Group #11782658 — subgroups

Subgroups — #11782658

Order 1152.

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

normal subgroups only

This group has 660 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×#493	C₂	1	1	yes	maximal, characteristic
2	#10592775	C₂	1	2	yes	maximal, complemented
3	#10592769	C₂	1	2	yes	maximal, complemented
4	#10592379	C₂	1	1	yes	maximal, characteristic, complemented
5	#10589321	C₂	1	1	yes	maximal, characteristic, complemented
6	#71277	—	3	4	no	maximal
7	C₂×C₃²×D₈	—	2	2	no	—
8	C₃²×#127	C₂²	1	1	yes	characteristic
9	C₃²×#127	C₂²	1	1	yes	characteristic
10	C₂×#3754	—	2	4	no	—
11	#64078	C₂²	1	2	yes	—
12	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic
13	#63659	—	2	4	no	—
14	#63644	—	2	2	no	—
15	C₄×C₃⋊(C₃⋊C₈)	C₂²	1	2	yes	—
16	C₃×#493	D₃	1	4	yes	—
17	#5076	—	3	8	no	—
18	#5070	—	3	8	no	—
19	#4680	—	3	4	no	—
20	#4455	—	3	4	no	—
21	C₂×C₃²×D₄	—	2	2	no	—
22	C₂×C₃²×D₄	—	2	2	no	—
23	C₂×C₃²×D₄	—	2	1	no	—
24	C₂×C₃²×D₄	—	2	1	no	—
25	C₂×#634	—	2	2	no	—
26	C₃²×D₈	—	4	4	no	—
27	C₂×C₃²×C₈	D₄	1	2	yes	—
28	C₃²×C₄²	C₂³	1	1	yes	characteristic
29	#3754	—	4	8	no	—
30	C₄⋊(C₃⋊Dic₃)	—	2	2	no	—
31	C₄⋊(C₃⋊Dic₃)	—	2	2	no	—
32	C₂×C₃⋊(C₃⋊C₈)	D₄	1	4	yes	—
33	#1715	—	9	1	no	Sylow
34	C₂×C₃×D₈	—	2	8	no	—
35	C₃×#127	C₂×D₃	1	4	yes	—
36	C₃×#127	C₂×D₃	1	4	yes	—
37	C₂×#214	—	6	16	no	—
38	#869	—	3	8	no	—
39	C₃×C₄×C₈	C₂×D₃	1	4	yes	—
40	#832	—	6	16	no	—
41	#817	—	6	8	no	—
42	C₄×C₃⋊C₈	—	3	8	no	—
43	C₂³×C₃²	—	4	1	no	—
44	C₂³×C₃²	—	4	1	no	—
45	C₃²×D₄	—	4	2	no	—
46	C₃²×D₄	—	4	2	no	—
47	C₃²×D₄	—	4	4	no	—
48	C₃²×D₄	—	4	4	no	—
49	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
50	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
51	C₂×C₃⋊Dic₃	—	4	2	no	—
52	#634	—	4	4	no	—
53	C₃²×C₈	SD₁₆	1	4	yes	complemented
54	C₃⋊(C₃⋊C₈)	—	2	4	no	—
55	#498	—	9	1	no	—
56	#493	C₃⋊D₃	1	1	yes	characteristic
57	#492	—	9	2	no	—
58	#486	—	9	2	no	—
59	#322	—	9	1	no	—
60	C₂×C₃×D₄	—	2	8	no	—
61	C₂×C₃×D₄	—	2	8	no	—
62	C₂×C₃×D₄	—	2	4	no	—
63	C₂×C₃×D₄	—	2	4	no	—
64	C₂×Dic₆	—	6	8	no	—
65	C₃×D₈	—	4	16	no	—
66	C₂×C₃×C₈	#67	1	8	yes	—
67	C₃×C₄²	C₂²×D₃	1	4	yes	—
68	#214	—	12	32	no	—
69	C₄⋊Dic₃	—	6	8	no	—
70	C₄⋊Dic₃	—	6	8	no	—
