Group #14647574 — subgroups

Subgroups — #14647574

Order 2816.

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

normal subgroups only

This group has 354 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	#13068788	C₂	1	2	yes	maximal
2	#13067372	C₂	1	4	yes	maximal
3	C₂×C₈²×C₁₁	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
5	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
6	C₂×#66883	—	2	4	no	—
7	#10622537	C₂²	1	4	yes	—
8	C₈²×C₁₁	C₄	1	1	yes	characteristic
9	C₈²×C₁₁	C₄	1	2	yes	—
10	C₈²×C₁₁	C₄	1	1	yes	characteristic
11	#10622095	—	2	8	no	—
12	C₂²×C₈×C₁₁	D₄	1	2	yes	—
13	C₂²×C₈×C₁₁	Q₈	1	4	yes	—
14	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
15	C₂×#4318	—	2	4	no	—
16	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
17	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
18	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
19	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
20	C₄×C₈×C₁₁	D₄	1	4	yes	—
21	C₄×C₈×C₁₁	Q₈	1	2	yes	—
22	#66883	—	4	8	no	—
23	C₄⋊(C₁₁⋊C₈)	—	2	8	no	—
24	#8822	—	11	1	no	maximal, Sylow
25	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
26	C₂²×C₄×C₁₁	C₂×Q₈	1	2	yes	—
27	C₂×C₈×C₁₁	—	2	8	no	—
28	C₂×C₈×C₁₁	C₄⋊C₄	1	4	yes	—
29	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
30	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
31	C₂×C₈×C₁₁	C₄⋊C₄	1	4	yes	—
32	C₂×C₈×C₁₁	SD₁₆	1	8	yes	—
33	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
34	C₄²×C₁₁	C₂×D₄	1	2	yes	—
35	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
36	#4318	—	4	8	no	—
37	C₂×C₁₁⋊C₈	—	4	4	no	—
38	#1848	—	11	2	no	—
39	#1566	—	11	4	no	—
40	C₂×C₈²	D₁₁	1	1	yes	characteristic
41	C₂³×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
42	C₂×C₄×C₁₁	—	2	4	no	—
43	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
44	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
45	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
46	C₂×C₄×C₁₁	C₄⋊Q₈	1	2	yes	—
47	C₂×C₄×C₁₁	C₂×SD₁₆	1	4	yes	—
48	C₈×C₁₁	—	2	4	no	—
49	C₈×C₁₁	#106	1	4	yes	—
50	C₈×C₁₁	#106	1	4	yes	—
51	C₈×C₁₁	#108	1	8	yes	complemented
52	C₁₁⋊C₈	—	8	4	no	—
53	C₂×#108	—	22	4	no	—
54	#423	—	11	4	no	—
55	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
56	C₂×C₄×C₈	C₂×D₁₁	1	2	yes	—
57	#334	—	22	8	no	—
58	C₈²	Dic₁₁	1	1	yes	characteristic
59	C₈²	Dic₁₁	1	2	yes	—
60	C₈²	Dic₁₁	1	1	yes	characteristic
61	C₂²×C₁₁	—	2	2	no	—
62	C₂²×C₁₁	#384	1	1	yes	characteristic
63	C₂²×C₁₁	#498	1	2	yes	—
64	C₄×C₁₁	—	2	2	no	—
65	C₄×C₁₁	C₂×#106	1	2	yes	—
66	C₄×C₁₁	C₂×#108	1	4	yes	—
67	C₄×C₁₁	#492	1	2	yes	—
68	C₂×M₁₆	—	22	4	no	—
69	C₂²×C₈	Dic₂₂	1	4	yes	—
70	C₂²×C₈	D₄₄	1	2	yes	—
71	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
72	#108	—	44	8	no	—
73	C₄⋊C₈	—	22	8	no	—
74	C₄×C₈	Dic₂₂	1	2	yes	—
75	C₄×C₈	D₄₄	1	4	yes	—
76	C₄×C₈	C₂×Dic₁₁	1	2	yes	—
77	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
78	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
79	C₄×C₈	C₂×Dic₁₁	1	2	yes	—
80	C₂×C₁₁	—	2	2	no	—
81	C₂×C₁₁	#1844	1	1	yes	characteristic
82	C₂×C₁₁	#1848	1	2	yes	—
83	C₂²×C₄	C₂×Dic₂₂	1	2	yes	—
84	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
85	M₁₆	—	44	8	no	—
86	C₂×C₈	—	2	8	no	—
87	C₂×C₈	—	44	4	no	—
88	C₂×C₈	#4314	1	8	yes	—
89	C₂×C₈	C₄⋊Dic₁₁	1	4	yes	—
90	C₂×C₈	C₄⋊Dic₁₁	1	2	yes	—
91	C₂×C₈	C₄⋊Dic₁₁	1	2	yes	—
92	C₂×C₈	C₄⋊Dic₁₁	1	4	yes	—
93	C₄²	C₂×Dic₂₂	1	1	yes	characteristic
94	C₄²	C₂×D₄₄	1	2	yes	—
95	C₄²	C₂²×Dic₁₁	1	1	yes	characteristic
96	C₁₁	#8822	1	1	yes	characteristic, complemented, Sylow
97	C₂³	#66922	1	1	yes	characteristic
98	C₂×C₄	—	2	4	no	—
99	C₂×C₄	#66922	1	2	yes	—
100	C₂×C₄	#66927	1	1	yes	characteristic
101	C₂×C₄	C₂×#4314	1	4	yes	—
102	C₂×C₄	C₂×C₄⋊Dic₁₁	1	2	yes	—
103	C₂×C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
104	C₈	—	2	4	no	—
105	C₈	—	88	4	no	—
106	C₈	#66881	1	4	yes	—
107	C₈	#66881	1	4	yes	—
108	C₈	#66883	1	8	yes	complemented
109	C₂²	—	2	2	no	—
110	C₂²	#10622293	1	2	yes	—
111	C₂²	#10622548	1	1	yes	characteristic
112	C₄	—	2	2	no	—
113	C₄	#10622306	1	2	yes	—
114	C₄	C₂×#66881	1	2	yes	—
115	C₄	C₂×#66883	1	4	yes	—
116	C₂	—	2	2	no	—
117	C₂	#13068773	1	1	yes	characteristic
118	C₂	#13068788	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13068788

