Group #14754161 — subgroups

Subgroups — #14754161

Order 2816.

1118 conjugacy classes of subgroups; only the 571 normal subgroups are shown.

normal subgroups only

This group has 1118 conjugacy classes of subgroups — too many to draw. Only its 571 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×#10622537	C₂	1	6	yes	maximal
2	#13068770	C₂	1	8	yes	maximal, complemented
3	C₂×C₁₁×#376	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄²×C₁₁	C₂²	1	3	yes	—
5	C₂²×#4318	C₂²	1	4	yes	—
6	C₁₁×#376	C₄	1	4	yes	—
7	C₁₁×#376	C₂²	1	4	yes	—
8	C₂×C₁₁×#95	C₄	1	4	yes	—
9	#10622537	—	2	24	no	—
10	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	24	yes	—
11	C₂³×C₄×C₁₁	C₂×C₄	1	6	yes	—
12	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
13	C₂×C₄²×C₁₁	C₂×C₄	1	6	yes	—
14	C₂×C₄²×C₁₁	D₄	1	12	yes	—
15	C₂×C₄²×C₁₁	Q₈	1	12	yes	—
16	C₂×C₄²×C₁₁	C₂³	1	6	yes	—
17	C₂×#4318	—	2	24	no	—
18	C₂²×C₁₁⋊C₈	C₂³	1	8	yes	—
19	C₁₁×#95	C₂×C₄	1	16	yes	—
20	C₄⋊(C₁₁⋊C₈)	—	2	48	no	—
21	#20792	—	11	1	no	maximal, Sylow
22	C₂⁴×C₁₁	C₂²×C₄	1	1	yes	characteristic
23	C₂²×C₄×C₁₁	—	4	12	no	—
24	C₂²×C₄×C₁₁	C₄⋊C₄	1	24	yes	—
25	C₂²×C₄×C₁₁	C₂²×C₄	1	12	yes	—
26	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
27	C₂²×C₄×C₁₁	C₂×D₄	1	6	yes	—
28	C₂²×C₄×C₁₁	C₂×Q₈	1	6	yes	—
29	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
30	C₄²×C₁₁	C₄⋊C₄	1	24	yes	—
31	C₄²×C₁₁	C₂×D₄	1	12	yes	—
32	C₄²×C₁₁	C₂×Q₈	1	12	yes	—
33	#4318	—	4	16	no	—
34	C₂×C₁₁⋊C₈	—	2	24	no	—
35	C₂×#423	—	11	6	no	—
36	C₂×#376	D₁₁	1	1	yes	characteristic
37	#1843	—	11	8	no	—
38	C₂³×C₁₁	—	2	4	no	—
39	C₂³×C₁₁	C₂×C₄⋊C₄	1	6	yes	—
40	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
41	C₂×C₄×C₁₁	—	2	24	no	—
42	C₂×C₄×C₁₁	—	4	24	no	—
43	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	24	yes	—
44	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	6	yes	—
45	C₂×C₄×C₁₁	#127	1	4	yes	—
46	C₂×C₄×C₁₁	C₄⋊Q₈	1	12	yes	—
47	C₂×C₄×C₁₁	C₂²×D₄	1	3	yes	—
48	C₂×C₄×C₁₁	C₂²×Q₈	1	3	yes	—
