Group #14670193 — subgroups

Subgroups — #14670193

Order 2816.

342 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 203 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×#10622101	C₂	1	4	yes	maximal
2	#13070372	C₂	1	2	yes	maximal
3	C₁₁×#1726	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₁×#97	C₄	1	2	yes	—
5	C₂×C₁₁×#97	C₄	1	1	yes	characteristic
6	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
7	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
8	C₁₁×#376	C₄	1	1	yes	characteristic
9	C₂×#66876	C₂²	1	4	yes	—
10	#10622101	—	2	8	no	—
11	C₄⋊(C₁₁⋊C₁₆)	—	2	4	no	—
12	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
13	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
14	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
15	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
16	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
17	C₁₁×#97	—	2	4	no	—
18	C₁₁×#97	C₈	1	4	yes	—
19	C₄×C₈×C₁₁	D₄	1	2	yes	—
20	C₄×C₈×C₁₁	D₄	1	4	yes	—
21	C₄×C₈×C₁₁	Q₈	1	4	yes	—
22	C₄×C₈×C₁₁	Q₈	1	2	yes	—
23	C₁₁×#95	—	2	2	no	—
24	#66876	—	2	8	no	—
25	C₂×C₁₁⋊C₁₆	—	2	4	no	—
26	#12901	—	11	1	no	maximal, Sylow
27	C₂²×C₄×C₁₁	—	2	2	no	—
28	C₂²×C₄×C₁₁	M₁₆	1	2	yes	—
29	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
30	C₂×C₈×C₁₁	—	2	2	no	—
31	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
32	C₂×C₈×C₁₁	C₄⋊C₄	1	4	yes	—
33	C₂×C₈×C₁₁	C₂×C₈	1	4	yes	—
34	C₂×C₈×C₁₁	M₁₆	1	4	yes	—
35	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
36	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
37	C₂×C₈×C₁₁	C₂×Q₈	1	2	yes	—
38	C₂×C₈×C₁₁	C₂×Q₈	1	1	yes	characteristic
39	C₄²×C₁₁	—	2	2	no	—
40	C₄²×C₁₁	C₄⋊C₄	1	4	yes	—
41	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
42	C₄²×C₁₁	C₂×C₈	1	2	yes	—
43	C₁₁⋊C₁₆	—	4	4	no	—
44	C₂×#364	—	11	4	no	—
45	#2150	—	11	2	no	—
46	#1726	D₁₁	1	1	yes	characteristic
47	C₂³×C₁₁	C₂×M₁₆	1	1	yes	characteristic
48	C₂×C₄×C₁₁	—	2	4	no	—
49	C₂×C₄×C₁₁	—	4	2	no	—
50	C₂×C₄×C₁₁	—	4	4	no	—
51	C₂×C₄×C₁₁	C₄⋊C₈	1	4	yes	—
52	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
53	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
54	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
55	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
56	C₈×C₁₁	—	2	2	no	—
57	C₈×C₁₁	C₄⋊C₈	1	8	yes	—
58	C₈×C₁₁	#127	1	1	yes	characteristic
59	C₈×C₁₁	C₄⋊Q₈	1	2	yes	—
60	C₈×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
61	C₂×M₃₂	—	11	4	no	—
