Group #11771882 — subgroups

Subgroups — #11771882

Order 1152.

342 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 95 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	#10592814	C₂	1	1	yes	maximal, characteristic
2	C₃²×#341	C₂	1	1	yes	maximal, characteristic, complemented
3	#10589415	C₂	1	1	yes	maximal, characteristic, complemented
4	#67487	—	3	4	no	maximal
5	C₂×C₃²×M₁₆	—	2	1	no	—
6	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
7	#64139	—	2	1	no	—
8	C₂×#3745	C₄	1	1	yes	characteristic
9	#63648	—	2	1	no	—
10	#63645	C₄	1	1	yes	characteristic
11	C₂×C₃⋊(C₃⋊C₁₆)	—	2	1	no	—
12	#5115	—	3	4	no	—
13	C₃×#341	D₃	1	4	yes	complemented
14	#4549	—	3	4	no	—
15	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
16	C₂×#638	—	4	1	no	—
17	C₂×C₄⋊(C₃⋊D₃)	—	2	1	no	—
18	C₃²×M₁₆	—	2	2	no	—
19	C₃²×M₁₆	—	4	1	no	—
20	C₂×C₃²×C₈	—	4	1	no	—
21	C₂×C₃²×C₈	—	4	1	no	—
22	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
23	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
24	#3752	—	4	1	no	—
25	C₄⋊(C₃⋊Dic₃)	—	2	1	no	—
26	#3745	—	4	1	no	—
27	C₃⋊(C₃⋊C₁₆)	—	4	1	no	—
28	#1349	—	9	1	no	Sylow
29	C₂×C₃×M₁₆	—	2	4	no	—
30	C₂²×C₃×C₈	C₂×D₃	1	4	yes	—
31	#930	—	6	4	no	—
32	C₂×D₂₄	—	3	4	no	—
33	#821	—	6	4	no	—
34	#818	—	3	4	no	—
35	C₂×C₃⋊C₁₆	—	6	4	no	—
36	C₂³×C₃²	SD₁₆	1	1	yes	characteristic
37	C₂²×C₃⋊D₃	—	4	1	no	—
38	C₂×C₃²×C₄	—	2	1	no	—
39	C₂×C₃²×C₄	—	2	1	no	—
40	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
41	C₂×C₃²×C₄	D₈	1	1	yes	characteristic
42	#638	—	8	2	no	—
43	C₂×C₃⋊Dic₃	—	4	1	no	—
44	C₄⋊(C₃⋊D₃)	—	4	1	no	—
45	C₄⋊(C₃⋊D₃)	—	4	1	no	—
46	C₃²×C₈	—	2	1	no	—
47	C₃²×C₈	—	2	1	no	—
48	C₃²×C₈	—	4	2	no	—
49	#466	—	9	1	no	—
50	C₂²⋊C₁₆	—	9	1	no	—
51	#341	C₃⋊D₃	1	1	yes	characteristic, complemented
52	C₂²×C₃×C₄	#67	1	4	yes	—
53	C₂×#67	—	12	4	no	—
54	C₂×D₁₂	—	6	4	no	—
55	C₃×M₁₆	—	2	8	no	—
56	C₃×M₁₆	—	4	4	no	—
57	C₂×C₃×C₈	—	4	4	no	—
58	C₂×C₃×C₈	—	4	4	no	—
59	C₂×C₃×C₈	C₄×D₃	1	4	yes	—
60	C₂×C₃×C₈	D₁₂	1	4	yes	—
61	(C₂×D₃)⋊C₄	—	12	4	no	—
62	C₄⋊Dic₃	—	6	4	no	—
63	D₂₄	—	12	4	no	—
64	C₃⋊C₁₆	—	12	4	no	—
65	C₂²×C₃²	—	2	1	no	—
66	C₂²×C₃²	—	2	1	no	—
67	C₂²×C₃²	—	2	1	no	—
68	C₂²×C₃²	#102	1	1	yes	characteristic
69	C₂×C₃⋊D₃	—	8	1	no	—
70	C₂×C₃⋊D₃	—	8	1	no	—
71	C₂×C₃⋊D₃	—	8	1	no	—
72	C₃²×C₄	—	2	1	no	—
73	C₃²×C₄	#99	1	1	yes	characteristic
74	C₃²×C₄	#104	1	1	yes	characteristic
