Group #14668151 — subgroups

Subgroups — #14668151

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	#13070524	C₂	1	1	yes	maximal, characteristic
2	#13068017	C₂	1	2	yes	maximal
3	#13066690	C₂	1	1	yes	maximal, characteristic
4	#13066674	C₂	1	2	yes	maximal
5	C₁₁×#2252	C₂	1	1	yes	maximal, characteristic
6	C₁₁×#500	C₂²	1	2	yes	—
7	#10622704	—	2	2	no	—
8	C₈×Dic₂₂	C₂²	1	1	yes	characteristic
9	C₁₁×#366	—	2	1	no	—
10	C₁₁×#366	—	2	1	no	—
11	C₄×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
12	#10622184	—	2	2	no	—
13	#10622140	—	2	1	no	—
14	Dic₁₁⋊C₁₆	—	2	1	no	—
15	C₄⋊(C₁₁⋊C₁₆)	C₂²	1	1	yes	characteristic
16	#10622096	C₂²	1	2	yes	—
17	C₁₁×C₄⋊Q₈	—	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×#107	—	2	2	no	—
22	C₁₁×#107	—	2	2	no	—
23	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
24	Dic₁₁⋊C₈	—	2	1	no	—
25	C₈×Dic₁₁	—	2	1	no	—
26	C₂×C₁₁⋊C₁₆	—	2	1	no	—
27	#66874	—	4	2	no	—
28	#66871	—	4	2	no	—
29	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
30	C₄⋊(C₁₁⋊C₈)	D₄	1	1	yes	characteristic
31	#12461	—	11	1	no	maximal, Sylow
32	C₂×Q₈×C₁₁	—	4	2	no	—
33	C₂×Dic₂₂	D₈	1	1	yes	characteristic
34	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
35	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
36	C₁₁×C₄⋊C₄	—	4	2	no	—
37	C₁₁×C₄⋊C₄	—	4	2	no	—
38	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
39	C₄⋊Dic₁₁	D₈	1	1	yes	characteristic
40	Dic₁₁⋊C₄	—	2	1	no	—
41	C₄×Dic₁₁	—	2	1	no	—
42	C₂×C₁₁⋊C₈	—	2	1	no	—
43	C₂×C₁₁⋊C₈	—	4	2	no	—
44	C₁₁×C₁₆	—	2	1	no	—
45	C₁₁×C₁₆	Q₁₆	1	2	yes	—
46	C₁₁⋊C₁₆	—	4	1	no	—
47	#2252	D₁₁	1	1	yes	characteristic
48	#2183	—	11	1	no	—
49	#1676	—	11	2	no	—
50	#1372	—	11	1	no	—
51	#1365	—	11	2	no	—
52	Q₈×C₁₁	—	16	2	no	—
53	C₂×C₄×C₁₁	—	8	2	no	—
54	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
55	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
56	C₂×C₄×C₁₁	#135	1	1	yes	characteristic
57	C₂×Dic₁₁	—	2	1	no	—
58	C₂×Dic₁₁	—	2	1	no	—
59	Dic₂₂	—	2	2	no	—
60	C₈×C₁₁	—	2	1	no	—
61	C₈×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
62	C₈×C₁₁	#137	1	1	yes	characteristic
63	C₁₁⋊C₈	—	4	1	no	—
64	C₁₁⋊C₈	—	8	2	no	—
65	#500	C₂×D₁₁	1	2	yes	—
66	#477	—	22	2	no	—
67	C₈×Q₈	—	11	1	no	—
68	#366	—	2	1	no	—
69	#366	—	2	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	—	11	2	no	—
75	#333	—	22	2	no	—
76	C₂²×C₁₁	#466	1	1	yes	characteristic
77	C₄×C₁₁	—	2	1	no	—
78	C₄×C₁₁	—	16	2	no	—
79	C₄×C₁₁	#462	1	1	yes	characteristic
80	C₄×C₁₁	#473	1	1	yes	characteristic
81	C₄×C₁₁	#510	1	2	yes	—
82	Dic₁₁	—	4	1	no	—
83	Dic₁₁	—	4	1	no	—
84	C₄⋊Q₈	—	2	2	no	—
85	C₄×Q₈	—	11	1	no	—
86	C₂×C₁₆	—	22	1	no	—
87	C₂×C₁₆	C₂²⋊D₁₁	1	1	yes	characteristic
88	C₂×C₁₆	C₂²⋊D₁₁	1	1	yes	characteristic
89	#107	—	2	2	no	—
90	#107	—	2	2	no	—
91	#107	—	44	2	no	—
92	C₄⋊C₈	—	11	1	no	—
93	C₄⋊C₈	—	22	1	no	—
94	C₄⋊C₈	—	22	2	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	—	4	2	no	—
102	C₂×Q₈	—	11	1	no	—
103	C₂×C₈	—	22	1	no	—
104	C₂×C₈	—	44	2	no	—
105	C₂×C₈	#4341	1	1	yes	characteristic
106	C₂×C₈	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
107	C₄⋊C₄	—	4	2	no	—
108	C₄⋊C₄	—	4	2	no	—
109	C₄⋊C₄	—	11	1	no	—
110	C₄⋊C₄	—	22	1	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	#4326	1	2	yes	—
116	C₁₁	#12461	1	1	yes	characteristic, complemented, Sylow
117	Q₈	—	16	2	no	—
118	Q₈	—	22	2	no	—
119	C₂×C₄	—	8	2	no	—
120	C₂×C₄	—	22	1	no	—
121	C₂×C₄	—	22	1	no	—
122	C₂×C₄	D₈×D₁₁	1	1	yes	characteristic
123	C₂×C₄	#66965	1	1	yes	characteristic
124	C₂×C₄	#66991	1	1	yes	characteristic
125	C₈	—	2	1	no	—
126	C₈	—	44	1	no	—
127	C₈	—	88	2	no	—
128	C₈	#66995	1	1	yes	characteristic
129	C₈	C₂×#4326	1	1	yes	characteristic
130	C₂²	#10622770	1	1	yes	characteristic
131	C₄	—	2	1	no	—
132	C₄	—	16	2	no	—
133	C₄	—	44	1	no	—
134	C₄	—	44	1	no	—
135	C₄	#10622531	1	2	yes	—
136	C₄	#10622703	1	1	yes	characteristic
137	C₄	#10622805	1	1	yes	characteristic
138	C₂	#13068007	1	1	yes	characteristic
139	C₂	#13070721	1	1	yes	characteristic
140	C₂	#13070733	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13070524

