Group #14640607 — subgroups

Subgroups — #14640607

Order 2816.

262 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 151 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	C₄×#66876	C₂	1	2	yes	maximal
2	C₂×C₁₁×#322	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₈×C₁₁	C₄	1	2	yes	—
4	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
5	C₂×#66876	C₄	1	4	yes	—
6	C₁₁×#322	—	2	2	no	—
7	#10622099	—	2	2	no	—
8	C₄×C₁₁⋊C₁₆	—	2	2	no	—
9	C₂²×C₈×C₁₁	C₈	1	4	yes	—
10	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
11	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
12	C₄×C₈×C₁₁	—	2	2	no	—
13	C₄×C₈×C₁₁	—	2	2	no	—
14	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
15	C₄×C₈×C₁₁	D₄	1	2	yes	—
16	C₄×C₈×C₁₁	Q₈	1	1	yes	characteristic
17	#66876	—	2	4	no	—
18	#66876	C₈	1	8	yes	complemented
19	C₂×C₁₁⋊C₁₆	—	2	4	no	—
20	#7139	—	11	1	no	maximal, Sylow
21	C₂²×C₄×C₁₁	C₄²	1	1	yes	characteristic
22	C₂²×C₄×C₁₁	C₂×C₈	1	2	yes	—
23	C₂×C₈×C₁₁	—	2	4	no	—
24	C₂×C₈×C₁₁	—	4	4	no	—
25	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
26	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
27	C₂×C₈×C₁₁	C₂×C₈	1	4	yes	—
28	C₂×C₈×C₁₁	M₁₆	1	4	yes	—
29	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
30	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
31	C₄²×C₁₁	M₁₆	1	2	yes	—
32	C₁₁⋊C₁₆	—	2	8	no	—
33	C₄×M₃₂	—	11	2	no	—
34	C₂×#322	D₁₁	1	1	yes	characteristic
35	C₂³×C₁₁	C₄×C₈	1	1	yes	characteristic
36	C₂×C₄×C₁₁	—	2	4	no	—
37	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
38	C₂×C₄×C₁₁	C₄×C₈	1	2	yes	—
39	C₂×C₄×C₁₁	#97	1	1	yes	characteristic
40	C₂×C₄×C₁₁	#97	1	2	yes	—
41	C₂×C₄×C₁₁	C₂²⋊C₈	1	2	yes	—
42	C₂×C₄×C₁₁	C₄⋊C₈	1	2	yes	—
43	C₈×C₁₁	—	4	4	no	—
44	C₈×C₁₁	C₂²⋊C₈	1	4	yes	—
45	C₈×C₁₁	C₄⋊C₈	1	4	yes	—
46	C₂×M₃₂	—	11	4	no	—
47	C₂×C₄×C₈	Dic₁₁	1	2	yes	—
48	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
49	#346	—	22	2	no	—
50	C₄×C₁₆	—	22	2	no	—
51	#322	—	2	2	no	—
52	C₂²×C₁₁	—	2	2	no	—
53	C₂²×C₁₁	C₈²	1	1	yes	characteristic
54	C₂²×C₁₁	#322	1	1	yes	characteristic
55	C₂²×C₁₁	#336	1	1	yes	characteristic
56	C₄×C₁₁	—	2	2	no	—
57	C₄×C₁₁	#322	1	2	yes	—
58	C₄×C₁₁	#336	1	2	yes	—
59	C₄×C₁₁	#349	1	4	yes	—
60	C₂²×C₈	C₁₁⋊C₈	1	4	yes	—
61	C₂²×C₈	C₄×D₁₁	1	2	yes	—
62	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
63	M₃₂	—	11	8	no	—
64	M₃₂	—	22	4	no	—
65	C₂×C₁₆	—	22	4	no	—
66	C₄×C₈	—	2	2	no	—
67	C₄×C₈	—	2	2	no	—
68	C₄×C₈	Dic₂₂	1	1	yes	characteristic
69	C₄×C₈	D₄₄	1	1	yes	characteristic
70	C₄×C₈	C₂²⋊D₁₁	1	2	yes	—
71	C₂×C₁₁	—	2	1	no	—
72	C₂×C₁₁	—	2	1	no	—
73	C₂×C₁₁	#1273	1	1	yes	characteristic
74	C₂×C₁₁	#1377	1	2	yes	—
75	C₂²×C₄	C₂×C₁₁⋊C₈	1	2	yes	—
76	C₂²×C₄	C₄×Dic₁₁	1	1	yes	characteristic
77	C₂×C₈	—	2	4	no	—
78	C₂×C₈	—	4	4	no	—
79	C₂×C₈	C₈×D₁₁	1	4	yes	—
80	C₂×C₈	#4313	1	4	yes	—
81	C₂×C₈	Dic₁₁⋊C₄	1	2	yes	—
82	C₂×C₈	(C₂×D₁₁)⋊C₄	1	2	yes	—
83	C₄²	#4318	1	2	yes	—
84	C₄²	C₄⋊Dic₁₁	1	1	yes	characteristic
85	C₄²	C₂²⋊Dic₁₁	1	1	yes	characteristic
86	C₁₆	—	22	8	no	—
87	C₁₁	#7139	1	1	yes	characteristic, complemented, Sylow
88	C₂³	C₄×C₁₁⋊C₈	1	1	yes	characteristic
89	C₂×C₄	—	2	4	no	—
90	C₂×C₄	#66867	1	1	yes	characteristic
91	C₂×C₄	C₄⋊(C₁₁⋊C₈)	1	2	yes	—
92	C₂×C₄	C₈×Dic₁₁	1	2	yes	—
93	C₂×C₄	#66879	1	2	yes	—
94	C₂×C₄	C₂²⋊(C₁₁⋊C₈)	1	2	yes	—
95	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
96	C₈	—	4	4	no	—
97	C₈	Dic₁₁⋊C₈	1	4	yes	—
98	C₈	(C₂×D₁₁)⋊C₈	1	4	yes	—
99	C₂²	—	2	2	no	—
100	C₂²	C₈×C₁₁⋊C₈	1	1	yes	characteristic
101	C₂²	#10622093	1	1	yes	characteristic
102	C₂²	#10622162	1	1	yes	characteristic
103	C₄	—	2	2	no	—
104	C₄	#10622092	1	2	yes	—
105	C₄	#10622188	1	2	yes	—
106	C₄	#10622191	1	4	yes	—
107	C₂	—	2	1	no	—
108	C₂	—	2	1	no	—
109	C₂	C₁₁⋊#1273	1	1	yes	characteristic
110	C₂	#13066700	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#66876

