Group #36444860 — subgroups

Subgroups — #36444860

Order 22784.

414 conjugacy classes of subgroups; only the 187 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 187 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	C₄×#15667923	C₂	1	1	yes	maximal, characteristic
3	#26018079	C₂	1	4	yes	maximal
4	C₈₉×#1744	C₂	1	1	yes	maximal, characteristic
5	C₂×#15667923	C₄	1	4	yes	—
6	C₂×C₄×#10623494	C₂²	1	2	yes	—
7	C₂×C₄×#10623494	C₂²	1	2	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	#15667923	—	2	8	no	—
15	C₄×#10623494	—	2	4	no	—
16	C₄×#10623494	—	2	4	no	—
17	C₂²×C₈×C₈₉	C₂×C₄	1	4	yes	—
18	C₂×C₄²×C₈₉	C₂×C₄	1	2	yes	—
19	C₂×C₄²×C₈₉	C₂×C₄	1	2	yes	—
20	C₂×C₄²×C₈₉	C₂×C₄	1	2	yes	—
21	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
22	C₄×C₈×C₈₉	—	2	4	no	—
23	C₂×#10623494	—	2	4	no	—
24	C₂×#10623494	—	2	4	no	—
25	C₂×#10623494	—	2	4	no	—
26	C₂×#10623494	—	2	8	no	—
27	C₂×#10623494	M₁₆	1	8	yes	—
28	C₂²×C₄×C₈₉	C₄²	1	4	yes	—
29	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
30	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
31	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₈×C₈₉	—	2	4	no	—
33	C₂×C₈×C₈₉	—	2	8	no	—
34	C₄²×C₈₉	—	2	4	no	—
35	C₄²×C₈₉	—	2	4	no	—
36	C₄²×C₈₉	—	2	4	no	—
37	C₄²×C₈₉	#41	1	4	yes	—
38	C₂³×C₈₉	C₂×C₄²	1	1	yes	characteristic
39	C₂×C₄×C₈₉	—	2	4	no	—
40	C₂×C₄×C₈₉	—	2	4	no	—
41	C₂×C₄×C₈₉	—	2	4	no	—
42	C₂×C₄×C₈₉	#117	1	2	yes	—
43	C₂×C₄×C₈₉	#117	1	2	yes	—
44	C₂×C₄×C₈₉	#117	1	2	yes	—
45	C₂×C₄×C₈₉	C₂×M₁₆	1	4	yes	—
46	C₂×C₄×C₈₉	#131	1	4	yes	—
47	C₂×C₄×C₈₉	#131	1	4	yes	—
48	C₈×C₈₉	—	4	4	no	—
49	#10623494	—	2	8	no	—
50	#10623494	—	4	4	no	—
51	C₂²×C₈₉	#376	1	1	yes	characteristic
52	C₂²×C₈₉	C₄×M₁₆	1	2	yes	—
53	C₂²×C₈₉	#405	1	2	yes	—
54	C₂²×C₈₉	#405	1	2	yes	—
55	C₄×C₈₉	—	4	4	no	—
56	C₄×C₈₉	#432	1	4	yes	—
57	C₄×C₈₉	#433	1	4	yes	—
58	C₄×C₈₉	#433	1	4	yes	—
59	#8134	—	89	1	no	maximal, Sylow
60	C₂×C₈₉	#1453	1	4	yes	—
61	C₂×C₈₉	#1745	1	1	yes	characteristic
62	C₂×C₈₉	#1746	1	1	yes	characteristic
63	C₂×C₈₉	#1746	1	1	yes	characteristic
64	#1744	—	89	1	no	—
65	#1744	D₈₉	1	1	yes	characteristic
66	C₄×#97	—	89	1	no	—
67	#1273	—	89	4	no	—
68	C₈₉	#8134	1	1	yes	characteristic, complemented, Sylow
69	C₂×#97	—	89	4	no	—
70	C₂×C₄×C₈	—	89	2	no	—
71	C₂×C₄×C₈	—	89	2	no	—
72	C₂×C₄×C₈	C₂×D₈₉	1	2	yes	—
73	C₄³	C₂×D₈₉	1	1	yes	characteristic
74	#336	—	89	4	no	—
75	#336	Dic₈₉	1	4	yes	—
76	C₂²×C₈	—	89	4	no	—
77	C₂²×C₈	—	89	4	no	—
78	C₂²×C₈	C₂×Dic₈₉	1	4	yes	—
79	C₂×C₄²	C₄×D₈₉	1	2	yes	—
80	C₂×C₄²	C₄×D₈₉	1	2	yes	—
81	C₂×C₄²	C₂×Dic₈₉	1	2	yes	—
82	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
83	#97	—	178	8	no	—
84	C₄×C₈	—	2	4	no	—
85	C₄×C₈	—	178	4	no	—
86	C₄×C₈	—	178	4	no	—
87	C₂²×C₄	C₄×Dic₈₉	1	4	yes	—
88	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
89	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
90	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
91	C₂×C₈	—	2	4	no	—
92	C₂×C₈	—	2	8	no	—
93	C₂×C₈	—	89	8	no	—
94	C₂×C₈	—	178	4	no	—
95	C₂×C₈	—	178	8	no	—
96	C₂×C₈	—	178	4	no	—
97	C₂×C₈	—	178	4	no	—
98	C₄²	—	2	4	no	—
99	C₄²	—	2	4	no	—
100	C₄²	—	2	4	no	—
101	C₄²	#13083574	1	4	yes	—
102	C₂³	C₂×C₄×Dic₈₉	1	1	yes	characteristic
103	C₂×C₄	—	2	4	no	—
104	C₂×C₄	—	2	4	no	—
105	C₂×C₄	—	2	4	no	—
106	C₂×C₄	#15667969	1	2	yes	—
107	C₂×C₄	#15667969	1	2	yes	—
108	C₂×C₄	#15667971	1	2	yes	—
109	C₂×C₄	M₁₆×D₈₉	1	4	yes	—
110	C₂×C₄	#15668018	1	4	yes	—
111	C₂×C₄	#15668019	1	4	yes	—
112	C₈	—	4	4	no	—
113	C₈	—	356	4	no	—
114	C₈	—	178	8	no	—
115	C₂²	#19151444	1	1	yes	characteristic
116	C₂²	M₁₆×Dic₈₉	1	2	yes	—
117	C₂²	#19151553	1	2	yes	—
118	C₂²	#19151554	1	2	yes	—
119	C₄	—	4	4	no	—
120	C₄	#19151653	1	4	yes	—
121	C₄	#19151657	1	4	yes	—
122	C₄	#19151659	1	4	yes	—
123	C₂	#26018547	1	4	yes	—
124	C₂	#26020000	1	1	yes	characteristic
125	C₂	#26020003	1	1	yes	characteristic
126	C₂	#26020004	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#26019998

