Group #19143697 — subgroups

Subgroups — #19143697

Order 5504.

330 conjugacy classes of subgroups; only the 205 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 205 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	#14583030	C₂	1	4	yes	maximal, complemented
2	Q₈×C₄₃⋊C₈	C₂	1	4	yes	maximal, complemented
3	#14582960	C₂	1	4	yes	maximal
4	#14582952	C₂	1	2	yes	maximal
5	C₄₃×#533	C₂	1	1	yes	maximal, characteristic
6	C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
7	C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
8	C₄⋊(C₄₃⋊C₈)	C₂²	1	8	yes	—
9	C₂²⋊(C₄₃⋊C₈)	C₂²	1	4	yes	—
10	#13063236	C₂²	1	4	yes	—
11	C₄×C₄₃⋊C₈	C₂²	1	4	yes	—
12	C₄×C₄₃⋊C₈	C₂²	1	4	yes	—
13	C₄⋊Q₈×C₄₃	C₄	1	2	yes	—
14	#125×C₄₃	C₄	1	2	yes	—
15	C₂²⋊Q₈×C₄₃	C₄	1	4	yes	—
16	C₄×Q₈×C₄₃	C₂²	1	4	yes	—
17	#117×C₄₃	C₂²	1	2	yes	—
18	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×Q₈×C₄₃	C₂×C₄	1	4	yes	—
20	C₂²×C₄×C₄₃	C₂×C₄	1	2	yes	—
21	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
22	C₄⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
23	C₄⋊C₄×C₄₃	C₂×C₄	1	8	yes	—
24	C₄⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
25	C₂²⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
26	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
27	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
28	C₄²×C₄₃	C₂³	1	2	yes	—
29	C₄²×C₄₃	C₂³	1	4	yes	—
30	C₂×C₄₃⋊C₈	C₂³	1	4	yes	—
31	C₂×C₄₃⋊C₈	C₂³	1	4	yes	—
32	C₂³×C₄₃	C₂²×C₄	1	1	yes	characteristic
33	Q₈×C₄₃	—	2	8	no	—
34	C₂×C₄×C₄₃	—	2	4	no	—
35	C₂×C₄×C₄₃	—	2	2	no	—
36	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
38	C₂×C₄×C₄₃	C₂²×C₄	1	8	yes	—
39	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
40	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
41	C₄₃⋊C₈	—	2	4	no	—
42	C₄₃⋊C₈	—	2	4	no	—
43	C₂²×C₄₃	—	2	1	no	—
44	C₂²×C₄₃	—	2	2	no	—
45	C₂²×C₄₃	C₂³×C₄	1	1	yes	characteristic
46	C₄×C₄₃	—	2	1	no	—
47	C₄×C₄₃	—	2	2	no	—
48	C₄×C₄₃	—	2	8	no	—
49	C₄×C₄₃	#131	1	4	yes	—
50	C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
51	#2986	—	43	1	no	maximal, Sylow
52	C₂×C₄₃	—	4	1	no	—
53	C₂×C₄₃	#519	1	1	yes	characteristic
54	C₂×C₄₃	C₂×#131	1	2	yes	—
55	#533	D₄₃	1	1	yes	characteristic
56	#446	—	43	4	no	—
57	C₈×Q₈	—	43	4	no	—
58	#433	—	43	4	no	—
59	#431	—	43	2	no	—
60	C₄₃	#2986	1	1	yes	characteristic, complemented, Sylow
61	C₄⋊Q₈	Dic₄₃	1	2	yes	—
62	#125	Dic₄₃	1	2	yes	—
63	C₂²⋊Q₈	Dic₄₃	1	4	yes	—
64	C₄×Q₈	C₂×D₄₃	1	4	yes	—
65	#117	C₂×D₄₃	1	2	yes	—
66	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
67	C₄⋊C₈	—	43	2	no	—
68	C₄⋊C₈	—	43	2	no	—
69	C₄⋊C₈	—	43	8	no	—
70	C₂²⋊C₈	—	43	4	no	—
71	#97	—	43	4	no	—
72	C₄×C₈	—	43	4	no	—
73	C₄×C₈	—	43	4	no	—
74	C₂×Q₈	C₂×Dic₄₃	1	4	yes	—
75	C₂²×C₄	C₂×Dic₄₃	1	2	yes	—
76	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
77	C₂×C₈	—	43	4	no	—
78	C₂×C₈	—	43	4	no	—
79	C₄⋊C₄	C₂×Dic₄₃	1	4	yes	—
80	C₄⋊C₄	C₂×Dic₄₃	1	8	yes	—
81	C₄⋊C₄	C₂×Dic₄₃	1	4	yes	—
82	C₂²⋊C₄	C₂×Dic₄₃	1	4	yes	—
83	C₄²	C₂×Dic₄₃	1	1	yes	characteristic
84	C₄²	C₂×Dic₄₃	1	1	yes	characteristic
85	C₄²	C₂²×D₄₃	1	2	yes	—
86	C₄²	C₂²×D₄₃	1	4	yes	—
87	C₂³	C₂²×Dic₄₃	1	1	yes	characteristic
88	Q₈	—	2	8	no	—
89	C₂×C₄	—	2	4	no	—
90	C₂×C₄	—	2	2	no	—
91	C₂×C₄	C₂²×Dic₄₃	1	2	yes	—
92	C₂×C₄	C₂²×Dic₄₃	1	8	yes	—
93	C₂×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
94	C₂×C₄	C₂²×Dic₄₃	1	2	yes	—
95	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
96	C₈	—	86	4	no	—
97	C₈	—	86	4	no	—
98	C₂²	—	2	1	no	—
99	C₂²	—	2	2	no	—
100	C₂²	C₂³×Dic₄₃	1	1	yes	characteristic
101	C₄	—	2	1	no	—
102	C₄	—	2	2	no	—
103	C₄	—	2	8	no	—
104	C₄	#13063332	1	4	yes	—
105	C₄	#13063373	1	2	yes	—
106	C₂	—	4	1	no	—
107	C₂	#14583377	1	1	yes	characteristic
108	C₂	C₂×#13063332	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14583030

