Group #14668133 — subgroups

Subgroups — #14668133

Order 2816.

204 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 69 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	C₁₆×Dic₂₂	C₂	1	1	yes	maximal, characteristic
3	#13068011	C₂	1	2	yes	maximal
4	#13066672	C₂	1	2	yes	maximal
5	C₁₁×#1371	C₂	1	1	yes	maximal, characteristic
6	#10622462	—	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	Dic₁₁⋊C₁₆	—	2	1	no	—
14	C₁₆×Dic₁₁	—	2	1	no	—
15	#10622120	—	2	2	no	—
16	C₄⋊(C₁₁⋊C₁₆)	C₂²	1	1	yes	characteristic
17	C₂×Dic₄₄	—	4	2	no	—
18	#66922	—	2	2	no	—
19	C₄×Dic₂₂	D₄	1	1	yes	characteristic
20	C₂×C₁₁×C₁₆	D₄	1	1	yes	characteristic
21	C₂×C₁₁×C₁₆	D₄	1	1	yes	characteristic
22	C₁₁×C₄⋊C₈	—	2	2	no	—
23	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
24	#66882	—	2	2	no	—
25	#66882	—	2	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	#12457	—	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	Dic₄₄	—	8	4	no	—
45	C₁₁×C₁₆	—	2	1	no	—
46	C₁₁×C₁₆	Q₁₆	1	2	yes	complemented
47	C₁₁⋊C₁₆	—	4	1	no	—
48	#2252	—	11	1	no	—
49	Q₈×C₁₆	—	11	1	no	—
50	#1674	—	11	2	no	—
51	#1371	D₁₁	1	1	yes	characteristic
52	#1364	—	11	2	no	—
53	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
54	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
55	C₂×C₄×C₁₁	#135	1	1	yes	characteristic
56	C₂×Dic₁₁	—	2	1	no	—
57	C₂×Dic₁₁	—	2	1	no	—
58	C₂×Dic₁₁	—	8	2	no	—
59	Dic₂₂	—	2	1	no	—
60	Dic₂₂	—	8	2	no	—
61	Dic₂₂	—	8	2	no	—
62	Dic₂₂	D₁₆	1	2	yes	—
63	C₈×C₁₁	—	2	1	no	—
64	C₈×C₁₁	—	8	2	no	—
65	C₈×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
66	C₈×C₁₁	#137	1	1	yes	characteristic
67	C₁₁⋊C₈	—	4	1	no	—
68	#500	—	11	2	no	—
69	#462	—	22	2	no	—
70	C₈×Q₈	—	11	1	no	—
71	#366	—	22	1	no	—
72	#366	—	22	1	no	—
73	C₄⋊C₁₆	—	11	1	no	—
74	C₄⋊C₁₆	—	22	1	no	—
75	C₄×C₁₆	—	22	1	no	—
76	C₄×C₁₆	C₂×D₁₁	1	1	yes	characteristic
77	#335	C₂×D₁₁	1	2	yes	—
78	#332	—	22	2	no	—
79	C₂²×C₁₁	#466	1	1	yes	characteristic
80	C₄×C₁₁	—	2	1	no	—
81	C₄×C₁₁	#462	1	1	yes	characteristic