71	C₂×C₃⋊C₈	—	3	16	no	—
72	C₂²×C₃²	—	8	1	no	—
73	C₂²×C₃²	—	8	1	no	—
74	C₂²×C₃²	—	8	2	no	—
75	C₂²×C₃²	—	8	2	no	—
76	C₂²×C₃²	#127	1	1	yes	characteristic
77	C₃²×C₄	C₂×SD₁₆	1	2	yes	—
78	C₃²×C₄	AGL(1,ℤ/8)	1	4	yes	—
79	C₃⋊Dic₃	—	8	2	no	—
80	C₂×SD₁₆	—	18	4	no	—
81	C₂×D₈	—	2	2	no	—
82	C₄⋊Q₈	—	9	2	no	—
83	#127	C₂×C₃⋊D₃	1	1	yes	characteristic
84	#127	C₂×C₃⋊D₃	1	1	yes	characteristic
85	#106	—	18	2	no	—
86	#102	—	18	4	no	—
87	C₄×C₈	—	9	2	no	—
88	C₄×C₈	C₂×C₃⋊D₃	1	1	yes	characteristic
89	C₂³×C₃	—	4	4	no	—
90	C₂³×C₃	—	4	4	no	—
91	C₃×D₄	—	4	16	no	—
92	C₃×D₄	—	4	16	no	—
93	C₃×D₄	—	4	8	no	—
94	C₃×D₄	—	4	8	no	—
95	C₂×C₃×C₄	D₃×D₄	1	8	yes	—
96	C₂×C₃×C₄	C₂×#67	1	4	yes	—
97	C₂×Dic₃	—	12	8	no	—
98	Dic₆	—	12	16	no	—
99	C₃×C₈	#214	1	16	yes	complemented
100	C₃⋊C₈	—	6	16	no	—
101	C₂×C₃²	—	16	1	no	—
102	C₂×C₃²	—	16	1	no	—
103	C₂×C₃²	#492	1	1	yes	characteristic
104	C₂×C₃²	#496	1	2	yes	—
105	C₂×Q₈	—	18	2	no	—
106	C₂×D₄	—	2	2	no	—
107	C₂×D₄	—	2	2	no	—
108	C₂×D₄	—	2	1	no	—
109	C₂×D₄	—	2	1	no	—
110	SD₁₆	—	36	8	no	—
111	D₈	—	4	4	no	—
112	C₂×C₈	—	9	4	no	—
113	C₂×C₈	#638	1	2	yes	—
114	C₄⋊C₄	—	18	2	no	—
115	C₄⋊C₄	—	18	2	no	—
116	C₄²	C₂²×C₃⋊D₃	1	1	yes	characteristic
117	C₂²×C₃	—	8	8	no	—
118	C₂²×C₃	—	8	8	no	—
119	C₂²×C₃	—	8	4	no	—
120	C₂²×C₃	—	8	4	no	—
121	C₂²×C₃	#940	1	4	yes	—
122	C₃×C₄	#911	1	16	yes	—
123	C₃×C₄	C₂×#214	1	8	yes	—
124	Dic₃	—	24	8	no	—
125	C₃²	#1715	1	1	yes	characteristic, complemented, Sylow
126	C₂³	—	4	1	no	—
127	C₂³	—	4	1	no	—
128	Q₈	—	36	4	no	—
129	D₄	—	4	4	no	—
130	D₄	—	4	4	no	—
131	D₄	—	4	2	no	—
132	D₄	—	4	2	no	—
133	C₂×C₄	—	36	2	no	—
134	C₂×C₄	D₄×C₃⋊D₃	1	2	yes	—
135	C₂×C₄	C₂×#638	1	1	yes	characteristic
136	C₈	—	18	4	no	—
137	C₈	#3754	1	4	yes	complemented
138	C₂×C₃	—	16	4	no	—
139	C₂×C₃	—	16	4	no	—
140	C₂×C₃	#5076	1	4	yes	—
141	C₂×C₃	#5154	1	8	yes	—
142	C₂²	—	8	1	no	—
143	C₂²	—	8	1	no	—
144	C₂²	—	8	2	no	—
145	C₂²	—	8	2	no	—
146	C₂²	#64149	1	1	yes	characteristic
147	C₄	—	72	2	no	—
148	C₄	#64120	1	4	yes	—
149	C₄	C₂×#3754	1	2	yes	—
150	C₃	#71277	1	4	yes	complemented
151	C₂	—	16	1	no	—
152	C₂	—	16	1	no	—
153	C₂	#10592775	1	1	yes	characteristic
154	C₂	#10592853	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃²×#493

