Group #11857079 — subgroups

Subgroups — #11857079

Order 1152.

972 conjugacy classes of subgroups; only the 310 normal subgroups are shown.

normal subgroups only

This group has 972 conjugacy classes of subgroups — too many to draw. Only its 310 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×#63450	C₂	1	6	yes	maximal
2	C₉×#384	C₂	1	1	yes	maximal, characteristic
3	#10588655	C₂	1	6	yes	maximal
4	#10588615	C₂	1	1	yes	maximal, characteristic
5	C₄²×Dic₉	C₂	1	1	yes	maximal, characteristic
6	#74356	—	3	1	no	maximal
7	C₂²×Dic₁₈	C₂²	1	4	yes	—
8	C₂×C₉×C₄⋊C₄	C₂²	1	6	yes	—
9	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₉	C₂²	1	6	yes	—
11	C₂×Dic₉⋊C₄	C₂²	1	12	yes	—
12	C₂×C₄×Dic₉	C₂²	1	3	yes	—
13	C₂×C₄×Dic₉	C₂²	1	3	yes	—
14	#63450	—	2	24	no	—
15	C₂×#888	—	3	6	no	—
16	C₃×#384	D₃	1	1	yes	characteristic
17	#4975	—	3	6	no	—
18	#4935	—	3	1	no	—
19	C₄²×Dic₃	—	3	1	no	—
20	C₂²×C₄×C₉	C₂³	1	4	yes	—
21	C₂²×C₄×C₉	C₂³	1	3	yes	—
22	C₂²×Dic₉	C₂³	1	4	yes	—
23	C₂²×Dic₉	C₂³	1	1	yes	characteristic
24	C₂²×Dic₉	C₂³	1	3	yes	—
25	C₂×Dic₁₈	—	2	24	no	—
26	C₉×C₄⋊C₄	—	2	12	no	—
27	C₄²×C₉	Q₈	1	4	yes	complemented
28	C₄⋊Dic₉	—	2	12	no	—
29	Dic₉⋊C₄	—	2	24	no	—
30	C₄×Dic₉	D₄	1	12	yes	—
31	C₄×Dic₉	Q₈	1	12	yes	complemented
32	#2868	—	9	1	no	Sylow
33	C₂²×Dic₆	—	3	4	no	—
34	C₂×C₃×C₄⋊C₄	C₂×D₃	1	6	yes	—
35	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
36	C₂×C₄⋊Dic₃	—	3	6	no	—
37	C₂×Dic₃⋊C₄	—	3	12	no	—
38	C₂×C₄×Dic₃	—	3	3	no	—
39	C₂×C₄×Dic₃	—	3	3	no	—
40	#888	—	6	24	no	—
41	C₂³×C₉	C₂⁴	1	1	yes	characteristic
42	C₂×C₄×C₉	—	2	12	no	—
43	C₂×C₄×C₉	C₂×D₄	1	6	yes	—
44	C₂×C₄×C₉	C₂×Q₈	1	6	yes	—
45	C₂×C₄×C₉	C₂×Q₈	1	6	yes	—
46	C₂×Dic₉	—	2	12	no	—
47	C₂×Dic₉	C₂×D₄	1	6	yes	—
48	C₂×Dic₉	C₂×D₄	1	6	yes	—
49	C₂×Dic₉	C₂×Q₈	1	12	yes	—
50	Dic₁₈	—	4	16	no	—
51	C₂×C₄⋊Q₈	—	9	6	no	—
52	#384	—	9	6	no	—
53	#384	—	9	1	no	—
54	#384	D₉	1	1	yes	characteristic
55	C₄³	—	9	1	no	—
56	C₂²×C₃×C₄	C₂²×D₃	1	4	yes	—
57	C₂²×C₃×C₄	C₂²×D₃	1	3	yes	—
58	C₂²×Dic₃	—	3	3	no	—
59	C₂²×Dic₃	—	3	1	no	—
60	C₂²×Dic₃	—	3	4	no	—
61	C₂×Dic₆	—	6	24	no	—
62	C₃×C₄⋊C₄	—	2	12	no	—
63	C₃×C₄²	Dic₆	1	4	yes	—
64	C₄⋊Dic₃	—	6	12	no	—
65	Dic₃⋊C₄	—	6	24	no	—
66	C₄×Dic₃	—	3	12	no	—
