Group #11795888 — subgroups

Subgroups — #11795888

Order 1152.

314 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 114 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×#63773	C₂	1	1	yes	maximal, characteristic
2	C₂²×#3708	C₂	1	1	yes	maximal, characteristic
3	#10592696	C₂	1	1	yes	maximal, characteristic
4	#10590148	C₂	1	2	yes	maximal, complemented
5	C₄×#3708	C₂	1	2	yes	maximal, 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	#63773	C₄	1	4	yes	complemented
10	C₂×#3708	C₄	1	4	yes	complemented
11	C₂×#3708	C₂²	1	1	yes	characteristic
12	C₂×#3708	C₂²	1	2	yes	—
13	C₂×#3708	C₂²	1	1	yes	characteristic
14	#63630	C₄	1	2	yes	—
15	C₄×C₃⋊(C₃⋊C₈)	C₂²	1	2	yes	—
16	#4997	—	6	2	no	—
17	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
18	C₃²×C₄⋊C₄	C₈	1	2	yes	—
19	C₃²×C₂²⋊C₄	C₈	1	2	yes	—
20	C₃²×C₄²	C₂×C₄	1	2	yes	—
21	#3748	C₈	1	4	yes	—
22	C₂×C₃⋊(C₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
23	C₂×C₃⋊(C₃⋊C₈)	C₂×C₄	1	2	yes	—
24	C₂×C₃⋊(C₃⋊C₈)	C₂×C₄	1	2	yes	—
25	C₂×C₃⋊(C₃⋊C₈)	C₂×C₄	1	2	yes	—
26	C₂×C₃⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
27	#3708	C₂×C₄	1	2	yes	—
28	#3708	C₂×C₄	1	2	yes	—
29	#3708	C₂×C₄	1	4	yes	—
30	#2108	—	9	1	no	maximal, Sylow
31	C₃×#117	—	2	2	no	—
32	C₂×#208	—	6	2	no	—
33	C₂²×C₃⋊C₈	—	6	2	no	—
34	#803	—	6	4	no	—
35	C₄×C₃⋊C₈	—	6	4	no	—
36	C₂³×C₃²	C₂×C₈	1	1	yes	characteristic
37	C₂×C₃²×C₄	C₄²	1	2	yes	—
38	C₂×C₃²×C₄	C₂×C₈	1	4	yes	—
39	C₂×C₃²×C₄	C₂×C₈	1	1	yes	characteristic
40	C₂×C₃²×C₄	C₂×C₈	1	2	yes	—
41	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
42	C₃⋊(C₃⋊C₈)	C₄²	1	2	yes	—
43	C₃⋊(C₃⋊C₈)	C₂×C₈	1	4	yes	—
44	C₃⋊(C₃⋊C₈)	C₂²×C₄	1	1	yes	characteristic
45	C₃⋊(C₃⋊C₈)	C₂²×C₄	1	1	yes	characteristic
46	C₂×M₃₂	—	9	1	no	—
47	C₂²×C₁₆	—	9	1	no	—
48	#405	—	9	1	no	—
49	#346	—	9	2	no	—
50	C₄×C₁₆	—	9	2	no	—
51	C₂²×C₃×C₄	—	2	2	no	—
52	C₃×C₄⋊C₄	—	2	4	no	—
53	C₃×C₂²⋊C₄	—	2	4	no	—
54	C₃×C₄²	—	2	4	no	—
55	#208	—	6	8	no	—
56	C₂×C₃⋊C₈	—	6	2	no	—
57	C₂×C₃⋊C₈	—	6	4	no	—
58	C₂×C₃⋊C₈	—	6	2	no	—
59	C₂×C₃⋊C₈	—	6	4	no	—
60	C₂×C₃⋊C₈	—	6	4	no	—
61	C₂²×C₃²	—	2	2	no	—
62	C₂²×C₃²	C₄×C₈	1	2	yes	—
63	C₂²×C₃²	C₂²×C₈	1	1	yes	characteristic
64	C₃²×C₄	—	2	4	no	—
65	C₃²×C₄	C₄×C₈	1	2	yes	—
66	C₃²×C₄	C₂×C₄²	1	1	yes	characteristic
67	C₃²×C₄	C₂²×C₈	1	1	yes	characteristic
68	C₂×M₁₆	—	9	1	no	—
69	C₂²×C₈	—	9	1	no	—
70	#117	#157	1	1	yes	characteristic
71	M₃₂	—	9	4	no	—
72	C₂×C₁₆	—	9	4	no	—
73	C₂×C₁₆	—	9	1	no	—
74	C₂×C₁₆	—	9	2	no	—
75	C₂×C₁₆	—	9	1	no	—
76	#97	—	9	2	no	—
77	C₄×C₈	—	9	2	no	—
78	C₂³×C₃	—	2	2	no	—
79	C₂×C₃×C₄	—	2	2	no	—
80	C₂×C₃×C₄	—	2	4	no	—
81	C₂×C₃×C₄	—	2	4	no	—
82	C₂×C₃×C₄	—	2	2	no	—
83	C₂×C₃×C₄	—	2	8	no	—
84	C₃⋊C₈	—	6	4	no	—
85	C₃⋊C₈	—	6	8	no	—
86	C₃⋊C₈	—	6	2	no	—
87	C₃⋊C₈	—	6	2	no	—
88	C₂×C₃²	—	2	2	no	—
89	C₂×C₃²	C₂×C₄×C₈	1	1	yes	characteristic
90	C₂×C₃²	#504	1	2	yes	—
91	C₂²×C₄	C₂×#157	1	1	yes	characteristic
92	M₁₆	—	9	4	no	—
93	C₂×C₈	—	9	1	no	—
94	C₂×C₈	—	9	2	no	—
95	C₂×C₈	—	9	1	no	—
96	C₂×C₈	—	9	2	no	—
97	C₂×C₈	—	9	2	no	—
98	C₄⋊C₄	#622	1	2	yes	—
99	C₂²⋊C₄	#622	1	2	yes	—
100	C₄²	C₂×#157	1	2	yes	—
101	C₁₆	—	9	2	no	—
102	C₁₆	—	9	2	no	—
103	C₁₆	—	9	4	no	—
104	C₂²×C₃	—	2	4	no	—
105	C₂²×C₃	—	2	2	no	—
106	C₂²×C₃	—	4	4	no	—
107	C₃×C₄	—	2	2	no	—
108	C₃×C₄	—	2	2	no	—
109	C₃×C₄	—	2	4	no	—
110	C₃×C₄	—	4	8	no	—
111	C₃²	#2108	1	1	yes	characteristic, complemented, Sylow
112	C₂³	C₂×#622	1	1	yes	characteristic
113	C₂×C₄	#3787	1	2	yes	—
114	C₂×C₄	C₄×#157	1	2	yes	—
115	C₂×C₄	C₂×#622	1	4	yes	—
116	C₂×C₄	C₂×#622	1	1	yes	characteristic
117	C₂×C₄	C₂²×#157	1	1	yes	characteristic
118	C₈	—	9	4	no	—
119	C₈	—	9	1	no	—
120	C₈	—	9	1	no	—
121	C₈	—	9	2	no	—
122	C₂×C₃	—	2	2	no	—
123	C₂×C₃	—	2	4	no	—
124	C₂×C₃	—	4	4	no	—
125	C₂²	—	2	2	no	—
126	C₂²	C₄×#622	1	2	yes	—
127	C₂²	C₂²×#622	1	1	yes	characteristic
128	C₄	—	2	4	no	—
129	C₄	C₄×#622	1	2	yes	—
130	C₄	C₂×#3787	1	1	yes	characteristic
131	C₄	C₂×C₄×#157	1	1	yes	characteristic
132	C₃	—	2	2	no	—
133	C₂	—	2	2	no	—
134	C₂	C₂×C₄×#622	1	1	yes	characteristic
135	C₂	#10593838	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#63773

