Group #19142587 — subgroups

Subgroups — #19142587

Order 5504.

432 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 149 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	#14582819	C₂	1	3	yes	maximal
2	#14582818	C₂	1	2	yes	maximal
3	#14582804	C₂	1	3	yes	maximal
4	#14582803	C₂	1	6	yes	maximal
5	C₄₃×#395	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₈₆	C₂²	1	1	yes	characteristic
7	C₂²×Dic₈₆	C₂²	1	3	yes	—
8	C₂×Dic₄₃⋊C₄	C₂²	1	6	yes	—
9	C₂×C₄×Dic₄₃	C₂²	1	3	yes	—
10	C₄₃⋊#95	C₂²	1	6	yes	—
11	C₄₃⋊#95	C₂²	1	6	yes	—
12	C₄₃⋊#95	C₂²	1	3	yes	—
13	C₂²×Q₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊C₄×C₄₃	C₂²	1	3	yes	—
15	#95×C₄₃	C₂²	1	3	yes	—
16	C₂×Q₈×C₄₃	—	4	3	no	—
17	C₂²×C₄×C₄₃	C₂³	1	3	yes	—
18	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
19	C₂²×C₄×C₄₃	C₂³	1	3	yes	—
20	C₂²×Dic₄₃	C₂³	1	2	yes	—
21	C₂²×Dic₄₃	C₂³	1	6	yes	—
22	C₂×Dic₈₆	—	4	3	no	—
23	C₂×Dic₈₆	—	4	3	no	—
24	C₂×Dic₈₆	—	4	3	no	—
25	C₂×Dic₈₆	Q₈	1	12	yes	complemented
26	C₄⋊C₄×C₄₃	—	4	3	no	—
27	Dic₄₃⋊C₄	—	4	6	no	—
28	C₄×Dic₄₃	—	4	3	no	—
29	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
30	Q₈×C₄₃	—	4	4	no	—
31	C₂×C₄×C₄₃	—	2	3	no	—
32	C₂×C₄×C₄₃	—	2	3	no	—
33	C₂×C₄×C₄₃	—	2	6	no	—
34	C₂×C₄×C₄₃	—	2	3	no	—
35	C₂×C₄×C₄₃	—	2	3	no	—
36	C₂×C₄×C₄₃	C₂×Q₈	1	6	yes	—
37	C₂×Dic₄₃	—	2	6	no	—
38	C₂×Dic₄₃	—	2	6	no	—
39	C₂×Dic₄₃	—	2	6	no	—
40	C₂×Dic₄₃	C₂×Q₈	1	12	yes	—
41	Dic₈₆	—	4	12	no	—
42	Dic₈₆	—	4	4	no	—
43	C₂²×C₄₃	C₂²×Q₈	1	3	yes	—
44	C₂²×C₄₃	H(5,𝔽₂)	1	3	yes	—
45	C₂²×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
46	C₄×C₄₃	—	2	6	no	—
47	C₄×C₄₃	—	4	1	no	—
48	C₄×C₄₃	—	4	3	no	—
49	Dic₄₃	—	2	12	no	—
50	Dic₄₃	—	4	2	no	—
51	#2811	—	43	1	no	maximal, Sylow
52	C₂×C₄₃	#543	1	3	yes	—
53	C₂×C₄₃	Q₈²	1	3	yes	—
54	C₂×C₄₃	H(3,𝔽₄)	1	1	yes	characteristic
55	#395	—	43	2	no	—
56	#395	—	43	3	no	—
57	#395	D₄₃	1	1	yes	characteristic
58	#391	—	43	3	no	—
59	#391	—	43	6	no	—
60	C₄₃	#2811	1	1	yes	characteristic, complemented, Sylow
61	C₂²×Q₈	—	43	3	no	—
62	C₂²×Q₈	—	43	1	no	—
63	C₂²×Q₈	C₂×D₄₃	1	1	yes	characteristic
64	C₂×C₄⋊C₄	—	43	6	no	—
65	C₂×C₄⋊C₄	C₂×D₄₃	1	3	yes	—
66	C₂×C₄²	—	43	3	no	—
67	#95	—	43	3	no	—
68	#95	—	43	6	no	—
69	#95	—	43	6	no	—
70	#95	C₂×D₄₃	1	3	yes	—
71	C₂×Q₈	—	4	3	no	—
72	C₂×Q₈	—	43	12	no	—
73	C₂×Q₈	—	172	3	no	—
74	C₂×Q₈	—	172	3	no	—
75	C₂×Q₈	—	172	3	no	—
76	C₂²×C₄	—	43	6	no	—
77	C₂²×C₄	—	43	2	no	—
78	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
79	C₂²×C₄	C₂²×D₄₃	1	3	yes	—
80	C₂²×C₄	C₂²×D₄₃	1	3	yes	—
81	C₄⋊C₄	—	4	3	no	—
82	C₄⋊C₄	—	172	6	no	—
83	C₄²	—	172	3	no	—
84	C₂³	C₂³×D₄₃	1	1	yes	characteristic
85	Q₈	—	4	4	no	—
86	Q₈	—	172	12	no	—
87	Q₈	—	172	4	no	—
88	C₂×C₄	—	2	3	no	—
89	C₂×C₄	—	2	3	no	—
90	C₂×C₄	—	2	3	no	—
91	C₂×C₄	—	2	3	no	—
92	C₂×C₄	—	2	6	no	—
93	C₂×C₄	—	43	12	no	—
94	C₂×C₄	—	86	6	no	—
95	C₂×C₄	—	86	6	no	—
96	C₂×C₄	—	86	6	no	—
97	C₂×C₄	Q₈×D₄₃	1	6	yes	—
98	C₂²	C₂×Q₈×D₄₃	1	3	yes	—
99	C₂²	#13063370	1	3	yes	—
100	C₂²	#13063371	1	1	yes	characteristic
101	C₄	—	2	6	no	—
102	C₄	—	4	3	no	—
103	C₄	—	4	1	no	—
104	C₄	—	86	12	no	—
105	C₄	—	172	2	no	—
106	C₂	#14583524	1	3	yes	—
107	C₂	#14583629	1	3	yes	—
108	C₂	#14583642	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14582819

