Group #14647575 — subgroups

Subgroups — #14647575

Order 2816.

354 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 171 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	#13068788	C₂	1	1	yes	maximal, characteristic
2	#13067374	C₂	1	4	yes	maximal
3	C₂×C₈×C₁₁⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1848	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₁×#108	—	2	2	no	—
6	C₁₁×#423	C₂²	1	2	yes	—
7	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
8	C₂×#66883	—	2	2	no	—
9	#10622537	C₂²	1	2	yes	—
10	C₂×C₄×C₁₁⋊C₈	C₂²	1	2	yes	—
11	#10622117	—	2	8	no	—
12	C₈×C₁₁⋊C₈	C₄	1	1	yes	characteristic
13	C₈×C₁₁⋊C₈	C₄	1	2	yes	—
14	C₈×C₁₁⋊C₈	C₄	1	1	yes	characteristic
15	C₂×C₁₁×M₁₆	—	2	2	no	—
16	C₂²×C₈×C₁₁	D₄	1	2	yes	—
17	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
18	C₂×#4318	—	2	2	no	—
19	C₂²×C₁₁⋊C₈	Q₈	1	4	yes	—
20	C₁₁×#108	—	4	4	no	—
21	C₁₁×C₄⋊C₈	—	2	4	no	—
22	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
23	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
24	C₄×C₈×C₁₁	Q₈	1	2	yes	—
25	#66883	—	4	4	no	—
26	C₄⋊(C₁₁⋊C₈)	—	2	4	no	—
27	C₄×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
28	C₄×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
29	C₄×C₁₁⋊C₈	D₄	1	4	yes	—
30	#8823	—	11	1	no	maximal, Sylow
31	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
32	C₂²×C₄×C₁₁	C₂×Q₈	1	2	yes	—
33	C₁₁×M₁₆	—	4	4	no	—
34	C₂×C₈×C₁₁	—	4	2	no	—
35	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
36	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
37	C₂×C₈×C₁₁	D₈	1	4	yes	—
38	C₂×C₈×C₁₁	Q₁₆	1	4	yes	—
39	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
40	C₄²×C₁₁	C₂×D₄	1	2	yes	—
41	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
42	#4318	—	4	4	no	—
43	C₂×C₁₁⋊C₈	—	2	8	no	—
44	C₂×C₁₁⋊C₈	—	4	2	no	—
45	C₂×C₁₁⋊C₈	C₄⋊C₄	1	4	yes	—
46	C₂×C₁₁⋊C₈	C₄⋊C₄	1	4	yes	—
47	#1848	—	11	1	no	—
48	#1848	D₁₁	1	1	yes	characteristic
49	#1567	—	11	4	no	—
50	C₂×C₈²	—	11	1	no	—
51	C₂³×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
52	C₂×C₄×C₁₁	—	2	4	no	—
53	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
54	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
55	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
56	C₂×C₄×C₁₁	C₄⋊Q₈	1	2	yes	—
57	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
58	C₂×C₄×C₁₁	C₂×Q₁₆	1	2	yes	—
59	C₈×C₁₁	—	8	2	no	—
60	C₈×C₁₁	#107	1	4	yes	—
61	C₈×C₁₁	#107	1	4	yes	—
62	C₁₁⋊C₈	—	2	4	no	—
63	C₁₁⋊C₈	—	8	2	no	—
64	C₁₁⋊C₈	#108	1	8	yes	complemented
65	C₂×#108	—	2	2	no	—
66	C₂×#108	—	22	2	no	—
67	#423	—	11	2	no	—
68	#423	C₂×D₁₁	1	2	yes	—
69	C₂×C₄×C₈	—	11	2	no	—
70	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
71	#335	—	22	8	no	—
72	C₈²	—	11	1	no	—
73	C₈²	—	11	2	no	—
74	C₈²	—	11	1	no	—
75	C₂²×C₁₁	—	2	2	no	—
76	C₂²×C₁₁	#384	1	1	yes	characteristic
77	C₂²×C₁₁	#500	1	2	yes	—
78	C₄×C₁₁	—	2	2	no	—
79	C₄×C₁₁	C₂×#107	1	2	yes	—
80	C₄×C₁₁	C₂×#108	1	4	yes	—
81	C₄×C₁₁	#493	1	1	yes	characteristic
82	C₄×C₁₁	#494	1	1	yes	characteristic
83	C₂×M₁₆	—	2	2	no	—
84	C₂×M₁₆	—	22	2	no	—
85	C₂²×C₈	—	11	4	no	—
86	C₂²×C₈	C₂²⋊D₁₁	1	2	yes	—
87	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
88	#108	—	4	4	no	—
89	#108	—	44	4	no	—
90	C₄⋊C₈	—	2	4	no	—
91	C₄⋊C₈	—	22	4	no	—
92	C₄×C₈	—	11	2	no	—
93	C₄×C₈	—	11	2	no	—
94	C₄×C₈	—	11	4	no	—
95	C₄×C₈	Dic₂₂	1	2	yes	—
96	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
97	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
98	C₂×C₁₁	—	2	2	no	—
99	C₂×C₁₁	#1845	1	1	yes	characteristic
100	C₂×C₁₁	#1848	1	2	yes	—
101	C₂²×C₄	Q₈×D₁₁	1	2	yes	—
102	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
103	M₁₆	—	4	4	no	—
104	M₁₆	—	44	4	no	—
105	C₂×C₈	—	4	2	no	—
106	C₂×C₈	—	11	4	no	—
107	C₂×C₈	—	11	4	no	—
108	C₂×C₈	—	22	8	no	—
109	C₂×C₈	—	44	2	no	—
110	C₂×C₈	Dic₁₁⋊C₄	1	2	yes	—
111	C₂×C₈	Dic₁₁⋊C₄	1	2	yes	—
112	C₂×C₈	#4323	1	4	yes	—
113	C₂×C₈	#4326	1	4	yes	—
114	C₄²	C₂×Dic₂₂	1	1	yes	characteristic
115	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
116	C₄²	D₄×D₁₁	1	2	yes	—
117	C₁₁	#8823	1	1	yes	characteristic, complemented, Sylow
118	C₂³	#66997	1	1	yes	characteristic
119	C₂×C₄	—	2	4	no	—
120	C₂×C₄	#66941	1	2	yes	—
121	C₂×C₄	C₄⋊C₄×D₁₁	1	2	yes	—
122	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
123	C₂×C₄	C₂×#4323	1	2	yes	—
124	C₂×C₄	#66993	1	1	yes	characteristic
125	C₂×C₄	C₂×#4326	1	2	yes	—
126	C₈	—	8	2	no	—
127	C₈	—	11	8	no	—
128	C₈	—	22	4	no	—
129	C₈	—	88	2	no	—
130	C₈	#66871	1	4	yes	—
131	C₈	#66871	1	4	yes	—
132	C₂²	—	2	2	no	—
133	C₂²	#10622589	1	1	yes	characteristic
134	C₂²	#10622691	1	2	yes	—
135	C₄	—	2	2	no	—
136	C₄	D₁₁×#108	1	4	yes	—
137	C₄	C₂×#66871	1	2	yes	—
138	C₄	#10622686	1	1	yes	characteristic
139	C₄	#10622705	1	1	yes	characteristic
140	C₂	—	2	2	no	—
141	C₂	#13068775	1	1	yes	characteristic
142	C₂	#13068786	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13068788