75	C₃⋊Dic₃	—	8	1	no	—
76	C₂×D₈	—	9	1	no	—
77	C₂×M₁₆	—	2	1	no	—
78	C₂²×C₈	C₂×C₃⋊D₃	1	1	yes	characteristic
79	#121	—	18	1	no	—
80	C₂×C₁₆	—	18	1	no	—
81	#107	—	9	1	no	—
82	#102	—	18	1	no	—
83	C₂³×C₃	#215	1	4	yes	—
84	C₂²×D₃	—	12	4	no	—
85	C₂×C₃×C₄	—	2	4	no	—
86	C₂×C₃×C₄	—	2	4	no	—
87	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	4	yes	—
88	C₂×C₃×C₄	#213	1	4	yes	—
89	#67	—	24	8	no	—
90	C₂×Dic₃	—	12	4	no	—
91	D₁₂	—	12	4	no	—
92	D₁₂	—	12	4	no	—
93	C₃×C₈	—	2	4	no	—
94	C₃×C₈	—	2	4	no	—
95	C₃×C₈	—	4	8	no	—
96	C₂×C₃²	—	4	1	no	—
97	C₂×C₃²	#327	1	1	yes	characteristic
98	C₂×C₃²	#359	1	1	yes	characteristic
99	C₂×C₃²	#361	1	1	yes	characteristic
100	C₃⋊D₃	—	16	1	no	—
101	C₂×D₄	—	18	1	no	—
102	C₂×D₄	—	36	1	no	—
103	C₂²×C₄	#638	1	1	yes	characteristic
104	D₈	—	36	1	no	—
105	M₁₆	—	2	2	no	—
106	M₁₆	—	4	1	no	—
107	C₂×C₈	—	4	1	no	—
108	C₂×C₈	—	4	1	no	—
109	C₂×C₈	C₄×C₃⋊D₃	1	1	yes	characteristic
110	C₂×C₈	C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
111	C₄⋊C₄	—	18	1	no	—
112	C₂²⋊C₄	—	36	1	no	—
113	C₁₆	—	36	1	no	—
114	C₂²×C₃	—	2	4	no	—
115	C₂²×C₃	—	2	4	no	—
116	C₂²×C₃	—	2	4	no	—
117	C₂²×C₃	#809	1	4	yes	—
118	C₂×D₃	—	24	4	no	—
119	C₂×D₃	—	24	4	no	—
120	C₂×D₃	—	24	4	no	—
121	C₃×C₄	—	2	4	no	—
122	C₃×C₄	#805	1	4	yes	—
123	C₃×C₄	#806	1	4	yes	—
124	Dic₃	—	24	4	no	—
125	C₃²	#1349	1	1	yes	characteristic, complemented, Sylow
126	C₂³	—	36	1	no	—
127	C₂³	#3755	1	1	yes	characteristic
128	D₄	—	36	1	no	—
129	D₄	—	36	1	no	—
130	D₄	—	72	2	no	—
131	C₂×C₄	—	2	1	no	—
132	C₂×C₄	—	2	1	no	—
133	C₂×C₄	—	36	1	no	—
134	C₂×C₄	#3752	1	1	yes	characteristic
135	C₂×C₄	#3753	1	1	yes	characteristic
136	C₈	—	2	1	no	—
137	C₈	—	2	1	no	—
138	C₈	—	4	2	no	—
139	C₂×C₃	—	4	4	no	—
140	C₂×C₃	#4451	1	4	yes	—
141	C₂×C₃	#4495	1	4	yes	—
142	C₂×C₃	#4497	1	4	yes	—
143	D₃	—	48	4	no	—
144	C₂²	—	2	1	no	—
145	C₂²	—	2	1	no	—
146	C₂²	—	2	1	no	—
147	C₂²	—	72	1	no	—
148	C₂²	—	72	1	no	—
149	C₂²	—	72	1	no	—
150	C₂²	#63636	1	1	yes	characteristic
151	C₄	—	2	1	no	—
152	C₄	—	72	1	no	—
153	C₄	#63632	1	1	yes	characteristic
154	C₄	#63633	1	1	yes	characteristic
155	C₃	#67487	1	4	yes	complemented
156	C₂	—	4	1	no	—
157	C₂	—	144	1	no	—
158	C₂	#10589317	1	1	yes	characteristic
159	C₂	#10589361	1	1	yes	characteristic
160	C₂	#10589363	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#10592814

