₂×C₉×C₄⋊C₄	C₂²	1	4	yes	—
10	C₂×C₄²×C₉	C₂²	1	4	yes	—
11	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
12	C₉×#95	C₂²	1	8	yes	—
13	C₉×#95	C₂²	1	4	yes	—
14	C₉×#95	C₂²	1	8	yes	—
15	C₂×C₃×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic
16	C₃×#391	C₂×C₃	1	4	yes	—
17	C₃×#387	C₂×C₃	1	8	yes	—
18	C₃×#383	C₂×C₃	1	2	yes	—
19	C₂×Q₈×C₉	—	4	2	no	—
20	C₂×Q₈×C₉	—	4	2	no	—
21	C₂×Q₈×C₉	C₂×C₄	1	8	yes	—
22	C₂²×C₄×C₉	C₂³	1	8	yes	—
23	C₂²×C₄×C₉	C₂³	1	4	yes	—
24	C₂²×C₄×C₉	C₂³	1	2	yes	—
25	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
26	C₉×C₄⋊C₄	—	4	4	no	—
27	C₉×C₄⋊C₄	C₂×C₄	1	16	yes	—
28	C₄²×C₉	—	4	4	no	—
29	C₄²×C₉	C₂×C₄	1	4	yes	—
30	#2381	C₉	1	1	yes	characteristic, direct product factor, Sylow
31	C₂²×C₃×Q₈	C₂²×C₃	1	2	yes	—
32	C₃×C₄⋊Q₈	C₃×C₄	1	8	yes	—
33	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
34	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
35	C₂×C₃×C₄²	C₂²×C₃	1	4	yes	—
36	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
37	C₃×#95	C₂²×C₃	1	8	yes	—
38	C₃×#95	C₂²×C₃	1	4	yes	—
39	C₃×#95	C₂²×C₃	1	8	yes	—
40	C₂³×C₉	C₂⁴	1	1	yes	characteristic
41	Q₈×C₉	—	4	8	no	—
42	C₂×C₄×C₉	—	2	4	no	—
43	C₂×C₄×C₉	—	2	4	no	—
44	C₂×C₄×C₉	—	2	2	no	—
45	C₂×C₄×C₉	—	2	4	no	—
46	C₂×C₄×C₉	—	2	8	no	—
47	C₂×C₄×C₉	—	2	16	no	—
48	C₂×C₄×C₉	C₂²×C₄	1	4	yes	—
49	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
50	C₂×C₄×C₉	C₂²×C₄	1	8	yes	—
51	C₂×C₄⋊Q₈	C₂×C₉	1	1	yes	characteristic
52	#391	C₂×C₉	1	4	yes	—
53	#387	C₂×C₉	1	8	yes	—
54	#383	C₂×C₉	1	2	yes	—
55	C₂×C₃×Q₈	—	4	2	no	—
56	C₂×C₃×Q₈	—	4	2	no	—
57	C₂×C₃×Q₈	C₂×C₃×C₄	1	8	yes	—
58	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
59	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
60	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
61	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
62	C₃×C₄⋊C₄	—	4	4	no	—
63	C₃×C₄⋊C₄	C₂×C₃×C₄	1	16	yes	—
64	C₃×C₄²	—	4	4	no	—
65	C₃×C₄²	C₂×C₃×C₄	1	4	yes	—
66	C₂²×C₉	C₂³×C₄	1	1	yes	characteristic
67	C₂²×C₉	H(5,𝔽₂)	1	2	yes	—
68	C₂²×C₉	2₋¹⁺⁴	1	4	yes	—
69	C₄×C₉	—	2	8	no	—
70	C₄×C₉	—	2	2	no	—
71	C₄×C₉	—	2	4	no	—
