Group #19149089 — subgroups

Subgroups — #19149089

Order 5504.

890 conjugacy classes of subgroups; only the 455 normal subgroups are shown.

normal subgroups only

This group has 890 conjugacy classes of subgroups — too many to draw. Only its 455 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	C₄₃⋊#564	C₂	1	3	yes	maximal, complemented
2	#14583626	C₂	1	12	yes	maximal, complemented
3	#14583508	C₂	1	12	yes	maximal
4	#14583455	C₂	1	3	yes	maximal
5	C₄₃×#564	C₂	1	1	yes	maximal, characteristic, complemented
6	#13063324	C₂²	1	6	yes	—
7	#13063324	C₂²	1	12	yes	—
8	#13063320	C₂²	1	12	yes	—
9	#13063319	C₂²	1	4	yes	—
10	#13063317	C₂²	1	3	yes	—
11	#13063316	C₂²	1	12	yes	—
12	#13063315	C₂²	1	12	yes	—
13	#13063315	C₂²	1	12	yes	—
14	#13063315	C₂²	1	12	yes	—
15	#13063303	C₂²	1	12	yes	—
16	C₄×Dic₈₆	C₂²	1	12	yes	—
17	#13063290	C₂²	1	12	yes	—
18	#13063290	C₂²	1	12	yes	—
19	#13063283	C₂²	1	6	yes	—
20	C₄²×D₄₃	C₂²	1	1	yes	characteristic
21	#125×C₄₃	C₂²	1	12	yes	—
22	#125×C₄₃	C₂²	1	3	yes	—
23	C₂×C₄×D₄₃	C₂³	1	3	yes	—
24	C₂×Dic₈₆	C₂³	1	12	yes	—
25	C₄⋊C₄×C₄₃	C₂³	1	6	yes	—
26	C₄⋊C₄×C₄₃	C₂³	1	12	yes	—
27	C₄⋊C₄×C₄₃	C₂³	1	12	yes	—
28	C₄²×C₄₃	C₂³	1	1	yes	characteristic
29	C₄²×C₄₃	C₂³	1	4	yes	—
30	(C₂×D₄₃)⋊C₄	C₂³	1	12	yes	—
31	C₄⋊Dic₄₃	C₂³	1	6	yes	—
32	C₄⋊Dic₄₃	C₂³	1	12	yes	—
33	Dic₄₃⋊C₄	C₂³	1	12	yes	—
34	Dic₄₃⋊C₄	C₂³	1	12	yes	—
35	Dic₄₃⋊C₄	C₂³	1	12	yes	—
36	Dic₄₃⋊C₄	C₂³	1	12	yes	—
37	C₄×Dic₄₃	C₂³	1	3	yes	—
38	C₄×Dic₄₃	C₂³	1	12	yes	—
39	C₄×Dic₄₃	C₂³	1	12	yes	—
40	C₂²×D₄₃	C₂⁴	1	1	yes	characteristic
41	C₂×C₄×C₄₃	C₂⁴	1	12	yes	—
42	C₂×C₄×C₄₃	C₂⁴	1	3	yes	—
43	C₂×Dic₄₃	C₂⁴	1	12	yes	—
44	C₂×Dic₄₃	C₂⁴	1	3	yes	—
