Group #14653166 — subgroups

Subgroups — #14653166

Order 2816.

370 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 119 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	#13068747	C₂	1	1	yes	maximal, characteristic
2	#13067180	C₂	1	4	yes	maximal
3	#13066908	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#3160	C₂	1	1	yes	maximal, characteristic
5	C₁₁×#533	C₂²	1	2	yes	—
6	C₁₁×#500	C₄	1	2	yes	complemented
7	C₁₁×#499	—	2	2	no	—
8	C₁₁×#498	C₄	1	2	yes	complemented
9	C₁₁×#427	—	2	2	no	—
10	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
11	#10622549	C₂²	1	2	yes	—
12	#10622538	C₂²	1	2	yes	—
13	#10622189	—	2	2	no	—
14	#10622176	—	2	8	no	—
15	#10622092	—	2	2	no	—
16	C₂²×C₈×C₁₁	D₄	1	2	yes	—
17	C₁₁×C₄⋊Q₈	C₂×C₄	1	4	yes	—
18	C₁₁×#125	—	2	2	no	—
19	C₁₁×C₂²⋊Q₈	—	2	4	no	—
20	C₄×Q₈×C₁₁	—	2	4	no	—
21	C₁₁×#117	—	2	2	no	—
22	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
23	C₂×C₄⋊Dic₁₁	—	2	2	no	—
24	C₁₁×#107	—	2	4	no	—
25	C₁₁×#106	—	2	4	no	—
26	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
27	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
28	C₄×C₈×C₁₁	D₄	1	2	yes	—
29	C₁₁⋊#95	—	2	4	no	—
30	C₂²⋊(C₁₁⋊C₈)	D₄	1	4	yes	—
31	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
32	C₄×C₁₁⋊C₈	—	2	2	no	—
33	#9759	—	11	1	no	maximal, Sylow
34	C₂×Q₈×C₁₁	—	2	4	no	—
35	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
36	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
37	C₂²×Dic₁₁	—	4	2	no	—
38	C₂×C₈×C₁₁	—	2	4	no	—
39	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
40	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
41	C₁₁×C₄⋊C₄	—	2	4	no	—
42	C₁₁×C₄⋊C₄	—	2	4	no	—
43	C₁₁×C₄⋊C₄	—	4	4	no	—
44	C₁₁×C₂²⋊C₄	—	4	2	no	—
45	C₄²×C₁₁	—	4	2	no	—
46	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
47	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
48	C₄²×C₁₁	#41	1	2	yes	—
49	C₄⋊Dic₁₁	—	4	4	no	—
50	C₂×C₁₁⋊C₈	—	2	4	no	—
51	#3160	D₁₁	1	1	yes	characteristic
52	#1835	—	11	1	no	—
53	#1518	—	11	4	no	—
54	#1452	—	11	1	no	—
55	C₂³×C₁₁	#127	1	1	yes	characteristic
56	Q₈×C₁₁	—	8	4	no	—
57	C₂×C₄×C₁₁	—	4	2	no	—
58	C₂×C₄×C₁₁	—	4	4	no	—
59	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
60	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
61	C₂×C₄×C₁₁	#121	1	2	yes	—
62	C₂×C₄×C₁₁	#124	1	1	yes	characteristic
63	C₂×C₄×C₁₁	#137	1	4	yes	—
64	C₂×Dic₁₁	—	8	4	no	—
65	C₂×Dic₁₁	—	8	2	no	—
66	C₈×C₁₁	—	2	2	no	—
67	C₈×C₁₁	—	2	2	no	—
68	C₁₁⋊C₈	—	4	4	no	—
69	#533	C₂×D₁₁	1	2	yes	—
70	#500	Dic₁₁	1	2	yes	complemented
71	#499	—	2	2	no	—
72	#498	Dic₁₁	1	2	yes	complemented
73	#431	—	11	2	no	—
74	#427	—	2	2	no	—
75	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
76	#382	—	11	2	no	—
77	#340	—	22	2	no	—
78	#328	—	22	8	no	—
79	#322	—	22	2	no	—
80	C₂²×C₁₁	—	2	2	no	—
81	C₂²×C₁₁	#390	1	1	yes	characteristic
82	C₂²×C₁₁	#497	1	2	yes	—
83	C₄×C₁₁	—	2	2	no	—
84	C₄×C₁₁	—	2	2	no	—
85	C₄×C₁₁	—	8	4	no	—
86	C₄×C₁₁	#419	1	2	yes	—
87	C₄×C₁₁	#491	1	2	yes	—
88	Dic₁₁	—	16	2	no	—
89	C₂²×C₈	C₂²⋊D₁₁	1	2	yes	—
90	C₄⋊Q₈	C₂×Dic₁₁	1	4	yes	—
91	#125	—	2	2	no	—
92	C₂²⋊Q₈	—	2	4	no	—
93	C₄×Q₈	—	2	4	no	—
94	#117	—	2	2	no	—
95	C₂×C₄⋊C₄	—	22	2	no	—
96	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
97	#107	—	2	4	no	—
98	#106	—	2	4	no	—
99	C₄⋊C₈	—	22	2	no	—
100	C₂²⋊C₈	—	11	4	no	—
101	C₄×C₈	—	22	2	no	—
102	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
103	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
104	C₄×C₈	C₂²⋊D₁₁	1	2	yes	—
105	#95	—	22	4	no	—
106	C₂×C₁₁	—	2	2	no	—
107	C₂×C₁₁	#1960	1	1	yes	characteristic
108	C₂×C₁₁	#1976	1	2	yes	—
109	C₂×Q₈	—	2	4	no	—
110	C₂²×C₄	—	44	2	no	—
111	C₂²×C₄	D₄×D₁₁	1	2	yes	—
112	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
113	C₂×C₈	—	2	4	no	—
114	C₂×C₈	—	22	4	no	—
115	C₂×C₈	C₂²⋊Dic₁₁	1	2	yes	—
116	C₂×C₈	C₂²⋊Dic₁₁	1	2	yes	—
117	C₄⋊C₄	—	2	4	no	—
118	C₄⋊C₄	—	2	4	no	—
119	C₄⋊C₄	—	4	4	no	—
120	C₄⋊C₄	—	44	4	no	—
121	C₂²⋊C₄	—	4	2	no	—
122	C₄²	—	4	2	no	—
123	C₄²	#4341	1	2	yes	—
124	C₄²	C₂²×Dic₁₁	1	1	yes	characteristic
125	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
126	C₁₁	#9759	1	1	yes	characteristic, complemented, Sylow
127	C₂³	#66993	1	1	yes	characteristic
128	Q₈	—	8	4	no	—
129	C₂×C₄	—	4	2	no	—
130	C₂×C₄	—	4	4	no	—
131	C₂×C₄	—	88	4	no	—
132	C₂×C₄	—	88	2	no	—
133	C₂×C₄	D₄×Dic₁₁	1	2	yes	—
134	C₂×C₄	#66989	1	1	yes	characteristic
135	C₂×C₄	#66991	1	2	yes	—
136	C₂×C₄	#66995	1	4	yes	—
137	C₂×C₄	C₂×C₂²⋊Dic₁₁	1	1	yes	characteristic
138	C₈	—	2	2	no	—
139	C₈	—	2	2	no	—
140	C₈	—	44	4	no	—
141	C₂²	—	2	2	no	—
142	C₂²	#10622699	1	2	yes	—
143	C₂²	#10622834	1	1	yes	characteristic
144	C₄	—	2	2	no	—
145	C₄	—	2	2	no	—
146	C₄	—	8	4	no	—
147	C₄	—	176	2	no	—
148	C₄	#10622695	1	2	yes	—
149	C₄	#10622838	1	2	yes	—
150	C₂	—	2	2	no	—
151	C₂	#13069437	1	1	yes	characteristic
152	C₂	#13069515	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13068747

