Group #13077001 — subgroups

Subgroups — #13077001

Order 1408.

400 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 157 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	C₁₁×#382	C₂	1	1	yes	maximal, characteristic
2	#10622598	C₂	1	2	yes	maximal
3	#10622586	C₂	1	2	yes	maximal
4	#10622549	C₂	1	1	yes	maximal, characteristic
5	C₄²×Dic₁₁	C₂	1	1	yes	maximal, characteristic
6	#10622268	C₂	1	4	yes	maximal
7	#10622267	C₂	1	4	yes	maximal
8	C₂×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
9	C₂×C₄²×C₁₁	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₁₁	C₂²	1	4	yes	—
11	C₂×C₄⋊Dic₁₁	C₂²	1	2	yes	—
12	C₂×Dic₁₁⋊C₄	C₂²	1	4	yes	—
13	C₂×C₄×Dic₁₁	C₂²	1	2	yes	—
14	C₂×C₄×Dic₁₁	C₂²	1	2	yes	—
15	C₂×C₄×Dic₁₁	C₂²	1	1	yes	characteristic
16	C₂×C₄×Dic₁₁	C₂²	1	1	yes	characteristic
17	C₁₁×#95	C₂²	1	2	yes	—
18	C₁₁×#95	C₂²	1	2	yes	—
19	C₁₁⋊#95	C₂²	1	2	yes	—
20	C₁₁⋊#95	C₂²	1	4	yes	—
21	C₁₁⋊#95	C₂²	1	4	yes	—
22	C₁₁⋊#95	C₂²	1	2	yes	—
23	C₂²×C₄×C₁₁	C₂³	1	4	yes	—
24	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
25	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
26	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
27	C₂²×Dic₁₁	C₂³	1	4	yes	—
28	C₂²×Dic₁₁	C₂³	1	2	yes	—
29	C₂²×Dic₁₁	C₂³	1	2	yes	—
30	C₁₁×C₄⋊C₄	—	2	4	no	—
31	C₄²×C₁₁	Q₈	1	4	yes	—
32	C₄⋊Dic₁₁	—	2	8	no	—
33	C₄⋊Dic₁₁	—	2	4	no	—
34	Dic₁₁⋊C₄	—	2	8	no	—
35	C₄×Dic₁₁	—	2	4	no	—
36	C₄×Dic₁₁	—	2	4	no	—
37	C₄×Dic₁₁	—	2	2	no	—
38	C₄×Dic₁₁	—	2	2	no	—
39	#2864	—	11	1	no	maximal, Sylow
40	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
41	C₂×C₄×C₁₁	—	2	2	no	—
42	C₂×C₄×C₁₁	—	2	2	no	—
43	C₂×C₄×C₁₁	—	2	4	no	—
44	C₂×C₄×C₁₁	—	2	4	no	—
45	C₂×C₄×C₁₁	—	2	4	no	—
46	C₂×C₄×C₁₁	C₂×Q₈	1	2	yes	—
47	C₂×C₄×C₁₁	C₂×Q₈	1	2	yes	—
48	C₂×C₄×C₁₁	C₂×Q₈	1	2	yes	—
49	C₂×C₄×C₁₁	#41	1	2	yes	—
50	C₂×C₄×C₁₁	#41	1	2	yes	—
51	C₂×Dic₁₁	—	2	2	no	—
52	C₂×Dic₁₁	—	2	2	no	—
53	C₂×Dic₁₁	—	2	2	no	—
54	C₂×Dic₁₁	—	2	2	no	—
55	C₂×Dic₁₁	—	2	4	no	—
56	C₂×Dic₁₁	—	2	4	no	—
57	C₂×Dic₁₁	—	2	4	no	—
58	C₂×Dic₁₁	#41	1	4	yes	—
59	C₂×Dic₁₁	#41	1	4	yes	—
60	#389	—	11	2	no	—
61	#389	—	11	2	no	—
62	#387	—	11	4	no	—
63	#387	—	11	4	no	—
64	#382	—	11	1	no	—
65	#382	D₁₁	1	1	yes	characteristic
66	C₄³	—	11	1	no	—
67	C₂²×C₁₁	C₂²×Q₈	1	1	yes	characteristic
68	C₂²×C₁₁	C₂×#41	1	1	yes	characteristic
69	C₂²×C₁₁	C₂×#41	1	1	yes	characteristic