82	C₄×C₁₁	#473	1	1	yes	characteristic
83	C₄×C₁₁	C₂×D₁₆	1	1	yes	characteristic
84	C₄×C₁₁	#508	1	1	yes	characteristic
85	Dic₁₁	—	2	2	no	—
86	Dic₁₁	—	4	1	no	—
87	Dic₁₁	—	16	2	no	—
88	C₂×Q₁₆	—	44	2	no	—
89	C₄⋊Q₈	—	22	2	no	—
90	C₄×Q₈	—	11	1	no	—
91	C₂×C₁₆	—	22	1	no	—
92	C₂×C₁₆	D₄₄	1	1	yes	characteristic
93	C₂×C₁₆	D₄₄	1	1	yes	characteristic
94	#107	—	22	2	no	—
95	#107	—	22	2	no	—
96	C₄⋊C₈	—	2	2	no	—
97	C₄⋊C₈	—	11	1	no	—
98	C₄⋊C₈	—	22	1	no	—
99	#103	—	44	2	no	—
100	C₄×C₈	—	22	1	no	—
101	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
102	C₂×C₁₁	#1674	1	1	yes	characteristic
103	C₂×C₁₁	#2215	1	1	yes	characteristic
104	C₂×C₁₁	#2222	1	1	yes	characteristic
105	C₂×Q₈	—	11	1	no	—
106	C₂×Q₈	—	44	2	no	—
107	Q₁₆	—	88	4	no	—
108	C₂×C₈	—	4	2	no	—
109	C₂×C₈	—	22	1	no	—
110	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
111	C₂×C₈	#4343	1	1	yes	characteristic
112	C₄⋊C₄	—	11	1	no	—
113	C₄⋊C₄	—	22	1	no	—
114	C₄⋊C₄	—	44	2	no	—
115	C₄⋊C₄	—	44	2	no	—
116	C₄²	—	22	1	no	—
117	C₄²	D₄×D₁₁	1	1	yes	characteristic
118	C₁₆	—	2	1	no	—
119	C₁₆	—	44	1	no	—
120	C₁₆	Dic₄₄	1	2	yes	complemented
121	C₁₁	#12457	1	1	yes	characteristic, complemented, Sylow
122	Q₈	—	11	2	no	—
123	Q₈	—	22	1	no	—
124	Q₈	—	88	2	no	—
125	Q₈	—	88	2	no	—
126	C₂×C₄	—	22	1	no	—
127	C₂×C₄	—	22	1	no	—
128	C₂×C₄	—	88	2	no	—
129	C₂×C₄	#66948	1	1	yes	characteristic
130	C₂×C₄	D₈×D₁₁	1	1	yes	characteristic
131	C₂×C₄	#66972	1	1	yes	characteristic
132	C₈	—	2	1	no	—
133	C₈	—	8	2	no	—
134	C₈	—	44	1	no	—
135	C₈	C₂×Dic₄₄	1	1	yes	characteristic
136	C₈	#66962	1	1	yes	characteristic
137	C₂²	#10622496	1	1	yes	characteristic
138	C₄	—	2	1	no	—
139	C₄	—	22	2	no	—
140	C₄	—	44	1	no	—
141	C₄	—	176	2	no	—
142	C₄	#10622462	1	1	yes	characteristic
143	C₄	#10622509	1	1	yes	characteristic
144	C₄	D₁₁×D₁₆	1	1	yes	characteristic
145	C₄	#10622532	1	1	yes	characteristic
146	C₂	#13068011	1	1	yes	characteristic
147	C₂	#13070703	1	1	yes	characteristic
148	C₂	#13070742	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13070891