C₂

yes

maximal, characteristic

#13067374

C₂

yes

maximal

C₂×C₈×C₁₁⋊C₈

C₂

yes

maximal, characteristic

C₁₁×#1848

C₂

yes

maximal, characteristic

C₂×C₁₁×#108

—

C₁₁×#423

C₂²

yes

—

C₂×C₄×C₈×C₁₁

C₂²

yes

characteristic

C₂×#66883

—

#10622537

C₂²

yes

—

C₂×C₄×C₁₁⋊C₈

C₂²

yes

—

#10622117

—

C₈×C₁₁⋊C₈

C₄

yes

characteristic

C₈×C₁₁⋊C₈

C₄

yes

—

C₈×C₁₁⋊C₈

C₄

yes

characteristic

C₂×C₁₁×M₁₆

—

C₂²×C₈×C₁₁

D₄

yes

—

C₂×C₄²×C₁₁

C₂³

yes

characteristic

C₂×#4318

—

C₂²×C₁₁⋊C₈

Q₈

yes

—

C₁₁×#108

—

C₁₁×C₄⋊C₈

—

C₄×C₈×C₁₁

C₂×C₄

yes

characteristic

C₄×C₈×C₁₁

C₂×C₄

yes

characteristic

C₄×C₈×C₁₁

Q₈

yes

—

#66883

—

C₄⋊(C₁₁⋊C₈)

