Group #10595783 — subgroups

Subgroups — C₃×C₃⋊#564 #10595783

Order 576.

372 conjugacy classes of subgroups; only the 182 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 182 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	C₃²×#125	C₂	1	1	yes	maximal, characteristic
2	C₃×#890	C₂	1	4	yes	maximal
3	C₃×#889	C₂	1	4	yes	maximal
4	C₃×#889	C₂	1	4	yes	maximal
5	C₃×#870	C₂	1	2	yes	maximal
6	C₃×#564	—	3	1	no	maximal
7	C₃⋊#564	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₃²×C₄⋊C₄	C₂²	1	2	yes	—
9	C₃²×C₄⋊C₄	C₂²	1	4	yes	—
10	C₃²×C₄²	C₂²	1	1	yes	characteristic
11	C₃×C₄⋊Dic₃	C₂²	1	2	yes	—
12	C₃×C₄⋊Dic₃	C₂²	1	4	yes	—
13	C₃×C₄⋊Dic₃	C₂²	1	2	yes	—
14	C₃×Dic₃⋊C₄	C₂²	1	4	yes	—
15	C₃×Dic₃⋊C₄	C₂²	1	4	yes	—
16	C₃×Dic₃⋊C₄	C₂²	1	4	yes	—
17	C₃×Dic₃⋊C₄	C₂²	1	4	yes	—
18	C₃×C₄×Dic₃	C₂²	1	4	yes	—
19	C₃×#125	—	2	1	no	—
20	C₃×#125	—	3	4	no	—
21	C₃×#125	—	3	4	no	—
22	C₃×#125	—	3	4	no	—
23	C₃×#125	—	3	2	no	—
24	C₃×#125	D₃	1	1	yes	characteristic
25	C₃×#125	C₂×C₃	1	1	yes	characteristic
26	#890	C₂×C₃	1	4	yes	—
27	#889	C₂×C₃	1	4	yes	—
28	#889	C₂×C₃	1	4	yes	—
29	#870	C₂×C₃	1	2	yes	—
30	C₂×C₃²×C₄	C₂³	1	4	yes	—
31	C₂×C₃²×C₄	C₂³	1	1	yes	characteristic
32	C₂×C₃²×C₄	C₂³	1	2	yes	—
33	C₂×C₃×Dic₃	C₂³	1	4	yes	—
34	C₂×C₃×Dic₃	C₂³	1	4	yes	—
35	#564	—	3	1	no	Sylow
36	C₃×C₄⋊C₄	—	2	2	no	—
37	C₃×C₄⋊C₄	—	2	4	no	—
38	C₃×C₄⋊C₄	—	3	4	no	—
39	C₃×C₄⋊C₄	—	3	4	no	—
40	C₃×C₄⋊C₄	—	3	4	no	—
41	C₃×C₄⋊C₄	—	3	4	no	—
42	C₃×C₄⋊C₄	—	3	4	no	—
43	C₃×C₄⋊C₄	—	3	2	no	—
44	C₃×C₄⋊C₄	—	3	2	no	—
45	C₃×C₄⋊C₄	C₂×D₃	1	2	yes	—
46	C₃×C₄⋊C₄	C₂×D₃	1	4	yes	—
47	C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
48	C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
49	C₃×C₄²	—	2	1	no	—
50	C₃×C₄²	—	3	4	no	—
51	C₃×C₄²	C₂×D₃	1	1	yes	characteristic
52	C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
53	C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
54	C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
55	C₄⋊Dic₃	C₂²×C₃	1	4	yes	—
56	Dic₃⋊C₄	C₂²×C₃	1	4	yes	—
57	Dic₃⋊C₄	C₂²×C₃	1	4	yes	—
58	Dic₃⋊C₄	C₂²×C₃	1	4	yes	—
59	Dic₃⋊C₄	C₂²×C₃	1	4	yes	—
60	C₄×Dic₃	C₂²×C₃	1	4	yes	—
61	C₂²×C₃²	C₂⁴	1	1	yes	characteristic
62	C₃²×C₄	—	2	1	no	—