C₂

yes

maximal

#13067372

C₂

yes

maximal

C₂×C₈²×C₁₁

C₂

yes

maximal, characteristic

C₂×C₄×C₈×C₁₁

C₂²

yes

—

C₂×C₄×C₈×C₁₁

C₂²

yes

characteristic

C₂×#66883

—

#10622537

C₂²

yes

—

C₈²×C₁₁

C₄

yes

characteristic

C₈²×C₁₁

C₄

yes

—

C₈²×C₁₁

C₄

yes

characteristic

#10622095

—

C₂²×C₈×C₁₁

D₄

yes

—

C₂²×C₈×C₁₁

Q₈

yes

—

C₂×C₄²×C₁₁

C₂³

yes

characteristic

C₂×#4318

—

C₄×C₈×C₁₁

C₂×C₄

yes

—

C₄×C₈×C₁₁

C₂×C₄

yes

characteristic

C₄×C₈×C₁₁

C₂×C₄

yes

characteristic

C₄×C₈×C₁₁

C₂×C₄

yes

—

C₄×C₈×C₁₁

D₄

yes

—

C₄×C₈×C₁₁

Q₈

yes

—

#66883

—

C₄⋊(C₁₁⋊C₈)

—

#8822

—

maximal, Sylow

C₂²×C₄×C₁₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₁

C₂×Q₈

yes

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

C₄⋊C₄

yes

—

C₂×C₈×C₁₁

C₄⋊C₄

yes

—

C₂×C₈×C₁₁

C₄⋊C₄

yes

—

C₂×C₈×C₁₁

C₄⋊C₄

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

—

#1848

—

#1566

—

C₂×C₈²

D₁₁

yes

characteristic

C₂³×C₁₁

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₁

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₁₁

#127

yes

characteristic

C₂×C₄×C₁₁

C₄⋊Q₈

yes

—

C₂×C₄×C₁₁

C₂×SD₁₆

yes

—

C₈×C₁₁

—

C₈×C₁₁

#106

yes

—

C₈×C₁₁

#106

yes

—

C₈×C₁₁

#108

yes

complemented

C₁₁⋊C₈

—

C₂×#108

—

#423

—

C₂×C₄×C₈

C₂×D₁₁

yes

characteristic

C₂×C₄×C₈

C₂×D₁₁

yes

—

#334

—

C₈²

Dic₁₁

yes

characteristic

C₈²

Dic₁₁

yes

—

C₈²

Dic₁₁

yes

characteristic

C₂²×C₁₁

—

C₂²×C₁₁

#384

yes

characteristic

C₂²×C₁₁

#498

yes

—

C₄×C₁₁

—

C₄×C₁₁

C₂×#106

yes

—

C₄×C₁₁

C₂×#108

yes

—

C₄×C₁₁

#492

yes

—

C₂×M₁₆

—

C₂²×C₈

Dic₂₂

yes

—

C₂²×C₈

D₄₄

yes

—

C₂×C₄²

C₂²×D₁₁

yes

characteristic

#108

—

C₄⋊C₈

—

C₄×C₈

Dic₂₂

yes

—

C₄×C₈

D₄₄

yes

—

C₄×C₈

C₂×Dic₁₁

yes

—

C₄×C₈

C₂×Dic₁₁

yes

characteristic

C₄×C₈

C₂×Dic₁₁

yes

characteristic

C₄×C₈

C₂×Dic₁₁

yes

—

C₂×C₁₁

—

C₂×C₁₁

#1844

yes

characteristic

C₂×C₁₁

#1848

yes

—

C₂²×C₄

C₂×Dic₂₂

yes

—

C₂²×C₄

C₂×D₄₄

