Group #36475447 — subgroups

Subgroups — #36475447

Order 22784.

158 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 67 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	#26022526	C₂	1	2	yes	maximal
2	#26018452	C₂	1	1	yes	maximal, characteristic
3	#26018451	C₂	1	2	yes	maximal
4	C₃₂×Dic₈₉	C₂	1	1	yes	maximal, characteristic
5	C₈₉×#1423	C₂	1	1	yes	maximal, characteristic
6	#19152002	—	2	2	no	—
7	C₂×#15667918	C₂²	1	1	yes	characteristic
8	#19151424	C₂²	1	2	yes	—
9	#19151423	—	2	2	no	—
10	C₁₆×Dic₈₉	C₂²	1	1	yes	characteristic
11	C₂×C₃₂×C₈₉	C₂²	1	1	yes	characteristic
12	#366×C₈₉	C₂²	1	2	yes	—
13	#15668011	—	4	2	no	—
14	C₂×#13083549	D₄	1	1	yes	characteristic
15	#15667946	—	2	2	no	—
16	#15667945	—	4	2	no	—
17	C₈×Dic₈₉	D₄	1	1	yes	characteristic
18	#15667918	Q₈	1	2	yes	complemented
19	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
20	#107×C₈₉	—	2	2	no	—
21	C₃₂×C₈₉	Q₈	1	2	yes	complemented
22	C₂×Dic₁₇₈	—	8	2	no	—
23	C₂×#10623494	D₈	1	1	yes	characteristic
24	C₄⋊Dic₈₉	—	4	2	no	—
25	#13083553	—	8	2	no	—
26	C₄×Dic₈₉	D₈	1	1	yes	characteristic
27	#13083549	Q₁₆	1	2	yes	—
28	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
29	C₄⋊C₄×C₈₉	—	4	2	no	—
30	C₁₆×C₈₉	C₂×Q₈	1	1	yes	characteristic
31	C₁₆×C₈₉	C₂×Q₈	1	1	yes	characteristic
32	C₂×C₄×C₈₉	—	8	2	no	—
33	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
34	C₂×Dic₈₉	—	8	2	no	—
35	C₂×Dic₈₉	D₁₆	1	1	yes	characteristic
36	C₂×Dic₈₉	D₁₆	1	1	yes	characteristic
37	Dic₁₇₈	—	16	4	no	—
38	C₈×C₈₉	C₄⋊Q₈	1	1	yes	characteristic
39	C₈×C₈₉	C₂×Q₁₆	1	1	yes	characteristic
40	#10623494	Q₃₂	1	2	yes	—
41	C₂²×C₈₉	C₂×D₁₆	1	1	yes	characteristic
42	C₄×C₈₉	—	16	2	no	—
43	C₄×C₈₉	#500	1	1	yes	characteristic
44	C₄×C₈₉	C₂×Q₃₂	1	1	yes	characteristic