C₂

yes

maximal, characteristic

#13068017

C₂

yes

maximal

#13066690

C₂

yes

maximal, characteristic

#13066674

C₂

yes

maximal

C₁₁×#2252

C₂

yes

maximal, characteristic

C₁₁×#500

C₂²

yes

—

#10622704

—

C₈×Dic₂₂

C₂²

yes

characteristic

C₁₁×#366

—

C₁₁×#366

—

C₄×C₁₁×C₁₆

C₂²

yes

characteristic

#10622184

—

#10622140

—

Dic₁₁⋊C₁₆

—

C₄⋊(C₁₁⋊C₁₆)

C₂²

yes

characteristic

#10622096

C₂²

yes

—

C₁₁×C₄⋊Q₈

—

C₄×Dic₂₂

D₄

yes

characteristic

C₂×C₁₁×C₁₆

D₄

yes

characteristic

C₂×C₁₁×C₁₆

D₄

yes

characteristic

C₁₁×#107

—

C₁₁×#107

—

C₄×C₈×C₁₁

C₂³

yes

characteristic

Dic₁₁⋊C₈

—

C₈×Dic₁₁

—

C₂×C₁₁⋊C₁₆

—

#66874

—

#66871

—

C₄⋊(C₁₁⋊C₈)

—

C₄⋊(C₁₁⋊C₈)

