Group #11766751 — subgroups

Subgroups — C₉×#2030 #11766751

Order 1152.

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

normal subgroups only

This group has 435 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	C₉×#543	C₂	1	1	yes	maximal, characteristic
2	C₉×#381	C₂	1	3	yes	maximal
3	C₉×#342	C₂	1	3	yes	maximal
4	C₃×#2030	C₃	1	1	yes	maximal, characteristic
5	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
6	C₉×C₂²⋊Q₈	—	2	6	no	—
7	C₂×C₉×C₂²⋊C₄	C₂²	1	3	yes	—
8	C₂×C₉×C₂²⋊C₄	C₂²	1	3	yes	—
9	C₉×#95	—	2	6	no	—
10	C₃×#543	C₂×C₃	1	1	yes	characteristic
11	C₃×#381	C₂×C₃	1	3	yes	—
12	C₃×#342	C₂×C₃	1	3	yes	—
13	C₂⁴×C₉	C₂³	1	1	yes	characteristic
14	C₂×Q₈×C₉	—	2	2	no	—
15	C₂²×C₄×C₉	—	2	3	no	—
16	C₂²×C₄×C₉	—	2	3	no	—
17	C₂²×C₄×C₉	—	2	3	no	—
18	C₂²×C₄×C₉	D₄	1	6	yes	—
19	C₂²×C₄×C₉	Q₈	1	2	yes	complemented
20	C₉×C₄⋊C₄	—	2	6	no	—
21	C₉×C₂²⋊C₄	—	2	6	no	—
22	C₉×C₂²⋊C₄	—	2	6	no	—
23	#2030	C₉	1	1	yes	characteristic, direct product factor, Sylow
24	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
25	C₃×C₂²⋊Q₈	—	2	6	no	—
26	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	3	yes	—
27	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	3	yes	—
28	C₃×#95	—	2	6	no	—
29	C₂³×C₉	—	4	2	no	—
30	C₂³×C₉	C₂×D₄	1	3	yes	—
31	C₂³×C₉	C₂×Q₈	1	1	yes	characteristic
32	C₂³×C₉	#41	1	3	yes	—
33	Q₈×C₉	—	8	2	no	—
34	C₂×C₄×C₉	—	2	6	no	—
35	C₂×C₄×C₉	—	2	6	no	—
36	C₂×C₄×C₉	—	4	1	no	—
37	C₂×C₄×C₉	—	4	3	no	—
38	C₂×C₄×C₉	—	4	6	no	—
39	C₂×C₄×C₉	—	4	6	no	—
40	C₂×C₄×C₉	—	4	3	no	—
41	#543	C₂×C₉	1	1	yes	characteristic
42	#381	C₂×C₉	1	3	yes	—
43	#342	C₂×C₉	1	3	yes	—
44	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
45	C₂×C₃×Q₈	—	2	2	no	—
46	C₂²×C₃×C₄	—	2	3	no	—
47	C₂²×C₃×C₄	—	2	3	no	—
48	C₂²×C₃×C₄	—	2	3	no	—
49	C₂²×C₃×C₄	C₃×D₄	1	6	yes	—
50	C₂²×C₃×C₄	C₃×Q₈	1	2	yes	—
51	C₃×C₄⋊C₄	—	2	6	no	—
52	C₃×C₂²⋊C₄	—	2	6	no	—
53	C₃×C₂²⋊C₄	—	2	6	no	—
54	C₂²×C₉	—	2	6	no	—
55	C₂²×C₉	—	4	1	no	—
56	C₂²×C₉	—	4	3	no	—
57	C₂²×C₉	#120	1	1	yes	characteristic
58	C₂²×C₉	C₂²⋊Q₈	1	3	yes	—
