Group #25096847 — subgroups

Subgroups — #25096847

Order 11008.

1062 conjugacy classes of subgroups; only the 411 normal subgroups are shown.

normal subgroups only

This group has 1062 conjugacy classes of subgroups — too many to draw. Only its 411 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	#19134738	C₂	1	8	yes	maximal, complemented
2	#19134289	C₂	1	6	yes	maximal
3	C₂×C₄³×C₄₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×#10621877	C₂²	1	4	yes	—
5	#14582654	C₂²	1	24	yes	—
6	C₂²×C₄²×C₄₃	C₄	1	4	yes	—
7	C₂²×C₄²×C₄₃	C₂²	1	3	yes	—
8	C₄³×C₄₃	C₄	1	4	yes	—
9	C₄³×C₄₃	C₂²	1	4	yes	—
10	C₂×#10621877	—	2	24	no	—
11	C₂²×C₄₃⋊C₈	C₂³	1	8	yes	—
12	C₂³×C₄×C₄₃	C₂×C₄	1	6	yes	—
13	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
14	C₂×C₄²×C₄₃	—	2	12	no	—
15	C₂×C₄²×C₄₃	—	2	16	no	—
16	C₂×C₄²×C₄₃	C₂×C₄	1	12	yes	—
17	C₂×C₄²×C₄₃	C₂×C₄	1	6	yes	—
18	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
19	C₂×C₄²×C₄₃	C₂³	1	6	yes	—
20	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
21	C₂²×C₄×C₄₃	—	2	24	no	—
22	C₂²×C₄×C₄₃	—	2	12	no	—
23	C₂²×C₄×C₄₃	C₂²×C₄	1	12	yes	—
24	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
25	C₂²×C₄×C₄₃	#41	1	12	yes	—
26	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
27	C₄²×C₄₃	—	2	12	no	—
28	C₄²×C₄₃	—	2	24	no	—
29	C₄²×C₄₃	—	2	12	no	—
30	C₄²×C₄₃	M₁₆	1	16	yes	complemented
31	#10621877	—	4	16	no	—
32	C₂×C₄₃⋊C₈	—	2	24	no	—
33	C₂³×C₄₃	—	2	4	no	—
34	C₂³×C₄₃	#117	1	6	yes	—
35	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
36	C₂×C₄×C₄₃	—	2	48	no	—
37	C₂×C₄×C₄₃	—	2	12	no	—
38	C₂×C₄×C₄₃	—	2	12	no	—
39	C₂×C₄×C₄₃	#117	1	6	yes	—
40	C₂×C₄×C₄₃	#126	1	16	yes	—
41	C₂×C₄×C₄₃	C₂×M₁₆	1	24	yes	—
42	C₂×C₄×C₄₃	C₂×#41	1	6	yes	—
43	C₄₃⋊C₈	—	4	8	no	—
44	#20772	—	43	1	no	maximal, Sylow
45	C₂²×C₄₃	—	2	12	no	—
46	C₂²×C₄₃	#383	1	4	yes	—
47	C₂²×C₄₃	C₂×#117	1	3	yes	—
