Group #36444862 — subgroups

Subgroups — #36444862

Order 22784.

382 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 167 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	#26019997	C₂	1	3	yes	maximal
2	#26018079	C₂	1	3	yes	maximal
3	C₈₉×#1273	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×#10623494	C₂²	1	3	yes	—
5	C₄²×Dic₈₉	C₂²	1	1	yes	characteristic
6	#19151352	C₄	1	6	yes	—
7	#19151352	C₄	1	6	yes	—
8	C₂×C₄×C₈×C₈₉	C₂²	1	3	yes	—
9	C₂²×#10623494	C₂×C₄	1	6	yes	—
10	C₂×C₄×Dic₈₉	C₂×C₄	1	3	yes	—
11	C₂×C₄×Dic₈₉	C₂×C₄	1	3	yes	—
12	C₄×#10623494	—	2	3	no	—
13	C₄×#10623494	—	2	3	no	—
14	C₂²×C₈×C₈₉	C₂×C₄	1	6	yes	—
15	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
16	C₄×C₈×C₈₉	—	2	6	no	—
17	C₂²×Dic₈₉	C₄²	1	1	yes	characteristic
18	C₂²×Dic₈₉	C₄²	1	3	yes	—
19	C₂×#10623494	—	2	6	no	—
20	C₂×#10623494	—	2	6	no	—
21	C₂×#10623494	—	2	6	no	—
22	C₄×Dic₈₉	—	2	6	no	—
23	C₄×Dic₈₉	—	2	6	no	—
24	C₂²×C₄×C₈₉	C₂²×C₄	1	3	yes	—
25	C₂×C₈×C₈₉	—	2	6	no	—
26	C₂×C₈×C₈₉	—	2	6	no	—
27	C₂×C₈×C₈₉	—	2	6	no	—
28	C₄²×C₈₉	#41	1	3	yes	—
29	C₄²×C₈₉	#41	1	1	yes	characteristic
30	C₂³×C₈₉	C₂×C₄²	1	1	yes	characteristic
31	C₂×C₄×C₈₉	#117	1	3	yes	—
32	C₂×C₄×C₈₉	#117	1	3	yes	—
33	C₂×C₄×C₈₉	#131	1	6	yes	—
34	C₂×C₄×C₈₉	#131	1	6	yes	—
35	C₂×Dic₈₉	—	2	3	no	—
36	C₂×Dic₈₉	—	2	3	no	—
37	C₂×Dic₈₉	—	2	6	no	—
38	C₈×C₈₉	—	4	6	no	—
39	#10623494	—	4	6	no	—
40	C₂²×C₈₉	#376	1	1	yes	characteristic
41	C₂²×C₈₉	#405	1	3	yes	—
42	C₂²×C₈₉	#405	1	3	yes	—
43	C₄×C₈₉	#433	1	6	yes	—
44	C₄×C₈₉	#433	1	6	yes	—
45	Dic₈₉	—	4	1	no	—
46	Dic₈₉	—	4	3	no	—
47	#8135	—	89	1	no	maximal, Sylow
48	C₂×C₈₉	#1454	1	1	yes	characteristic
49	C₂×C₈₉	#1454	1	3	yes	—
50	C₂×C₈₉	#1746	1	3	yes	—
51	#1744	—	89	3	no	—
52	#1273	—	89	3	no	—
53	#1273	D₈₉	1	1	yes	characteristic
54	C₈₉	#8135	1	1	yes	characteristic, complemented, Sylow
55	C₂×C₄×C₈	—	89	3	no	—
56	C₂×C₄×C₈	C₂×D₈₉	1	3	yes	—
57	C₄³	—	89	1	no	—
58	#336	—	89	6	no	—
59	#336	—	89	6	no	—
60	C₂²×C₈	—	89	6	no	—
61	C₂²×C₈	C₄×D₈₉	1	6	yes	—
62	C₂×C₄²	—	89	3	no	—
63	C₂×C₄²	—	89	3	no	—
64	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
65	C₄×C₈	—	2	6	no	—
66	C₄×C₈	—	178	3	no	—
67	C₄×C₈	—	178	3	no	—
68	C₂²×C₄	—	89	1	no	—
69	C₂²×C₄	—	89	3	no	—
70	C₂²×C₄	C₂×C₄×D₈₉	1	3	yes	—
71	C₂×C₈	—	2	6	no	—
72	C₂×C₈	—	2	6	no	—
73	C₂×C₈	—	2	6	no	—
74	C₂×C₈	—	178	6	no	—
75	C₂×C₈	—	178	6	no	—
76	C₂×C₈	—	178	6	no	—
77	C₄²	—	178	6	no	—
78	C₄²	—	178	6	no	—
79	C₄²	#13083573	1	3	yes	—
80	C₄²	#13083575	1	1	yes	characteristic
81	C₂³	C₄²×D₈₉	1	1	yes	characteristic
82	C₂×C₄	—	178	3	no	—
83	C₂×C₄	—	178	3	no	—
84	C₂×C₄	—	178	6	no	—
85	C₂×C₄	#15667968	1	3	yes	—
86	C₂×C₄	#15667970	1	3	yes	—
87	C₂×C₄	#15668018	1	6	yes	—
88	C₂×C₄	#15668020	1	6	yes	—
89	C₈	—	4	6	no	—
90	C₈	—	356	6	no	—
91	C₂²	#19151443	1	1	yes	characteristic
92	C₂²	#19151552	1	3	yes	—
93	C₂²	#19151555	1	3	yes	—
94	C₄	—	356	1	no	—
95	C₄	—	356	3	no	—
96	C₄	#19151656	1	6	yes	—
97	C₄	#19151658	1	6	yes	—
98	C₂	#26018551	1	1	yes	characteristic
99	C₂	#26018553	1	3	yes	—
100	C₂	#26020002	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#26019997

