Group #11782431 — subgroups

Subgroups — #11782431

Order 1152.

336 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 94 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	C₉×#493	C₂	1	1	yes	maximal, characteristic
2	#10588753	C₂	1	2	yes	maximal, complemented
3	#10588750	C₂	1	2	yes	maximal, complemented
4	#10588362	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈×C₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	#71274	—	3	1	no	maximal
7	C₂×C₉×D₈	—	2	2	no	—
8	C₉×#127	C₂²	1	2	yes	—
9	C₂×#3672	—	2	4	no	—
10	#63431	C₂²	1	2	yes	—
11	C₄×C₈×C₉	C₂²	1	1	yes	characteristic
12	#63392	—	2	4	no	—
13	#63378	—	2	2	no	—
14	C₄×C₉⋊C₈	C₂²	1	1	yes	characteristic
15	C₄×C₉⋊C₈	C₂²	1	1	yes	characteristic
16	C₃×#493	D₃	1	1	yes	characteristic
17	#5076	—	3	2	no	—
18	#5070	—	3	2	no	—
19	#4682	—	3	1	no	—
20	C₈×C₃⋊C₈	—	3	1	no	—
21	C₂×D₄×C₉	—	2	2	no	—
22	C₂×D₄×C₉	—	2	2	no	—
23	C₂×D₄×C₉	—	2	2	no	—
24	C₂×Dic₁₈	—	2	2	no	—
25	C₉×D₈	—	4	4	no	—
26	C₂×C₈×C₉	D₄	1	2	yes	—
27	C₄²×C₉	C₂³	1	1	yes	characteristic
28	#3672	—	4	8	no	—
29	C₄⋊Dic₉	—	2	2	no	—
30	C₄⋊Dic₉	—	2	2	no	—
31	C₂×C₉⋊C₈	D₄	1	2	yes	—
32	C₂×C₉⋊C₈	D₄	1	2	yes	—
33	#1706	—	9	1	no	Sylow
34	C₂×C₃×D₈	—	2	2	no	—
35	C₃×#127	C₂×D₃	1	2	yes	—
36	C₂×#214	—	6	4	no	—
37	#869	—	3	2	no	—
38	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
39	#832	—	6	4	no	—
40	#818	—	6	2	no	—
41	C₄×C₃⋊C₈	—	3	1	no	—
42	C₄×C₃⋊C₈	—	3	1	no	—
43	C₂³×C₉	—	4	2	no	—
44	D₄×C₉	—	4	4	no	—
45	D₄×C₉	—	4	4	no	—
46	D₄×C₉	—	4	4	no	—
47	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
50	C₂×Dic₉	—	4	2	no	—
51	Dic₁₈	—	4	4	no	—
52	C₈×C₉	SD₁₆	1	4	yes	complemented
53	C₉⋊C₈	—	2	2	no	—
54	C₉⋊C₈	D₈	1	4	yes	complemented
55	#500	—	9	1	no	—
56	#493	D₉	1	1	yes	characteristic
57	#492	—	9	2	no	—
58	#486	—	9	2	no	—
59	C₈²	—	9	1	no	—
60	C₂×C₃×D₄	—	2	2	no	—
61	C₂×C₃×D₄	—	2	2	no	—
62	C₂×C₃×D₄	—	2	2	no	—
63	C₂×Dic₆	—	6	2	no	—
64	C₃×D₈	—	4	4	no	—
65	C₂×C₃×C₈	#67	1	2	yes	—
66	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
67	#214	—	12	8	no	—
68	C₄⋊Dic₃	—	6	2	no	—
69	C₄⋊Dic₃	—	6	2	no	—
70	C₂×C₃⋊C₈	—	3	2	no	—
71	C₂×C₃⋊C₈	—	3	2	no	—
72	C₂²×C₉	—	8	2	no	—
73	C₂²×C₉	—	8	2	no	—
74	C₂²×C₉	—	8	2	no	—
75	C₂²×C₉	#127	1	1	yes	characteristic