C₂

yes

maximal, characteristic

#13067180

C₂

yes

maximal

#13066908

C₂

yes

maximal, characteristic

C₁₁×#3160

C₂

yes

maximal, characteristic

C₁₁×#533

C₂²

yes

—

C₁₁×#500

C₄

yes

complemented

C₁₁×#499

—

C₁₁×#498

C₄

yes

complemented

C₁₁×#427

—

C₂×C₄×C₈×C₁₁

C₂²

yes

characteristic

#10622549

C₂²

yes

—

#10622538

C₂²

yes

—

#10622189

—

#10622176

—

#10622092

—

C₂²×C₈×C₁₁

D₄

yes

—

C₁₁×C₄⋊Q₈

C₂×C₄

yes

—

C₁₁×#125

—

C₁₁×C₂²⋊Q₈

—

C₄×Q₈×C₁₁

—

C₁₁×#117

—

C₂×C₄²×C₁₁

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₁

—

C₁₁×#107

—

C₁₁×#106

—

C₄×C₈×C₁₁

C₂×C₄

yes

characteristic

C₄×C₈×C₁₁

C₂×C₄

yes

characteristic

C₄×C₈×C₁₁

D₄

yes

—

C₁₁⋊#95

—

C₂²⋊(C₁₁⋊C₈)

D₄

yes

—

C₄⋊(C₁₁⋊C₈)

—

C₄×C₁₁⋊C₈

—

#9759

—

maximal, Sylow

C₂×Q₈×C₁₁

—

C₂²×C₄×C₁₁

C₂×D₄

yes

—

C₂²×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂²×Dic₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