D₄

yes

characteristic

#12461

—

maximal, Sylow

C₂×Q₈×C₁₁

—

C₂×Dic₂₂

D₈

yes

characteristic

C₂×C₈×C₁₁

C₂×D₄

yes

characteristic

C₂×C₈×C₁₁

#41

yes

characteristic

C₁₁×C₄⋊C₄

—

C₁₁×C₄⋊C₄

—

C₄²×C₁₁

C₂×D₄

yes

characteristic

C₄⋊Dic₁₁

D₈

yes

characteristic

Dic₁₁⋊C₄

—

C₄×Dic₁₁

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

—

C₁₁×C₁₆

—

C₁₁×C₁₆

Q₁₆

yes

—

C₁₁⋊C₁₆

—

#2252

D₁₁

yes

—

—

—

—

Q₈×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

#121

yes

characteristic

C₂×C₄×C₁₁

C₂×D₈

yes

characteristic

C₂×C₄×C₁₁

#135

yes

characteristic

C₂×Dic₁₁

—

C₂×Dic₁₁

—

Dic₂₂

—

C₈×C₁₁

—

C₈×C₁₁

C₂×Q₁₆

yes

characteristic

C₈×C₁₁

#137

yes

characteristic

C₁₁⋊C₈

—

C₁₁⋊C₈

—

#500

C₂×D₁₁

yes

—

#477

—

C₈×Q₈

—

#366

—

#366

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

#346

—

C₄×C₁₆

C₂×D₁₁

yes

characteristic

#335

—

#333

—

C₂²×C₁₁

#466

yes

characteristic

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

yes

C₄×C₁₁

yes

C₄×C₁₁

yes

—

Dic₁₁

—

Dic₁₁

—

C₄⋊Q₈

—

C₄×Q₈

—

C₂×C₁₆

—

C₂×C₁₆

C₂²⋊D₁₁

yes

characteristic

C₂×C₁₆

C₂²⋊D₁₁

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

#4341

yes

characteristic

106

C₂×C₈

C₂×C₂²⋊D₁₁

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

#4326

yes

—

116

C₁₁

#12461

yes

characteristic, complemented, Sylow

117

Q₈

—

118

Q₈

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

D₈×D₁₁

yes

characteristic

123

C₂×C₄

#66965

yes

characteristic

124

C₂×C₄

#66991

yes

characteristic

125

C₈

—

126

C₈

—

127

C₈

—

128

C₈

#66995

yes

characteristic

129

C₈

C₂×#4326

yes

characteristic

130

C₂²

#10622770

yes

characteristic

131

C₄

—

132

C₄

—

133

C₄

—

134

C₄

—

135

C₄

#10622531

yes

—

136

C₄

#10622703

yes

characteristic

137

C₄

#10622805

yes

characteristic

138

C₂

#13068007

yes

characteristic

139

C₂

#13070721

yes

characteristic

140

C₂

#13070733

yes

characteristic

	subgroup	G/H
center	C₂²	#10622770
commutator, cosocle	C₄×C₈×C₁₁	C₂³
Frattini	C₄×C₈	C₂²×D₁₁
Fitting	C₁₁×#2252	C₂
socle, prime radical	C₂²×C₁₁	#466
hypercenter	#2252	D₁₁
hypocenter	C₁₁	#12461
LCS	G ▷ C₄×C₈×C₁₁ ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #2252

subgroup

G/H

center

C₂²

#10622770

commutator, cosocle

C₄×C₈×C₁₁

C₂³

Frattini

C₄×C₈

C₂²×D₁₁

Fitting

C₁₁×#2252

C₂

C₂²×C₁₁

D₁₁

C₁₁

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

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #2252

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
#13070524	2
#13068017	2
#13066690	2
#13066674	2
C₁₁×#2252	2
#12461	11

subgroup

index

C₁₁×#2252

Subgroups — #14668151

Conjugacy classes of subgroups

Complements

Maximal subgroups