Group #36444863 — subgroups

Subgroups — #36444863

Order 22784.

382 conjugacy classes of subgroups; only the 179 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 179 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	#26019998	C₂	1	1	yes	maximal, characteristic
2	#26019998	C₂	1	1	yes	maximal, characteristic
3	#26018079	C₂	1	4	yes	maximal
4	C₈₉×#1744	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×#10623494	C₂²	1	2	yes	—
6	C₂×C₄×#10623494	C₂²	1	2	yes	—
7	#19151353	C₄	1	4	yes	—
8	#19151353	C₄	1	4	yes	—
9	C₂×C₄×C₈×C₈₉	C₂²	1	2	yes	—
10	C₄³×C₈₉	C₂²	1	1	yes	characteristic
11	#336×C₈₉	C₄	1	4	yes	—
12	C₂²×#10623494	C₂×C₄	1	4	yes	—
13	C₂²×#10623494	C₂×C₄	1	4	yes	—
14	C₄×#10623494	—	2	4	no	—
15	C₄×#10623494	—	2	4	no	—
16	C₂²×C₈×C₈₉	C₂×C₄	1	4	yes	—
17	C₂×C₄²×C₈₉	C₂×C₄	1	2	yes	—
18	C₂×C₄²×C₈₉	C₂×C₄	1	2	yes	—
19	C₂×C₄²×C₈₉	C₂×C₄	1	2	yes	—
20	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
21	C₄×C₈×C₈₉	—	2	4	no	—
22	C₂×#10623494	—	2	4	no	—
23	C₂×#10623494	—	2	4	no	—
24	C₂×#10623494	—	2	8	no	—
25	C₂×#10623494	—	2	8	no	—
26	C₂²×C₄×C₈₉	C₄²	1	4	yes	—
27	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
28	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
29	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
30	C₂×C₈×C₈₉	—	2	4	no	—
31	C₂×C₈×C₈₉	—	2	8	no	—
32	C₄²×C₈₉	—	2	4	no	—
33	C₄²×C₈₉	—	2	4	no	—
34	C₄²×C₈₉	—	2	4	no	—
35	C₄²×C₈₉	#41	1	4	yes	—
36	C₂³×C₈₉	C₂×C₄²	1	1	yes	characteristic
37	C₂×C₄×C₈₉	—	2	4	no	—
38	C₂×C₄×C₈₉	—	2	4	no	—
39	C₂×C₄×C₈₉	—	2	4	no	—
40	C₂×C₄×C₈₉	#117	1	2	yes	—
41	C₂×C₄×C₈₉	#117	1	2	yes	—
42	C₂×C₄×C₈₉	#117	1	2	yes	—
43	C₂×C₄×C₈₉	#131	1	4	yes	—
44	C₂×C₄×C₈₉	#131	1	4	yes	—
45	C₂×C₄×C₈₉	#131	1	4	yes	—
46	C₈×C₈₉	—	4	4	no	—
47	#10623494	—	4	4	no	—
48	#10623494	—	4	4	no	—
49	C₂²×C₈₉	#376	1	1	yes	characteristic
50	C₂²×C₈₉	#405	1	2	yes	—
51	C₂²×C₈₉	#405	1	2	yes	—
52	C₂²×C₈₉	#405	1	2	yes	—
53	C₄×C₈₉	—	4	4	no	—
54	C₄×C₈₉	#433	1	4	yes	—
55	C₄×C₈₉	#433	1	4	yes	—
56	C₄×C₈₉	#433	1	4	yes	—
