Group #14653274 — subgroups

Subgroups — #14653274

Order 2816.

454 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 127 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	#13068754	C₂	1	1	yes	maximal, characteristic
2	#13067288	C₂	1	4	yes	maximal
3	#13066908	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₁×#494	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₁₁×Q₁₆	—	2	2	no	—
6	C₂×C₁₁×C₄⋊Q₈	C₂²	1	2	yes	—
7	C₁₁×#494	—	2	2	no	—
8	C₁₁×#494	C₄	1	4	yes	—
9	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
10	#10622538	C₂²	1	2	yes	—
11	#10622537	C₂²	1	2	yes	—
12	#10622190	—	2	2	no	—
13	#10622185	—	2	8	no	—
14	#10622092	—	2	2	no	—
15	C₂²×Q₈×C₁₁	—	2	2	no	—
16	C₂×C₁₁×Q₁₆	—	2	8	no	—
17	C₂×C₁₁×Q₁₆	—	4	8	no	—
18	C₂²×C₈×C₁₁	D₄	1	2	yes	—
19	C₁₁×C₄⋊Q₈	—	2	4	no	—
20	C₁₁×C₄⋊Q₈	—	2	2	no	—
21	C₁₁×C₄⋊Q₈	C₂×C₄	1	4	yes	—
22	C₂×C₁₁×C₄⋊C₄	—	2	4	no	—
23	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
24	C₂×#4318	—	2	2	no	—
25	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
26	C₄×C₈×C₁₁	D₄	1	2	yes	—
27	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
28	C₄⋊(C₁₁⋊C₈)	—	2	4	no	—
29	C₄⋊(C₁₁⋊C₈)	D₄	1	4	yes	—
30	C₄×C₁₁⋊C₈	—	2	2	no	—
31	#9779	—	11	1	no	maximal, Sylow
32	C₂×Q₈×C₁₁	—	2	4	no	—
33	C₂×Q₈×C₁₁	—	4	2	no	—
34	C₂×Q₈×C₁₁	—	4	8	no	—
35	C₂²×C₄×C₁₁	—	4	2	no	—
36	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
37	C₂²×C₄×C₁₁	#41	1	2	yes	—
38	C₁₁×Q₁₆	—	4	16	no	—
39	C₂×C₈×C₁₁	—	2	4	no	—
40	C₂×C₈×C₁₁	C₂²⋊C₄	1	4	yes	—
41	C₁₁×C₄⋊C₄	—	2	8	no	—
42	C₁₁×C₄⋊C₄	—	4	4	no	—
43	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
44	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
45	C₄²×C₁₁	C₂×D₄	1	2	yes	—
46	#4318	—	4	4	no	—
47	C₂×C₁₁⋊C₈	—	2	4	no	—
48	C₂×C₁₁⋊C₈	—	4	2	no	—
49	C₂×#494	D₁₁	1	1	yes	characteristic
50	#1837	—	11	1	no	—
51	#1546	—	11	4	no	—
52	#1452	—	11	1	no	—
53	C₂³×C₁₁	#124	1	1	yes	characteristic
54	Q₈×C₁₁	—	4	8	no	—
55	Q₈×C₁₁	—	8	4	no	—
56	C₂×C₄×C₁₁	—	2	4	no	—
57	C₂×C₄×C₁₁	—	4	4	no	—
58	C₂×C₄×C₁₁	—	8	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	C₈×C₁₁	—	2	4	no	—
65	C₁₁⋊C₈	—	4	4	no	—
66	C₁₁⋊C₈	—	8	2	no	—
67	C₂²×Q₁₆	—	2	2	no	—
68	C₂×C₄⋊Q₈	C₂×D₁₁	1	2	yes	—
69	#494	—	2	2	no	—
70	#494	Dic₁₁	1	4	yes	—
71	#431	—	11	2	no	—
72	#423	—	11	2	no	—
73	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
74	#341	—	22	2	no	—
75	#332	—	22	8	no	—
76	#322	—	22	2	no	—
77	C₂²×C₁₁	—	2	2	no	—
78	C₂²×C₁₁	#390	1	1	yes	characteristic
79	C₂²×C₁₁	#490	1	2	yes	—
80	C₄×C₁₁	—	2	2	no	—
81	C₄×C₁₁	—	8	4	no	—
82	C₄×C₁₁	#418	1	2	yes	—
83	C₄×C₁₁	#473	1	4	yes	—
84	C₄×C₁₁	#496	1	2	yes	—
85	C₂²×Q₈	—	2	2	no	—
86	C₂×Q₁₆	—	2	8	no	—
87	C₂×Q₁₆	—	4	8	no	—
88	C₂×M₁₆	—	22	2	no	—
89	C₂²×C₈	C₂²⋊D₁₁	1	2	yes	—
90	C₄⋊Q₈	—	2	4	no	—
91	C₄⋊Q₈	—	2	2	no	—
92	C₄⋊Q₈	C₂×Dic₁₁	1	4	yes	—
93	C₂×C₄⋊C₄	—	2	4	no	—
94	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
95	C₄⋊C₈	—	11	4	no	—
96	C₄⋊C₈	—	22	4	no	—
97	C₂²⋊C₈	—	22	2	no	—
98	C₄×C₈	—	22	2	no	—
99	C₄×C₈	C₂×Dic₁₁	1	2	yes	—
100	C₄×C₈	C₂²⋊D₁₁	1	2	yes	—
101	C₂×C₁₁	—	2	2	no	—
102	C₂×C₁₁	#1961	1	1	yes	characteristic
103	C₂×C₁₁	#1979	1	2	yes	—
104	C₂×Q₈	—	2	4	no	—
105	C₂×Q₈	—	4	2	no	—
106	C₂×Q₈	—	4	8	no	—
107	C₂²×C₄	—	4	2	no	—
108	C₂²×C₄	#4341	1	2	yes	—
109	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
110	Q₁₆	—	4	16	no	—
111	M₁₆	—	44	4	no	—
112	C₂×C₈	—	2	4	no	—
113	C₂×C₈	—	22	4	no	—
114	C₂×C₈	—	44	2	no	—
115	C₂×C₈	C₂²⋊Dic₁₁	1	4	yes	—
116	C₄⋊C₄	—	2	8	no	—
117	C₄⋊C₄	—	4	4	no	—
118	C₄²	D₄×D₁₁	1	2	yes	—
119	C₄²	C₂²×Dic₁₁	1	1	yes	characteristic
120	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
121	C₁₁	#9779	1	1	yes	characteristic, complemented, Sylow
122	C₂³	#66989	1	1	yes	characteristic
123	Q₈	—	4	8	no	—
124	Q₈	—	8	4	no	—
125	C₂×C₄	—	2	4	no	—
126	C₂×C₄	—	4	4	no	—
127	C₂×C₄	—	8	4	no	—
128	C₂×C₄	#66985	1	4	yes	—
129	C₂×C₄	D₄×Dic₁₁	1	2	yes	—
130	C₂×C₄	#66991	1	2	yes	—
131	C₂×C₄	#66993	1	1	yes	characteristic
132	C₂×C₄	C₂×C₂²⋊Dic₁₁	1	1	yes	characteristic
133	C₈	—	2	4	no	—
134	C₈	—	44	4	no	—
135	C₈	—	88	2	no	—
136	C₂²	—	2	2	no	—
137	C₂²	#10622684	1	2	yes	—
138	C₂²	#10622834	1	1	yes	characteristic
139	C₄	—	2	2	no	—
140	C₄	—	8	4	no	—
141	C₄	#10622687	1	2	yes	—
142	C₄	#10622805	1	4	yes	—
143	C₄	#10622828	1	2	yes	—
144	C₂	—	2	2	no	—
145	C₂	#13069441	1	1	yes	characteristic
146	C₂	#13069532	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13068754

