Group #14653276 — subgroups

Subgroups — #14653276

Order 2816.

558 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 119 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×#10622308	C₂	1	1	yes	maximal, characteristic
2	#13067285	C₂	1	4	yes	maximal, complemented
3	#13066908	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#1837	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₈₈	—	2	2	no	—
6	C₂×#66927	C₂²	1	2	yes	—
7	C₁₁×#423	C₂²	1	2	yes	—
8	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
9	#10622538	C₂²	1	2	yes	—
10	#10622308	—	2	2	no	—
11	#10622308	C₄	1	4	yes	—
12	C₁₁×#341	—	2	2	no	—
13	#10622123	—	2	8	no	—
14	#10622092	—	2	2	no	—
15	C₂²×D₄₄	—	2	2	no	—
16	C₂²×D₄₄	—	2	4	no	—
17	C₂×C₁₁×M₁₆	—	2	2	no	—
18	C₂²×C₈×C₁₁	D₄	1	2	yes	—
19	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
20	C₂×D₈₈	—	2	8	no	—
21	C₂×D₈₈	—	4	8	no	—
22	#66927	—	2	2	no	—
23	#66927	—	2	4	no	—
24	#66927	C₂×C₄	1	4	yes	—
25	C₁₁×C₄⋊C₈	—	2	4	no	—
26	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
27	C₄×C₈×C₁₁	D₄	1	2	yes	—
28	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
29	C₄⋊(C₁₁⋊C₈)	D₄	1	4	yes	—
30	C₄×C₁₁⋊C₈	—	2	2	no	—
31	#9780	—	11	1	no	maximal, Sylow
32	C₂³×D₁₁	—	4	2	no	—
33	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
34	C₂²×C₄×C₁₁	#41	1	2	yes	—
35	C₂×D₄₄	—	2	4	no	—
36	C₂×D₄₄	—	2	8	no	—
37	C₂×D₄₄	—	4	4	no	—
38	C₂×D₄₄	—	4	2	no	—
39	C₂×D₄₄	—	4	8	no	—
40	C₂×D₄₄	—	8	8	no	—
41	C₁₁×M₁₆	—	4	4	no	—
42	C₂×C₈×C₁₁	—	2	4	no	—
43	C₂×C₈×C₁₁	—	4	2	no	—
44	C₂×C₈×C₁₁	C₂²⋊C₄	1	4	yes	—
45	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
46	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
47	C₄²×C₁₁	C₂×D₄	1	2	yes	—
48	C₂×C₁₁⋊C₈	—	2	4	no	—
49	D₈₈	—	4	16	no	—
50	C₂×#493	—	11	1	no	—
51	#1837	D₁₁	1	1	yes	characteristic, complemented
52	#1545	—	11	4	no	—
53	#1452	—	11	1	no	—
54	C₂³×C₁₁	#124	1	1	yes	characteristic
55	C₂²×D₁₁	—	4	4	no	—
56	C₂²×D₁₁	—	8	8	no	—
57	C₂²×D₁₁	—	8	4	no	—
58	C₂×C₄×C₁₁	—	2	4	no	—
59	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
60	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
61	C₂×C₄×C₁₁	#121	1	2	yes	—
62	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
63	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	4	yes	—
64	D₄₄	—	4	8	no	—
65	D₄₄	—	8	8	no	—
66	D₄₄	—	8	8	no	—
67	D₄₄	—	8	4	no	—
68	C₈×C₁₁	—	2	4	no	—
69	C₈×C₁₁	—	8	2	no	—
70	C₁₁⋊C₈	—	4	4	no	—
71	C₂²×D₈	—	22	2	no	—
72	C₂×#127	—	11	2	no	—
73	#493	—	11	4	no	—
74	#493	—	22	2	no	—
75	#431	—	11	2	no	—
76	#423	C₂×D₁₁	1	2	yes	—
77	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
78	#341	—	2	2	no	—
79	#331	—	22	8	no	—
80	#322	—	22	2	no	—
81	C₂²×C₁₁	—	2	2	no	—
82	C₂²×C₁₁	#390	1	1	yes	characteristic
83	C₂²×C₁₁	#490	1	2	yes	—
84	C₂×D₁₁	—	8	4	no	—
85	C₂×D₁₁	—	8	8	no	—
86	C₂×D₁₁	—	16	8	no	—
87	C₄×C₁₁	—	2	2	no	—
88	C₄×C₁₁	#418	1	2	yes	—
89	C₄×C₁₁	#472	1	4	yes	—
90	C₄×C₁₁	#496	1	2	yes	—
91	C₂²×D₄	—	22	4	no	—
92	C₂²×D₄	—	22	2	no	—
93	C₂×D₈	—	22	8	no	—
94	C₂×D₈	—	44	8	no	—
95	C₂×M₁₆	—	2	2	no	—
96	C₂²×C₈	C₂²⋊D₁₁	1	2	yes	—
97	#127	—	11	4	no	—
98	#127	—	22	2	no	—
99	#127	—	22	4	no	—
100	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
101	C₄⋊C₈	—	2	4	no	—
102	C₄⋊C₈	—	11	4	no	—
103	C₂²⋊C₈	—	22	2	no	—
104	C₄×C₈	—	22	2	no	—
105	C₄×C₈	C₄×D₁₁	1	2	yes	—
106	C₄×C₈	D₄₄	1	2	yes	—
107	C₂×C₁₁	—	2	2	no	—
108	C₂×C₁₁	#1961	1	1	yes	characteristic
109	C₂×C₁₁	#1978	1	2	yes	—
110	D₁₁	—	16	4	no	—
111	C₂⁴	—	44	2	no	—
112	C₂×D₄	—	22	8	no	—
113	C₂×D₄	—	22	4	no	—
114	C₂×D₄	—	44	4	no	—
115	C₂×D₄	—	44	2	no	—
116	C₂×D₄	—	44	8	no	—
117	C₂×D₄	—	88	8	no	—
118	C₂²×C₄	#4343	1	2	yes	—
119	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
120	D₈	—	44	16	no	—
121	M₁₆	—	4	4	no	—
122	C₂×C₈	—	2	4	no	—
123	C₂×C₈	—	4	2	no	—
124	C₂×C₈	—	22	4	no	—
125	C₂×C₈	(C₂×D₁₁)⋊C₄	1	4	yes	—
126	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
127	C₄²	C₂×D₄₄	1	1	yes	characteristic
128	C₄²	D₄×D₁₁	1	2	yes	—
129	C₁₁	#9780	1	1	yes	characteristic, complemented, Sylow
130	C₂³	—	44	4	no	—
131	C₂³	—	88	8	no	—
132	C₂³	—	88	4	no	—
133	C₂³	#67000	1	1	yes	characteristic
134	D₄	—	44	8	no	—
135	D₄	—	88	8	no	—
136	D₄	—	88	8	no	—
137	D₄	—	88	4	no	—
138	C₂×C₄	—	2	4	no	—
139	C₂×C₄	#66946	1	2	yes	—
140	C₂×C₄	#66948	1	2	yes	—
141	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
142	C₂×C₄	#66993	1	1	yes	characteristic
143	C₂×C₄	#67002	1	4	yes	—
144	C₈	—	2	4	no	—
145	C₈	—	8	2	no	—
146	C₈	—	44	4	no	—
147	C₂²	—	2	2	no	—
148	C₂²	—	88	4	no	—
149	C₂²	—	88	8	no	—
150	C₂²	—	176	8	no	—
151	C₂²	#10622601	1	1	yes	characteristic
152	C₂²	#10622680	1	2	yes	—
153	C₄	—	2	2	no	—
154	C₄	#10622510	1	4	yes	—
155	C₄	#10622614	1	2	yes	—
156	C₄	#10622671	1	2	yes	—
157	C₂	—	2	2	no	—
158	C₂	—	176	4	no	—
159	C₂	#13069439	1	1	yes	characteristic
160	C₂	#13069524	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10622308

