Group #11795298 — subgroups

Subgroups — #11795298

Order 1152.

528 conjugacy classes of subgroups; only the 187 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 187 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	#10592820	C₂	1	2	yes	maximal
2	C₂×#63645	C₂	1	1	yes	maximal, characteristic
3	#10592801	C₂	1	1	yes	maximal, characteristic
4	C₃²×#341	C₂	1	1	yes	maximal, characteristic
5	#10589420	C₂	1	2	yes	maximal
6	#68923	—	3	4	no	maximal
7	C₂×C₃²×M₁₆	C₂²	1	2	yes	—
8	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
9	#64135	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊(C₃⋊Dic₃)	C₂²	1	2	yes	—
11	C₂×#3748	C₂²	1	1	yes	characteristic
12	#63645	—	2	2	no	—
13	#63645	—	2	2	no	—
14	#63644	—	2	2	no	—
15	#63641	—	2	2	no	—
16	#5121	—	3	8	no	—
17	C₂×#818	—	3	4	no	—
18	#5102	—	3	4	no	—
19	C₃×#341	D₃	1	4	yes	—
20	#4554	—	3	8	no	—
21	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
22	C₂²×C₃⋊Dic₃	—	2	2	no	—
23	C₃²×M₁₆	—	2	2	no	—
24	C₃²×M₁₆	Q₈	1	4	yes	—
25	C₂×C₃²×C₈	—	2	2	no	—
26	C₂×C₃²×C₈	—	2	2	no	—
27	C₂×C₃²×C₈	D₄	1	2	yes	—
28	#3757	—	2	1	no	—
29	C₄⋊(C₃⋊Dic₃)	—	2	2	no	—
30	C₄⋊(C₃⋊Dic₃)	—	2	2	no	—
31	C₄⋊(C₃⋊Dic₃)	D₄	1	1	yes	characteristic
32	C₄⋊(C₃⋊Dic₃)	D₄	1	1	yes	characteristic
33	C₄×C₃⋊Dic₃	—	2	1	no	—
34	#3748	—	2	2	no	—
35	C₂×C₃⋊(C₃⋊C₈)	—	2	1	no	—
36	#2089	—	9	1	no	Sylow
37	C₂×C₃×M₁₆	C₂×D₃	1	8	yes	—
38	C₂²×C₃×C₈	C₂×D₃	1	4	yes	—
39	#926	—	3	4	no	—
40	C₂×C₄⋊Dic₃	—	3	8	no	—
41	C₂×#208	—	3	4	no	—
42	#818	—	6	8	no	—
43	#818	—	6	8	no	—
44	#817	—	6	8	no	—
45	Dic₃⋊C₈	—	6	8	no	—
46	C₂³×C₃²	#41	1	1	yes	characteristic
47	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
48	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
49	C₂×C₃²×C₄	C₂×Q₈	1	2	yes	—
50	C₂×C₃²×C₄	#41	1	2	yes	—
51	C₂×C₃⋊Dic₃	—	2	1	no	—
52	C₂×C₃⋊Dic₃	—	2	1	no	—
53	C₂×C₃⋊Dic₃	—	4	2	no	—
54	C₂×C₃⋊Dic₃	—	8	2	no	—
55	C₃²×C₈	—	2	4	no	—
56	C₃²×C₈	—	2	2	no	—
57	C₃⋊(C₃⋊C₈)	—	4	1	no	—
58	#428	—	9	2	no	—
59	C₂×#107	—	9	1	no	—
60	#424	—	9	1	no	—
61	#343	—	9	2	no	—
62	#341	C₃⋊D₃	1	1	yes	characteristic
63	C₂²×C₃×C₄	C₂²×D₃	1	4	yes	—
64	C₂²×Dic₃	—	6	8	no	—
65	C₃×M₁₆	—	2	8	no	—
66	C₃×M₁₆	Dic₆	1	16	yes	—
67	C₂×C₃×C₈	—	2	8	no	—
68	C₂×C₃×C₈	—	2	8	no	—
69	C₂×C₃×C₈	D₁₂	1	8	yes	—
70	#217	—	6	4	no	—
71	C₄⋊Dic₃	—	3	4	no	—
72	C₄⋊Dic₃	—	3	4	no	—
73	C₄⋊Dic₃	—	6	8	no	—
74	C₄⋊Dic₃	—	6	8	no	—
75	C₄×Dic₃	—	6	4	no	—
76	#208	—	6	8	no	—
77	C₂×C₃⋊C₈	—	6	4	no	—
78	C₂²×C₃²	—	2	1	no	—
79	C₂²×C₃²	—	2	1	no	—
80	C₂²×C₃²	#121	1	1	yes	characteristic