C₂

yes

maximal, characteristic

#13067288

C₂

yes

maximal

#13066908

C₂

yes

maximal, characteristic

C₂×C₁₁×#494

C₂

yes

maximal, characteristic

C₂²×C₁₁×Q₁₆

—

C₂×C₁₁×C₄⋊Q₈

C₂²

yes

—

C₁₁×#494

—

C₁₁×#494

C₄

yes

—

C₂×C₄×C₈×C₁₁

C₂²

yes

characteristic

#10622538

C₂²

yes

—

#10622537

C₂²

yes

—

#10622190

—

#10622185

—

#10622092

—

C₂²×Q₈×C₁₁

—

C₂×C₁₁×Q₁₆

—

C₂×C₁₁×Q₁₆

—

C₂²×C₈×C₁₁

D₄

yes

—

C₁₁×C₄⋊Q₈

—

C₁₁×C₄⋊Q₈

—

C₁₁×C₄⋊Q₈

C₂×C₄

yes

—

C₂×C₁₁×C₄⋊C₄

—

C₂×C₄²×C₁₁

C₂³

yes

characteristic

C₂×#4318

—

C₄×C₈×C₁₁

C₂×C₄

yes

—

C₄×C₈×C₁₁

D₄

yes

—

C₂²⋊(C₁₁⋊C₈)

—

C₄⋊(C₁₁⋊C₈)