49	C₁₁⋊C₈	—	4	8	no	—
50	C₂²×M₁₆	—	11	4	no	—
51	C₂²×C₄²	C₂×D₁₁	1	3	yes	—
52	#423	—	22	24	no	—
53	C₂×C₄⋊C₈	—	11	24	no	—
54	#376	Dic₁₁	1	4	yes	—
55	#376	C₂×D₁₁	1	4	yes	—
56	C₂×#95	Dic₁₁	1	4	yes	—
57	C₂²×C₁₁	—	2	12	no	—
58	C₂²×C₁₁	#384	1	4	yes	—
59	C₂²×C₁₁	C₂²×C₄⋊C₄	1	3	yes	—
60	C₂²×C₁₁	#568	1	4	yes	—
61	C₄×C₁₁	—	2	24	no	—
62	C₄×C₁₁	#384	1	4	yes	—
63	C₄×C₁₁	C₂×#127	1	1	yes	characteristic
64	C₄×C₁₁	C₂×C₄⋊Q₈	1	3	yes	—
65	C₂³×C₄	C₂×Dic₁₁	1	6	yes	—
66	C₂³×C₄	C₂²×D₁₁	1	1	yes	characteristic
67	C₂×M₁₆	—	22	24	no	—
68	C₂²×C₈	—	11	8	no	—
69	C₂×C₄²	Dic₂₂	1	12	yes	—
70	C₂×C₄²	D₄₄	1	12	yes	—
71	C₂×C₄²	C₂×Dic₁₁	1	6	yes	—
72	C₂×C₄²	C₂²×D₁₁	1	6	yes	—
73	C₄⋊C₈	—	22	48	no	—
74	#95	C₂×Dic₁₁	1	16	yes	—
75	C₂×C₁₁	—	2	4	no	—
76	C₂×C₁₁	C₂×#384	1	1	yes	characteristic
77	C₂×C₁₁	#2905	1	6	yes	—
78	C₂⁴	C₂²×Dic₁₁	1	1	yes	characteristic
79	C₂²×C₄	—	4	12	no	—
80	C₂²×C₄	C₄⋊Dic₁₁	1	24	yes	—
81	C₂²×C₄	C₂×Dic₂₂	1	6	yes	—
82	C₂²×C₄	C₂×D₄₄	1	6	yes	—
83	C₂²×C₄	C₂²×Dic₁₁	1	12	yes	—
84	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
85	C₂²×C₄	C₂³×D₁₁	1	1	yes	characteristic
86	M₁₆	—	44	16	no	—
87	C₂×C₈	—	22	24	no	—
88	C₄²	C₄⋊Dic₁₁	1	24	yes	—
89	C₄²	C₂×Dic₂₂	1	12	yes	—
90	C₄²	C₂×D₄₄	1	12	yes	—
91	C₁₁	#20792	1	1	yes	characteristic, complemented, Sylow
92	C₂³	—	2	4	no	—
93	C₂³	C₂×C₄⋊Dic₁₁	1	6	yes	—
94	C₂³	C₂³×Dic₁₁	1	1	yes	characteristic
95	C₂×C₄	—	2	24	no	—
96	C₂×C₄	—	4	24	no	—
97	C₂×C₄	#66922	1	12	yes	—
98	C₂×C₄	#66927	1	4	yes	—
99	C₂×C₄	C₂×C₄⋊Dic₁₁	1	24	yes	—
100	C₂×C₄	C₂×C₄⋊Dic₁₁	1	6	yes	—
101	C₂×C₄	C₂²×Dic₂₂	1	3	yes	—
102	C₂×C₄	C₂²×D₄₄	1	3	yes	—
103	C₈	—	44	8	no	—
104	C₂²	—	2	12	no	—
105	C₂²	#10622548	1	4	yes	—
106	C₂²	C₂²×C₄⋊Dic₁₁	1	3	yes	—
107	C₂²	#10623350	1	4	yes	—
108	C₄	—	2	24	no	—
109	C₄	#10622548	1	4	yes	—
110	C₄	C₂×#66922	1	3	yes	—
111	C₄	C₂×#66927	1	1	yes	characteristic
112	C₂	—	2	4	no	—
113	C₂	C₂×#10622548	1	1	yes	characteristic
114	C₂	#13077180	1	6	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10622537

