Group #10588331 — subgroups

Subgroups — #10588331

Order 576.

207 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 207 conjugacy classes of subgroups — too many to draw. Only its 85 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	C₂×C₄×Dic₉	C₂	1	1	yes	maximal, characteristic
2	C₉×#95	C₂	1	1	yes	maximal, characteristic
3	C₉⋊#95	C₂	1	1	yes	maximal, characteristic
4	C₉⋊#95	C₂	1	2	yes	maximal
5	C₉⋊#95	C₂	1	2	yes	maximal
6	#4651	—	3	1	no	maximal
7	C₂²×C₄×C₉	C₂²	1	2	yes	—
8	C₂²×C₄×C₉	C₂²	1	1	yes	characteristic
9	C₂²×Dic₉	C₂²	1	2	yes	—
10	C₂²×Dic₉	C₂²	1	1	yes	characteristic
11	C₂²×Dic₉	C₂²	1	1	yes	characteristic
12	C₄×Dic₉	C₄	1	4	yes	complemented
13	C₂×C₄×Dic₃	—	3	1	no	—
14	C₃×#95	D₃	1	1	yes	characteristic
15	C₃⋊#95	—	3	2	no	—
16	C₃⋊#95	—	3	2	no	—
17	C₃⋊#95	—	3	1	no	—
18	C₂³×C₉	C₂³	1	1	yes	characteristic
19	C₂×C₄×C₉	—	2	2	no	—
20	C₂×C₄×C₉	—	2	2	no	—
21	C₂×C₄×C₉	—	2	2	no	—
22	C₂×C₄×C₉	—	2	2	no	—
23	C₂×C₄×C₉	C₂×C₄	1	2	yes	—
24	C₂×Dic₉	—	2	2	no	—
25	C₂×Dic₉	—	2	1	no	—
26	C₂×Dic₉	—	2	1	no	—
27	C₂×Dic₉	—	2	2	no	—
28	C₂×Dic₉	—	2	2	no	—
29	C₂×Dic₉	—	2	2	no	—
30	C₂×Dic₉	C₂×C₄	1	2	yes	—
31	C₂×Dic₉	C₂×C₄	1	2	yes	—
32	#383	—	9	1	no	Sylow
33	C₂²×C₃×C₄	C₂×D₃	1	2	yes	—
34	C₂²×C₃×C₄	C₂×D₃	1	1	yes	characteristic
35	C₂²×Dic₃	—	3	1	no	—
36	C₂²×Dic₃	—	3	1	no	—
37	C₂²×Dic₃	—	3	2	no	—
38	C₄×Dic₃	—	3	4	no	—
39	C₂²×C₉	C₂²×C₄	1	1	yes	characteristic
40	C₂²×C₉	#41	1	2	yes	—
41	C₂²×C₉	#41	1	2	yes	—
42	C₂²×C₉	#41	1	1	yes	characteristic
43	C₂²×C₉	#41	1	1	yes	characteristic
44	C₄×C₉	—	2	2	no	—
45	C₄×C₉	—	4	2	no	—
46	Dic₉	—	2	2	no	—
47	Dic₉	—	2	2	no	—
48	Dic₉	—	4	2	no	—
49	C₂×C₄²	—	9	1	no	—
50	#95	—	9	2	no	—
51	#95	—	9	2	no	—
52	#95	—	9	1	no	—
53	#95	D₉	1	1	yes	characteristic
54	C₂³×C₃	C₂²×D₃	1	1	yes	characteristic
55	C₂×C₃×C₄	—	2	2	no	—
56	C₂×C₃×C₄	—	2	2	no	—
57	C₂×C₃×C₄	—	2	2	no	—
58	C₂×C₃×C₄	—	2	2	no	—
