Group #24987019 — subgroups

Subgroups — #24987019

Order 11008.

574 conjugacy classes of subgroups; only the 291 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 291 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	C₄×C₈×Dic₄₃	C₂	1	3	yes	maximal
2	C₄₃⋊#1273	C₂	1	3	yes	maximal
3	C₄₃×#1273	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₄₃⋊C₈	C₂²	1	3	yes	—
5	C₂×C₈×Dic₄₃	C₄	1	6	yes	—
6	C₂×C₈×Dic₄₃	C₄	1	6	yes	—
7	C₄²×Dic₄₃	C₂²	1	1	yes	characteristic
8	C₂×C₄×C₈×C₄₃	C₂²	1	3	yes	—
9	C₂²×C₄₃⋊C₈	C₂×C₄	1	6	yes	—
10	C₂×C₄×Dic₄₃	C₂×C₄	1	3	yes	—
11	C₂×C₄×Dic₄₃	C₂×C₄	1	3	yes	—
12	C₄×C₄₃⋊C₈	—	2	3	no	—
13	C₄×C₄₃⋊C₈	—	2	3	no	—
14	C₈×Dic₄₃	—	2	12	no	—
15	C₈×Dic₄₃	C₈	1	24	yes	complemented
16	C₂²×C₈×C₄₃	C₂×C₄	1	6	yes	—
17	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
18	C₄×C₈×C₄₃	—	2	6	no	—
19	C₂²×C₄×C₄₃	C₂²×C₄	1	3	yes	—
20	C₂²×Dic₄₃	C₄²	1	1	yes	characteristic
21	C₂²×Dic₄₃	C₄²	1	3	yes	—
22	C₂×C₈×C₄₃	—	2	6	no	—
23	C₂×C₈×C₄₃	—	2	6	no	—
24	C₂×C₈×C₄₃	C₂×C₈	1	12	yes	—
25	C₄²×C₄₃	#41	1	3	yes	—
26	C₄²×C₄₃	#41	1	1	yes	characteristic
27	C₄×Dic₄₃	C₂×C₈	1	12	yes	—
28	C₄×Dic₄₃	M₁₆	1	12	yes	—
29	C₂×C₄₃⋊C₈	—	2	6	no	—
30	C₂×C₄₃⋊C₈	—	2	6	no	—
31	C₂×C₄₃⋊C₈	C₂×C₈	1	12	yes	—
32	C₂³×C₄₃	C₂×C₄²	1	1	yes	characteristic
33	C₂×C₄×C₄₃	#117	1	3	yes	—
34	C₂×C₄×C₄₃	#117	1	3	yes	—
35	C₂×C₄×C₄₃	C₂²×C₈	1	6	yes	—
36	C₂×C₄×C₄₃	C₂×M₁₆	1	6	yes	—
37	C₂×Dic₄₃	C₄×C₈	1	6	yes	—
38	C₂×Dic₄₃	C₄×C₈	1	6	yes	—
39	C₂×Dic₄₃	#97	1	12	yes	—
40	C₈×C₄₃	—	2	12	no	—
41	C₄₃⋊C₈	—	2	12	no	—
42	#8131	—	43	1	no	maximal, Sylow
43	C₂²×C₄₃	#376	1	1	yes	characteristic
44	C₂²×C₄₃	C₂×C₄×C₈	1	3	yes	—
45	C₂²×C₄₃	C₂×#97	1	3	yes	—