C₂

yes

maximal

#13068770

C₂

yes

maximal, complemented

C₂×C₁₁×#376

C₂

yes

maximal, characteristic

C₂²×C₄²×C₁₁

C₂²

yes

—

C₂²×#4318

C₂²

yes

—

C₁₁×#376

C₄

yes

—

C₁₁×#376

C₂²

yes

—

C₂×C₁₁×#95

C₄

yes

—

#10622537

—

C₂×C₄⋊(C₁₁⋊C₈)

C₂²

yes

—

C₂³×C₄×C₁₁

C₂×C₄

yes

—

C₂³×C₄×C₁₁

C₂³

yes

characteristic

C₂×C₄²×C₁₁

C₂×C₄

yes

—

C₂×C₄²×C₁₁

D₄

yes

—

C₂×C₄²×C₁₁

Q₈

yes

—

C₂×C₄²×C₁₁

C₂³

yes

—

C₂×#4318

—

C₂²×C₁₁⋊C₈

C₂³

yes

—

C₁₁×#95

C₂×C₄

yes

—

C₄⋊(C₁₁⋊C₈)

—

#20792

—

maximal, Sylow

C₂⁴×C₁₁

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₁

—

C₂²×C₄×C₁₁

C₄⋊C₄

yes

—

C₂²×C₄×C₁₁

C₂²×C₄

yes

—

C₂²×C₄×C₁₁

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₁

C₂×D₄

yes

—

C₂²×C₄×C₁₁

C₂×Q₈

yes

—

C₂²×C₄×C₁₁

C₂⁴

yes

characteristic

C₄²×C₁₁

C₄⋊C₄

yes

—

C₄²×C₁₁

C₂×D₄

yes

—

C₄²×C₁₁

C₂×Q₈

yes

—

#4318

—

C₂×C₁₁⋊C₈

—

C₂×#423

—

C₂×#376

D₁₁

yes

characteristic

#1843

—

C₂³×C₁₁

—

C₂³×C₁₁

C₂×C₄⋊C₄

yes

—

C₂³×C₁₁

C₂³×C₄

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₁₁

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₁₁

#127

yes

—

C₂×C₄×C₁₁

C₄⋊Q₈

yes

—

C₂×C₄×C₁₁

C₂²×D₄

yes

—

C₂×C₄×C₁₁

C₂²×Q₈

yes

—

C₁₁⋊C₈

—

C₂²×M₁₆

—

C₂²×C₄²

C₂×D₁₁

yes

—

#423

—

C₂×C₄⋊C₈

—

#376

Dic₁₁

yes

—

#376

C₂×D₁₁

yes

—

C₂×#95

Dic₁₁

yes

—

C₂²×C₁₁

—

C₂²×C₁₁

#384

yes

—

C₂²×C₁₁

C₂²×C₄⋊C₄

yes

—

C₂²×C₁₁

#568

yes

—

C₄×C₁₁

—

C₄×C₁₁

#384

yes

—

C₄×C₁₁

C₂×#127

yes

characteristic

C₄×C₁₁

C₂×C₄⋊Q₈

yes

—

C₂³×C₄

C₂×Dic₁₁

yes

—

C₂³×C₄

C₂²×D₁₁

yes

characteristic

C₂×M₁₆

—

C₂²×C₈

—

C₂×C₄²

Dic₂₂

yes

—

C₂×C₄²

D₄₄

yes

—

C₂×C₄²

C₂×Dic₁₁

yes

—

C₂×C₄²

C₂²×D₁₁

yes

—

C₄⋊C₈

—

#95

C₂×Dic₁₁

yes

—

C₂×C₁₁

—

C₂×C₁₁

C₂×#384

yes

characteristic

C₂×C₁₁

#2905

yes

—

C₂⁴

C₂²×Dic₁₁

yes

characteristic

C₂²×C₄

—

C₂²×C₄

C₄⋊Dic₁₁

yes

—

C₂²×C₄

C₂×Dic₂₂

yes

—

C₂²×C₄

C₂×D₄₄

yes

—

C₂²×C₄

C₂²×Dic₁₁

yes

—

C₂²×C₄

C₂²×Dic₁₁

yes

characteristic

C₂²×C₄

C₂³×D₁₁

yes

characteristic

M₁₆

—

C₂×C₈

—

C₄²

C₄⋊Dic₁₁

yes

—

C₄²

C₂×Dic₂₂

yes

—

C₄²

C₂×D₄₄

yes

—

C₁₁

#20792

yes

characteristic, complemented, Sylow

C₂³

—

C₂³

C₂×C₄⋊Dic₁₁

yes

—

C₂³

C₂³×Dic₁₁

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#66922

yes

—

C₂×C₄

#66927

yes

—

C₂×C₄

C₂×C₄⋊Dic₁₁

yes

—

100

C₂×C₄

C₂×C₄⋊Dic₁₁

yes

—

101

C₂×C₄

C₂²×Dic₂₂

yes

—

102

C₂×C₄

C₂²×D₄₄

yes

—

103

C₈

—

104

C₂²

—

105

C₂²

#10622548

yes

—

106

C₂²

C₂²×C₄⋊Dic₁₁

yes

—

107

C₂²

#10623350

yes

—

108

C₄

—

109

C₄

#10622548

yes

—

110

C₄

C₂×#66922

yes

—

111

C₄

C₂×#66927

yes

characteristic

112

C₂

—

113

C₂

C₂×#10622548

yes

characteristic

114

C₂

#13077180

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₁
commutator, socle	C₂³×C₁₁	C₂³×C₄
Fitting	C₂×C₁₁×#376	C₂
prime radical	C₂⁴×C₁₁	C₂²×C₄
cosocle	C₂²×C₄×C₁₁	C₂⁴
hypercenter	C₂×#376	D₁₁
hypocenter	C₁₁	#20792
LCS	G ▷ C₂³×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#376

subgroup

G/H

center, Frattini

C₂²×C₄

C₂³×D₁₁

commutator, socle

C₂³×C₁₁

C₂³×C₄

Fitting

C₂×C₁₁×#376

C₂

prime radical

C₂⁴×C₁₁

C₂²×C₄

cosocle

C₂²×C₄×C₁₁

C₂⁴

D₁₁

C₁₁

G ▷ C₂³×C₁₁ ▷ C₁₁

C₁ ◁ C₂²×C₄ ◁ C₂×#376

N	H ≅ G/N	type
2. #13068770	C₂	semidirect
91. C₁₁	#20792	semidirect

H ≅ G/N

type

2. #13068770

C₂

semidirect

91. C₁₁

#20792

semidirect

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

subgroup	index
C₂×#10622537	2
#13068770	2
C₂×C₁₁×#376	2
#20792	11

subgroup

index

C₂×#10622537

#13068770

C₂×C₁₁×#376

#20792

Subgroups — #14754161

Conjugacy classes of subgroups

Complements

Maximal subgroups