C₂

yes

maximal, characteristic

C₄×#15667923

C₂

yes

maximal, characteristic

#26018079

C₂

yes

maximal

C₈₉×#1744

C₂

yes

maximal, characteristic

C₂×#15667923

C₄

yes

—

C₂×C₄×#10623494

C₂²

yes

—

C₂×C₄×#10623494

C₂²

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

—

#15667923

—

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

—

—

—

—

—

M₁₆

yes

—

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

C₂×M₁₆

yes

—

C₂×C₄×C₈₉

#131

yes

—

C₂×C₄×C₈₉

#131

yes

—

C₈×C₈₉

—

#10623494

—

#10623494

—

C₂²×C₈₉

#376

yes

characteristic

C₂²×C₈₉

C₄×M₁₆

yes

—

C₂²×C₈₉

#405

yes

—

C₂²×C₈₉

#405

yes

—

C₄×C₈₉

—

C₄×C₈₉

#432

yes

—

C₄×C₈₉

#433

yes

—

C₄×C₈₉

#433

yes

—

#8134

—

maximal, Sylow

C₂×C₈₉

#1453

yes

—

C₂×C₈₉

yes

C₂×C₈₉

yes

C₂×C₈₉

yes

—

D₈₉

yes

characteristic

C₄×#97

—

#1273

—

C₈₉

#8134

yes

characteristic, complemented, Sylow

C₂×#97

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₈₉

yes

—

C₄³

C₂×D₈₉

yes

characteristic

#336

—

#336

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

#97

—

178

—

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

—

C₂×C₈

—

178

—

C₂×C₈

—

178

—

C₂×C₈

—

178

—

C₂×C₈

—

178

—

C₄²

—

C₄²

—

100

C₄²

—

101

C₄²

#13083574

yes

—

102

C₂³

C₂×C₄×Dic₈₉

yes

characteristic

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

#15667969

yes

—

107

C₂×C₄

#15667969

yes

—

108

C₂×C₄

#15667971

yes

—

109

C₂×C₄

M₁₆×D₈₉

yes

—

110

C₂×C₄

#15668018

yes

—

111

C₂×C₄

#15668019

yes

—

112

C₈

—

113

C₈

—

356

—

114

C₈

—

178

—

115

C₂²

#19151444

yes

characteristic

116

C₂²

M₁₆×Dic₈₉

yes

—

117

C₂²

#19151553

yes

—

118

C₂²

#19151554

yes

—

119

C₄

—

120

C₄

#19151653

yes

—

121

C₄

#19151657

yes

—

122

C₄

#19151659

yes

—

123

C₂

#26018547

yes

—

124

C₂

#26020000

yes

characteristic

125

C₂

#26020003

yes

characteristic

126

C₂

#26020004

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	#8134
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
68. C₈₉	#8134	semidirect

H ≅ G/N

type

68. C₈₉

#8134

semidirect

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

subgroup	index
#26019998	2
C₄×#15667923	2
#26018079	2
C₈₉×#1744	2
#8134	89

subgroup

index

C₈₉×#1744

Subgroups — #36444860

Conjugacy classes of subgroups

Complements

Maximal subgroups