Group #11770870 — subgroups

Subgroups — #11770870

Order 1152.

214 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 57 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	#10593726	C₂	1	1	yes	maximal, characteristic
2	#10593725	C₂	1	1	yes	maximal, characteristic
3	C₄×#3788	C₂	1	1	yes	maximal, characteristic
4	C₂×#3788	C₄	1	2	yes	—
5	C₂×#3787	C₄	1	2	yes	—
6	C₄²×C₃⋊D₃	C₂²	1	1	yes	characteristic
7	#63779	—	2	1	no	—
8	#63779	—	2	1	no	—
9	#63778	C₄	1	2	yes	—
10	#63777	—	2	1	no	—
11	C₄⋊#622	—	2	1	no	—
12	C₄×#622	—	2	1	no	—
13	C₄×#622	—	2	1	no	—
14	C₂×C₄×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
17	C₂×#622	—	2	2	no	—
18	C₂×#622	—	2	2	no	—
19	C₂×#622	—	2	2	no	—
20	#3788	—	2	2	no	—
21	#3788	C₈	1	4	yes	complemented
22	#3787	—	4	2	no	—
23	C₃²×C₄²	Q₈	1	1	yes	characteristic
24	C₄×C₃⋊Dic₃	D₄	1	1	yes	characteristic
25	C₄×C₃⋊Dic₃	D₄	1	1	yes	characteristic
26	C₄×C₃⋊Dic₃	D₄	1	1	yes	characteristic
27	#1283	—	9	1	no	maximal, Sylow
28	C₄²×D₃	—	12	1	no	—
29	C₂²×C₃⋊D₃	C₄²	1	1	yes	characteristic
30	C₂×C₃²×C₄	C₄⋊C₄	1	1	yes	characteristic
31	C₂×C₃²×C₄	C₄⋊C₄	1	1	yes	characteristic
32	C₂×C₃²×C₄	C₄⋊C₄	1	1	yes	characteristic
33	C₂×C₃⋊Dic₃	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×C₃⋊Dic₃	C₂²⋊C₄	1	1	yes	characteristic
35	C₂×C₃⋊Dic₃	C₂²⋊C₄	1	1	yes	characteristic
36	C₄×C₃⋊D₃	—	2	1	no	—
37	C₄×C₃⋊D₃	—	2	1	no	—
38	C₄×C₃⋊D₃	—	4	1	no	—
39	C₄×C₃⋊D₃	C₂×C₈	1	2	yes	—
40	C₄×C₃⋊D₃	M₁₆	1	2	yes	—
41	#622	—	2	4	no	—
42	#622	—	4	2	no	—
43	#622	—	4	2	no	—
44	#431	—	9	1	no	—
45	C₂×C₄⋊C₈	—	9	1	no	—
46	C₄×M₁₆	—	9	1	no	—
47	C₂×C₄×D₃	—	12	1	no	—
48	C₂×C₄×D₃	—	12	1	no	—
49	C₂×C₄×D₃	—	12	1	no	—
50	C₃×C₄²	—	4	1	no	—
51	C₄×Dic₃	—	12	1	no	—
52	C₄×Dic₃	—	12	1	no	—
53	C₄×Dic₃	—	12	1	no	—
54	C₂²×C₃²	#95	1	1	yes	characteristic
55	C₂×C₃⋊D₃	—	2	1	no	—
56	C₂×C₃⋊D₃	—	2	1	no	—
57	C₂×C₃⋊D₃	C₄×C₈	1	1	yes	characteristic
58	C₂×C₃⋊D₃	#97	1	1	yes	characteristic
59	C₃²×C₄	—	2	1	no	—
60	C₃²×C₄	—	2	1	no	—
61	C₃²×C₄	C₄⋊C₈	1	2	yes	—
62	C₃⋊Dic₃	—	2	1	no	—
63	C₃⋊Dic₃	C₂²⋊C₈	1	2	yes	—
64	C₃⋊Dic₃	#100	1	1	yes	characteristic
65	C₃⋊Dic₃	#101	1	1	yes	characteristic
66	C₂×M₁₆	—	9	2	no	—
67	C₂²×C₈	—	9	2	no	—
68	C₂×C₄²	—	9	1	no	—