63	C₃²×C₄	—	2	4	no	—
64	C₃²×C₄	—	2	2	no	—
65	C₃×Dic₃	—	2	4	no	—
66	C₃×Dic₃	—	2	4	no	—
67	#125	—	3	4	no	—
68	#125	—	3	4	no	—
69	#125	—	3	4	no	—
70	#125	—	3	2	no	—
71	#125	C₃×D₃	1	1	yes	characteristic
72	C₂×C₃×C₄	—	2	1	no	—
73	C₂×C₃×C₄	—	2	2	no	—
74	C₂×C₃×C₄	—	2	4	no	—
75	C₂×C₃×C₄	—	3	4	no	—
76	C₂×C₃×C₄	—	3	4	no	—
77	C₂×C₃×C₄	C₂²×D₃	1	4	yes	—
78	C₂×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
79	C₂×C₃×C₄	C₂²×D₃	1	2	yes	—
80	C₂×C₃×C₄	C₂³×C₃	1	4	yes	—
81	C₂×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
82	C₂×C₃×C₄	C₂³×C₃	1	2	yes	—
83	C₂×Dic₃	C₂³×C₃	1	4	yes	—
84	C₂×Dic₃	C₂³×C₃	1	4	yes	—
85	C₂×C₃²	2₋¹⁺⁴	1	1	yes	characteristic
86	C₂×C₃²	2₋¹⁺⁴	1	2	yes	—
87	C₄⋊C₄	—	3	4	no	—
88	C₄⋊C₄	—	3	4	no	—
89	C₄⋊C₄	—	3	4	no	—
90	C₄⋊C₄	—	3	4	no	—
91	C₄⋊C₄	—	3	4	no	—
92	C₄⋊C₄	—	3	2	no	—
93	C₄⋊C₄	—	3	2	no	—
94	C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
95	C₄⋊C₄	C₂×C₃×D₃	1	4	yes	—
96	C₄²	—	3	4	no	—
97	C₄²	C₂×C₃×D₃	1	1	yes	characteristic
98	C₂²×C₃	—	2	1	no	—
99	C₂²×C₃	C₂³×D₃	1	1	yes	characteristic
100	C₂²×C₃	C₂⁴×C₃	1	1	yes	characteristic
101	C₃×C₄	—	2	2	no	—
102	C₃×C₄	—	2	1	no	—
103	C₃×C₄	—	2	4	no	—
104	C₃×C₄	—	2	2	no	—
105	C₃×C₄	—	2	1	no	—
106	C₃×C₄	—	2	4	no	—
107	C₃×C₄	—	2	2	no	—
108	C₃×C₄	—	4	2	no	—
109	C₃×C₄	—	4	4	no	—
110	C₃×C₄	—	6	4	no	—
111	C₃×C₄	—	6	4	no	—
112	Dic₃	—	2	4	no	—
113	Dic₃	—	2	4	no	—
114	C₃²	#564	1	1	yes	characteristic, complemented, Sylow
115	C₂×C₄	—	3	4	no	—
116	C₂×C₄	—	3	4	no	—
117	C₂×C₄	C₂²×C₃×D₃	1	4	yes	—
118	C₂×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
119	C₂×C₄	C₂²×C₃×D₃	1	2	yes	—
120	C₂×C₃	—	2	1	no	—
121	C₂×C₃	—	2	2	no	—
122	C₂×C₃	#1007	1	1	yes	characteristic
123	C₂×C₃	#1010	1	2	yes	—
124	C₂×C₃	C₃×2₋¹⁺⁴	1	1	yes	characteristic
125	C₂×C₃	C₃×2₋¹⁺⁴	1	2	yes	—
126	C₂²	C₂³×C₃×D₃	1	1	yes	characteristic
127	C₄	—	2	1	no	—
128	C₄	—	2	4	no	—
129	C₄	—	2	2	no	—
130	C₄	—	6	4	no	—
131	C₄	—	6	4	no	—
132	C₃	—	2	1	no	—
133	C₃	C₃⋊#564	1	1	yes	characteristic, direct product factor
134	C₃	C₃×#564	1	1	yes	characteristic, complemented
135	C₂	C₃×#1007	1	1	yes	characteristic
136	C₂	C₃×#1010	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃²×#125