59	C₂×C₃×C₄	C₄×D₃	1	2	yes	—
60	C₂×Dic₃	—	3	2	no	—
61	C₂×Dic₃	—	3	2	no	—
62	C₂×Dic₃	—	6	2	no	—
63	C₂×Dic₃	—	6	1	no	—
64	C₂×Dic₃	—	6	1	no	—
65	C₂×Dic₃	—	6	2	no	—
66	C₂×Dic₃	—	6	2	no	—
67	C₂×Dic₃	—	6	2	no	—
68	C₂×C₉	#117	1	1	yes	characteristic
69	C₂×C₉	#117	1	1	yes	characteristic
70	C₂×C₉	#117	1	1	yes	characteristic
71	C₂×C₉	#126	1	2	yes	—
72	C₂×C₉	#126	1	2	yes	—
73	C₂²×C₄	—	9	1	no	—
74	C₂²×C₄	—	9	1	no	—
75	C₂²×C₄	—	9	2	no	—
76	C₂²×C₄	C₂×D₉	1	2	yes	—
77	C₂²×C₄	C₂×D₉	1	1	yes	characteristic
78	C₄²	—	9	4	no	—
79	C₂²×C₃	C₂×C₄×D₃	1	1	yes	characteristic
80	C₂²×C₃	#235	1	2	yes	—
81	C₂²×C₃	#237	1	2	yes	—
82	C₂²×C₃	#237	1	1	yes	characteristic
83	C₂²×C₃	#239	1	1	yes	characteristic
84	C₃×C₄	—	2	2	no	—
85	C₃×C₄	—	4	2	no	—
86	Dic₃	—	6	2	no	—
87	Dic₃	—	6	2	no	—
88	Dic₃	—	12	2	no	—
89	C₉	#383	1	1	yes	characteristic, complemented, Sylow
90	C₂³	C₂²×D₉	1	1	yes	characteristic
91	C₂×C₄	—	2	2	no	—
92	C₂×C₄	—	2	2	no	—
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	—	2	2	no	—
95	C₂×C₄	—	9	2	no	—
96	C₂×C₄	—	9	2	no	—
97	C₂×C₄	—	18	2	no	—
98	C₂×C₄	—	18	1	no	—
99	C₂×C₄	—	18	1	no	—
100	C₂×C₄	—	18	2	no	—
101	C₂×C₄	—	18	2	no	—
102	C₂×C₄	—	18	2	no	—
103	C₂×C₄	C₄×D₉	1	2	yes	—
104	C₂×C₃	#872	1	1	yes	characteristic
105	C₂×C₃	#877	1	1	yes	characteristic
106	C₂×C₃	#879	1	2	yes	—
107	C₂×C₃	#892	1	1	yes	characteristic
108	C₂×C₃	#898	1	2	yes	—
109	C₂²	C₂×C₄×D₉	1	1	yes	characteristic
110	C₂²	#3697	1	2	yes	—
111	C₂²	#3699	1	2	yes	—
112	C₂²	#3699	1	1	yes	characteristic
113	C₂²	#3701	1	1	yes	characteristic
114	C₄	—	2	2	no	—
115	C₄	—	4	2	no	—
116	C₄	—	18	2	no	—
117	C₄	—	18	2	no	—
118	C₄	—	36	2	no	—
119	C₃	#4651	1	1	yes	characteristic
120	C₂	#63434	1	1	yes	characteristic
121	C₂	#63439	1	1	yes	characteristic
122	C₂	#63441	1	2	yes	—
123	C₂	#63454	1	1	yes	characteristic
124	C₂	#63460	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄×Dic₉

