Group #14909275 — subgroups

Subgroups — #14909275

Order 2816.

482 conjugacy classes of subgroups; only the 219 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 219 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	#13079130	C₂	1	2	yes	maximal
2	#13070902	C₂	1	8	yes	maximal, complemented
3	#13070400	C₂	1	4	yes	maximal
4	C₂×C₁₁×#346	C₂	1	1	yes	maximal, characteristic
5	#10623001	—	2	2	no	—
6	C₂²×C₁₁×C₁₆	C₂²	1	2	yes	—
7	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
8	#10622719	—	2	2	no	—
9	#10622719	C₂²	1	4	yes	—
10	#10622296	—	2	2	no	—
11	#10622296	C₂²	1	4	yes	—
12	#10622295	C₂²	1	4	yes	—
13	#10622293	—	2	2	no	—
14	C₁₁×#346	C₂²	1	4	yes	—
15	#10622143	C₂²	1	8	yes	—
16	#10622142	C₂²	1	8	yes	—
17	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
18	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
19	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
20	#66979	—	2	4	no	—
21	#66977	—	4	4	no	—
22	#66923	—	2	4	no	—
23	#66922	—	2	4	no	—
24	C₄×Dic₂₂	—	4	4	no	—
25	C₂×C₁₁×C₁₆	Q₈	1	8	yes	complemented
26	C₂×C₁₁×C₁₆	C₂³	1	4	yes	—
27	C₄×C₈×C₁₁	D₄	1	2	yes	—
28	C₄×C₈×C₁₁	C₂³	1	2	yes	—
29	#66882	—	2	4	no	—
30	#66882	C₂³	1	8	yes	—
31	#66881	—	2	4	no	—
32	#66881	—	2	4	no	—
33	#33728	—	11	1	no	maximal, Sylow
34	C₂²×C₄×C₁₁	D₈	1	2	yes	—
35	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
36	C₂×Dic₂₂	—	4	4	no	—
37	C₂×C₈×C₁₁	Q₁₆	1	4	yes	—
38	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
39	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
40	C₂×C₈×C₁₁	C₂×Q₈	1	4	yes	—
41	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
42	C₄²×C₁₁	D₈	1	2	yes	—
43	C₄²×C₁₁	C₂×D₄	1	2	yes	—
44	C₂²⋊Dic₁₁	—	4	4	no	—
45	C₄⋊Dic₁₁	—	2	8	no	—
46	C₄⋊Dic₁₁	—	4	4	no	—
47	Dic₁₁⋊C₄	—	4	8	no	—
48	C₄×Dic₁₁	—	4	4	no	—
49	C₁₁×C₁₆	C₂×Q₈	1	8	yes	—
50	#3160	—	11	2	no	—
51	#2255	—	11	8	no	—
52	#2158	—	11	4	no	—
53	C₂×#346	D₁₁	1	1	yes	characteristic
54	C₂³×C₁₁	C₂×D₈	1	1	yes	characteristic
55	C₂×C₄×C₁₁	—	4	2	no	—
56	C₂×C₄×C₁₁	C₄⋊Q₈	1	2	yes	—
57	C₂×C₄×C₁₁	C₂×D₈	1	4	yes	—
58	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
59	C₂×C₄×C₁₁	C₂×Q₁₆	1	2	yes	—
60	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
61	C₂×Dic₁₁	—	4	8	no	—
62	Dic₂₂	—	8	8	no	—
63	C₈×C₁₁	C₄⋊Q₈	1	2	yes	—
64	C₈×C₁₁	C₂×Q₁₆	1	4	yes	—
65	C₈×C₁₁	C₂²×Q₈	1	2	yes	—
66	#533	—	22	2	no	—
67	C₂²×C₁₆	C₂×D₁₁	1	2	yes	—