C₂

yes

maximal

#14582818

C₂

yes

maximal

#14582804

C₂

yes

maximal

#14582803

C₂

yes

maximal

C₄₃×#395

C₂

yes

maximal, characteristic

C₂²×Dic₈₆

C₂²

yes

characteristic

C₂²×Dic₈₆

C₂²

yes

—

C₂×Dic₄₃⋊C₄

C₂²

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₂²×Q₈×C₄₃

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₄₃

C₂²

yes

—

#95×C₄₃

C₂²

yes

—

C₂×Q₈×C₄₃

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

Q₈

yes

complemented

C₄⋊C₄×C₄₃

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₂³×C₄₃

C₂⁴

yes

characteristic

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×Q₈

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

C₂×Q₈

yes

—

Dic₈₆

—

Dic₈₆

—

C₂²×C₄₃

C₂²×Q₈

yes

—

C₂²×C₄₃

H(5,𝔽₂)

yes

—

C₂²×C₄₃

H(5,𝔽₂)

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

Dic₄₃

—

Dic₄₃

—

#2811

—

maximal, Sylow

C₂×C₄₃

#543

yes

—

C₂×C₄₃

Q₈²

yes

—

C₂×C₄₃

yes

—

—

D₄₃

yes

characteristic

#391

—

#391

—

C₄₃

#2811

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂²×Q₈

—

C₂²×Q₈

C₂×D₄₃

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₃

yes

—

C₂×C₄²

—

—

—

—

C₂×D₄₃

yes

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

172

—

C₂×Q₈

—

172

—

C₂×Q₈

—

172

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

C₂²×C₄

C₂²×D₄₃

yes

—

C₂²×C₄

C₂²×D₄₃

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

172

—

C₄²

—

172

—

C₂³

C₂³×D₄₃

yes

characteristic

Q₈

—

Q₈

—

172

—

Q₈

—

172

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

Q₈×D₄₃

yes

—

C₂²

C₂×Q₈×D₄₃

yes

—

C₂²

#13063370

yes

—

100

C₂²

#13063371

yes

characteristic

101

C₄

—

102

C₄

—

103

C₄

—

104

C₄

—

105

C₄

—

172

—

106

C₂

#14583524

yes

—

107

C₂

#14583629

yes

—

108

C₂

#14583642

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₃
commutator, socle	C₂³×C₄₃	C₂⁴
Fitting	C₄₃×#395	C₂
hypercenter	#395	D₄₃
hypocenter	C₄₃	#2811
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ #395

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₃

commutator, socle

C₂³×C₄₃

C₂⁴

Fitting

C₄₃×#395

C₂

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₄₃

C₁ ◁ C₂³ ◁ #395

N	H ≅ G/N	type
25. C₂×Dic₈₆	Q₈	semidirect
60. C₄₃	#2811	semidirect

H ≅ G/N

type

25. C₂×Dic₈₆

Q₈

semidirect

60. C₄₃

#2811

semidirect

Subgroups — #19142587

Conjugacy classes of subgroups

Complements