C₂²⋊C₄

yes

—

C₂×C₈×C₁₁

C₂²⋊C₄

yes

—

C₁₁×C₄⋊C₄

—

C₁₁×C₄⋊C₄

—

C₁₁×C₄⋊C₄

—

C₁₁×C₂²⋊C₄

—

C₄²×C₁₁

—

C₄²×C₁₁

C₂²×C₄

yes

characteristic

C₄²×C₁₁

C₂×D₄

yes

characteristic

C₄²×C₁₁

#41

yes

—

C₄⋊Dic₁₁

—

C₂×C₁₁⋊C₈

—

#3160

D₁₁

yes

—

—

—

C₂³×C₁₁

#127

yes

characteristic

Q₈×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₁

C₄×D₄

yes

—

C₂×C₄×C₁₁

#121

yes

—

C₂×C₄×C₁₁

#124

yes

characteristic

C₂×C₄×C₁₁

#137

yes

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₈×C₁₁

—

C₈×C₁₁

—

C₁₁⋊C₈

—

#533

C₂×D₁₁

yes

—

#500

Dic₁₁

yes

complemented

#499

—

#498

Dic₁₁

yes

complemented

#431

—

#427

—

C₂×C₄×C₈

C₂×D₁₁

yes

—

—

—

—

C₂²×C₁₁

—

C₂²×C₁₁

#390

yes

characteristic

C₂²×C₁₁

#497

yes

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

#419

yes

—

C₄×C₁₁

#491

yes

—

Dic₁₁

—

C₂²×C₈

C₂²⋊D₁₁

yes

—

C₄⋊Q₈

C₂×Dic₁₁

yes

—

#125

—

C₂²⋊Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂²×D₁₁

yes

characteristic

#107

—

#106

—

C₄⋊C₈

—

100

C₂²⋊C₈

—

101

C₄×C₈

—

102

C₄×C₈

C₂×Dic₁₁

yes

characteristic

103

C₄×C₈

C₂×Dic₁₁

yes

characteristic

104

C₄×C₈

C₂²⋊D₁₁

yes

—

105

#95

—

106

C₂×C₁₁

—

107

C₂×C₁₁

#1960

yes

characteristic

108

C₂×C₁₁

#1976

yes

—

109

C₂×Q₈

—

110

C₂²×C₄

—

111

C₂²×C₄

D₄×D₁₁

yes

—

112

C₂²×C₄

C₂×C₂²⋊D₁₁

yes

characteristic

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

C₂²⋊Dic₁₁

yes

—

116

C₂×C₈

C₂²⋊Dic₁₁

yes

—

117

C₄⋊C₄

—

118

C₄⋊C₄

—

119

C₄⋊C₄

—

120

C₄⋊C₄

—

121

C₂²⋊C₄

—

122

C₄²

—

123

C₄²

#4341

yes

—

124

C₄²

C₂²×Dic₁₁

yes

characteristic

125

C₄²

C₂×C₂²⋊D₁₁

yes

characteristic

126

C₁₁

#9759

yes

characteristic, complemented, Sylow

127

C₂³

#66993

yes

characteristic

128

Q₈

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

D₄×Dic₁₁

yes

—

134

C₂×C₄

#66989

yes

characteristic

135

C₂×C₄

#66991

yes

—

136

C₂×C₄

#66995

yes

—

137

C₂×C₄

C₂×C₂²⋊Dic₁₁

yes

characteristic

138

C₈

—

139

C₈

—

140

C₈

—

141

C₂²

—

142

C₂²

#10622699

yes

—

143

C₂²

#10622834

yes

characteristic

144

C₄

—

145

C₄

—

146

C₄

—

147

C₄

—

176

—

148

C₄

#10622695

yes

—

149

C₄

#10622838

yes

—

150

C₂

—

151

C₂

#13069437

yes

characteristic

152

C₂

#13069515

yes

—

	subgroup	G/H
center	C₂²	#10622834
commutator	C₄²×C₁₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₁₁×#3160	C₂
socle	C₂²×C₁₁	#390
prime radical	C₂³×C₁₁	#127
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	#3160	D₁₁
hypocenter	C₁₁	#9759
LCS	G ▷ C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3160

subgroup

G/H

center

C₂²

#10622834

commutator

C₄²×C₁₁

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₁

Fitting

C₁₁×#3160

C₂

C₂²×C₁₁

C₂³×C₁₁

C₂×C₄²×C₁₁

C₂³

D₁₁

C₁₁

G ▷ C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3160

N	H ≅ G/N	type
6. C₁₁×#500	C₄	semidirect
8. C₁₁×#498	C₄	semidirect
70. #500	Dic₁₁	semidirect
72. #498	Dic₁₁	semidirect
126. C₁₁	#9759	semidirect

H ≅ G/N

type

6. C₁₁×#500

C₄

semidirect

8. C₁₁×#498

C₄

semidirect

70. #500

Dic₁₁

semidirect

72. #498

Dic₁₁

semidirect

126. C₁₁

#9759

semidirect

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

subgroup	index
#13068747	2
#13067180	2
#13066908	2
C₁₁×#3160	2
#9759	11

subgroup

index

C₁₁×#3160

Subgroups — #14653166

Conjugacy classes of subgroups

Complements

Maximal subgroups