59	C₂²×C₉	#124	1	3	yes	—
60	C₄×C₉	—	4	2	no	—
61	C₄×C₉	—	4	6	no	—
62	C₄×C₉	—	8	3	no	—
63	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
64	C₂²⋊Q₈	—	2	6	no	—
65	C₂×C₂²⋊C₄	C₂²×C₉	1	3	yes	—
66	C₂×C₂²⋊C₄	C₂²×C₉	1	3	yes	—
67	#95	—	2	6	no	—
68	C₂³×C₃	—	4	2	no	—
69	C₂³×C₃	C₂×C₃×D₄	1	3	yes	—
70	C₂³×C₃	C₂×C₃×Q₈	1	1	yes	characteristic
71	C₂³×C₃	C₃×#41	1	3	yes	—
72	C₃×Q₈	—	8	2	no	—
73	C₂×C₃×C₄	—	2	6	no	—
74	C₂×C₃×C₄	—	2	6	no	—
75	C₂×C₃×C₄	—	4	1	no	—
76	C₂×C₃×C₄	—	4	3	no	—
77	C₂×C₃×C₄	—	4	6	no	—
78	C₂×C₃×C₄	—	4	6	no	—
79	C₂×C₃×C₄	—	4	3	no	—
80	C₂×C₉	—	2	3	no	—
81	C₂×C₉	—	2	3	no	—
82	C₂×C₉	#393	1	1	yes	characteristic
83	C₂×C₉	#458	1	2	yes	—
84	C₂⁴	C₂³×C₉	1	1	yes	characteristic
85	C₂×Q₈	—	2	2	no	—
86	C₂²×C₄	—	2	3	no	—
87	C₂²×C₄	—	2	3	no	—
88	C₂²×C₄	—	2	3	no	—
89	C₂²×C₄	D₄×C₉	1	6	yes	—
90	C₂²×C₄	Q₈×C₉	1	2	yes	complemented
91	C₄⋊C₄	—	2	6	no	—
92	C₂²⋊C₄	—	2	6	no	—
93	C₂²⋊C₄	—	2	6	no	—
94	C₂²×C₃	—	2	6	no	—
95	C₂²×C₃	—	4	1	no	—
96	C₂²×C₃	—	4	3	no	—
97	C₂²×C₃	C₃×#120	1	1	yes	characteristic
98	C₂²×C₃	C₃×C₂²⋊Q₈	1	3	yes	—
99	C₂²×C₃	C₃×#124	1	3	yes	—
100	C₃×C₄	—	4	2	no	—
101	C₃×C₄	—	4	6	no	—
102	C₃×C₄	—	8	3	no	—
103	C₉	#2030	1	1	yes	characteristic, direct product factor, Sylow
104	C₂³	—	4	2	no	—
105	C₂³	C₂×D₄×C₉	1	3	yes	—
106	C₂³	C₂×Q₈×C₉	1	1	yes	characteristic
107	C₂³	C₉×#41	1	3	yes	—
108	Q₈	—	8	2	no	—
109	C₂×C₄	—	2	6	no	—
110	C₂×C₄	—	2	6	no	—
111	C₂×C₄	—	4	1	no	—
112	C₂×C₄	—	4	3	no	—
113	C₂×C₄	—	4	6	no	—
114	C₂×C₄	—	4	6	no	—
115	C₂×C₄	—	4	3	no	—
116	C₂×C₃	—	2	3	no	—
117	C₂×C₃	—	2	3	no	—
118	C₂×C₃	C₃×#393	1	1	yes	characteristic
119	C₂×C₃	C₃×#458	1	2	yes	—
120	C₂²	—	2	6	no	—
121	C₂²	—	4	1	no	—
122	C₂²	—	4	3	no	—
123	C₂²	C₉×#120	1	1	yes	characteristic
124	C₂²	C₉×C₂²⋊Q₈	1	3	yes	—
125	C₂²	C₉×#124	1	3	yes	—
126	C₄	—	4	2	no	—
127	C₄	—	4	6	no	—
128	C₄	—	8	3	no	—
129	C₃	C₃×#2030	1	1	yes	characteristic
130	C₂	—	2	3	no	—
131	C₂	—	2	3	no	—
132	C₂	C₉×#393	1	1	yes	characteristic
133	C₂	C₉×#458	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₉×#543