70	C₂²×C₁₁	C₂×#41	1	2	yes	—
71	C₂²×C₁₁	C₂×#41	1	2	yes	—
72	C₄×C₁₁	—	2	2	no	—
73	C₄×C₁₁	—	2	2	no	—
74	C₄×C₁₁	—	4	4	no	—
75	C₄×C₁₁	#125	1	4	yes	—
76	Dic₁₁	—	2	4	no	—
77	Dic₁₁	—	2	4	no	—
78	Dic₁₁	—	4	4	no	—
79	C₂×C₄⋊C₄	—	11	2	no	—
80	C₂×C₄⋊C₄	—	11	4	no	—
81	C₂×C₄⋊C₄	—	11	4	no	—
82	C₂×C₄⋊C₄	C₂×D₁₁	1	2	yes	—
83	C₂×C₄²	—	11	2	no	—
84	C₂×C₄²	—	11	2	no	—
85	C₂×C₄²	—	11	1	no	—
86	C₂×C₄²	—	11	1	no	—
87	C₂×C₄²	C₂×D₁₁	1	1	yes	characteristic
88	#95	—	11	2	no	—
89	#95	—	11	2	no	—
90	#95	—	11	4	no	—
91	#95	—	11	4	no	—
92	#95	C₂×D₁₁	1	2	yes	—
93	#95	C₂×D₁₁	1	2	yes	—
94	C₂×C₁₁	C₂×#125	1	1	yes	characteristic
95	C₂×C₁₁	#529	1	2	yes	—
96	C₂×C₁₁	#529	1	2	yes	—
97	C₂×C₁₁	#533	1	1	yes	characteristic
98	C₂×C₁₁	#533	1	1	yes	characteristic
99	C₂²×C₄	—	11	2	no	—
100	C₂²×C₄	—	11	2	no	—
101	C₂²×C₄	—	11	4	no	—
102	C₂²×C₄	C₂²×D₁₁	1	4	yes	—
103	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
104	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
105	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
106	C₄⋊C₄	—	2	4	no	—
107	C₄⋊C₄	—	22	8	no	—
108	C₄⋊C₄	—	22	8	no	—
109	C₄⋊C₄	—	22	4	no	—
110	C₄²	—	22	4	no	—
111	C₄²	—	22	4	no	—
112	C₄²	—	22	2	no	—
113	C₄²	—	22	2	no	—
114	C₄²	Dic₂₂	1	4	yes	—
115	C₁₁	#2864	1	1	yes	characteristic, complemented, Sylow
116	C₂³	C₂³×D₁₁	1	1	yes	characteristic
117	C₂×C₄	—	2	2	no	—
118	C₂×C₄	—	2	2	no	—
119	C₂×C₄	—	2	4	no	—
120	C₂×C₄	—	2	4	no	—
121	C₂×C₄	—	2	4	no	—
122	C₂×C₄	—	11	4	no	—
123	C₂×C₄	—	11	4	no	—
124	C₂×C₄	—	22	2	no	—
125	C₂×C₄	—	22	2	no	—
126	C₂×C₄	—	22	2	no	—
127	C₂×C₄	—	22	2	no	—
128	C₂×C₄	—	22	4	no	—
129	C₂×C₄	—	22	4	no	—
130	C₂×C₄	—	22	4	no	—
131	C₂×C₄	C₂×Dic₂₂	1	2	yes	—
132	C₂×C₄	C₂×Dic₂₂	1	2	yes	—
133	C₂×C₄	C₂×Dic₂₂	1	2	yes	—
134	C₂×C₄	#4341	1	2	yes	—
135	C₂×C₄	#4343	1	2	yes	—
136	C₂²	C₂²×Dic₂₂	1	1	yes	characteristic
137	C₂²	C₂×#4341	1	1	yes	characteristic
138	C₂²	C₂×#4343	1	1	yes	characteristic
139	C₂²	#41×D₁₁	1	2	yes	—
140	C₂²	#41×D₁₁	1	2	yes	—
141	C₄	—	2	2	no	—
142	C₄	—	2	2	no	—
143	C₄	—	4	4	no	—
144	C₄	—	22	4	no	—
145	C₄	—	22	4	no	—
146	C₄	—	44	4	no	—
147	C₄	#66943	1	4	yes	—
148	C₂	C₂×#66943	1	1	yes	characteristic
149	C₂	#10623048	1	1	yes	characteristic
150	C₂	#10623048	1	1	yes	characteristic
151	C₂	#10623211	1	2	yes	—
152	C₂	#10623222	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₁×#382

