Group #36446884 — subgroups

Subgroups — #36446884

Order 22784.

656 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 656 conjugacy classes of subgroups — too many to draw. Only its 147 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	#26021222	C₂	1	3	yes	maximal
2	C₂×#19151340	C₂	1	3	yes	maximal
3	C₂×#564×C₈₉	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	#19151340	—	2	6	no	—
8	#564×C₈₉	—	2	6	no	—
9	#564×C₈₉	C₄	1	4	yes	complemented
10	C₂×#125×C₈₉	—	2	6	no	—
11	C₂×#125×C₈₉	C₂²	1	3	yes	—
12	C₂²×#10623494	—	2	3	no	—
13	C₂×C₄⋊Dic₈₉	—	2	3	no	—
14	#15667923	—	2	6	no	—
15	#125×C₈₉	—	2	24	no	—
16	#125×C₈₉	—	2	24	no	—
17	#125×C₈₉	—	2	6	no	—
18	#125×C₈₉	C₂×C₄	1	6	yes	—
19	#125×C₈₉	D₄	1	6	yes	—
20	C₂×C₄⋊C₄×C₈₉	—	2	6	no	—
21	C₂×C₄⋊C₄×C₈₉	—	2	6	no	—
22	C₂×C₄⋊C₄×C₈₉	D₄	1	6	yes	—
23	C₂×C₄²×C₈₉	—	2	2	no	—
24	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
25	C₂²×Dic₈₉	—	4	1	no	—
26	C₂×#10623494	—	2	6	no	—
27	C₂×#10623494	—	4	3	no	—
28	C₂×#10623494	—	4	3	no	—
29	C₄⋊Dic₈₉	—	4	6	no	—
30	C₂²×C₄×C₈₉	—	2	6	no	—
31	C₂²×C₄×C₈₉	C₂×D₄	1	3	yes	—
32	C₄⋊C₄×C₈₉	—	2	24	no	—
33	C₄⋊C₄×C₈₉	—	2	12	no	—
34	C₄⋊C₄×C₈₉	—	2	12	no	—
35	C₄⋊C₄×C₈₉	—	2	6	no	—
36	C₄⋊C₄×C₈₉	C₂²⋊C₄	1	12	yes	—
37	C₄²×C₈₉	—	2	8	no	—
38	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
39	C₄²×C₈₉	C₂×D₄	1	3	yes	—
40	C₂³×C₈₉	#120	1	1	yes	characteristic
41	C₂×C₄×C₈₉	—	2	3	no	—
42	C₂×C₄×C₈₉	—	2	3	no	—
43	C₂×C₄×C₈₉	—	2	12	no	—
44	C₂×C₄×C₈₉	—	4	6	no	—
45	C₂×C₄×C₈₉	—	4	6	no	—
46	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	3	yes	—
47	C₂×C₄×C₈₉	#120	1	3	yes	—
48	C₂×Dic₈₉	—	8	3	no	—
49	#10623494	—	4	6	no	—
50	C₂²×C₈₉	#379	1	1	yes	characteristic
51	C₂²×C₈₉	#454	1	3	yes	—
52	C₂²×C₈₉	#456	1	3	yes	—
53	C₄×C₈₉	—	2	3	no	—
54	C₄×C₈₉	—	2	3	no	—
55	C₄×C₈₉	—	4	12	no	—
56	Dic₈₉	—	16	1	no	—
57	#8509	—	89	1	no	maximal, Sylow
58	C₂×C₈₉	#1658	1	1	yes	characteristic
59	C₂×C₈₉	#1663	1	3	yes	—
60	C₂×C₈₉	#1793	1	3	yes	—
61	C₂×#564	D₈₉	1	1	yes	characteristic
62	#1992	—	89	3	no	—
63	C₂×#330	—	89	3	no	—
64	C₈₉	#8509	1	1	yes	characteristic, complemented, Sylow
65	#564	—	2	6	no	—
66	#564	Dic₈₉	1	4	yes	complemented
67	C₂×#125	—	2	6	no	—
68	C₂×#125	C₂×D₈₉	1	3	yes	—
69	C₂×#97	—	89	3	no	—
70	#384	—	89	1	no	—
71	#340	—	178	6	no	—
72	#330	—	178	6	no	—
73	C₂²×C₈	—	178	3	no	—
74	#125	—	2	24	no	—
75	#125	—	2	24	no	—
76	#125	—	2	6	no	—
77	#125	C₂×Dic₈₉	1	6	yes	—
78	#125	C₂²⋊D₈₉	1	6	yes	—
79	C₂×C₄⋊C₄	—	2	6	no	—
80	C₂×C₄⋊C₄	—	2	6	no	—
81	C₂×C₄⋊C₄	—	178	3	no	—
82	C₂×C₄⋊C₄	C₂²⋊D₈₉	1	6	yes	—
83	C₂×C₄²	—	2	2	no	—
84	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
85	#97	—	178	6	no	—
86	C₂²×C₄	—	2	6	no	—
87	C₂²×C₄	—	356	1	no	—
88	C₂²×C₄	C₂×C₂²⋊D₈₉	1	3	yes	—
89	C₂×C₈	—	356	3	no	—
90	C₂×C₈	—	356	3	no	—
91	C₂×C₈	—	178	6	no	—
92	C₄⋊C₄	—	2	24	no	—
93	C₄⋊C₄	—	2	12	no	—
94	C₄⋊C₄	—	2	6	no	—
95	C₄⋊C₄	—	2	12	no	—
96	C₄⋊C₄	—	356	6	no	—
97	C₄⋊C₄	C₂²⋊Dic₈₉	1	12	yes	—
98	C₄²	—	2	8	no	—
99	C₄²	C₂²×Dic₈₉	1	1	yes	characteristic
100	C₄²	C₂×C₂²⋊D₈₉	1	3	yes	—
101	C₂³	#15667981	1	1	yes	characteristic
102	C₂×C₄	—	2	3	no	—
103	C₂×C₄	—	2	3	no	—
104	C₂×C₄	—	2	12	no	—
105	C₂×C₄	—	4	6	no	—
106	C₂×C₄	—	4	6	no	—
107	C₂×C₄	—	712	3	no	—
108	C₂×C₄	C₂×C₂²⋊Dic₈₉	1	3	yes	—
109	C₂×C₄	#15667981	1	3	yes	—
110	C₈	—	356	6	no	—
111	C₂²	#19151454	1	1	yes	characteristic
112	C₂²	#19151771	1	3	yes	—
113	C₂²	#19151781	1	3	yes	—
114	C₄	—	2	3	no	—
115	C₄	—	2	3	no	—
116	C₄	—	4	12	no	—
117	C₄	—	1424	1	no	—
118	C₂	#26019554	1	1	yes	characteristic
119	C₂	#26019580	1	3	yes	—
120	C₂	#26020211	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#26021222

