Group #25017616 — subgroups

Subgroups — #25017616

Order 11008.

158 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 67 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	#19136869	C₂	1	2	yes	maximal
2	#19132795	C₂	1	1	yes	maximal, characteristic
3	#19132794	C₂	1	2	yes	maximal
4	C₃₂×Dic₄₃	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#1423	C₂	1	1	yes	maximal, characteristic
6	#14583303	—	2	2	no	—
7	C₂×C₄₃⋊C₃₂	C₂²	1	1	yes	characteristic
8	#14582725	C₂²	1	2	yes	—
9	#14582724	—	2	2	no	—
10	C₁₆×Dic₄₃	C₂²	1	1	yes	characteristic
11	C₂×C₃₂×C₄₃	C₂²	1	1	yes	characteristic
12	C₄₃×#366	C₂²	1	2	yes	—
13	#13063324	—	4	2	no	—
14	C₂×C₄₃⋊C₁₆	D₄	1	1	yes	characteristic
15	#13063259	—	2	2	no	—
16	#13063258	—	4	2	no	—
17	C₈×Dic₄₃	D₄	1	1	yes	characteristic
18	C₄₃⋊C₃₂	Q₈	1	2	yes	complemented
19	C₂×C₁₆×C₄₃	C₂³	1	1	yes	characteristic
20	#107×C₄₃	—	2	2	no	—
21	C₃₂×C₄₃	Q₈	1	2	yes	complemented
22	C₂×Dic₈₆	—	8	2	no	—
23	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
24	C₄⋊C₄×C₄₃	—	4	2	no	—
25	C₄⋊Dic₄₃	—	4	2	no	—
26	Dic₄₃⋊C₄	—	8	2	no	—
27	C₄×Dic₄₃	D₈	1	1	yes	characteristic
28	C₂×C₄₃⋊C₈	D₈	1	1	yes	characteristic
29	C₁₆×C₄₃	C₂×Q₈	1	1	yes	characteristic
30	C₁₆×C₄₃	C₂×Q₈	1	1	yes	characteristic
31	C₄₃⋊C₁₆	Q₁₆	1	2	yes	—
32	C₂×C₄×C₄₃	—	8	2	no	—
33	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
34	C₂×Dic₄₃	—	8	2	no	—
35	C₂×Dic₄₃	D₁₆	1	1	yes	characteristic
36	C₂×Dic₄₃	D₁₆	1	1	yes	characteristic
37	Dic₈₆	—	16	4	no	—
38	C₈×C₄₃	C₄⋊Q₈	1	1	yes	characteristic
39	C₈×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
40	C₄₃⋊C₈	Q₃₂	1	2	yes	—
41	#13731	—	43	1	no	maximal, Sylow
42	C₂²×C₄₃	C₂×D₁₆	1	1	yes	characteristic
43	C₄×C₄₃	—	16	2	no	—
