Group #24987031 — subgroups

Subgroups — #24987031

Order 11008.

382 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 167 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	#19134340	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	C₄²×Dic₄₃	C₂²	1	1	yes	characteristic
6	#14582653	C₄	1	6	yes	—
7	#14582653	C₄	1	6	yes	—
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	C₂²×C₈×C₄₃	C₂×C₄	1	6	yes	—
15	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
16	C₄×C₈×C₄₃	—	2	6	no	—
17	C₂²×C₄×C₄₃	C₂²×C₄	1	3	yes	—
18	C₂²×Dic₄₃	C₄²	1	1	yes	characteristic
19	C₂²×Dic₄₃	C₄²	1	3	yes	—
20	C₂×C₈×C₄₃	—	2	6	no	—
21	C₂×C₈×C₄₃	—	2	6	no	—
22	C₂×C₈×C₄₃	—	2	6	no	—
23	C₄²×C₄₃	#41	1	3	yes	—
24	C₄²×C₄₃	#41	1	1	yes	characteristic
25	C₄×Dic₄₃	—	2	6	no	—
26	C₄×Dic₄₃	—	2	6	no	—
27	C₂×C₄₃⋊C₈	—	2	6	no	—
28	C₂×C₄₃⋊C₈	—	2	6	no	—
29	C₂×C₄₃⋊C₈	—	2	6	no	—
30	C₂³×C₄₃	C₂×C₄²	1	1	yes	characteristic
31	C₂×C₄×C₄₃	#117	1	3	yes	—
32	C₂×C₄×C₄₃	#117	1	3	yes	—
33	C₂×C₄×C₄₃	#131	1	6	yes	—
34	C₂×C₄×C₄₃	#131	1	6	yes	—
35	C₂×Dic₄₃	—	2	3	no	—
36	C₂×Dic₄₃	—	2	3	no	—
37	C₂×Dic₄₃	—	2	6	no	—
38	C₈×C₄₃	—	4	6	no	—
39	C₄₃⋊C₈	—	4	6	no	—
40	#8135	—	43	1	no	maximal, Sylow
41	C₂²×C₄₃	#376	1	1	yes	characteristic
42	C₂²×C₄₃	#405	1	3	yes	—
43	C₂²×C₄₃	#405	1	3	yes	—
44	C₄×C₄₃	#433	1	6	yes	—
45	C₄×C₄₃	#433	1	6	yes	—
46	Dic₄₃	—	4	1	no	—
47	Dic₄₃	—	4	3	no	—
48	#1744	—	43	3	no	—
49	#1273	—	43	3	no	—
50	#1273	D₄₃	1	1	yes	characteristic
51	C₂×C₄₃	#1454	1	1	yes	characteristic
52	C₂×C₄₃	#1454	1	3	yes	—
53	C₂×C₄₃	#1746	1	3	yes	—
54	C₂×C₄×C₈	—	43	3	no	—
55	C₂×C₄×C₈	C₂×D₄₃	1	3	yes	—
56	C₄³	—	43	1	no	—
57	#336	—	43	6	no	—
58	#336	—	43	6	no	—
59	C₄₃	#8135	1	1	yes	characteristic, complemented, Sylow
60	C₂²×C₈	—	43	6	no	—
61	C₂²×C₈	C₄×D₄₃	1	6	yes	—
62	C₂×C₄²	—	43	3	no	—
63	C₂×C₄²	—	43	3	no	—
64	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
65	C₄×C₈	—	2	6	no	—
66	C₄×C₈	—	86	3	no	—
67	C₄×C₈	—	86	3	no	—
68	C₂²×C₄	—	43	1	no	—
69	C₂²×C₄	—	43	3	no	—
70	C₂²×C₄	C₂×C₄×D₄₃	1	3	yes	—
71	C₂×C₈	—	2	6	no	—
72	C₂×C₈	—	2	6	no	—
73	C₂×C₈	—	2	6	no	—
74	C₂×C₈	—	86	6	no	—
75	C₂×C₈	—	86	6	no	—
76	C₂×C₈	—	86	6	no	—
77	C₄²	—	86	6	no	—
78	C₄²	—	86	6	no	—
79	C₄²	#10621900	1	3	yes	—
80	C₄²	#10621902	1	1	yes	characteristic
81	C₂³	C₄²×D₄₃	1	1	yes	characteristic
82	C₂×C₄	—	86	3	no	—
83	C₂×C₄	—	86	3	no	—
84	C₂×C₄	—	86	6	no	—
85	C₂×C₄	#13063281	1	3	yes	—
86	C₂×C₄	#13063283	1	3	yes	—
87	C₂×C₄	#13063331	1	6	yes	—
88	C₂×C₄	#13063333	1	6	yes	—
89	C₈	—	4	6	no	—
90	C₈	—	172	6	no	—
91	C₂²	#14582744	1	1	yes	characteristic
92	C₂²	#14582853	1	3	yes	—
93	C₂²	#14582856	1	3	yes	—
94	C₄	—	172	1	no	—
95	C₄	—	172	3	no	—
96	C₄	#14582957	1	6	yes	—
97	C₄	#14582959	1	6	yes	—
98	C₂	#19132894	1	1	yes	characteristic
99	C₂	#19132896	1	3	yes	—
100	C₂	#19134345	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19134340

