Group #11797356 — subgroups

Subgroups — #11797356

Order 1152.

268 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 70 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	#10592696	C₂	1	1	yes	maximal, characteristic
2	C₂²⋊#3708	C₂	1	2	yes	maximal
3	#10590148	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄⋊#3708	C₂	1	2	yes	maximal, complemented
5	C₄×#3708	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃²×#117	C₄	1	1	yes	characteristic
7	C₂×#3748	C₄	1	1	yes	characteristic
8	C₂²×C₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
9	C₂×#3708	C₂²	1	2	yes	—
10	C₂×#3708	C₂²	1	2	yes	—
11	#63630	C₄	1	1	yes	characteristic
12	#63630	C₄	1	1	yes	characteristic
13	C₄×C₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
14	C₄×C₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
15	#4997	—	6	2	no	—
16	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
17	C₃²×C₄⋊C₄	C₈	1	2	yes	—
18	C₃²×C₂²⋊C₄	C₈	1	2	yes	—
19	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
20	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
21	#3748	—	2	2	no	—
22	C₂×C₃⋊(C₃⋊C₈)	—	2	2	no	—
23	C₂×C₃⋊(C₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
24	C₂×C₃⋊(C₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
25	C₂×C₃⋊(C₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
26	C₂×C₃⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
27	#3708	—	2	2	no	—
28	#3708	—	2	2	no	—
29	#2164	—	9	1	no	maximal, Sylow
30	C₃×#117	—	2	2	no	—
31	C₂×#208	—	6	2	no	—
32	C₂²×C₃⋊C₈	—	6	2	no	—
33	#803	—	6	2	no	—
34	#803	—	6	2	no	—
35	C₄×C₃⋊C₈	—	6	2	no	—
36	C₄×C₃⋊C₈	—	6	2	no	—
37	C₂³×C₃²	C₂×C₈	1	1	yes	characteristic
38	C₂×C₃²×C₄	—	2	1	no	—
39	C₂×C₃²×C₄	—	2	1	no	—
40	C₂×C₃²×C₄	C₂×C₈	1	2	yes	—
41	C₂×C₃²×C₄	C₂×C₈	1	2	yes	—
42	C₂×C₃²×C₄	C₂×C₈	1	1	yes	characteristic
43	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
44	C₃⋊(C₃⋊C₈)	—	2	1	no	—
45	C₃⋊(C₃⋊C₈)	—	2	1	no	—
46	C₃⋊(C₃⋊C₈)	M₁₆	1	2	yes	—
47	C₃⋊(C₃⋊C₈)	#41	1	2	yes	—
48	#405	—	9	1	no	—
49	C₄⋊C₁₆	—	9	2	no	—
50	C₂²⋊C₁₆	—	9	2	no	—
51	#346	—	9	1	no	—
52	C₄×C₁₆	—	9	1	no	—
53	C₂²×C₃×C₄	—	2	2	no	—
54	C₃×C₄⋊C₄	—	2	4	no	—
55	C₃×C₂²⋊C₄	—	2	4	no	—
56	C₃×C₄²	—	2	2	no	—
57	C₃×C₄²	—	2	2	no	—
58	#208	—	6	8	no	—
59	C₂×C₃⋊C₈	—	6	2	no	—
60	C₂×C₃⋊C₈	—	6	2	no	—
61	C₂×C₃⋊C₈	—	6	2	no	—
62	C₂×C₃⋊C₈	—	6	2	no	—
63	C₂×C₃⋊C₈	—	6	8	no	—
64	C₂²×C₃²	—	2	1	no	—
65	C₂²×C₃²	—	2	2	no	—
66	C₂²×C₃²	C₂²×C₈	1	1	yes	characteristic
67	C₃²×C₄	—	2	1	no	—
68	C₃²×C₄	—	2	2	no	—
69	C₃²×C₄	—	2	2	no	—
70	C₃²×C₄	#117	1	1	yes	characteristic
71	C₃²×C₄	C₂×M₁₆	1	1	yes	characteristic
72	C₂×M₁₆	—	9	1	no	—
73	C₂²×C₈	—	9	1	no	—
74	#117	#157	1	1	yes	characteristic
75	C₂×C₁₆	—	9	2	no	—
76	C₂×C₁₆	—	9	2	no	—
77	#97	—	9	1	no	—
78	#97	—	9	1	no	—
79	C₄×C₈	—	9	1	no	—
80	C₄×C₈	—	9	1	no	—
81	C₂³×C₃	—	2	2	no	—
82	C₂×C₃×C₄	—	2	4	no	—
83	C₂×C₃×C₄	—	2	4	no	—
84	C₂×C₃×C₄	—	2	2	no	—
85	C₂×C₃×C₄	—	2	2	no	—
86	C₂×C₃×C₄	—	2	4	no	—
87	C₂×C₃×C₄	—	2	4	no	—
88	C₃⋊C₈	—	6	4	no	—
89	C₃⋊C₈	—	6	4	no	—
90	C₃⋊C₈	—	6	4	no	—
91	C₃⋊C₈	—	6	4	no	—
92	C₂×C₃²	—	4	1	no	—
93	C₂×C₃²	#431	1	1	yes	characteristic
94	C₂×C₃²	#504	1	2	yes	—
95	C₂²×C₄	C₂×#157	1	1	yes	characteristic
96	M₁₆	—	18	2	no	—
97	C₂×C₈	—	9	1	no	—
98	C₂×C₈	—	9	1	no	—
99	C₂×C₈	—	9	1	no	—
100	C₂×C₈	—	9	1	no	—
101	C₂×C₈	—	18	2	no	—
102	C₄⋊C₄	#622	1	2	yes	—
103	C₂²⋊C₄	#622	1	2	yes	—
104	C₄²	C₂×#157	1	1	yes	characteristic
105	C₄²	C₂×#157	1	1	yes	characteristic
106	C₁₆	—	18	2	no	—
107	C₁₆	—	18	2	no	—
108	C₂²×C₃	—	2	4	no	—
109	C₂²×C₃	—	2	2	no	—
110	C₂²×C₃	—	4	4	no	—
111	C₃×C₄	—	2	4	no	—
112	C₃×C₄	—	2	2	no	—
113	C₃×C₄	—	2	2	no	—
114	C₃×C₄	—	4	4	no	—
115	C₃×C₄	—	4	4	no	—
116	C₃²	#2164	1	1	yes	characteristic, complemented, Sylow
117	C₂³	C₂×#622	1	1	yes	characteristic
118	C₂×C₄	—	2	1	no	—
119	C₂×C₄	—	2	1	no	—
120	C₂×C₄	C₂×#622	1	2	yes	—
121	C₂×C₄	C₂×#622	1	2	yes	—
122	C₂×C₄	C₂×#622	1	1	yes	characteristic
123	C₂×C₄	C₂²×#157	1	1	yes	characteristic
124	C₈	—	9	2	no	—
125	C₈	—	9	2	no	—
126	C₈	—	18	1	no	—
127	C₈	—	18	1	no	—
128	C₂×C₃	—	2	2	no	—
129	C₂×C₃	—	2	4	no	—
130	C₂×C₃	—	4	4	no	—
131	C₂²	—	2	1	no	—
132	C₂²	—	2	2	no	—
133	C₂²	C₂²×#622	1	1	yes	characteristic
134	C₄	—	2	1	no	—
135	C₄	—	2	2	no	—
136	C₄	—	2	2	no	—
137	C₄	#64283	1	1	yes	characteristic
138	C₄	#64286	1	1	yes	characteristic
139	C₃	—	2	2	no	—
140	C₂	—	4	1	no	—
141	C₂	#10593795	1	1	yes	characteristic
142	C₂	#10593838	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#10592696

