Group #19148743 — subgroups

Subgroups — #19148743

Order 5504.

930 conjugacy classes of subgroups; only the 451 normal subgroups are shown.

normal subgroups only

This group has 930 conjugacy classes of subgroups — too many to draw. Only its 451 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	#14583653	C₂	1	10	yes	maximal, complemented
2	#14583647	C₂	1	5	yes	maximal, complemented
3	#14583455	C₂	1	5	yes	maximal, complemented
4	#14583434	C₂	1	10	yes	maximal, complemented
5	C₄₃×#564	C₂	1	1	yes	maximal, characteristic, complemented
6	#13063324	C₂²	1	10	yes	—
7	#13063320	C₂²	1	20	yes	—
8	#13063317	C₂²	1	5	yes	—
9	#13063313	C₂²	1	10	yes	—
10	#13063310	C₂²	1	20	yes	—
11	#13063305	C₂²	1	10	yes	—
12	#13063303	C₂²	1	20	yes	—
13	#13063300	C₂²	1	10	yes	—
14	#13063290	C₂²	1	10	yes	—
15	#13063287	C₂²	1	10	yes	—
16	#13063283	C₂²	1	10	yes	—
17	C₄²×D₄₃	C₂²	1	5	yes	—
18	#125×C₄₃	C₂²	1	5	yes	—
19	#125×C₄₃	C₂²	1	10	yes	—
20	C₂×D₁₇₂	C₂³	1	10	yes	—
21	C₂×C₄×D₄₃	C₂³	1	5	yes	—
22	C₂×C₄×D₄₃	C₂³	1	10	yes	—
23	C₂×Dic₈₆	C₂³	1	10	yes	—
24	C₄⋊C₄×C₄₃	C₂³	1	10	yes	—
25	C₄⋊C₄×C₄₃	C₂³	1	10	yes	—
26	C₄⋊C₄×C₄₃	C₂³	1	10	yes	—
27	C₄²×C₄₃	C₂³	1	5	yes	—
28	(C₂×D₄₃)⋊C₄	C₂³	1	20	yes	—
29	(C₂×D₄₃)⋊C₄	C₂³	1	20	yes	—
30	C₄⋊Dic₄₃	C₂³	1	10	yes	—
31	Dic₄₃⋊C₄	C₂³	1	20	yes	—
32	C₄×Dic₄₃	C₂³	1	10	yes	—
33	C₄×Dic₄₃	C₂³	1	5	yes	—
34	C₂²×D₄₃	C₂⁴	1	5	yes	—
35	C₂×C₄×C₄₃	C₂⁴	1	10	yes	—
36	C₂×C₄×C₄₃	C₂⁴	1	5	yes	—
37	C₂×Dic₄₃	C₂⁴	1	10	yes	—
38	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
39	D₁₇₂	—	4	10	no	—
40	C₄×D₄₃	—	2	10	no	—
41	C₄×D₄₃	—	4	10	no	—
42	Dic₈₆	—	4	10	no	—
43	C₂²×C₄₃	C₂⁵	1	1	yes	characteristic
44	C₂×D₄₃	—	2	5	no	—
45	C₂×D₄₃	—	2	10	no	—
46	C₄×C₄₃	—	2	5	no	—
47	C₄×C₄₃	—	2	10	no	—
48	Dic₄₃	—	2	10	no	—
49	Dic₄₃	2₋¹⁺⁴	1	2	yes	—
50	#3531	—	43	1	no	maximal, Sylow
51	C₂×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
52	C₂×C₄₃	#585	1	2	yes	—
53	D₄₃	—	4	5	no	—
54	#564	D₄₃	1	1	yes	characteristic, complemented
55	#563	—	43	10	no	—
56	#562	—	43	5	no	—
57	#533	—	43	5	no	—
58	#529	—	43	10	no	—
59	C₄₃	#3531	1	1	yes	characteristic, complemented, Sylow
60	C₄⋊Q₈	—	43	10	no	—
61	#126	—	43	20	no	—
62	#125	—	43	5	no	—
63	#125	C₂×D₄₃	1	10	yes	—
64	#125	C₂×D₄₃	1	5	yes	—
65	#124	—	43	10	no	—
66	#123	—	43	20	no	—
67	C₂²⋊Q₈	—	43	10	no	—
68	C₂²⋊Q₈	—	43	20	no	—
69	#121	—	43	10	no	—
70	C₄×Q₈	—	43	10	no	—
71	C₄×D₄	—	43	10	no	—
72	#117	—	43	10	no	—
73	C₂×C₄²	—	43	5	no	—
74	C₂×Q₈	—	43	10	no	—
75	C₂×D₄	—	43	10	no	—
76	C₂²×C₄	—	43	5	no	—
77	C₂²×C₄	—	43	10	no	—
78	C₄⋊C₄	—	43	10	no	—
79	C₄⋊C₄	—	43	20	no	—
80	C₄⋊C₄	C₂²×D₄₃	1	10	yes	—
81	C₄⋊C₄	C₂²×D₄₃	1	10	yes	—
82	C₄⋊C₄	C₂²×D₄₃	1	10	yes	—
83	C₂²⋊C₄	—	43	20	no	—
84	C₂²⋊C₄	—	43	20	no	—
85	C₄²	—	43	10	no	—
86	C₄²	—	43	5	no	—
87	C₄²	C₂²×D₄₃	1	5	yes	—
88	C₂³	—	43	5	no	—
89	Q₈	—	172	10	no	—
90	D₄	—	172	10	no	—
91	C₂×C₄	—	43	1	no	—
92	C₂×C₄	—	43	10	no	—
93	C₂×C₄	—	86	10	no	—
94	C₂×C₄	—	172	10	no	—
95	C₂×C₄	C₂³×D₄₃	1	5	yes	—
96	C₂×C₄	C₂³×D₄₃	1	10	yes	—
97	C₂²	—	86	5	no	—
98	C₂²	—	86	10	no	—
99	C₂²	C₂⁴×D₄₃	1	1	yes	characteristic
100	C₄	—	2	5	no	—
101	C₄	—	2	10	no	—
102	C₄	—	43	2	no	—
103	C₄	—	86	10	no	—
104	C₂	—	172	5	no	—
105	C₂	2₋¹⁺⁴×D₄₃	1	1	yes	characteristic
106	C₂	#14583736	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14583653