45	Dic₈₉	—	16	2	no	—
46	Dic₈₉	D₃₂	1	2	yes	—
47	Dic₈₉	Q₆₄	1	2	yes	—
48	#13731	—	89	1	no	maximal, Sylow
49	C₂×C₈₉	#2252	1	1	yes	characteristic
50	C₂×C₈₉	C₂×D₃₂	1	1	yes	characteristic
51	C₂×C₈₉	C₂×Q₆₄	1	1	yes	characteristic
52	#2252	—	89	2	no	—
53	#1423	—	89	1	no	—
54	#1423	—	89	2	no	—
55	#1423	D₈₉	1	1	yes	characteristic
56	C₄×C₃₂	—	89	1	no	—
57	C₈₉	#13731	1	1	yes	characteristic, complemented, Sylow
58	#500	—	178	2	no	—
59	C₂×C₃₂	—	89	1	no	—
60	C₂×C₃₂	C₂×D₈₉	1	1	yes	characteristic
61	#366	—	89	2	no	—
62	#366	—	178	2	no	—
63	#366	C₂×D₈₉	1	2	yes	—
64	C₄×C₁₆	—	89	1	no	—
65	C₄⋊Q₈	—	356	2	no	—
66	C₂×C₁₆	—	89	1	no	—
67	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
68	#107	—	2	2	no	—
69	#107	—	356	2	no	—
70	#107	—	178	2	no	—
71	C₄×C₈	—	89	1	no	—
72	C₃₂	—	89	2	no	—
73	C₃₂	Dic₁₇₈	1	2	yes	complemented
74	C₂×Q₈	—	712	2	no	—
75	C₂×C₈	—	89	1	no	—
76	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
77	C₄⋊C₄	—	4	2	no	—
78	C₄⋊C₄	—	356	2	no	—
79	C₄⋊C₄	—	712	2	no	—
80	C₄²	—	89	1	no	—
81	C₁₆	—	89	2	no	—
82	C₁₆	Q₈×D₈₉	1	1	yes	characteristic
83	C₁₆	C₂×Dic₁₇₈	1	1	yes	characteristic
84	Q₈	—	1424	4	no	—
85	C₂×C₄	—	8	2	no	—
86	C₂×C₄	—	89	1	no	—
87	C₂×C₄	—	89	1	no	—
88	C₂×C₄	—	712	2	no	—
89	C₂×C₄	D₈×D₈₉	1	1	yes	characteristic
90	C₈	—	89	2	no	—
91	C₈	#15668011	1	1	yes	characteristic
92	C₈	Q₁₆×D₈₉	1	1	yes	characteristic
93	C₂²	D₁₆×D₈₉	1	1	yes	characteristic
94	C₄	—	16	2	no	—
95	C₄	—	89	2	no	—
96	C₄	—	89	2	no	—
97	C₄	—	1424	2	no	—
98	C₄	#19152002	1	1	yes	characteristic
99	C₄	Q₃₂×D₈₉	1	1	yes	characteristic
100	C₂	#26022526	1	1	yes	characteristic
101	C₂	D₃₂×D₈₉	1	1	yes	characteristic
102	C₂	Q₆₄×D₈₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#26022526