—

C₄×C₁₁⋊C₈

C₂×C₄

yes

—

C₄×C₁₁⋊C₈

C₂×C₄

yes

—

C₄×C₁₁⋊C₈

D₄

yes

—

#8823

—

maximal, Sylow

C₂²×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₁

C₂×Q₈

yes

—

C₁₁×M₁₆

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

C₄⋊C₄

yes

—

C₂×C₈×C₁₁

C₄⋊C₄

yes

—

C₂×C₈×C₁₁

D₈

yes

—

C₂×C₈×C₁₁

Q₁₆

yes

—

C₄²×C₁₁

C₂²×C₄

yes

characteristic

C₄²×C₁₁

C₂×D₄

yes

—

C₄²×C₁₁

C₂×Q₈

yes

characteristic

#4318

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

C₄⋊C₄

yes

—

C₂×C₁₁⋊C₈

C₄⋊C₄

yes

—

#1848

—

#1848

D₁₁

yes

characteristic

#1567

—

C₂×C₈²

—

C₂³×C₁₁

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₁₁

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₁

#127

yes

characteristic

C₂×C₄×C₁₁

C₄⋊Q₈

yes

—

C₂×C₄×C₁₁

C₂×D₈

yes

—

C₂×C₄×C₁₁

C₂×Q₁₆

yes

—

C₈×C₁₁

—

C₈×C₁₁

#107

yes

—

C₈×C₁₁

#107

yes

—

C₁₁⋊C₈

—

C₁₁⋊C₈

—

C₁₁⋊C₈

yes

—

—

—

C₂×D₁₁

yes

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₁₁

yes

characteristic

#335

—

C₈²

—

C₈²

—

C₈²

—

C₂²×C₁₁

—

C₂²×C₁₁

#384

yes

characteristic

C₂²×C₁₁

#500

yes

—

C₄×C₁₁

—

C₄×C₁₁

C₂×#107

yes

—

C₄×C₁₁

C₂×#108

yes

—

C₄×C₁₁

yes

C₄×C₁₁

yes

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

C₂²⋊D₁₁

yes

—

C₂×C₄²

C₂²×D₁₁

yes

characteristic

#108

—

#108

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

Dic₂₂

yes

—

C₄×C₈

C₄×D₁₁

yes

characteristic

C₄×C₈

C₄×D₁₁

yes

characteristic

C₂×C₁₁

—

C₂×C₁₁

#1845

yes

characteristic

100

C₂×C₁₁

#1848

yes

—

101

C₂²×C₄

Q₈×D₁₁

yes

—

102

C₂²×C₄

C₂×C₂²⋊D₁₁

yes

characteristic

103

M₁₆

—

104

M₁₆

—

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

Dic₁₁⋊C₄

yes

—

111

C₂×C₈

Dic₁₁⋊C₄

yes

—

112

C₂×C₈

#4323

yes

—

113

C₂×C₈

#4326

yes

—

114

C₄²

C₂×Dic₂₂

yes

characteristic

115

C₄²

C₂×C₄×D₁₁

yes

characteristic

116

C₄²

D₄×D₁₁

yes

—

117

C₁₁

#8823

yes

characteristic, complemented, Sylow

118

C₂³

#66997

yes

characteristic

119

C₂×C₄

—

120

C₂×C₄

#66941

yes

—

121

C₂×C₄

C₄⋊C₄×D₁₁

yes

—

122

C₂×C₄

C₂×Dic₁₁⋊C₄

yes

characteristic

123

C₂×C₄

C₂×#4323

yes

—

124

C₂×C₄

#66993

yes

characteristic

125

C₂×C₄

C₂×#4326

yes

—

126

C₈

—

127

C₈

—

128

C₈

—

129

C₈

—

130

C₈

#66871

yes

—

131

C₈

#66871

yes

—

132

C₂²

—

133

C₂²

#10622589

yes

characteristic

134

C₂²

#10622691

yes

—

135

C₄

—

136

C₄

D₁₁×#108

yes

—

137

C₄

C₂×#66871

yes

—

138

C₄

#10622686

yes

characteristic

139

C₄

#10622705

yes

characteristic

140

C₂

—

141

C₂

#13068775

yes

characteristic

142

C₂

#13068786

yes

—

	subgroup	G/H
center	C₂×C₄	#66993
commutator	C₄²×C₁₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₁₁×#1848	C₂
socle	C₂²×C₁₁	#384
prime radical	C₂³×C₁₁	C₄⋊Q₈
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	#1848	D₁₁
hypocenter	C₁₁	#8823
LCS	G ▷ C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1848

subgroup

G/H

center

C₂×C₄

#66993

commutator

C₄²×C₁₁

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₁

Fitting

C₁₁×#1848

C₂

socle

C₂²×C₁₁

#384

prime radical

C₂³×C₁₁

C₄⋊Q₈

cosocle

C₂×C₄²×C₁₁

C₂³

D₁₁

C₁₁

G ▷ C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1848

N	H ≅ G/N	type
64. C₁₁⋊C₈	#108	semidirect
117. C₁₁	#8823	semidirect

H ≅ G/N

type

64. C₁₁⋊C₈

#108

semidirect

117. C₁₁

#8823

semidirect

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

subgroup	index
#13068788	2
#13067374	2
C₂×C₈×C₁₁⋊C₈	2
C₁₁×#1848	2
#8823	11

subgroup

index

#13068788

#13067374

C₂×C₈×C₁₁⋊C₈

C₁₁×#1848

#8823

Subgroups — #14647575

Conjugacy classes of subgroups

Complements

Maximal subgroups