Group #26019581 — subgroups

Subgroups — #26019581

Order 11392.

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

normal subgroups only

This group has 172 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
2	#19152007	C₂	1	2	yes	maximal
3	#19151968	C₂	1	1	yes	maximal, characteristic
4	#19151339	C₂	1	2	yes	maximal
5	#330×C₈₉	C₂	1	1	yes	maximal, characteristic
6	#15668012	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	#15667946	—	2	2	no	—
12	#15667944	—	2	2	no	—
13	#15667935	—	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×Dic₁₇₈	—	2	1	no	—
18	C₂×#10623494	—	2	1	no	—
19	C₄⋊Dic₈₉	—	2	2	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	C₂×C₄×C₈₉	—	2	2	no	—
33	C₂×C₄×C₈₉	C₂×D₄	1	2	yes	—
34	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
35	C₂×Dic₈₉	—	2	2	no	—
36	C₂×Dic₈₉	—	2	2	no	—
37	C₂×Dic₈₉	—	4	1	no	—
38	Dic₁₇₈	—	4	2	no	—
39	C₈×C₈₉	—	2	4	no	—
40	#10623494	—	4	1	no	—
41	C₂²×C₈₉	#120	1	1	yes	characteristic
42	C₄×C₈₉	—	2	1	no	—
43	C₄×C₈₉	—	2	2	no	—
44	C₄×C₈₉	—	4	2	no	—
45	Dic₈₉	—	4	2	no	—
46	Dic₈₉	—	4	2	no	—
47	Dic₈₉	—	8	1	no	—
48	C₂×C₈₉	#454	1	1	yes	characteristic
49	C₂×C₈₉	#456	1	2	yes	—
50	#1663	—	89	1	no	maximal, Sylow
51	C₈₉	#1663	1	1	yes	characteristic, complemented, Sylow
52	#564	—	89	1	no	—
53	#501	—	89	2	no	—
54	#491	—	89	1	no	—
55	#330	—	89	2	no	—
56	#330	D₈₉	1	1	yes	characteristic
57	C₄⋊Q₈	—	89	1	no	—
58	#125	—	89	2	no	—
59	#125	—	178	2	no	—
60	#125	—	178	2	no	—
61	#125	—	178	2	no	—
62	#125	C₂×D₈₉	1	1	yes	characteristic
63	#107	—	178	2	no	—
64	#106	—	178	2	no	—
65	#103	—	178	2	no	—
66	#97	—	89	1	no	—
67	#97	C₂×D₈₉	1	2	yes	—
68	C₂×Q₈	—	178	1	no	—
69	C₂×C₈	—	2	2	no	—
70	C₂×C₈	—	178	1	no	—
71	C₄⋊C₄	—	2	2	no	—
72	C₄⋊C₄	—	89	2	no	—
73	C₄⋊C₄	—	89	2	no	—
74	C₄⋊C₄	—	178	2	no	—
75	C₄⋊C₄	—	178	2	no	—
76	C₄⋊C₄	—	178	2	no	—
77	C₄⋊C₄	—	178	2	no	—
78	C₄⋊C₄	—	178	2	no	—
79	C₄⋊C₄	—	178	2	no	—
80	C₄⋊C₄	D₃₅₆	1	2	yes	—
81	C₄²	—	178	2	no	—
82	C₄²	C₂²×D₈₉	1	1	yes	characteristic
83	Q₈	—	356	2	no	—
84	C₂×C₄	—	2	2	no	—
85	C₂×C₄	—	356	1	no	—
86	C₂×C₄	—	178	2	no	—
87	C₂×C₄	—	178	2	no	—
88	C₂×C₄	D₄×D₈₉	1	2	yes	—
89	C₂×C₄	C₂×D₃₅₆	1	1	yes	characteristic
90	C₈	—	2	4	no	—
91	C₈	—	356	1	no	—
92	C₂²	#15667982	1	1	yes	characteristic
93	C₄	—	2	1	no	—
94	C₄	—	2	2	no	—
95	C₄	—	4	2	no	—
96	C₄	—	356	2	no	—
97	C₄	—	356	2	no	—
98	C₄	—	712	1	no	—
99	C₂	#19151773	1	1	yes	characteristic
100	C₂	#19151782	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₈₉⋊#564

C₂

yes

maximal, characteristic

#19152007

C₂

yes

maximal

#19151968

C₂

yes

maximal, characteristic

#19151339

C₂

yes

maximal

#330×C₈₉

C₂

yes

maximal, characteristic

#15668012

C₂²

yes

characteristic

#15668004

C₂²

yes

—

—

—

—

—

—

—

C₂²

yes

characteristic

#125×C₈₉

C₂²

yes

characteristic

#97×C₈₉

C₂²

yes

—

C₂×Dic₁₇₈

—

C₂×#10623494

—

C₄⋊Dic₈₉

—

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

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

C₂×D₄

yes

—

C₂×C₄×C₈₉

C₂×D₄

yes

characteristic

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

Dic₁₇₈

—

C₈×C₈₉

—

#10623494

—

C₂²×C₈₉

#120

yes

characteristic

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

—

Dic₈₉

—

Dic₈₉

—

Dic₈₉

—

C₂×C₈₉

#454

yes

characteristic

C₂×C₈₉

#456

yes

—

#1663

—

maximal, Sylow

C₈₉

#1663

yes

characteristic, complemented, Sylow

—

—

—

—

D₈₉

yes

characteristic

C₄⋊Q₈

—

#125

—

#125

—

178

—

#125

—

178

—

#125

—

178

—

#125

C₂×D₈₉

yes

characteristic

#107

—

178

—

#106

—

178

—

#103

—

178

—

#97

—

#97

C₂×D₈₉

yes

—

C₂×Q₈

—

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

—

178

—

C₄⋊C₄

D₃₅₆

yes

—

C₄²

—

178

—

C₄²

C₂²×D₈₉

yes

characteristic

Q₈

—

356

—

C₂×C₄

—

C₂×C₄

—

356

—

C₂×C₄

—

178

—

C₂×C₄

—

178

—

C₂×C₄

D₄×D₈₉

yes

—

C₂×C₄

C₂×D₃₅₆

yes

characteristic

C₈

—

C₈

—

356

—

C₂²

#15667982

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

356

—

C₄

—

356

—

C₄

—

712

—

C₂

#19151773

yes

characteristic

100

C₂

#19151782

yes

—

	subgroup	G/H
center	C₂²	#15667982
commutator, cosocle	C₄²×C₈₉	C₂³
Frattini	C₄²	C₂²×D₈₉
Fitting	#330×C₈₉	C₂
socle, prime radical	C₂²×C₈₉	#120
hypercenter	#330	D₈₉
hypocenter	C₈₉	#1663
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

D₈₉

C₈₉

G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #330

N	H ≅ G/N	type
51. C₈₉	#1663	semidirect

H ≅ G/N

type

51. C₈₉

#1663

semidirect

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

subgroup	index
C₈₉⋊#564	2
#19152007	2
#19151968	2
#19151339	2
#330×C₈₉	2
#1663	89

subgroup

index

C₈₉⋊#564

#330×C₈₉

Subgroups — #26019581

Conjugacy classes of subgroups

Complements

Maximal subgroups