Group #14668155 — subgroups

Subgroups — #14668155

Order 2816.

188 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 67 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	#13070891	C₂	1	1	yes	maximal, characteristic
2	#13070524	C₂	1	1	yes	maximal, characteristic
3	#13068021	C₂	1	2	yes	maximal
4	#13066675	C₂	1	2	yes	maximal
5	C₁₁×#1372	C₂	1	1	yes	maximal, characteristic
6	#10622463	—	2	2	no	—
7	#10622295	C₂²	1	2	yes	—
8	C₈×Dic₂₂	C₂²	1	1	yes	characteristic
9	C₄×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
10	C₁₁×#335	C₂²	1	2	yes	—
11	#10622142	—	2	1	no	—
12	#10622142	—	2	1	no	—
13	#10622140	—	2	1	no	—
14	Dic₁₁⋊C₁₆	—	2	1	no	—
15	#10622119	—	2	2	no	—
16	C₄⋊(C₁₁⋊C₁₆)	C₂²	1	1	yes	characteristic
17	#66922	—	2	2	no	—
18	C₄×Dic₂₂	D₄	1	1	yes	characteristic
19	C₂×C₁₁×C₁₆	D₄	1	1	yes	characteristic
20	C₂×C₁₁×C₁₆	D₄	1	1	yes	characteristic
21	C₁₁×C₄⋊C₈	—	2	2	no	—
22	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
23	#66882	—	2	2	no	—
24	#66882	—	2	2	no	—
25	#66882	—	4	2	no	—
26	#66880	—	4	2	no	—
27	Dic₁₁⋊C₈	—	2	1	no	—
28	C₈×Dic₁₁	—	2	1	no	—
29	C₂×C₁₁⋊C₁₆	—	2	1	no	—
30	C₄⋊(C₁₁⋊C₈)	D₄	1	1	yes	characteristic
31	#12461	—	11	1	no	maximal, Sylow
32	C₂×Dic₂₂	—	4	2	no	—
33	C₂×Dic₂₂	D₈	1	1	yes	characteristic
34	C₂×C₈×C₁₁	—	4	2	no	—
35	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
36	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
37	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
38	C₄⋊Dic₁₁	—	4	2	no	—
39	C₄⋊Dic₁₁	—	4	2	no	—
40	C₄⋊Dic₁₁	D₈	1	1	yes	characteristic
41	Dic₁₁⋊C₄	—	2	1	no	—
42	C₄×Dic₁₁	—	2	1	no	—
43	C₂×C₁₁⋊C₈	—	2	1	no	—
44	C₁₁×C₁₆	—	2	1	no	—
45	C₁₁×C₁₆	Q₁₆	1	2	yes	—
46	C₁₁⋊C₁₆	—	4	1	no	—
47	#2252	—	11	1	no	—
48	#2183	—	11	1	no	—
49	#1676	—	11	2	no	—
50	#1372	D₁₁	1	1	yes	characteristic
51	#1365	—	11	2	no	—
52	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
53	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
54	C₂×C₄×C₁₁	#135	1	1	yes	characteristic
55	C₂×Dic₁₁	—	2	1	no	—
56	C₂×Dic₁₁	—	2	1	no	—
57	C₂×Dic₁₁	—	8	2	no	—
58	Dic₂₂	—	2	2	no	—
59	Dic₂₂	—	16	2	no	—
60	C₈×C₁₁	—	2	1	no	—
61	C₈×C₁₁	—	8	2	no	—
62	C₈×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
63	C₈×C₁₁	#137	1	1	yes	characteristic
