Group #26019555 — subgroups

Subgroups — #26019555

Order 11392.

182 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 45 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	C₈₉⋊#564	C₂	1	1	yes	maximal, characteristic, complemented
2	#19151964	C₂	1	1	yes	maximal, characteristic
3	#19151963	C₂	1	2	yes	maximal
4	#19151339	C₂	1	2	yes	maximal, complemented
5	#330×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#15668009	C₂²	1	1	yes	characteristic
7	#15668004	C₂²	1	2	yes	—
8	#15668003	—	2	2	no	—
9	#15668002	—	2	2	no	—
10	#15668002	—	2	2	no	—
11	#15667934	—	2	2	no	—
12	#15667934	—	2	2	no	—
13	#15667932	—	2	2	no	—
14	#15667923	C₂²	1	1	yes	characteristic
15	#125×C₈₉	C₂²	1	1	yes	characteristic
16	#97×C₈₉	C₂²	1	2	yes	—
17	C₂×D₃₅₆	—	2	1	no	—
18	C₂×D₃₅₆	—	2	2	no	—
19	C₂×#10623494	—	2	1	no	—
20	C₄⋊Dic₈₉	—	2	2	no	—
21	C₄⋊Dic₈₉	D₄	1	2	yes	—
22	C₄⋊Dic₈₉	D₄	1	2	yes	—
23	#13083553	—	2	2	no	—
24	#13083553	—	2	2	no	—
25	#13083553	—	2	2	no	—
26	#13083553	—	2	2	no	—
27	C₄×Dic₈₉	—	2	2	no	—
28	C₂×C₈×C₈₉	—	2	2	no	—
29	C₄⋊C₄×C₈₉	—	2	2	no	—
30	C₄⋊C₄×C₈₉	D₄	1	2	yes	—
31	C₄²×C₈₉	C₂³	1	1	yes	characteristic
32	C₂²×D₈₉	—	4	1	no	—
33	C₂×C₄×C₈₉	—	2	2	no	—
34	C₂×C₄×C₈₉	C₂×D₄	1	2	yes	—
35	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
36	C₂×Dic₈₉	—	2	2	no	—
37	C₂×Dic₈₉	—	2	2	no	—
38	D₃₅₆	—	4	2	no	—
39	D₃₅₆	—	4	4	no	—
40	C₈×C₈₉	—	4	2	no	—
41	#10623494	—	4	1	no	—
42	C₂²×C₈₉	#120	1	1	yes	characteristic
43	C₂×D₈₉	—	8	2	no	—
44	C₂×D₈₉	—	8	1	no	—
45	C₄×C₈₉	—	2	1	no	—
46	C₄×C₈₉	—	2	2	no	—
47	C₄×C₈₉	—	4	2	no	—
48	Dic₈₉	—	4	2	no	—
49	Dic₈₉	—	4	2	no	—
50	C₂×C₈₉	#454	1	2	yes	—
51	C₂×C₈₉	#454	1	1	yes	characteristic
52	D₈₉	—	16	1	no	—
53	#1658	—	89	1	no	maximal, Sylow
54	C₈₉	#1658	1	1	yes	characteristic, complemented, Sylow
55	#564	—	89	1	no	—
56	#490	—	89	1	no	—
57	#490	—	89	2	no	—
58	#330	—	89	2	no	—
59	#330	D₈₉	1	1	yes	characteristic, complemented
60	#127	—	89	1	no	—
61	#125	—	89	2	no	—
62	#125	—	178	2	no	—
63	#125	—	178	2	no	—
64	#125	—	178	2	no	—
65	#125	C₂×D₈₉	1	1	yes	characteristic
66	#102	—	178	2	no	—
67	#102	—	178	2	no	—
68	#102	—	178	2	no	—
69	#97	—	89	1	no	—
70	#97	C₂×D₈₉	1	2	yes	—
71	C₂×D₄	—	178	2	no	—
72	C₂×D₄	—	178	1	no	—
73	C₂×C₈	—	2	2	no	—
74	C₂×C₈	—	178	1	no	—
75	C₄⋊C₄	—	2	2	no	—
76	C₄⋊C₄	—	89	2	no	—
77	C₄⋊C₄	—	89	2	no	—
78	C₄⋊C₄	—	178	2	no	—
79	C₄⋊C₄	—	178	2	no	—
80	C₄⋊C₄	—	178	2	no	—
81	C₄⋊C₄	—	178	2	no	—
82	C₄⋊C₄	—	178	2	no	—
83	C₄⋊C₄	D₃₅₆	1	2	yes	—
84	C₄²	—	178	2	no	—
85	C₄²	C₂²×D₈₉	1	1	yes	characteristic
86	C₂³	—	356	1	no	—
87	D₄	—	356	4	no	—
88	D₄	—	356	2	no	—
89	C₂×C₄	—	2	2	no	—
90	C₂×C₄	—	178	2	no	—
91	C₂×C₄	—	178	2	no	—
92	C₂×C₄	D₄×D₈₉	1	2	yes	—
93	C₂×C₄	C₂×D₃₅₆	1	1	yes	characteristic
94	C₈	—	4	2	no	—
95	C₈	—	356	1	no	—
96	C₂²	—	712	2	no	—
97	C₂²	—	712	1	no	—
98	C₂²	#15667982	1	1	yes	characteristic
99	C₄	—	2	2	no	—
100	C₄	—	2	1	no	—
101	C₄	—	4	2	no	—
102	C₄	—	356	2	no	—
103	C₄	—	356	2	no	—
104	C₂	—	1424	1	no	—
105	C₂	#19151772	1	2	yes	—
106	C₂	#19151773	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₈₉⋊#564