C₂

yes

maximal, characteristic

C₃²×#341

C₂

yes

maximal, characteristic, complemented

#10589415

C₂

yes

maximal, characteristic, complemented

#67487

—

maximal

C₂×C₃²×M₁₆

—

C₂²×C₃²×C₈

C₂²

yes

characteristic

#64139

—

C₂×#3745

C₄

yes

characteristic

#63648

—

#63645

C₄

yes

characteristic

C₂×C₃⋊(C₃⋊C₁₆)

—

#5115

—

C₃×#341

D₃

yes

complemented

#4549

—

C₂²×C₃²×C₄

D₄

yes

characteristic

C₂×#638

—

C₂×C₄⋊(C₃⋊D₃)

—

C₃²×M₁₆

—

C₃²×M₁₆

—

C₂×C₃²×C₈

—

C₂×C₃²×C₈

—

C₂×C₃²×C₈

C₂×C₄

yes

characteristic

C₂×C₃²×C₈

D₄

yes

characteristic

#3752

—

C₄⋊(C₃⋊Dic₃)

—

#3745

—

C₃⋊(C₃⋊C₁₆)

—

#1349

—

Sylow

C₂×C₃×M₁₆

—

C₂²×C₃×C₈

C₂×D₃

yes

—

#930

—

C₂×D₂₄

—

#821

—

#818

—

C₂×C₃⋊C₁₆

—

C₂³×C₃²

SD₁₆

yes

characteristic

C₂²×C₃⋊D₃

—

C₂×C₃²×C₄

—

C₂×C₃²×C₄

—

C₂×C₃²×C₄

C₂²⋊C₄

yes

characteristic

C₂×C₃²×C₄

D₈

yes

characteristic

#638

—

C₂×C₃⋊Dic₃

—

C₄⋊(C₃⋊D₃)

—

C₄⋊(C₃⋊D₃)

—

C₃²×C₈

—

C₃²×C₈

—

C₃²×C₈

—

#466

—

C₂²⋊C₁₆

—

#341

C₃⋊D₃

yes

characteristic, complemented

C₂²×C₃×C₄

#67

yes

—

C₂×#67

—

C₂×D₁₂

—

C₃×M₁₆

—

C₃×M₁₆

—

C₂×C₃×C₈

—

C₂×C₃×C₈

—

C₂×C₃×C₈

C₄×D₃

yes

—

C₂×C₃×C₈

D₁₂

yes

—

(C₂×D₃)⋊C₄

—

C₄⋊Dic₃

—

D₂₄

—

C₃⋊C₁₆

—

C₂²×C₃²

—

C₂²×C₃²

—

C₂²×C₃²

—

C₂²×C₃²

#102

yes

characteristic

C₂×C₃⋊D₃

—

C₂×C₃⋊D₃

—

C₂×C₃⋊D₃

—

C₃²×C₄

—

C₃²×C₄

yes

C₃²×C₄

yes

C₃⋊Dic₃

—

C₂×D₈

—

C₂×M₁₆

—

C₂²×C₈

C₂×C₃⋊D₃

yes

characteristic

#121

—

C₂×C₁₆

—

#107

—

#102

—

C₂³×C₃

#215

yes

—

C₂²×D₃

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

(C₂×D₃)⋊C₄

yes

—

C₂×C₃×C₄

#213

yes

—

#67

—

C₂×Dic₃

—

D₁₂

—

D₁₂

—

C₃×C₈

—

C₃×C₈

—

C₃×C₈

—

C₂×C₃²

—

C₂×C₃²

yes

C₂×C₃²

yes

C₂×C₃²

yes

100

C₃⋊D₃

—

101

C₂×D₄

—

102

C₂×D₄

—

103

C₂²×C₄

#638

yes

characteristic

104

D₈

—

105

M₁₆

—

106

M₁₆

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

C₄×C₃⋊D₃

yes

characteristic

110

C₂×C₈

C₄⋊(C₃⋊D₃)