C₂

yes

maximal, complemented

#14583647

C₂

yes

maximal, complemented

#14583455

C₂

yes

maximal, complemented

#14583434

C₂

yes

maximal, complemented

C₄₃×#564

C₂

yes

maximal, characteristic, complemented

#13063324

C₂²

yes

—

#13063320

C₂²

yes

—

#13063317

C₂²

yes

—

#13063313

C₂²

yes

—

#13063310

C₂²

yes

—

#13063305

C₂²

yes

—

#13063303

C₂²

yes

—

#13063300

C₂²

yes

—

#13063290

C₂²

yes

—

#13063287

C₂²

yes

—

#13063283

C₂²

yes

—

C₄²×D₄₃

C₂²

yes

—

#125×C₄₃

C₂²

yes

—

#125×C₄₃

C₂²

yes

—

C₂×D₁₇₂

C₂³

yes

—

C₂×C₄×D₄₃

C₂³

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

—

(C₂×D₄₃)⋊C₄

C₂³

yes

—

(C₂×D₄₃)⋊C₄

C₂³

yes

—

C₄⋊Dic₄₃

C₂³

yes

—

Dic₄₃⋊C₄

C₂³

yes

—

C₄×Dic₄₃

C₂³

yes

—

C₄×Dic₄₃

C₂³

yes

—

C₂²×D₄₃

C₂⁴

yes

—

C₂×C₄×C₄₃

C₂⁴

yes

—

C₂×C₄×C₄₃

C₂⁴

yes

—

C₂×Dic₄₃

C₂⁴

yes

—

C₂×Dic₄₃

C₂⁴

yes

characteristic

D₁₇₂

—

C₄×D₄₃

—

C₄×D₄₃

—

Dic₈₆

—

C₂²×C₄₃

C₂⁵

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

Dic₄₃

—

Dic₄₃

2₋¹⁺⁴

yes

—

#3531

—

maximal, Sylow

C₂×C₄₃

C₂×2₋¹⁺⁴

yes

characteristic

C₂×C₄₃

#585

yes

—

D₄₃

—

#564

D₄₃

yes

characteristic, complemented

—

—

—

—

C₄₃

#3531

yes

characteristic, complemented, Sylow

C₄⋊Q₈

—

#126

—

#125

—

#125

C₂×D₄₃

yes

—

#125

C₂×D₄₃

yes

—

#124

—

#123

—

C₂²⋊Q₈

—

C₂²⋊Q₈

—

#121

—

C₄×Q₈

—

C₄×D₄

—

#117

—

C₂×C₄²

—

C₂×Q₈

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂²×D₄₃

yes

—

C₄⋊C₄

C₂²×D₄₃

yes

—

C₄⋊C₄

C₂²×D₄₃

yes

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

C₂²×D₄₃

yes

—

C₂³

—

Q₈

—

172

—

D₄

—

172

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

172

—

C₂×C₄

C₂³×D₄₃

yes

—

C₂×C₄

C₂³×D₄₃

yes

—

C₂²

—

C₂²

—

C₂²

C₂⁴×D₄₃

yes

characteristic

100

C₄

—

101

C₄

—

102

C₄

—

103

C₄

—

104

C₂

—

172

—

105

C₂

2₋¹⁺⁴×D₄₃

yes

characteristic

106

C₂

#14583736

yes

—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₃
commutator, socle	C₂²×C₄₃	C₂⁵
Fitting	C₄₃×#564	C₂
hypercenter	#564	D₄₃
hypocenter	C₄₃	#3531
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. #14583653	C₂	semidirect
2. #14583647	C₂	semidirect
3. #14583455	C₂	semidirect
4. #14583434	C₂	semidirect
5. C₄₃×#564	C₂	semidirect
54. #564	D₄₃	semidirect
59. C₄₃	#3531	semidirect

H ≅ G/N

type

1. #14583653

C₂

semidirect

2. #14583647

C₂

semidirect

3. #14583455

C₂

semidirect

4. #14583434

C₂

semidirect

5. C₄₃×#564

C₂

semidirect

54. #564

D₄₃

semidirect

59. C₄₃

#3531

semidirect

Subgroups — #19148743

Conjugacy classes of subgroups

Complements