62	C₂×#97	Dic₁₁	1	2	yes	—
63	C₂×#97	Dic₁₁	1	1	yes	characteristic
64	C₂×C₄×C₈	C₂×D₁₁	1	2	yes	—
65	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
66	#376	Dic₁₁	1	1	yes	characteristic
67	#364	—	22	8	no	—
68	C₄⋊C₁₆	—	22	4	no	—
69	C₂²×C₁₁	—	2	2	no	—
70	C₂²×C₁₁	C₂×C₄⋊C₈	1	1	yes	characteristic
71	C₂²×C₁₁	#423	1	2	yes	—
72	C₄×C₁₁	—	2	4	no	—
73	C₄×C₁₁	—	4	4	no	—
74	C₄×C₁₁	#384	1	1	yes	characteristic
75	C₄×C₁₁	C₂×C₄⋊C₈	1	2	yes	—
76	C₄×C₁₁	#423	1	1	yes	characteristic
77	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
78	C₂²×C₈	C₂×Dic₁₁	1	2	yes	—
79	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
80	C₂×C₄²	C₂×Dic₁₁	1	2	yes	—
81	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
82	M₃₂	—	22	8	no	—
83	C₂×C₁₆	—	22	4	no	—
84	#97	—	2	4	no	—
85	#97	C₁₁⋊C₈	1	4	yes	—
86	C₄×C₈	Dic₂₂	1	4	yes	—
87	C₄×C₈	Dic₂₂	1	2	yes	—
88	C₄×C₈	D₄₄	1	4	yes	—
89	C₄×C₈	D₄₄	1	2	yes	—
90	#95	—	2	2	no	—
91	C₂×C₁₁	—	2	2	no	—
92	C₂×C₁₁	#1842	1	1	yes	characteristic
93	C₂×C₁₁	#2153	1	2	yes	—
94	C₂²×C₄	—	2	2	no	—
95	C₂²×C₄	#4318	1	2	yes	—
96	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
97	C₂×C₈	—	2	2	no	—
98	C₂×C₈	C₂×C₁₁⋊C₈	1	4	yes	—
99	C₂×C₈	#4318	1	4	yes	—
100	C₂×C₈	C₄⋊Dic₁₁	1	2	yes	—
101	C₂×C₈	C₄⋊Dic₁₁	1	4	yes	—
102	C₂×C₈	C₂×Dic₂₂	1	1	yes	characteristic
103	C₂×C₈	C₂×Dic₂₂	1	2	yes	—
104	C₂×C₈	C₂×D₄₄	1	2	yes	—
105	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
106	C₄²	—	2	2	no	—
107	C₄²	C₂×C₁₁⋊C₈	1	2	yes	—
108	C₄²	C₄⋊Dic₁₁	1	4	yes	—
109	C₄²	C₄⋊Dic₁₁	1	2	yes	—
110	C₁₆	—	44	4	no	—
111	C₁₁	#12901	1	1	yes	characteristic, complemented, Sylow
112	C₂³	C₂×#4318	1	1	yes	characteristic
113	C₂×C₄	—	2	4	no	—
114	C₂×C₄	—	4	2	no	—
115	C₂×C₄	—	4	4	no	—
116	C₂×C₄	C₄⋊(C₁₁⋊C₈)	1	4	yes	—
117	C₂×C₄	C₂²×C₁₁⋊C₈	1	1	yes	characteristic
118	C₂×C₄	C₂×#4318	1	2	yes	—
119	C₂×C₄	C₂×C₄⋊Dic₁₁	1	2	yes	—
120	C₂×C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
121	C₈	—	2	2	no	—
122	C₈	C₄⋊(C₁₁⋊C₈)	1	8	yes	—
123	C₈	#66922	1	2	yes	—
124	C₈	#66922	1	1	yes	characteristic
125	C₈	#66927	1	1	yes	characteristic
126	C₂²	—	2	2	no	—
127	C₂²	C₂×C₄⋊(C₁₁⋊C₈)	1	1	yes	characteristic
128	C₂²	#10622537	1	2	yes	—
129	C₄	—	2	4	no	—
130	C₄	—	4	4	no	—
131	C₄	C₂×C₄⋊(C₁₁⋊C₈)	1	2	yes	—
132	C₄	#10622537	1	1	yes	characteristic
133	C₄	#10622548	1	1	yes	characteristic
134	C₂	—	2	2	no	—
135	C₂	#13068768	1	1	yes	characteristic
136	C₂	#13070382	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10622101