72	C₄×C₉	—	4	8	no	—
73	C₂²×Q₈	C₂²×C₉	1	2	yes	—
74	C₄⋊Q₈	C₄×C₉	1	8	yes	complemented
75	C₂×C₄⋊C₄	C₂²×C₉	1	4	yes	—
76	C₂×C₄⋊C₄	C₂²×C₉	1	4	yes	—
77	C₂×C₄²	C₂²×C₉	1	4	yes	—
78	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
79	#95	C₂²×C₉	1	8	yes	—
80	#95	C₂²×C₉	1	4	yes	—
81	#95	C₂²×C₉	1	8	yes	—
82	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
83	C₃×Q₈	—	4	8	no	—
84	C₂×C₃×C₄	—	2	4	no	—
85	C₂×C₃×C₄	—	2	4	no	—
86	C₂×C₃×C₄	—	2	2	no	—
87	C₂×C₃×C₄	—	2	4	no	—
88	C₂×C₃×C₄	—	2	8	no	—
89	C₂×C₃×C₄	—	2	16	no	—
90	C₂×C₃×C₄	C₂²×C₃×C₄	1	4	yes	—
91	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
92	C₂×C₃×C₄	C₂²×C₃×C₄	1	8	yes	—
93	C₂×C₉	#518	1	1	yes	characteristic
94	C₂×C₉	#519	1	2	yes	—
95	C₂×C₉	#563	1	4	yes	—
96	C₂×Q₈	—	4	2	no	—
97	C₂×Q₈	—	4	2	no	—
98	C₂×Q₈	C₂×C₄×C₉	1	8	yes	—
99	C₂²×C₄	C₂³×C₉	1	8	yes	—
100	C₂²×C₄	C₂³×C₉	1	2	yes	—
101	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
102	C₂²×C₄	C₂³×C₉	1	4	yes	—
103	C₄⋊C₄	—	4	4	no	—
104	C₄⋊C₄	C₂×C₄×C₉	1	16	yes	—
105	C₄²	—	4	4	no	—
106	C₄²	C₂×C₄×C₉	1	4	yes	—
107	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
108	C₂²×C₃	C₃×H(5,𝔽₂)	1	2	yes	—
109	C₂²×C₃	C₃×2₋¹⁺⁴	1	4	yes	—
110	C₃×C₄	—	2	2	no	—
111	C₃×C₄	—	2	8	no	—
112	C₃×C₄	—	2	4	no	—
113	C₃×C₄	—	4	8	no	—
114	C₉	#2381	1	1	yes	characteristic, direct product factor, Sylow
115	C₂³	C₂⁴×C₉	1	1	yes	characteristic
116	Q₈	—	4	8	no	—
117	C₂×C₄	—	2	4	no	—
118	C₂×C₄	—	2	4	no	—
119	C₂×C₄	—	2	2	no	—
120	C₂×C₄	—	2	4	no	—
121	C₂×C₄	—	2	8	no	—
122	C₂×C₄	—	2	16	no	—
123	C₂×C₄	C₂²×C₄×C₉	1	4	yes	—
124	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
125	C₂×C₄	C₂²×C₄×C₉	1	8	yes	—
126	C₂×C₃	C₃×#518	1	1	yes	characteristic
127	C₂×C₃	C₃×#519	1	2	yes	—
128	C₂×C₃	C₃×#563	1	4	yes	—
129	C₂²	C₂³×C₄×C₉	1	1	yes	characteristic
130	C₂²	C₉×H(5,𝔽₂)	1	2	yes	—
131	C₂²	C₉×2₋¹⁺⁴	1	4	yes	—
132	C₄	—	2	2	no	—
133	C₄	—	2	8	no	—
134	C₄	—	2	4	no	—
135	C₄	—	4	8	no	—
136	C₃	C₃×#2381	1	1	yes	characteristic
137	C₂	C₉×#518	1	1	yes	characteristic
138	C₂	C₉×#519	1	2	yes	—
139	C₂	C₉×#563	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₉×C₄⋊Q₈