46	C₄×C₄₃	#431	1	6	yes	—
47	C₄×C₄₃	#431	1	6	yes	—
48	Dic₄₃	C₈²	1	4	yes	—
49	Dic₄₃	#322	1	12	yes	—
50	C₄²×C₈	—	43	3	no	—
51	#1273	—	43	3	no	—
52	#1273	D₄₃	1	1	yes	characteristic
53	C₂×C₄₃	C₂×C₈²	1	1	yes	characteristic
54	C₂×C₄₃	C₂×#322	1	3	yes	—
55	C₂×C₄₃	#1744	1	3	yes	—
56	C₂×C₄×C₈	—	43	6	no	—
57	C₂×C₄×C₈	—	43	6	no	—
58	C₂×C₄×C₈	—	43	3	no	—
59	C₂×C₄×C₈	C₂×D₄₃	1	3	yes	—
60	C₄³	—	43	1	no	—
61	C₄₃	#8131	1	1	yes	characteristic, complemented, Sylow
62	C₂²×C₈	—	43	6	no	—
63	C₂²×C₈	C₄×D₄₃	1	6	yes	—
64	C₂×C₄²	—	43	3	no	—
65	C₂×C₄²	—	43	3	no	—
66	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
67	C₄×C₈	—	2	6	no	—
68	C₄×C₈	—	43	24	no	—
69	C₄×C₈	—	86	12	no	—
70	C₄×C₈	—	86	3	no	—
71	C₄×C₈	—	86	3	no	—
72	C₂²×C₄	—	43	1	no	—
73	C₂²×C₄	—	43	3	no	—
74	C₂²×C₄	C₂×C₄×D₄₃	1	3	yes	—
75	C₂×C₈	—	2	6	no	—
76	C₂×C₈	—	2	6	no	—
77	C₂×C₈	—	43	12	no	—
78	C₂×C₈	—	86	6	no	—
79	C₂×C₈	—	86	6	no	—
80	C₂×C₈	C₈×D₄₃	1	12	yes	—
81	C₄²	—	43	12	no	—
82	C₄²	—	43	12	no	—
83	C₄²	#10621900	1	3	yes	—
84	C₄²	#10621902	1	1	yes	characteristic
85	C₂³	C₄²×D₄₃	1	1	yes	characteristic
86	C₂×C₄	—	43	6	no	—
87	C₂×C₄	—	43	6	no	—
88	C₂×C₄	—	43	12	no	—
89	C₂×C₄	#13063281	1	3	yes	—
90	C₂×C₄	#13063283	1	3	yes	—
91	C₂×C₄	C₂×C₈×D₄₃	1	6	yes	—
92	C₂×C₄	M₁₆×D₄₃	1	6	yes	—
93	C₈	—	2	12	no	—
94	C₈	—	86	12	no	—
95	C₂²	#14582744	1	1	yes	characteristic
96	C₂²	C₄×C₈×D₄₃	1	3	yes	—
97	C₂²	#97×D₄₃	1	3	yes	—
98	C₄	—	43	4	no	—
99	C₄	—	43	12	no	—
100	C₄	#14582949	1	6	yes	—
101	C₄	#14582951	1	6	yes	—
102	C₂	C₈²×D₄₃	1	1	yes	characteristic
103	C₂	#322×D₄₃	1	3	yes	—
104	C₂	#19134339	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×C₈×Dic₄₃