C₂

yes

maximal

#13070372

C₂

yes

maximal

C₁₁×#1726

C₂

yes

maximal, characteristic

C₂×C₁₁×#97

C₄

yes

—

C₂×C₁₁×#97

C₄

yes

characteristic

C₂×C₄×C₈×C₁₁

C₂²

yes

—

C₂×C₄×C₈×C₁₁

C₂²

yes

characteristic

C₁₁×#376

C₄

yes

characteristic

C₂×#66876

C₂²

yes

—

#10622101

—

C₄⋊(C₁₁⋊C₁₆)

—

C₂²×C₈×C₁₁

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₁

C₂×C₄

yes

—

C₂²×C₈×C₁₁

C₂³

yes

characteristic

C₂×C₄²×C₁₁

C₂×C₄

yes

—

C₂×C₄²×C₁₁

C₂×C₄

yes

characteristic

C₁₁×#97

—

C₁₁×#97

C₈

yes

—

C₄×C₈×C₁₁

D₄

yes

—

C₄×C₈×C₁₁

D₄

yes

—

C₄×C₈×C₁₁

Q₈

yes

—

C₄×C₈×C₁₁

Q₈

yes

—

C₁₁×#95

—

#66876

—

C₂×C₁₁⋊C₁₆

—

#12901

—

maximal, Sylow

C₂²×C₄×C₁₁

—

C₂²×C₄×C₁₁

M₁₆

yes

—

C₂²×C₄×C₁₁

C₂²×C₄

yes

characteristic

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

C₄⋊C₄

yes

—

C₂×C₈×C₁₁

C₄⋊C₄

yes

—

C₂×C₈×C₁₁

C₂×C₈

yes

—

C₂×C₈×C₁₁

M₁₆

yes

—

C₂×C₈×C₁₁

C₂×D₄

yes

—

C₂×C₈×C₁₁

C₂×D₄

yes

characteristic

C₂×C₈×C₁₁

C₂×Q₈

yes

—

C₂×C₈×C₁₁

C₂×Q₈

yes

characteristic

C₄²×C₁₁

—

C₄²×C₁₁

C₄⋊C₄

yes

—

C₄²×C₁₁

C₄⋊C₄

yes

—

C₄²×C₁₁

C₂×C₈

yes

—

C₁₁⋊C₁₆

—

C₂×#364

—

#2150

—

#1726

D₁₁

yes

characteristic

C₂³×C₁₁

C₂×M₁₆

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

C₄⋊C₈

yes

—

C₂×C₄×C₁₁

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₁₁

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₁

C₂²×C₈

yes

characteristic

C₂×C₄×C₁₁

C₂×M₁₆

yes

—

C₈×C₁₁

—

C₈×C₁₁

C₄⋊C₈

yes

—

C₈×C₁₁

#127

yes

characteristic

C₈×C₁₁

C₄⋊Q₈

yes

—

C₈×C₁₁

C₄⋊Q₈

yes

characteristic

C₂×M₃₂

—

C₂×#97

Dic₁₁

yes

—

C₂×#97

Dic₁₁

yes

characteristic

C₂×C₄×C₈

C₂×D₁₁

yes

—

C₂×C₄×C₈

C₂×D₁₁

yes

characteristic

#376

Dic₁₁

yes

characteristic

#364

—

C₄⋊C₁₆

—

C₂²×C₁₁

—

C₂²×C₁₁

C₂×C₄⋊C₈

yes

characteristic

C₂²×C₁₁

#423

yes

—

C₄×C₁₁

—

C₄×C₁₁

—

C₄×C₁₁

#384

yes

characteristic

C₄×C₁₁

C₂×C₄⋊C₈

yes

—

C₄×C₁₁

#423

yes

characteristic

C₂²×C₈

C₂×Dic₁₁

yes

characteristic

C₂²×C₈

C₂×Dic₁₁

yes

—

C₂²×C₈

C₂²×D₁₁

yes

characteristic

C₂×C₄²

C₂×Dic₁₁

yes

—

C₂×C₄²

C₂×Dic₁₁

yes

characteristic

M₃₂

—

C₂×C₁₆

—

#97

—

#97

C₁₁⋊C₈

yes

—

C₄×C₈

Dic₂₂

yes

—

C₄×C₈

Dic₂₂

yes

—

C₄×C₈

D₄₄

yes

