Group #11782026 — subgroups

Subgroups — #11782026

Order 1152.

210 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 76 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	#10588514	C₂	1	2	yes	maximal
2	#10588362	C₂	1	1	yes	maximal, characteristic
3	#10588359	C₂	1	1	yes	maximal, characteristic
4	C₉×#334	C₂	1	1	yes	maximal, characteristic
5	#10588158	C₂	1	2	yes	maximal
6	#68553	—	3	1	no	maximal
7	#63431	C₂²	1	2	yes	—
8	C₄×Dic₁₈	C₂²	1	1	yes	characteristic
9	C₉×C₄⋊C₈	C₂²	1	2	yes	—
10	C₄×C₈×C₉	C₂²	1	1	yes	characteristic
11	#63378	—	2	1	no	—
12	#63378	—	2	1	no	—
13	#63378	—	2	2	no	—
14	#63376	—	2	2	no	—
15	#63375	—	2	1	no	—
16	Dic₉⋊C₈	—	2	1	no	—
17	C₄⋊(C₉⋊C₈)	C₂²	1	1	yes	characteristic
18	#4850	—	3	2	no	—
19	#4682	—	3	1	no	—
20	#4679	—	3	1	no	—
21	C₃×#334	D₃	1	1	yes	characteristic
22	#4481	—	3	2	no	—
23	C₂×Dic₁₈	—	2	2	no	—
24	C₂×Dic₁₈	D₄	1	1	yes	characteristic
25	C₂×C₈×C₉	—	2	2	no	—
26	C₂×C₈×C₉	D₄	1	1	yes	characteristic
27	C₂×C₈×C₉	D₄	1	1	yes	characteristic
28	C₄²×C₉	C₂³	1	1	yes	characteristic
29	C₄⋊Dic₉	—	2	2	no	—
30	C₄⋊Dic₉	—	2	2	no	—
31	C₄⋊Dic₉	D₄	1	1	yes	characteristic
32	Dic₉⋊C₄	—	2	1	no	—
33	C₄×Dic₉	—	2	1	no	—
34	C₂×C₉⋊C₈	—	2	1	no	—
35	#1696	—	9	1	no	Sylow
36	#869	—	3	2	no	—
37	C₄×Dic₆	—	3	1	no	—
38	C₃×C₄⋊C₈	C₂×D₃	1	2	yes	—
39	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
40	#818	—	6	2	no	—
41	#818	—	6	1	no	—
42	#818	—	6	1	no	—
43	#816	—	6	2	no	—
44	#815	—	6	1	no	—
45	Dic₃⋊C₈	—	6	1	no	—
46	C₄⋊(C₃⋊C₈)	—	3	1	no	—
47	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄×C₉	#41	1	1	yes	characteristic
50	C₂×Dic₉	—	2	1	no	—
51	C₂×Dic₉	—	2	1	no	—
52	C₂×Dic₉	—	4	2	no	—
53	Dic₁₈	—	2	2	no	—
54	Dic₁₈	—	8	2	no	—
55	C₈×C₉	—	2	1	no	—
56	C₈×C₉	—	4	2	no	—
57	C₈×C₉	Q₁₆	1	2	yes	—
58	C₉⋊C₈	—	4	1	no	—
59	#500	—	9	1	no	—
60	#477	—	9	2	no	—
61	#446	—	9	1	no	—
62	#334	D₉	1	1	yes	characteristic
63	#333	—	9	2	no	—
64	C₂×Dic₆	—	3	1	no	—
65	C₂×Dic₆	—	6	2	no	—
66	C₂×C₃×C₈	—	2	2	no	—
67	C₂×C₃×C₈	D₁₂	1	1	yes	characteristic
68	C₂×C₃×C₈	D₁₂	1	1	yes	characteristic
69	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
70	C₄⋊Dic₃	—	3	1	no	—
71	C₄⋊Dic₃	—	6	2	no	—
72	C₄⋊Dic₃	—	6	2	no	—
73	Dic₃⋊C₄	—	6	1	no	—
74	C₄×Dic₃	—	6	1	no	—
75	C₂×C₃⋊C₈	—	6	1	no	—
76	C₂²×C₉	#121	1	1	yes	characteristic
77	C₄×C₉	—	2	1	no	—
78	C₄×C₉	C₂×Q₁₆	1	1	yes	characteristic
79	C₄×C₉	#137	1	1	yes	characteristic
80	C₄×C₉	#137	1	2	yes	—
81	Dic₉	—	4	1	no	—
82	Dic₉	—	4	1	no	—
83	Dic₉	—	8	2	no	—
84	C₄⋊Q₈	—	9	2	no	—
85	C₄×Q₈	—	9	1	no	—
86	#107	—	18	2	no	—
87	#107	—	18	1	no	—
88	#107	—	18	1	no	—
89	C₄⋊C₈	—	9	1	no	—
90	C₄⋊C₈	—	18	1	no	—
91	C₄⋊C₈	C₂×D₉	1	2	yes	—
92	#103	—	18	2	no	—
93	#97	—	18	1	no	—
94	C₄×C₈	C₂×D₉	1	1	yes	characteristic
95	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
96	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
97	C₂×C₃×C₄	#239	1	1	yes	characteristic
98	C₂×Dic₃	—	6	1	no	—
99	C₂×Dic₃	—	6	1	no	—
100	C₂×Dic₃	—	12	2	no	—
101	Dic₆	—	6	2	no	—
102	Dic₆	—	24	2	no	—
103	C₃×C₈	—	2	1	no	—
104	C₃×C₈	—	4	2	no	—
105	C₃×C₈	Dic₁₂	1	2	yes	—
106	C₃⋊C₈	—	12	1	no	—
107	C₂×C₉	#462	1	1	yes	characteristic
108	C₂×C₉	#470	1	1	yes	characteristic
109	C₂×C₉	#472	1	1	yes	characteristic
110	C₂×Q₈	—	9	1	no	—
111	C₂×Q₈	—	18	2	no	—
112	C₂×C₈	—	2	2	no	—
113	C₂×C₈	—	18	1	no	—
114	C₂×C₈	D₃₆	1	1	yes	characteristic
115	C₂×C₈	D₃₆	1	1	yes	characteristic
116	C₄⋊C₄	—	9	1	no	—
117	C₄⋊C₄	—	18	1	no	—
118	C₄⋊C₄	—	18	2	no	—
119	C₄⋊C₄	—	18	2	no	—
120	C₄²	—	18	1	no	—
121	C₄²	C₂²×D₉	1	1	yes	characteristic
122	C₂²×C₃	#895	1	1	yes	characteristic
123	C₃×C₄	—	2	1	no	—
124	C₃×C₄	C₂×Dic₁₂	1	1	yes	characteristic
125	C₃×C₄	#909	1	1	yes	characteristic
126	C₃×C₄	#915	1	2	yes	—
127	Dic₃	—	12	1	no	—
128	Dic₃	—	12	1	no	—
129	Dic₃	—	24	2	no	—
130	C₉	#1696	1	1	yes	characteristic, complemented, Sylow
131	Q₈	—	18	2	no	—
132	Q₈	—	72	2	no	—
133	C₂×C₄	—	18	1	no	—
134	C₂×C₄	—	18	1	no	—
135	C₂×C₄	—	36	2	no	—
136	C₂×C₄	C₂×D₃₆	1	1	yes	characteristic
137	C₂×C₄	D₄×D₉	1	1	yes	characteristic
138	C₂×C₄	#3701	1	1	yes	characteristic
139	C₈	—	2	1	no	—
140	C₈	—	4	2	no	—
141	C₈	—	36	1	no	—
142	C₈	Dic₃₆	1	2	yes	—
143	C₂×C₃	#4849	1	1	yes	characteristic
144	C₂×C₃	#4867	1	1	yes	characteristic
145	C₂×C₃	#4897	1	1	yes	characteristic
146	C₂²	#63457	1	1	yes	characteristic
147	C₄	—	2	1	no	—
148	C₄	—	36	1	no	—
149	C₄	—	36	1	no	—
150	C₄	—	72	2	no	—
151	C₄	C₂×Dic₃₆	1	1	yes	characteristic
152	C₄	#63471	1	1	yes	characteristic
153	C₄	#63477	1	2	yes	—
154	C₃	#68553	1	1	yes	characteristic
155	C₂	#10588513	1	1	yes	characteristic
156	C₂	#10588547	1	1	yes	characteristic
157	C₂	#10588577	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#10588514