57	#8135	—	89	1	no	maximal, Sylow
58	C₂×C₈₉	#1454	1	4	yes	—
59	C₂×C₈₉	#1746	1	1	yes	characteristic
60	C₂×C₈₉	#1746	1	1	yes	characteristic
61	C₂×C₈₉	#1746	1	1	yes	characteristic
62	#1744	—	89	1	no	—
63	#1744	—	89	1	no	—
64	#1744	D₈₉	1	1	yes	characteristic
65	#1273	—	89	4	no	—
66	C₈₉	#8135	1	1	yes	characteristic, complemented, Sylow
67	C₂×C₄×C₈	—	89	2	no	—
68	C₂×C₄×C₈	—	89	2	no	—
69	C₂×C₄×C₈	C₂×D₈₉	1	2	yes	—
70	C₄³	C₂×D₈₉	1	1	yes	characteristic
71	#336	—	89	4	no	—
72	#336	—	89	4	no	—
73	#336	Dic₈₉	1	4	yes	—
74	C₂²×C₈	—	89	4	no	—
75	C₂²×C₈	—	89	4	no	—
76	C₂²×C₈	C₂×Dic₈₉	1	4	yes	—
77	C₂×C₄²	C₄×D₈₉	1	2	yes	—
78	C₂×C₄²	C₄×D₈₉	1	2	yes	—
79	C₂×C₄²	C₂×Dic₈₉	1	2	yes	—
80	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
81	C₄×C₈	—	2	4	no	—
82	C₄×C₈	—	178	4	no	—
83	C₄×C₈	—	178	4	no	—
84	C₂²×C₄	C₄×Dic₈₉	1	4	yes	—
85	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
86	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
87	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
88	C₂×C₈	—	2	4	no	—
89	C₂×C₈	—	2	8	no	—
90	C₂×C₈	—	178	4	no	—
91	C₂×C₈	—	178	4	no	—
92	C₂×C₈	—	178	8	no	—
93	C₂×C₈	—	178	8	no	—
94	C₄²	—	2	4	no	—
95	C₄²	—	2	4	no	—
96	C₄²	—	2	4	no	—
97	C₄²	#13083574	1	4	yes	—
98	C₂³	C₂×C₄×Dic₈₉	1	1	yes	characteristic
99	C₂×C₄	—	2	4	no	—
100	C₂×C₄	—	2	4	no	—
101	C₂×C₄	—	2	4	no	—
102	C₂×C₄	#15667969	1	2	yes	—
103	C₂×C₄	#15667969	1	2	yes	—
104	C₂×C₄	#15667971	1	2	yes	—
105	C₂×C₄	#15668018	1	4	yes	—
106	C₂×C₄	#15668019	1	4	yes	—
107	C₂×C₄	#15668020	1	4	yes	—
108	C₈	—	4	4	no	—
109	C₈	—	356	4	no	—
110	C₈	—	356	4	no	—
111	C₂²	#19151444	1	1	yes	characteristic
112	C₂²	#19151553	1	2	yes	—
113	C₂²	#19151554	1	2	yes	—
114	C₂²	#19151556	1	2	yes	—
115	C₄	—	4	4	no	—
116	C₄	#19151657	1	4	yes	—
117	C₄	#19151659	1	4	yes	—
118	C₄	#19151660	1	4	yes	—
119	C₂	#26018552	1	4	yes	—
120	C₂	#26020003	1	1	yes	characteristic
121	C₂	#26020004	1	1	yes	characteristic
122	C₂	#26020005	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#26019998

