Group #14670225 — subgroups

Subgroups — #14670225

Order 2816.

306 conjugacy classes of subgroups; only the 179 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 179 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×#10622144	C₂	1	4	yes	maximal
2	#13068788	C₂	1	2	yes	maximal
3	C₂×C₁₁×#346	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₁₁×C₁₆	C₂²	1	2	yes	—
5	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
6	C₂×#66883	—	2	2	no	—
7	C₂×#66883	C₂²	1	4	yes	—
8	#10622537	—	2	2	no	—
9	C₁₁×#346	C₄	1	4	yes	—
10	#10622144	—	2	8	no	—
11	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
12	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
13	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
14	C₂×#4318	—	2	4	no	—
15	C₂×C₁₁×C₁₆	C₂×C₄	1	4	yes	—
16	C₂×C₁₁×C₁₆	D₄	1	4	yes	—
17	C₂×C₁₁×C₁₆	Q₈	1	4	yes	—
18	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
19	C₄×C₈×C₁₁	Q₈	1	2	yes	—
20	#66883	—	2	8	no	—
21	#66883	—	4	4	no	—
22	C₄⋊(C₁₁⋊C₈)	—	4	4	no	—
23	#12910	—	11	1	no	maximal, Sylow
24	C₂²×C₄×C₁₁	Q₁₆	1	2	yes	—
25	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
26	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
27	C₂×C₈×C₁₁	D₈	1	2	yes	—
28	C₂×C₈×C₁₁	Q₁₆	1	2	yes	—
29	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
30	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
31	C₂×C₈×C₁₁	C₂×Q₈	1	1	yes	characteristic
32	C₂×C₈×C₁₁	C₂×Q₈	1	2	yes	—
33	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
34	C₄²×C₁₁	D₈	1	2	yes	—
35	#4318	—	4	4	no	—
36	#4318	—	4	4	no	—
37	C₂×C₁₁⋊C₈	—	4	4	no	—
38	C₁₁×C₁₆	C₄⋊C₄	1	8	yes	—
39	C₂×#368	—	11	4	no	—
40	C₂×#346	D₁₁	1	1	yes	characteristic
41	#1848	—	11	2	no	—
42	C₂³×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
43	C₂×C₄×C₁₁	—	4	2	no	—
44	C₂×C₄×C₁₁	#107	1	4	yes	—
45	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
46	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
47	C₂×C₄×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
48	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
49	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
50	C₂×C₄×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
51	C₈×C₁₁	#107	1	4	yes	—
52	C₈×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
53	C₈×C₁₁	C₄⋊Q₈	1	2	yes	—
54	C₁₁⋊C₈	—	8	4	no	—
55	C₂²×C₁₆	C₂×D₁₁	1	2	yes	—
56	C₂×#108	—	11	4	no	—
57	C₂×#108	—	22	2	no	—
58	#423	—	22	2	no	—
59	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
60	#368	—	22	8	no	—
61	#346	Dic₁₁	1	4	yes	—
62	C₂²×C₁₁	—	2	2	no	—
63	C₂²×C₁₁	C₂×#107	1	1	yes	characteristic
64	C₂²×C₁₁	#494	1	1	yes	characteristic
65	C₂²×C₁₁	#500	1	1	yes	characteristic
66	C₄×C₁₁	—	2	4	no	—
67	C₄×C₁₁	#384	1	1	yes	characteristic
68	C₄×C₁₁	C₂×#107	1	1	yes	characteristic
69	C₄×C₁₁	#493	1	1	yes	characteristic
70	C₄×C₁₁	#500	1	1	yes	characteristic
71	C₂×M₁₆	—	22	4	no	—
72	C₂²×C₈	D₄₄	1	1	yes	characteristic
73	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
74	C₂×C₄²	D₄₄	1	1	yes	characteristic
75	C₂×C₁₆	Dic₂₂	1	4	yes	—
76	C₂×C₁₆	D₄₄	1	4	yes	—
77	C₂×C₁₆	C₂×Dic₁₁	1	4	yes	—
78	#108	—	22	8	no	—
79	#108	—	44	4	no	—
80	C₄⋊C₈	—	44	4	no	—
81	C₄×C₈	Dic₂₂	1	2	yes	—
82	C₄×C₈	C₂×Dic₁₁	1	2	yes	—
83	C₂×C₁₁	—	2	1	no	—
84	C₂×C₁₁	—	2	1	no	—
85	C₂×C₁₁	#1845	1	1	yes	characteristic
86	C₂×C₁₁	#2161	1	2	yes	—
87	C₂²×C₄	Dic₄₄	1	2	yes	—
88	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
89	M₁₆	—	44	4	no	—
90	M₁₆	—	44	4	no	—
91	C₂×C₈	—	44	4	no	—
92	C₂×C₈	D₈₈	1	2	yes	—
93	C₂×C₈	Dic₄₄	1	2	yes	—
94	C₂×C₈	C₄⋊Dic₁₁	1	2	yes	—
95	C₂×C₈	C₂×Dic₂₂	1	1	yes	characteristic
96	C₂×C₈	C₂×Dic₂₂	1	2	yes	—
97	C₂×C₈	C₂×D₄₄	1	2	yes	—
98	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
99	C₄²	D₈₈	1	2	yes	—
100	C₄²	C₄⋊Dic₁₁	1	2	yes	—
101	C₁₆	C₄⋊Dic₁₁	1	8	yes	—
102	C₁₁	#12910	1	1	yes	characteristic, complemented, Sylow
103	C₂³	C₂×Dic₄₄	1	1	yes	characteristic
104	C₂×C₄	—	4	2	no	—
105	C₂×C₄	#66882	1	4	yes	—
106	C₂×C₄	#66922	1	1	yes	characteristic
107	C₂×C₄	#66927	1	1	yes	characteristic
108	C₂×C₄	C₂×D₈₈	1	1	yes	characteristic
109	C₂×C₄	C₂×D₈₈	1	1	yes	characteristic
110	C₂×C₄	C₂×Dic₄₄	1	1	yes	characteristic
111	C₂×C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
112	C₈	—	88	4	no	—
113	C₈	#66882	1	4	yes	—
114	C₈	#66922	1	2	yes	—
115	C₈	C₂×C₄⋊Dic₁₁	1	2	yes	—
116	C₂²	—	2	2	no	—
117	C₂²	#10622295	1	1	yes	characteristic
118	C₂²	#10622312	1	1	yes	characteristic
119	C₂²	C₂×#66882	1	1	yes	characteristic
120	C₄	—	2	4	no	—
121	C₄	#10622295	1	1	yes	characteristic
122	C₄	#10622308	1	1	yes	characteristic
123	C₄	#10622548	1	1	yes	characteristic
124	C₄	C₂×#66882	1	1	yes	characteristic
125	C₂	—	2	1	no	—
126	C₂	—	2	1	no	—
127	C₂	#13068776	1	1	yes	characteristic
128	C₂	#13070411	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10622144