C₂

yes

maximal

C₄₃⋊#1273

C₂

yes

maximal

C₄₃×#1273

C₂

yes

maximal, characteristic

C₂×C₄×C₄₃⋊C₈

C₂²

yes

—

C₂×C₈×Dic₄₃

C₄

yes

—

C₂×C₈×Dic₄₃

C₄

yes

—

C₄²×Dic₄₃

C₂²

yes

characteristic

C₂×C₄×C₈×C₄₃

C₂²

yes

—

C₂²×C₄₃⋊C₈

C₂×C₄

yes

—

C₂×C₄×Dic₄₃

C₂×C₄

yes

—

C₂×C₄×Dic₄₃

C₂×C₄

yes

—

C₄×C₄₃⋊C₈

—

C₄×C₄₃⋊C₈

—

C₈×Dic₄₃

—

C₈×Dic₄₃

C₈

yes

complemented

C₂²×C₈×C₄₃

C₂×C₄

yes

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₄×C₈×C₄₃

—

C₂²×C₄×C₄₃

C₂²×C₄

yes

—

C₂²×Dic₄₃

C₄²

yes

characteristic

C₂²×Dic₄₃

C₄²

yes

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂×C₈

yes

—

C₄²×C₄₃

#41

yes

—

C₄²×C₄₃

#41

yes

characteristic

C₄×Dic₄₃

C₂×C₈

yes

—

C₄×Dic₄₃

M₁₆

yes

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

C₂×C₈

yes

—

C₂³×C₄₃

C₂×C₄²

yes

characteristic

C₂×C₄×C₄₃

#117

yes

—

C₂×C₄×C₄₃

#117

yes

—

C₂×C₄×C₄₃

C₂²×C₈

yes

—

C₂×C₄×C₄₃

C₂×M₁₆

yes

—

C₂×Dic₄₃

C₄×C₈

yes

—

C₂×Dic₄₃

C₄×C₈

yes

—

C₂×Dic₄₃

#97

yes

—

C₈×C₄₃

—

C₄₃⋊C₈

—

—

C₂²×C₄₃

yes

C₂²×C₄₃

C₂×C₄×C₈

yes

—

C₂²×C₄₃

C₂×#97

yes

—

C₄×C₄₃

#431

yes

—

C₄×C₄₃

#431

yes

—

Dic₄₃

C₈²

yes

—

Dic₄₃

#322

yes

—

C₄²×C₈

—

#1273

—

#1273

D₄₃

yes

characteristic

C₂×C₄₃

C₂×C₈²

yes

characteristic

C₂×C₄₃

C₂×#322

yes

—

C₂×C₄₃

#1744

yes

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₄₃

yes

—

C₄³

—

C₄₃

#8131

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

C₄×D₄₃

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂²×D₄₃

yes

characteristic

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×C₄×D₄₃

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₈×D₄₃

yes

—

C₄²

—

C₄²

—

C₄²

#10621900

yes

—

C₄²

#10621902

yes

characteristic

C₂³

C₄²×D₄₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#13063281

yes

—

C₂×C₄

#13063283

yes

—

C₂×C₄

C₂×C₈×D₄₃

yes

—

C₂×C₄

M₁₆×D₄₃

yes

—

C₈

—

C₈

—

C₂²

#14582744

yes

characteristic

C₂²

C₄×C₈×D₄₃

yes

—

C₂²

#97×D₄₃

yes

—

C₄

—

C₄

—

100

C₄

#14582949

yes

—

101

C₄

#14582951

yes

—

102

C₂

C₈²×D₄₃

yes

characteristic

103

C₂

#322×D₄₃

yes

—

104

C₂

#19134339

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₄₃
commutator	C₂×C₄₃	C₂×C₈²
Fitting	C₄₃×#1273	C₂
socle, prime radical	C₂³×C₄₃	C₂×C₄²
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1273	D₄₃
hypocenter	C₄₃	#8131
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄² ◁ #1273

subgroup

G/H

center, Frattini

C₂×C₄²

C₂²×D₄₃

commutator

C₂×C₄₃

C₂×C₈²

Fitting

C₄₃×#1273

C₂

socle, prime radical

C₂³×C₄₃

C₂×C₄²

cosocle

C₂×C₄²×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂×C₄₃ ▷ C₄₃

C₁ ◁ C₂×C₄² ◁ #1273

N	H ≅ G/N	type
15. C₈×Dic₄₃	C₈	semidirect
61. C₄₃	#8131	semidirect

H ≅ G/N

type

15. C₈×Dic₄₃

C₈

semidirect

61. C₄₃

#8131

semidirect

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

subgroup	index
C₄×C₈×Dic₄₃	2
C₄₃⋊#1273	2
C₄₃×#1273	2
#8131	43

subgroup

index

C₄×C₈×Dic₄₃

C₄₃⋊#1273

C₄₃×#1273

#8131

Subgroups — #24987019

Conjugacy classes of subgroups

Complements

Maximal subgroups