64	C₁₁⋊C₈	—	4	1	no	—
65	#500	—	11	2	no	—
66	#477	—	22	2	no	—
67	C₈×Q₈	—	11	1	no	—
68	#366	—	22	1	no	—
69	#366	—	22	1	no	—
70	C₄⋊C₁₆	—	11	1	no	—
71	C₄⋊C₁₆	—	22	1	no	—
72	#346	—	22	1	no	—
73	C₄×C₁₆	C₂×D₁₁	1	1	yes	characteristic
74	#335	C₂×D₁₁	1	2	yes	—
75	#333	—	22	2	no	—
76	C₂²×C₁₁	#466	1	1	yes	characteristic
77	C₄×C₁₁	—	2	1	no	—
78	C₄×C₁₁	#462	1	1	yes	characteristic
79	C₄×C₁₁	#473	1	1	yes	characteristic
80	C₄×C₁₁	#510	1	2	yes	—
81	Dic₁₁	—	4	1	no	—
82	Dic₁₁	—	4	1	no	—
83	Dic₁₁	—	16	2	no	—
84	C₄⋊Q₈	—	22	2	no	—
85	C₄×Q₈	—	11	1	no	—
86	C₂×C₁₆	—	22	1	no	—
87	C₂×C₁₆	D₄₄	1	1	yes	characteristic
88	C₂×C₁₆	D₄₄	1	1	yes	characteristic
89	#107	—	22	2	no	—
90	#107	—	22	2	no	—
91	#107	—	44	2	no	—
92	C₄⋊C₈	—	2	2	no	—
93	C₄⋊C₈	—	11	1	no	—
94	C₄⋊C₈	—	22	1	no	—
95	#103	—	44	2	no	—
96	C₄×C₈	—	22	1	no	—
97	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
98	C₂×C₁₁	#1674	1	1	yes	characteristic
99	C₂×C₁₁	#2219	1	1	yes	characteristic
100	C₂×C₁₁	#2221	1	1	yes	characteristic
101	C₂×Q₈	—	11	1	no	—
102	C₂×Q₈	—	44	2	no	—
103	C₂×C₈	—	4	2	no	—
104	C₂×C₈	—	22	1	no	—
105	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
106	C₂×C₈	#4343	1	1	yes	characteristic
107	C₄⋊C₄	—	11	1	no	—
108	C₄⋊C₄	—	22	1	no	—
109	C₄⋊C₄	—	44	2	no	—
110	C₄⋊C₄	—	44	2	no	—
111	C₄²	—	22	1	no	—
112	C₄²	D₄×D₁₁	1	1	yes	characteristic
113	C₁₆	—	2	1	no	—
114	C₁₆	—	44	1	no	—
115	C₁₆	Dic₄₄	1	2	yes	—
116	C₁₁	#12461	1	1	yes	characteristic, complemented, Sylow
117	Q₈	—	22	2	no	—
118	Q₈	—	176	2	no	—
119	C₂×C₄	—	22	1	no	—
120	C₂×C₄	—	22	1	no	—
121	C₂×C₄	—	88	2	no	—
122	C₂×C₄	#66948	1	1	yes	characteristic
123	C₂×C₄	D₈×D₁₁	1	1	yes	characteristic
124	C₂×C₄	#66972	1	1	yes	characteristic
125	C₈	—	2	1	no	—
126	C₈	—	8	2	no	—
127	C₈	—	44	1	no	—
128	C₈	C₂×Dic₄₄	1	1	yes	characteristic
129	C₈	#66962	1	1	yes	characteristic
130	C₂²	#10622496	1	1	yes	characteristic
131	C₄	—	2	1	no	—
132	C₄	—	44	1	no	—
133	C₄	—	44	1	no	—
134	C₄	—	176	2	no	—
135	C₄	#10622462	1	1	yes	characteristic
136	C₄	#10622509	1	1	yes	characteristic
137	C₄	#10622528	1	2	yes	—
138	C₂	#13068011	1	1	yes	characteristic
139	C₂	#13070725	1	1	yes	characteristic
140	C₂	#13070737	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13070891