C₂

yes

maximal, characteristic

C₁₆×Dic₂₂

C₂

yes

maximal, characteristic

#13068011

C₂

yes

maximal

#13066672

C₂

yes

maximal

C₁₁×#1371

C₂

yes

maximal, characteristic

#10622462

—

#10622295

C₂²

yes

—

C₈×Dic₂₂

C₂²

yes

characteristic

C₄×C₁₁×C₁₆

C₂²

yes

characteristic

C₁₁×#335

C₂²

yes

—

#10622142

—

#10622142

—

Dic₁₁⋊C₁₆

—

C₁₆×Dic₁₁

—

#10622120

—

C₄⋊(C₁₁⋊C₁₆)

C₂²

yes

characteristic

C₂×Dic₄₄

—

#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

#12457

—

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

—

Dic₄₄

—

C₁₁×C₁₆

—

C₁₁×C₁₆

Q₁₆

yes

complemented

C₁₁⋊C₁₆

—

#2252

—

Q₈×C₁₆

—

#1674

—

#1371

D₁₁

yes

characteristic

#1364

—

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

—

Dic₂₂

—

Dic₂₂

D₁₆

yes

—

C₈×C₁₁

—

C₈×C₁₁

—

C₈×C₁₁

C₂×Q₁₆

yes

characteristic

C₈×C₁₁

#137

yes

characteristic

C₁₁⋊C₈

—

#500

—

#462

—

C₈×Q₈

—

#366

—

#366

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

C₄×C₁₆

—

C₄×C₁₆

C₂×D₁₁

yes

characteristic

#335

C₂×D₁₁

yes

—

#332

—

C₂²×C₁₁

#466

yes

characteristic

C₄×C₁₁

—

C₄×C₁₁

yes

C₄×C₁₁

yes

C₄×C₁₁

C₂×D₁₆

yes

characteristic

C₄×C₁₁

#508

yes

characteristic

Dic₁₁

—

Dic₁₁

—

Dic₁₁

—

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄×Q₈

—

C₂×C₁₆

—

C₂×C₁₆

D₄₄

yes

characteristic

C₂×C₁₆

D₄₄

yes

characteristic

#107

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

#103

—

100

C₄×C₈

—

101

C₄×C₈

C₂²×D₁₁

yes

characteristic

102

C₂×C₁₁

#1674

yes

characteristic

103

C₂×C₁₁

#2215

yes

characteristic

104

C₂×C₁₁

#2222

yes

characteristic

105

C₂×Q₈

—

106

C₂×Q₈

—

107

Q₁₆

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

C₂×D₄₄

yes

characteristic

111

C₂×C₈

#4343

yes

characteristic

112

C₄⋊C₄

—

113

C₄⋊C₄

—

114

C₄⋊C₄

—

115

C₄⋊C₄

—

116

C₄²

—

117

C₄²

D₄×D₁₁

yes

characteristic

118

C₁₆

—

119

C₁₆

—

120

C₁₆

Dic₄₄

yes

complemented

121

C₁₁

#12457

yes

characteristic, complemented, Sylow

122

Q₈

—

123

Q₈

—

124

Q₈

—

125

Q₈

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

#66948

yes

characteristic

130

C₂×C₄

D₈×D₁₁

yes

characteristic

131

C₂×C₄

#66972

yes

characteristic

132

C₈

—

133

C₈

—

134

C₈

—

135

C₈

C₂×Dic₄₄

yes

characteristic

136

C₈

#66962

yes

characteristic

137

C₂²

#10622496

yes

characteristic

138

C₄

—

139

C₄

—

140

C₄

—

141

C₄

—

176

—

142

C₄

#10622462

yes

characteristic

143

C₄

#10622509

yes

characteristic

144

C₄

D₁₁×D₁₆

yes

characteristic

145

C₄

#10622532

yes

characteristic

146

C₂

#13068011

yes

characteristic

147

C₂

#13070703

yes

characteristic

148

C₂

#13070742

yes

characteristic

	subgroup	G/H
center	C₂²	#10622496
commutator, cosocle	C₄×C₈×C₁₁	C₂³
Frattini	C₄×C₈	C₂²×D₁₁
Fitting	C₁₁×#1371	C₂
socle, prime radical	C₂²×C₁₁	#466
hypercenter	#1371	D₁₁
hypocenter	C₁₁	#12457
LCS	G ▷ C₄×C₈×C₁₁ ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #1371

subgroup

G/H

center

C₂²

#10622496

commutator, cosocle

C₄×C₈×C₁₁

C₂³

Frattini

C₄×C₈

C₂²×D₁₁

Fitting

C₁₁×#1371

C₂

C₂²×C₁₁

D₁₁

C₁₁

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

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #1371

N	H ≅ G/N	type
46. C₁₁×C₁₆	Q₁₆	semidirect
120. C₁₆	Dic₄₄	semidirect
121. C₁₁	#12457	semidirect

H ≅ G/N

type

46. C₁₁×C₁₆

Q₁₆

semidirect

120. C₁₆

Dic₄₄

semidirect

121. C₁₁

#12457

semidirect

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

subgroup	index
#13070891	2
C₁₆×Dic₂₂	2
#13068011	2
#13066672	2
C₁₁×#1371	2
#12457	11

subgroup

index

C₁₆×Dic₂₂

C₁₁×#1371

Subgroups — #14668133

Conjugacy classes of subgroups

Complements

Maximal subgroups