81	C₂²×C₃²	#125	1	2	yes	—
82	C₃²×C₄	C₂²⋊Q₈	1	2	yes	—
83	C₃²×C₄	#123	1	1	yes	characteristic
84	C₃²×C₄	C₄⋊Q₈	1	1	yes	characteristic
85	C₃⋊Dic₃	—	4	1	no	—
86	C₃⋊Dic₃	—	4	1	no	—
87	C₃⋊Dic₃	—	8	2	no	—
88	C₂×M₁₆	—	9	1	no	—
89	C₂×M₁₆	C₂×C₃⋊D₃	1	2	yes	—
90	C₂²×C₈	C₂×C₃⋊D₃	1	1	yes	characteristic
91	#117	—	9	1	no	—
92	C₂×C₄⋊C₄	—	9	2	no	—
93	#107	—	18	2	no	—
94	#107	—	18	2	no	—
95	#106	—	18	2	no	—
96	C₄⋊C₈	—	18	2	no	—
97	C₂³×C₃	#239	1	4	yes	—
98	C₂×C₃×C₄	C₂×Dic₆	1	8	yes	—
99	C₂×C₃×C₄	C₂×D₁₂	1	4	yes	—
100	C₂×C₃×C₄	D₃×D₄	1	4	yes	—
101	C₂×C₃×C₄	#237	1	8	yes	—
102	C₂×Dic₃	—	6	4	no	—
103	C₂×Dic₃	—	6	4	no	—
104	C₂×Dic₃	—	12	8	no	—
105	C₂×Dic₃	—	24	8	no	—
106	C₃×C₈	—	2	16	no	—
107	C₃×C₈	—	2	8	no	—
108	C₃⋊C₈	—	12	4	no	—
109	C₂×C₃²	—	2	2	no	—
110	C₂×C₃²	#398	1	1	yes	characteristic
111	C₂×C₃²	#472	1	1	yes	characteristic
112	C₂×C₃²	#473	1	1	yes	characteristic
113	C₂²×C₄	—	18	2	no	—
114	C₂²×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
115	M₁₆	—	2	2	no	—
116	M₁₆	—	18	2	no	—
117	M₁₆	#634	1	4	yes	—
118	C₂×C₈	—	2	2	no	—
119	C₂×C₈	—	2	2	no	—
120	C₂×C₈	—	18	1	no	—
121	C₂×C₈	C₄⋊(C₃⋊D₃)	1	2	yes	—
122	C₄⋊C₄	—	9	1	no	—
123	C₄⋊C₄	—	9	1	no	—
124	C₄⋊C₄	—	18	2	no	—
125	C₄⋊C₄	—	18	2	no	—
126	C₂²⋊C₄	—	18	1	no	—
127	C₄²	—	18	1	no	—
128	C₂²×C₃	—	2	4	no	—
129	C₂²×C₃	—	2	4	no	—
130	C₂²×C₃	#890	1	8	yes	—
131	C₂²×C₃	#895	1	4	yes	—
132	C₃×C₄	#869	1	4	yes	—
133	C₃×C₄	#878	1	8	yes	—
134	C₃×C₄	#886	1	4	yes	—
135	Dic₃	—	12	4	no	—
136	Dic₃	—	12	4	no	—
137	Dic₃	—	24	8	no	—
138	C₃²	#2089	1	1	yes	characteristic, complemented, Sylow
139	C₂³	#3832	1	1	yes	characteristic
140	C₂×C₄	—	18	1	no	—
141	C₂×C₄	—	18	1	no	—
142	C₂×C₄	—	36	2	no	—
143	C₂×C₄	—	72	2	no	—
144	C₂×C₄	C₂×#634	1	2	yes	—
145	C₂×C₄	C₂×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
146	C₂×C₄	D₄×C₃⋊D₃	1	1	yes	characteristic
147	C₂×C₄	#3830	1	2	yes	—
148	C₈	—	2	4	no	—
149	C₈	—	2	2	no	—
150	C₈	—	36	1	no	—
151	C₂×C₃	—	2	8	no	—
152	C₂×C₃	#4661	1	4	yes	—
153	C₂×C₃	#4896	1	4	yes	—
154	C₂×C₃	#4897	1	4	yes	—
155	C₂²	—	2	1	no	—
156	C₂²	—	2	1	no	—
157	C₂²	#64099	1	2	yes	—
158	C₂²	#64104	1	1	yes	characteristic
159	C₄	—	36	1	no	—
160	C₄	—	36	1	no	—
161	C₄	—	72	2	no	—
162	C₄	#64078	1	1	yes	characteristic
163	C₄	#64087	1	2	yes	—
164	C₄	#64095	1	1	yes	characteristic
165	C₃	#68923	1	4	yes	complemented
166	C₂	—	2	2	no	—
167	C₂	#10592360	1	1	yes	characteristic
168	C₂	#10592595	1	1	yes	characteristic
169	C₂	#10592596	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#10592820

