Group #36458937 — subgroups

Subgroups — #36458937

Order 22784.

350 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 97 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	#26020385	C₂	1	3	yes	maximal
2	#26018133	C₂	1	3	yes	maximal
3	C₈₉×#2845	C₂	1	1	yes	maximal, characteristic
4	C₂×#15667923	C₂²	1	3	yes	—
5	#19151468	C₂²	1	1	yes	characteristic
6	#19151360	—	2	6	no	—
7	#398×C₈₉	—	2	6	no	—
8	#382×C₈₉	C₂²	1	3	yes	—
9	C₂²×#10623494	—	2	3	no	—
10	C₂×C₄⋊Dic₈₉	—	2	3	no	—
11	#15667923	—	2	3	no	—
12	#15667923	Q₈	1	6	yes	—
13	C₂×C₄⋊C₄×C₈₉	—	2	6	no	—
14	C₂×C₄⋊C₄×C₈₉	D₄	1	6	yes	—
15	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
16	#95×C₈₉	—	2	2	no	—
17	#95×C₈₉	—	2	6	no	—
18	C₂²×Dic₈₉	—	4	1	no	—
19	C₂×#10623494	—	2	6	no	—
20	C₂×#10623494	—	4	3	no	—
21	C₂×#10623494	—	4	3	no	—
22	C₄⋊Dic₈₉	—	4	6	no	—
23	C₂²×C₄×C₈₉	—	2	6	no	—
24	C₂²×C₄×C₈₉	C₂×D₄	1	3	yes	—
25	C₄⋊C₄×C₈₉	—	4	6	no	—
26	C₄⋊C₄×C₈₉	—	8	6	no	—
27	C₄²×C₈₉	C₂×Q₈	1	3	yes	—
28	C₄²×C₈₉	#41	1	1	yes	characteristic
29	C₂³×C₈₉	#120	1	1	yes	characteristic
30	C₂×C₄×C₈₉	—	2	3	no	—
31	C₂×C₄×C₈₉	—	2	3	no	—
32	C₂×C₄×C₈₉	—	4	6	no	—
33	C₂×C₄×C₈₉	—	4	6	no	—
34	C₂×C₄×C₈₉	—	4	6	no	—
35	C₂×C₄×C₈₉	C₂²⋊Q₈	1	3	yes	—
36	C₂×C₄×C₈₉	C₄⋊Q₈	1	3	yes	—
37	C₂×Dic₈₉	—	8	3	no	—
38	#10623494	—	4	6	no	—
39	C₂²×C₈₉	#395	1	1	yes	characteristic
40	C₂²×C₈₉	#454	1	3	yes	—
41	C₂²×C₈₉	#455	1	3	yes	—
42	C₄×C₈₉	—	2	3	no	—
43	C₄×C₈₉	—	2	3	no	—
44	C₄×C₈₉	—	8	6	no	—
45	Dic₈₉	—	16	1	no	—
46	#10586	—	89	1	no	maximal, Sylow
47	C₂×C₈₉	#1658	1	1	yes	characteristic
48	C₂×C₈₉	#1662	1	3	yes	—
49	C₂×C₈₉	#2061	1	3	yes	—
50	#2845	D₈₉	1	1	yes	characteristic
51	#1836	—	89	3	no	—
52	#1295	—	89	3	no	—
53	C₈₉	#10586	1	1	yes	characteristic, complemented, Sylow
54	C₂×#97	—	89	3	no	—
55	#398	—	2	6	no	—
56	#384	—	89	1	no	—
57	#382	C₂×D₈₉	1	3	yes	—
58	#340	—	178	6	no	—
59	C₂²×C₈	—	178	3	no	—
60	C₂×C₄⋊C₄	—	2	6	no	—
61	C₂×C₄⋊C₄	—	178	3	no	—
62	C₂×C₄⋊C₄	C₂²⋊D₈₉	1	6	yes	—
63	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
64	#97	—	89	6	no	—
65	#97	—	178	3	no	—
66	#95	—	2	2	no	—
67	#95	—	2	6	no	—
68	C₂²×C₄	—	2	6	no	—
69	C₂²×C₄	—	356	1	no	—
70	C₂²×C₄	C₂×C₂²⋊D₈₉	1	3	yes	—
71	C₂×C₈	—	356	3	no	—
72	C₂×C₈	—	356	3	no	—
73	C₂×C₈	—	178	6	no	—
74	C₄⋊C₄	—	4	6	no	—
75	C₄⋊C₄	—	8	6	no	—
76	C₄⋊C₄	—	356	6	no	—
77	C₄²	Q₈×D₈₉	1	3	yes	—
78	C₄²	#13083575	1	1	yes	characteristic
79	C₂³	#15667981	1	1	yes	characteristic
80	C₂×C₄	—	2	3	no	—
81	C₂×C₄	—	2	3	no	—
82	C₂×C₄	—	4	6	no	—
83	C₂×C₄	—	4	6	no	—
84	C₂×C₄	—	4	6	no	—
85	C₂×C₄	—	712	3	no	—
86	C₂×C₄	#15667988	1	3	yes	—
87	C₂×C₄	#15668010	1	3	yes	—
88	C₈	—	356	6	no	—
89	C₂²	#19151517	1	1	yes	characteristic
90	C₂²	#19151771	1	3	yes	—
91	C₂²	#19151776	1	3	yes	—
92	C₄	—	2	3	no	—
93	C₄	—	2	3	no	—
94	C₄	—	8	6	no	—
95	C₄	—	1424	1	no	—
96	C₂	#26019554	1	1	yes	characteristic
97	C₂	#26019575	1	3	yes	—
98	C₂	#26021599	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#26020385