C₂

yes

maximal

#10588362

C₂

yes

maximal, characteristic

#10588359

C₂

yes

maximal, characteristic

C₉×#334

C₂

yes

maximal, characteristic

#10588158

C₂

yes

—

C₂²

yes

—

C₄×Dic₁₈

C₂²

yes

characteristic

C₉×C₄⋊C₈

C₂²

yes

—

C₄×C₈×C₉

C₂²

yes

—

—

—

—

—

Dic₉⋊C₈

—

C₄⋊(C₉⋊C₈)

C₂²

yes

—

—

—

D₃

yes

characteristic

#4481

—

C₂×Dic₁₈

—

C₂×Dic₁₈

D₄

yes

characteristic

C₂×C₈×C₉

—

C₂×C₈×C₉

D₄

yes

characteristic

C₂×C₈×C₉

D₄

yes

characteristic

C₄²×C₉

C₂³

yes

characteristic

C₄⋊Dic₉

—

C₄⋊Dic₉

—

C₄⋊Dic₉

D₄

yes

characteristic

Dic₉⋊C₄

—

C₄×Dic₉

—

C₂×C₉⋊C₈

—

#1696

—

Sylow

#869

—

C₄×Dic₆

—

C₃×C₄⋊C₈

C₂×D₃

yes

—

C₃×C₄×C₈

C₂×D₃

yes

—

—

—

—

—

Dic₃⋊C₈

—

C₄⋊(C₃⋊C₈)

