Group #11765996 — subgroups

Subgroups — C₉×#1275 #11765996

Order 1152.

228 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 132 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×#431	C₂	1	2	yes	maximal
2	C₂×C₉×#97	C₂	1	1	yes	maximal, characteristic
3	C₃×#1275	C₃	1	1	yes	maximal, characteristic
4	C₂²×C₈×C₉	C₄	1	2	yes	—
5	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
6	C₉×C₄⋊C₈	—	2	2	no	—
7	C₉×C₂²⋊C₈	—	2	2	no	—
8	C₉×#97	—	2	2	no	—
9	C₄×C₈×C₉	C₄	1	4	yes	—
10	C₃×#431	C₂×C₃	1	2	yes	—
11	C₂×C₃×#97	C₂×C₃	1	1	yes	characteristic
12	C₂²×C₄×C₉	C₂×C₄	1	1	yes	characteristic
13	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
14	C₂²×C₄×C₉	Q₈	1	1	yes	characteristic
15	C₂×C₈×C₉	—	2	2	no	—
16	C₂×C₈×C₉	—	2	2	no	—
17	C₂×C₈×C₉	—	2	4	no	—
18	C₂×C₈×C₉	C₈	1	4	yes	complemented
19	C₄²×C₉	C₂×C₄	1	2	yes	—
20	C₄²×C₉	D₄	1	2	yes	—
21	#1275	C₉	1	1	yes	characteristic, direct product factor, Sylow
22	C₂²×C₃×C₈	C₃×C₄	1	2	yes	—
23	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
24	C₃×C₄⋊C₈	—	2	2	no	—
25	C₃×C₂²⋊C₈	—	2	2	no	—
26	C₃×#97	—	2	2	no	—
27	C₃×C₄×C₈	C₃×C₄	1	4	yes	—
28	C₂³×C₉	C₄⋊C₄	1	1	yes	characteristic
29	C₂×C₄×C₉	—	4	1	no	—
30	C₂×C₄×C₉	—	4	1	no	—
31	C₂×C₄×C₉	C₄²	1	1	yes	characteristic
32	C₂×C₄×C₉	C₂²⋊C₄	1	2	yes	—
33	C₂×C₄×C₉	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₉	C₄⋊C₄	1	2	yes	—
35	C₂×C₄×C₉	C₂×C₈	1	2	yes	—
36	C₂×C₄×C₉	M₁₆	1	2	yes	—
37	C₈×C₉	—	2	4	no	—
38	C₈×C₉	—	4	4	no	—
39	#431	C₂×C₉	1	2	yes	—
40	C₂×#97	C₂×C₉	1	1	yes	characteristic
41	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
42	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
43	C₂²×C₃×C₄	C₃×Q₈	1	1	yes	characteristic
44	C₂×C₃×C₈	—	2	2	no	—
45	C₂×C₃×C₈	—	2	2	no	—
46	C₂×C₃×C₈	—	2	4	no	—
47	C₂×C₃×C₈	C₃×C₈	1	4	yes	—
48	C₃×C₄²	C₂×C₃×C₄	1	2	yes	—
49	C₃×C₄²	C₃×D₄	1	2	yes	—
50	C₂²×C₉	—	2	1	no	—
51	C₂²×C₉	—	2	1	no	—
52	C₂²×C₉	#95	1	1	yes	characteristic
53	C₂²×C₉	C₄⋊C₈	1	2	yes	—
54	C₄×C₉	—	2	2	no	—
55	C₄×C₉	—	2	2	no	—
56	C₄×C₉	C₄×C₈	1	1	yes	characteristic
57	C₄×C₉	#97	1	1	yes	characteristic
58	C₄×C₉	C₂²⋊C₈	1	2	yes	—
59	C₂²×C₈	C₄×C₉	1	2	yes	—
60	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