C₂

yes

maximal

C₄₃⋊#1273

C₂

yes

maximal

C₄₃×#1273

C₂

yes

maximal, characteristic

C₂×C₄×C₄₃⋊C₈

C₂²

yes

—

C₄²×Dic₄₃

C₂²

yes

characteristic

#14582653

C₄

yes

—

#14582653

C₄

yes

—

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

—

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

—

C₄²×C₄₃

#41

yes

—

C₄²×C₄₃

#41

yes

characteristic

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

C₂×C₄²

yes

characteristic

C₂×C₄×C₄₃

#117

yes

—

C₂×C₄×C₄₃

#117

yes

—

C₂×C₄×C₄₃

#131

yes

—

C₂×C₄×C₄₃

#131

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

—

C₂²×C₄₃

yes

C₂²×C₄₃

yes

—

C₂²×C₄₃

#405

yes

—

C₄×C₄₃

#433

yes

—

C₄×C₄₃

#433

yes

—

Dic₄₃

—

Dic₄₃

—

#1744

—

#1273

—

#1273

D₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

C₂×C₄₃

#1746

yes

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₄₃

yes

—

C₄³

—

#336

—

#336

—

C₄₃

#8135

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

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×C₄×D₄₃

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

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

#13063331

yes

—

C₂×C₄

#13063333

yes

—

C₈

—

C₈

—

172

—

C₂²

#14582744

yes

characteristic

C₂²

#14582853

yes

—

C₂²

#14582856

yes

—

C₄

—

172

—

C₄

—

172

—

C₄

#14582957

yes

—

C₄

#14582959

yes

—

C₂

#19132894

yes

characteristic

C₂

#19132896

yes

—

100

C₂

#19134345

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₄₃
commutator, socle, prime radical	C₂³×C₄₃	C₂×C₄²
Fitting	C₄₃×#1273	C₂
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1273	D₄₃
hypocenter	C₄₃	#8135
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄² ◁ #1273

subgroup

G/H

center, Frattini

C₂×C₄²

C₂²×D₄₃

commutator, socle, prime radical

C₂³×C₄₃

C₂×C₄²

Fitting

C₄₃×#1273

C₂

cosocle

C₂×C₄²×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₄₃

C₁ ◁ C₂×C₄² ◁ #1273

N	H ≅ G/N	type
59. C₄₃	#8135	semidirect

H ≅ G/N

type

59. C₄₃

#8135

semidirect

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

subgroup	index
#19134340	2
C₄₃⋊#1273	2
C₄₃×#1273	2
#8135	43

subgroup

index

#19134340

C₄₃⋊#1273

C₄₃×#1273

#8135

Subgroups — #24987031

Conjugacy classes of subgroups

Complements

Maximal subgroups