Group #14647582 — subgroups

Subgroups — #14647582

Order 2816.

338 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 163 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	#13068788	C₂	1	1	yes	maximal, characteristic
2	#13067371	C₂	1	4	yes	maximal
3	C₂×#10622093	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1848	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₁×#108	—	2	2	no	—
6	C₁₁×#423	C₂²	1	2	yes	—
7	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
8	C₂×#66883	—	2	2	no	—
9	#10622537	C₂²	1	2	yes	—
10	C₂×C₄×C₁₁⋊C₈	C₂²	1	2	yes	—
11	#10622118	—	2	8	no	—
12	#10622093	C₄	1	4	yes	—
13	C₂×C₁₁×M₁₆	—	2	2	no	—
14	C₂²×C₈×C₁₁	D₄	1	2	yes	—
15	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
16	C₂×#4318	—	2	2	no	—
17	C₂²×C₁₁⋊C₈	Q₈	1	4	yes	—
18	C₁₁×#108	—	4	4	no	—
19	C₁₁×C₄⋊C₈	—	2	4	no	—
20	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
21	C₄×C₈×C₁₁	Q₈	1	2	yes	—
22	#66883	—	4	4	no	—
23	C₄⋊(C₁₁⋊C₈)	—	2	4	no	—
24	C₄×C₁₁⋊C₈	C₂×C₄	1	4	yes	—
25	C₄×C₁₁⋊C₈	D₄	1	4	yes	—
26	#8825	—	11	1	no	maximal, Sylow
27	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
28	C₂²×C₄×C₁₁	C₂×Q₈	1	2	yes	—
29	C₁₁×M₁₆	—	4	4	no	—
30	C₂×C₈×C₁₁	—	4	2	no	—
31	C₂×C₈×C₁₁	C₄⋊C₄	1	4	yes	—
32	C₂×C₈×C₁₁	SD₁₆	1	4	yes	—
33	C₂×C₈×C₁₁	SD₁₆	1	4	yes	—
34	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
35	C₄²×C₁₁	C₂×D₄	1	2	yes	—
36	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
37	#4318	—	4	4	no	—
38	C₂×C₁₁⋊C₈	—	4	4	no	—
39	C₂×C₁₁⋊C₈	—	4	2	no	—
40	C₂×C₁₁⋊C₈	C₄⋊C₄	1	8	yes	—
41	#1848	—	11	1	no	—
42	#1848	D₁₁	1	1	yes	characteristic
43	#1566	—	11	4	no	—
44	C₂×#322	—	11	1	no	—
45	C₂³×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
46	C₂×C₄×C₁₁	—	2	4	no	—
47	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
48	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
49	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
50	C₂×C₄×C₁₁	C₄⋊Q₈	1	2	yes	—
51	C₂×C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
52	C₂×C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
53	C₈×C₁₁	—	8	2	no	—
54	C₈×C₁₁	#106	1	8	yes	—
55	C₁₁⋊C₈	—	2	8	no	—