C₂

yes

maximal, characteristic

C₂²⋊#3708

C₂

yes

maximal

#10590148

C₂

yes

maximal, characteristic, complemented

C₄⋊#3708

C₂

yes

maximal, complemented

C₄×#3708

C₂

yes

maximal, characteristic, complemented

C₃²×#117

C₄

yes

characteristic

C₂×#3748

C₄

yes

characteristic

C₂²×C₃⋊(C₃⋊C₈)

C₂²

yes

characteristic

C₂×#3708

C₂²

yes

—

C₂×#3708

C₂²

yes

—

#63630

C₄

yes

characteristic

#63630

C₄

yes

characteristic

C₄×C₃⋊(C₃⋊C₈)

C₂²

yes

characteristic

C₄×C₃⋊(C₃⋊C₈)

C₂²

yes

characteristic

#4997

—

C₂²×C₃²×C₄

C₂×C₄

yes

characteristic

C₃²×C₄⋊C₄

C₈

yes

—

C₃²×C₂²⋊C₄

C₈

yes

—

C₃²×C₄²

C₂×C₄

yes

characteristic

C₃²×C₄²

C₂×C₄

yes

characteristic

#3748

—

C₂×C₃⋊(C₃⋊C₈)

—

C₂×C₃⋊(C₃⋊C₈)

C₂×C₄

yes

characteristic

C₂×C₃⋊(C₃⋊C₈)

C₂×C₄

yes

characteristic

C₂×C₃⋊(C₃⋊C₈)

C₂×C₄

yes

characteristic

C₂×C₃⋊(C₃⋊C₈)

