Group #19133309 — subgroups

Subgroups — #19133309

Order 5504.

332 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 85 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	#14582956	C₂	1	2	yes	maximal, complemented
2	#14582643	C₂	1	4	yes	maximal, complemented
3	C₂×#127×C₄₃	C₂	1	1	yes	maximal, characteristic
4	C₄⋊(C₄₃⋊C₈)	C₂²	1	4	yes	complemented
5	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
6	#13063236	—	2	2	no	—
7	C₂²×D₄×C₄₃	—	2	2	no	—
8	C₂²×D₄×C₄₃	C₄	1	2	yes	—
9	#127×C₄₃	—	2	2	no	—
10	#127×C₄₃	C₄	1	2	yes	—
11	#127×C₄₃	C₂²	1	2	yes	—
12	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄₃	—	2	2	no	—
14	C₂×D₄×C₄₃	—	2	2	no	—
15	C₂×D₄×C₄₃	—	2	4	no	—
16	C₂×D₄×C₄₃	—	2	4	no	—
17	C₂×D₄×C₄₃	—	4	8	no	—
18	C₂×D₄×C₄₃	—	4	4	no	—
19	C₂×D₄×C₄₃	C₂×C₄	1	4	yes	—
20	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₄×C₄₃	D₄	1	2	yes	—
22	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
23	C₄²×C₄₃	D₄	1	2	yes	—
24	C₄²×C₄₃	C₂³	1	1	yes	characteristic
25	C₂×C₄₃⋊C₈	—	2	4	no	—
26	C₂³×C₄₃	—	2	4	no	—
27	C₂³×C₄₃	—	4	8	no	—
28	C₂³×C₄₃	—	4	4	no	—
29	C₂³×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
30	D₄×C₄₃	—	4	4	no	—
31	D₄×C₄₃	—	4	4	no	—
32	D₄×C₄₃	—	4	8	no	—
33	D₄×C₄₃	—	4	8	no	—
34	C₂×C₄×C₄₃	—	2	2	no	—
35	C₂×C₄×C₄₃	—	2	4	no	—
36	C₂×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
37	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
38	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
39	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
40	C₄₃⋊C₈	—	4	4	no	—
41	C₂²×C₄₃	—	2	2	no	—
42	C₂²×C₄₃	—	4	4	no	—
43	C₂²×C₄₃	—	4	8	no	—
44	C₂²×C₄₃	—	8	8	no	—
45	C₂²×C₄₃	#100	1	2	yes	—
46	C₂²×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
47	C₄×C₄₃	—	2	1	no	—
48	C₄×C₄₃	—	2	1	no	—
49	C₄×C₄₃	—	2	2	no	—
50	C₄×C₄₃	AGL(1,ℤ/8)	1	4	yes	—
51	#1555	—	43	1	no	maximal, Sylow
52	C₂×C₄₃	—	2	2	no	—
53	C₂×C₄₃	—	8	4	no	—
54	C₂×C₄₃	C₂×#100	1	1	yes	characteristic
55	C₂×C₄₃	#418	1	2	yes	—
56	C₂×#127	D₄₃	1	1	yes	characteristic
57	#432	—	43	2	no	—
58	#331	—	43	4	no	—
59	C₄₃	#1555	1	1	yes	characteristic, complemented, Sylow
60	C₂²×D₄	—	2	2	no	—
61	C₂²×D₄	Dic₄₃	1	2	yes	—
62	#127	—	2	2	no	—
63	#127	Dic₄₃	1	2	yes	—
64	#127	C₂×D₄₃	1	2	yes	—
65	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
66	C₄⋊C₈	—	43	4	no	—
67	C₂²⋊C₈	—	86	2	no	—
68	#97	—	86	2	no	—
69	C₂⁴	—	2	2	no	—
70	C₂×D₄	—	2	2	no	—
71	C₂×D₄	—	2	4	no	—
72	C₂×D₄	—	2	4	no	—
73	C₂×D₄	—	4	4	no	—
74	C₂×D₄	—	4	8	no	—
75	C₂×D₄	C₂×Dic₄₃	1	4	yes	—
76	C₂²×C₄	C₂×Dic₄₃	1	1	yes	characteristic
77	C₂²×C₄	C₂²⋊D₄₃	1	2	yes	—
78	C₂×C₈	—	86	4	no	—
79	C₄²	C₂×Dic₄₃	1	1	yes	characteristic
80	C₄²	C₂²⋊D₄₃	1	2	yes	—
81	C₄²	C₂²×D₄₃	1	1	yes	characteristic
82	C₂³	—	2	4	no	—
83	C₂³	—	4	8	no	—
84	C₂³	—	4	4	no	—
85	C₂³	C₂²⋊Dic₄₃	1	1	yes	characteristic
86	D₄	—	4	4	no	—
87	D₄	—	4	4	no	—
88	D₄	—	4	8	no	—
89	D₄	—	4	8	no	—
90	C₂×C₄	—	2	2	no	—
91	C₂×C₄	—	2	4	no	—
92	C₂×C₄	C₂²⋊Dic₄₃	1	2	yes	—
93	C₂×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
94	C₂×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
95	C₂×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
96	C₈	—	172	4	no	—
97	C₂²	—	2	2	no	—
98	C₂²	—	4	4	no	—
99	C₂²	—	4	8	no	—
100	C₂²	—	8	8	no	—
101	C₂²	#13063242	1	2	yes	—
102	C₂²	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
103	C₄	—	2	1	no	—
104	C₄	—	2	1	no	—
105	C₄	—	2	2	no	—
106	C₄	#13063351	1	4	yes	—
107	C₂	—	2	2	no	—
108	C₂	—	8	4	no	—
109	C₂	C₂×#13063242	1	1	yes	characteristic
110	C₂	#14582904	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14582956

