Group #14670165 — subgroups

Subgroups — #14670165

Order 2816.

274 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 139 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	C₂×#10622099	C₂	1	1	yes	maximal, characteristic
2	#13068788	C₂	1	1	yes	maximal, characteristic
3	#13066709	C₂	1	4	yes	maximal
4	C₁₁×#1848	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₁×#108	—	2	1	no	—
6	C₂×C₁₁×#108	C₂²	1	2	yes	—
7	C₁₁×#423	—	2	1	no	—
8	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
9	C₂×#66883	—	2	1	no	—
10	C₂×#66883	C₂²	1	2	yes	—
11	C₂²×C₁₁⋊C₁₆	C₂²	1	2	yes	—
12	#10622537	—	2	1	no	—
13	#10622099	C₄	1	4	yes	—
14	C₂×C₁₁×M₁₆	—	2	2	no	—
15	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
16	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
17	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
18	C₂×#4318	—	2	2	no	—
19	C₁₁×#108	—	2	4	no	—
20	C₁₁×#108	—	4	2	no	—
21	C₁₁×C₄⋊C₈	—	4	2	no	—
22	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
23	C₄×C₈×C₁₁	Q₈	1	2	yes	—
24	#66883	—	2	4	no	—
25	#66883	—	4	2	no	—
26	C₂×C₁₁⋊C₁₆	—	2	2	no	—
27	C₂×C₁₁⋊C₁₆	—	2	2	no	—
28	C₂×C₁₁⋊C₁₆	C₂×C₄	1	4	yes	—
29	C₄⋊(C₁₁⋊C₈)	—	4	2	no	—
30	#12892	—	11	1	no	maximal, Sylow
31	C₂²×C₄×C₁₁	Q₁₆	1	2	yes	—
32	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
33	C₁₁×M₁₆	—	4	2	no	—
34	C₁₁×M₁₆	—	4	2	no	—
35	C₂×C₈×C₁₁	—	4	2	no	—
36	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
37	C₂×C₈×C₁₁	SD₁₆	1	2	yes	—
38	C₂×C₈×C₁₁	SD₁₆	1	2	yes	—
39	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
40	C₂×C₈×C₁₁	C₂×Q₈	1	1	yes	characteristic
41	C₂×C₈×C₁₁	#41	1	2	yes	—
42	C₂×C₈×C₁₁	#41	1	2	yes	—
43	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
44	C₄²×C₁₁	D₈	1	2	yes	—
45	#4318	—	4	2	no	—
46	#4318	—	4	2	no	—
47	C₂×C₁₁⋊C₈	—	4	2	no	—
48	C₁₁⋊C₁₆	—	2	4	no	—
49	C₂×#346	—	11	1	no	—
50	#1848	—	11	1	no	—
51	#1848	D₁₁	1	1	yes	characteristic
52	#1381	—	11	4	no	—
53	C₂³×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
54	C₂×C₄×C₁₁	—	4	2	no	—
55	C₂×C₄×C₁₁	#107	1	4	yes	—
56	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
57	C₂×C₄×C₁₁	#124	1	1	yes	characteristic
58	C₂×C₄×C₁₁	#124	1	1	yes	characteristic
59	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
60	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
61	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
62	C₈×C₁₁	—	8	2	no	—
63	C₈×C₁₁	#106	1	4	yes	—
64	C₈×C₁₁	#117	1	2	yes	—
65	C₈×C₁₁	#125	1	2	yes	—
66	C₁₁⋊C₈	—	8	2	no	—
67	C₂²×C₁₆	—	11	2	no	—
68	C₂×#108	—	2	1	no	—
69	C₂×#108	—	11	2	no	—
70	C₂×#108	—	22	1	no	—
71	C₂×#108	C₂×D₁₁	1	2	yes	—
72	#423	—	2	1	no	—
73	#423	—	22	1	no	—
74	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
75	#346	—	11	4	no	—
76	C₂²×C₁₁	—	2	2	no	—
77	C₂²×C₁₁	C₂×#107	1	1	yes	characteristic
78	C₂²×C₁₁	#487	1	1	yes	characteristic
79	C₂²×C₁₁	#487	1	1	yes	characteristic
80	C₄×C₁₁	—	2	4	no	—
81	C₄×C₁₁	#382	1	1	yes	characteristic
82	C₄×C₁₁	C₂×#106	1	1	yes	characteristic
83	C₄×C₁₁	#486	1	1	yes	characteristic
84	C₄×C₁₁	#486	1	1	yes	characteristic
85	C₂×M₁₆	—	2	2	no	—
86	C₂×M₁₆	—	22	2	no	—
87	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
88	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
89	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
90	C₂×C₁₆	—	11	4	no	—
91	C₂×C₁₆	—	22	2	no	—
92	C₂×C₁₆	—	22	2	no	—
93	#108	—	2	4	no	—
94	#108	—	4	2	no	—
95	#108	—	22	4	no	—
96	#108	—	44	2	no	—
97	C₄⋊C₈	—	4	2	no	—
98	C₄⋊C₈	—	44	2	no	—
99	C₄×C₈	Dic₂₂	1	2	yes	—
100	C₄×C₈	C₄×D₁₁	1	2	yes	—
101	C₂×C₁₁	—	2	1	no	—
102	C₂×C₁₁	—	2	1	no	—
103	C₂×C₁₁	#1834	1	1	yes	characteristic
104	C₂×C₁₁	#2161	1	2	yes	—
105	C₂²×C₄	#4326	1	2	yes	—
106	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
107	M₁₆	—	4	2	no	—
108	M₁₆	—	4	2	no	—
109	M₁₆	—	44	2	no	—
110	M₁₆	—	44	2	no	—
111	C₂×C₈	—	4	2	no	—
112	C₂×C₈	—	44	2	no	—
113	C₂×C₈	Dic₁₁⋊C₄	1	2	yes	—
114	C₂×C₈	#4324	1	2	yes	—
115	C₂×C₈	#4325	1	2	yes	—
116	C₂×C₈	C₂×Dic₂₂	1	1	yes	characteristic
117	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
118	C₂×C₈	#4341	1	2	yes	—
119	C₂×C₈	#4343	1	2	yes	—
120	C₄²	Dic₁₁⋊C₄	1	2	yes	—
121	C₄²	#4323	1	2	yes	—
122	C₁₆	—	22	4	no	—
123	C₁₁	#12892	1	1	yes	characteristic, complemented, Sylow
124	C₂³	C₂×#4326	1	1	yes	characteristic
125	C₂×C₄	—	4	2	no	—
126	C₂×C₄	#66871	1	4	yes	—
127	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
128	C₂×C₄	C₂×#4323	1	1	yes	characteristic
129	C₂×C₄	C₂×#4324	1	1	yes	characteristic
130	C₂×C₄	#66989	1	1	yes	characteristic
131	C₂×C₄	C₂×#4325	1	1	yes	characteristic
132	C₂×C₄	#67000	1	1	yes	characteristic
133	C₈	—	8	2	no	—
134	C₈	—	88	2	no	—
135	C₈	#66872	1	4	yes	—
136	C₈	#66943	1	2	yes	—
137	C₈	#66945	1	2	yes	—
138	C₂²	—	2	2	no	—
139	C₂²	C₂×#66871	1	1	yes	characteristic
140	C₂²	#10622694	1	1	yes	characteristic
141	C₂²	#10622706	1	1	yes	characteristic
142	C₄	—	2	4	no	—
143	C₄	C₂×#66872	1	1	yes	characteristic
144	C₄	#10622590	1	1	yes	characteristic
145	C₄	#10622683	1	1	yes	characteristic
146	C₄	#10622701	1	1	yes	characteristic
147	C₂	—	2	1	no	—
148	C₂	—	2	1	no	—
149	C₂	#13068743	1	1	yes	characteristic
150	C₂	#13070410	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10622099