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

#4314

yes

—

C₂×C₈

C₄⋊Dic₁₁

yes

—

C₂×C₈

C₄⋊Dic₁₁

yes

—

C₂×C₈

C₄⋊Dic₁₁

yes

—

C₂×C₈

C₄⋊Dic₁₁

yes

—

C₄²

C₂×Dic₂₂

yes

characteristic

C₄²

C₂×D₄₄

yes

—

C₄²

C₂²×Dic₁₁

yes

characteristic

C₁₁

#8822

yes

characteristic, complemented, Sylow

C₂³

#66922

yes

characteristic

C₂×C₄

—

C₂×C₄

#66922

yes

—

100

C₂×C₄

#66927

yes

characteristic

101

C₂×C₄

C₂×#4314

yes

—

102

C₂×C₄

C₂×C₄⋊Dic₁₁

yes

—

103

C₂×C₄

C₂×C₄⋊Dic₁₁

yes

characteristic

104

C₈

—

105

C₈

—

106

C₈

#66881

yes

—

107

C₈

#66881

yes

—

108

C₈

#66883

yes

complemented

109

C₂²

—

110

C₂²

#10622293

yes

—

111

C₂²

#10622548

yes

characteristic

112

C₄

—

113

C₄

#10622306

yes

—

114

C₄

C₂×#66881

yes

—

115

C₄

C₂×#66883

yes

—

116

C₂

—

117

C₂

#13068773

yes

characteristic

118

C₂

#13068788

yes

—

	subgroup	G/H
center	C₂×C₄	#66927
commutator	C₄²×C₁₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₂×C₈²×C₁₁	C₂
socle	C₂²×C₁₁	#384
prime radical	C₂³×C₁₁	C₄⋊Q₈
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	C₂×C₈²	D₁₁
hypocenter	C₁₁	#8822
LCS	G ▷ C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₈²

subgroup

G/H

center

C₂×C₄

#66927

commutator

C₄²×C₁₁

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₁

Fitting

C₂×C₈²×C₁₁

C₂

socle

C₂²×C₁₁

#384

prime radical

C₂³×C₁₁

C₄⋊Q₈

cosocle

C₂×C₄²×C₁₁

C₂³

hypercenter

C₂×C₈²

D₁₁

hypocenter

C₁₁

#8822

LCS

G ▷ C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₈²

N	H ≅ G/N	type
51. C₈×C₁₁	#108	semidirect
96. C₁₁	#8822	semidirect
108. C₈	#66883	semidirect

H ≅ G/N

type

51. C₈×C₁₁

#108

semidirect

96. C₁₁

#8822

semidirect

108. C₈

#66883

semidirect

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

subgroup	index
#13068788	2
#13067372	2
C₂×C₈²×C₁₁	2
#8822	11

subgroup

index

#13068788

#13067372

C₂×C₈²×C₁₁

#8822

Subgroups — #14647574

Conjugacy classes of subgroups

Complements

Maximal subgroups