Group #19143701 — subgroups

Subgroups — #19143701

Order 5504.

314 conjugacy classes of subgroups; only the 197 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 197 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	8	yes	maximal, complemented
2	#14582960	C₂	1	4	yes	maximal
3	#14582956	C₂	1	2	yes	maximal
4	C₄₃×#533	C₂	1	1	yes	maximal, characteristic
5	C₄⋊(C₄₃⋊C₈)	C₂²	1	4	yes	—
6	C₄⋊(C₄₃⋊C₈)	C₂²	1	8	yes	—
7	C₂²⋊(C₄₃⋊C₈)	C₂²	1	4	yes	—
8	#13063236	C₂²	1	4	yes	—
9	#13063236	C₂²	1	4	yes	—
10	C₄×C₄₃⋊C₈	C₂²	1	4	yes	—
11	C₄⋊Q₈×C₄₃	C₄	1	2	yes	—
12	#125×C₄₃	C₄	1	2	yes	—
13	C₂²⋊Q₈×C₄₃	C₄	1	4	yes	—
14	C₄×Q₈×C₄₃	C₂²	1	4	yes	—
15	#117×C₄₃	C₂²	1	2	yes	—
16	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×Q₈×C₄₃	C₂×C₄	1	4	yes	—
18	C₂²×C₄×C₄₃	C₂×C₄	1	2	yes	—
19	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
20	C₄⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
21	C₄⋊C₄×C₄₃	C₂×C₄	1	8	yes	—
22	C₄⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
23	C₂²⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
24	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
25	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
26	C₄²×C₄₃	C₂³	1	2	yes	—
27	C₄²×C₄₃	C₂³	1	4	yes	—
28	C₂×C₄₃⋊C₈	C₂³	1	8	yes	—
29	C₂³×C₄₃	C₂²×C₄	1	1	yes	characteristic
30	Q₈×C₄₃	—	4	4	no	—
31	C₂×C₄×C₄₃	—	2	2	no	—
32	C₂×C₄×C₄₃	—	4	2	no	—
33	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
34	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
35	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
36	C₂×C₄×C₄₃	C₂²×C₄	1	8	yes	—
37	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
38	C₄₃⋊C₈	—	2	8	no	—
39	C₂²×C₄₃	—	2	1	no	—
40	C₂²×C₄₃	—	2	2	no	—
41	C₂²×C₄₃	C₂³×C₄	1	1	yes	characteristic
42	C₄×C₄₃	—	2	1	no	—
43	C₄×C₄₃	—	2	2	no	—
44	C₄×C₄₃	—	2	2	no	—
45	C₄×C₄₃	—	2	8	no	—
46	C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
47	#2987	—	43	1	no	maximal, Sylow
48	C₂×C₄₃	—	4	1	no	—
49	C₂×C₄₃	#519	1	1	yes	characteristic
50	C₂×C₄₃	#568	1	2	yes	—
51	#533	D₄₃	1	1	yes	characteristic
52	#446	—	43	8	no	—
53	#433	—	43	4	no	—
54	#432	—	43	2	no	—
55	C₄₃	#2987	1	1	yes	characteristic, complemented, Sylow
56	C₄⋊Q₈	Dic₄₃	1	2	yes	—
57	#125	Dic₄₃	1	2	yes	—
58	C₂²⋊Q₈	Dic₄₃	1	4	yes	—
59	C₄×Q₈	C₂×D₄₃	1	4	yes	—
60	#117	C₂×D₄₃	1	2	yes	—
61	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
62	C₄⋊C₈	—	43	4	no	—
63	C₄⋊C₈	—	43	8	no	—
64	C₂²⋊C₈	—	43	4	no	—
65	#97	—	43	4	no	—
66	#97	—	43	4	no	—
67	C₄×C₈	—	43	4	no	—
68	C₂×Q₈	C₂×Dic₄₃	1	4	yes	—
69	C₂²×C₄	C₂×Dic₄₃	1	2	yes	—
70	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
71	C₂×C₈	—	43	8	no	—
72	C₄⋊C₄	C₂×Dic₄₃	1	4	yes	—
73	C₄⋊C₄	C₂×Dic₄₃	1	8	yes	—
74	C₄⋊C₄	C₂×Dic₄₃	1	4	yes	—
75	C₂²⋊C₄	C₂×Dic₄₃	1	4	yes	—
76	C₄²	C₂×Dic₄₃	1	1	yes	characteristic
77	C₄²	C₂×Dic₄₃	1	1	yes	characteristic
78	C₄²	C₂²×D₄₃	1	4	yes	—
79	C₄²	C₂²×D₄₃	1	2	yes	—
80	C₂³	C₂²×Dic₄₃	1	1	yes	characteristic
81	Q₈	—	4	4	no	—
82	C₂×C₄	—	2	2	no	—
83	C₂×C₄	—	4	2	no	—
84	C₂×C₄	C₂²×Dic₄₃	1	2	yes	—
85	C₂×C₄	C₂²×Dic₄₃	1	2	yes	—
86	C₂×C₄	C₂²×Dic₄₃	1	8	yes	—
87	C₂×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
88	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
89	C₈	—	86	8	no	—
90	C₂²	—	2	1	no	—
91	C₂²	—	2	2	no	—
92	C₂²	C₂³×Dic₄₃	1	1	yes	characteristic
93	C₄	—	2	1	no	—
94	C₄	—	2	2	no	—
95	C₄	—	2	2	no	—
96	C₄	—	2	8	no	—
97	C₄	#13063373	1	2	yes	—
98	C₂	—	4	1	no	—
99	C₂	#14583377	1	1	yes	characteristic
100	C₂	#14583666	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14583030

C₂

yes

maximal, complemented

#14582960

C₂

yes

maximal

#14582956

C₂

yes

maximal

C₄₃×#533

C₂

yes

maximal, characteristic

C₄⋊(C₄₃⋊C₈)

C₂²

yes

—

C₄⋊(C₄₃⋊C₈)

C₂²

yes

—

C₂²⋊(C₄₃⋊C₈)

C₂²

yes

—

#13063236

C₂²

yes

—

#13063236

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

—

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

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂³×C₄

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

2₋¹⁺⁴

yes

—

#2987

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

#519

yes

characteristic

C₂×C₄₃

#568

yes

—

#533

D₄₃

yes

—

—

—

C₄₃

#2987

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

—

C₂²⋊C₈

—

#97

—

#97

—

C₄×C₈

—

C₂×Q₈

C₂×Dic₄₃

yes

—

C₂²×C₄

C₂×Dic₄₃

yes

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

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

—

C₂×C₄

C₂²×Dic₄₃

yes

characteristic

C₂×C₄

C₂³×D₄₃

yes

characteristic

C₈

—

C₂²

—

C₂²

—

C₂²

C₂³×Dic₄₃

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

C₄

#13063373

yes

—

C₂

—

C₂

#14583377

yes

characteristic

100

C₂

#14583666

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	#2987
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
55. C₄₃	#2987	semidirect

H ≅ G/N

type

1. #14583030

C₂

semidirect

55. C₄₃

#2987

semidirect

Subgroups — #19143701

Conjugacy classes of subgroups

Complements