C₂

yes

maximal, characteristic

#10622598

C₂

yes

maximal

#10622586

C₂

yes

maximal

#10622549

C₂

yes

maximal, characteristic

C₄²×Dic₁₁

C₂

yes

maximal, characteristic

#10622268

C₂

yes

maximal

#10622267

C₂

yes

maximal

C₂×C₁₁×C₄⋊C₄

C₂²

yes

—

C₂×C₄²×C₁₁

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₁

C₂²

yes

—

C₂×C₄⋊Dic₁₁

C₂²

yes

—

C₂×Dic₁₁⋊C₄

C₂²

yes

—

C₂×C₄×Dic₁₁

C₂²

yes

—

C₂×C₄×Dic₁₁

C₂²

yes

—

C₂×C₄×Dic₁₁

C₂²

yes

characteristic

C₂×C₄×Dic₁₁

C₂²

yes

characteristic

C₁₁×#95

C₂²

yes

—

C₁₁×#95

C₂²

yes

—

C₁₁⋊#95

C₂²

yes

—

C₁₁⋊#95

C₂²

yes

—

C₁₁⋊#95

C₂²

yes

—

C₁₁⋊#95

C₂²

yes

—

C₂²×C₄×C₁₁

C₂³

yes

—

C₂²×C₄×C₁₁

C₂³

yes

characteristic

C₂²×C₄×C₁₁

C₂³

yes

characteristic

C₂²×C₄×C₁₁

C₂³

yes

characteristic

C₂²×Dic₁₁

C₂³

yes

—

C₂²×Dic₁₁

C₂³

yes

—

C₂²×Dic₁₁

C₂³

yes

—

C₁₁×C₄⋊C₄

—

C₄²×C₁₁

Q₈

yes

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

Dic₁₁⋊C₄

—

C₄×Dic₁₁

—

C₄×Dic₁₁

—

C₄×Dic₁₁

—

C₄×Dic₁₁

—

#2864

—

maximal, Sylow

C₂³×C₁₁

C₂⁴

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

C₂×Q₈

yes

—

C₂×C₄×C₁₁

C₂×Q₈

yes

—

C₂×C₄×C₁₁

C₂×Q₈

yes

—

C₂×C₄×C₁₁

#41

yes

—

C₂×C₄×C₁₁

#41

yes

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

#41

yes

—

C₂×Dic₁₁

#41

yes

—

—

—

—

—

—

D₁₁

yes

characteristic

C₄³

—

C₂²×C₁₁

C₂²×Q₈

yes

characteristic

C₂²×C₁₁

C₂×#41

yes

characteristic

C₂²×C₁₁

C₂×#41

yes

characteristic

C₂²×C₁₁

C₂×#41

yes

—

C₂²×C₁₁

C₂×#41

yes

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

#125

yes

—

Dic₁₁

—

Dic₁₁

—

Dic₁₁

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₁

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₁₁

yes

—

—

—

—

C₂×D₁₁

yes

—

#95

C₂×D₁₁

yes

—

C₂×C₁₁

C₂×#125

yes

characteristic

C₂×C₁₁

#529

yes

—

C₂×C₁₁

#529

yes

—

C₂×C₁₁

yes

C₂×C₁₁

yes

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

—

102

C₂²×C₄

C₂²×D₁₁

yes

—

103

C₂²×C₄

C₂²×D₁₁

yes

characteristic

104

C₂²×C₄

C₂²×D₁₁

yes

characteristic

105

C₂²×C₄

C₂²×D₁₁

yes

characteristic

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₄⋊C₄

—

109

C₄⋊C₄

—

110

C₄²

—

111

C₄²

—

112

C₄²

—

113

C₄²

—

114

C₄²

Dic₂₂

yes

—

115

C₁₁

#2864

yes

characteristic, complemented, Sylow

116

C₂³

C₂³×D₁₁

yes

characteristic

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

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

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

C₂×Dic₂₂

yes

—

132

C₂×C₄

C₂×Dic₂₂

yes

—

133

C₂×C₄

C₂×Dic₂₂

yes

—

134

C₂×C₄

#4341

yes

—

135

C₂×C₄

#4343

yes

—

136

C₂²

C₂²×Dic₂₂

yes

characteristic

137

C₂²

C₂×#4341

yes

characteristic

138

C₂²

C₂×#4343

yes

characteristic

139

C₂²

#41×D₁₁

yes

—

140

C₂²

#41×D₁₁

yes

—

141

C₄

—

142

C₄

—

143

C₄

—

144

C₄

—

145

C₄

—

146

C₄

—

147

C₄

#66943

yes

—

148

C₂

C₂×#66943

yes

characteristic

149

C₂

#10623048

yes

characteristic

150

C₂

#10623048

yes

characteristic

151

C₂

#10623211

yes

—

152

C₂

#10623222

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₁
commutator, socle, prime radical, cosocle	C₂³×C₁₁	C₂⁴
Fitting	C₁₁×#382	C₂
hypercenter	#382	D₁₁
hypocenter	C₁₁	#2864
LCS	G ▷ C₂³×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ #382

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₁

commutator, socle, prime radical, cosocle

C₂³×C₁₁

C₂⁴

Fitting

C₁₁×#382

C₂

D₁₁

C₁₁

G ▷ C₂³×C₁₁ ▷ C₁₁

C₁ ◁ C₂³ ◁ #382

N	H ≅ G/N	type
115. C₁₁	#2864	semidirect

H ≅ G/N

type

115. C₁₁

#2864

semidirect

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

subgroup	index
C₁₁×#382	2
#10622598	2
#10622586	2
#10622549	2
C₄²×Dic₁₁	2
#10622268	2
#10622267	2
#2864	11

subgroup

index

C₁₁×#382

C₄²×Dic₁₁

Subgroups — #13077001

Conjugacy classes of subgroups

Complements

Maximal subgroups