56	C₁₁⋊C₈	—	8	2	no	—
57	C₂×#108	—	2	2	no	—
58	C₂×#108	—	22	2	no	—
59	#423	—	11	2	no	—
60	#423	C₂×D₁₁	1	2	yes	—
61	C₂×C₄×C₈	—	11	2	no	—
62	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
63	#334	—	22	8	no	—
64	#322	—	11	4	no	—
65	C₂²×C₁₁	—	2	2	no	—
66	C₂²×C₁₁	#384	1	1	yes	characteristic
67	C₂²×C₁₁	#498	1	2	yes	—
68	C₄×C₁₁	—	2	2	no	—
69	C₄×C₁₁	C₂×#106	1	2	yes	—
70	C₄×C₁₁	#430	1	4	yes	—
71	C₄×C₁₁	#492	1	1	yes	characteristic
72	C₄×C₁₁	#492	1	1	yes	characteristic
73	C₂×M₁₆	—	2	2	no	—
74	C₂×M₁₆	—	22	2	no	—
75	C₂²×C₈	—	11	4	no	—
76	C₂²×C₈	C₂²⋊D₁₁	1	2	yes	—
77	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
78	#108	—	4	4	no	—
79	#108	—	44	4	no	—
80	C₄⋊C₈	—	2	4	no	—
81	C₄⋊C₈	—	22	4	no	—
82	C₄×C₈	—	11	4	no	—
83	C₄×C₈	—	11	4	no	—
84	C₄×C₈	Dic₂₂	1	2	yes	—
85	C₄×C₈	C₄×D₁₁	1	2	yes	—
86	C₂×C₁₁	—	2	2	no	—
87	C₂×C₁₁	#1844	1	1	yes	characteristic
88	C₂×C₁₁	#1849	1	2	yes	—
89	C₂²×C₄	Q₈×D₁₁	1	2	yes	—
90	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
91	M₁₆	—	4	4	no	—
92	M₁₆	—	44	4	no	—
93	C₂×C₈	—	4	2	no	—
94	C₂×C₈	—	11	8	no	—
95	C₂×C₈	—	44	4	no	—
96	C₂×C₈	—	44	2	no	—
97	C₂×C₈	Dic₁₁⋊C₄	1	4	yes	—
98	C₂×C₈	#4324	1	4	yes	—
99	C₂×C₈	#4325	1	4	yes	—
100	C₄²	C₂×Dic₂₂	1	1	yes	characteristic
101	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
102	C₄²	D₄×D₁₁	1	2	yes	—
103	C₁₁	#8825	1	1	yes	characteristic, complemented, Sylow
104	C₂³	#66997	1	1	yes	characteristic
105	C₂×C₄	—	2	4	no	—
106	C₂×C₄	#66941	1	2	yes	—
107	C₂×C₄	C₄⋊C₄×D₁₁	1	2	yes	—
108	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
109	C₂×C₄	C₂×#4324	1	2	yes	—
110	C₂×C₄	#66993	1	1	yes	characteristic
111	C₂×C₄	C₂×#4325	1	2	yes	—
112	C₈	—	8	2	no	—
113	C₈	—	22	8	no	—
114	C₈	—	88	2	no	—
115	C₈	#66872	1	8	yes	—
116	C₂²	—	2	2	no	—
117	C₂²	#10622589	1	1	yes	characteristic
118	C₂²	#10622692	1	2	yes	—
119	C₄	—	2	2	no	—
120	C₄	#10622506	1	4	yes	—
121	C₄	C₂×#66872	1	2	yes	—
122	C₄	#10622689	1	1	yes	characteristic
123	C₄	#10622698	1	1	yes	characteristic
124	C₂	—	2	2	no	—
125	C₂	#13068772	1	1	yes	characteristic
126	C₂	#13068789	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13068788

