Group #14640384 — subgroups

Subgroups — #14640384

Order 2816.

304 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 115 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	#13068469	C₂	1	2	yes	maximal
2	C₁₁×#1831	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₁×C₄⋊C₈	C₄	1	2	yes	—
4	C₄³×C₁₁	C₂²	1	1	yes	characteristic
5	C₂×C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
6	C₂×#66867	—	2	2	no	—
7	C₁₁×#336	—	2	2	no	—
8	#10622162	C₄	1	4	yes	—
9	C₂²×C₈×C₁₁	—	2	2	no	—
10	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
11	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
13	C₂×C₄²×C₁₁	D₄	1	2	yes	—
14	C₂×C₄²×C₁₁	Q₈	1	1	yes	characteristic
15	C₂²×C₁₁⋊C₈	—	2	4	no	—
16	C₁₁×C₄⋊C₈	—	4	2	no	—
17	C₄⋊(C₁₁⋊C₈)	—	2	8	no	—
18	#66867	—	4	2	no	—
19	#66867	—	4	2	no	—
20	#7049	—	11	1	no	maximal, Sylow
21	C₂²×C₄×C₁₁	C₄²	1	1	yes	characteristic
22	C₂²×C₄×C₁₁	C₂²⋊C₄	1	2	yes	—
23	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
24	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
25	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
26	C₂×C₈×C₁₁	—	4	2	no	—
27	C₂×C₈×C₁₁	—	4	4	no	—
28	C₄²×C₁₁	—	2	1	no	—
29	C₄²×C₁₁	—	2	1	no	—
30	C₄²×C₁₁	—	2	4	no	—
31	C₄²×C₁₁	—	4	2	no	—
32	C₄²×C₁₁	—	4	1	no	—
33	C₄²×C₁₁	D₈	1	1	yes	characteristic
34	C₄²×C₁₁	SD₁₆	1	2	yes	—
35	C₄²×C₁₁	Q₁₆	1	1	yes	characteristic
36	C₂×C₁₁⋊C₈	—	2	8	no	—
37	C₂×C₁₁⋊C₈	—	4	4	no	—
38	C₂×C₁₁⋊C₈	—	4	4	no	—
39	#1831	D₁₁	1	1	yes	characteristic
40	#1767	—	11	2	no	—
41	C₂³×C₁₁	#95	1	1	yes	characteristic
42	C₂×C₄×C₁₁	—	2	1	no	—
43	C₂×C₄×C₁₁	—	2	2	no	—
44	C₂×C₄×C₁₁	—	2	1	no	—
45	C₂×C₄×C₁₁	—	2	2	no	—
46	C₂×C₄×C₁₁	—	2	2	no	—
47	C₂×C₄×C₁₁	—	2	2	no	—
48	C₂×C₄×C₁₁	—	2	1	no	—
49	C₂×C₄×C₁₁	—	2	2	no	—
50	C₂×C₄×C₁₁	—	2	2	no	—
51	C₂×C₄×C₁₁	#100	1	1	yes	characteristic
52	C₂×C₄×C₁₁	#101	1	1	yes	characteristic
53	C₂×C₄×C₁₁	#102	1	2	yes	—
54	C₂×C₄×C₁₁	#103	1	2	yes	—
55	C₂×C₄×C₁₁	#104	1	4	yes	—
56	C₂×C₄×C₁₁	#106	1	1	yes	characteristic
57	C₂×C₄×C₁₁	#107	1	1	yes	characteristic
58	C₈×C₁₁	—	8	2	no	—
59	C₁₁⋊C₈	—	4	8	no	—
60	C₂×C₄⋊C₈	—	22	2	no	—
61	C₂×C₄⋊C₈	Dic₁₁	1	2	yes	—
62	C₂×#97	—	22	2	no	—
63	C₄³	C₂×D₁₁	1	1	yes	characteristic
64	#336	—	2	2	no	—
65	#336	—	11	4	no	—
66	C₂²×C₁₁	#338	1	1	yes	characteristic
67	C₂²×C₁₁	#339	1	2	yes	—
68	C₂²×C₁₁	#340	1	1	yes	characteristic
69	C₂²×C₁₁	#343	1	1	yes	characteristic
70	C₂²×C₁₁	#344	1	2	yes	—