C₂

yes

maximal, characteristic

#10592775

C₂

yes

maximal, complemented

#10592769

C₂

yes

maximal, complemented

#10592379

C₂

yes

maximal, characteristic, complemented

#10589321

C₂

yes

maximal, characteristic, complemented

#71277

—

maximal

C₂×C₃²×D₈

—

C₃²×#127

C₂²

yes

characteristic

C₃²×#127

C₂²

yes

characteristic

C₂×#3754

—

#64078

C₂²

yes

—

C₃²×C₄×C₈

C₂²

yes

characteristic

#63659

—

#63644

—

C₄×C₃⋊(C₃⋊C₈)

C₂²

yes

—

C₃×#493

D₃

yes

—

—

—

—

—

C₂×C₃²×D₄

—

C₂×C₃²×D₄

—

C₂×C₃²×D₄

—

C₂×C₃²×D₄

—

C₂×#634

—

C₃²×D₈

—

C₂×C₃²×C₈

D₄

yes

—

C₃²×C₄²

C₂³

yes

characteristic

#3754

—

C₄⋊(C₃⋊Dic₃)

—

C₄⋊(C₃⋊Dic₃)

—

C₂×C₃⋊(C₃⋊C₈)

D₄

yes

—

#1715

—

Sylow

C₂×C₃×D₈

—

C₃×#127

C₂×D₃

yes

—

C₃×#127

C₂×D₃

yes

—

C₂×#214

—

#869

—

C₃×C₄×C₈

C₂×D₃

yes

—

#832

—

#817

—

C₄×C₃⋊C₈

—

C₂³×C₃²

—

C₂³×C₃²

—

C₃²×D₄

—

C₃²×D₄

—

C₃²×D₄

—

C₃²×D₄

—

C₂×C₃²×C₄

C₂×D₄

yes

—

C₂×C₃²×C₄

C₂×D₄

yes

characteristic

C₂×C₃⋊Dic₃

—

#634

—

C₃²×C₈

SD₁₆

yes

complemented

C₃⋊(C₃⋊C₈)

—

#498

—

#493

C₃⋊D₃

yes

—

—

—

C₂×C₃×D₄

—

C₂×C₃×D₄

—

C₂×C₃×D₄

—

C₂×C₃×D₄

—

C₂×Dic₆

—

C₃×D₈

—

C₂×C₃×C₈

#67

yes

—

C₃×C₄²

C₂²×D₃

yes

—

#214

—

C₄⋊Dic₃

—

C₄⋊Dic₃

—

C₂×C₃⋊C₈

—

C₂²×C₃²

—

C₂²×C₃²

—

C₂²×C₃²

—

C₂²×C₃²

—

C₂²×C₃²

#127

yes

characteristic

C₃²×C₄

C₂×SD₁₆

yes

—

C₃²×C₄

AGL(1,ℤ/8)

