Group #14665776 — subgroups

Subgroups — #14665776

Order 2816.

206 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 83 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	#13067513	C₂	1	2	yes	maximal
2	#13066690	C₂	1	1	yes	maximal, characteristic
3	#13066580	C₂	1	2	yes	maximal
4	#13066532	C₂	1	1	yes	maximal, characteristic
5	C₄×C₁₁×Q₃₂	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₁×Q₃₂	C₄	1	1	yes	characteristic
7	C₄×C₁₁×Q₁₆	C₂²	1	2	yes	—
8	#10622637	—	2	2	no	—
9	C₁₁×#366	C₄	1	1	yes	characteristic
10	C₁₁×#358	C₄	1	2	yes	—
11	C₄×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
12	Q₈⋊(C₁₁⋊C₈)	—	2	2	no	—
13	C₄×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
14	#10622096	C₂²	1	2	yes	—
15	C₈×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₁×Q₁₆	C₂×C₄	1	2	yes	—
17	C₄×Q₈×C₁₁	—	2	2	no	—
18	C₁₁×Q₃₂	—	2	2	no	—
19	C₂×C₁₁×C₁₆	C₂×C₄	1	1	yes	characteristic
20	C₂×C₁₁×C₁₆	C₂×C₄	1	1	yes	characteristic
21	C₁₁×#107	C₂×C₄	1	2	yes	—
22	C₁₁×#103	—	2	2	no	—
23	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
24	C₂×C₁₁⋊C₁₆	—	2	1	no	—
25	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
26	C₄⋊(C₁₁⋊C₈)	—	4	2	no	—
27	#66867	—	4	2	no	—
28	C₄×C₁₁⋊C₈	D₄	1	1	yes	characteristic
29	C₄×C₁₁⋊C₈	D₄	1	1	yes	characteristic
30	#12085	—	11	1	no	maximal, Sylow
31	C₂×Q₈×C₁₁	—	2	2	no	—
32	C₁₁×Q₁₆	—	2	2	no	—
33	C₁₁×Q₁₆	—	2	2	no	—
34	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
36	C₁₁×C₄⋊C₄	—	2	2	no	—
37	C₁₁×C₄⋊C₄	—	4	2	no	—
38	C₄²×C₁₁	—	4	2	no	—
39	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
40	C₂×C₁₁⋊C₈	—	2	1	no	—
41	C₂×C₁₁⋊C₈	—	4	2	no	—
42	C₂×C₁₁⋊C₈	D₈	1	2	yes	—
43	C₁₁×C₁₆	—	2	1	no	—
44	C₁₁×C₁₆	M₁₆	1	2	yes	—
45	C₁₁⋊C₁₆	—	2	2	no	—
46	C₄×Q₃₂	D₁₁	1	1	yes	characteristic
47	#1591	—	11	2	no	—
48	#1372	—	11	1	no	—
49	#1332	—	11	2	no	—
50	#1311	—	11	1	no	—
51	Q₈×C₁₁	—	4	2	no	—
52	Q₈×C₁₁	—	4	2	no	—
53	C₂×C₄×C₁₁	—	4	2	no	—
54	C₂×C₄×C₁₁	—	4	2	no	—
55	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
56	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
57	C₂×C₄×C₁₁	#135	1	1	yes	characteristic
58	C₈×C₁₁	—	2	1	no	—
59	C₈×C₁₁	C₂×M₁₆	1	1	yes	characteristic
60	C₈×C₁₁	#131	1	1	yes	characteristic
61	C₁₁⋊C₈	—	2	2	no	—
62	C₁₁⋊C₈	—	4	1	no	—
63	C₁₁⋊C₈	—	8	2	no	—
64	C₂×Q₃₂	Dic₁₁	1	1	yes	characteristic
65	#446	—	22	2	no	—
66	C₄×Q₁₆	C₂×D₁₁	1	2	yes	—
67	#366	Dic₁₁	1	1	yes	characteristic
68	#358	Dic₁₁	1	2	yes	—
69	C₄×C₁₆	—	11	1	no	—
70	C₄×C₁₆	C₂×D₁₁	1	1	yes	characteristic
71	#335	—	11	2	no	—
72	Q₈⋊C₈	—	22	2	no	—
73	C₈²	—	11	1	no	—
74	C₂²×C₁₁	C₄×D₈	1	1	yes	characteristic
75	C₄×C₁₁	—	2	1	no	—
76	C₄×C₁₁	—	8	2	no	—
77	C₄×C₁₁	—	8	2	no	—
78	C₄×C₁₁	#436	1	1	yes	characteristic
79	C₄×C₁₁	#443	1	1	yes	characteristic
80	C₄×C₁₁	#510	1	2	yes	—
81	C₂×Q₁₆	C₂×Dic₁₁	1	2	yes	—
82	C₄×Q₈	—	2	2	no	—
83	Q₃₂	—	2	2	no	—
84	C₂×C₁₆	—	22	1	no	—
85	C₂×C₁₆	C₂×Dic₁₁	1	1	yes	characteristic
86	C₂×C₁₆	C₂×Dic₁₁	1	1	yes	characteristic
87	#107	C₂×Dic₁₁	1	2	yes	—
88	C₄⋊C₈	—	22	2	no	—
89	C₄⋊C₈	—	44	2	no	—
90	#103	—	2	2	no	—
91	#97	—	44	2	no	—
92	C₄×C₈	—	11	1	no	—
93	C₄×C₈	—	11	1	no	—
94	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
95	C₂×C₁₁	#1589	1	1	yes	characteristic
96	C₂×C₁₁	#2176	1	1	yes	characteristic
97	C₂×C₁₁	#2179	1	1	yes	characteristic
98	C₂×Q₈	—	2	2	no	—
99	Q₁₆	—	2	2	no	—
100	Q₁₆	—	2	2	no	—
101	C₂×C₈	—	11	2	no	—
102	C₂×C₈	—	22	1	no	—
103	C₂×C₈	—	44	2	no	—
104	C₂×C₈	#4341	1	1	yes	characteristic
105	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
106	C₄⋊C₄	—	2	2	no	—
107	C₄⋊C₄	—	4	2	no	—
108	C₄²	—	4	2	no	—
109	C₄²	D₄×D₁₁	1	1	yes	characteristic
110	C₁₆	—	2	1	no	—
111	C₁₆	—	22	2	no	—
112	C₁₆	#4318	1	2	yes	—
113	C₁₁	#12085	1	1	yes	characteristic, complemented, Sylow
114	Q₈	—	4	2	no	—
115	Q₈	—	4	2	no	—
116	C₂×C₄	—	4	2	no	—
117	C₂×C₄	—	4	2	no	—
118	C₂×C₄	D₈×D₁₁	1	1	yes	characteristic
119	C₂×C₄	#66965	1	1	yes	characteristic
120	C₂×C₄	D₄×Dic₁₁	1	1	yes	characteristic
121	C₈	—	2	1	no	—
122	C₈	—	22	2	no	—
123	C₈	—	44	1	no	—
124	C₈	—	88	2	no	—
125	C₈	C₂×#4318	1	1	yes	characteristic
126	C₈	#67001	1	1	yes	characteristic
127	C₂²	D₈×Dic₁₁	1	1	yes	characteristic
128	C₄	—	2	1	no	—
129	C₄	—	8	2	no	—
130	C₄	—	8	2	no	—
131	C₄	#10622531	1	2	yes	—
132	C₄	#10622625	1	1	yes	characteristic
133	C₄	#10622809	1	1	yes	characteristic
134	C₂	#13067501	1	1	yes	characteristic
135	C₂	#13070487	1	1	yes	characteristic
136	C₂	#13070502	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13067513