C₂

yes

maximal, characteristic

#13067371

C₂

yes

maximal

C₂×#10622093

C₂

yes

maximal, characteristic

C₁₁×#1848

C₂

yes

maximal, characteristic

C₂×C₁₁×#108

—

C₁₁×#423

C₂²

yes

—

C₂×C₄×C₈×C₁₁

C₂²

yes

characteristic

C₂×#66883

—

#10622537

C₂²

yes

—

C₂×C₄×C₁₁⋊C₈

C₂²

yes

—

#10622118

—

#10622093

C₄

yes

—

C₂×C₁₁×M₁₆

—

C₂²×C₈×C₁₁

D₄

yes

—

C₂×C₄²×C₁₁

C₂³

yes

characteristic

C₂×#4318

—

C₂²×C₁₁⋊C₈

Q₈

yes

—

C₁₁×#108

—

C₁₁×C₄⋊C₈

—

C₄×C₈×C₁₁

C₂×C₄

yes

—

C₄×C₈×C₁₁

Q₈

yes

—

#66883

—

C₄⋊(C₁₁⋊C₈)

—

C₄×C₁₁⋊C₈

C₂×C₄

yes

—

C₄×C₁₁⋊C₈

D₄

yes

—

#8825

—

maximal, Sylow

C₂²×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₁

C₂×Q₈

yes

—

C₁₁×M₁₆

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

C₄⋊C₄

yes

—

C₂×C₈×C₁₁

SD₁₆

yes

—

C₂×C₈×C₁₁

SD₁₆

yes

—

C₄²×C₁₁

C₂²×C₄

yes

characteristic

C₄²×C₁₁

C₂×D₄

yes

—

C₄²×C₁₁

C₂×Q₈

yes

characteristic

#4318

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

C₄⋊C₄

yes

—

#1848

—

#1848

D₁₁

yes

characteristic

#1566

—

C₂×#322

—

C₂³×C₁₁

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₁₁

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₁

#127

yes

characteristic

C₂×C₄×C₁₁

C₄⋊Q₈

yes

—

C₂×C₄×C₁₁

C₂×SD₁₆

yes

—

C₂×C₄×C₁₁

C₂×SD₁₆

yes

—

C₈×C₁₁

—

C₈×C₁₁

#106

yes

—

C₁₁⋊C₈

—

C₁₁⋊C₈

—

—

—

—

C₂×D₁₁

yes

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₁₁

yes

characteristic

#334

—

#322

—

C₂²×C₁₁

—

C₂²×C₁₁

#384

yes

characteristic

C₂²×C₁₁

#498

yes

—

C₄×C₁₁

—

C₄×C₁₁

C₂×#106

yes

—

C₄×C₁₁

#430

yes

—

C₄×C₁₁

yes

C₄×C₁₁

yes

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

C₂²⋊D₁₁

yes

—

C₂×C₄²

C₂²×D₁₁

yes

characteristic

#108

—

#108

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

Dic₂₂

yes

—

C₄×C₈

C₄×D₁₁

yes

—

C₂×C₁₁

—

C₂×C₁₁

#1844

yes

characteristic

C₂×C₁₁

#1849

yes

—

C₂²×C₄

Q₈×D₁₁

yes

—

C₂²×C₄

C₂×C₂²⋊D₁₁

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

Dic₁₁⋊C₄

yes

—

C₂×C₈

#4324

yes

—

C₂×C₈

#4325

yes

—

100

C₄²

C₂×Dic₂₂

yes

characteristic

101

C₄²

C₂×C₄×D₁₁

yes

characteristic

102

C₄²

D₄×D₁₁

yes

—

103

C₁₁

#8825

yes

characteristic, complemented, Sylow

104

C₂³

#66997

yes

characteristic

105

C₂×C₄

—

106

C₂×C₄

#66941

yes

—

107

C₂×C₄

C₄⋊C₄×D₁₁

yes

—

108

C₂×C₄

C₂×Dic₁₁⋊C₄

yes

characteristic

109

C₂×C₄

C₂×#4324

yes

—

110

C₂×C₄

#66993

yes

characteristic

111

C₂×C₄

C₂×#4325

yes

—

112

C₈

—

113

C₈

—

114

C₈

—

115

C₈

#66872

yes

—

116

C₂²

—

117

C₂²

#10622589

yes

characteristic

118

C₂²

#10622692

yes

—

119

C₄

—

120

C₄

#10622506

yes

—

121

C₄

C₂×#66872

yes

—

122

C₄

#10622689

yes

characteristic

123

C₄

#10622698

yes

characteristic

124

C₂

—

125

C₂

#13068772

yes

characteristic

126

C₂

#13068789

yes

—

	subgroup	G/H
center	C₂×C₄	#66993
commutator	C₄²×C₁₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₁₁×#1848	C₂
socle	C₂²×C₁₁	#384
prime radical	C₂³×C₁₁	C₄⋊Q₈
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	#1848	D₁₁
hypocenter	C₁₁	#8825
LCS	G ▷ C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1848

subgroup

G/H

center

C₂×C₄

#66993

commutator

C₄²×C₁₁

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₁

Fitting

C₁₁×#1848

C₂

socle

C₂²×C₁₁

#384

prime radical

C₂³×C₁₁

C₄⋊Q₈

cosocle

C₂×C₄²×C₁₁

C₂³

D₁₁

C₁₁

G ▷ C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1848

N	H ≅ G/N	type
103. C₁₁	#8825	semidirect

H ≅ G/N

type

103. C₁₁

#8825

semidirect

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

subgroup	index
#13068788	2
#13067371	2
C₂×#10622093	2
C₁₁×#1848	2
#8825	11

subgroup

index

C₁₁×#1848

Subgroups — #14647582

Conjugacy classes of subgroups

Complements

Maximal subgroups