61	C₄⋊C₈	—	2	2	no	—
62	C₂²⋊C₈	—	2	2	no	—
63	#97	—	2	2	no	—
64	C₄×C₈	C₄×C₉	1	4	yes	—
65	C₂³×C₃	C₃×C₄⋊C₄	1	1	yes	characteristic
66	C₂×C₃×C₄	—	4	1	no	—
67	C₂×C₃×C₄	—	4	1	no	—
68	C₂×C₃×C₄	C₃×C₄²	1	1	yes	characteristic
69	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	2	yes	—
70	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
71	C₂×C₃×C₄	C₃×C₄⋊C₄	1	2	yes	—
72	C₂×C₃×C₄	C₂×C₃×C₈	1	2	yes	—
73	C₂×C₃×C₄	C₃×M₁₆	1	2	yes	—
74	C₃×C₈	—	2	4	no	—
75	C₃×C₈	—	4	4	no	—
76	C₂×C₉	—	2	2	no	—
77	C₂×C₉	#336	1	1	yes	characteristic
78	C₂×C₉	H(3,ℤ/4)	1	1	yes	characteristic
79	C₂×C₉	#338	1	1	yes	characteristic
80	C₂²×C₄	C₂×C₄×C₉	1	1	yes	characteristic
81	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
82	C₂²×C₄	Q₈×C₉	1	1	yes	characteristic
83	C₂×C₈	—	2	2	no	—
84	C₂×C₈	—	2	2	no	—
85	C₂×C₈	—	2	4	no	—
86	C₂×C₈	C₈×C₉	1	4	yes	complemented
87	C₄²	C₂×C₄×C₉	1	2	yes	—
88	C₄²	D₄×C₉	1	2	yes	—
89	C₂²×C₃	—	2	1	no	—
90	C₂²×C₃	—	2	1	no	—
91	C₂²×C₃	C₃×#95	1	1	yes	characteristic
92	C₂²×C₃	C₃×C₄⋊C₈	1	2	yes	—
93	C₃×C₄	—	2	2	no	—
94	C₃×C₄	—	2	2	no	—
95	C₃×C₄	C₃×C₄×C₈	1	1	yes	characteristic
96	C₃×C₄	C₃×#97	1	1	yes	characteristic
97	C₃×C₄	C₃×C₂²⋊C₈	1	2	yes	—
98	C₉	#1275	1	1	yes	characteristic, direct product factor, Sylow
99	C₂³	C₉×C₄⋊C₄	1	1	yes	characteristic
100	C₂×C₄	—	4	1	no	—
101	C₂×C₄	—	4	1	no	—
102	C₂×C₄	C₄²×C₉	1	1	yes	characteristic
103	C₂×C₄	C₉×C₂²⋊C₄	1	2	yes	—
104	C₂×C₄	C₉×C₂²⋊C₄	1	1	yes	characteristic
105	C₂×C₄	C₉×C₄⋊C₄	1	2	yes	—
106	C₂×C₄	C₂×C₈×C₉	1	2	yes	—
107	C₂×C₄	C₉×M₁₆	1	2	yes	—
108	C₈	—	2	4	no	—
109	C₈	—	4	4	no	—
110	C₂×C₃	—	2	2	no	—
111	C₂×C₃	C₃×#336	1	1	yes	characteristic
112	C₂×C₃	C₃×H(3,ℤ/4)	1	1	yes	characteristic
113	C₂×C₃	C₃×#338	1	1	yes	characteristic
114	C₂²	—	2	1	no	—
115	C₂²	—	2	1	no	—
116	C₂²	C₉×#95	1	1	yes	characteristic
117	C₂²	C₉×C₄⋊C₈	1	2	yes	—
118	C₄	—	2	2	no	—
119	C₄	—	2	2	no	—
120	C₄	C₄×C₈×C₉	1	1	yes	characteristic
121	C₄	C₉×#97	1	1	yes	characteristic
122	C₄	C₉×C₂²⋊C₈	1	2	yes	—
123	C₃	C₃×#1275	1	1	yes	characteristic
124	C₂	—	2	2	no	—
125	C₂	C₉×#336	1	1	yes	characteristic
126	C₂	C₉×H(3,ℤ/4)	1	1	yes	characteristic
127	C₂	C₉×#338	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₉×#431