C₂

yes

maximal

#26018133

C₂

yes

maximal

C₈₉×#2845

C₂

yes

maximal, characteristic

C₂×#15667923

C₂²

yes

—

#19151468

C₂²

yes

characteristic

#19151360

—

#398×C₈₉

—

#382×C₈₉

C₂²

yes

—

C₂²×#10623494

—

C₂×C₄⋊Dic₈₉

—

#15667923

—

#15667923

Q₈

yes

—

C₂×C₄⋊C₄×C₈₉

—

C₂×C₄⋊C₄×C₈₉

D₄

yes

—

C₂×C₄²×C₈₉

C₂³

yes

characteristic

#95×C₈₉

—

#95×C₈₉

—

C₂²×Dic₈₉

—

C₂×#10623494

—

C₂×#10623494

—

C₂×#10623494

—

C₄⋊Dic₈₉

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

C₂×D₄

yes

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄²×C₈₉

C₂×Q₈

yes

—

C₄²×C₈₉

yes

C₂³×C₈₉

yes

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₈₉

C₄⋊Q₈

yes

—

C₂×Dic₈₉

—

#10623494

—

C₂²×C₈₉

#395

yes

characteristic

C₂²×C₈₉

#454

yes

—

C₂²×C₈₉

#455

yes

—

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

—

Dic₈₉

—

—

C₂×C₈₉

yes

C₂×C₈₉

yes

—

C₂×C₈₉

#2061

yes

—

#2845

D₈₉

yes

characteristic

#1836

—

#1295

—

C₈₉

#10586

yes

characteristic, complemented, Sylow

C₂×#97

—

#398

—

#384

—

#382

C₂×D₈₉

yes

—

#340

—

178

—

C₂²×C₈

—

178

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

178

—

C₂×C₄⋊C₄

C₂²⋊D₈₉

yes

—

C₂×C₄²

C₂²×D₈₉

yes

characteristic

#97

—

#97

—

178

—

#95

—

#95

—

C₂²×C₄

—

C₂²×C₄

—

356

—

C₂²×C₄

C₂×C₂²⋊D₈₉

yes

—

C₂×C₈

—

356

—

C₂×C₈

—

356

—

C₂×C₈

—

178

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

356

—

C₄²

Q₈×D₈₉

yes

—

C₄²

yes

C₂³

yes

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

712

—

C₂×C₄

#15667988

yes

—

C₂×C₄

#15668010

yes

—

C₈

—

356

—

C₂²

#19151517

yes

characteristic

C₂²

#19151771

yes

—

C₂²

#19151776

yes

—

C₄

—

C₄

—

C₄

—

C₄

—

1424

—

C₂

#26019554

yes

characteristic

C₂

#26019575

yes

—

C₂

#26021599

yes

—

	subgroup	G/H
center	C₂³	#15667981
commutator, cosocle	C₂×C₄²×C₈₉	C₂³
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₈₉×#2845	C₂
socle, prime radical	C₂³×C₈₉	#120
hypercenter	#2845	D₈₉
hypocenter	C₈₉	#10586
LCS	G ▷ C₂×C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2845

subgroup

G/H

center

C₂³

#15667981

commutator, cosocle

C₂×C₄²×C₈₉

C₂³

Frattini

C₂×C₄²

C₂²×D₈₉

Fitting

C₈₉×#2845

C₂

C₂³×C₈₉

D₈₉

C₈₉

G ▷ C₂×C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2845

N	H ≅ G/N	type
53. C₈₉	#10586	semidirect

H ≅ G/N

type

53. C₈₉

#10586

semidirect

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

subgroup	index
#26020385	2
#26018133	2
C₈₉×#2845	2
#10586	89

subgroup

index

#26020385

#26018133

C₈₉×#2845

#10586

Subgroups — #36458937

Conjugacy classes of subgroups

Complements

Maximal subgroups