Group #14647446 — subgroups

Subgroups — #14647446

Order 2816.

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

normal subgroups only

This group has 322 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	#13068733	C₂	1	1	yes	maximal, characteristic
2	#13068362	C₂	1	1	yes	maximal, characteristic
3	#13066450	C₂	1	4	yes	maximal
4	C₁₁×#1831	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
6	C₄³×C₁₁	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
8	C₂×C₄×C₁₁⋊C₈	C₂²	1	2	yes	—
9	C₁₁×#336	—	2	2	no	—
10	#10622162	—	2	2	no	—
11	#10622162	C₄	1	2	yes	—
12	#10622162	C₄	1	2	yes	—
13	C₂²×C₈×C₁₁	—	2	2	no	—
14	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄²×C₁₁	D₄	1	2	yes	—
17	C₂×C₄²×C₁₁	Q₈	1	2	yes	—
18	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
19	C₂²×C₁₁⋊C₈	—	2	2	no	—
20	C₂²×C₁₁⋊C₈	C₂×C₄	1	4	yes	—
21	C₁₁×C₄⋊C₈	—	2	4	no	—
22	C₄⋊(C₁₁⋊C₈)	—	2	4	no	—
23	C₄×C₁₁⋊C₈	—	2	2	no	—
24	C₄×C₁₁⋊C₈	—	2	2	no	—
25	#8788	—	11	1	no	maximal, Sylow
26	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
27	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
28	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
29	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
30	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
31	C₂×C₈×C₁₁	—	4	2	no	—
32	C₂×C₈×C₁₁	—	4	4	no	—
33	C₄²×C₁₁	—	2	2	no	—
34	C₄²×C₁₁	—	2	2	no	—
35	C₄²×C₁₁	—	2	4	no	—
36	C₄²×C₁₁	—	4	2	no	—
37	C₄²×C₁₁	#41	1	2	yes	—
38	C₄²×C₁₁	#41	1	2	yes	—
39	C₂×C₁₁⋊C₈	—	2	4	no	—
40	C₂×C₁₁⋊C₈	—	2	4	no	—
41	C₂×C₁₁⋊C₈	—	2	4	no	—
42	C₂×C₁₁⋊C₈	—	4	2	no	—
43	C₂×C₁₁⋊C₈	—	4	4	no	—
44	#1831	—	11	1	no	—
45	#1831	D₁₁	1	1	yes	characteristic
46	#1744	—	11	1	no	—
47	#1277	—	11	4	no	—
48	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
49	C₂×C₄×C₁₁	—	2	2	no	—
50	C₂×C₄×C₁₁	—	2	2	no	—
51	C₂×C₄×C₁₁	—	2	2	no	—
52	C₂×C₄×C₁₁	—	2	2	no	—
53	C₂×C₄×C₁₁	—	2	2	no	—
54	C₂×C₄×C₁₁	—	2	2	no	—
55	C₂×C₄×C₁₁	—	2	2	no	—
56	C₂×C₄×C₁₁	#117	1	2	yes	—
57	C₂×C₄×C₁₁	#124	1	1	yes	characteristic
58	C₂×C₄×C₁₁	#124	1	1	yes	characteristic
59	C₂×C₄×C₁₁	#125	1	2	yes	—
60	C₂×C₄×C₁₁	#131	1	2	yes	—
61	C₂×C₄×C₁₁	#131	1	2	yes	—
62	C₂×C₄×C₁₁	#135	1	4	yes	—
63	C₈×C₁₁	—	8	2	no	—
64	C₁₁⋊C₈	—	4	4	no	—
65	C₁₁⋊C₈	—	8	2	no	—
66	C₂×C₄⋊C₈	—	11	2	no	—
67	C₂×C₄⋊C₈	C₂×D₁₁	1	2	yes	—
68	C₂×C₄×C₈	—	11	2	no	—
69	C₄³	C₂×D₁₁	1	1	yes	characteristic
70	#336	—	2	2	no	—
71	#336	—	11	2	no	—
72	#336	—	11	2	no	—
73	#336	—	22	2	no	—
74	C₂²×C₁₁	#382	1	1	yes	characteristic
