Group #11782504 — subgroups

Subgroups — #11782504

Order 1152.

285 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 285 conjugacy classes of subgroups — too many to draw. Only its 90 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×#498	C₂	1	1	yes	maximal, characteristic, complemented
2	#10588773	C₂	1	2	yes	maximal
3	#10588759	C₂	1	2	yes	maximal, complemented
4	#10588375	C₂	1	1	yes	maximal, characteristic
5	C₈×C₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	#71334	—	3	1	no	maximal
7	C₉×C₄⋊Q₈	C₂²	1	2	yes	—
8	C₂×#3664	—	2	2	no	—
9	#63436	C₂²	1	1	yes	characteristic
10	#63431	C₂²	1	1	yes	characteristic
11	C₉×#106	—	2	2	no	—
12	C₄×C₈×C₉	C₂²	1	1	yes	characteristic
13	#63395	—	2	4	no	—
14	#63369	—	2	4	no	—
15	C₄×C₉⋊C₈	C₂²	1	2	yes	—
16	C₃×#498	D₃	1	1	yes	characteristic
17	#5088	—	3	2	no	—
18	#5079	—	3	2	no	—
19	#4693	—	3	1	no	—
20	C₈×C₃⋊C₈	—	3	1	no	—
21	C₂×Q₈×C₉	—	2	2	no	—
22	C₂×D₃₆	—	2	2	no	—
23	C₂×D₃₆	—	2	1	no	—
24	C₂×Dic₁₈	—	2	1	no	—
25	C₂×C₈×C₉	D₄	1	2	yes	—
26	C₉×C₄⋊C₄	—	2	2	no	—
27	C₉×C₄⋊C₄	—	2	2	no	—
28	C₄²×C₉	C₂³	1	1	yes	characteristic
29	C₄⋊Dic₉	—	2	2	no	—
30	C₂×C₉⋊C₈	D₄	1	4	yes	—
31	#3664	—	4	4	no	—
32	#1708	—	9	1	no	Sylow
33	C₃×C₄⋊Q₈	C₂×D₃	1	2	yes	—
34	C₂×#204	—	6	2	no	—
35	#874	—	3	1	no	—
36	#869	—	3	1	no	—
37	C₃×#106	—	2	2	no	—
38	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
39	#835	—	6	4	no	—
40	#809	—	6	4	no	—
41	C₄×C₃⋊C₈	—	3	2	no	—
42	C₂²×D₉	—	4	1	no	—
43	Q₈×C₉	—	4	4	no	—
44	C₂×C₄×C₉	—	4	2	no	—
45	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
46	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
47	C₂×Dic₉	—	4	1	no	—
48	D₃₆	—	4	2	no	—
49	D₃₆	—	4	4	no	—
50	Dic₁₈	—	4	2	no	—
51	C₈×C₉	SD₁₆	1	4	yes	—
52	C₉⋊C₈	—	2	4	no	—
53	#498	D₉	1	1	yes	characteristic, complemented
54	#492	—	9	1	no	—
55	#487	—	9	2	no	—
56	#486	—	9	2	no	—
57	C₈²	—	9	1	no	—
58	C₂×C₃×Q₈	—	2	2	no	—
59	C₂×D₁₂	—	6	2	no	—
60	C₂×D₁₂	—	6	1	no	—
61	C₂×Dic₆	—	6	1	no	—
62	C₂×C₃×C₈	#67	1	2	yes	—
63	C₃×C₄⋊C₄	—	2	2	no	—
64	C₃×C₄⋊C₄	—	2	2	no	—
65	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
66	C₄⋊Dic₃	—	6	2	no	—
67	C₂×C₃⋊C₈	—	3	4	no	—
68	#204	—	12	4	no	—
69	C₂²×C₉	#127	1	1	yes	characteristic
70	C₂×D₉	—	8	1	no	—
71	C₂×D₉	—	8	2	no	—
72	C₄×C₉	—	8	2	no	—
73	C₄×C₉	C₂×SD₁₆	1	2	yes	—
74	C₄×C₉	#135	1	4	yes	—
75	Dic₉	—	8	1	no	—
76	C₂×SD₁₆	—	18	2	no	—