C₂

yes

maximal, characteristic

#13067285

C₂

yes

maximal, complemented

#13066908

C₂

yes

maximal, characteristic, complemented

C₁₁×#1837

C₂

yes

maximal, characteristic, complemented

C₂²×D₈₈

—

C₂×#66927

C₂²

yes

—

C₁₁×#423

C₂²

yes

—

C₂×C₄×C₈×C₁₁

C₂²

yes

characteristic

#10622538

C₂²

yes

—

#10622308

—

#10622308

C₄

yes

—

C₁₁×#341

—

#10622123

—

#10622092

—

C₂²×D₄₄

—

C₂²×D₄₄

—

C₂×C₁₁×M₁₆

—

C₂²×C₈×C₁₁

D₄

yes

—

C₂×C₄²×C₁₁

C₂³

yes

characteristic

C₂×D₈₈

—

C₂×D₈₈

—

#66927

—

#66927

—

#66927

C₂×C₄

yes

—

C₁₁×C₄⋊C₈

—

C₄×C₈×C₁₁

C₂×C₄

yes

—

C₄×C₈×C₁₁

D₄

yes

—

C₂²⋊(C₁₁⋊C₈)

—

C₄⋊(C₁₁⋊C₈)

D₄

yes

—

C₄×C₁₁⋊C₈

—

#9780

—

maximal, Sylow

C₂³×D₁₁

—

C₂²×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₁

#41

yes

—

C₂×D₄₄

—

C₂×D₄₄

—

C₂×D₄₄

—

C₂×D₄₄

—

C₂×D₄₄

—

C₂×D₄₄

—

C₁₁×M₁₆

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

C₂²⋊C₄

yes

—

C₄²×C₁₁

C₂²×C₄

yes

characteristic

C₄²×C₁₁

C₂×D₄

yes

characteristic

C₄²×C₁₁

C₂×D₄

yes

—

C₂×C₁₁⋊C₈

—

D₈₈

—

C₂×#493

—

#1837

D₁₁

yes

characteristic, complemented

#1545

—

#1452

—

C₂³×C₁₁

#124

yes

characteristic

C₂²×D₁₁

—

C₂²×D₁₁

—

C₂²×D₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₁

C₄×D₄

yes

—

C₂×C₄×C₁₁

#121

yes

—

C₂×C₄×C₁₁

#127

yes

characteristic

C₂×C₄×C₁₁

AGL(1,ℤ/8)