71	C₄×C₁₁	—	2	1	no	—
72	C₄×C₁₁	—	2	1	no	—
73	C₄×C₁₁	—	2	2	no	—
74	C₄×C₁₁	—	2	2	no	—
75	C₄×C₁₁	—	4	2	no	—
76	C₄×C₁₁	—	4	1	no	—
77	C₄×C₁₁	#329	1	2	yes	—
78	C₄×C₁₁	#330	1	2	yes	—
79	C₂²×C₈	—	2	2	no	—
80	C₂²×C₈	—	22	4	no	—
81	C₂×C₄²	Dic₂₂	1	1	yes	characteristic
82	C₂×C₄²	C₄×D₁₁	1	2	yes	—
83	C₂×C₄²	D₄₄	1	1	yes	characteristic
84	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
85	C₂×C₄²	C₂²⋊D₁₁	1	2	yes	—
86	C₄⋊C₈	—	4	2	no	—
87	C₄⋊C₈	—	22	8	no	—
88	#97	—	44	2	no	—
89	#97	—	44	2	no	—
90	C₂×C₁₁	#1291	1	2	yes	—
91	C₂×C₁₁	#1292	1	1	yes	characteristic
92	C₂×C₁₁	#1295	1	1	yes	characteristic
93	C₂×C₁₁	#1303	1	2	yes	—
94	C₂×C₁₁	#1307	1	1	yes	characteristic
95	C₂²×C₄	C₄×Dic₁₁	1	1	yes	characteristic
96	C₂²×C₄	Dic₁₁⋊C₄	1	2	yes	—
97	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
98	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	2	yes	—
99	C₂²×C₄	C₂²⋊Dic₁₁	1	1	yes	characteristic
100	C₂×C₈	—	4	2	no	—
101	C₂×C₈	—	4	4	no	—
102	C₂×C₈	—	22	8	no	—
103	C₂×C₈	—	44	4	no	—
104	C₂×C₈	—	44	4	no	—
105	C₄²	—	2	1	no	—
106	C₄²	—	2	1	no	—
107	C₄²	—	2	4	no	—
108	C₄²	—	4	1	no	—
109	C₄²	—	4	2	no	—
110	C₄²	#4314	1	2	yes	—
111	C₄²	D₈₈	1	1	yes	characteristic
112	C₄²	Dic₄₄	1	1	yes	characteristic
113	C₁₁	#7049	1	1	yes	characteristic, complemented, Sylow
114	C₂³	C₁₁⋊#95	1	1	yes	characteristic
115	C₂×C₄	—	2	1	no	—
116	C₂×C₄	—	2	2	no	—
117	C₂×C₄	—	2	2	no	—
118	C₂×C₄	—	2	1	no	—
119	C₂×C₄	—	2	1	no	—
120	C₂×C₄	—	2	2	no	—
121	C₂×C₄	—	2	2	no	—
122	C₂×C₄	—	2	2	no	—
123	C₂×C₄	—	2	2	no	—
124	C₂×C₄	#66880	1	2	yes	—
125	C₂×C₄	#66881	1	1	yes	characteristic
126	C₂×C₄	#66882	1	1	yes	characteristic
127	C₂×C₄	#66885	1	2	yes	—
128	C₂×C₄	#66897	1	1	yes	characteristic
129	C₂×C₄	#66900	1	1	yes	characteristic
130	C₂×C₄	#66901	1	4	yes	—
131	C₈	—	8	2	no	—
132	C₈	—	44	8	no	—
133	C₂²	#10622168	1	1	yes	characteristic
134	C₂²	#10622170	1	2	yes	—
135	C₂²	#10622189	1	1	yes	characteristic
136	C₂²	#10622197	1	2	yes	—
137	C₂²	C₁₁⋊#338	1	1	yes	characteristic
138	C₄	—	2	2	no	—
139	C₄	—	2	2	no	—
140	C₄	—	2	1	no	—
141	C₄	—	2	1	no	—
142	C₄	—	4	1	no	—
143	C₄	—	4	2	no	—
144	C₄	#10622178	1	2	yes	—
145	C₄	#10622181	1	2	yes	—
146	C₂	#13066487	1	2	yes	—
147	C₂	#13066491	1	1	yes	characteristic
148	C₂	#13066497	1	1	yes	characteristic
149	C₂	#13066518	1	2	yes	—
150	C₂	#13066527	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13068469