C₂

yes

maximal

C₂×C₉×#97

C₂

yes

maximal, characteristic

C₃×#1275

C₃

yes

maximal, characteristic

C₂²×C₈×C₉

C₄

yes

—

C₂×C₄²×C₉

C₂²

yes

characteristic

C₉×C₄⋊C₈

—

C₉×C₂²⋊C₈

—

C₉×#97

—

C₄×C₈×C₉

C₄

yes

—

C₃×#431

C₂×C₃

yes

—

C₂×C₃×#97

C₂×C₃

yes

characteristic

C₂²×C₄×C₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₉

D₄

yes

characteristic

C₂²×C₄×C₉

Q₈

yes

characteristic

C₂×C₈×C₉

—

C₂×C₈×C₉

—

C₂×C₈×C₉

—

C₂×C₈×C₉

C₈

yes

complemented

C₄²×C₉

C₂×C₄

yes

—

C₄²×C₉

D₄

yes

—

#1275

C₉

yes

characteristic, direct product factor, Sylow

C₂²×C₃×C₈

C₃×C₄

yes

—

C₂×C₃×C₄²

C₂²×C₃

yes

characteristic

C₃×C₄⋊C₈

—

C₃×C₂²⋊C₈

—

C₃×#97

—

C₃×C₄×C₈

C₃×C₄

yes

—

C₂³×C₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

C₄²

yes

characteristic

C₂×C₄×C₉

C₂²⋊C₄

yes

—

C₂×C₄×C₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₉

C₄⋊C₄

yes

—

C₂×C₄×C₉

C₂×C₈

yes

—

C₂×C₄×C₉

M₁₆

yes

—

C₈×C₉

—

C₈×C₉

—

#431

C₂×C₉

yes

—

C₂×#97

C₂×C₉

yes

characteristic

C₂²×C₃×C₄

C₂×C₃×C₄

yes

characteristic

C₂²×C₃×C₄

C₃×D₄

yes

characteristic

C₂²×C₃×C₄

C₃×Q₈

yes

characteristic

C₂×C₃×C₈

—

C₂×C₃×C₈

—

C₂×C₃×C₈

—

C₂×C₃×C₈

C₃×C₈

yes

—

C₃×C₄²

C₂×C₃×C₄

yes

—

C₃×C₄²

C₃×D₄

yes

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

#95

yes

characteristic

C₂²×C₉

C₄⋊C₈

yes

—

C₄×C₉

—

C₄×C₉

—

C₄×C₉

C₄×C₈

yes

characteristic

C₄×C₉

#97

yes

characteristic

C₄×C₉

C₂²⋊C₈

yes

—

C₂²×C₈

C₄×C₉

yes

—

C₂×C₄²

C₂²×C₉

yes

characteristic

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

C₄×C₈

C₄×C₉

yes

—

C₂³×C₃

C₃×C₄⋊C₄

yes

characteristic

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

C₃×C₄²

yes

characteristic

C₂×C₃×C₄

C₃×C₂²⋊C₄

yes

—

C₂×C₃×C₄

C₃×C₂²⋊C₄

yes

characteristic

C₂×C₃×C₄

C₃×C₄⋊C₄

yes

—

C₂×C₃×C₄

C₂×C₃×C₈

yes

—

C₂×C₃×C₄

C₃×M₁₆

yes

—

C₃×C₈

—

C₃×C₈

—

C₂×C₉

—

C₂×C₉

yes

C₂×C₉

yes

C₂×C₉

yes

C₂²×C₄

C₂×C₄×C₉

yes

characteristic

C₂²×C₄

D₄×C₉

yes

characteristic

C₂²×C₄

Q₈×C₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₈×C₉

yes

complemented

C₄²

C₂×C₄×C₉

yes

—

C₄²

D₄×C₉

yes

—

C₂²×C₃

—

C₂²×C₃

—

C₂²×C₃

C₃×#95

yes

characteristic

C₂²×C₃

C₃×C₄⋊C₈

yes

—

C₃×C₄

—

C₃×C₄

—

C₃×C₄

C₃×C₄×C₈

yes

characteristic

C₃×C₄

C₃×#97

yes

characteristic

C₃×C₄

C₃×C₂²⋊C₈

yes

—

C₉

#1275

yes

characteristic, direct product factor, Sylow

C₂³

C₉×C₄⋊C₄

yes

characteristic

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

C₄²×C₉

yes

characteristic

103

C₂×C₄

C₉×C₂²⋊C₄

yes

—

104

C₂×C₄

C₉×C₂²⋊C₄

yes

characteristic

105

C₂×C₄

C₉×C₄⋊C₄

yes

—

106

C₂×C₄

C₂×C₈×C₉

yes

—

107

C₂×C₄

C₉×M₁₆

yes

—

108

C₈

—

109

C₈

—

110

C₂×C₃

—

111

C₂×C₃

C₃×#336

yes

characteristic

112

C₂×C₃

C₃×H(3,ℤ/4)

yes

characteristic

113

C₂×C₃

C₃×#338

yes

characteristic

114

C₂²

—

115

C₂²

—

116

C₂²

C₉×#95

yes

characteristic

117

C₂²

C₉×C₄⋊C₈

yes

—

118

C₄

—

119

C₄

—

120

C₄

C₄×C₈×C₉

yes

characteristic

121

C₄

C₉×#97

yes

characteristic

122

C₄

C₉×C₂²⋊C₈

yes

—

123

C₃

C₃×#1275

yes

characteristic

124

C₂

—

125

C₂

C₉×#336

yes

characteristic

126

C₂

C₉×H(3,ℤ/4)

yes

characteristic

127

C₂

C₉×#338

yes

characteristic

	subgroup	G/H
center	C₂×C₄×C₉	C₄²
commutator	C₄	C₄×C₈×C₉
Frattini, cosocle	C₂×C₃×C₄²	C₂²×C₃
socle	C₂²×C₃	C₃×#95
prime radical	C₂³×C₃	C₃×C₄⋊C₄
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₉ ◁ G

subgroup

G/H

center

C₂×C₄×C₉

C₄²

commutator

C₄

C₄×C₈×C₉

Frattini, cosocle

C₂×C₃×C₄²

C₂²×C₃

socle

C₂²×C₃

C₃×#95

prime radical

C₂³×C₃

C₃×C₄⋊C₄

LCS

G ▷ C₄ ▷ C₁

UCS

C₁ ◁ C₂×C₄×C₉ ◁ G

N	H ≅ G/N	type
18. C₂×C₈×C₉	C₈	semidirect
21. #1275	C₉	direct (N × H)
86. C₂×C₈	C₈×C₉	semidirect
98. C₉	#1275	direct (N × H)

H ≅ G/N

type

18. C₂×C₈×C₉

C₈

semidirect

21. #1275

C₉

direct (N × H)

86. C₂×C₈

C₈×C₉

semidirect

98. C₉

#1275

direct (N × H)

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

subgroup	index
C₉×#431	2
C₂×C₉×#97	2
C₃×#1275	3

subgroup

index

C₉×#431

C₂×C₉×#97

C₃×#1275

Subgroups — C₉×#1275 #11765996

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C9×#1275 #11765996

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#1275 #11765996