C₂

yes

maximal, characteristic

C₉×#391

C₂

yes

maximal

C₉×#387

C₂

yes

maximal

C₉×#383

C₂

yes

maximal

C₃×#2381

C₃

yes

maximal, characteristic

C₂²×Q₈×C₉

C₂²

yes

—

C₉×C₄⋊Q₈

C₄

yes

complemented

C₂×C₉×C₄⋊C₄

C₂²

yes

—

C₂×C₉×C₄⋊C₄

C₂²

yes

—

C₂×C₄²×C₉

C₂²

yes

—

C₂×C₄²×C₉

C₂²

yes

characteristic

C₉×#95

C₂²

yes

—

C₉×#95

C₂²

yes

—

C₉×#95

C₂²

yes

—

C₂×C₃×C₄⋊Q₈

C₂×C₃

yes

characteristic

C₃×#391

C₂×C₃

yes

—

C₃×#387

C₂×C₃

yes

—

C₃×#383

C₂×C₃

yes

—

C₂×Q₈×C₉

—

C₂×Q₈×C₉

—

C₂×Q₈×C₉

C₂×C₄

yes

—

C₂²×C₄×C₉

C₂³

yes

—

C₂²×C₄×C₉

C₂³

yes

—

C₂²×C₄×C₉

C₂³

yes

—

C₂²×C₄×C₉

C₂³

yes

characteristic

C₉×C₄⋊C₄

—

C₉×C₄⋊C₄

C₂×C₄

yes

—

C₄²×C₉

—

C₄²×C₉

C₂×C₄

yes

—

#2381

C₉

yes

characteristic, direct product factor, Sylow

C₂²×C₃×Q₈

C₂²×C₃

yes

—

C₃×C₄⋊Q₈

C₃×C₄

yes

—

C₂×C₃×C₄⋊C₄

C₂²×C₃

yes

—

C₂×C₃×C₄⋊C₄

C₂²×C₃

yes

—

C₂×C₃×C₄²

C₂²×C₃

yes

—

C₂×C₃×C₄²

C₂²×C₃

yes

characteristic

C₃×#95

C₂²×C₃

yes

—

C₃×#95

C₂²×C₃

yes

—

C₃×#95

C₂²×C₃

yes

—

C₂³×C₉

C₂⁴

yes

characteristic

Q₈×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

C₂²×C₄

yes

—

C₂×C₄×C₉

C₂²×C₄

yes

—

C₂×C₄×C₉

C₂²×C₄

yes

—

C₂×C₄⋊Q₈

C₂×C₉

yes

characteristic

#391

C₂×C₉

yes

—

#387

C₂×C₉

yes

—

#383

C₂×C₉

yes

—

C₂×C₃×Q₈

—

C₂×C₃×Q₈

—

C₂×C₃×Q₈

C₂×C₃×C₄

yes

—

C₂²×C₃×C₄

C₂³×C₃

yes

—

C₂²×C₃×C₄

C₂³×C₃

yes

—

C₂²×C₃×C₄

C₂³×C₃

yes

characteristic

C₂²×C₃×C₄

C₂³×C₃

yes

—

C₃×C₄⋊C₄

—

C₃×C₄⋊C₄

C₂×C₃×C₄

yes

—

C₃×C₄²

—

C₃×C₄²

C₂×C₃×C₄

yes

—

C₂²×C₉

C₂³×C₄

yes

characteristic

C₂²×C₉

H(5,𝔽₂)