C₂³

yes

—

—

—

—

—

C₂²×C₃⋊C₈

—

#803

—

#803

—

C₄×C₃⋊C₈

—

C₄×C₃⋊C₈

—

C₂³×C₃²

C₂×C₈

yes

characteristic

C₂×C₃²×C₄

—

C₂×C₃²×C₄

—

C₂×C₃²×C₄

C₂×C₈

yes

—

C₂×C₃²×C₄

C₂×C₈

yes

—

C₂×C₃²×C₄

C₂×C₈

yes

characteristic

C₂×C₃²×C₄

C₂²×C₄

yes

characteristic

C₃⋊(C₃⋊C₈)

—

C₃⋊(C₃⋊C₈)

—

C₃⋊(C₃⋊C₈)

M₁₆

yes

—

C₃⋊(C₃⋊C₈)

#41

yes

—

#405

—

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

#346

—

C₄×C₁₆

—

C₂²×C₃×C₄

—

C₃×C₄⋊C₄

—

C₃×C₂²⋊C₄

—

C₃×C₄²

—

C₃×C₄²

—

#208

—

C₂×C₃⋊C₈

—

C₂×C₃⋊C₈

—

C₂×C₃⋊C₈

—

C₂×C₃⋊C₈

—

C₂×C₃⋊C₈

—

C₂²×C₃²

—

C₂²×C₃²

—

C₂²×C₃²

C₂²×C₈

yes

characteristic

C₃²×C₄

—

C₃²×C₄

—

C₃²×C₄

—

C₃²×C₄

#117

yes

characteristic

C₃²×C₄

C₂×M₁₆

yes

characteristic

C₂×M₁₆

—

C₂²×C₈

—

#117

#157

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

#97

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₂³×C₃

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₃⋊C₈

—

C₃⋊C₈

—

C₃⋊C₈

—

C₃⋊C₈

—

C₂×C₃²

—

C₂×C₃²

#431

yes

characteristic

C₂×C₃²

#504

yes

—

C₂²×C₄

C₂×#157

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₄⋊C₄

#622

yes

—

103

C₂²⋊C₄

#622

yes

—

104

C₄²

C₂×#157

yes

characteristic

105

C₄²

C₂×#157

yes

characteristic

106

C₁₆

—

107

C₁₆

—

108

C₂²×C₃

—

109

C₂²×C₃

—

110

C₂²×C₃

—

111

C₃×C₄

—

112

C₃×C₄

—

113

C₃×C₄

—

114

C₃×C₄

—

115

C₃×C₄

—

116

C₃²

#2164

yes

characteristic, complemented, Sylow

117

C₂³

C₂×#622

yes

characteristic

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

C₂×#622

yes

—

121

C₂×C₄

C₂×#622

yes

—

122

C₂×C₄

C₂×#622

yes

characteristic

123

C₂×C₄

C₂²×#157

yes

characteristic

124

C₈

—

125

C₈

—

126

C₈

—

127

C₈

—

128

C₂×C₃

—

129

C₂×C₃

—

130

C₂×C₃

—

131

C₂²

—

132

C₂²

—

133

C₂²

C₂²×#622

yes

characteristic

134

C₄

—

135

C₄

—

136

C₄

—

137

C₄

#64283

yes

characteristic

138

C₄

#64286

yes

characteristic

139

C₃

—

140

C₂

—

141

C₂

#10593795

yes

characteristic

142

C₂

#10593838

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#157
commutator, socle	C₂²×C₃²	C₂²×C₈
Fitting	C₃²×#117	C₄
prime radical	C₂³×C₃²	C₂×C₈
cosocle	C₂×C₃⋊(C₃⋊C₈)	C₂³
hypercenter	#117	#157
hypocenter	C₃²	#2164
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₄ ◁ #117

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#157

commutator, socle

C₂²×C₃²

C₂²×C₈

Fitting

C₃²×#117

C₄

prime radical

C₂³×C₃²

C₂×C₈

cosocle

C₂×C₃⋊(C₃⋊C₈)

C₂³

C₃²

G ▷ C₂²×C₃² ▷ C₃²

C₁ ◁ C₂×C₄ ◁ #117

N	H ≅ G/N	type
3. #10590148	C₂	semidirect
4. C₄⋊#3708	C₂	semidirect
5. C₄×#3708	C₂	semidirect
116. C₃²	#2164	semidirect

H ≅ G/N

type

3. #10590148

C₂

semidirect

4. C₄⋊#3708

C₂

semidirect

5. C₄×#3708

C₂

semidirect

116. C₃²

#2164

semidirect

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

subgroup	index
#10592696	2
C₂²⋊#3708	2
#10590148	2
C₄⋊#3708	2
C₄×#3708	2
#2164	9

subgroup

index

C₂²⋊#3708

Subgroups — #11797356

Conjugacy classes of subgroups

Complements

Maximal subgroups