C₂

yes

maximal

#26018452

C₂

yes

maximal, characteristic

#26018451

C₂

yes

maximal

C₃₂×Dic₈₉

C₂

yes

maximal, characteristic

C₈₉×#1423

C₂

yes

maximal, characteristic

#19152002

—

C₂×#15667918

C₂²

yes

characteristic

#19151424

C₂²

yes

—

#19151423

—

C₁₆×Dic₈₉

C₂²

yes

characteristic

C₂×C₃₂×C₈₉

C₂²

yes

characteristic

#366×C₈₉

C₂²

yes

—

#15668011

—

C₂×#13083549

D₄

yes

characteristic

#15667946

—

#15667945

—

C₈×Dic₈₉

D₄

yes

characteristic

#15667918

Q₈

yes

complemented

C₂×C₁₆×C₈₉

C₂³

yes

characteristic

#107×C₈₉

—

C₃₂×C₈₉

Q₈

yes

complemented

C₂×Dic₁₇₈

—

C₂×#10623494

D₈

yes

characteristic

C₄⋊Dic₈₉

—

#13083553

—

C₄×Dic₈₉

D₈

yes

characteristic

#13083549

Q₁₆

yes

—

C₂×C₈×C₈₉

C₂×D₄

yes

characteristic

C₄⋊C₄×C₈₉

—

C₁₆×C₈₉

C₂×Q₈

yes

characteristic

C₁₆×C₈₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

C₂×D₈

yes

characteristic

C₂×Dic₈₉

—

C₂×Dic₈₉

D₁₆

yes

characteristic

C₂×Dic₈₉

D₁₆

yes

characteristic

Dic₁₇₈

—

C₈×C₈₉

C₄⋊Q₈

yes

characteristic

C₈×C₈₉

C₂×Q₁₆

yes

characteristic

#10623494

Q₃₂

yes

—

C₂²×C₈₉

C₂×D₁₆

yes

characteristic

C₄×C₈₉

—

C₄×C₈₉

#500

yes

characteristic

C₄×C₈₉

C₂×Q₃₂

yes

characteristic

Dic₈₉

—

Dic₈₉

D₃₂

yes

—

Dic₈₉

Q₆₄

yes

—

—

C₂×C₈₉

yes

C₂×C₈₉

C₂×D₃₂

yes

characteristic

C₂×C₈₉

C₂×Q₆₄

yes

—

—

—

D₈₉

yes

characteristic

C₄×C₃₂

—

C₈₉

#13731

yes

characteristic, complemented, Sylow

#500

—

178

—

C₂×C₃₂

—

C₂×C₃₂

C₂×D₈₉

yes

characteristic

#366

—

#366

—

178

—

#366

C₂×D₈₉

yes

—

C₄×C₁₆

—

C₄⋊Q₈

—

356

—

C₂×C₁₆

—

C₂×C₁₆

C₂²×D₈₉

yes

characteristic

#107

—

#107

—

356

—

#107

—

178

—

C₄×C₈

—

C₃₂

—

C₃₂

Dic₁₇₈

yes

complemented

C₂×Q₈

—

712

—

C₂×C₈

—

C₂×C₈

D₄×D₈₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

356

—

C₄⋊C₄

—

712

—

C₄²

—

C₁₆

—

C₁₆

Q₈×D₈₉

yes

characteristic

C₁₆

C₂×Dic₁₇₈

yes

characteristic

Q₈

—

1424

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

712

—

C₂×C₄

D₈×D₈₉

yes

characteristic

C₈

—

C₈

#15668011

yes

characteristic

C₈

Q₁₆×D₈₉

yes

characteristic

C₂²

D₁₆×D₈₉

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

1424

—

C₄

#19152002

yes

characteristic

C₄

Q₃₂×D₈₉

yes

characteristic

100

C₂

#26022526

yes

characteristic

101

C₂

D₃₂×D₈₉

yes

characteristic

102

C₂

Q₆₄×D₈₉

yes

characteristic

	subgroup	G/H
center	C₂²	D₁₆×D₈₉
commutator, cosocle	C₂×C₁₆×C₈₉	C₂³
Frattini	C₂×C₁₆	C₂²×D₈₉
Fitting	C₈₉×#1423	C₂
socle, prime radical	C₂²×C₈₉	C₂×D₁₆
hypercenter	#1423	D₈₉
hypocenter	C₈₉	#13731
LCS	G ▷ C₂×C₁₆×C₈₉ ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #1423

subgroup

G/H

center

C₂²

D₁₆×D₈₉

commutator, cosocle

C₂×C₁₆×C₈₉

C₂³

Frattini

C₂×C₁₆

C₂²×D₈₉

Fitting

C₈₉×#1423

C₂

socle, prime radical

C₂²×C₈₉

C₂×D₁₆

D₈₉

C₈₉

G ▷ C₂×C₁₆×C₈₉ ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #1423

N	H ≅ G/N	type
18. #15667918	Q₈	semidirect
21. C₃₂×C₈₉	Q₈	semidirect
57. C₈₉	#13731	semidirect
73. C₃₂	Dic₁₇₈	semidirect

H ≅ G/N

type

18. #15667918

Q₈

semidirect

21. C₃₂×C₈₉

Q₈

semidirect

57. C₈₉

#13731

semidirect

73. C₃₂

Dic₁₇₈

semidirect

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

subgroup	index
#26022526	2
#26018452	2
#26018451	2
C₃₂×Dic₈₉	2
C₈₉×#1423	2
#13731	89

subgroup

index

#26022526

#26018452

#26018451

C₃₂×Dic₈₉

C₈₉×#1423

#13731

Subgroups — #36475447

Conjugacy classes of subgroups

Complements

Maximal subgroups