yes

characteristic

111

C₄⋊C₄

—

112

C₂²⋊C₄

—

113

C₁₆

—

114

C₂²×C₃

—

115

C₂²×C₃

—

116

C₂²×C₃

—

117

C₂²×C₃

#809

yes

—

118

C₂×D₃

—

119

C₂×D₃

—

120

C₂×D₃

—

121

C₃×C₄

—

122

C₃×C₄

#805

yes

—

123

C₃×C₄

#806

yes

—

124

Dic₃

—

125

C₃²

#1349

yes

characteristic, complemented, Sylow

126

C₂³

—

127

C₂³

#3755

yes

characteristic

128

D₄

—

129

D₄

—

130

D₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

#3752

yes

characteristic

135

C₂×C₄

#3753

yes

characteristic

136

C₈

—

137

C₈

—

138

C₈

—

139

C₂×C₃

—

140

C₂×C₃

#4451

yes

—

141

C₂×C₃

#4495

yes

—

142

C₂×C₃

#4497

yes

—

143

D₃

—

144

C₂²

—

145

C₂²

—

146

C₂²

—

147

C₂²

—

148

C₂²

—

149

C₂²

—

150

C₂²

#63636

yes

characteristic

151

C₄

—

152

C₄

—

153

C₄

#63632

yes

characteristic

154

C₄

#63633

yes

characteristic

155

C₃

#67487

yes

complemented

156

C₂

—

157

C₂

—

144

—

158

C₂

#10589317

yes

characteristic

159

C₂

#10589361

yes

characteristic

160

C₂

#10589363

yes

characteristic

	subgroup	G/H
center	C₂²	#63636
commutator	C₂×C₃²×C₈	C₂×C₄
Frattini	C₂²×C₈	C₂×C₃⋊D₃
Fitting	C₃²×#341	C₂
socle	C₂²×C₃²	#102
prime radical	#10592814	C₂
cosocle	C₂²×C₃²×C₈	C₂²
hypercenter	#341	C₃⋊D₃
hypocenter	C₃²	#1349
LCS	G ▷ C₂×C₃²×C₈ ▷ C₂×C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #341

subgroup

G/H

center

C₂²

#63636

commutator

C₂×C₃²×C₈

C₂×C₄

Frattini

C₂²×C₈

C₂×C₃⋊D₃

Fitting

C₃²×#341

C₂

C₂²×C₃²

C₂

C₂²×C₃²×C₈

C₂²

C₃⋊D₃

C₃²

G ▷ C₂×C₃²×C₈ ▷ C₂×C₃²×C₄ ▷ C₂×C₃² ▷ C₃²

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #341

N	H ≅ G/N	type
2. C₃²×#341	C₂	semidirect
3. #10589415	C₂	semidirect
13. C₃×#341	D₃	semidirect
51. #341	C₃⋊D₃	semidirect
125. C₃²	#1349	semidirect
155. C₃	#67487	semidirect

H ≅ G/N

type

2. C₃²×#341

C₂

semidirect

3. #10589415

C₂

semidirect

13. C₃×#341

D₃

semidirect

51. #341

C₃⋊D₃

semidirect

125. C₃²

#1349

semidirect

155. C₃

#67487

semidirect

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

subgroup	index
#10592814	2
C₃²×#341	2
#10589415	2
#67487	3

subgroup

index

#10592814

C₃²×#341

#10589415

#67487

Subgroups — #11771882

Conjugacy classes of subgroups

Complements

Maximal subgroups