76	C₄×C₉	C₂×D₈	1	2	yes	—
77	C₄×C₉	C₂×SD₁₆	1	2	yes	—
78	C₄×C₉	#135	1	2	yes	—
79	Dic₉	—	8	2	no	—
80	C₂×SD₁₆	—	18	4	no	—
81	C₂×D₈	—	2	2	no	—
82	C₄⋊Q₈	—	9	2	no	—
83	#127	C₂×D₉	1	2	yes	—
84	#107	—	18	2	no	—
85	#102	—	18	4	no	—
86	C₄×C₈	—	9	1	no	—
87	C₄×C₈	—	9	1	no	—
88	C₄×C₈	C₂×D₉	1	1	yes	characteristic
89	C₂³×C₃	—	4	2	no	—
90	C₃×D₄	—	4	4	no	—
91	C₃×D₄	—	4	4	no	—
92	C₃×D₄	—	4	4	no	—
93	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
94	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
95	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
96	C₂×Dic₃	—	12	2	no	—
97	Dic₆	—	12	4	no	—
98	C₃×C₈	#214	1	4	yes	—
99	C₃⋊C₈	—	3	4	no	—
100	C₃⋊C₈	—	6	2	no	—
101	C₂×C₉	—	16	2	no	—
102	C₂×C₉	#492	1	1	yes	characteristic
103	C₂×C₉	#493	1	1	yes	characteristic
104	C₂×C₉	#495	1	1	yes	characteristic
105	C₂×Q₈	—	18	2	no	—
106	C₂×D₄	—	2	2	no	—
107	C₂×D₄	—	2	2	no	—
108	C₂×D₄	—	2	2	no	—
109	SD₁₆	—	36	8	no	—
110	D₈	—	4	4	no	—
111	C₂×C₈	—	9	2	no	—
112	C₂×C₈	—	9	2	no	—
113	C₂×C₈	#611	1	2	yes	—
114	C₄⋊C₄	—	18	2	no	—
115	C₄⋊C₄	—	18	2	no	—
116	C₄²	C₂²×D₉	1	1	yes	characteristic
117	C₂²×C₃	—	8	2	no	—
118	C₂²×C₃	—	8	2	no	—
119	C₂²×C₃	—	8	2	no	—
120	C₂²×C₃	#940	1	1	yes	characteristic
121	C₃×C₄	D₃×D₈	1	2	yes	—
122	C₃×C₄	#912	1	2	yes	—
123	C₃×C₄	C₂×#214	1	2	yes	—
124	Dic₃	—	24	2	no	—
125	C₉	#1706	1	1	yes	characteristic, complemented, Sylow
126	C₂³	—	4	2	no	—
127	Q₈	—	36	4	no	—
128	D₄	—	4	4	no	—
129	D₄	—	4	4	no	—
130	D₄	—	4	4	no	—
131	C₂×C₄	—	36	2	no	—
132	C₂×C₄	D₄×D₉	1	1	yes	characteristic
133	C₂×C₄	D₄×D₉	1	1	yes	characteristic
134	C₂×C₄	C₂×#611	1	1	yes	characteristic
135	C₈	—	9	4	no	—
136	C₈	—	18	2	no	—
137	C₈	#3672	1	4	yes	complemented
138	C₂×C₃	—	16	2	no	—
139	C₂×C₃	#5076	1	1	yes	characteristic
140	C₂×C₃	#5151	1	1	yes	characteristic
141	C₂×C₃	#5155	1	1	yes	characteristic
142	C₂²	—	8	2	no	—
143	C₂²	—	8	2	no	—
144	C₂²	—	8	2	no	—
145	C₂²	#63502	1	1	yes	characteristic
146	C₄	—	72	2	no	—
147	C₄	D₈×D₉	1	2	yes	—
148	C₄	#63474	1	2	yes	—
149	C₄	C₂×#3672	1	2	yes	—
150	C₃	#71274	1	1	yes	characteristic
151	C₂	—	16	2	no	—
152	C₂	#10588753	1	1	yes	characteristic
153	C₂	#10588831	1	1	yes	characteristic
154	C₂	#10588835	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₉×#493