C₂

yes

maximal, characteristic

C₂²×#3708

C₂

yes

maximal, characteristic

#10592696

C₂

yes

maximal, characteristic

#10590148

C₂

yes

maximal, complemented

C₄×#3708

C₂

yes

maximal, complemented

C₃²×#117

C₄

yes

characteristic

C₂×#3748

C₄

yes

characteristic

C₂²×C₃⋊(C₃⋊C₈)

C₂²

yes

characteristic

#63773

C₄

yes

complemented

C₂×#3708

C₄

yes

complemented

C₂×#3708

C₂²

yes

characteristic

C₂×#3708

C₂²

yes

—

C₂×#3708

C₂²

yes

characteristic

#63630

C₄

yes

—

C₄×C₃⋊(C₃⋊C₈)

C₂²

yes

—

#4997

—

C₂²×C₃²×C₄

C₂×C₄

yes

characteristic

C₃²×C₄⋊C₄

C₈

yes

—

C₃²×C₂²⋊C₄

C₈

yes

—

C₃²×C₄²

C₂×C₄

yes

—

#3748

C₈

yes

—

C₂×C₃⋊(C₃⋊C₈)

C₂×C₄

yes

characteristic

C₂×C₃⋊(C₃⋊C₈)

C₂×C₄

yes

—

C₂×C₃⋊(C₃⋊C₈)

C₂×C₄

yes

—

C₂×C₃⋊(C₃⋊C₈)

C₂×C₄

yes

—

C₂×C₃⋊(C₃⋊C₈)