C₂

yes

maximal

#13066690

C₂

yes

maximal, characteristic

#13066580

C₂

yes

maximal

#13066532

C₂

yes

maximal, characteristic

C₄×C₁₁×Q₃₂

C₂

yes

maximal, characteristic

C₂×C₁₁×Q₃₂

C₄

yes

characteristic

C₄×C₁₁×Q₁₆

C₂²

yes

—

#10622637

—

C₁₁×#366

C₄

yes

characteristic

C₁₁×#358

C₄

yes

—

C₄×C₁₁×C₁₆

C₂²

yes

characteristic

Q₈⋊(C₁₁⋊C₈)

—

C₄×C₁₁⋊C₁₆

C₂²

yes

characteristic

#10622096

C₂²

yes

—

C₈×C₁₁⋊C₈

C₂²

yes

characteristic

C₂×C₁₁×Q₁₆

C₂×C₄

yes

—

C₄×Q₈×C₁₁

—

C₁₁×Q₃₂

—

C₂×C₁₁×C₁₆

C₂×C₄

yes

characteristic

C₂×C₁₁×C₁₆

C₂×C₄

yes

characteristic

C₁₁×#107

C₂×C₄

yes

—

C₁₁×#103

—

C₄×C₈×C₁₁

C₂³

yes

characteristic

C₂×C₁₁⋊C₁₆

—

C₄⋊(C₁₁⋊C₈)

—

C₄⋊(C₁₁⋊C₈)