C₂

yes

maximal, complemented

#14582643

C₂

yes

maximal, complemented

C₂×#127×C₄₃

C₂

yes

maximal, characteristic

C₄⋊(C₄₃⋊C₈)

C₂²

yes

complemented

C₂²⋊(C₄₃⋊C₈)

—

#13063236

—

C₂²×D₄×C₄₃

—

C₂²×D₄×C₄₃

C₄

yes

—

#127×C₄₃

—

#127×C₄₃

C₄

yes

—

#127×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₂⁴×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

C₂×C₄

yes

—

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₃

D₄

yes

—

C₄²×C₄₃

C₂×C₄

yes

characteristic

C₄²×C₄₃

D₄

yes

—

C₄²×C₄₃

C₂³

yes

characteristic

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

C₂²⋊C₄

yes

characteristic

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#100

yes

—

C₂²×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

AGL(1,ℤ/8)

yes

—

#1555

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

C₂×#100

yes

characteristic

C₂×C₄₃

#418

yes

—

C₂×#127

D₄₃

yes

characteristic

#432

—

#331

—

C₄₃

#1555

yes

characteristic, complemented, Sylow

C₂²×D₄

—

C₂²×D₄

Dic₄₃

yes

—

#127

—

#127

Dic₄₃

yes

—

#127

C₂×D₄₃

yes

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

C₂⁴

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

C₂×Dic₄₃

yes

—

C₂²×C₄

C₂×Dic₄₃

yes

characteristic

C₂²×C₄

C₂²⋊D₄₃

yes

—

C₂×C₈

—

C₄²

C₂×Dic₄₃

yes

characteristic

C₄²

C₂²⋊D₄₃

yes

—

C₄²

C₂²×D₄₃

yes

characteristic

C₂³

—

C₂³

—

C₂³

—

C₂³

C₂²⋊Dic₄₃

yes

characteristic

D₄

—

D₄

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²⋊Dic₄₃

yes

—

C₂×C₄

C₂²⋊Dic₄₃

yes

characteristic

C₂×C₄

C₂²×Dic₄₃

yes

characteristic

C₂×C₄

C₂×C₂²⋊D₄₃

yes

—

C₈

—

172

—

C₂²

—

C₂²

—

C₂²

—

100

C₂²

—

101

C₂²

#13063242

yes

—

102

C₂²

C₂×C₂²⋊Dic₄₃

yes

characteristic

103

C₄

—

104

C₄

—

105

C₄

—

106

C₄

#13063351

yes

—

107

C₂

—

108

C₂

—

109

C₂

C₂×#13063242

yes

characteristic

110

C₂

#14582904

yes

—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊Dic₄₃
commutator	C₂×C₄×C₄₃	C₂²×C₄
Frattini	C₄²	C₂²×D₄₃
Fitting	C₂×#127×C₄₃	C₂
socle	C₂²×C₄₃	C₂×C₂²⋊C₄
hypercenter	C₂×#127	D₄₃
hypocenter	C₄₃	#1555
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#127

subgroup

G/H

center

C₂²

C₂×C₂²⋊Dic₄₃

commutator

C₂×C₄×C₄₃

C₂²×C₄

Frattini

C₄²

C₂²×D₄₃

Fitting

C₂×#127×C₄₃

C₂

socle

C₂²×C₄₃

C₂×C₂²⋊C₄

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#127

N	H ≅ G/N	type
1. #14582956	C₂	semidirect
2. #14582643	C₂	semidirect
4. C₄⋊(C₄₃⋊C₈)	C₂²	semidirect
59. C₄₃	#1555	semidirect

H ≅ G/N

type

1. #14582956

C₂

semidirect

2. #14582643

C₂

semidirect

4. C₄⋊(C₄₃⋊C₈)

C₂²

semidirect

59. C₄₃

#1555

semidirect

Subgroups — #19133309

Conjugacy classes of subgroups

Complements