Group #19142864 — subgroups

Subgroups — #19142864

Order 5504.

348 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 133 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	#14582838	C₂	1	3	yes	maximal
2	#14582832	C₂	1	6	yes	maximal
3	#14582819	C₂	1	3	yes	maximal
4	#14582767	C₂	1	2	yes	maximal
5	C₄₃×#384	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₈₆	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊Dic₄₃	C₂²	1	3	yes	—
8	C₂×Dic₄₃⋊C₄	C₂²	1	6	yes	—
9	C₄₃⋊#95	C₂²	1	6	yes	—
10	C₄₃⋊#95	C₂²	1	3	yes	—
11	C₄₃⋊#95	C₂²	1	3	yes	—
12	C₄₃⋊#95	C₂²	1	6	yes	—
13	C₂×C₄⋊C₄×C₄₃	C₂²	1	3	yes	—
14	C₂×C₄⋊C₄×C₄₃	C₂²	1	3	yes	—
15	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
16	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
17	C₂²×C₄×C₄₃	C₂³	1	3	yes	—
18	C₂²×C₄×C₄₃	C₂³	1	3	yes	—
19	C₂²×Dic₄₃	C₂³	1	6	yes	—
20	C₂²×Dic₄₃	C₂³	1	2	yes	—
21	C₂×Dic₈₆	—	4	3	no	—
22	C₄⋊C₄×C₄₃	—	4	3	no	—
23	C₄⋊C₄×C₄₃	—	4	3	no	—
24	C₄²×C₄₃	Q₈	1	4	yes	complemented
25	C₄⋊Dic₄₃	—	4	3	no	—
26	Dic₄₃⋊C₄	—	4	6	no	—
27	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
28	C₂×C₄×C₄₃	—	2	3	no	—
29	C₂×C₄×C₄₃	—	2	3	no	—
30	C₂×C₄×C₄₃	—	2	6	no	—
31	C₂×C₄×C₄₃	—	2	3	no	—
32	C₂×C₄×C₄₃	—	2	3	no	—
33	C₂×C₄×C₄₃	C₂×Q₈	1	6	yes	—
34	C₂×Dic₄₃	—	2	6	no	—
35	C₂×Dic₄₃	—	2	6	no	—
36	C₂×Dic₄₃	—	2	12	no	—
37	Dic₈₆	—	4	4	no	—
38	C₂²×C₄₃	C₂²×Q₈	1	1	yes	characteristic
39	C₂²×C₄₃	H(5,𝔽₂)	1	3	yes	—
40	C₂²×C₄₃	2₋¹⁺⁴	1	3	yes	—
41	C₄×C₄₃	—	2	6	no	—
42	C₄×C₄₃	—	4	1	no	—
43	C₄×C₄₃	—	4	3	no	—
44	Dic₄₃	—	4	2	no	—
45	Dic₄₃	—	4	6	no	—
46	#2843	—	43	1	no	maximal, Sylow
47	C₂×C₄₃	#544	1	3	yes	—
48	C₂×C₄₃	#560	1	1	yes	characteristic
49	C₂×C₄₃	#563	1	3	yes	—
50	#400	—	43	3	no	—
51	#398	—	43	6	no	—
52	#395	—	43	3	no	—
53	#384	D₄₃	1	1	yes	characteristic
54	#383	—	43	2	no	—
55	C₄₃	#2843	1	1	yes	characteristic, complemented, Sylow
56	C₂²×Q₈	—	43	1	no	—
57	C₂×C₄⋊C₄	—	43	6	no	—
58	C₂×C₄⋊C₄	—	43	3	no	—
59	C₂×C₄⋊C₄	C₂×D₄₃	1	3	yes	—
60	C₂×C₄⋊C₄	C₂×D₄₃	1	3	yes	—
61	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
62	#95	—	43	6	no	—
63	#95	—	43	6	no	—
64	#95	—	43	3	no	—
65	#95	—	43	3	no	—
66	C₂×Q₈	—	172	3	no	—
67	C₂²×C₄	—	43	6	no	—
68	C₂²×C₄	—	43	2	no	—
69	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
70	C₂²×C₄	C₂²×D₄₃	1	3	yes	—
71	C₂²×C₄	C₂²×D₄₃	1	3	yes	—
72	C₄⋊C₄	—	4	3	no	—
73	C₄⋊C₄	—	4	3	no	—
74	C₄⋊C₄	—	172	6	no	—
75	C₄⋊C₄	—	172	3	no	—
76	C₄²	Dic₈₆	1	4	yes	complemented
77	C₂³	C₂³×D₄₃	1	1	yes	characteristic
78	Q₈	—	172	4	no	—
79	C₂×C₄	—	2	3	no	—
80	C₂×C₄	—	2	3	no	—
81	C₂×C₄	—	2	6	no	—
82	C₂×C₄	—	2	3	no	—
83	C₂×C₄	—	2	3	no	—
84	C₂×C₄	—	86	6	no	—
85	C₂×C₄	—	86	6	no	—
86	C₂×C₄	—	86	12	no	—
87	C₂×C₄	C₂×Dic₈₆	1	6	yes	—
88	C₂²	C₂²×Dic₈₆	1	1	yes	characteristic
89	C₂²	#13063370	1	3	yes	—
90	C₂²	#13063373	1	3	yes	—
91	C₄	—	2	6	no	—
92	C₄	—	4	1	no	—
93	C₄	—	4	3	no	—
94	C₄	—	172	2	no	—
95	C₄	—	172	6	no	—
96	C₂	#14583530	1	3	yes	—
97	C₂	#14583636	1	1	yes	characteristic
98	C₂	#14583648	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14582838