—

C₄⋊(C₁₁⋊C₈)

D₄

yes

—

C₄×C₁₁⋊C₈

—

#9779

—

maximal, Sylow

C₂×Q₈×C₁₁

—

C₂×Q₈×C₁₁

—

C₂×Q₈×C₁₁

—

C₂²×C₄×C₁₁

—

C₂²×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₁

#41

yes

—

C₁₁×Q₁₆

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

C₂²⋊C₄

yes

—

C₁₁×C₄⋊C₄

—

C₁₁×C₄⋊C₄

—

C₄²×C₁₁

C₂²×C₄

yes

characteristic

C₄²×C₁₁

C₂×D₄

yes

characteristic

C₄²×C₁₁

C₂×D₄

yes

—

#4318

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

—

C₂×#494

D₁₁

yes

—

—

—

C₂³×C₁₁

#124

yes

characteristic

Q₈×C₁₁

—

Q₈×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

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

—

C₈×C₁₁

—

C₁₁⋊C₈

—

C₁₁⋊C₈

—

C₂²×Q₁₆

—

C₂×C₄⋊Q₈

C₂×D₁₁

yes

—

#494

—

#494

Dic₁₁

yes

—

#431

—

#423

—

C₂×C₄×C₈

C₂×D₁₁

yes

—

—

—

C₂²×C₁₁

—

C₂²×C₁₁

#390

yes

characteristic

C₂²×C₁₁

#490

yes

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

#418

yes

—

C₄×C₁₁

#473

yes

—

C₄×C₁₁

#496

yes

—

C₂²×Q₈

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×M₁₆

—

C₂²×C₈

C₂²⋊D₁₁

yes

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×Dic₁₁

yes

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂²×D₁₁

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

—

C₄×C₈

C₂×Dic₁₁

yes

—

100

C₄×C₈

C₂²⋊D₁₁

yes

—

101

C₂×C₁₁

—

102

C₂×C₁₁

#1961

yes

characteristic

103

C₂×C₁₁

#1979

yes

—

104

C₂×Q₈

—

105

C₂×Q₈

—

106

C₂×Q₈

—

107

C₂²×C₄

—

108

C₂²×C₄

#4341

yes

—

109

C₂²×C₄

C₂×C₂²⋊D₁₁

yes

characteristic

110

Q₁₆

—

111

M₁₆

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

C₂²⋊Dic₁₁

yes

—

116

C₄⋊C₄

—

117

C₄⋊C₄

—

118

C₄²

D₄×D₁₁

yes

—

119

C₄²

C₂²×Dic₁₁

yes

characteristic

120

C₄²

C₂×C₂²⋊D₁₁

yes

characteristic

121

C₁₁

#9779

yes

characteristic, complemented, Sylow

122

C₂³

#66989

yes

characteristic

123

Q₈

—

124

Q₈

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

#66985

yes

—

129

C₂×C₄

D₄×Dic₁₁

yes

—

130

C₂×C₄

#66991

yes

—

131

C₂×C₄

#66993

yes

characteristic

132

C₂×C₄

C₂×C₂²⋊Dic₁₁

yes

characteristic

133

C₈

—

134

C₈

—

135

C₈

—

136

C₂²

—

137

C₂²

#10622684

yes

—

138

C₂²

#10622834

yes

characteristic

139

C₄

—

140

C₄

—

141

C₄

#10622687

yes

—

142

C₄

#10622805

yes

—

143

C₄

#10622828

yes

—

144

C₂

—

145

C₂

#13069441

yes

characteristic

146

C₂

#13069532

yes

—

	subgroup	G/H
center	C₂²	#10622834
commutator	C₄²×C₁₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₂×C₁₁×#494	C₂
socle	C₂²×C₁₁	#390
prime radical	C₂³×C₁₁	#124
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	C₂×#494	D₁₁
hypocenter	C₁₁	#9779
LCS	G ▷ C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#494

subgroup

G/H

center

C₂²

#10622834

commutator

C₄²×C₁₁

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₁

Fitting

C₂×C₁₁×#494

C₂

C₂²×C₁₁

C₂³×C₁₁

C₂×C₄²×C₁₁

C₂³

D₁₁

C₁₁

G ▷ C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#494

N	H ≅ G/N	type
121. C₁₁	#9779	semidirect

H ≅ G/N

type

121. C₁₁

#9779

semidirect

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

subgroup	index
#13068754	2
#13067288	2
#13066908	2
C₂×C₁₁×#494	2
#9779	11

subgroup

index

C₂×C₁₁×#494

Subgroups — #14653274

Conjugacy classes of subgroups

Complements

Maximal subgroups