45	C₄×D₄₃	—	2	6	no	—
46	Dic₈₆	—	2	24	no	—
47	C₂²×C₄₃	C₂⁵	1	1	yes	characteristic
48	C₂×D₄₃	—	2	3	no	—
49	C₄×C₄₃	—	2	12	no	—
50	C₄×C₄₃	—	2	3	no	—
51	Dic₄₃	—	2	12	no	—
52	Dic₄₃	2₋¹⁺⁴	1	6	yes	—
53	#3556	—	43	1	no	maximal, Sylow
54	C₂×C₄₃	C₂×2₋¹⁺⁴	1	3	yes	—
55	D₄₃	—	4	1	no	—
56	#564	—	43	3	no	—
57	#564	D₄₃	1	1	yes	characteristic, complemented
58	#557	—	43	12	no	—
59	#541	—	43	12	no	—
60	#533	—	43	3	no	—
61	C₄₃	#3556	1	1	yes	characteristic, complemented, Sylow
62	C₄⋊Q₈	—	43	6	no	—
63	C₄⋊Q₈	—	43	12	no	—
64	#126	—	43	12	no	—
65	#126	—	43	4	no	—
66	#125	—	43	12	no	—
67	#125	—	43	12	no	—
68	#125	—	43	12	no	—
69	#125	—	43	12	no	—
70	#125	—	43	3	no	—
71	#125	C₂×D₄₃	1	3	yes	—
72	#125	C₂×D₄₃	1	12	yes	—
73	C₂²⋊Q₈	—	43	12	no	—
74	C₄×Q₈	—	43	12	no	—
75	C₄×Q₈	—	43	12	no	—
76	C₄×Q₈	—	43	12	no	—
77	#117	—	43	6	no	—
78	C₂×C₄²	—	43	1	no	—
79	C₂×Q₈	—	43	12	no	—
80	C₂²×C₄	—	43	3	no	—
81	C₄⋊C₄	—	43	6	no	—
82	C₄⋊C₄	—	43	12	no	—
83	C₄⋊C₄	—	43	12	no	—
84	C₄⋊C₄	—	43	12	no	—
85	C₄⋊C₄	—	43	12	no	—
86	C₄⋊C₄	—	43	12	no	—
87	C₄⋊C₄	C₂²×D₄₃	1	6	yes	—
88	C₄⋊C₄	C₂²×D₄₃	1	12	yes	—
89	C₄⋊C₄	C₂²×D₄₃	1	12	yes	—
90	C₂²⋊C₄	—	43	12	no	—
91	C₄²	—	43	3	no	—
92	C₄²	—	43	12	no	—
93	C₄²	—	43	12	no	—
94	C₄²	C₂²×D₄₃	1	1	yes	characteristic
95	C₄²	C₂²×D₄₃	1	4	yes	—
96	C₂³	—	43	1	no	—
97	Q₈	—	86	24	no	—
98	C₂×C₄	—	43	3	no	—
99	C₂×C₄	—	43	12	no	—
100	C₂×C₄	—	86	6	no	—
101	C₂×C₄	C₂³×D₄₃	1	12	yes	—
102	C₂×C₄	C₂³×D₄₃	1	3	yes	—
103	C₂²	—	86	3	no	—
104	C₂²	C₂⁴×D₄₃	1	1	yes	characteristic
105	C₄	—	2	3	no	—
106	C₄	—	2	12	no	—
107	C₄	—	43	6	no	—
108	C₄	—	86	12	no	—
109	C₂	—	172	1	no	—
110	C₂	2₋¹⁺⁴×D₄₃	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄₃⋊#564