C₂

yes

maximal

C₂×#19151340

C₂

yes

maximal

C₂×#564×C₈₉

C₂

yes

maximal, characteristic

C₂×#15667923

C₂²

yes

—

#19151468

C₂²

yes

characteristic

#19151360

—

#19151340

—

#564×C₈₉

—

#564×C₈₉

C₄

yes

complemented

C₂×#125×C₈₉

—

C₂×#125×C₈₉

C₂²

yes

—

C₂²×#10623494

—

C₂×C₄⋊Dic₈₉

—

#15667923

—

#125×C₈₉

—

#125×C₈₉

—

#125×C₈₉

—

#125×C₈₉

C₂×C₄

yes

—

#125×C₈₉

D₄

yes

—

C₂×C₄⋊C₄×C₈₉

—

C₂×C₄⋊C₄×C₈₉

—

C₂×C₄⋊C₄×C₈₉

D₄

yes

—

C₂×C₄²×C₈₉

—

C₂×C₄²×C₈₉

C₂³

yes

characteristic

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

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

C₂²⋊C₄

yes

—

C₄²×C₈₉

—

C₄²×C₈₉

C₂²×C₄

yes

characteristic

C₄²×C₈₉

C₂×D₄

yes

—

C₂³×C₈₉

#120

yes

characteristic

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

C₂×C₂²⋊C₄

yes

—

C₂×C₄×C₈₉

#120

yes

—

C₂×Dic₈₉

—

#10623494

—

C₂²×C₈₉

#379

yes

characteristic

C₂²×C₈₉

#454

yes

—

C₂²×C₈₉

#456

yes

—

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

—

Dic₈₉

—

—

C₂×C₈₉

yes

C₂×C₈₉

yes

—

C₂×C₈₉

#1793

yes

—

C₂×#564

D₈₉

yes

characteristic

#1992

—

C₂×#330

—

C₈₉

#8509

yes

characteristic, complemented, Sylow

#564

—

#564

Dic₈₉

yes

complemented

C₂×#125

—

C₂×#125

C₂×D₈₉

yes

—

C₂×#97

—

#384

—

#340

—

178

—

#330

—

178

—

C₂²×C₈

—

178

—

—

—

—

C₂×Dic₈₉

yes

—

#125

C₂²⋊D₈₉

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

178

—

C₂×C₄⋊C₄

C₂²⋊D₈₉

yes

—

C₂×C₄²

—

C₂×C₄²

C₂²×D₈₉

yes

characteristic

#97

—

178

—

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

—

C₄⋊C₄

—

C₄⋊C₄

—

356

—

C₄⋊C₄

C₂²⋊Dic₈₉

yes

—

C₄²

—

C₄²

C₂²×Dic₈₉

yes

characteristic

100

C₄²

C₂×C₂²⋊D₈₉

yes

—

101

C₂³

#15667981

yes

characteristic

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

712

—

108

C₂×C₄

C₂×C₂²⋊Dic₈₉

yes

—

109

C₂×C₄

#15667981

yes

—

110

C₈

—

356

—

111

C₂²

#19151454

yes

characteristic

112

C₂²

#19151771

yes

—

113

C₂²

#19151781

yes

—

114

C₄

—

115

C₄

—

116

C₄

—

117

C₄

—

1424

—

118

C₂

#26019554

yes

characteristic

119

C₂

#26019580

yes

—

120

C₂

#26020211

yes

—

	subgroup	G/H
center	C₂³	#15667981
commutator	C₄²×C₈₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₂×#564×C₈₉	C₂
socle, prime radical	C₂³×C₈₉	#120
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	C₂×#564	D₈₉
hypocenter	C₈₉	#8509
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#564

subgroup

G/H

center

C₂³

#15667981

commutator

C₄²×C₈₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₈₉

Fitting

C₂×#564×C₈₉

C₂

socle, prime radical

C₂³×C₈₉

#120

cosocle

C₂×C₄²×C₈₉

C₂³

D₈₉

C₈₉

G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#564

N	H ≅ G/N	type
9. #564×C₈₉	C₄	semidirect
64. C₈₉	#8509	semidirect
66. #564	Dic₈₉	semidirect

H ≅ G/N

type

9. #564×C₈₉

C₄

semidirect

64. C₈₉

#8509

semidirect

66. #564

Dic₈₉

semidirect

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

subgroup	index
#26021222	2
C₂×#19151340	2
C₂×#564×C₈₉	2
#8509	89

subgroup

index

#26021222

C₂×#19151340

C₂×#564×C₈₉

#8509

Subgroups — #36446884

Conjugacy classes of subgroups

Complements

Maximal subgroups