67	C₄×Dic₃	—	3	12	no	—
68	C₂²×C₉	C₂²×D₄	1	3	yes	—
69	C₂²×C₉	C₂²×Q₈	1	1	yes	characteristic
70	C₂²×C₉	C₂²×Q₈	1	3	yes	—
71	C₄×C₉	—	4	4	no	—
72	C₄×C₉	C₄⋊Q₈	1	12	yes	complemented
73	Dic₉	—	4	4	no	—
74	Dic₉	#127	1	4	yes	—
75	Dic₉	C₄⋊Q₈	1	12	yes	complemented
76	C₂²×Q₈	—	9	4	no	—
77	C₄⋊Q₈	—	18	24	no	—
78	C₂×C₄⋊C₄	—	9	12	no	—
79	C₂×C₄⋊C₄	—	9	6	no	—
80	C₂×C₄⋊C₄	C₂×D₉	1	6	yes	—
81	C₂×C₄²	—	9	3	no	—
82	C₂×C₄²	—	9	3	no	—
83	C₂×C₄²	C₂×D₉	1	1	yes	characteristic
84	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
85	C₂×C₃×C₄	—	2	12	no	—
86	C₂×C₃×C₄	C₂×Dic₆	1	6	yes	—
87	C₂×C₃×C₄	D₃×D₄	1	6	yes	—
88	C₂×C₃×C₄	D₃×Q₈	1	6	yes	—
89	C₂×Dic₃	—	3	6	no	—
90	C₂×Dic₃	—	3	6	no	—
91	C₂×Dic₃	—	3	12	no	—
92	C₂×Dic₃	—	6	12	no	—
93	Dic₆	—	12	16	no	—
94	C₂×C₉	C₂×#127	1	1	yes	characteristic
95	C₂×C₉	C₂×C₄⋊Q₈	1	3	yes	—
96	C₂×C₉	C₂×C₄⋊Q₈	1	3	yes	—
97	C₂×Q₈	—	18	24	no	—
98	C₂²×C₄	—	9	3	no	—
99	C₂²×C₄	—	9	1	no	—
100	C₂²×C₄	—	9	4	no	—
101	C₂²×C₄	C₂²×D₉	1	4	yes	—
102	C₂²×C₄	C₂²×D₉	1	3	yes	—
103	C₄⋊C₄	—	2	12	no	—
104	C₄⋊C₄	—	18	24	no	—
105	C₄⋊C₄	—	18	12	no	—
106	C₄²	—	9	12	no	—
107	C₄²	—	9	12	no	—
108	C₄²	Dic₁₈	1	4	yes	complemented
109	C₂²×C₃	C₂²×Dic₆	1	1	yes	characteristic
110	C₂²×C₃	C₂×D₃×D₄	1	3	yes	—
111	C₂²×C₃	C₂×D₃×Q₈	1	3	yes	—
112	C₃×C₄	—	4	4	no	—
113	C₃×C₄	#888	1	12	yes	—
114	Dic₃	—	3	4	no	—
115	Dic₃	—	3	12	no	—
116	Dic₃	—	12	4	no	—
117	C₉	#2868	1	1	yes	characteristic, complemented, Sylow
118	C₂³	C₂³×D₉	1	1	yes	characteristic
119	Q₈	—	36	16	no	—
120	C₂×C₄	—	2	12	no	—
121	C₂×C₄	—	9	6	no	—
122	C₂×C₄	—	9	6	no	—
123	C₂×C₄	—	9	12	no	—
124	C₂×C₄	—	18	12	no	—
125	C₂×C₄	C₂×Dic₁₈	1	6	yes	—
126	C₂×C₄	D₄×D₉	1	6	yes	—
127	C₂×C₄	Q₈×D₉	1	6	yes	—
128	C₂×C₃	C₂×#888	1	3	yes	—
129	C₂×C₃	D₃×#127	1	1	yes	characteristic
130	C₂×C₃	D₃×C₄⋊Q₈	1	3	yes	—
131	C₂²	C₂²×Dic₁₈	1	1	yes	characteristic
132	C₂²	C₂×D₄×D₉	1	3	yes	—
133	C₂²	C₂×Q₈×D₉	1	3	yes	—
134	C₄	—	4	4	no	—
135	C₄	—	9	4	no	—
136	C₄	—	9	12	no	—
137	C₄	—	36	4	no	—
138	C₄	#63450	1	12	yes	complemented
139	C₃	#74356	1	1	yes	characteristic
140	C₂	C₂×#63450	1	3	yes	—
141	C₂	D₉×#127	1	1	yes	characteristic
142	C₂	D₉×C₄⋊Q₈	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#63450

