Group #14640370 — subgroups

Subgroups — #14640370

Order 2816.

304 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 107 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	C₄	1	4	yes	—
7	C₁₁×#336	—	2	2	no	—
8	#10622162	—	2	2	no	—
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	4	no	—
19	#7042	—	11	1	no	maximal, Sylow
20	C₂²×C₄×C₁₁	C₄²	1	1	yes	characteristic
21	C₂²×C₄×C₁₁	C₂²⋊C₄	1	2	yes	—
22	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
23	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
24	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
25	C₂×C₈×C₁₁	—	4	2	no	—
26	C₂×C₈×C₁₁	—	4	4	no	—
27	C₄²×C₁₁	—	2	2	no	—
28	C₄²×C₁₁	—	2	1	no	—
29	C₄²×C₁₁	—	2	1	no	—
30	C₄²×C₁₁	—	2	2	no	—
31	C₄²×C₁₁	—	2	4	no	—
32	C₄²×C₁₁	—	2	2	no	—
33	C₄²×C₁₁	—	4	1	no	—
34	C₂×C₁₁⋊C₈	—	2	8	no	—
35	C₂×C₁₁⋊C₈	—	4	4	no	—
36	C₂×C₁₁⋊C₈	—	4	4	no	—
37	#1831	D₁₁	1	1	yes	characteristic
38	#1767	—	11	2	no	—
39	C₂³×C₁₁	#95	1	1	yes	characteristic
40	C₂×C₄×C₁₁	—	2	2	no	—
41	C₂×C₄×C₁₁	—	2	1	no	—
42	C₂×C₄×C₁₁	—	2	2	no	—
43	C₂×C₄×C₁₁	—	2	1	no	—
44	C₂×C₄×C₁₁	—	2	2	no	—
45	C₂×C₄×C₁₁	—	2	2	no	—
46	C₂×C₄×C₁₁	—	2	1	no	—
47	C₂×C₄×C₁₁	—	2	2	no	—
48	C₂×C₄×C₁₁	—	2	2	no	—
49	C₂×C₄×C₁₁	#100	1	2	yes	—
50	C₂×C₄×C₁₁	#100	1	1	yes	characteristic
51	C₂×C₄×C₁₁	#101	1	2	yes	—
52	C₂×C₄×C₁₁	#101	1	1	yes	characteristic
53	C₂×C₄×C₁₁	#104	1	4	yes	—
54	C₂×C₄×C₁₁	#108	1	2	yes	—
55	C₈×C₁₁	—	8	2	no	—
56	C₁₁⋊C₈	—	4	8	no	—
57	C₂×C₄⋊C₈	—	22	2	no	—
58	C₂×C₄⋊C₈	Dic₁₁	1	2	yes	—
59	C₂×#97	—	11	4	no	—
60	C₄³	C₂×D₁₁	1	1	yes	characteristic
61	#336	—	2	2	no	—
62	#336	—	22	2	no	—
63	C₂²×C₁₁	H(3,ℤ/4)	1	1	yes	characteristic
64	C₂²×C₁₁	#339	1	2	yes	—
65	C₂²×C₁₁	#341	1	1	yes	characteristic
66	C₂²×C₁₁	#343	1	1	yes	characteristic
67	C₂²×C₁₁	#343	1	2	yes	—
68	C₄×C₁₁	—	2	2	no	—
69	C₄×C₁₁	—	2	2	no	—
70	C₄×C₁₁	—	2	2	no	—
71	C₄×C₁₁	—	4	2	no	—
72	C₄×C₁₁	—	4	1	no	—
73	C₄×C₁₁	#329	1	2	yes	—
74	C₄×C₁₁	#330	1	2	yes	—
75	C₂²×C₈	—	2	2	no	—
76	C₂²×C₈	—	22	4	no	—
77	C₂×C₄²	Dic₂₂	1	1	yes	characteristic
78	C₂×C₄²	C₄×D₁₁	1	2	yes	—
79	C₂×C₄²	D₄₄	1	1	yes	characteristic
80	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
81	C₂×C₄²	C₂²⋊D₁₁	1	2	yes	—
82	C₄⋊C₈	—	4	2	no	—
83	C₄⋊C₈	—	22	8	no	—
84	#97	—	44	4	no	—
85	C₂×C₁₁	#1285	1	2	yes	—
86	C₂×C₁₁	#1290	1	1	yes	characteristic
87	C₂×C₁₁	#1295	1	1	yes	characteristic
88	C₂×C₁₁	#1299	1	2	yes	—
89	C₂×C₁₁	#1309	1	1	yes	characteristic
90	C₂²×C₄	C₄×Dic₁₁	1	1	yes	characteristic
91	C₂²×C₄	Dic₁₁⋊C₄	1	2	yes	—
92	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
93	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	2	yes	—
94	C₂²×C₄	C₂²⋊Dic₁₁	1	1	yes	characteristic
95	C₂×C₈	—	4	2	no	—
96	C₂×C₈	—	4	4	no	—
97	C₂×C₈	—	22	8	no	—
98	C₂×C₈	—	44	4	no	—
99	C₂×C₈	—	44	4	no	—
100	C₄²	—	2	2	no	—
101	C₄²	—	2	2	no	—
102	C₄²	—	2	2	no	—
103	C₄²	—	2	1	no	—
104	C₄²	—	2	1	no	—
105	C₄²	—	2	4	no	—
106	C₄²	—	4	1	no	—
107	C₁₁	#7042	1	1	yes	characteristic, complemented, Sylow
108	C₂³	C₁₁⋊#95	1	1	yes	characteristic
109	C₂×C₄	—	2	1	no	—
110	C₂×C₄	—	2	2	no	—
111	C₂×C₄	—	2	2	no	—
112	C₂×C₄	—	2	1	no	—
113	C₂×C₄	—	2	1	no	—
114	C₂×C₄	—	2	2	no	—
115	C₂×C₄	—	2	2	no	—
116	C₂×C₄	—	2	2	no	—
117	C₂×C₄	—	2	2	no	—
118	C₂×C₄	#66883	1	2	yes	—
119	C₂×C₄	#66887	1	2	yes	—
120	C₂×C₄	#66888	1	2	yes	—
121	C₂×C₄	#66897	1	1	yes	characteristic
122	C₂×C₄	#66900	1	1	yes	characteristic
123	C₂×C₄	#66901	1	4	yes	—
124	C₈	—	8	2	no	—
125	C₈	—	44	8	no	—
126	C₂²	#10622168	1	1	yes	characteristic
127	C₂²	#10622170	1	2	yes	—
128	C₂²	#10622190	1	1	yes	characteristic
129	C₂²	#10622192	1	2	yes	—
130	C₂²	#10622195	1	1	yes	characteristic
131	C₄	—	2	2	no	—
132	C₄	—	2	2	no	—
133	C₄	—	2	2	no	—
134	C₄	—	4	2	no	—
135	C₄	—	4	1	no	—
136	C₄	#10622178	1	2	yes	—
137	C₄	#10622181	1	2	yes	—
138	C₂	#13066473	1	2	yes	—
139	C₂	#13066486	1	1	yes	characteristic
140	C₂	#13066497	1	1	yes	characteristic
141	C₂	#13066507	1	2	yes	—
142	C₂	C₁₁⋊#1309	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