C₂

yes

maximal, characteristic

#13068788

C₂

yes

maximal, characteristic

#13066709

C₂

yes

maximal

C₁₁×#1848

C₂

yes

maximal, characteristic

C₂×C₁₁×#108

—

C₂×C₁₁×#108

C₂²

yes

—

C₁₁×#423

—

C₂×C₄×C₈×C₁₁

C₂²

yes

characteristic

C₂×#66883

—

C₂×#66883

C₂²

yes

—

C₂²×C₁₁⋊C₁₆

C₂²

yes

—

#10622537

—

#10622099

C₄

yes

—

C₂×C₁₁×M₁₆

—

C₂²×C₈×C₁₁

D₄

yes

characteristic

C₂²×C₈×C₁₁

C₂³

yes

characteristic

C₂×C₄²×C₁₁

D₄

yes

characteristic

C₂×#4318

—

C₁₁×#108

—

C₁₁×#108

—

C₁₁×C₄⋊C₈

—

C₄×C₈×C₁₁

C₂×C₄

yes

—

C₄×C₈×C₁₁

Q₈

yes

—

#66883

—

#66883

—

C₂×C₁₁⋊C₁₆

—

C₂×C₁₁⋊C₁₆

—

C₂×C₁₁⋊C₁₆

C₂×C₄

yes

—

C₄⋊(C₁₁⋊C₈)

