Group #19133898 — subgroups

Subgroups — #19133898

Order 5504.

182 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 45 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	1	yes	maximal, characteristic, complemented
2	#14583265	C₂	1	1	yes	maximal, characteristic
3	#14583264	C₂	1	2	yes	maximal
4	#14582640	C₂	1	2	yes	maximal, complemented
5	C₄₃×#330	C₂	1	1	yes	maximal, characteristic, complemented
6	#13063322	C₂²	1	1	yes	characteristic
7	#13063317	C₂²	1	2	yes	—
8	#13063316	—	2	2	no	—
9	#13063315	—	2	2	no	—
10	#13063315	—	2	2	no	—
11	#13063247	—	2	2	no	—
12	#13063247	—	2	2	no	—
13	#13063245	—	2	2	no	—
14	#13063236	C₂²	1	1	yes	characteristic
15	#125×C₄₃	C₂²	1	1	yes	characteristic
16	#97×C₄₃	C₂²	1	2	yes	—
17	C₂×D₁₇₂	—	2	1	no	—
18	C₂×D₁₇₂	—	2	2	no	—
19	C₂×C₈×C₄₃	—	2	2	no	—
20	C₄⋊C₄×C₄₃	—	2	2	no	—
21	C₄⋊C₄×C₄₃	D₄	1	2	yes	—
22	C₄²×C₄₃	C₂³	1	1	yes	characteristic
23	C₄⋊Dic₄₃	—	2	2	no	—
24	C₄⋊Dic₄₃	D₄	1	2	yes	—
25	C₄⋊Dic₄₃	D₄	1	2	yes	—
26	Dic₄₃⋊C₄	—	2	2	no	—
27	Dic₄₃⋊C₄	—	2	2	no	—
28	Dic₄₃⋊C₄	—	2	2	no	—
29	Dic₄₃⋊C₄	—	2	2	no	—
30	C₄×Dic₄₃	—	2	2	no	—
31	C₂×C₄₃⋊C₈	—	2	1	no	—
32	C₂²×D₄₃	—	4	1	no	—
33	C₂×C₄×C₄₃	—	2	2	no	—
34	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
35	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
36	C₂×Dic₄₃	—	2	2	no	—
37	C₂×Dic₄₃	—	2	2	no	—
38	D₁₇₂	—	4	2	no	—
39	D₁₇₂	—	4	4	no	—
40	C₈×C₄₃	—	4	2	no	—
41	C₄₃⋊C₈	—	4	1	no	—
42	C₂²×C₄₃	#120	1	1	yes	characteristic
43	C₂×D₄₃	—	8	2	no	—
44	C₂×D₄₃	—	8	1	no	—
45	C₄×C₄₃	—	2	1	no	—
46	C₄×C₄₃	—	2	2	no	—
47	C₄×C₄₃	—	4	2	no	—
48	Dic₄₃	—	4	2	no	—
49	Dic₄₃	—	4	2	no	—
50	#1658	—	43	1	no	maximal, Sylow
51	C₂×C₄₃	#454	1	2	yes	—
52	C₂×C₄₃	#454	1	1	yes	characteristic
53	D₄₃	—	16	1	no	—
54	#564	—	43	1	no	—
55	#490	—	43	1	no	—
56	#490	—	43	2	no	—
57	#330	—	43	2	no	—
58	#330	D₄₃	1	1	yes	characteristic, complemented
59	C₄₃	#1658	1	1	yes	characteristic, complemented, Sylow
60	#127	—	43	1	no	—
61	#125	—	43	2	no	—
62	#125	—	86	2	no	—
63	#125	—	86	2	no	—
64	#125	—	86	2	no	—
65	#125	C₂×D₄₃	1	1	yes	characteristic
66	#102	—	86	2	no	—
67	#102	—	86	2	no	—
68	#102	—	86	2	no	—
69	#97	—	43	1	no	—
70	#97	C₂×D₄₃	1	2	yes	—
71	C₂×D₄	—	86	1	no	—
72	C₂×D₄	—	86	2	no	—
73	C₂×C₈	—	2	2	no	—
74	C₂×C₈	—	86	1	no	—
75	C₄⋊C₄	—	2	2	no	—
76	C₄⋊C₄	—	43	2	no	—
77	C₄⋊C₄	—	43	2	no	—
78	C₄⋊C₄	—	86	2	no	—
79	C₄⋊C₄	—	86	2	no	—
80	C₄⋊C₄	—	86	2	no	—
81	C₄⋊C₄	—	86	2	no	—
82	C₄⋊C₄	—	86	2	no	—
83	C₄⋊C₄	D₁₇₂	1	2	yes	—
84	C₄²	—	86	2	no	—
85	C₄²	C₂²×D₄₃	1	1	yes	characteristic
86	C₂³	—	172	1	no	—
87	D₄	—	172	4	no	—
88	D₄	—	172	2	no	—
89	C₂×C₄	—	2	2	no	—
90	C₂×C₄	—	86	2	no	—
91	C₂×C₄	—	86	2	no	—
92	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
93	C₂×C₄	D₄×D₄₃	1	2	yes	—
94	C₈	—	4	2	no	—
95	C₈	—	172	1	no	—
96	C₂²	—	344	2	no	—
97	C₂²	—	344	1	no	—
98	C₂²	#13063295	1	1	yes	characteristic
99	C₄	—	2	2	no	—
100	C₄	—	2	1	no	—
101	C₄	—	4	2	no	—
102	C₄	—	172	2	no	—
103	C₄	—	172	2	no	—
104	C₂	—	688	1	no	—
105	C₂	#14583073	1	2	yes	—
106	C₂	#14583074	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄₃⋊#564