C₂

yes

maximal

C₉×#384

C₂

yes

maximal, characteristic

#10588655

C₂

yes

maximal

#10588615

C₂

yes

maximal, characteristic

C₄²×Dic₉

C₂

yes

maximal, characteristic

#74356

—

maximal

C₂²×Dic₁₈

C₂²

yes

—

C₂×C₉×C₄⋊C₄

C₂²

yes

—

C₂×C₄²×C₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₉

C₂²

yes

—

C₂×Dic₉⋊C₄

C₂²

yes

—

C₂×C₄×Dic₉

C₂²

yes

—

C₂×C₄×Dic₉

C₂²

yes

—

#63450

—

C₂×#888

—

C₃×#384

D₃

yes

characteristic

#4975

—

#4935

—

C₄²×Dic₃

—

C₂²×C₄×C₉

C₂³

yes

—

C₂²×C₄×C₉

C₂³

yes

—

C₂²×Dic₉

C₂³

yes

—

C₂²×Dic₉

C₂³

yes

characteristic

C₂²×Dic₉

C₂³

yes

—

C₂×Dic₁₈

—

C₉×C₄⋊C₄

—

C₄²×C₉

Q₈

yes

complemented

C₄⋊Dic₉

—

Dic₉⋊C₄

—

C₄×Dic₉

D₄

yes

—

C₄×Dic₉

Q₈

yes

complemented

#2868

—

Sylow

C₂²×Dic₆

—

C₂×C₃×C₄⋊C₄

C₂×D₃

yes

—

C₂×C₃×C₄²

C₂×D₃

yes

characteristic

C₂×C₄⋊Dic₃

—

C₂×Dic₃⋊C₄

—

C₂×C₄×Dic₃

—

C₂×C₄×Dic₃

—

#888

—

C₂³×C₉

C₂⁴

yes

characteristic

C₂×C₄×C₉

—

C₂×C₄×C₉

C₂×D₄

yes

—

C₂×C₄×C₉

C₂×Q₈

yes

—

C₂×C₄×C₉

C₂×Q₈

yes

—

C₂×Dic₉

—

C₂×Dic₉

C₂×D₄

yes

—

C₂×Dic₉

C₂×D₄

yes

—

C₂×Dic₉

C₂×Q₈

yes

—

Dic₁₈

—

C₂×C₄⋊Q₈

—

#384

—

#384

—

#384

D₉

yes

characteristic

C₄³

—

C₂²×C₃×C₄

C₂²×D₃

yes

—

C₂²×C₃×C₄

C₂²×D₃

yes

—

C₂²×Dic₃

—

C₂²×Dic₃

—

C₂²×Dic₃

—

C₂×Dic₆

—

C₃×C₄⋊C₄

—

C₃×C₄²

Dic₆

yes

—

C₄⋊Dic₃

—

Dic₃⋊C₄

—

C₄×Dic₃

—

C₄×Dic₃

—

C₂²×C₉

C₂²×D₄

yes

—

C₂²×C₉

C₂²×Q₈

yes

characteristic

C₂²×C₉

C₂²×Q₈

yes

—

C₄×C₉

—

C₄×C₉

C₄⋊Q₈

yes

complemented

Dic₉

—

Dic₉

#127

yes

—

Dic₉

C₄⋊Q₈

yes

complemented

C₂²×Q₈

—

C₄⋊Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₉

yes

characteristic

C₂³×C₃

C₂³×D₃

yes

characteristic

C₂×C₃×C₄

—

C₂×C₃×C₄

C₂×Dic₆

yes

—

C₂×C₃×C₄

D₃×D₄

yes

—

C₂×C₃×C₄

D₃×Q₈

yes

—

C₂×Dic₃

—

C₂×Dic₃

—

C₂×Dic₃

—

C₂×Dic₃

—

Dic₆

—

C₂×C₉

C₂×#127

yes

characteristic

C₂×C₉

C₂×C₄⋊Q₈

yes

—

C₂×C₉

C₂×C₄⋊Q₈

yes

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

C₂²×D₉

yes