C₂

yes

maximal

C₂×#63645

C₂

yes

maximal, characteristic

#10592801

C₂

yes

maximal, characteristic

C₃²×#341

C₂

yes

maximal, characteristic

#10589420

C₂

yes

maximal

#68923

—

maximal

C₂×C₃²×M₁₆

C₂²

yes

—

C₂²×C₃²×C₈

C₂²

yes

characteristic

#64135

C₂²

yes

characteristic

C₂×C₄⋊(C₃⋊Dic₃)

C₂²

yes

—

C₂×#3748

C₂²

yes

—

—

—

—

—

—

—

D₃

yes

—

#4554

—

C₂²×C₃²×C₄

C₂³

yes

characteristic

C₂²×C₃⋊Dic₃

—

C₃²×M₁₆

—

C₃²×M₁₆

Q₈

yes

—

C₂×C₃²×C₈

—

C₂×C₃²×C₈

—

C₂×C₃²×C₈

D₄

yes

—

#3757

—

C₄⋊(C₃⋊Dic₃)

—

C₄⋊(C₃⋊Dic₃)

—

C₄⋊(C₃⋊Dic₃)

D₄

yes

characteristic

C₄⋊(C₃⋊Dic₃)

D₄

yes

characteristic

C₄×C₃⋊Dic₃

—

#3748

—

C₂×C₃⋊(C₃⋊C₈)

—

#2089

—

Sylow

C₂×C₃×M₁₆

C₂×D₃

yes

—

C₂²×C₃×C₈

C₂×D₃

yes

—

#926

—

C₂×C₄⋊Dic₃

—

—

—

—

—

Dic₃⋊C₈

—

C₂³×C₃²

#41

yes

characteristic

C₂×C₃²×C₄

C₂×D₄

yes

characteristic

C₂×C₃²×C₄

C₂×D₄

yes

characteristic

C₂×C₃²×C₄

C₂×Q₈

yes

—

C₂×C₃²×C₄

#41

yes

—

C₂×C₃⋊Dic₃

—

C₂×C₃⋊Dic₃

—

C₂×C₃⋊Dic₃

—

C₂×C₃⋊Dic₃

—

C₃²×C₈

—

C₃²×C₈

—

C₃⋊(C₃⋊C₈)