68	#500	—	11	4	no	—
69	#499	—	11	4	no	—
70	#499	—	22	2	no	—
71	#498	—	22	2	no	—
72	#427	—	11	4	no	—
73	#427	—	22	2	no	—
74	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
75	#367	—	11	8	no	—
76	#366	—	11	8	no	—
77	#346	C₂×D₁₁	1	4	yes	—
78	C₂²×C₁₁	—	2	2	no	—
79	C₂²×C₁₁	#500	1	2	yes	—
80	C₂²×C₁₁	C₂²×D₈	1	1	yes	characteristic
81	C₄×C₁₁	—	2	4	no	—
82	C₄×C₁₁	#500	1	2	yes	—
83	C₄×C₁₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
84	C₄×C₁₁	C₂²×Q₁₆	1	1	yes	characteristic
85	Dic₁₁	—	8	8	no	—
86	C₂²×C₈	D₄₄	1	1	yes	characteristic
87	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
88	C₄⋊Q₈	—	22	4	no	—
89	#125	—	22	4	no	—
90	C₂²⋊Q₈	—	44	4	no	—
91	C₄×Q₈	—	44	4	no	—
92	#117	—	22	4	no	—
93	C₂×C₄²	D₄₄	1	1	yes	characteristic
94	C₂×C₁₆	Dic₂₂	1	8	yes	complemented
95	C₂×C₁₆	C₂²×D₁₁	1	4	yes	—
96	#107	—	11	8	no	—
97	#107	—	22	4	no	—
98	#106	—	22	4	no	—
99	#106	—	22	4	no	—
100	C₄×C₈	D₄₄	1	2	yes	—
101	C₄×C₈	C₂²×D₁₁	1	2	yes	—
102	C₂×C₁₁	—	2	2	no	—
103	C₂×C₁₁	C₂×#500	1	1	yes	characteristic
104	C₂×C₁₁	#3414	1	2	yes	—
105	C₂×Q₈	—	44	4	no	—
106	C₂²×C₄	D₈₈	1	2	yes	—
107	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
108	C₂×C₈	Dic₄₄	1	4	yes	—
109	C₂×C₈	C₂×Dic₂₂	1	4	yes	—
110	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
111	C₂×C₈	C₂×D₄₄	1	2	yes	—
112	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
113	C₄⋊C₄	—	22	8	no	—
114	C₄⋊C₄	—	44	8	no	—
115	C₄⋊C₄	—	44	4	no	—
116	C₂²⋊C₄	—	44	4	no	—
117	C₄²	—	44	4	no	—
118	C₄²	D₈₈	1	2	yes	—
119	C₄²	C₂×D₄₄	1	2	yes	—
120	C₁₆	C₂×Dic₂₂	1	8	yes	—
121	C₁₁	#33728	1	1	yes	characteristic, complemented, Sylow
122	C₂³	C₂×D₈₈	1	1	yes	characteristic
123	Q₈	—	88	8	no	—
124	C₂×C₄	—	4	2	no	—
125	C₂×C₄	—	44	8	no	—
126	C₂×C₄	#66922	1	2	yes	—
127	C₂×C₄	C₂×D₈₈	1	4	yes	—
128	C₂×C₄	C₂×D₈₈	1	1	yes	characteristic
129	C₂×C₄	C₂×Dic₄₄	1	2	yes	—
130	C₂×C₄	C₂²×D₄₄	1	1	yes	characteristic
131	C₈	#66922	1	2	yes	—
132	C₈	C₂×Dic₄₄	1	4	yes	—
133	C₈	C₂²×Dic₂₂	1	2	yes	—
134	C₂²	—	2	2	no	—
135	C₂²	#10622295	1	2	yes	—
136	C₂²	C₂²×D₈₈	1	1	yes	characteristic
137	C₄	—	2	4	no	—
138	C₄	—	88	8	no	—
139	C₄	#10622295	1	2	yes	—
140	C₄	C₂×#66922	1	1	yes	characteristic
141	C₄	C₂²×Dic₄₄	1	1	yes	characteristic
142	C₂	—	2	2	no	—
143	C₂	C₂×#10622295	1	1	yes	characteristic
144	C₂	#13081752	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13079130