C₂³

yes

characteristic

#3708

C₂×C₄

yes

—

#3708

C₂×C₄

yes

—

#3708

C₂×C₄

yes

—

—

—

—

C₂²×C₃⋊C₈

—

#803

—

C₄×C₃⋊C₈

—

C₂³×C₃²

C₂×C₈

yes

characteristic

C₂×C₃²×C₄

C₄²

yes

—

C₂×C₃²×C₄

C₂×C₈

yes

—

C₂×C₃²×C₄

C₂×C₈

yes

characteristic

C₂×C₃²×C₄

C₂×C₈

yes

—

C₂×C₃²×C₄

C₂²×C₄

yes

characteristic

C₃⋊(C₃⋊C₈)

C₄²

yes

—

C₃⋊(C₃⋊C₈)

C₂×C₈

yes

—

C₃⋊(C₃⋊C₈)

C₂²×C₄

yes

characteristic

C₃⋊(C₃⋊C₈)

C₂²×C₄

yes

characteristic

C₂×M₃₂

—

C₂²×C₁₆

—

#405

—

#346

—

C₄×C₁₆

—

C₂²×C₃×C₄

—

C₃×C₄⋊C₄

—

C₃×C₂²⋊C₄

—

C₃×C₄²

—

#208

—

C₂×C₃⋊C₈

—

C₂×C₃⋊C₈

—

C₂×C₃⋊C₈

—

C₂×C₃⋊C₈

—

C₂×C₃⋊C₈

—

C₂²×C₃²

—

C₂²×C₃²

C₄×C₈

yes

—

C₂²×C₃²

C₂²×C₈

yes

characteristic

C₃²×C₄

—

C₃²×C₄

C₄×C₈

yes

—

C₃²×C₄

C₂×C₄²

yes

characteristic

C₃²×C₄

C₂²×C₈

yes

characteristic

C₂×M₁₆

—

C₂²×C₈

—

#117

#157

yes

characteristic

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

#97

—

C₄×C₈

—

C₂³×C₃

—

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

C₂×C₄×C₈

yes

characteristic

C₂×C₃²

#504

yes

—

C₂²×C₄

C₂×#157

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

#622

yes

—

C₂²⋊C₄

#622

yes

—

100

C₄²

C₂×#157

yes

—

101

C₁₆

—

102

C₁₆

—

103

C₁₆

—

104

C₂²×C₃

—

105

C₂²×C₃

—

106

C₂²×C₃

—

107

C₃×C₄

—

108

C₃×C₄

—

109

C₃×C₄

—

110

C₃×C₄

—

111

C₃²

#2108

yes

characteristic, complemented, Sylow

112

C₂³

C₂×#622

yes

characteristic

113

C₂×C₄

#3787

yes

—

114

C₂×C₄

C₄×#157

yes

—

115

C₂×C₄

C₂×#622

yes

—

116

C₂×C₄

C₂×#622

yes

characteristic

117

C₂×C₄

C₂²×#157

yes

characteristic

118

C₈

—

119

C₈

—

120

C₈

—

121

C₈

—

122

C₂×C₃

—

123

C₂×C₃

—

124

C₂×C₃

—

125

C₂²

—

126

C₂²

C₄×#622

yes

—

127

C₂²

C₂²×#622

yes

characteristic

128

C₄

—

129

C₄

C₄×#622

yes

—

130

C₄

C₂×#3787

yes

characteristic

131

C₄

C₂×C₄×#157

yes

characteristic

132

C₃

—

133

C₂

—

134

C₂

C₂×C₄×#622

yes

characteristic

135

C₂

#10593838

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#157
commutator	C₂×C₃²	C₂×C₄×C₈
Fitting	C₃²×#117	C₄
socle	C₂²×C₃²	C₂²×C₈
prime radical	C₂³×C₃²	C₂×C₈
cosocle	C₂×C₃⋊(C₃⋊C₈)	C₂³
hypercenter	#117	#157
hypocenter	C₃²	#2108
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₄ ◁ #117

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#157

commutator

C₂×C₃²

C₂×C₄×C₈

Fitting

C₃²×#117

C₄

socle

C₂²×C₃²

C₂²×C₈

prime radical

C₂³×C₃²

C₂×C₈

cosocle

C₂×C₃⋊(C₃⋊C₈)

C₂³

C₃²

G ▷ C₂×C₃² ▷ C₃²

C₁ ◁ C₂×C₄ ◁ #117

N	H ≅ G/N	type
4. #10590148	C₂	semidirect
5. C₄×#3708	C₂	semidirect
9. #63773	C₄	semidirect
10. C₂×#3708	C₄	semidirect
111. C₃²	#2108	semidirect

H ≅ G/N

type

4. #10590148

C₂

semidirect

5. C₄×#3708

C₂

semidirect

9. #63773

C₄

semidirect

10. C₂×#3708

C₄

semidirect

111. C₃²

#2108

semidirect

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

subgroup	index
C₂×#63773	2
C₂²×#3708	2
#10592696	2
#10590148	2
C₄×#3708	2
#2108	9

subgroup

index

C₂²×#3708

Subgroups — #11795888

Conjugacy classes of subgroups

Complements

Maximal subgroups