48	C₂²×C₄₃	C₂²×M₁₆	1	4	yes	—
49	C₄×C₄₃	—	2	24	no	—
50	C₄×C₄₃	#383	1	4	yes	—
51	C₄×C₄₃	C₂×#126	1	4	yes	—
52	C₂×C₄³	D₄₃	1	1	yes	characteristic
53	#1839	—	43	8	no	—
54	#1728	—	43	6	no	—
55	C₂×C₄₃	—	2	4	no	—
56	C₂×C₄₃	C₂×#383	1	1	yes	characteristic
57	C₂×C₄₃	#2920	1	6	yes	—
58	C₂²×M₁₆	—	43	4	no	—
59	C₂²×C₄²	Dic₄₃	1	4	yes	—
60	C₂²×C₄²	C₂×D₄₃	1	3	yes	—
61	C₄³	Dic₄₃	1	4	yes	—
62	C₄³	C₂×D₄₃	1	4	yes	—
63	#336	—	43	24	no	—
64	C₄₃	#20772	1	1	yes	characteristic, complemented, Sylow
65	C₂³×C₄	C₂×Dic₄₃	1	6	yes	—
66	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
67	C₂×M₁₆	—	86	24	no	—
68	C₂²×C₈	—	43	8	no	—
69	C₂×C₄²	—	2	12	no	—
70	C₂×C₄²	—	2	16	no	—
71	C₂×C₄²	C₂×Dic₄₃	1	6	yes	—
72	C₂×C₄²	C₂×Dic₄₃	1	12	yes	—
73	C₂×C₄²	C₂×Dic₄₃	1	4	yes	—
74	C₂×C₄²	C₂²×D₄₃	1	6	yes	—
75	C₂⁴	C₂²×Dic₄₃	1	1	yes	characteristic
76	C₂²×C₄	—	2	12	no	—
77	C₂²×C₄	—	2	24	no	—
78	C₂²×C₄	#10621898	1	12	yes	—
79	C₂²×C₄	C₂²×Dic₄₃	1	12	yes	—
80	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
81	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
82	M₁₆	—	172	16	no	—
83	C₂×C₈	—	86	24	no	—
84	C₄²	—	2	12	no	—
85	C₄²	—	2	24	no	—
86	C₄²	—	2	12	no	—
87	C₄²	#10621877	1	16	yes	complemented
88	C₂³	—	2	4	no	—
89	C₂³	#13063284	1	6	yes	—
90	C₂³	C₂³×Dic₄₃	1	1	yes	characteristic
91	C₂×C₄	—	2	48	no	—
92	C₂×C₄	—	2	12	no	—
93	C₂×C₄	—	2	12	no	—
94	C₂×C₄	#13063284	1	6	yes	—
95	C₂×C₄	#13063319	1	16	yes	—
96	C₂×C₄	C₂×#10621877	1	24	yes	—
97	C₂×C₄	C₂×#10621898	1	6	yes	—
98	C₈	—	172	8	no	—
99	C₂²	—	2	12	no	—
100	C₂²	#14582767	1	4	yes	—
101	C₂²	C₂×#13063284	1	3	yes	—
102	C₂²	C₂²×#10621877	1	4	yes	—
103	C₄	—	2	24	no	—
104	C₄	#14582767	1	4	yes	—
105	C₄	C₂×#13063319	1	4	yes	—
106	C₂	—	2	4	no	—
107	C₂	C₂×#14582767	1	1	yes	characteristic
108	C₂	#19143228	1	6	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19134738