—

—

—

—

—

C₃⋊D₃

yes

characteristic

C₂²×C₃×C₄

C₂²×D₃

yes

—

C₂²×Dic₃

—

C₃×M₁₆

—

C₃×M₁₆

Dic₆

yes

—

C₂×C₃×C₈

—

C₂×C₃×C₈

—

C₂×C₃×C₈

D₁₂

yes

—

#217

—

C₄⋊Dic₃

—

C₄⋊Dic₃

—

C₄⋊Dic₃

—

C₄⋊Dic₃

—

C₄×Dic₃

—

#208

—

C₂×C₃⋊C₈

—

C₂²×C₃²

—

C₂²×C₃²

—

C₂²×C₃²

#121

yes

characteristic

C₂²×C₃²

#125

yes

—

C₃²×C₄

C₂²⋊Q₈

yes

—

C₃²×C₄

#123

yes

characteristic

C₃²×C₄

C₄⋊Q₈

yes

characteristic

C₃⋊Dic₃

—

C₃⋊Dic₃

—

C₃⋊Dic₃

—

C₂×M₁₆

—

C₂×M₁₆

C₂×C₃⋊D₃

yes

—

C₂²×C₈

C₂×C₃⋊D₃

yes

characteristic

#117

—

C₂×C₄⋊C₄

—

#107

—

#107

—

#106

—

C₄⋊C₈

—

C₂³×C₃

#239

yes

—

C₂×C₃×C₄

C₂×Dic₆

yes

—

C₂×C₃×C₄

C₂×D₁₂

yes

—

100

C₂×C₃×C₄

D₃×D₄

yes

—

101

C₂×C₃×C₄

#237

yes

—

102

C₂×Dic₃

—

103

C₂×Dic₃

—

104

C₂×Dic₃

—

105

C₂×Dic₃

—

106

C₃×C₈

—

107

C₃×C₈

—

108

C₃⋊C₈

—

109

C₂×C₃²

—

110

C₂×C₃²

#398

yes

characteristic

111

C₂×C₃²

#472

yes

characteristic

112

C₂×C₃²

#473

yes

characteristic

113

C₂²×C₄

—

114

C₂²×C₄

C₂²×C₃⋊D₃

yes

characteristic

115

M₁₆

—

116

M₁₆

—

117

M₁₆

#634

yes

—

118

C₂×C₈

—

119

C₂×C₈

—

120

C₂×C₈

—

121

C₂×C₈

C₄⋊(C₃⋊D₃)

yes

—

122

C₄⋊C₄

—

123

C₄⋊C₄

—

124

C₄⋊C₄

—

125

C₄⋊C₄

—

126

C₂²⋊C₄

—

127

C₄²

—

128

C₂²×C₃

—

129

C₂²×C₃

—

130

C₂²×C₃

#890

yes

—

131

C₂²×C₃

#895

yes

—

132

C₃×C₄

#869

yes

—

133

C₃×C₄

#878

yes

—

134

C₃×C₄

#886

yes

—

135

Dic₃

—

136

Dic₃

—

137

Dic₃

—

138

C₃²

#2089

yes

characteristic, complemented, Sylow

139

C₂³

#3832

yes

characteristic

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

C₂×#634

yes

—

145

C₂×C₄

C₂×C₄⋊(C₃⋊D₃)

yes

characteristic

146

C₂×C₄

D₄×C₃⋊D₃

yes

characteristic

147

C₂×C₄

#3830

yes

—

148

C₈

—

149

C₈

—

150

C₈

—

151

C₂×C₃

—

152

C₂×C₃

#4661

yes

—

153

C₂×C₃

#4896

yes

—

154

C₂×C₃

#4897

yes

—

155

C₂²

—

156

C₂²

—

157

C₂²

#64099

yes

—

158

C₂²

#64104

yes

characteristic

159

C₄

—

160

C₄

—

161

C₄

—

162

C₄

#64078

yes

characteristic

163

C₄

#64087

yes

—

164

C₄

#64095

yes

characteristic

165

C₃

#68923

yes

complemented

166

C₂

—

167

C₂

#10592360

yes

characteristic

168

C₂

#10592595

yes

characteristic

169

C₂

#10592596

yes

characteristic

	subgroup	G/H
center	C₂²	#64104
commutator, cosocle	C₂²×C₃²×C₄	C₂³
Frattini	C₂²×C₄	C₂²×C₃⋊D₃
Fitting	C₃²×#341	C₂
socle	C₂²×C₃²	#121
prime radical	C₂³×C₃²	#41
hypercenter	#341	C₃⋊D₃
hypocenter	C₃²	#2089
LCS	G ▷ C₂²×C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #341

subgroup

G/H

center

C₂²

#64104

commutator, cosocle

C₂²×C₃²×C₄

C₂³

Frattini

C₂²×C₄

C₂²×C₃⋊D₃

Fitting

C₃²×#341

C₂

C₂²×C₃²

C₂³×C₃²

C₃⋊D₃

C₃²

G ▷ C₂²×C₃²×C₄ ▷ C₂×C₃² ▷ C₃²

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #341

N	H ≅ G/N	type
138. C₃²	#2089	semidirect
165. C₃	#68923	semidirect

H ≅ G/N

type

138. C₃²

#2089

semidirect

165. C₃

#68923

semidirect

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

subgroup	index
#10592820	2
C₂×#63645	2
#10592801	2
C₃²×#341	2
#10589420	2
#68923	3

subgroup

index

C₃²×#341

Subgroups — #11795298

Conjugacy classes of subgroups

Complements

Maximal subgroups