—

C₂×C₄×C₉

C₂×D₄

yes

characteristic

C₂×C₄×C₉

C₂×D₄

yes

characteristic

C₂×C₄×C₉

#41

yes

characteristic

C₂×Dic₉

—

C₂×Dic₉

—

C₂×Dic₉

—

Dic₁₈

—

Dic₁₈

—

C₈×C₉

—

C₈×C₉

—

C₈×C₉

Q₁₆

yes

—

C₉⋊C₈

—

—

—

—

D₉

yes

characteristic

#333

—

C₂×Dic₆

—

C₂×Dic₆

—

C₂×C₃×C₈

—

C₂×C₃×C₈

D₁₂

yes

characteristic

C₂×C₃×C₈

D₁₂

yes

characteristic

C₃×C₄²

C₂²×D₃

yes

characteristic

C₄⋊Dic₃

—

C₄⋊Dic₃

—

C₄⋊Dic₃

—

Dic₃⋊C₄

—

C₄×Dic₃

—

C₂×C₃⋊C₈

—

C₂²×C₉

#121

yes

characteristic

C₄×C₉

—

C₄×C₉

C₂×Q₁₆

yes

C₄×C₉

yes

C₄×C₉

yes

—

Dic₉

—

Dic₉

—

Dic₉

—

C₄⋊Q₈

—

C₄×Q₈

—

#107

—

#107

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₉

yes

—

#103

—

#97

—

C₄×C₈

C₂×D₉

yes

characteristic

C₂×C₃×C₄

C₂×D₁₂

yes

characteristic

C₂×C₃×C₄

D₃×D₄

yes

characteristic

C₂×C₃×C₄

#239

yes

characteristic

C₂×Dic₃

—

C₂×Dic₃

—

100

C₂×Dic₃

—

101

Dic₆

—

102

Dic₆

—

103

C₃×C₈

—

104

C₃×C₈

—

105

C₃×C₈

Dic₁₂

yes

—

106

C₃⋊C₈

—

107

C₂×C₉

#462

yes

characteristic

108

C₂×C₉

#470

yes

characteristic

109

C₂×C₉

#472

yes

characteristic

110

C₂×Q₈

—

111

C₂×Q₈

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

D₃₆

yes

characteristic

115

C₂×C₈

D₃₆

yes

characteristic

116

C₄⋊C₄

—

117

C₄⋊C₄

—

118

C₄⋊C₄

—

119

C₄⋊C₄

—

120

C₄²

—

121

C₄²

C₂²×D₉

yes

characteristic

122

C₂²×C₃

#895

yes

characteristic

123

C₃×C₄

—

124

C₃×C₄

C₂×Dic₁₂

yes

characteristic

125

C₃×C₄

#909

yes

characteristic

126

C₃×C₄

#915

yes

—

127

Dic₃

—

128

Dic₃

—

129

Dic₃

—

130

C₉

#1696

yes

characteristic, complemented, Sylow

131

Q₈

—

132

Q₈

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

C₂×D₃₆

yes

characteristic

137

C₂×C₄

D₄×D₉

yes

characteristic

138

C₂×C₄

#3701

yes

characteristic

139

C₈

—

140

C₈

—

141

C₈

—

142

C₈

Dic₃₆

yes

—

143

C₂×C₃

#4849

yes

characteristic

144

C₂×C₃

#4867

yes

characteristic

145

C₂×C₃

#4897

yes

characteristic

146

C₂²

#63457

yes

characteristic

147

C₄

—

148

C₄

—

149

C₄

—

150

C₄

—

151

C₄

C₂×Dic₃₆

yes

characteristic

152

C₄

#63471

yes

characteristic

153

C₄

#63477

yes

—

154

C₃

#68553

yes

characteristic

155

C₂

#10588513

yes

characteristic

156

C₂

#10588547

yes

characteristic

157

C₂

#10588577

yes

characteristic

	subgroup	G/H
center	C₂²	#63457
commutator, cosocle	C₄²×C₉	C₂³
Frattini	C₃×C₄²	C₂²×D₃
Fitting	C₉×#334	C₂
socle, prime radical	C₂²×C₃	#895
hypercenter	#334	D₉
hypocenter	C₉	#1696
LCS	G ▷ C₄²×C₉ ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #334

subgroup

G/H

center

C₂²

#63457

commutator, cosocle

C₄²×C₉

C₂³

Frattini

C₃×C₄²

C₂²×D₃

C₂

C₂²×C₃

D₉

C₉

G ▷ C₄²×C₉ ▷ C₂²×C₉ ▷ C₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #334

N	H ≅ G/N	type
130. C₉	#1696	semidirect

H ≅ G/N

type

130. C₉

#1696

semidirect

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

subgroup	index
#10588514	2
#10588362	2
#10588359	2
C₉×#334	2
#10588158	2
#68553	3

subgroup

index

Subgroups — #11782026

Conjugacy classes of subgroups

Complements

Maximal subgroups