Group #11782939 — subgroups

Subgroups — #11782939

Order 1152.

594 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 165 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×#494	C₂	1	1	yes	maximal, characteristic, complemented
2	#10592787	C₂	1	2	yes	maximal
3	#10592777	C₂	1	2	yes	maximal, complemented
4	#10592392	C₂	1	1	yes	maximal, characteristic
5	#10589321	C₂	1	1	yes	maximal, characteristic, complemented
6	#71301	—	3	4	no	maximal
7	C₂×C₃²×Q₁₆	—	2	2	no	—
8	C₃²×C₄⋊Q₈	C₂²	1	2	yes	—
9	C₂×#3744	—	2	2	no	—
10	#64083	C₂²	1	1	yes	characteristic
11	#64078	C₂²	1	1	yes	characteristic
12	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic
13	#63636	—	2	4	no	—
14	#63634	—	2	4	no	—
15	C₄×C₃⋊(C₃⋊C₈)	C₂²	1	2	yes	—
16	C₃×#494	D₃	1	4	yes	complemented
17	#5088	—	3	8	no	—
18	#5078	—	3	8	no	—
19	#4693	—	3	4	no	—
20	#4455	—	3	4	no	—
21	C₂×C₃²×Q₈	—	2	2	no	—
22	C₂×C₄⋊(C₃⋊D₃)	—	2	1	no	—
23	C₂×C₄⋊(C₃⋊D₃)	—	2	2	no	—
24	C₂×#634	—	2	1	no	—
25	C₃²×Q₁₆	—	4	4	no	—
26	C₂×C₃²×C₈	D₄	1	2	yes	—
27	C₃²×C₄⋊C₄	—	2	2	no	—
28	C₃²×C₄⋊C₄	—	2	2	no	—
29	C₃²×C₄²	C₂³	1	1	yes	characteristic
30	C₄⋊(C₃⋊Dic₃)	—	2	2	no	—
31	C₂×C₃⋊(C₃⋊C₈)	D₄	1	4	yes	—
32	#3744	—	4	4	no	—
33	#1722	—	9	1	no	Sylow
34	C₂×C₃×Q₁₆	—	2	8	no	—
35	C₃×C₄⋊Q₈	C₂×D₃	1	8	yes	—
36	C₂×#204	—	6	8	no	—
37	#874	—	3	4	no	—
38	#869	—	3	4	no	—
39	C₃×C₄×C₈	C₂×D₃	1	4	yes	—
40	#809	—	6	16	no	—
41	#807	—	6	16	no	—
42	C₄×C₃⋊C₈	—	3	8	no	—
43	C₂²×C₃⋊D₃	—	4	1	no	—
44	C₃²×Q₈	—	4	4	no	—
45	C₂×C₃²×C₄	—	4	2	no	—
46	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
47	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
48	C₂×C₃⋊Dic₃	—	4	1	no	—
49	C₄⋊(C₃⋊D₃)	—	4	2	no	—
50	C₄⋊(C₃⋊D₃)	—	4	4	no	—
51	#634	—	4	2	no	—
52	C₃²×C₈	D₈	1	4	yes	—
53	C₃⋊(C₃⋊C₈)	—	2	4	no	—
54	#500	—	9	2	no	—
55	#494	C₃⋊D₃	1	1	yes	characteristic, complemented
56	#492	—	9	1	no	—
57	#486	—	9	2	no	—
58	#322	—	9	1	no	—
59	C₂×C₃×Q₈	—	2	8	no	—
60	C₂×D₁₂	—	6	8	no	—
61	C₂×D₁₂	—	6	4	no	—
62	C₂×Dic₆	—	6	4	no	—
63	C₃×Q₁₆	—	4	16	no	—
64	C₂×C₃×C₈	#67	1	8	yes	—
65	C₃×C₄⋊C₄	—	2	8	no	—
66	C₃×C₄⋊C₄	—	2	8	no	—
67	C₃×C₄²	C₂²×D₃	1	4	yes	—
68	C₄⋊Dic₃	—	6	8	no	—
69	C₂×C₃⋊C₈	—	3	16	no	—
70	#204	—	12	16	no	—
71	C₂²×C₃²	#127	1	1	yes	characteristic
72	C₂×C₃⋊D₃	—	8	1	no	—
73	C₂×C₃⋊D₃	—	8	2	no	—
74	C₃²×C₄	—	8	2	no	—
75	C₃²×C₄	C₂×D₈	1	2	yes	—
76	C₃²×C₄	#137	1	4	yes	—
77	C₃⋊Dic₃	—	8	1	no	—
78	C₂×Q₁₆	—	2	2	no	—
79	C₂×SD₁₆	—	18	2	no	—
80	C₄⋊Q₈	—	9	1	no	—
81	C₄⋊Q₈	C₂×C₃⋊D₃	1	2	yes	—
82	#127	—	9	1	no	—
83	#107	—	18	4	no	—
84	#102	—	18	4	no	—
85	C₄×C₈	—	9	2	no	—
86	C₄×C₈	C₂×C₃⋊D₃	1	1	yes	characteristic
87	C₂²×D₃	—	12	4	no	—
88	C₃×Q₈	—	4	16	no	—
89	C₂×C₃×C₄	—	4	8	no	—
90	C₂×C₃×C₄	D₃×D₄	1	8	yes	—
91	C₂×C₃×C₄	C₂×#67	1	4	yes	—
92	C₂×Dic₃	—	12	4	no	—
93	D₁₂	—	12	16	no	—
94	D₁₂	—	12	8	no	—
95	Dic₆	—	12	8	no	—
96	C₃×C₈	#213	1	16	yes	—
97	C₃⋊C₈	—	6	16	no	—
98	C₂×C₃²	#493	1	1	yes	characteristic
99	C₂×C₃²	#497	1	2	yes	—
100	C₃⋊D₃	—	16	1	no	—
101	C₂×Q₈	—	2	2	no	—
102	C₂×Q₈	—	18	1	no	—
103	C₂×D₄	—	18	2	no	—
104	C₂×D₄	—	18	1	no	—
105	Q₁₆	—	4	4	no	—
106	SD₁₆	—	36	4	no	—
107	C₂×C₈	—	9	4	no	—
108	C₂×C₈	#638	1	2	yes	—
109	C₄⋊C₄	—	2	2	no	—
110	C₄⋊C₄	—	2	2	no	—
111	C₄⋊C₄	—	18	2	no	—
112	C₄²	C₂²×C₃⋊D₃	1	1	yes	characteristic
113	C₂²×C₃	#940	1	4	yes	—
114	C₂×D₃	—	24	8	no	—
115	C₂×D₃	—	24	4	no	—
116	C₃×C₄	—	8	8	no	—
117	C₃×C₄	#918	1	16	yes	—
118	C₃×C₄	C₂×#213	1	8	yes	—
119	Dic₃	—	24	4	no	—
120	C₃²	#1722	1	1	yes	characteristic, complemented, Sylow
121	C₂³	—	36	1	no	—
122	Q₈	—	4	4	no	—
123	Q₈	—	36	2	no	—
124	D₄	—	36	4	no	—
125	D₄	—	36	2	no	—
126	C₂×C₄	—	4	2	no	—
127	C₂×C₄	—	36	1	no	—
128	C₂×C₄	D₄×C₃⋊D₃	1	2	yes	—
129	C₂×C₄	C₂×#638	1	1	yes	characteristic
130	C₈	—	18	4	no	—
131	C₈	#3753	1	4	yes	—
132	C₂×C₃	#5073	1	4	yes	—
133	C₂×C₃	#5190	1	8	yes	—
134	D₃	—	48	4	no	—
135	C₂²	—	72	1	no	—
136	C₂²	—	72	2	no	—
137	C₂²	#64149	1	1	yes	characteristic
138	C₄	—	8	2	no	—
139	C₄	—	72	1	no	—
140	C₄	#64127	1	4	yes	—
141	C₄	C₂×#3753	1	2	yes	—
142	C₃	#71301	1	4	yes	complemented
143	C₂	—	144	1	no	—
144	C₂	#10592772	1	1	yes	characteristic
145	C₂	#10592889	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃²×#494