C₂

yes

maximal

C₂×C₁₁×#322

C₂

yes

maximal, characteristic

C₂×C₄×C₈×C₁₁

C₄

yes

—

C₂×C₄×C₈×C₁₁

C₂²

yes

characteristic

C₂×#66876

C₄

yes

—

C₁₁×#322

—

#10622099

—

C₄×C₁₁⋊C₁₆

—

C₂²×C₈×C₁₁

C₈

yes

—

C₂²×C₈×C₁₁

C₂×C₄

yes

—

C₂×C₄²×C₁₁

C₂×C₄

yes

characteristic

C₄×C₈×C₁₁

—

C₄×C₈×C₁₁

—

C₄×C₈×C₁₁

D₄

yes

characteristic

C₄×C₈×C₁₁

D₄

yes

—

C₄×C₈×C₁₁

Q₈

yes

characteristic

#66876

—

#66876

C₈

yes

complemented

C₂×C₁₁⋊C₁₆

—

#7139

—

maximal, Sylow

C₂²×C₄×C₁₁

C₄²

yes

characteristic

C₂²×C₄×C₁₁

C₂×C₈

yes

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

—

C₂×C₈×C₁₁

C₂²⋊C₄

yes

—

C₂×C₈×C₁₁

C₄⋊C₄

yes

—

C₂×C₈×C₁₁

C₂×C₈

yes

—

C₂×C₈×C₁₁

M₁₆

yes

—

C₄²×C₁₁

C₂²⋊C₄

yes

characteristic

C₄²×C₁₁

C₄⋊C₄

yes

characteristic

C₄²×C₁₁

M₁₆

yes

—

C₁₁⋊C₁₆

—

C₄×M₃₂

—

C₂×#322

D₁₁

yes

characteristic

C₂³×C₁₁

C₄×C₈

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

#95

yes

characteristic

C₂×C₄×C₁₁

C₄×C₈

yes

—

C₂×C₄×C₁₁

#97

yes

characteristic

C₂×C₄×C₁₁

#97

yes

—

C₂×C₄×C₁₁

C₂²⋊C₈

yes

—

C₂×C₄×C₁₁

C₄⋊C₈

yes

—

C₈×C₁₁

—

C₈×C₁₁

C₂²⋊C₈

yes

—

C₈×C₁₁

C₄⋊C₈

yes

—

C₂×M₃₂

—

C₂×C₄×C₈

Dic₁₁

yes

—

C₂×C₄×C₈

C₂×D₁₁

yes

characteristic

#346

—

C₄×C₁₆

—

#322

—

C₂²×C₁₁

—

C₂²×C₁₁

C₈²

yes

C₂²×C₁₁

yes

C₂²×C₁₁

yes

C₄×C₁₁

—

C₄×C₁₁

#322

yes

—

C₄×C₁₁

#336

yes

—

C₄×C₁₁

#349

yes

—

C₂²×C₈

C₁₁⋊C₈

yes

—

C₂²×C₈

C₄×D₁₁

yes

—

C₂×C₄²

C₂×Dic₁₁

yes

characteristic

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

Dic₂₂

yes

characteristic

C₄×C₈

D₄₄

yes

characteristic

C₄×C₈

C₂²⋊D₁₁

yes

—

C₂×C₁₁

—

C₂×C₁₁

—

C₂×C₁₁

#1273

yes

characteristic

C₂×C₁₁

#1377

yes

—

C₂²×C₄

C₂×C₁₁⋊C₈

yes

—

C₂²×C₄

C₄×Dic₁₁

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₈×D₁₁

yes

—