C₂

yes

maximal, characteristic

C₃×#890

C₂

yes

maximal

C₃×#889

C₂

yes

maximal

C₃×#889

C₂

yes

maximal

C₃×#870

C₂

yes

—

C₃

yes

maximal, characteristic, direct product factor

C₃²×C₄⋊C₄

C₂²

yes

—

C₃²×C₄⋊C₄

C₂²

yes

—

C₃²×C₄²

C₂²

yes

characteristic

C₃×C₄⋊Dic₃

C₂²

yes

—

C₃×C₄⋊Dic₃

C₂²

yes

—

C₃×C₄⋊Dic₃

C₂²

yes

—

C₃×Dic₃⋊C₄

C₂²

yes

—

C₃×Dic₃⋊C₄

C₂²

yes

—

C₃×Dic₃⋊C₄

C₂²

yes

—

C₃×Dic₃⋊C₄

C₂²

yes

—

C₃×C₄×Dic₃

C₂²

yes

—

—

—

—

—

—

D₃

yes

characteristic

C₃×#125

C₂×C₃

yes

characteristic

#890

C₂×C₃

yes

—

#889

C₂×C₃

yes

—

#889

C₂×C₃

yes

—

#870

C₂×C₃

yes

—

C₂×C₃²×C₄

C₂³

yes

—

C₂×C₃²×C₄

C₂³

yes

characteristic

C₂×C₃²×C₄

C₂³

yes

—

C₂×C₃×Dic₃

C₂³

yes

—

C₂×C₃×Dic₃

C₂³

yes

—

#564

—

Sylow

C₃×C₄⋊C₄

—

C₃×C₄⋊C₄

—

C₃×C₄⋊C₄

—

C₃×C₄⋊C₄

—

C₃×C₄⋊C₄

—

C₃×C₄⋊C₄

—

C₃×C₄⋊C₄

—

C₃×C₄⋊C₄

—

C₃×C₄⋊C₄

—

C₃×C₄⋊C₄

C₂×D₃

yes

—

C₃×C₄⋊C₄

C₂×D₃

yes

—

C₃×C₄⋊C₄

C₂²×C₃

yes

—

C₃×C₄⋊C₄

C₂²×C₃

yes

—

C₃×C₄²

—

C₃×C₄²

—

C₃×C₄²

C₂×D₃

yes

characteristic

C₃×C₄²

C₂²×C₃

yes

characteristic

C₄⋊Dic₃

C₂²×C₃

yes

—

C₄⋊Dic₃

C₂²×C₃

yes

—

C₄⋊Dic₃

C₂²×C₃

yes

—

Dic₃⋊C₄

C₂²×C₃

yes

—

Dic₃⋊C₄

C₂²×C₃

yes

—

Dic₃⋊C₄

C₂²×C₃

yes

—

Dic₃⋊C₄

C₂²×C₃

yes

—

C₄×Dic₃

C₂²×C₃

yes

—

C₂²×C₃²

C₂⁴

yes

characteristic

C₃²×C₄

—

C₃²×C₄

—

C₃²×C₄

—

C₃×Dic₃

—

C₃×Dic₃

—

—

—

—

—

C₃×D₃

yes

characteristic

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

C₂²×D₃

yes

—

C₂×C₃×C₄

C₂²×D₃

yes

characteristic

C₂×C₃×C₄

C₂²×D₃

yes

—

C₂×C₃×C₄

C₂³×C₃

yes

—

C₂×C₃×C₄

C₂³×C₃

yes

characteristic

C₂×C₃×C₄

C₂³×C₃

yes

—

C₂×Dic₃

C₂³×C₃

yes

—

C₂×Dic₃

C₂³×C₃

yes

—

C₂×C₃²

2₋¹⁺⁴

yes

characteristic

C₂×C₃²

2₋¹⁺⁴

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂×C₃×D₃

yes

—

C₄⋊C₄

C₂×C₃×D₃

yes

—

C₄²

—

C₄²

C₂×C₃×D₃

yes

characteristic

C₂²×C₃

—

C₂²×C₃

C₂³×D₃

yes

characteristic

100

C₂²×C₃

C₂⁴×C₃