75	C₂²×C₁₁	#424	1	1	yes	characteristic
76	C₂²×C₁₁	#424	1	1	yes	characteristic
77	C₂²×C₁₁	#427	1	2	yes	—
78	C₂²×C₁₁	#430	1	2	yes	—
79	C₄×C₁₁	—	2	2	no	—
80	C₄×C₁₁	—	4	2	no	—
81	C₄×C₁₁	—	4	2	no	—
82	C₄×C₁₁	#433	1	4	yes	—
83	C₄×C₁₁	#488	1	2	yes	—
84	C₄×C₁₁	#488	1	2	yes	—
85	C₂²×C₈	—	2	2	no	—
86	C₂²×C₈	—	11	4	no	—
87	C₂²×C₈	—	22	2	no	—
88	C₂×C₄²	Dic₂₂	1	2	yes	—
89	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
90	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
91	C₂×C₄²	C₂²⋊D₁₁	1	2	yes	—
92	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
93	C₄⋊C₈	—	2	4	no	—
94	C₄⋊C₈	—	22	4	no	—
95	C₄×C₈	—	22	2	no	—
96	C₄×C₈	—	22	2	no	—
97	C₂×C₁₁	#1572	1	2	yes	—
98	C₂×C₁₁	#1572	1	2	yes	—
99	C₂×C₁₁	#1832	1	1	yes	characteristic
100	C₂×C₁₁	#1835	1	1	yes	characteristic
101	C₂×C₁₁	#1838	1	1	yes	characteristic
102	C₂²×C₄	Dic₁₁⋊C₄	1	2	yes	—
103	C₂²×C₄	Dic₁₁⋊C₄	1	2	yes	—
104	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
105	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
106	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
107	C₂×C₈	—	4	2	no	—
108	C₂×C₈	—	4	4	no	—
109	C₂×C₈	—	22	4	no	—
110	C₂×C₈	—	22	4	no	—
111	C₂×C₈	—	22	4	no	—
112	C₂×C₈	—	44	2	no	—
113	C₂×C₈	—	44	4	no	—
114	C₄²	—	2	2	no	—
115	C₄²	—	2	2	no	—
116	C₄²	—	2	4	no	—
117	C₄²	—	4	2	no	—
118	C₄²	#4341	1	2	yes	—
119	C₄²	#4343	1	2	yes	—
120	C₁₁	#8788	1	1	yes	characteristic, complemented, Sylow
121	C₂³	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
122	C₂×C₄	—	2	2	no	—
123	C₂×C₄	—	2	2	no	—
124	C₂×C₄	—	2	2	no	—
125	C₂×C₄	—	2	2	no	—
126	C₂×C₄	—	2	2	no	—
127	C₂×C₄	—	2	2	no	—
128	C₂×C₄	—	2	2	no	—
129	C₂×C₄	#66943	1	2	yes	—
130	C₂×C₄	#66945	1	2	yes	—
131	C₂×C₄	#66954	1	2	yes	—
132	C₂×C₄	#66960	1	2	yes	—
133	C₂×C₄	#66989	1	1	yes	characteristic
134	C₂×C₄	#67000	1	1	yes	characteristic
135	C₂×C₄	#67003	1	4	yes	—
136	C₈	—	8	2	no	—
137	C₈	—	44	4	no	—
138	C₈	—	88	2	no	—
139	C₂²	#10622590	1	1	yes	characteristic
140	C₂²	#10622611	1	2	yes	—
141	C₂²	#10622715	1	1	yes	characteristic
142	C₂²	#10622732	1	1	yes	characteristic
143	C₂²	#10622737	1	2	yes	—
144	C₄	—	2	2	no	—
145	C₄	—	4	2	no	—
146	C₄	—	4	2	no	—
147	C₄	#10622453	1	4	yes	—
148	C₄	#10622669	1	2	yes	—
149	C₄	#10622681	1	2	yes	—
150	C₂	#13067394	1	2	yes	—
151	C₂	#13067397	1	2	yes	—
152	C₂	#13068735	1	1	yes	characteristic
153	C₂	#13068746	1	1	yes	characteristic
154	C₂	#13068756	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13068733