C₂

yes

maximal, characteristic

#26019998

C₂

yes

maximal, characteristic

#26018079

C₂

yes

maximal

C₈₉×#1744

C₂

yes

maximal, characteristic

C₂×C₄×#10623494

C₂²

yes

—

C₂×C₄×#10623494

C₂²

yes

—

#19151353

C₄

yes

—

#19151353

C₄

yes

—

C₂×C₄×C₈×C₈₉

C₂²

yes

—

C₄³×C₈₉

C₂²

yes

characteristic

#336×C₈₉

C₄

yes

—

C₂²×#10623494

C₂×C₄

yes

—

C₂²×#10623494

C₂×C₄

yes

—

C₄×#10623494

—

C₄×#10623494

—

C₂²×C₈×C₈₉

C₂×C₄

yes

—

C₂×C₄²×C₈₉

C₂×C₄

yes

—

C₂×C₄²×C₈₉

C₂×C₄

yes

—

C₂×C₄²×C₈₉

C₂×C₄

yes

—

C₂×C₄²×C₈₉

C₂³

yes

characteristic

C₄×C₈×C₈₉

—

—

—

—

—

C₂²×C₄×C₈₉

C₄²

yes

—

C₂²×C₄×C₈₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₈₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₈₉

C₂²×C₄

yes

characteristic

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₄²×C₈₉

—

C₄²×C₈₉

—

C₄²×C₈₉

—

C₄²×C₈₉

#41

yes

—

C₂³×C₈₉

C₂×C₄²

yes

characteristic

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

#117

yes

—

C₂×C₄×C₈₉

#117

yes

—

C₂×C₄×C₈₉

#117

yes

—

C₂×C₄×C₈₉

#131

yes

—

C₂×C₄×C₈₉

#131

yes

—

C₂×C₄×C₈₉

#131

yes

—

C₈×C₈₉

—

#10623494

—

#10623494

—

C₂²×C₈₉

#376

yes

characteristic

C₂²×C₈₉

#405

yes

—

C₂²×C₈₉

#405

yes

—

C₂²×C₈₉

#405

yes

—

C₄×C₈₉

—

C₄×C₈₉

#433

yes

—

C₄×C₈₉

#433

yes

—

C₄×C₈₉

#433

yes

—

#8135

—

maximal, Sylow

C₂×C₈₉

#1454

yes

—

C₂×C₈₉

yes

C₂×C₈₉

yes

C₂×C₈₉

yes

—

—

D₈₉

yes

characteristic

#1273

—

C₈₉

#8135

yes

characteristic, complemented, Sylow

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₈₉

yes

—

C₄³

C₂×D₈₉

yes

—

—

Dic₈₉

yes

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

C₂×Dic₈₉

yes

—

C₂×C₄²

C₄×D₈₉

yes

—

C₂×C₄²

C₄×D₈₉

yes

—

C₂×C₄²

C₂×Dic₈₉

yes

—

C₂×C₄²

C₂²×D₈₉

yes

characteristic

C₄×C₈

—

C₄×C₈

—

178

—

C₄×C₈

—

178

—

C₂²×C₄

C₄×Dic₈₉

yes

—

C₂²×C₄

C₂×C₄×D₈₉

yes

characteristic

C₂²×C₄

C₂×C₄×D₈₉

yes

characteristic

C₂²×C₄

C₂²×Dic₈₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

178

—

C₂×C₈

—

178

—

C₂×C₈

—

178

—

C₂×C₈

—

178

—

C₄²

—

C₄²

—

C₄²

—

C₄²

#13083574

yes

—

C₂³

C₂×C₄×Dic₈₉

yes

characteristic

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

#15667969

yes

—

103

C₂×C₄

#15667969

yes

—

104

C₂×C₄

#15667971

yes

—

105

C₂×C₄

#15668018

yes

—

106

C₂×C₄

#15668019

yes

—

107

C₂×C₄

#15668020

yes

—

108

C₈

—

109

C₈

—

356

—

110

C₈

—

356

—

111

C₂²

#19151444

yes

characteristic

112

C₂²

#19151553

yes

—

113

C₂²

#19151554

yes

—

114

C₂²

#19151556

yes

—

115

C₄

—

116

C₄

#19151657

yes

—

117

C₄

#19151659

yes

—

118

C₄

#19151660

yes

—

119

C₂

#26018552

yes

—

120

C₂

#26020003

yes

characteristic

121

C₂

#26020004

yes

characteristic

122

C₂

#26020005

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₈₉
commutator, socle, prime radical	C₂³×C₈₉	C₂×C₄²
Fitting	C₈₉×#1744	C₂
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	#1744	D₈₉
hypocenter	C₈₉	#8135
LCS	G ▷ C₂³×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄² ◁ #1744

subgroup

G/H

center, Frattini

C₂×C₄²

C₂²×D₈₉

commutator, socle, prime radical

C₂³×C₈₉

C₂×C₄²

Fitting

C₈₉×#1744

C₂

cosocle

C₂×C₄²×C₈₉

C₂³

D₈₉

C₈₉

G ▷ C₂³×C₈₉ ▷ C₈₉

C₁ ◁ C₂×C₄² ◁ #1744

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

H ≅ G/N

type

66. C₈₉

#8135

semidirect

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

subgroup	index
#26019998	2
#26018079	2
C₈₉×#1744	2
#8135	89

subgroup

index

#26019998

#26018079

C₈₉×#1744

#8135

Subgroups — #36444863

Conjugacy classes of subgroups

Complements

Maximal subgroups