yes

—

D₄₄

—

D₄₄

—

D₄₄

—

D₄₄

—

C₈×C₁₁

—

C₈×C₁₁

—

C₁₁⋊C₈

—

C₂²×D₈

—

—

—

—

—

C₂×D₁₁

yes

—

C₂×C₄×C₈

C₂×D₁₁

yes

—

—

—

C₂²×C₁₁

—

C₂²×C₁₁

#390

yes

characteristic

C₂²×C₁₁

#490

yes

—

C₂×D₁₁

—

C₂×D₁₁

—

C₂×D₁₁

—

C₄×C₁₁

—

C₄×C₁₁

#418

yes

—

C₄×C₁₁

#472

yes

—

C₄×C₁₁

#496

yes

—

C₂²×D₄

—

C₂²×D₄

—

C₂×D₈

—

C₂×D₈

—

C₂×M₁₆

—

C₂²×C₈

C₂²⋊D₁₁

yes

—

#127

—

#127

—

#127

—

100

C₂×C₄²

C₂²×D₁₁

yes

characteristic

101

C₄⋊C₈

—

102

C₄⋊C₈

—

103

C₂²⋊C₈

—

104

C₄×C₈

—

105

C₄×C₈

C₄×D₁₁

yes

—

106

C₄×C₈

D₄₄

yes

—

107

C₂×C₁₁

—

108

C₂×C₁₁

#1961

yes

characteristic

109

C₂×C₁₁

#1978

yes

—

110

D₁₁

—

111

C₂⁴

—

112

C₂×D₄

—

113

C₂×D₄

—

114

C₂×D₄

—

115

C₂×D₄

—

116

C₂×D₄

—

117

C₂×D₄

—

118

C₂²×C₄

#4343

yes

—

119

C₂²×C₄

C₂×C₂²⋊D₁₁

yes

characteristic

120

D₈

—

121

M₁₆

—

122

C₂×C₈

—

123

C₂×C₈

—

124

C₂×C₈

—

125

C₂×C₈

(C₂×D₁₁)⋊C₄

yes

—

126

C₄²

C₂×C₄×D₁₁

yes

characteristic

127

C₄²

C₂×D₄₄

yes

characteristic

128

C₄²

D₄×D₁₁

yes

—

129

C₁₁

#9780

yes

characteristic, complemented, Sylow

130

C₂³

—

131

C₂³

—

132

C₂³

—

133

C₂³

#67000

yes

characteristic

134

D₄

—

135

D₄

—

136

D₄

—

137

D₄

—

138

C₂×C₄

—

139

C₂×C₄

#66946

yes

—

140

C₂×C₄

#66948

yes

—

141

C₂×C₄

C₂×(C₂×D₁₁)⋊C₄

yes

characteristic

142

C₂×C₄

#66993

yes

characteristic

143

C₂×C₄

#67002

yes

—

144

C₈

—

145

C₈

—

146

C₈

—

147

C₂²

—

148

C₂²

—

149

C₂²

—

150

C₂²

—

176

—

151

C₂²

#10622601

yes

characteristic

152

C₂²

#10622680

yes

—

153

C₄

—

154

C₄

#10622510

yes

—

155

C₄

#10622614

yes

—

156

C₄

#10622671

yes

—

157

C₂

—

158

C₂

—

176

—

159

C₂

#13069439

yes

characteristic

160

C₂

#13069524

yes

—

	subgroup	G/H
center	C₂²	#10622601
commutator	C₄²×C₁₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₁₁×#1837	C₂
socle	C₂²×C₁₁	#390
prime radical	C₂×#10622308	C₂
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	#1837	D₁₁
hypocenter	C₁₁	#9780
LCS	G ▷ C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1837

subgroup

G/H

center

C₂²

#10622601

commutator

C₄²×C₁₁

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₁

Fitting

C₁₁×#1837

C₂

C₂²×C₁₁

C₂

C₂×C₄²×C₁₁

C₂³

D₁₁

C₁₁

G ▷ C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1837

N	H ≅ G/N	type
2. #13067285	C₂	semidirect
3. #13066908	C₂	semidirect
4. C₁₁×#1837	C₂	semidirect
51. #1837	D₁₁	semidirect
129. C₁₁	#9780	semidirect

H ≅ G/N

type

2. #13067285

C₂

semidirect

3. #13066908

C₂

semidirect

4. C₁₁×#1837

C₂

semidirect

51. #1837

D₁₁

semidirect

129. C₁₁

#9780

semidirect

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

subgroup	index
C₂×#10622308	2
#13067285	2
#13066908	2
C₁₁×#1837	2
#9780	11

subgroup

index

C₁₁×#1837

Subgroups — #14653276

Conjugacy classes of subgroups

Complements

Maximal subgroups