C₂

yes

maximal, complemented

Q₈×C₄₃⋊C₈

C₂

yes

maximal, complemented

#14582960

C₂

yes

maximal

#14582952

C₂

yes

maximal

C₄₃×#533

C₂

yes

maximal, characteristic

C₄⋊(C₄₃⋊C₈)

C₂²

yes

—

C₄⋊(C₄₃⋊C₈)

C₂²

yes

—

C₄⋊(C₄₃⋊C₈)

C₂²

yes

—

C₂²⋊(C₄₃⋊C₈)

C₂²

yes

—

#13063236

C₂²

yes

—

C₄×C₄₃⋊C₈

C₂²

yes

—

C₄×C₄₃⋊C₈

C₂²

yes

—

C₄⋊Q₈×C₄₃

C₄

yes

—

#125×C₄₃

C₄

yes

—

C₂²⋊Q₈×C₄₃

C₄

yes

—

C₄×Q₈×C₄₃

C₂²

yes

—

#117×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₂×Q₈×C₄₃

C₂×C₄

yes

—

C₂²×C₄×C₄₃

C₂×C₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₄⋊C₄×C₄₃

C₂×C₄

yes

—

C₄⋊C₄×C₄₃

C₂×C₄

yes

—

C₄⋊C₄×C₄₃

C₂×C₄

yes

—

C₂²⋊C₄×C₄₃

C₂×C₄

yes

—

C₄²×C₄₃

C₂×C₄

yes

characteristic

C₄²×C₄₃

C₂×C₄

yes

characteristic

C₄²×C₄₃

C₂³

yes

—

C₄²×C₄₃

C₂³

yes

—

C₂×C₄₃⋊C₈

C₂³

yes

—

C₂×C₄₃⋊C₈

C₂³

yes

—

C₂³×C₄₃

C₂²×C₄

yes

characteristic

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂⁴

yes

characteristic

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂³×C₄

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#131

yes

—

C₄×C₄₃

2₋¹⁺⁴

yes

—

#2986

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

#519

yes

characteristic

C₂×C₄₃

C₂×#131

yes

—

#533

D₄₃

yes

characteristic

#446

—

C₈×Q₈

—

#433

—

#431

—

C₄₃

#2986

yes

characteristic, complemented, Sylow

C₄⋊Q₈

Dic₄₃

yes

—

#125

Dic₄₃

yes

—

C₂²⋊Q₈

Dic₄₃

yes

—

C₄×Q₈

C₂×D₄₃

yes

—

#117

C₂×D₄₃

yes

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₂×Q₈

C₂×Dic₄₃

yes

—

C₂²×C₄

C₂×Dic₄₃

yes

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

C₂×Dic₄₃

yes

—

C₄⋊C₄

C₂×Dic₄₃

yes

—

C₄⋊C₄

C₂×Dic₄₃

yes

—

C₂²⋊C₄

C₂×Dic₄₃

yes

—

C₄²

C₂×Dic₄₃

yes

characteristic

C₄²

C₂×Dic₄₃

yes

characteristic

C₄²

C₂²×D₄₃

yes

—

C₄²

C₂²×D₄₃

yes

—

C₂³

C₂²×Dic₄₃

yes

characteristic

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²×Dic₄₃

yes

—

C₂×C₄

C₂²×Dic₄₃

yes

—

C₂×C₄

C₂²×Dic₄₃

yes

characteristic

C₂×C₄

C₂²×Dic₄₃

yes

—

C₂×C₄

C₂³×D₄₃

yes

characteristic

C₈

—

C₈

—

C₂²

—

C₂²

—

100

C₂²

C₂³×Dic₄₃

yes

characteristic

101

C₄

—

102

C₄

—

103

C₄

—

104

C₄

#13063332

yes

—

105

C₄

#13063373

yes

—

106

C₂

—

107

C₂

#14583377

yes

characteristic

108

C₂

C₂×#13063332

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₄₃
commutator, socle	C₂²×C₄₃	C₂³×C₄
Fitting	C₄₃×#533	C₂
hypercenter	#533	D₄₃
hypocenter	C₄₃	#2986
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ #533

subgroup

G/H

center, Frattini

C₂×C₄

C₂³×D₄₃

commutator, socle

C₂²×C₄₃

C₂³×C₄

Fitting

C₄₃×#533

C₂

D₄₃

C₄₃

G ▷ C₂²×C₄₃ ▷ C₄₃

C₁ ◁ C₂×C₄ ◁ #533

N	H ≅ G/N	type
1. #14583030	C₂	semidirect
2. Q₈×C₄₃⋊C₈	C₂	semidirect
60. C₄₃	#2986	semidirect

H ≅ G/N

type

1. #14583030

C₂

semidirect

2. Q₈×C₄₃⋊C₈

C₂

semidirect

60. C₄₃

#2986

semidirect

Subgroups — #19143697

Conjugacy classes of subgroups

Complements