C₂

yes

maximal, characteristic

#10588753

C₂

yes

maximal, complemented

#10588750

C₂

yes

maximal, complemented

#10588362

C₂

yes

maximal, characteristic, complemented

C₈×C₉⋊C₈

C₂

yes

maximal, characteristic, complemented

#71274

—

maximal

C₂×C₉×D₈

—

C₉×#127

C₂²

yes

—

C₂×#3672

—

#63431

C₂²

yes

—

C₄×C₈×C₉

C₂²

yes

characteristic

#63392

—

#63378

—

C₄×C₉⋊C₈

C₂²

yes

characteristic

C₄×C₉⋊C₈

C₂²

yes

characteristic

C₃×#493

D₃

yes

—

—

—

C₈×C₃⋊C₈

—

C₂×D₄×C₉

—

C₂×D₄×C₉

—

C₂×D₄×C₉

—

C₂×Dic₁₈

—

C₉×D₈

—

C₂×C₈×C₉

D₄

yes

—

C₄²×C₉

C₂³

yes

characteristic

#3672

—

C₄⋊Dic₉

—

C₄⋊Dic₉

—

C₂×C₉⋊C₈

D₄

yes

—

C₂×C₉⋊C₈

D₄

yes

—

#1706

—

Sylow

C₂×C₃×D₈

—

C₃×#127

C₂×D₃

yes

—

C₂×#214

—

#869

—

C₃×C₄×C₈

C₂×D₃

yes

characteristic

#832

—

#818

—

C₄×C₃⋊C₈

—

C₄×C₃⋊C₈

—

C₂³×C₉

—

D₄×C₉

—

D₄×C₉

—

D₄×C₉

—

C₂×C₄×C₉

C₂×D₄

yes

characteristic

C₂×C₄×C₉

C₂×D₄

yes

characteristic

C₂×C₄×C₉

C₂×D₄

yes

characteristic

C₂×Dic₉

—

Dic₁₈

—

C₈×C₉

SD₁₆

yes

complemented

C₉⋊C₈

—

C₉⋊C₈

D₈

yes

complemented

#500

—

#493

D₉

yes

characteristic

#492

—

#486

—

C₈²

—

C₂×C₃×D₄

—

C₂×C₃×D₄

—

C₂×C₃×D₄

—

C₂×Dic₆

—

C₃×D₈

—

C₂×C₃×C₈

#67

yes

—

C₃×C₄²

C₂²×D₃

yes

characteristic

#214

—

C₄⋊Dic₃

—

C₄⋊Dic₃

—

C₂×C₃⋊C₈

—

C₂×C₃⋊C₈

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

#127

yes

characteristic

C₄×C₉

C₂×D₈

yes

—

C₄×C₉

C₂×SD₁₆

yes

—

C₄×C₉

#135

yes

—

Dic₉

—

C₂×SD₁₆

—

C₂×D₈

—

C₄⋊Q₈

—

#127

C₂×D₉

yes

—

#107

—

#102

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₉

yes

characteristic

C₂³×C₃

—

C₃×D₄

—

C₃×D₄

—

C₃×D₄

—

C₂×C₃×C₄

D₃×D₄

yes

characteristic

C₂×C₃×C₄

D₃×D₄

yes

characteristic

C₂×C₃×C₄

C₂×#67

yes

characteristic

C₂×Dic₃

—

Dic₆

—

C₃×C₈

#214

yes

—

C₃⋊C₈

—

100

C₃⋊C₈

—

101

C₂×C₉

—

102

C₂×C₉

#492

yes

characteristic

103

C₂×C₉

#493

yes

characteristic

104

C₂×C₉

#495

yes

characteristic

105

C₂×Q₈

—

106

C₂×D₄

—

107

C₂×D₄

—

108

C₂×D₄

—

109

SD₁₆

—

110

D₈

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

#611

yes

—

114

C₄⋊C₄

—

115

C₄⋊C₄

—

116

C₄²

C₂²×D₉

yes

characteristic

117

C₂²×C₃

—

118

C₂²×C₃

—

119

C₂²×C₃

—

120

C₂²×C₃

#940

yes

characteristic

121

C₃×C₄

D₃×D₈

yes

—

122

C₃×C₄

#912

yes

—

123

C₃×C₄

C₂×#214

yes

—

124

Dic₃

—

125

C₉

#1706

yes

characteristic, complemented, Sylow

126

C₂³

—

127

Q₈

—

128

D₄

—

129

D₄

—

130

D₄

—

131

C₂×C₄

—

132

C₂×C₄

D₄×D₉

yes

characteristic

133

C₂×C₄

D₄×D₉

yes

characteristic

134

C₂×C₄

C₂×#611

yes

characteristic

135

C₈

—

136

C₈

—

137

C₈

#3672

yes

complemented

138

C₂×C₃

—

139

C₂×C₃

#5076

yes

characteristic

140

C₂×C₃

#5151

yes

characteristic

141

C₂×C₃

#5155

yes

characteristic

142

C₂²

—

143

C₂²

—

144

C₂²

—

145

C₂²

#63502

yes

characteristic

146

C₄

—

147

C₄

D₈×D₉

yes

—

148

C₄

#63474

yes

—

149

C₄

C₂×#3672

yes

—

150

C₃

#71274

yes

characteristic

151

C₂

—

152

C₂

#10588753

yes

characteristic

153

C₂

#10588831

yes

characteristic

154

C₂

#10588835

yes

characteristic

	subgroup	G/H
center	C₂²	#63502
commutator, cosocle	C₄²×C₉	C₂³
Frattini	C₃×C₄²	C₂²×D₃
Fitting	C₉×#493	C₂
socle	C₂²×C₃	#940
prime radical	C₃×#493	D₃
hypercenter	#493	D₉
hypocenter	C₉	#1706
LCS	G ▷ C₄²×C₉ ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #493

subgroup

G/H

center

C₂²

#63502

commutator, cosocle

C₄²×C₉

C₂³

Frattini

C₃×C₄²

C₂²×D₃

C₂

C₂²×C₃

D₃

D₉

C₉

G ▷ C₄²×C₉ ▷ C₂²×C₉ ▷ C₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #493

N	H ≅ G/N	type
2. #10588753	C₂	semidirect
3. #10588750	C₂	semidirect
4. #10588362	C₂	semidirect
5. C₈×C₉⋊C₈	C₂	semidirect
52. C₈×C₉	SD₁₆	semidirect
54. C₉⋊C₈	D₈	semidirect
125. C₉	#1706	semidirect
137. C₈	#3672	semidirect

H ≅ G/N

type

2. #10588753

C₂

semidirect

3. #10588750

C₂

semidirect

4. #10588362

C₂

semidirect

5. C₈×C₉⋊C₈

C₂

semidirect

52. C₈×C₉

SD₁₆

semidirect

54. C₉⋊C₈

D₈

semidirect

125. C₉

#1706

semidirect

137. C₈

#3672

semidirect

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

subgroup	index
C₉×#493	2
#10588753	2
#10588750	2
#10588362	2
C₈×C₉⋊C₈	2
#71274	3

subgroup

index

C₈×C₉⋊C₈

Subgroups — #11782431

Conjugacy classes of subgroups

Complements

Maximal subgroups