69	C₄⋊C₈	—	18	1	no	—
70	C₄⋊C₈	—	18	1	no	—
71	C₄⋊C₈	—	18	1	no	—
72	C₂²⋊C₈	—	9	2	no	—
73	#97	—	18	1	no	—
74	C₄×C₈	—	18	1	no	—
75	C₄×C₈	—	18	1	no	—
76	C₂²×D₃	—	12	1	no	—
77	C₂×C₃×C₄	—	4	1	no	—
78	C₂×C₃×C₄	—	4	1	no	—
79	C₂×C₃×C₄	—	4	1	no	—
80	C₂×Dic₃	—	12	1	no	—
81	C₂×Dic₃	—	12	1	no	—
82	C₂×Dic₃	—	12	1	no	—
83	C₄×D₃	—	12	2	no	—
84	C₄×D₃	—	12	2	no	—
85	C₄×D₃	—	12	2	no	—
86	C₄×D₃	—	12	2	no	—
87	C₄×D₃	—	12	4	no	—
88	C₂×C₃²	#336	1	1	yes	characteristic
89	C₂×C₃²	#343	1	1	yes	characteristic
90	C₂×C₃²	#344	1	1	yes	characteristic
91	C₃⋊D₃	—	2	1	no	—
92	C₃⋊D₃	—	2	1	no	—
93	C₂²×C₄	—	9	1	no	—
94	C₂²×C₄	—	9	1	no	—
95	C₂²×C₄	—	9	1	no	—
96	M₁₆	—	9	4	no	—
97	M₁₆	—	18	2	no	—
98	C₂×C₈	—	18	2	no	—
99	C₂×C₈	—	18	2	no	—
100	C₂×C₈	—	18	2	no	—
101	C₂×C₈	—	36	2	no	—
102	C₄²	—	9	1	no	—
103	C₄²	—	9	1	no	—
104	C₄²	—	9	1	no	—
105	C₄²	PSU(3,𝔽₂)	1	1	yes	characteristic
106	C₂²×C₃	—	4	1	no	—
107	C₂×D₃	—	12	1	no	—
108	C₂×D₃	—	12	1	no	—
109	C₂×D₃	—	12	2	no	—
110	C₂×D₃	—	12	2	no	—
111	C₃×C₄	—	4	2	no	—
112	C₃×C₄	—	4	2	no	—
113	C₃×C₄	—	4	2	no	—
114	Dic₃	—	12	2	no	—
115	Dic₃	—	12	1	no	—
116	Dic₃	—	12	1	no	—
117	Dic₃	—	12	2	no	—
118	C₃²	#1283	1	1	yes	characteristic, complemented, Sylow
119	C₂³	—	9	1	no	—
120	C₂×C₄	—	9	1	no	—
121	C₂×C₄	—	9	1	no	—
122	C₂×C₄	—	9	2	no	—
123	C₂×C₄	—	9	2	no	—
124	C₂×C₄	—	9	1	no	—
125	C₂×C₄	—	18	1	no	—
126	C₂×C₄	—	18	1	no	—
127	C₂×C₄	—	36	1	no	—
128	C₂×C₄	#3777	1	1	yes	characteristic
129	C₂×C₄	#3777	1	1	yes	characteristic
130	C₂×C₄	#3777	1	1	yes	characteristic
131	C₈	—	18	4	no	—
132	C₈	—	36	2	no	—
133	C₈	—	36	2	no	—
134	C₂×C₃	—	4	1	no	—
135	C₂×C₃	—	4	1	no	—
136	C₂×C₃	—	4	1	no	—
137	D₃	—	12	2	no	—
138	D₃	—	12	2	no	—
139	C₂²	—	9	1	no	—
140	C₂²	—	9	1	no	—
141	C₂²	—	18	1	no	—
142	C₂²	—	18	1	no	—
143	C₂²	#63747	1	1	yes	characteristic
144	C₄	—	2	1	no	—
145	C₄	—	2	1	no	—
146	C₄	—	9	2	no	—
147	C₄	—	9	1	no	—
148	C₄	—	9	1	no	—
149	C₄	—	18	1	no	—
150	C₄	#63744	1	2	yes	—
151	C₃	—	4	1	no	—
152	C₂	—	18	1	no	—
153	C₂	—	18	1	no	—
154	C₂	#10590090	1	1	yes	characteristic
155	C₂	#10590094	1	1	yes	characteristic
156	C₂	#10590095	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#10593726