yes

characteristic

101

C₃×C₄

—

102

C₃×C₄

—

103

C₃×C₄

—

104

C₃×C₄

—

105

C₃×C₄

—

106

C₃×C₄

—

107

C₃×C₄

—

108

C₃×C₄

—

109

C₃×C₄

—

110

C₃×C₄

—

111

C₃×C₄

—

112

Dic₃

—

113

Dic₃

—

114

C₃²

#564

yes

characteristic, complemented, Sylow

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

C₂²×C₃×D₃

yes

—

118

C₂×C₄

C₂²×C₃×D₃

yes

characteristic

119

C₂×C₄

C₂²×C₃×D₃

yes

—

120

C₂×C₃

—

121

C₂×C₃

—

122

C₂×C₃

#1007

yes

characteristic

123

C₂×C₃

#1010

yes

—

124

C₂×C₃

C₃×2₋¹⁺⁴

yes

characteristic

125

C₂×C₃

C₃×2₋¹⁺⁴

yes

—

126

C₂²

C₂³×C₃×D₃

yes

characteristic

127

C₄

—

128

C₄

—

129

C₄

—

130

C₄

—

131

C₄

—

132

C₃

—

133

C₃

C₃⋊#564

yes

characteristic, direct product factor

134

C₃

C₃×#564

yes

characteristic, complemented

135

C₂

C₃×#1007

yes

characteristic

136

C₂

C₃×#1010

yes

—

	subgroup	G/H
center	C₂²×C₃	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁴×C₃
Frattini	C₂²	C₂³×C₃×D₃
Fitting	C₃²×#125	C₂
socle, prime radical	C₂²×C₃²	C₂⁴
hypercenter	C₃×#125	D₃
hypocenter	C₃	C₃×#564
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#125

subgroup

G/H

center

C₂²×C₃

C₂³×D₃

commutator, cosocle

C₂²×C₃

C₂⁴×C₃

Frattini

C₂²

C₂³×C₃×D₃

Fitting

C₃²×#125

C₂

socle, prime radical

C₂²×C₃²

C₂⁴

D₃

C₃

G ▷ C₂²×C₃ ▷ C₃

C₁ ◁ C₂²×C₃ ◁ C₃×#125

N	H ≅ G/N	type
7. C₃⋊#564	C₃	direct (N × H)
114. C₃²	#564	semidirect
133. C₃	C₃⋊#564	direct (N × H)
134. C₃	C₃×#564	semidirect

H ≅ G/N

type

7. C₃⋊#564

C₃

direct (N × H)

114. C₃²

#564

semidirect

133. C₃

C₃⋊#564

direct (N × H)

134. C₃

C₃×#564

semidirect

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

subgroup	index
C₃²×#125	2
C₃×#890	2
C₃×#889	2
C₃×#870	2
C₃×#564	3
C₃⋊#564	3

subgroup

index

C₃²×#125

Subgroups — C₃×C₃⋊#564 #10595783

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C3×C3⋊#564 #10595783

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₃⋊#564 #10595783