C₂

yes

maximal, characteristic, complemented

#10592787

C₂

yes

maximal

#10592777

C₂

yes

maximal, complemented

#10592392

C₂

yes

maximal, characteristic

#10589321

C₂

yes

maximal, characteristic, complemented

#71301

—

maximal

C₂×C₃²×Q₁₆

—

C₃²×C₄⋊Q₈

C₂²

yes

—

C₂×#3744

—

#64083

C₂²

yes

characteristic

#64078

C₂²

yes

characteristic

C₃²×C₄×C₈

C₂²

yes

characteristic

#63636

—

#63634

—

C₄×C₃⋊(C₃⋊C₈)

C₂²

yes

—

C₃×#494

D₃

yes

—

—

—

—

C₂×C₃²×Q₈

—

C₂×C₄⋊(C₃⋊D₃)

—

C₂×C₄⋊(C₃⋊D₃)

—

C₂×#634

—

C₃²×Q₁₆

—

C₂×C₃²×C₈

D₄

yes

—

C₃²×C₄⋊C₄

—

C₃²×C₄⋊C₄

—

C₃²×C₄²

C₂³

yes

characteristic

C₄⋊(C₃⋊Dic₃)

—

C₂×C₃⋊(C₃⋊C₈)

D₄

yes

—

#3744

—

#1722

—

Sylow

C₂×C₃×Q₁₆

—

C₃×C₄⋊Q₈

C₂×D₃

yes

—

C₂×#204

—

#874

—

#869

—

C₃×C₄×C₈

C₂×D₃

yes

—

#809

—

#807

—

C₄×C₃⋊C₈

—

C₂²×C₃⋊D₃

—

C₃²×Q₈

—

C₂×C₃²×C₄

—

C₂×C₃²×C₄

C₂×D₄

yes

—

C₂×C₃²×C₄

C₂×D₄

yes

characteristic

C₂×C₃⋊Dic₃

—

C₄⋊(C₃⋊D₃)