—

C₄×C₈

D₄₄

yes

—

#95

—

C₂×C₁₁

—

C₂×C₁₁

#1842

yes

characteristic

C₂×C₁₁

#2153

yes

—

C₂²×C₄

—

C₂²×C₄

#4318

yes

—

C₂²×C₄

C₂²×Dic₁₁

yes

characteristic

C₂×C₈

—

C₂×C₈

C₂×C₁₁⋊C₈

yes

—

C₂×C₈

#4318

yes

—

100

C₂×C₈

C₄⋊Dic₁₁

yes

—

101

C₂×C₈

C₄⋊Dic₁₁

yes

—

102

C₂×C₈

C₂×Dic₂₂

yes

characteristic

103

C₂×C₈

C₂×Dic₂₂

yes

—

104

C₂×C₈

C₂×D₄₄

yes

—

105

C₂×C₈

C₂×D₄₄

yes

characteristic

106

C₄²

—

107

C₄²

C₂×C₁₁⋊C₈

yes

—

108

C₄²

C₄⋊Dic₁₁

yes

—

109

C₄²

C₄⋊Dic₁₁

yes

—

110

C₁₆

—

111

C₁₁

#12901

yes

characteristic, complemented, Sylow

112

C₂³

C₂×#4318

yes

characteristic

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

C₄⋊(C₁₁⋊C₈)

yes

—

117

C₂×C₄

C₂²×C₁₁⋊C₈

yes

characteristic

118

C₂×C₄

C₂×#4318

yes

—

119

C₂×C₄

C₂×C₄⋊Dic₁₁

yes

—

120

C₂×C₄

C₂×C₄⋊Dic₁₁

yes

characteristic

121

C₈

—

122

C₈

C₄⋊(C₁₁⋊C₈)

yes

—

123

C₈

#66922

yes

—

124

C₈

#66922

yes

characteristic

125

C₈

#66927

yes

characteristic

126

C₂²

—

127

C₂²

C₂×C₄⋊(C₁₁⋊C₈)

yes

characteristic

128

C₂²

#10622537

yes

—

129

C₄

—

130

C₄

—

131

C₄

C₂×C₄⋊(C₁₁⋊C₈)

yes

—

132

C₄

#10622537

yes

characteristic

133

C₄

#10622548

yes

characteristic

134

C₂

—

135

C₂

#13068768

yes

characteristic

136

C₂

#13070382

yes

—

	subgroup	G/H
center	C₂×C₈	C₂×D₄₄
commutator	C₂×C₄×C₁₁	C₂²×C₈
Frattini	C₂²×C₈	C₂²×D₁₁
Fitting	C₁₁×#1726	C₂
socle	C₂²×C₁₁	C₂×C₄⋊C₈
prime radical	C₂³×C₁₁	C₂×M₁₆
cosocle	C₂²×C₈×C₁₁	C₂³
hypercenter	#1726	D₁₁
hypocenter	C₁₁	#12901
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ #1726

subgroup

G/H

center

C₂×C₈

C₂×D₄₄

commutator

C₂×C₄×C₁₁

C₂²×C₈

Frattini

C₂²×C₈

C₂²×D₁₁

Fitting

C₁₁×#1726

C₂

socle

C₂²×C₁₁

C₂×C₄⋊C₈

prime radical

C₂³×C₁₁

C₂×M₁₆

cosocle

C₂²×C₈×C₁₁

C₂³

D₁₁

C₁₁

G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ #1726

N	H ≅ G/N	type
111. C₁₁	#12901	semidirect

H ≅ G/N

type

111. C₁₁

#12901

semidirect

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

subgroup	index
C₂×#10622101	2
#13070372	2
C₁₁×#1726	2
#12901	11

subgroup

index

C₂×#10622101

#13070372

C₁₁×#1726

#12901

Subgroups — #14670193

Conjugacy classes of subgroups

Complements

Maximal subgroups