C₂

yes

maximal, characteristic

#13068362

C₂

yes

maximal, characteristic

#13066450

C₂

yes

maximal

C₁₁×#1831

C₂

yes

maximal, characteristic

C₂×C₁₁×C₄⋊C₈

C₂²

yes

—

C₄³×C₁₁

C₂²

yes

characteristic

C₂×C₄⋊(C₁₁⋊C₈)

C₂²

yes

—

C₂×C₄×C₁₁⋊C₈

C₂²

yes

—

C₁₁×#336

—

#10622162

—

#10622162

C₄

yes

—

#10622162

C₄

yes

—

C₂²×C₈×C₁₁

—

C₂×C₄²×C₁₁

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₁

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₁

D₄

yes

—

C₂×C₄²×C₁₁

Q₈

yes

—

C₂×C₄²×C₁₁

C₂³

yes

characteristic

C₂²×C₁₁⋊C₈

—

C₂²×C₁₁⋊C₈

C₂×C₄

yes

—

C₁₁×C₄⋊C₈

—

C₄⋊(C₁₁⋊C₈)

—

C₄×C₁₁⋊C₈

—

C₄×C₁₁⋊C₈

—

#8788

—

maximal, Sylow

C₂²×C₄×C₁₁

C₄⋊C₄

yes

—

C₂²×C₄×C₁₁

C₄⋊C₄

yes

—

C₂²×C₄×C₁₁

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₁

C₂×Q₈

yes

characteristic

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₄²×C₁₁

—

C₄²×C₁₁

—

C₄²×C₁₁

—

C₄²×C₁₁

—

C₄²×C₁₁

#41

yes

—

C₄²×C₁₁

#41

yes

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

—

#1831

—

#1831

D₁₁

yes

characteristic

#1744

—

#1277

—

C₂³×C₁₁

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

#117

yes

—

C₂×C₄×C₁₁

yes

C₂×C₄×C₁₁

yes

C₂×C₄×C₁₁

yes

—

C₂×C₄×C₁₁

#131

yes

—

C₂×C₄×C₁₁

#131

yes

—

C₂×C₄×C₁₁

#135

yes

—

C₈×C₁₁

—

C₁₁⋊C₈

—

C₁₁⋊C₈

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

C₂×D₁₁

yes

—

C₂×C₄×C₈

—

C₄³

C₂×D₁₁

yes

—

—

—

—

C₂²×C₁₁

yes

C₂²×C₁₁

yes

C₂²×C₁₁

yes

C₂²×C₁₁

yes

—

C₂²×C₁₁

#430

yes

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

#433

yes

—

C₄×C₁₁

#488

yes

—

C₄×C₁₁

#488

yes

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

Dic₂₂

yes

—

C₂×C₄²

C₄×D₁₁

yes

characteristic

C₂×C₄²

C₄×D₁₁

yes

characteristic

C₂×C₄²

C₂²⋊D₁₁

yes

—

C₂×C₄²

C₂²×D₁₁

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₂×C₁₁

#1572

yes

—

C₂×C₁₁

#1572

yes

—

C₂×C₁₁

#1832

yes

characteristic

100

C₂×C₁₁

#1835

yes

characteristic

101

C₂×C₁₁

#1838

yes

characteristic

102

C₂²×C₄

Dic₁₁⋊C₄

yes

—

103

C₂²×C₄

Dic₁₁⋊C₄

yes

—

104

C₂²×C₄

C₂×Dic₂₂

yes

characteristic

105

C₂²×C₄

C₂×C₄×D₁₁

yes

characteristic

106

C₂²×C₄

C₂×C₂²⋊D₁₁

yes

characteristic

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₄²

—

115

C₄²

—

116

C₄²

—

117

C₄²

—

118

C₄²

#4341

yes

—

119

C₄²

#4343

yes

—

120

C₁₁

#8788

yes

characteristic, complemented, Sylow

121

C₂³

C₂×Dic₁₁⋊C₄

yes

characteristic

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

#66943

yes

—

130

C₂×C₄

#66945

yes

—

131

C₂×C₄

#66954

yes

—

132

C₂×C₄

#66960

yes

—

133

C₂×C₄

#66989

yes

characteristic

134

C₂×C₄

#67000

yes

characteristic

135

C₂×C₄

#67003

yes

—

136

C₈

—

137

C₈

—

138

C₈

—

139

C₂²

#10622590

yes

characteristic

140

C₂²

#10622611

yes

—

141

C₂²

#10622715

yes

characteristic

142

C₂²

#10622732

yes

characteristic

143

C₂²

#10622737

yes

—

144

C₄

—

145

C₄

—

146

C₄

—

147

C₄

#10622453

yes

—

148

C₄

#10622669

yes

—

149

C₄

#10622681

yes

—

150

C₂

#13067394

yes

—

151

C₂

#13067397

yes

—

152

C₂

#13068735

yes

characteristic

153

C₂

#13068746

yes

characteristic

154

C₂

#13068756

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₁₁
commutator	C₂²×C₄×C₁₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₁₁×#1831	C₂
socle, prime radical	C₂³×C₁₁	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	#1831	D₁₁
hypocenter	C₁₁	#8788
LCS	G ▷ C₂²×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ #1831

subgroup

G/H

center

C₂²×C₄

C₂×C₂²⋊D₁₁

commutator

C₂²×C₄×C₁₁

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₁

Fitting

C₁₁×#1831

C₂

socle, prime radical

C₂³×C₁₁

C₂×C₄⋊C₄

cosocle

C₂×C₄²×C₁₁

C₂³

D₁₁

C₁₁

G ▷ C₂²×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ #1831

N	H ≅ G/N	type
120. C₁₁	#8788	semidirect

H ≅ G/N

type

120. C₁₁

#8788

semidirect

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

subgroup	index
#13068733	2
#13068362	2
#13066450	2
C₁₁×#1831	2
#8788	11

subgroup

index

C₁₁×#1831

Subgroups — #14647446

Conjugacy classes of subgroups

Complements

Maximal subgroups