C₂×C₈

#4313

yes

—

C₂×C₈

Dic₁₁⋊C₄

yes

—

C₂×C₈

(C₂×D₁₁)⋊C₄

yes

—

C₄²

#4318

yes

—

C₄²

C₄⋊Dic₁₁

yes

characteristic

C₄²

C₂²⋊Dic₁₁

yes

characteristic

C₁₆

—

C₁₁

#7139

yes

characteristic, complemented, Sylow

C₂³

C₄×C₁₁⋊C₈

yes

characteristic

C₂×C₄

—

C₂×C₄

#66867

yes

characteristic

C₂×C₄

C₄⋊(C₁₁⋊C₈)

yes

—

C₂×C₄

C₈×Dic₁₁

yes

—

C₂×C₄

#66879

yes

—

C₂×C₄

C₂²⋊(C₁₁⋊C₈)

yes

—

C₂×C₄

C₁₁⋊#95

yes

characteristic

C₈

—

C₈

Dic₁₁⋊C₈

yes

—

C₈

(C₂×D₁₁)⋊C₈

yes

—

C₂²

—

100

C₂²

C₈×C₁₁⋊C₈

yes

characteristic

101

C₂²

#10622093

yes

characteristic

102

C₂²

#10622162

yes

characteristic

103

C₄

—

104

C₄

#10622092

yes

—

105

C₄

#10622188

yes

—

106

C₄

#10622191

yes

—

107

C₂

—

108

C₂

—

109

C₂

C₁₁⋊#1273

yes

characteristic

110

C₂

#13066700

yes

—

	subgroup	G/H
center	C₄²	C₂²⋊Dic₁₁
commutator	C₂²×C₁₁	C₈²
Frattini	C₂×C₄×C₈	C₂×D₁₁
Fitting	C₂×C₁₁×#322	C₂
socle	C₂²×C₁₁	#336
prime radical	C₂³×C₁₁	C₄×C₈
cosocle	C₂×C₄×C₈×C₁₁	C₂²
hypercenter	C₂×#322	D₁₁
hypocenter	C₁₁	#7139
LCS	G ▷ C₂²×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₄² ◁ C₂×C₄×C₈ ◁ C₂×#322

subgroup

G/H

center

C₄²

C₂²⋊Dic₁₁

commutator

C₂²×C₁₁

C₈²

Frattini

C₂×C₄×C₈

C₂×D₁₁

Fitting

C₂×C₁₁×#322

C₂

socle

C₂²×C₁₁

#336

prime radical

C₂³×C₁₁

C₄×C₈

cosocle

C₂×C₄×C₈×C₁₁

C₂²

D₁₁

C₁₁

G ▷ C₂²×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁

UCS

C₁ ◁ C₄² ◁ C₂×C₄×C₈ ◁ C₂×#322

N	H ≅ G/N	type
18. #66876	C₈	semidirect
87. C₁₁	#7139	semidirect

H ≅ G/N

type

18. #66876

C₈

semidirect

87. C₁₁

#7139

semidirect

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

subgroup	index
C₄×#66876	2
C₂×C₁₁×#322	2
#7139	11

subgroup

index

C₄×#66876

C₂×C₁₁×#322

#7139

Subgroups — #14640607

Conjugacy classes of subgroups

Complements

Maximal subgroups