—

102

C₂²×C₄

C₂²×D₉

yes

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄²

—

107

C₄²

—

108

C₄²

Dic₁₈

yes

complemented

109

C₂²×C₃

C₂²×Dic₆

yes

characteristic

110

C₂²×C₃

C₂×D₃×D₄

yes

—

111

C₂²×C₃

C₂×D₃×Q₈

yes

—

112

C₃×C₄

—

113

C₃×C₄

#888

yes

—

114

Dic₃

—

115

Dic₃

—

116

Dic₃

—

117

C₉

#2868

yes

characteristic, complemented, Sylow

118

C₂³

C₂³×D₉

yes

characteristic

119

Q₈

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

C₂×Dic₁₈

yes

—

126

C₂×C₄

D₄×D₉

yes

—

127

C₂×C₄

Q₈×D₉

yes

—

128

C₂×C₃

C₂×#888

yes

—

129

C₂×C₃

D₃×#127

yes

characteristic

130

C₂×C₃

D₃×C₄⋊Q₈

yes

—

131

C₂²

C₂²×Dic₁₈

yes

characteristic

132

C₂²

C₂×D₄×D₉

yes

—

133

C₂²

C₂×Q₈×D₉

yes

—

134

C₄

—

135

C₄

—

136

C₄

—

137

C₄

—

138

C₄

#63450

yes

complemented

139

C₃

#74356

yes

characteristic

140

C₂

C₂×#63450

yes

—

141

C₂

D₉×#127

yes

characteristic

142

C₂

D₉×C₄⋊Q₈

yes

—

	subgroup	G/H
center	C₂³	C₂³×D₉
commutator, cosocle	C₂³×C₉	C₂⁴
Frattini, socle, prime radical	C₂³×C₃	C₂³×D₃
Fitting	C₉×#384	C₂
hypercenter	#384	D₉
hypocenter	C₉	#2868
LCS	G ▷ C₂³×C₉ ▷ C₉
UCS	C₁ ◁ C₂³ ◁ #384

subgroup

G/H

center

C₂³

C₂³×D₉

commutator, cosocle

C₂³×C₉

C₂⁴

Frattini, socle, prime radical

C₂³×C₃

C₂³×D₃

C₂

D₉

C₉

G ▷ C₂³×C₉ ▷ C₉

C₁ ◁ C₂³ ◁ #384

N	H ≅ G/N	type
27. C₄²×C₉	Q₈	semidirect
31. C₄×Dic₉	Q₈	semidirect
72. C₄×C₉	C₄⋊Q₈	semidirect
75. Dic₉	C₄⋊Q₈	semidirect
108. C₄²	Dic₁₈	semidirect
117. C₉	#2868	semidirect
138. C₄	#63450	semidirect

H ≅ G/N

type

27. C₄²×C₉

Q₈

semidirect

31. C₄×Dic₉

Q₈

semidirect

72. C₄×C₉

C₄⋊Q₈

semidirect

75. Dic₉

C₄⋊Q₈

semidirect

108. C₄²

Dic₁₈

semidirect

117. C₉

#2868

semidirect

138. C₄

#63450

semidirect

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

subgroup	index
C₂×#63450	2
C₉×#384	2
#10588655	2
#10588615	2
C₄²×Dic₉	2
#74356	3

subgroup

index

C₄²×Dic₉

Subgroups — #11857079

Conjugacy classes of subgroups

Complements

Maximal subgroups