C₂

yes

maximal, characteristic

#13070524

C₂

yes

maximal, characteristic

#13068021

C₂

yes

maximal

#13066675

C₂

yes

maximal

C₁₁×#1372

C₂

yes

maximal, characteristic

#10622463

—

#10622295

C₂²

yes

—

C₈×Dic₂₂

C₂²

yes

characteristic

C₄×C₁₁×C₁₆

C₂²

yes

characteristic

C₁₁×#335

C₂²

yes

—

#10622142

—

#10622142

—

#10622140

—

Dic₁₁⋊C₁₆

—

#10622119

—

C₄⋊(C₁₁⋊C₁₆)

C₂²

yes

characteristic

#66922

—

C₄×Dic₂₂

D₄

yes

characteristic

C₂×C₁₁×C₁₆

D₄

yes

characteristic

C₂×C₁₁×C₁₆

D₄

yes

characteristic

C₁₁×C₄⋊C₈

—

C₄×C₈×C₁₁

C₂³

yes

—

—

—

—

Dic₁₁⋊C₈

—

C₈×Dic₁₁

—

C₂×C₁₁⋊C₁₆

—

C₄⋊(C₁₁⋊C₈)

D₄

yes

characteristic

#12461

—

maximal, Sylow

C₂×Dic₂₂

—

C₂×Dic₂₂

D₈

yes

characteristic

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

C₂×D₄

yes

characteristic

C₂×C₈×C₁₁

#41

yes

characteristic

C₄²×C₁₁

C₂×D₄

yes

characteristic

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

D₈

yes

characteristic

Dic₁₁⋊C₄

—

C₄×Dic₁₁

—

C₂×C₁₁⋊C₈

—

C₁₁×C₁₆

—

C₁₁×C₁₆

Q₁₆

yes

—

C₁₁⋊C₁₆

—

—

—

—

D₁₁

yes

characteristic

#1365

—

C₂×C₄×C₁₁

#121

yes

characteristic

C₂×C₄×C₁₁

C₂×D₈

yes

characteristic

C₂×C₄×C₁₁

#135

yes

characteristic

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

Dic₂₂

—

Dic₂₂

—

C₈×C₁₁

—

C₈×C₁₁

—

C₈×C₁₁

C₂×Q₁₆

yes

characteristic

C₈×C₁₁

#137

yes

characteristic

C₁₁⋊C₈

—

#500

—

#477

—

C₈×Q₈

—

#366

—

#366

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

#346

—

C₄×C₁₆

C₂×D₁₁

yes

characteristic

#335

C₂×D₁₁

yes

—

#333

—

C₂²×C₁₁

#466

yes

characteristic

C₄×C₁₁

—

C₄×C₁₁

yes

C₄×C₁₁

yes

C₄×C₁₁

yes

—

Dic₁₁

—

Dic₁₁

—

Dic₁₁

—

C₄⋊Q₈

—

C₄×Q₈

—

C₂×C₁₆

—

C₂×C₁₆

D₄₄

yes

characteristic

C₂×C₁₆

D₄₄

yes

—

—

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

#103

—

C₄×C₈

—

C₄×C₈

C₂²×D₁₁

yes

C₂×C₁₁

yes

C₂×C₁₁

yes

100

C₂×C₁₁

#2221

yes

characteristic

101

C₂×Q₈

—

102

C₂×Q₈

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

C₂×D₄₄

yes

characteristic

106

C₂×C₈

#4343

yes

characteristic

107

C₄⋊C₄

—

108

C₄⋊C₄

—

109

C₄⋊C₄

—

110

C₄⋊C₄

—

111

C₄²

—

112

C₄²

D₄×D₁₁

yes

characteristic

113

C₁₆

—

114

C₁₆

—

115

C₁₆

Dic₄₄

yes

—

116

C₁₁

#12461

yes

characteristic, complemented, Sylow

117

Q₈

—

118

Q₈

—

176

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

#66948

yes

characteristic

123

C₂×C₄

D₈×D₁₁

yes

characteristic

124

C₂×C₄

#66972

yes

characteristic

125

C₈

—

126

C₈

—

127

C₈

—

128

C₈

C₂×Dic₄₄

yes

characteristic

129

C₈

#66962

yes

characteristic

130

C₂²

#10622496

yes

characteristic

131

C₄

—

132

C₄

—

133

C₄

—

134

C₄

—

176

—

135

C₄

#10622462

yes

characteristic

136

C₄

#10622509

yes

characteristic

137

C₄

#10622528

yes

—

138

C₂

#13068011

yes

characteristic

139

C₂

#13070725

yes

characteristic

140

C₂

#13070737

yes

characteristic

	subgroup	G/H
center	C₂²	#10622496
commutator, cosocle	C₄×C₈×C₁₁	C₂³
Frattini	C₄×C₈	C₂²×D₁₁
Fitting	C₁₁×#1372	C₂
socle, prime radical	C₂²×C₁₁	#466
hypercenter	#1372	D₁₁
hypocenter	C₁₁	#12461
LCS	G ▷ C₄×C₈×C₁₁ ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #1372

subgroup

G/H

center

C₂²

#10622496

commutator, cosocle

C₄×C₈×C₁₁

C₂³

Frattini

C₄×C₈

C₂²×D₁₁

Fitting

C₁₁×#1372

C₂

C₂²×C₁₁

D₁₁

C₁₁

G ▷ C₄×C₈×C₁₁ ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #1372

N	H ≅ G/N	type
116. C₁₁	#12461	semidirect

H ≅ G/N

type

116. C₁₁

#12461

semidirect

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

subgroup	index
#13070891	2
#13070524	2
#13068021	2
#13066675	2
C₁₁×#1372	2
#12461	11

subgroup

index

C₁₁×#1372

Subgroups — #14668155

Conjugacy classes of subgroups

Complements

Maximal subgroups