C₂

yes

maximal, characteristic

#10593725

C₂

yes

maximal, characteristic

C₄×#3788

C₂

yes

maximal, characteristic

C₂×#3788

C₄

yes

—

C₂×#3787

C₄

yes

—

C₄²×C₃⋊D₃

C₂²

yes

—

—

C₄

yes

—

—

—

—

—

C₂×C₄×C₃⋊D₃

C₂×C₄

yes

characteristic

C₂×C₄×C₃⋊D₃

C₂×C₄

yes

characteristic

C₂×C₄×C₃⋊D₃

C₂×C₄

yes

—

—

—

—

C₈

yes

complemented

#3787

—

C₃²×C₄²

Q₈

yes

characteristic

C₄×C₃⋊Dic₃

D₄

yes

characteristic

C₄×C₃⋊Dic₃

D₄

yes

characteristic

C₄×C₃⋊Dic₃

D₄

yes

characteristic

#1283

—

maximal, Sylow

C₄²×D₃

—

C₂²×C₃⋊D₃

C₄²

yes

characteristic

C₂×C₃²×C₄

C₄⋊C₄

yes

characteristic

C₂×C₃²×C₄

C₄⋊C₄

yes

characteristic

C₂×C₃²×C₄

C₄⋊C₄

yes

characteristic

C₂×C₃⋊Dic₃

C₂²⋊C₄

yes

characteristic

C₂×C₃⋊Dic₃

C₂²⋊C₄

yes

characteristic

C₂×C₃⋊Dic₃

C₂²⋊C₄

yes

characteristic

C₄×C₃⋊D₃

—

C₄×C₃⋊D₃

—

C₄×C₃⋊D₃

—

C₄×C₃⋊D₃

C₂×C₈

yes

—

C₄×C₃⋊D₃

M₁₆

yes

—

—

—

—

—

C₂×C₄⋊C₈

—

C₄×M₁₆

—

C₂×C₄×D₃

—

C₂×C₄×D₃

—

C₂×C₄×D₃

—

C₃×C₄²

—

C₄×Dic₃

—

C₄×Dic₃

—

C₄×Dic₃

—

C₂²×C₃²

#95

yes

characteristic

C₂×C₃⋊D₃

—

C₂×C₃⋊D₃

—

C₂×C₃⋊D₃

C₄×C₈

yes

characteristic

C₂×C₃⋊D₃

#97

yes

characteristic

C₃²×C₄

—

C₃²×C₄

—

C₃²×C₄

C₄⋊C₈

yes

—

C₃⋊Dic₃

—

C₃⋊Dic₃

C₂²⋊C₈

yes

—

C₃⋊Dic₃

yes

C₃⋊Dic₃

yes

C₂×M₁₆

—

C₂²×C₈

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₂²×D₃

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×Dic₃

—

C₂×Dic₃

—

C₂×Dic₃

—

C₄×D₃

—

C₄×D₃

—

C₄×D₃

—

C₄×D₃

—

C₄×D₃

—

C₂×C₃²

yes

C₂×C₃²

yes

C₂×C₃²

yes

C₃⋊D₃

—

C₃⋊D₃

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₄²

—

103

C₄²

—

104

C₄²

—

105

C₄²

PSU(3,𝔽₂)

yes

characteristic

106

C₂²×C₃

—

107

C₂×D₃

—

108

C₂×D₃

—

109

C₂×D₃

—

110

C₂×D₃

—

111

C₃×C₄

—

112

C₃×C₄

—

113

C₃×C₄

—

114

Dic₃

—

115

Dic₃

—

116

Dic₃

—

117

Dic₃

—

118

C₃²

#1283

yes

characteristic, complemented, Sylow

119

C₂³

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

#3777

yes

characteristic

129

C₂×C₄

#3777

yes

characteristic

130

C₂×C₄

#3777

yes

characteristic

131

C₈

—

132

C₈

—

133

C₈

—

134

C₂×C₃

—

135

C₂×C₃

—

136

C₂×C₃

—

137

D₃

—

138

D₃

—

139

C₂²

—

140

C₂²

—

141

C₂²

—

142

C₂²

—

143

C₂²

#63747

yes

characteristic

144

C₄

—

145

C₄

—

146

C₄

—

147

C₄

—

148

C₄

—

149

C₄

—

150

C₄

#63744

yes

—

151

C₃

—

152

C₂

—

153

C₂

—

154

C₂

#10590090

yes

characteristic

155

C₂

#10590094

yes

characteristic

156

C₂

#10590095

yes

characteristic

	subgroup	G/H
center	C₂²	#63747
commutator	C₂×C₃⋊D₃	C₄×C₈
Frattini, hypercenter	C₄²	PSU(3,𝔽₂)
Fitting	C₃²×C₄²	Q₈
socle	C₂²×C₃²	#95
prime radical	C₂²×C₃⋊D₃	C₄²
cosocle	C₄²×C₃⋊D₃	C₂²
hypocenter	C₃²	#1283
LCS	G ▷ C₂×C₃⋊D₃ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂² ◁ C₄²

subgroup

G/H

center

C₂²

#63747

commutator

C₂×C₃⋊D₃

C₄×C₈

Frattini, hypercenter

C₄²

PSU(3,𝔽₂)

Fitting

C₃²×C₄²

Q₈

socle

C₂²×C₃²

#95

prime radical

C₂²×C₃⋊D₃

C₄²

cosocle

C₄²×C₃⋊D₃

C₂²

hypocenter

C₃²

#1283

LCS

G ▷ C₂×C₃⋊D₃ ▷ C₂×C₃² ▷ C₃²

UCS

C₁ ◁ C₂² ◁ C₄²

N	H ≅ G/N	type
21. #3788	C₈	semidirect
118. C₃²	#1283	semidirect

H ≅ G/N

type

21. #3788

C₈

semidirect

118. C₃²

#1283

semidirect

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

subgroup	index
#10593726	2
#10593725	2
C₄×#3788	2
#1283	9

subgroup

index

Subgroups — #11770870

Conjugacy classes of subgroups

Complements

Maximal subgroups