44	C₄×C₄₃	#500	1	1	yes	characteristic
45	C₄×C₄₃	C₂×Q₃₂	1	1	yes	characteristic
46	Dic₄₃	—	16	2	no	—
47	Dic₄₃	D₃₂	1	2	yes	—
48	Dic₄₃	Q₆₄	1	2	yes	—
49	#2252	—	43	2	no	—
50	#1423	—	43	1	no	—
51	#1423	—	43	2	no	—
52	#1423	D₄₃	1	1	yes	characteristic
53	C₄×C₃₂	—	43	1	no	—
54	C₂×C₄₃	#2252	1	1	yes	characteristic
55	C₂×C₄₃	C₂×D₃₂	1	1	yes	characteristic
56	C₂×C₄₃	C₂×Q₆₄	1	1	yes	characteristic
57	#500	—	86	2	no	—
58	C₂×C₃₂	—	43	1	no	—
59	C₂×C₃₂	C₂×D₄₃	1	1	yes	characteristic
60	#366	—	43	2	no	—
61	#366	—	86	2	no	—
62	#366	C₂×D₄₃	1	2	yes	—
63	C₄×C₁₆	—	43	1	no	—
64	C₄₃	#13731	1	1	yes	characteristic, complemented, Sylow
65	C₄⋊Q₈	—	172	2	no	—
66	C₂×C₁₆	—	43	1	no	—
67	C₂×C₁₆	C₂²×D₄₃	1	1	yes	characteristic
68	#107	—	2	2	no	—
69	#107	—	86	2	no	—
70	#107	—	172	2	no	—
71	C₄×C₈	—	43	1	no	—
72	C₃₂	—	43	2	no	—
73	C₃₂	Dic₈₆	1	2	yes	complemented
74	C₂×Q₈	—	344	2	no	—
75	C₂×C₈	—	43	1	no	—
76	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
77	C₄⋊C₄	—	4	2	no	—
78	C₄⋊C₄	—	344	2	no	—
79	C₄⋊C₄	—	172	2	no	—
80	C₄²	—	43	1	no	—
81	C₁₆	—	43	2	no	—
82	C₁₆	C₂×Dic₈₆	1	1	yes	characteristic
83	C₁₆	Q₈×D₄₃	1	1	yes	characteristic
84	Q₈	—	688	4	no	—
85	C₂×C₄	—	8	2	no	—
86	C₂×C₄	—	43	1	no	—
87	C₂×C₄	—	43	1	no	—
88	C₂×C₄	—	344	2	no	—
89	C₂×C₄	D₈×D₄₃	1	1	yes	characteristic
90	C₈	—	43	2	no	—
91	C₈	#13063324	1	1	yes	characteristic
92	C₈	Q₁₆×D₄₃	1	1	yes	characteristic
93	C₂²	D₁₆×D₄₃	1	1	yes	characteristic
94	C₄	—	16	2	no	—
95	C₄	—	43	2	no	—
96	C₄	—	43	2	no	—
97	C₄	—	688	2	no	—
98	C₄	#14583303	1	1	yes	characteristic
99	C₄	Q₃₂×D₄₃	1	1	yes	characteristic
100	C₂	#19136869	1	1	yes	characteristic
101	C₂	D₃₂×D₄₃	1	1	yes	characteristic
102	C₂	Q₆₄×D₄₃	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19136869