C₂

yes

maximal

#13068788

C₂

yes

maximal

C₂×C₁₁×#346

C₂

yes

maximal, characteristic

C₂²×C₁₁×C₁₆

C₂²

yes

—

C₂×C₄×C₈×C₁₁

C₂²

yes

characteristic

C₂×#66883

—

C₂×#66883

C₂²

yes

—

#10622537

—

C₁₁×#346

C₄

yes

—

#10622144

—

C₂²×C₈×C₁₁

D₄

yes

characteristic

C₂²×C₈×C₁₁

C₂³

yes

characteristic

C₂×C₄²×C₁₁

D₄

yes

characteristic

C₂×#4318

—

C₂×C₁₁×C₁₆

C₂×C₄

yes

—

C₂×C₁₁×C₁₆

D₄

yes

—

C₂×C₁₁×C₁₆

Q₈

yes

—

C₄×C₈×C₁₁

C₂×C₄

yes

—

C₄×C₈×C₁₁

Q₈

yes

—

#66883

—

#66883

—

C₄⋊(C₁₁⋊C₈)

—

#12910

—

maximal, Sylow

C₂²×C₄×C₁₁

Q₁₆

yes

—

C₂²×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂×C₈×C₁₁

C₄⋊C₄

yes

—

C₂×C₈×C₁₁

D₈

yes

—

C₂×C₈×C₁₁

Q₁₆

yes

—

C₂×C₈×C₁₁

C₂²×C₄

yes

characteristic

C₂×C₈×C₁₁

C₂×D₄

yes

—

C₂×C₈×C₁₁

C₂×Q₈

yes

characteristic

C₂×C₈×C₁₁

C₂×Q₈

yes

—

C₄²×C₁₁

C₄⋊C₄

yes

—

C₄²×C₁₁

D₈

yes

—

#4318

—

#4318

—

C₂×C₁₁⋊C₈

—

C₁₁×C₁₆

C₄⋊C₄

yes

—

C₂×#368

—

C₂×#346

D₁₁

yes

characteristic

#1848

—

C₂³×C₁₁

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

#107

yes

—

C₂×C₄×C₁₁

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₁

#127

yes

characteristic

C₂×C₄×C₁₁

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₁₁

C₂×D₈

yes

characteristic

C₂×C₄×C₁₁

C₂×D₈

yes

characteristic

C₂×C₄×C₁₁

C₂×Q₁₆

yes

characteristic

C₈×C₁₁

#107

yes

—

C₈×C₁₁

C₂×C₄⋊C₄

yes

—

C₈×C₁₁

C₄⋊Q₈

yes

—

C₁₁⋊C₈

—

C₂²×C₁₆

C₂×D₁₁

yes

—

C₂×#108

—

C₂×#108

—

#423

—

C₂×C₄×C₈

C₂×D₁₁

yes

characteristic

#368

—

#346

Dic₁₁

yes

—

C₂²×C₁₁

—

C₂²×C₁₁

yes

C₂²×C₁₁

yes

C₂²×C₁₁

yes

C₄×C₁₁

—

C₄×C₁₁

yes

C₄×C₁₁

yes

C₄×C₁₁

yes

C₄×C₁₁

yes

C₂×M₁₆

—

C₂²×C₈

D₄₄

yes

characteristic

C₂²×C₈

C₂²×D₁₁

yes

characteristic

C₂×C₄²

D₄₄

yes

characteristic

C₂×C₁₆

Dic₂₂

yes

—

C₂×C₁₆

D₄₄

yes

—

C₂×C₁₆

C₂×Dic₁₁

yes

—

#108

—

#108

—

C₄⋊C₈

—

C₄×C₈

Dic₂₂

yes

—

C₄×C₈

C₂×Dic₁₁

yes

—

C₂×C₁₁

—

C₂×C₁₁

—

C₂×C₁₁

#1845

yes

characteristic

C₂×C₁₁

#2161

yes

—

C₂²×C₄

Dic₄₄

yes

—

C₂²×C₄

C₂×D₄₄

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

D₈₈

yes