C₂

yes

maximal

#26018079

C₂

yes

maximal

C₈₉×#1273

C₂

yes

maximal, characteristic

C₂×C₄×#10623494

C₂²

yes

—

C₄²×Dic₈₉

C₂²

yes

characteristic

#19151352

C₄

yes

—

#19151352

C₄

yes

—

C₂×C₄×C₈×C₈₉

C₂²

yes

—

C₂²×#10623494

C₂×C₄

yes

—

C₂×C₄×Dic₈₉

C₂×C₄

yes

—

C₂×C₄×Dic₈₉

C₂×C₄

yes

—

C₄×#10623494

—

C₄×#10623494

—

C₂²×C₈×C₈₉

C₂×C₄

yes

—

C₂×C₄²×C₈₉

C₂³

yes

characteristic

C₄×C₈×C₈₉

—

C₂²×Dic₈₉

C₄²

yes

characteristic

C₂²×Dic₈₉

C₄²

yes

—

C₂×#10623494

—

C₂×#10623494

—

C₂×#10623494

—

C₄×Dic₈₉

—

C₄×Dic₈₉

—

C₂²×C₄×C₈₉

C₂²×C₄

yes

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₄²×C₈₉

#41

yes

—

C₄²×C₈₉

#41

yes

characteristic

C₂³×C₈₉

C₂×C₄²

yes

characteristic

C₂×C₄×C₈₉

#117

yes

—

C₂×C₄×C₈₉

#117

yes

—

C₂×C₄×C₈₉

#131

yes

—

C₂×C₄×C₈₉

#131

yes

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₈×C₈₉

—

#10623494

—

C₂²×C₈₉

#376

yes

characteristic

C₂²×C₈₉

#405

yes

—

C₂²×C₈₉

#405

yes

—

C₄×C₈₉

#433

yes

—

C₄×C₈₉

#433

yes

—

Dic₈₉

—

Dic₈₉

—

—

C₂×C₈₉

yes

C₂×C₈₉

yes

—

C₂×C₈₉

#1746

yes

—

#1744

—

#1273

—

#1273

D₈₉

yes

characteristic

C₈₉

#8135

yes

characteristic, complemented, Sylow

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₈₉

yes

—

C₄³

—

#336

—

#336

—

C₂²×C₈

—

C₂²×C₈

C₄×D₈₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂²×D₈₉

yes

characteristic

C₄×C₈

—

C₄×C₈

—

178

—

C₄×C₈

—

178

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×C₄×D₈₉

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

178

—

C₂×C₈

—

178

—

C₂×C₈

—

178

—

C₄²

—

178

—

C₄²

—

178

—

C₄²

#13083573

yes

—

C₄²

#13083575

yes

characteristic

C₂³

C₄²×D₈₉

yes

characteristic

C₂×C₄

—

178

—

C₂×C₄

—

178

—

C₂×C₄

—

178

—

C₂×C₄

#15667968

yes

—

C₂×C₄

#15667970

yes

—

C₂×C₄

#15668018

yes

—

C₂×C₄

#15668020

yes

—

C₈

—

C₈

—

356

—

C₂²

#19151443

yes

characteristic

C₂²

#19151552

yes

—

C₂²

#19151555

yes

—

C₄

—

356

—

C₄

—

356

—

C₄

#19151656

yes

—

C₄

#19151658

yes

—

C₂

#26018551

yes

characteristic

C₂

#26018553

yes

—

100

C₂

#26020002

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₈₉
commutator, socle, prime radical	C₂³×C₈₉	C₂×C₄²
Fitting	C₈₉×#1273	C₂
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	#1273	D₈₉
hypocenter	C₈₉	#8135
LCS	G ▷ C₂³×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄² ◁ #1273

subgroup

G/H

center, Frattini

C₂×C₄²

C₂²×D₈₉

commutator, socle, prime radical

C₂³×C₈₉

C₂×C₄²

Fitting

C₈₉×#1273

C₂

cosocle

C₂×C₄²×C₈₉

C₂³

D₈₉

C₈₉

G ▷ C₂³×C₈₉ ▷ C₈₉

C₁ ◁ C₂×C₄² ◁ #1273

N	H ≅ G/N	type
54. C₈₉	#8135	semidirect

H ≅ G/N

type

54. C₈₉

#8135

semidirect

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

subgroup	index
#26019997	2
#26018079	2
C₈₉×#1273	2
#8135	89

subgroup

index

#26019997

#26018079

C₈₉×#1273

#8135

Subgroups — #36444862

Conjugacy classes of subgroups

Complements

Maximal subgroups