C₂

yes

maximal

#13070902

C₂

yes

maximal, complemented

#13070400

C₂

yes

maximal

C₂×C₁₁×#346

C₂

yes

maximal, characteristic

#10623001

—

C₂²×C₁₁×C₁₆

C₂²

yes

—

C₂×C₄×C₈×C₁₁

C₂²

yes

characteristic

#10622719

—

#10622719

C₂²

yes

—

#10622296

—

#10622296

C₂²

yes

—

#10622295

C₂²

yes

—

#10622293

—

C₁₁×#346

C₂²

yes

—

#10622143

C₂²

yes

—

#10622142

C₂²

yes

—

C₂²×C₈×C₁₁

D₄

yes

characteristic

C₂²×C₈×C₁₁

C₂³

yes

characteristic

C₂×C₄²×C₁₁

D₄

yes

—

—

—

—

C₄×Dic₂₂

—

C₂×C₁₁×C₁₆

Q₈

yes

complemented

C₂×C₁₁×C₁₆

C₂³

yes

—

C₄×C₈×C₁₁

D₄

yes

—

C₄×C₈×C₁₁

C₂³

yes

—

#66882

—

#66882

C₂³

yes

—

—

—

—

C₂²×C₄×C₁₁

D₈

yes

—

C₂²×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂×Dic₂₂

—

C₂×C₈×C₁₁

Q₁₆

yes

—

C₂×C₈×C₁₁

C₂×D₄

yes

characteristic

C₂×C₈×C₁₁

C₂×D₄

yes

—

C₂×C₈×C₁₁

C₂×Q₈

yes

—

C₂×C₈×C₁₁

C₂⁴

yes

characteristic

C₄²×C₁₁

D₈

yes

—

C₄²×C₁₁

C₂×D₄

yes

—

C₂²⋊Dic₁₁

—

C₄⋊Dic₁₁

—

C₄⋊Dic₁₁

—

Dic₁₁⋊C₄

—

C₄×Dic₁₁

—

C₁₁×C₁₆

C₂×Q₈

yes

—

—

—

—

D₁₁

yes

characteristic

C₂³×C₁₁

C₂×D₈

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

C₄⋊Q₈

yes

—

C₂×C₄×C₁₁

C₂×D₈

yes

—

C₂×C₄×C₁₁

C₂×D₈

yes

characteristic

C₂×C₄×C₁₁

C₂×Q₁₆

yes

—

C₂×C₄×C₁₁

C₂²×D₄

yes

characteristic

C₂×Dic₁₁

—

Dic₂₂

—

C₈×C₁₁

C₄⋊Q₈

yes

—

C₈×C₁₁

C₂×Q₁₆

yes

—

C₈×C₁₁

C₂²×Q₈

yes

—

#533

—

C₂²×C₁₆

C₂×D₁₁

yes

—

—

—

—

—

—

—

C₂×C₄×C₈

C₂×D₁₁

yes

—

—

C₂×D₁₁

yes

—

C₂²×C₁₁

—

C₂²×C₁₁

#500

yes

—

C₂²×C₁₁

C₂²×D₈

yes

characteristic

C₄×C₁₁

—

C₄×C₁₁

#500

yes

—

C₄×C₁₁

C₂×C₄⋊Q₈

yes

characteristic

C₄×C₁₁

C₂²×Q₁₆

yes

characteristic

Dic₁₁

—

C₂²×C₈

D₄₄

yes

characteristic

C₂²×C₈

C₂²×D₁₁

yes

characteristic

C₄⋊Q₈

—

#125

—

C₂²⋊Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

D₄₄

yes

characteristic

C₂×C₁₆

Dic₂₂

yes

complemented

C₂×C₁₆

C₂²×D₁₁

yes

—

—

—

—

—

100

C₄×C₈

D₄₄

yes

—

101

C₄×C₈

C₂²×D₁₁

yes

—

102

C₂×C₁₁

—

103

C₂×C₁₁

C₂×#500

yes

characteristic

104

C₂×C₁₁

#3414

yes

—

105

C₂×Q₈

—

106

C₂²×C₄

D₈₈

yes