C₂

yes

maximal, complemented

#19134289

C₂

yes

maximal

C₂×C₄³×C₄₃

C₂

yes

maximal, characteristic

C₂²×#10621877

C₂²

yes

—

#14582654

C₂²

yes

—

C₂²×C₄²×C₄₃

C₄

yes

—

C₂²×C₄²×C₄₃

C₂²

yes

—

C₄³×C₄₃

C₄

yes

—

C₄³×C₄₃

C₂²

yes

—

C₂×#10621877

—

C₂²×C₄₃⋊C₈

C₂³

yes

—

C₂³×C₄×C₄₃

C₂×C₄

yes

—

C₂³×C₄×C₄₃

C₂³

yes

characteristic

C₂×C₄²×C₄₃

—

C₂×C₄²×C₄₃

—

C₂×C₄²×C₄₃

C₂×C₄

yes

—

C₂×C₄²×C₄₃

C₂×C₄

yes

—

C₂×C₄²×C₄₃

C₂×C₄

yes

—

C₂×C₄²×C₄₃

C₂³

yes

—

C₂⁴×C₄₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂²×C₄

yes

—

C₂²×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₃

#41

yes

—

C₂²×C₄×C₄₃

C₂⁴

yes

characteristic

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

M₁₆

yes

complemented

#10621877

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

—

C₂³×C₄₃

#117

yes

—

C₂³×C₄₃

C₂³×C₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

#117

yes

—

C₂×C₄×C₄₃

#126

yes

—

C₂×C₄×C₄₃

C₂×M₁₆

yes

—

C₂×C₄×C₄₃

C₂×#41

yes

—

C₄₃⋊C₈

—

#20772

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

#383

yes

—

C₂²×C₄₃

C₂×#117

yes

—

C₂²×C₄₃

C₂²×M₁₆

yes

—

C₄×C₄₃

—

C₄×C₄₃

#383

yes

—

C₄×C₄₃

C₂×#126

yes

—

C₂×C₄³

D₄₃

yes

characteristic

#1839

—

#1728

—

C₂×C₄₃

—

C₂×C₄₃

C₂×#383

yes

characteristic

C₂×C₄₃

#2920

yes

—

C₂²×M₁₆

—

C₂²×C₄²

Dic₄₃

yes

—

C₂²×C₄²

C₂×D₄₃

yes

—

C₄³

Dic₄₃

yes

—

C₄³

C₂×D₄₃

yes

—

#336

—

C₄₃

#20772

yes

characteristic, complemented, Sylow

C₂³×C₄

C₂×Dic₄₃

yes

—

C₂³×C₄

C₂²×D₄₃

yes

characteristic

C₂×M₁₆

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×Dic₄₃

yes

—

C₂×C₄²

C₂×Dic₄₃

yes

—

C₂×C₄²

C₂×Dic₄₃

yes

—

C₂×C₄²

C₂²×D₄₃

yes

—

C₂⁴

C₂²×Dic₄₃

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

#10621898

yes

—

C₂²×C₄

C₂²×Dic₄₃

yes

—

C₂²×C₄

C₂²×Dic₄₃

yes

characteristic

C₂²×C₄

C₂³×D₄₃

yes

characteristic

M₁₆

—

172

—

C₂×C₈

—

C₄²

—

C₄²

—

C₄²

—

C₄²

#10621877

yes

complemented

C₂³

—

C₂³

#13063284

yes

—

C₂³

C₂³×Dic₄₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#13063284

yes

—

C₂×C₄

#13063319

yes

—

C₂×C₄

C₂×#10621877

yes

—

C₂×C₄

C₂×#10621898

yes

—

C₈

—

172

—

C₂²

—

100

C₂²

#14582767

yes

—

101

C₂²

C₂×#13063284

yes

—

102

C₂²

C₂²×#10621877

yes

—

103

C₄

—

104

C₄

#14582767

yes

—

105

C₄

C₂×#13063319

yes

—

106

C₂

—

107

C₂

C₂×#14582767

yes

characteristic

108

C₂

#19143228

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₃
commutator, socle	C₂³×C₄₃	C₂³×C₄
Fitting	C₂×C₄³×C₄₃	C₂
prime radical	C₂⁴×C₄₃	C₂²×C₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₂×C₄³	D₄₃
hypocenter	C₄₃	#20772
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄³

subgroup

G/H

center, Frattini

C₂²×C₄

C₂³×D₄₃

commutator, socle

C₂³×C₄₃

C₂³×C₄

Fitting

C₂×C₄³×C₄₃

C₂

prime radical

C₂⁴×C₄₃

C₂²×C₄

cosocle

C₂²×C₄×C₄₃

C₂⁴

hypercenter

C₂×C₄³

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₄₃

C₁ ◁ C₂²×C₄ ◁ C₂×C₄³

N	H ≅ G/N	type
1. #19134738	C₂	semidirect
30. C₄²×C₄₃	M₁₆	semidirect
64. C₄₃	#20772	semidirect
87. C₄²	#10621877	semidirect

H ≅ G/N

type

1. #19134738

C₂

semidirect

30. C₄²×C₄₃

M₁₆

semidirect

64. C₄₃

#20772

semidirect

87. C₄²

#10621877

semidirect

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

subgroup	index
#19134738	2
#19134289	2
C₂×C₄³×C₄₃	2
#20772	43

subgroup

index

#19134738

#19134289

C₂×C₄³×C₄₃

#20772

Subgroups — #25096847

Conjugacy classes of subgroups

Complements

Maximal subgroups