C₄

yes

—

C₁₁×#336

—

#10622162

—

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)

—

#66867

—

#7042

—

maximal, Sylow

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

—

C₄²×C₁₁

—

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

#100

yes

—

C₂×C₄×C₁₁

#100

yes

characteristic

C₂×C₄×C₁₁

#101

yes

—

C₂×C₄×C₁₁

#101

yes

characteristic

C₂×C₄×C₁₁

#104

yes

—

C₂×C₄×C₁₁

#108

yes

—

C₈×C₁₁

—

C₁₁⋊C₈

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

Dic₁₁

yes

—

C₂×#97

—

C₄³

C₂×D₁₁

yes

characteristic

#336

—

#336

—

C₂²×C₁₁

H(3,ℤ/4)

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

#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

—

C₂×C₁₁

#1285

yes

—

C₂×C₁₁

yes

C₂×C₁₁

yes

C₂×C₁₁

yes

—

C₂×C₁₁

#1309

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

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

100

C₄²

—

101

C₄²

—

102

C₄²

—

103

C₄²

—

104

C₄²

—

105

C₄²

—

106

C₄²

—

107

C₁₁

#7042

yes

characteristic, complemented, Sylow

108

C₂³

C₁₁⋊#95

yes

characteristic

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

#66883

yes

—

119

C₂×C₄

#66887

yes

—

120

C₂×C₄

#66888

yes

—

121

C₂×C₄

#66897

yes

characteristic

122

C₂×C₄

#66900

yes

characteristic

123

C₂×C₄

#66901

yes

—

124

C₈

—

125

C₈

—

126

C₂²

#10622168

yes

characteristic

127

C₂²

#10622170

yes

—

128

C₂²

#10622190

yes

characteristic

129

C₂²

#10622192

yes

—

130

C₂²

#10622195

yes

characteristic

131

C₄

—

132

C₄

—

133

C₄

—

134

C₄

—

135

C₄

—

136

C₄

#10622178

yes

—

137

C₄

#10622181

yes

—

138

C₂

#13066473

yes

—

139

C₂

#13066486

yes

characteristic

140

C₂

#13066497

yes

characteristic

141

C₂

#13066507

yes

—

142

C₂

C₁₁⋊#1309

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	#7042
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
107. C₁₁	#7042	semidirect

H ≅ G/N

type

107. C₁₁

#7042

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
#7042	11

subgroup

index

#13068469

C₁₁×#1831

#7042

Subgroups — #14640370

Conjugacy classes of subgroups

Complements

Maximal subgroups