Group #24987033 — subgroups

Subgroups — #24987033

Order 11008.

478 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 203 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×#13063235	C₂	1	3	yes	maximal
2	C₄₃⋊#1273	C₂	1	3	yes	maximal
3	C₄₃×#1273	C₂	1	1	yes	maximal, characteristic
4	C₂×#13063235	C₄	1	6	yes	—
5	C₂×#13063235	C₄	1	6	yes	—
6	C₂×C₄×C₄₃⋊C₈	C₂²	1	3	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	#13063235	—	2	12	no	—
13	#13063235	—	2	12	no	—
14	C₄×C₄₃⋊C₈	—	2	3	no	—
15	C₄×C₄₃⋊C₈	—	2	3	no	—
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	M₁₆	1	12	yes	—
25	C₄²×C₄₃	#41	1	3	yes	—
26	C₄²×C₄₃	#41	1	1	yes	characteristic
27	C₄×Dic₄₃	—	2	6	no	—
28	C₄×Dic₄₃	—	2	6	no	—
29	C₂×C₄₃⋊C₈	—	2	6	no	—
30	C₂×C₄₃⋊C₈	—	2	6	no	—
31	C₂×C₄₃⋊C₈	M₁₆	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	C₂×M₁₆	1	6	yes	—
36	C₂×C₄×C₄₃	C₂×M₁₆	1	6	yes	—
37	C₂×Dic₄₃	—	2	3	no	—
38	C₂×Dic₄₃	—	2	3	no	—
39	C₂×Dic₄₃	—	2	6	no	—
40	C₈×C₄₃	—	2	12	no	—
41	C₄₃⋊C₈	—	2	12	no	—
42	#8136	—	43	1	no	maximal, Sylow
43	C₂²×C₄₃	#376	1	1	yes	characteristic
44	C₂²×C₄₃	C₄×M₁₆	1	3	yes	—
45	C₂²×C₄₃	C₄×M₁₆	1	3	yes	—
46	C₄×C₄₃	#432	1	6	yes	—
47	C₄×C₄₃	#432	1	6	yes	—
48	Dic₄₃	—	4	1	no	—
49	Dic₄₃	—	4	3	no	—
50	C₄×#97	—	43	3	no	—
51	#1273	—	43	3	no	—
52	#1273	D₄₃	1	1	yes	characteristic
53	C₂×C₄₃	#1455	1	1	yes	characteristic
54	C₂×C₄₃	#1455	1	3	yes	—
55	C₂×C₄₃	#1745	1	3	yes	—
56	C₂×#97	—	43	6	no	—
57	C₂×#97	—	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	#8136	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	#97	—	86	12	no	—
68	#97	—	86	12	no	—
69	C₄×C₈	—	2	6	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	#10621872	1	12	yes	—
81	C₄²	—	86	6	no	—
82	C₄²	—	86	6	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	—	86	3	no	—
87	C₂×C₄	—	86	3	no	—
88	C₂×C₄	—	86	6	no	—
89	C₂×C₄	#13063281	1	3	yes	—
90	C₂×C₄	#13063283	1	3	yes	—
91	C₂×C₄	M₁₆×D₄₃	1	6	yes	—
92	C₂×C₄	C₂×#10621872	1	6	yes	—
93	C₈	—	2	12	no	—
94	C₈	—	86	12	no	—
95	C₂²	#14582744	1	1	yes	characteristic
96	C₂²	C₄×#10621872	1	3	yes	—
97	C₂²	#14582851	1	3	yes	—
98	C₄	—	172	1	no	—
99	C₄	—	172	3	no	—
100	C₄	#14582953	1	6	yes	—
101	C₄	#14582955	1	6	yes	—
102	C₂	#19132897	1	1	yes	characteristic
103	C₂	#19132899	1	3	yes	—
104	C₂	#19134342	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#13063235

C₂

yes

maximal

C₄₃⋊#1273

C₂

yes

maximal

C₄₃×#1273

C₂

yes

maximal, characteristic

C₂×#13063235

C₄

yes

—

C₂×#13063235

C₄

yes

—

C₂×C₄×C₄₃⋊C₈

C₂²

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

—

#13063235

—

#13063235

—

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

M₁₆

yes

—

C₄²×C₄₃

#41

yes

—

C₄²×C₄₃

#41

yes

characteristic

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

M₁₆

yes

—

C₂³×C₄₃

C₂×C₄²

yes

characteristic

C₂×C₄×C₄₃

#117

yes

—

C₂×C₄×C₄₃

#117

yes

—

C₂×C₄×C₄₃

C₂×M₁₆

yes

—

C₂×C₄×C₄₃

C₂×M₁₆

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

—

C₂²×C₄₃

yes

C₂²×C₄₃

C₄×M₁₆

yes

—

C₂²×C₄₃

C₄×M₁₆

yes

—

C₄×C₄₃

#432

yes

—

C₄×C₄₃

#432

yes

—

Dic₄₃

—

Dic₄₃

—

C₄×#97

—

#1273

—

#1273

D₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

C₂×C₄₃

#1745

yes

—

C₂×#97

—

C₂×#97

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₄₃

yes

—

C₄³

—

C₄₃

#8136

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

C₄×D₄₃

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂²×D₄₃

yes

characteristic

#97

—

#97

—

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

#10621872

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

M₁₆×D₄₃

yes

—

C₂×C₄

C₂×#10621872

yes

—

C₈

—

C₈

—

C₂²

#14582744

yes

characteristic

C₂²

C₄×#10621872

yes

—

C₂²

#14582851

yes

—

C₄

—

172

—

C₄

—

172

—

100

C₄

#14582953

yes

—

101

C₄

#14582955

yes

—

102

C₂

#19132897

yes

characteristic

103

C₂

#19132899

yes

—

104

C₂

#19134342

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	#8136
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
61. C₄₃	#8136	semidirect

H ≅ G/N

type

61. C₄₃

#8136

semidirect

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

subgroup	index
C₄×#13063235	2
C₄₃⋊#1273	2
C₄₃×#1273	2
#8136	43

subgroup

index

C₄×#13063235

C₄₃⋊#1273

C₄₃×#1273

#8136

Subgroups — #24987033

Conjugacy classes of subgroups

Complements

Maximal subgroups