C₂

yes

maximal

#19132795

C₂

yes

maximal, characteristic

#19132794

C₂

yes

maximal

C₃₂×Dic₄₃

C₂

yes

maximal, characteristic

C₄₃×#1423

C₂

yes

maximal, characteristic

#14583303

—

C₂×C₄₃⋊C₃₂

C₂²

yes

characteristic

#14582725

C₂²

yes

—

#14582724

—

C₁₆×Dic₄₃

C₂²

yes

characteristic

C₂×C₃₂×C₄₃

C₂²

yes

characteristic

C₄₃×#366

C₂²

yes

—

#13063324

—

C₂×C₄₃⋊C₁₆

D₄

yes

characteristic

#13063259

—

#13063258

—

C₈×Dic₄₃

D₄

yes

characteristic

C₄₃⋊C₃₂

Q₈

yes

complemented

C₂×C₁₆×C₄₃

C₂³

yes

characteristic

#107×C₄₃

—

C₃₂×C₄₃

Q₈

yes

complemented

C₂×Dic₈₆

—

C₂×C₈×C₄₃

C₂×D₄

yes

characteristic

C₄⋊C₄×C₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

D₈

yes

characteristic

C₂×C₄₃⋊C₈

D₈

yes

characteristic

C₁₆×C₄₃

C₂×Q₈

yes

characteristic

C₁₆×C₄₃

C₂×Q₈

yes

characteristic

C₄₃⋊C₁₆

Q₁₆

yes

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₈

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

D₁₆

yes

characteristic

C₂×Dic₄₃

D₁₆

yes

characteristic

Dic₈₆

—

C₈×C₄₃

C₄⋊Q₈

yes

characteristic

C₈×C₄₃

C₂×Q₁₆

yes

characteristic

C₄₃⋊C₈

Q₃₂

yes

—

#13731

—

maximal, Sylow

C₂²×C₄₃

C₂×D₁₆

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

#500

yes

characteristic

C₄×C₄₃

C₂×Q₃₂

yes

characteristic

Dic₄₃

—

Dic₄₃

D₃₂

yes

—

Dic₄₃

Q₆₄

yes

—

—

—

—

D₄₃

yes

characteristic

C₄×C₃₂

—

C₂×C₄₃

#2252

yes

characteristic

C₂×C₄₃

C₂×D₃₂

yes

characteristic

C₂×C₄₃

C₂×Q₆₄

yes

characteristic

#500

—

C₂×C₃₂

—

C₂×C₃₂

C₂×D₄₃

yes

—

—

C₂×D₄₃

yes

—

C₄×C₁₆

—

C₄₃

#13731

yes

characteristic, complemented, Sylow

C₄⋊Q₈

—

172

—

C₂×C₁₆

—

C₂×C₁₆

C₂²×D₄₃

yes

—

—

—

172

—

C₄×C₈

—

C₃₂

—

C₃₂

Dic₈₆

yes

complemented

C₂×Q₈

—

344

—

C₂×C₈

—

C₂×C₈

D₄×D₄₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

344

—

C₄⋊C₄

—

172

—

C₄²

—

C₁₆

—

C₁₆

C₂×Dic₈₆

yes

characteristic

C₁₆

Q₈×D₄₃

yes

characteristic

Q₈

—

688

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

344

—

C₂×C₄

D₈×D₄₃

yes

characteristic

C₈

—

C₈

#13063324

yes

characteristic

C₈

Q₁₆×D₄₃

yes

characteristic

C₂²

D₁₆×D₄₃

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

688

—

C₄

#14583303

yes

characteristic

C₄

Q₃₂×D₄₃

yes

characteristic

100

C₂

#19136869

yes

characteristic

101

C₂

D₃₂×D₄₃

yes

characteristic

102

C₂

Q₆₄×D₄₃

yes

characteristic

	subgroup	G/H
center	C₂²	D₁₆×D₄₃
commutator, cosocle	C₂×C₁₆×C₄₃	C₂³
Frattini	C₂×C₁₆	C₂²×D₄₃
Fitting	C₄₃×#1423	C₂
socle, prime radical	C₂²×C₄₃	C₂×D₁₆
hypercenter	#1423	D₄₃
hypocenter	C₄₃	#13731
LCS	G ▷ C₂×C₁₆×C₄₃ ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #1423

subgroup

G/H

center

C₂²

D₁₆×D₄₃

commutator, cosocle

C₂×C₁₆×C₄₃

C₂³

Frattini

C₂×C₁₆

C₂²×D₄₃

Fitting

C₄₃×#1423

C₂

socle, prime radical

C₂²×C₄₃

C₂×D₁₆

D₄₃

C₄₃

G ▷ C₂×C₁₆×C₄₃ ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #1423

N	H ≅ G/N	type
18. C₄₃⋊C₃₂	Q₈	semidirect
21. C₃₂×C₄₃	Q₈	semidirect
64. C₄₃	#13731	semidirect
73. C₃₂	Dic₈₆	semidirect

H ≅ G/N

type

18. C₄₃⋊C₃₂

Q₈

semidirect

21. C₃₂×C₄₃

Q₈

semidirect

64. C₄₃

#13731

semidirect

73. C₃₂

Dic₈₆

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#19136869	2
#19132795	2
#19132794	2
C₃₂×Dic₄₃	2
C₄₃×#1423	2
#13731	43

subgroup

index

#19136869

#19132795

#19132794

C₃₂×Dic₄₃

C₄₃×#1423

#13731

Subgroups — #25017616

Conjugacy classes of subgroups

Complements

Maximal subgroups