—

107

C₂²×C₄

C₂×D₄₄

yes

characteristic

108

C₂×C₈

Dic₄₄

yes

—

109

C₂×C₈

C₂×Dic₂₂

yes

—

110

C₂×C₈

C₂×D₄₄

yes

characteristic

111

C₂×C₈

C₂×D₄₄

yes

—

112

C₂×C₈

C₂³×D₁₁

yes

characteristic

113

C₄⋊C₄

—

114

C₄⋊C₄

—

115

C₄⋊C₄

—

116

C₂²⋊C₄

—

117

C₄²

—

118

C₄²

D₈₈

yes

—

119

C₄²

C₂×D₄₄

yes

—

120

C₁₆

C₂×Dic₂₂

yes

—

121

C₁₁

#33728

yes

characteristic, complemented, Sylow

122

C₂³

C₂×D₈₈

yes

characteristic

123

Q₈

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

#66922

yes

—

127

C₂×C₄

C₂×D₈₈

yes

—

128

C₂×C₄

C₂×D₈₈

yes

characteristic

129

C₂×C₄

C₂×Dic₄₄

yes

—

130

C₂×C₄

C₂²×D₄₄

yes

characteristic

131

C₈

#66922

yes

—

132

C₈

C₂×Dic₄₄

yes

—

133

C₈

C₂²×Dic₂₂

yes

—

134

C₂²

—

135

C₂²

#10622295

yes

—

136

C₂²

C₂²×D₈₈

yes

characteristic

137

C₄

—

138

C₄

—

139

C₄

#10622295

yes

—

140

C₄

C₂×#66922

yes

characteristic

141

C₄

C₂²×Dic₄₄

yes

characteristic

142

C₂

—

143

C₂

C₂×#10622295

yes

characteristic

144

C₂

#13081752

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×D₈₈
commutator, cosocle	C₂×C₈×C₁₁	C₂⁴
Frattini	C₂×C₈	C₂³×D₁₁
Fitting	C₂×C₁₁×#346	C₂
socle	C₂²×C₁₁	C₂²×D₈
prime radical	C₂³×C₁₁	C₂×D₈
hypercenter	C₂×#346	D₁₁
hypocenter	C₁₁	#33728
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#346

subgroup

G/H

center

C₂×C₄

C₂×D₈₈

commutator, cosocle

C₂×C₈×C₁₁

C₂⁴

Frattini

C₂×C₈

C₂³×D₁₁

Fitting

C₂×C₁₁×#346

C₂

socle

C₂²×C₁₁

C₂²×D₈

prime radical

C₂³×C₁₁

C₂×D₈

D₁₁

C₁₁

G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#346

N	H ≅ G/N	type
2. #13070902	C₂	semidirect
25. C₂×C₁₁×C₁₆	Q₈	semidirect
94. C₂×C₁₆	Dic₂₂	semidirect
121. C₁₁	#33728	semidirect

H ≅ G/N

type

2. #13070902

C₂

semidirect

25. C₂×C₁₁×C₁₆

Q₈

semidirect

94. C₂×C₁₆

Dic₂₂

semidirect

121. C₁₁

#33728

semidirect

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

subgroup	index
#13079130	2
#13070902	2
#13070400	2
C₂×C₁₁×#346	2
#33728	11

subgroup

index

C₂×C₁₁×#346

Subgroups — #14909275

Conjugacy classes of subgroups

Complements

Maximal subgroups