—

#66867

—

C₄×C₁₁⋊C₈

D₄

yes

characteristic

C₄×C₁₁⋊C₈

D₄

yes

characteristic

#12085

—

maximal, Sylow

C₂×Q₈×C₁₁

—

C₁₁×Q₁₆

—

C₁₁×Q₁₆

—

C₂×C₈×C₁₁

C₂²×C₄

yes

characteristic

C₂×C₈×C₁₁

#41

yes

characteristic

C₁₁×C₄⋊C₄

—

C₁₁×C₄⋊C₄

—

C₄²×C₁₁

—

C₄²×C₁₁

C₂×D₄

yes

characteristic

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

D₈

yes

—

C₁₁×C₁₆

—

C₁₁×C₁₆

M₁₆

yes

—

C₁₁⋊C₁₆

—

C₄×Q₃₂

D₁₁

yes

—

—

—

—

Q₈×C₁₁

—

Q₈×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

C₄×D₄

yes

characteristic

C₂×C₄×C₁₁

C₂×D₈

yes

characteristic

C₂×C₄×C₁₁

#135

yes

characteristic

C₈×C₁₁

—

C₈×C₁₁

C₂×M₁₆

yes

characteristic

C₈×C₁₁

#131

yes

characteristic

C₁₁⋊C₈

—

C₁₁⋊C₈

—

C₁₁⋊C₈

—

C₂×Q₃₂

Dic₁₁

yes

characteristic

#446

—

C₄×Q₁₆

C₂×D₁₁

yes

—

#366

Dic₁₁

yes

characteristic

#358

Dic₁₁

yes

—

C₄×C₁₆

—

C₄×C₁₆

C₂×D₁₁

yes

characteristic

#335

—

Q₈⋊C₈

—

C₈²

—

C₂²×C₁₁

C₄×D₈

yes

characteristic

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

yes

C₄×C₁₁

yes

C₄×C₁₁

yes

—

C₂×Q₁₆

C₂×Dic₁₁

yes

—

C₄×Q₈

—

Q₃₂

—

C₂×C₁₆

—

C₂×C₁₆

C₂×Dic₁₁

yes

characteristic

C₂×C₁₆

C₂×Dic₁₁

yes

characteristic

#107

C₂×Dic₁₁

yes

—

C₄⋊C₈

—

C₄⋊C₈

—

#103

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂²×D₁₁

yes

C₂×C₁₁

yes

C₂×C₁₁

yes

C₂×C₁₁

yes

C₂×Q₈

—

Q₁₆

—

100

Q₁₆

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

#4341

yes

characteristic

105

C₂×C₈

C₂²×Dic₁₁

yes

characteristic

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₄²

—

109

C₄²

D₄×D₁₁

yes

characteristic

110

C₁₆

—

111

C₁₆

—

112

C₁₆

#4318

yes

—

113

C₁₁

#12085

yes

characteristic, complemented, Sylow

114

Q₈

—

115

Q₈

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

D₈×D₁₁

yes

characteristic

119

C₂×C₄

#66965

yes

characteristic

120

C₂×C₄

D₄×Dic₁₁

yes

characteristic

121

C₈

—

122

C₈

—

123

C₈

—

124

C₈

—

125

C₈

C₂×#4318

yes

characteristic

126

C₈

#67001

yes

characteristic

127

C₂²

D₈×Dic₁₁

yes

characteristic

128

C₄

—

129

C₄

—

130

C₄

—

131

C₄

#10622531

yes

—

132

C₄

#10622625

yes

characteristic

133

C₄

#10622809

yes

characteristic

134

C₂

#13067501

yes

characteristic

135

C₂

#13070487

yes

characteristic

136

C₂

#13070502

yes

characteristic

	subgroup	G/H
center	C₂×C₄	D₈×D₁₁
commutator	C₂×C₈×C₁₁	C₂²×C₄
Frattini	C₄×C₈	C₂²×D₁₁
Fitting	C₄×C₁₁×Q₃₂	C₂
socle, prime radical	C₂²×C₁₁	C₄×D₈
cosocle	C₄×C₈×C₁₁	C₂³
hypercenter	C₄×Q₃₂	D₁₁
hypocenter	C₁₁	#12085
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ C₄×Q₃₂

subgroup

G/H

center

C₂×C₄

D₈×D₁₁

commutator

C₂×C₈×C₁₁

C₂²×C₄

Frattini

C₄×C₈

C₂²×D₁₁

Fitting

C₄×C₁₁×Q₃₂

C₂

socle, prime radical

C₂²×C₁₁

C₄×D₈

cosocle

C₄×C₈×C₁₁

C₂³

hypercenter

C₄×Q₃₂

D₁₁

hypocenter

C₁₁

#12085

LCS

G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ C₄×Q₃₂

N	H ≅ G/N	type
113. C₁₁	#12085	semidirect

H ≅ G/N

type

113. C₁₁

#12085

semidirect

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

subgroup	index
#13067513	2
#13066690	2
#13066580	2
#13066532	2
C₄×C₁₁×Q₃₂	2
#12085	11

subgroup

index

C₄×C₁₁×Q₃₂

Subgroups — #14665776

Conjugacy classes of subgroups

Complements

Maximal subgroups