—

C₂×C₈

Dic₄₄

yes

—

C₂×C₈

C₄⋊Dic₁₁

yes

—

C₂×C₈

C₂×Dic₂₂

yes

characteristic

C₂×C₈

C₂×Dic₂₂

yes

—

C₂×C₈

C₂×D₄₄

yes

—

C₂×C₈

C₂²×Dic₁₁

yes

characteristic

C₄²

D₈₈

yes

—

100

C₄²

C₄⋊Dic₁₁

yes

—

101

C₁₆

C₄⋊Dic₁₁

yes

—

102

C₁₁

#12910

yes

characteristic, complemented, Sylow

103

C₂³

C₂×Dic₄₄

yes

characteristic

104

C₂×C₄

—

105

C₂×C₄

#66882

yes

—

106

C₂×C₄

#66922

yes

characteristic

107

C₂×C₄

#66927

yes

characteristic

108

C₂×C₄

C₂×D₈₈

yes

characteristic

109

C₂×C₄

C₂×D₈₈

yes

characteristic

110

C₂×C₄

C₂×Dic₄₄

yes

characteristic

111

C₂×C₄

C₂×C₄⋊Dic₁₁

yes

characteristic

112

C₈

—

113

C₈

#66882

yes

—

114

C₈

#66922

yes

—

115

C₈

C₂×C₄⋊Dic₁₁

yes

—

116

C₂²

—

117

C₂²

#10622295

yes

characteristic

118

C₂²

#10622312

yes

characteristic

119

C₂²

C₂×#66882

yes

characteristic

120

C₄

—

121

C₄

#10622295

yes

characteristic

122

C₄

#10622308

yes

characteristic

123

C₄

#10622548

yes

characteristic

124

C₄

C₂×#66882

yes

characteristic

125

C₂

—

126

C₂

—

127

C₂

#13068776

yes

characteristic

128

C₂

#13070411

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×D₈₈
commutator	C₂×C₈×C₁₁	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₁₁
Fitting	C₂×C₁₁×#346	C₂
socle	C₂²×C₁₁	C₂×#107
prime radical	C₂³×C₁₁	C₂×Q₁₆
cosocle	C₂²×C₈×C₁₁	C₂³
hypercenter	C₂×#346	D₁₁
hypocenter	C₁₁	#12910
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#346

subgroup

G/H

center

C₂×C₄

C₂×D₈₈

commutator

C₂×C₈×C₁₁

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₁₁

Fitting

C₂×C₁₁×#346

C₂

socle

C₂²×C₁₁

C₂×#107

prime radical

C₂³×C₁₁

C₂×Q₁₆

cosocle

C₂²×C₈×C₁₁

C₂³

D₁₁

C₁₁

G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#346

N	H ≅ G/N	type
102. C₁₁	#12910	semidirect

H ≅ G/N

type

102. C₁₁

#12910

semidirect

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

subgroup	index
C₂×#10622144	2
#13068788	2
C₂×C₁₁×#346	2
#12910	11

subgroup

index

C₂×#10622144

#13068788

C₂×C₁₁×#346

#12910

Subgroups — #14670225

Conjugacy classes of subgroups

Complements

Maximal subgroups