yes

—

C₂²×C₉

2₋¹⁺⁴

yes

—

C₄×C₉

—

C₄×C₉

—

C₄×C₉

—

C₄×C₉

—

C₂²×Q₈

C₂²×C₉

yes

—

C₄⋊Q₈

C₄×C₉

yes

complemented

C₂×C₄⋊C₄

C₂²×C₉

yes

—

C₂×C₄⋊C₄

C₂²×C₉

yes

—

C₂×C₄²

C₂²×C₉

yes

—

C₂×C₄²

C₂²×C₉

yes

characteristic

#95

C₂²×C₉

yes

—

#95

C₂²×C₉

yes

—

#95

C₂²×C₉

yes

—

C₂³×C₃

C₂⁴×C₃

yes

characteristic

C₃×Q₈

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

C₂²×C₃×C₄

yes

—

C₂×C₃×C₄

C₂²×C₃×C₄

yes

—

C₂×C₃×C₄

C₂²×C₃×C₄

yes

—

C₂×C₉

#518

yes

characteristic

C₂×C₉

#519

yes

—

C₂×C₉

#563

yes

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

C₂×C₄×C₉

yes

—

C₂²×C₄

C₂³×C₉

yes

—

100

C₂²×C₄

C₂³×C₉

yes

—

101

C₂²×C₄

C₂³×C₉

yes

characteristic

102

C₂²×C₄

C₂³×C₉

yes

—

103

C₄⋊C₄

—

104

C₄⋊C₄

C₂×C₄×C₉

yes

—

105

C₄²

—

106

C₄²

C₂×C₄×C₉

yes

—

107

C₂²×C₃

C₂³×C₃×C₄

yes

characteristic

108

C₂²×C₃

C₃×H(5,𝔽₂)

yes

—

109

C₂²×C₃

C₃×2₋¹⁺⁴

yes

—

110

C₃×C₄

—

111

C₃×C₄

—

112

C₃×C₄

—

113

C₃×C₄

—

114

C₉

#2381

yes

characteristic, direct product factor, Sylow

115

C₂³

C₂⁴×C₉

yes

characteristic

116

Q₈

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

C₂²×C₄×C₉

yes

—

124

C₂×C₄

C₂²×C₄×C₉

yes

—

125

C₂×C₄

C₂²×C₄×C₉

yes

—

126

C₂×C₃

C₃×#518

yes

characteristic

127

C₂×C₃

C₃×#519

yes

—

128

C₂×C₃

C₃×#563

yes

—

129

C₂²

C₂³×C₄×C₉

yes

characteristic

130

C₂²

C₉×H(5,𝔽₂)

yes

—

131

C₂²

C₉×2₋¹⁺⁴

yes

—

132

C₄

—

133

C₄

—

134

C₄

—

135

C₄

—

136

C₃

C₃×#2381

yes

characteristic

137

C₂

C₉×#518

yes

characteristic

138

C₂

C₉×#519

yes

—

139

C₂

C₉×#563

yes

—

	subgroup	G/H
center	C₂³×C₉	C₂⁴
commutator	C₂²	C₂³×C₄×C₉
Frattini, socle, prime radical, cosocle	C₂³×C₃	C₂⁴×C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₉ ◁ G

subgroup

G/H

center

C₂³×C₉

C₂⁴

commutator

C₂²

C₂³×C₄×C₉

Frattini, socle, prime radical, cosocle

C₂³×C₃

C₂⁴×C₃

LCS

G ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₉ ◁ G

N	H ≅ G/N	type
7. C₉×C₄⋊Q₈	C₄	semidirect
30. #2381	C₉	direct (N × H)
74. C₄⋊Q₈	C₄×C₉	semidirect
114. C₉	#2381	direct (N × H)

H ≅ G/N

type

7. C₉×C₄⋊Q₈

C₄

semidirect

30. #2381

C₉

direct (N × H)

74. C₄⋊Q₈

C₄×C₉

semidirect

114. C₉

#2381

direct (N × H)

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

subgroup	index
C₂×C₉×C₄⋊Q₈	2
C₉×#391	2
C₉×#387	2
C₉×#383	2
C₃×#2381	3

subgroup

index

C₂×C₉×C₄⋊Q₈

Subgroups — C₉×#2381 #11767102

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C9×#2381 #11767102

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2381 #11767102