C₂

yes

maximal

#14582832

C₂

yes

maximal

#14582819

C₂

yes

maximal

#14582767

C₂

yes

maximal

C₄₃×#384

C₂

yes

maximal, characteristic

C₂²×Dic₈₆

C₂²

yes

characteristic

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×Dic₄₃⋊C₄

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₂×C₄⋊C₄×C₄₃

C₂²

yes

—

C₂×C₄⋊C₄×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₂×Dic₈₆

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

Q₈

yes

complemented

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

C₂³×C₄₃

C₂⁴

yes

characteristic

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

—

Dic₈₆

—

C₂²×C₄₃

C₂²×Q₈

yes

characteristic

C₂²×C₄₃

H(5,𝔽₂)

yes

—

C₂²×C₄₃

2₋¹⁺⁴

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

Dic₄₃

—

Dic₄₃

—

#2843

—

maximal, Sylow

C₂×C₄₃

#544

yes

—

C₂×C₄₃

#560

yes

characteristic

C₂×C₄₃

#563

yes

—

—

—

—

D₄₃

yes

characteristic

#383

—

C₄₃

#2843

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₃

yes

—

C₂×C₄⋊C₄

C₂×D₄₃

yes

—

C₂×C₄²

C₂×D₄₃

yes

—

—

—

—

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

—

C₄⋊C₄

—

172

—

C₄⋊C₄

—

172

—

C₄²

Dic₈₆

yes

complemented

C₂³

C₂³×D₄₃

yes

characteristic

Q₈

—

172

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×Dic₈₆

yes

—

C₂²

C₂²×Dic₈₆

yes

characteristic

C₂²

#13063370

yes

—

C₂²

#13063373

yes

—

C₄

—

C₄

—

C₄

—

C₄

—

172

—

C₄

—

172

—

C₂

#14583530

yes

—

C₂

#14583636

yes

characteristic

C₂

#14583648

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₃
commutator, socle	C₂³×C₄₃	C₂⁴
Fitting	C₄₃×#384	C₂
hypercenter	#384	D₄₃
hypocenter	C₄₃	#2843
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ #384

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₃

commutator, socle

C₂³×C₄₃

C₂⁴

Fitting

C₄₃×#384

C₂

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₄₃

C₁ ◁ C₂³ ◁ #384

N	H ≅ G/N	type
24. C₄²×C₄₃	Q₈	semidirect
55. C₄₃	#2843	semidirect
76. C₄²	Dic₈₆	semidirect

H ≅ G/N

type

24. C₄²×C₄₃

Q₈

semidirect

55. C₄₃

#2843

semidirect

76. C₄²

Dic₈₆

semidirect

Subgroups — #19142864

Conjugacy classes of subgroups

Complements