C₂

yes

maximal, characteristic, complemented

#14583265

C₂

yes

maximal, characteristic

#14583264

C₂

yes

maximal

#14582640

C₂

yes

maximal, complemented

C₄₃×#330

C₂

yes

maximal, characteristic, complemented

#13063322

C₂²

yes

characteristic

#13063317

C₂²

yes

—

—

—

—

—

—

—

C₂²

yes

characteristic

#125×C₄₃

C₂²

yes

characteristic

#97×C₄₃

C₂²

yes

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×C₈×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

D₄

yes

—

C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

D₄

yes

—

C₄⋊Dic₄₃

D₄

yes

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂²×D₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

D₁₇₂

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₂²×C₄₃

#120

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

Dic₄₃

—

Dic₄₃

—

#1658

—

maximal, Sylow

C₂×C₄₃

#454

yes

—

C₂×C₄₃

#454

yes

characteristic

D₄₃

—

—

—

—

—

D₄₃

yes

characteristic, complemented

C₄₃

#1658

yes

characteristic, complemented, Sylow

—

—

—

—

—

C₂×D₄₃

yes

—

—

—

—

C₂×D₄₃

yes

—

C₂×D₄

—

C₂×D₄

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

D₁₇₂

yes

—

C₄²

—

C₄²

C₂²×D₄₃

yes

characteristic

C₂³

—

172

—

D₄

—

172

—

D₄

—

172

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×D₁₇₂

yes

characteristic

C₂×C₄

D₄×D₄₃

yes

—

C₈

—

C₈

—

172

—

C₂²

—

344

—

C₂²

—

344

—

C₂²

#13063295

yes

characteristic

C₄

—

100

C₄

—

101

C₄

—

102

C₄

—

172

—

103

C₄

—

172

—

104

C₂

—

688

—

105

C₂

#14583073

yes

—

106

C₂

#14583074

yes

characteristic

	subgroup	G/H
center	C₂²	#13063295
commutator	C₄²×C₄₃	C₂³
Frattini	C₄²	C₂²×D₄₃
Fitting	C₄₃×#330	C₂
socle	C₂²×C₄₃	#120
hypercenter	#330	D₄₃
hypocenter	C₄₃	#1658
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #330

subgroup

G/H

center

C₂²

#13063295

commutator

C₄²×C₄₃

C₂³

Frattini

C₄²

C₂²×D₄₃

Fitting

C₄₃×#330

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #330

N	H ≅ G/N	type
1. C₄₃⋊#564	C₂	semidirect
4. #14582640	C₂	semidirect
5. C₄₃×#330	C₂	semidirect
58. #330	D₄₃	semidirect
59. C₄₃	#1658	semidirect

H ≅ G/N

type

1. C₄₃⋊#564

C₂

semidirect

4. #14582640

C₂

semidirect

5. C₄₃×#330

C₂

semidirect

58. #330

D₄₃

semidirect

59. C₄₃

#1658

semidirect

Subgroups — #19133898

Conjugacy classes of subgroups

Complements