C₂

yes

maximal, characteristic

C₉×#381

C₂

yes

maximal

C₉×#342

C₂

yes

maximal

C₃×#2030

C₃

yes

maximal, characteristic

C₂³×C₄×C₉

C₂²

yes

characteristic

C₉×C₂²⋊Q₈

—

C₂×C₉×C₂²⋊C₄

C₂²

yes

—

C₂×C₉×C₂²⋊C₄

C₂²

yes

—

C₉×#95

—

C₃×#543

C₂×C₃

yes

characteristic

C₃×#381

C₂×C₃

yes

—

C₃×#342

C₂×C₃

yes

—

C₂⁴×C₉

C₂³

yes

characteristic

C₂×Q₈×C₉

—

C₂²×C₄×C₉

—

C₂²×C₄×C₉

—

C₂²×C₄×C₉

—

C₂²×C₄×C₉

D₄

yes

—

C₂²×C₄×C₉

Q₈

yes

complemented

C₉×C₄⋊C₄

—

C₉×C₂²⋊C₄

—

C₉×C₂²⋊C₄

—

#2030

C₉

yes

characteristic, direct product factor, Sylow

C₂³×C₃×C₄

C₂²×C₃

yes

characteristic

C₃×C₂²⋊Q₈

—

C₂×C₃×C₂²⋊C₄

C₂²×C₃

yes

—

C₂×C₃×C₂²⋊C₄

C₂²×C₃

yes

—

C₃×#95

—

C₂³×C₉

—

C₂³×C₉

C₂×D₄

yes

—

C₂³×C₉

C₂×Q₈

yes

characteristic

C₂³×C₉

#41

yes

—

Q₈×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

#543

C₂×C₉

yes

characteristic

#381

C₂×C₉

yes

—

#342

C₂×C₉

yes

—

C₂⁴×C₃

C₂³×C₃

yes

characteristic

C₂×C₃×Q₈

—

C₂²×C₃×C₄

—

C₂²×C₃×C₄

—

C₂²×C₃×C₄

—

C₂²×C₃×C₄

C₃×D₄

yes

—

C₂²×C₃×C₄

C₃×Q₈

yes

—

C₃×C₄⋊C₄

—

C₃×C₂²⋊C₄

—

C₃×C₂²⋊C₄

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

#120

yes

characteristic

C₂²×C₉

C₂²⋊Q₈

yes

—

C₂²×C₉

#124

yes

—

C₄×C₉

—

C₄×C₉

—

C₄×C₉

—

C₂³×C₄

C₂²×C₉

yes

characteristic

C₂²⋊Q₈

—

C₂×C₂²⋊C₄

C₂²×C₉

yes

—

C₂×C₂²⋊C₄

C₂²×C₉

yes

—

#95

—

C₂³×C₃

—

C₂³×C₃

C₂×C₃×D₄

yes

—

C₂³×C₃

C₂×C₃×Q₈

yes

characteristic

C₂³×C₃

C₃×#41

yes

—

C₃×Q₈

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₉

—

C₂×C₉

—

C₂×C₉

#393

yes

characteristic

C₂×C₉

#458

yes

—

C₂⁴

C₂³×C₉

yes

characteristic

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

D₄×C₉

yes

—

C₂²×C₄

Q₈×C₉

yes

complemented

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²×C₃

—

C₂²×C₃

—

C₂²×C₃

—

C₂²×C₃

C₃×#120

yes

characteristic

C₂²×C₃

C₃×C₂²⋊Q₈

yes

—

C₂²×C₃

C₃×#124

yes

—

100

C₃×C₄

—

101

C₃×C₄

—

102

C₃×C₄

—

103

C₉

#2030

yes

characteristic, direct product factor, Sylow

104

C₂³

—

105

C₂³

C₂×D₄×C₉

yes

—

106

C₂³

C₂×Q₈×C₉

yes

characteristic

107

C₂³

C₉×#41

yes

—

108

Q₈

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₃

—

117

C₂×C₃

—

118

C₂×C₃

C₃×#393

yes

characteristic

119

C₂×C₃

C₃×#458

yes

—

120

C₂²

—

121

C₂²

—

122

C₂²

—

123

C₂²

C₉×#120

yes

characteristic

124

C₂²

C₉×C₂²⋊Q₈

yes

—

125

C₂²

C₉×#124

yes

—

126

C₄

—

127

C₄

—

128

C₄

—

129

C₃

C₃×#2030

yes

characteristic

130

C₂

—

131

C₂

—

132

C₂

C₉×#393

yes

characteristic

133

C₂

C₉×#458

yes

—

	subgroup	G/H
center	C₂²×C₉	#120
commutator	C₂⁴	C₂³×C₉
Frattini, prime radical, cosocle	C₂⁴×C₃	C₂³×C₃
socle	C₂²×C₃	C₃×#120
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₂⁴×C₉ ◁ G

subgroup

G/H

center

C₂²×C₉

#120

commutator

C₂⁴

C₂³×C₉

Frattini, prime radical, cosocle

C₂⁴×C₃

C₂³×C₃

C₂²×C₃

G ▷ C₂⁴ ▷ C₂ ▷ C₁

C₁ ◁ C₂²×C₉ ◁ C₂⁴×C₉ ◁ G

N	H ≅ G/N	type
19. C₂²×C₄×C₉	Q₈	semidirect
23. #2030	C₉	direct (N × H)
90. C₂²×C₄	Q₈×C₉	semidirect
103. C₉	#2030	direct (N × H)

H ≅ G/N

type

19. C₂²×C₄×C₉

Q₈

semidirect

23. #2030

C₉

direct (N × H)

90. C₂²×C₄

Q₈×C₉

semidirect

103. C₉

#2030

direct (N × H)

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

subgroup	index
C₉×#543	2
C₉×#381	2
C₉×#342	2
C₃×#2030	3

subgroup

index

Subgroups — C₉×#2030 #11766751

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C9×#2030 #11766751

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2030 #11766751