—

#12892

—

maximal, Sylow

C₂²×C₄×C₁₁

Q₁₆

yes

—

C₂²×C₄×C₁₁

C₂×D₄

yes

characteristic

C₁₁×M₁₆

—

C₁₁×M₁₆

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

C₄⋊C₄

yes

—

C₂×C₈×C₁₁

SD₁₆

yes

—

C₂×C₈×C₁₁

SD₁₆

yes

—

C₂×C₈×C₁₁

C₂²×C₄

yes

characteristic

C₂×C₈×C₁₁

C₂×Q₈

yes

characteristic

C₂×C₈×C₁₁

#41

yes

—

C₂×C₈×C₁₁

#41

yes

—

C₄²×C₁₁

C₄⋊C₄

yes

—

C₄²×C₁₁

D₈

yes

—

#4318

—

#4318

—

C₂×C₁₁⋊C₈

—

C₁₁⋊C₁₆

—

C₂×#346

—

#1848

—

#1848

D₁₁

yes

characteristic

#1381

—

C₂³×C₁₁

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

#107

yes

—

C₂×C₄×C₁₁

C₂×C₄⋊C₄

yes

C₂×C₄×C₁₁

yes

C₂×C₄×C₁₁

yes

C₂×C₄×C₁₁

C₂×D₈

yes

characteristic

C₂×C₄×C₁₁

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₁₁

C₂×SD₁₆

yes

characteristic

C₈×C₁₁

—

C₈×C₁₁

#106

yes

—

C₈×C₁₁

#117

yes

—

C₈×C₁₁

#125

yes

—

C₁₁⋊C₈

—

C₂²×C₁₆

—

—

—

—

C₂×D₁₁

yes

—

#423

—

#423

—

C₂×C₄×C₈

C₂×D₁₁

yes

characteristic

#346

—

C₂²×C₁₁

—

C₂²×C₁₁

yes

C₂²×C₁₁

yes

C₂²×C₁₁

yes

C₄×C₁₁

—

C₄×C₁₁

yes

C₄×C₁₁

yes

C₄×C₁₁

yes

C₄×C₁₁

yes

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

C₂²⋊D₁₁

yes

characteristic

C₂²×C₈

C₂²×D₁₁

yes

characteristic

C₂×C₄²

C₂²⋊D₁₁

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

—

—

—

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄×C₈

Dic₂₂

yes

—

100

C₄×C₈

C₄×D₁₁

yes

—

101

C₂×C₁₁

—

102

C₂×C₁₁

—

103

C₂×C₁₁

#1834

yes

characteristic

104

C₂×C₁₁

#2161

yes

—

105

C₂²×C₄

#4326

yes

—

106

C₂²×C₄

C₂×C₂²⋊D₁₁

yes

characteristic

107

M₁₆

—

108

M₁₆

—

109

M₁₆

—

110

M₁₆

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

Dic₁₁⋊C₄

yes

—

114

C₂×C₈

#4324

yes

—

115

C₂×C₈

#4325

yes

—

116

C₂×C₈

C₂×Dic₂₂

yes

characteristic

117

C₂×C₈

C₂×C₄×D₁₁

yes

characteristic

118

C₂×C₈

#4341

yes

—

119

C₂×C₈

#4343

yes

—

120

C₄²

Dic₁₁⋊C₄

yes

—

121

C₄²

#4323

yes

—

122

C₁₆

—

123

C₁₁

#12892

yes

characteristic, complemented, Sylow

124

C₂³

C₂×#4326

yes

characteristic

125

C₂×C₄

—

126

C₂×C₄

#66871

yes

—

127

C₂×C₄

C₂×Dic₁₁⋊C₄

yes

characteristic

128

C₂×C₄

C₂×#4323

yes

characteristic

129

C₂×C₄

C₂×#4324

yes

characteristic

130

C₂×C₄

#66989

yes

characteristic

131

C₂×C₄

C₂×#4325

yes

characteristic

132

C₂×C₄

#67000

yes

characteristic

133

C₈

—

134

C₈

—

135

C₈

#66872

yes

—

136

C₈

#66943

yes

—

137

C₈

#66945

yes

—

138

C₂²

—

139

C₂²

C₂×#66871

yes

characteristic

140

C₂²

#10622694

yes

characteristic

141

C₂²

#10622706

yes

characteristic

142

C₄

—

143

C₄

C₂×#66872

yes

characteristic

144

C₄

#10622590

yes

characteristic

145

C₄

#10622683

yes

characteristic

146

C₄

#10622701

yes

characteristic

147

C₂

—

148

C₂

—

149

C₂

#13068743

yes

characteristic

150

C₂

#13070410

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×#4323
commutator	C₂×C₈×C₁₁	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₁₁
Fitting	C₁₁×#1848	C₂
socle	C₂²×C₁₁	C₂×#107
prime radical	C₂³×C₁₁	C₂×Q₁₆
cosocle	C₂²×C₈×C₁₁	C₂³
hypercenter	#1848	D₁₁
hypocenter	C₁₁	#12892
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #1848

subgroup

G/H

center

C₂×C₄

C₂×#4323

commutator

C₂×C₈×C₁₁

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₁₁

Fitting

C₁₁×#1848

C₂

socle

C₂²×C₁₁

C₂×#107

prime radical

C₂³×C₁₁

C₂×Q₁₆

cosocle

C₂²×C₈×C₁₁

C₂³

D₁₁

C₁₁

G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #1848

N	H ≅ G/N	type
123. C₁₁	#12892	semidirect

H ≅ G/N

type

123. C₁₁

#12892

semidirect

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

subgroup	index
C₂×#10622099	2
#13068788	2
#13066709	2
C₁₁×#1848	2
#12892	11

subgroup

index

C₁₁×#1848

Subgroups — #14670165

Conjugacy classes of subgroups

Complements

Maximal subgroups