—

C₄⋊(C₃⋊D₃)

—

#634

—

C₃²×C₈

D₈

yes

—

C₃⋊(C₃⋊C₈)

—

#500

—

#494

C₃⋊D₃

yes

characteristic, complemented

#492

—

#486

—

#322

—

C₂×C₃×Q₈

—

C₂×D₁₂

—

C₂×D₁₂

—

C₂×Dic₆

—

C₃×Q₁₆

—

C₂×C₃×C₈

#67

yes

—

C₃×C₄⋊C₄

—

C₃×C₄⋊C₄

—

C₃×C₄²

C₂²×D₃

yes

—

C₄⋊Dic₃

—

C₂×C₃⋊C₈

—

#204

—

C₂²×C₃²

#127

yes

characteristic

C₂×C₃⋊D₃

—

C₂×C₃⋊D₃

—

C₃²×C₄

—

C₃²×C₄

C₂×D₈

yes

—

C₃²×C₄

#137

yes

—

C₃⋊Dic₃

—

C₂×Q₁₆

—

C₂×SD₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×C₃⋊D₃

yes

—

#127

—

#107

—

#102

—

C₄×C₈

—

C₄×C₈

C₂×C₃⋊D₃

yes

characteristic

C₂²×D₃

—

C₃×Q₈

—

C₂×C₃×C₄

—

C₂×C₃×C₄

D₃×D₄

yes

—

C₂×C₃×C₄

C₂×#67

yes

—

C₂×Dic₃

—

D₁₂

—

D₁₂

—

Dic₆

—

C₃×C₈

#213

yes

—

C₃⋊C₈

—

C₂×C₃²

#493

yes

characteristic

C₂×C₃²

#497

yes

—

100

C₃⋊D₃

—

101

C₂×Q₈

—

102

C₂×Q₈

—

103

C₂×D₄

—

104

C₂×D₄

—

105

Q₁₆

—

106

SD₁₆

—

107

C₂×C₈

—

108

C₂×C₈

#638

yes

—

109

C₄⋊C₄

—

110

C₄⋊C₄

—

111

C₄⋊C₄

—

112

C₄²

C₂²×C₃⋊D₃

yes

characteristic

113

C₂²×C₃

#940

yes

—

114

C₂×D₃

—

115

C₂×D₃

—

116

C₃×C₄

—

117

C₃×C₄

#918

yes

—

118

C₃×C₄

C₂×#213

yes

—

119

Dic₃

—

120

C₃²

#1722

yes

characteristic, complemented, Sylow

121

C₂³

—

122

Q₈

—

123

Q₈

—

124

D₄

—

125

D₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

D₄×C₃⋊D₃

yes

—

129

C₂×C₄

C₂×#638

yes

characteristic

130

C₈

—

131

C₈

#3753

yes

—

132

C₂×C₃

#5073

yes

—

133

C₂×C₃

#5190

yes

—

134

D₃

—

135

C₂²

—

136

C₂²

—

137

C₂²

#64149

yes

characteristic

138

C₄

—

139

C₄

—

140

C₄

#64127

yes

—

141

C₄

C₂×#3753

yes

—

142

C₃

#71301

yes

complemented

143

C₂

—

144

—

144

C₂

#10592772

yes

characteristic

145

C₂

#10592889

yes

—

	subgroup	G/H
center	C₂²	#64149
commutator, cosocle	C₃²×C₄²	C₂³
Frattini	C₄²	C₂²×C₃⋊D₃
Fitting	C₃²×#494	C₂
socle	C₂²×C₃²	#127
prime radical	#64083	C₂²
hypercenter	#494	C₃⋊D₃
hypocenter	C₃²	#1722
LCS	G ▷ C₃²×C₄² ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #494

subgroup

G/H

center

C₂²

#64149

commutator, cosocle

C₃²×C₄²

C₂³

Frattini

C₄²

C₂²×C₃⋊D₃

Fitting

C₃²×#494

C₂

C₂²×C₃²

C₂²

C₃⋊D₃

C₃²

G ▷ C₃²×C₄² ▷ C₂²×C₃² ▷ C₃²

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #494

N	H ≅ G/N	type
1. C₃²×#494	C₂	semidirect
3. #10592777	C₂	semidirect
5. #10589321	C₂	semidirect
16. C₃×#494	D₃	semidirect
55. #494	C₃⋊D₃	semidirect
120. C₃²	#1722	semidirect
142. C₃	#71301	semidirect

H ≅ G/N

type

1. C₃²×#494

C₂

semidirect

3. #10592777

C₂

semidirect

5. #10589321

C₂

semidirect

16. C₃×#494

D₃

semidirect

55. #494

C₃⋊D₃

semidirect

120. C₃²

#1722

semidirect

142. C₃

#71301

semidirect

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

subgroup	index
C₃²×#494	2
#10592787	2
#10592777	2
#10592392	2
#10589321	2
#71301	3

subgroup

index

C₃²×#494

Subgroups — #11782939

Conjugacy classes of subgroups

Complements

Maximal subgroups