C₂

yes

maximal, complemented

#14583626

C₂

yes

maximal, complemented

#14583508

C₂

yes

maximal

#14583455

C₂

yes

maximal

C₄₃×#564

C₂

yes

maximal, characteristic, complemented

#13063324

C₂²

yes

—

#13063324

C₂²

yes

—

#13063320

C₂²

yes

—

#13063319

C₂²

yes

—

#13063317

C₂²

yes

—

#13063316

C₂²

yes

—

#13063315

C₂²

yes

—

#13063315

C₂²

yes

—

#13063315

C₂²

yes

—

#13063303

C₂²

yes

—

C₄×Dic₈₆

C₂²

yes

—

#13063290

C₂²

yes

—

#13063290

C₂²

yes

—

#13063283

C₂²

yes

—

C₄²×D₄₃

C₂²

yes

characteristic

#125×C₄₃

C₂²

yes

—

#125×C₄₃

C₂²

yes

—

C₂×C₄×D₄₃

C₂³

yes

—

C₂×Dic₈₆

C₂³

yes

—

C₄⋊C₄×C₄₃

C₂³

yes

—

C₄⋊C₄×C₄₃

C₂³

yes

—

C₄⋊C₄×C₄₃

C₂³

yes

—

C₄²×C₄₃

C₂³

yes

characteristic

C₄²×C₄₃

C₂³

yes

—

(C₂×D₄₃)⋊C₄

C₂³

yes

—

C₄⋊Dic₄₃

C₂³

yes

—

C₄⋊Dic₄₃

C₂³

yes

—

Dic₄₃⋊C₄

C₂³

yes

—

Dic₄₃⋊C₄

C₂³

yes

—

Dic₄₃⋊C₄

C₂³

yes

—

Dic₄₃⋊C₄

C₂³

yes

—

C₄×Dic₄₃

C₂³

yes

—

C₄×Dic₄₃

C₂³

yes

—

C₄×Dic₄₃

C₂³

yes

—

C₂²×D₄₃

C₂⁴

yes

characteristic

C₂×C₄×C₄₃

C₂⁴

yes

—

C₂×C₄×C₄₃

C₂⁴

yes

—

C₂×Dic₄₃

C₂⁴

yes

—

C₂×Dic₄₃

C₂⁴

yes

—

C₄×D₄₃

—

Dic₈₆

—

C₂²×C₄₃

C₂⁵

yes

characteristic

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

Dic₄₃

—

Dic₄₃

2₋¹⁺⁴

yes

—

#3556

—

maximal, Sylow

C₂×C₄₃

C₂×2₋¹⁺⁴

yes

—

D₄₃

—

#564

—

#564

D₄₃

yes

characteristic, complemented

#557

—

#541

—

#533

—

C₄₃

#3556

yes

characteristic, complemented, Sylow

C₄⋊Q₈

—

C₄⋊Q₈

—

—

—

—

—

—

—

—

C₂×D₄₃

yes

—

#125

C₂×D₄₃

yes

—

C₂²⋊Q₈

—

C₄×Q₈

—

C₄×Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

—

C₂×Q₈

—

C₂²×C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂²×D₄₃

yes

—

C₄⋊C₄

C₂²×D₄₃

yes

—

C₄⋊C₄

C₂²×D₄₃

yes

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂²×D₄₃

yes

characteristic

C₄²

C₂²×D₄₃

yes

—

C₂³

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

C₂³×D₄₃

yes

—

102

C₂×C₄

C₂³×D₄₃

yes

—

103

C₂²

—

104

C₂²

C₂⁴×D₄₃

yes

characteristic

105

C₄

—

106

C₄

—

107

C₄

—

108

C₄

—

109

C₂

—

172

—

110

C₂

2₋¹⁺⁴×D₄₃

yes

—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₃
commutator, socle	C₂²×C₄₃	C₂⁵
Fitting	C₄₃×#564	C₂
hypercenter	#564	D₄₃
hypocenter	C₄₃	#3556
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ #564

subgroup

G/H

center, Frattini

C₂²

C₂⁴×D₄₃

commutator, socle

C₂²×C₄₃

C₂⁵

Fitting

C₄₃×#564

C₂

D₄₃

C₄₃

G ▷ C₂²×C₄₃ ▷ C₄₃

C₁ ◁ C₂² ◁ #564

N	H ≅ G/N	type
1. C₄₃⋊#564	C₂	semidirect
2. #14583626	C₂	semidirect
5. C₄₃×#564	C₂	semidirect
57. #564	D₄₃	semidirect
61. C₄₃	#3556	semidirect

H ≅ G/N

type

1. C₄₃⋊#564

C₂

semidirect

2. #14583626

C₂

semidirect

5. C₄₃×#564

C₂

semidirect

57. #564

D₄₃

semidirect

61. C₄₃

#3556

semidirect

Subgroups — #19149089

Conjugacy classes of subgroups

Complements