C₂

yes

maximal

C₁₁×#1831

C₂

yes

maximal, characteristic

C₂×C₁₁×C₄⋊C₈

C₄

yes

—

C₄³×C₁₁

C₂²

yes

characteristic

C₂×C₄⋊(C₁₁⋊C₈)

—

C₂×#66867

—

C₁₁×#336

—

#10622162

C₄

yes

—

C₂²×C₈×C₁₁

—

C₂×C₄²×C₁₁

C₂×C₄

yes

—

C₂×C₄²×C₁₁

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₁

D₄

yes

characteristic

C₂×C₄²×C₁₁

D₄

yes

—

C₂×C₄²×C₁₁

Q₈

yes

characteristic

C₂²×C₁₁⋊C₈

—

C₁₁×C₄⋊C₈

—

C₄⋊(C₁₁⋊C₈)

—

—

—

—

C₂²×C₄×C₁₁

C₄²

yes

characteristic

C₂²×C₄×C₁₁

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₁

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₁

C₄⋊C₄

yes

—

C₂²×C₄×C₁₁

C₄⋊C₄

yes

characteristic

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₄²×C₁₁

—

C₄²×C₁₁

—

C₄²×C₁₁

—

C₄²×C₁₁

—

C₄²×C₁₁

—

C₄²×C₁₁

D₈

yes

characteristic

C₄²×C₁₁

SD₁₆

yes

—

C₄²×C₁₁

Q₁₆

yes

characteristic

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

—

#1831

D₁₁

yes

characteristic

#1767

—

C₂³×C₁₁

#95

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

yes

C₂×C₄×C₁₁

yes

C₂×C₄×C₁₁

yes

—

C₂×C₄×C₁₁

#103

yes

—

C₂×C₄×C₁₁

#104

yes

—

C₂×C₄×C₁₁

yes

C₂×C₄×C₁₁

yes

C₈×C₁₁

—

C₁₁⋊C₈

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

Dic₁₁

yes

—

C₂×#97

—

C₄³

C₂×D₁₁

yes

characteristic

#336

—

#336

—

C₂²×C₁₁

#338

yes

characteristic

C₂²×C₁₁

#339

yes

—

C₂²×C₁₁

yes

C₂²×C₁₁

yes

C₂²×C₁₁

yes

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

#329

yes

—

C₄×C₁₁

#330

yes

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

Dic₂₂

yes

characteristic

C₂×C₄²

C₄×D₁₁

yes

—

C₂×C₄²

D₄₄

yes

characteristic

C₂×C₄²

C₂×Dic₁₁

yes

characteristic

C₂×C₄²

C₂²⋊D₁₁

yes

—

C₄⋊C₈

—

C₄⋊C₈

—

#97

—

#97

—

C₂×C₁₁

#1291

yes

—

C₂×C₁₁

yes

C₂×C₁₁

yes

C₂×C₁₁

yes

—

C₂×C₁₁

#1307

yes

characteristic

C₂²×C₄

C₄×Dic₁₁

yes

characteristic

C₂²×C₄

Dic₁₁⋊C₄

yes

—

C₂²×C₄

C₄⋊Dic₁₁

yes

characteristic

C₂²×C₄

(C₂×D₁₁)⋊C₄

yes

—

C₂²×C₄

C₂²⋊Dic₁₁

yes

characteristic

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₄²

—

106

C₄²

—

107

C₄²

—

108

C₄²

—

109

C₄²

—

110

C₄²

#4314

yes

—

111

C₄²

D₈₈

yes

characteristic

112

C₄²

Dic₄₄

yes

characteristic

113

C₁₁

#7049

yes

characteristic, complemented, Sylow

114

C₂³

C₁₁⋊#95

yes

characteristic

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

#66880

yes

—

125

C₂×C₄

#66881

yes

characteristic

126

C₂×C₄

#66882

yes

characteristic

127

C₂×C₄

#66885

yes

—

128

C₂×C₄

#66897

yes

characteristic

129

C₂×C₄

#66900

yes

characteristic

130

C₂×C₄

#66901

yes

—

131

C₈

—

132

C₈

—

133

C₂²

#10622168

yes

characteristic

134

C₂²

#10622170

yes

—

135

C₂²

#10622189

yes

characteristic

136

C₂²

#10622197

yes

—

137

C₂²

C₁₁⋊#338

yes

characteristic

138

C₄

—

139

C₄

—

140

C₄

—

141

C₄

—

142

C₄

—

143

C₄

—

144

C₄

#10622178

yes

—

145

C₄

#10622181

yes

—

146

C₂

#13066487

yes

—

147

C₂

#13066491

yes

characteristic

148

C₂

#13066497

yes

characteristic

149

C₂

#13066518

yes

—

150

C₂

#13066527

yes

characteristic

	subgroup	G/H
center	C₂³	C₁₁⋊#95
commutator	C₂²×C₄×C₁₁	C₄²
Frattini	C₄³	C₂×D₁₁
Fitting	C₁₁×#1831	C₂
socle, prime radical	C₂³×C₁₁	#95
cosocle	C₄³×C₁₁	C₂²
hypercenter	#1831	D₁₁
hypocenter	C₁₁	#7049
LCS	G ▷ C₂²×C₄×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #1831

subgroup

G/H

center

C₂³

C₁₁⋊#95

commutator

C₂²×C₄×C₁₁

C₄²

Frattini

C₄³

C₂×D₁₁

Fitting

C₁₁×#1831

C₂

socle, prime radical

C₂³×C₁₁

#95

cosocle

C₄³×C₁₁

C₂²

D₁₁

C₁₁

G ▷ C₂²×C₄×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ #1831

N	H ≅ G/N	type
113. C₁₁	#7049	semidirect

H ≅ G/N

type

113. C₁₁

#7049

semidirect

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

subgroup	index
#13068469	2
C₁₁×#1831	2
#7049	11

subgroup

index

#13068469

C₁₁×#1831

#7049

Subgroups — #14640384

Conjugacy classes of subgroups

Complements

Maximal subgroups