C₂

yes

maximal, characteristic

C₉×#95

C₂

yes

maximal, characteristic

C₉⋊#95

C₂

yes

maximal, characteristic

C₉⋊#95

C₂

yes

maximal

C₉⋊#95

C₂

yes

maximal

#4651

—

maximal

C₂²×C₄×C₉

C₂²

yes

—

C₂²×C₄×C₉

C₂²

yes

characteristic

C₂²×Dic₉

C₂²

yes

—

C₂²×Dic₉

C₂²

yes

characteristic

C₂²×Dic₉

C₂²

yes

characteristic

C₄×Dic₉

C₄

yes

complemented

C₂×C₄×Dic₃

—

C₃×#95

D₃

yes

—

—

—

C₂³×C₉

C₂³

yes

characteristic

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

C₂×C₄

yes

—

C₂×Dic₉

—

C₂×Dic₉

—

C₂×Dic₉

—

C₂×Dic₉

—

C₂×Dic₉

—

C₂×Dic₉

—

C₂×Dic₉

C₂×C₄

yes

—

C₂×Dic₉

C₂×C₄

yes

—

#383

—

Sylow

C₂²×C₃×C₄

C₂×D₃

yes

—

C₂²×C₃×C₄

C₂×D₃

yes

characteristic

C₂²×Dic₃

—

C₂²×Dic₃

—

C₂²×Dic₃

—

C₄×Dic₃

—

C₂²×C₉

C₂²×C₄

yes

characteristic

C₂²×C₉

#41

yes

—

C₂²×C₉

#41

yes

—

C₂²×C₉

yes

C₂²×C₉

yes

C₄×C₉

—

C₄×C₉

—

Dic₉

—

Dic₉

—

Dic₉

—

C₂×C₄²

—

—

—

—

D₉

yes

characteristic

C₂³×C₃

C₂²×D₃

yes

characteristic

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

C₄×D₃

yes

—

C₂×Dic₃

—

C₂×Dic₃

—

C₂×Dic₃

—

C₂×Dic₃

—

C₂×Dic₃

—

C₂×Dic₃

—

C₂×Dic₃

—

C₂×Dic₃

—

C₂×C₉

yes

C₂×C₉

yes

C₂×C₉

yes

C₂×C₉

yes

—

C₂×C₉

#126

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×D₉

yes

—

C₂²×C₄

C₂×D₉

yes

characteristic

C₄²

—

C₂²×C₃

C₂×C₄×D₃

yes

characteristic

C₂²×C₃

#235

yes

—

C₂²×C₃

#237

yes

—

C₂²×C₃

yes

C₂²×C₃

yes

C₃×C₄

—

C₃×C₄

—

Dic₃

—

Dic₃

—

Dic₃

—

C₉

#383

yes

characteristic, complemented, Sylow

C₂³

C₂²×D₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

C₄×D₉

yes

—

104

C₂×C₃

#872

yes

characteristic

105

C₂×C₃

#877

yes

characteristic

106

C₂×C₃

#879

yes

—

107

C₂×C₃

#892

yes

characteristic

108

C₂×C₃

#898

yes

—

109

C₂²

C₂×C₄×D₉

yes

characteristic

110

C₂²

#3697

yes

—

111

C₂²

#3699

yes

—

112

C₂²

#3699

yes

characteristic

113

C₂²

#3701

yes

characteristic

114

C₄

—

115

C₄

—

116

C₄

—

117

C₄

—

118

C₄

—

119

C₃

#4651

yes

characteristic

120

C₂

#63434

yes

characteristic

121

C₂

#63439

yes

characteristic

122

C₂

#63441

yes

—

123

C₂

#63454

yes

characteristic

124

C₂

#63460

yes

—

	subgroup	G/H
center	C₂³	C₂²×D₉
commutator	C₂²×C₉	C₂²×C₄
Frattini, socle, prime radical	C₂³×C₃	C₂²×D₃
Fitting	C₉×#95	C₂
cosocle	C₂³×C₉	C₂³
hypercenter	#95	D₉
hypocenter	C₉	#383
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂³ ◁ #95

subgroup

G/H

center

C₂³

C₂²×D₉

commutator

C₂²×C₉

C₂²×C₄

Frattini, socle, prime radical

C₂³×C₃

C₂²×D₃

Fitting

C₉×#95

C₂

cosocle

C₂³×C₉

C₂³

D₉

C₉

G ▷ C₂²×C₉ ▷ C₉

C₁ ◁ C₂³ ◁ #95

N	H ≅ G/N	type
12. C₄×Dic₉	C₄	semidirect
89. C₉	#383	semidirect

H ≅ G/N

type

12. C₄×Dic₉

C₄

semidirect

89. C₉

#383

semidirect

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

subgroup	index
C₂×C₄×Dic₉	2
C₉×#95	2
C₉⋊#95	2
#4651	3

subgroup

index

C₂×C₄×Dic₉

C₉×#95

C₉⋊#95

#4651

Subgroups — #10588331

Conjugacy classes of subgroups

Complements

Maximal subgroups