yes

—

C₃⋊Dic₃

—

C₂×SD₁₆

—

C₂×D₈

—

C₄⋊Q₈

—

#127

C₂×C₃⋊D₃

yes

characteristic

#127

C₂×C₃⋊D₃

yes

characteristic

#106

—

#102

—

C₄×C₈

—

C₄×C₈

C₂×C₃⋊D₃

yes

characteristic

C₂³×C₃

—

C₂³×C₃

—

C₃×D₄

—

C₃×D₄

—

C₃×D₄

—

C₃×D₄

—

C₂×C₃×C₄

D₃×D₄

yes

—

C₂×C₃×C₄

C₂×#67

yes

—

C₂×Dic₃

—

Dic₆

—

C₃×C₈

#214

yes

complemented

100

C₃⋊C₈

—

101

C₂×C₃²

—

102

C₂×C₃²

—

103

C₂×C₃²

#492

yes

characteristic

104

C₂×C₃²

#496

yes

—

105

C₂×Q₈

—

106

C₂×D₄

—

107

C₂×D₄

—

108

C₂×D₄

—

109

C₂×D₄

—

110

SD₁₆

—

111

D₈

—

112

C₂×C₈

—

113

C₂×C₈

#638

yes

—

114

C₄⋊C₄

—

115

C₄⋊C₄

—

116

C₄²

C₂²×C₃⋊D₃

yes

characteristic

117

C₂²×C₃

—

118

C₂²×C₃

—

119

C₂²×C₃

—

120

C₂²×C₃

—

121

C₂²×C₃

#940

yes

—

122

C₃×C₄

#911

yes

—

123

C₃×C₄

C₂×#214

yes

—

124

Dic₃

—

125

C₃²

#1715

yes

characteristic, complemented, Sylow

126

C₂³

—

127

C₂³

—

128

Q₈

—

129

D₄

—

130

D₄

—

131

D₄

—

132

D₄

—

133

C₂×C₄

—

134

C₂×C₄

D₄×C₃⋊D₃

yes

—

135

C₂×C₄

C₂×#638

yes

characteristic

136

C₈

—

137

C₈

#3754

yes

complemented

138

C₂×C₃

—

139

C₂×C₃

—

140

C₂×C₃

#5076

yes

—

141

C₂×C₃

#5154

yes

—

142

C₂²

—

143

C₂²

—

144

C₂²

—

145

C₂²

—

146

C₂²

#64149

yes

characteristic

147

C₄

—

148

C₄

#64120

yes

—

149

C₄

C₂×#3754

yes

—

150

C₃

#71277

yes

complemented

151

C₂

—

152

C₂

—

153

C₂

#10592775

yes

characteristic

154

C₂

#10592853

yes

—

	subgroup	G/H
center	C₂²	#64149
commutator, cosocle	C₃²×C₄²	C₂³
Frattini	C₄²	C₂²×C₃⋊D₃
Fitting, prime radical	C₃²×#493	C₂
socle	C₂²×C₃²	#127
hypercenter	#493	C₃⋊D₃
hypocenter	C₃²	#1715
LCS	G ▷ C₃²×C₄² ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #493

subgroup

G/H

center

C₂²

#64149

commutator, cosocle

C₃²×C₄²

C₂³

Frattini

C₄²

C₂²×C₃⋊D₃

Fitting, prime radical

C₃²×#493

C₂

C₂²×C₃²

C₃⋊D₃

C₃²

G ▷ C₃²×C₄² ▷ C₂²×C₃² ▷ C₃²

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #493

N	H ≅ G/N	type
2. #10592775	C₂	semidirect
3. #10592769	C₂	semidirect
4. #10592379	C₂	semidirect
5. #10589321	C₂	semidirect
53. C₃²×C₈	SD₁₆	semidirect
99. C₃×C₈	#214	semidirect
125. C₃²	#1715	semidirect
137. C₈	#3754	semidirect
150. C₃	#71277	semidirect

H ≅ G/N

type

2. #10592775

C₂

semidirect

3. #10592769

C₂

semidirect

4. #10592379

C₂

semidirect

5. #10589321

C₂

semidirect

53. C₃²×C₈

SD₁₆

semidirect

99. C₃×C₈

#214

semidirect

125. C₃²

#1715

semidirect

137. C₈

#3754

semidirect

150. C₃

#71277

semidirect

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

subgroup	index
C₃²×#493	2
#10592775	2
#10592769	2
#10592379	2
#10589321	2
#71277	3

subgroup

index

C₃²×#493

Subgroups — #11782658

Conjugacy classes of subgroups

Complements

Maximal subgroups