C₂

yes

maximal, characteristic, complemented

#19151964

C₂

yes

maximal, characteristic

#19151963

C₂

yes

maximal

#19151339

C₂

yes

maximal, complemented

#330×C₈₉

C₂

yes

maximal, characteristic, complemented

#15668009

C₂²

yes

characteristic

#15668004

C₂²

yes

—

—

—

—

—

—

—

C₂²

yes

characteristic

#125×C₈₉

C₂²

yes

characteristic

#97×C₈₉

C₂²

yes

—

C₂×D₃₅₆

—

C₂×D₃₅₆

—

C₂×#10623494

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

D₄

yes

—

C₄⋊Dic₈₉

D₄

yes

—

—

—

—

—

C₄×Dic₈₉

—

C₂×C₈×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

D₄

yes

—

C₄²×C₈₉

C₂³

yes

characteristic

C₂²×D₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

C₂×D₄

yes

—

C₂×C₄×C₈₉

C₂×D₄

yes

characteristic

C₂×Dic₈₉

—

C₂×Dic₈₉

—

D₃₅₆

—

D₃₅₆

—

C₈×C₈₉

—

#10623494

—

C₂²×C₈₉

#120

yes

characteristic

C₂×D₈₉

—

C₂×D₈₉

—

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

—

Dic₈₉

—

Dic₈₉

—

C₂×C₈₉

#454

yes

—

C₂×C₈₉

#454

yes

characteristic

D₈₉

—

#1658

—

maximal, Sylow

C₈₉

#1658

yes

characteristic, complemented, Sylow

—

—

—

—

D₈₉

yes

characteristic, complemented

#127

—

#125

—

#125

—

178

—

#125

—

178

—

#125

—

178

—

#125

C₂×D₈₉

yes

characteristic

#102

—

178

—

#102

—

178

—

#102

—

178

—

#97

—

#97

C₂×D₈₉

yes

—

C₂×D₄

—

178

—

C₂×D₄

—

178

—

C₂×C₈

—

C₂×C₈

—

178

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

178

—

C₄⋊C₄

—

178

—

C₄⋊C₄

—

178

—

C₄⋊C₄

—

178

—

C₄⋊C₄

—

178

—

C₄⋊C₄

D₃₅₆

yes

—

C₄²

—

178

—

C₄²

C₂²×D₈₉

yes

characteristic

C₂³

—

356

—

D₄

—

356

—

D₄

—

356

—

C₂×C₄

—

C₂×C₄

—

178

—

C₂×C₄

—

178

—

C₂×C₄

D₄×D₈₉

yes

—

C₂×C₄

C₂×D₃₅₆

yes

characteristic

C₈

—

C₈

—

356

—

C₂²

—

712

—

C₂²

—

712

—

C₂²

#15667982

yes

characteristic

C₄

—

100

C₄

—

101

C₄

—

102

C₄

—

356

—

103

C₄

—

356

—

104

C₂

—

1424

—

105

C₂

#19151772

yes

—

106

C₂

#19151773

yes

characteristic

	subgroup	G/H
center	C₂²	#15667982
commutator, cosocle	C₄²×C₈₉	C₂³
Frattini	C₄²	C₂²×D₈₉
Fitting	#330×C₈₉	C₂
socle	C₂²×C₈₉	#120
prime radical	#15668009	C₂²
hypercenter	#330	D₈₉
hypocenter	C₈₉	#1658
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #330

subgroup

G/H

center

C₂²

#15667982

commutator, cosocle

C₄²×C₈₉

C₂³

Frattini

C₄²

C₂²×D₈₉

Fitting

#330×C₈₉

C₂

C₂²×C₈₉

C₂²

D₈₉

C₈₉

G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #330

N	H ≅ G/N	type
1. C₈₉⋊#564	C₂	semidirect
4. #19151339	C₂	semidirect
5. #330×C₈₉	C₂	semidirect
54. C₈₉	#1658	semidirect
59. #330	D₈₉	semidirect

H ≅ G/N

type

1. C₈₉⋊#564

C₂

semidirect

4. #19151339

C₂

semidirect

5. #330×C₈₉

C₂

semidirect

54. C₈₉

#1658

semidirect

59. #330

D₈₉

semidirect

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

subgroup	index
C₈₉⋊#564	2
#19151964	2
#19151963	2
#19151339	2
#330×C₈₉	2
#1658	89

subgroup

index

C₈₉⋊#564

#330×C₈₉

Subgroups — #26019555

Conjugacy classes of subgroups

Complements

Maximal subgroups