77	C₄⋊Q₈	—	9	1	no	—
78	C₄⋊Q₈	C₂×D₉	1	2	yes	—
79	#127	—	9	1	no	—
80	#106	—	2	2	no	—
81	#103	—	18	4	no	—
82	#102	—	18	4	no	—
83	C₄×C₈	—	9	2	no	—
84	C₄×C₈	C₂×D₉	1	1	yes	characteristic
85	C₂²×D₃	—	12	1	no	—
86	C₃×Q₈	—	4	4	no	—
87	C₂×C₃×C₄	—	4	2	no	—
88	C₂×C₃×C₄	D₃×D₄	1	2	yes	—
89	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
90	C₂×Dic₃	—	12	1	no	—
91	D₁₂	—	12	4	no	—
92	D₁₂	—	12	2	no	—
93	Dic₆	—	12	2	no	—
94	C₃×C₈	#215	1	4	yes	—
95	C₃⋊C₈	—	6	4	no	—
96	C₂×C₉	#492	1	1	yes	characteristic
97	C₂×C₉	#495	1	2	yes	—
98	D₉	—	16	1	no	—
99	C₂×Q₈	—	2	2	no	—
100	C₂×Q₈	—	18	1	no	—
101	C₂×D₄	—	18	2	no	—
102	C₂×D₄	—	18	1	no	—
103	SD₁₆	—	36	4	no	—
104	C₂×C₈	—	9	4	no	—
105	C₂×C₈	#611	1	2	yes	—
106	C₄⋊C₄	—	2	2	no	—
107	C₄⋊C₄	—	2	2	no	—
108	C₄⋊C₄	—	18	2	no	—
109	C₄²	C₂²×D₉	1	1	yes	characteristic
110	C₂²×C₃	#940	1	1	yes	characteristic
111	C₂×D₃	—	24	2	no	—
112	C₂×D₃	—	24	1	no	—
113	C₃×C₄	—	8	2	no	—
114	C₃×C₄	#916	1	4	yes	—
115	C₃×C₄	C₂×#215	1	2	yes	—
116	Dic₃	—	24	1	no	—
117	C₉	#1708	1	1	yes	characteristic, complemented, Sylow
118	C₂³	—	36	1	no	—
119	Q₈	—	4	4	no	—
120	Q₈	—	36	2	no	—
121	D₄	—	36	2	no	—
122	D₄	—	36	4	no	—
123	C₂×C₄	—	4	2	no	—
124	C₂×C₄	—	36	1	no	—
125	C₂×C₄	D₄×D₉	1	2	yes	—
126	C₂×C₄	C₂×#611	1	1	yes	characteristic
127	C₈	—	18	4	no	—
128	C₈	#3675	1	4	yes	—
129	C₂×C₃	#5085	1	1	yes	characteristic
130	C₂×C₃	#5168	1	2	yes	—
131	D₃	—	48	1	no	—
132	C₂²	—	72	1	no	—
133	C₂²	—	72	2	no	—
134	C₂²	#63502	1	1	yes	characteristic
135	C₄	—	8	2	no	—
136	C₄	—	72	1	no	—
137	C₄	#63478	1	4	yes	—
138	C₄	C₂×#3675	1	2	yes	—
139	C₃	#71334	1	1	yes	characteristic
140	C₂	—	144	1	no	—
141	C₂	#10588770	1	1	yes	characteristic
142	C₂	#10588848	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₉×#498

C₂

yes

maximal, characteristic, complemented

#10588773

C₂

yes

maximal

#10588759

C₂

yes

maximal, complemented

#10588375

C₂

yes

maximal, characteristic

C₈×C₉⋊C₈

C₂

yes

maximal, characteristic, complemented

#71334

—

maximal

C₉×C₄⋊Q₈

C₂²

yes

—

C₂×#3664

—

#63436

C₂²

yes

characteristic

#63431

C₂²

yes

characteristic

C₉×#106

—

C₄×C₈×C₉

C₂²

yes

characteristic

#63395

—

#63369

—

C₄×C₉⋊C₈

C₂²

yes

—

C₃×#498

D₃

yes

—

—

—

C₈×C₃⋊C₈

—

C₂×Q₈×C₉

—

C₂×D₃₆

—

C₂×D₃₆

—

C₂×Dic₁₈

—

C₂×C₈×C₉

D₄

yes

—

C₉×C₄⋊C₄

—

C₉×C₄⋊C₄

—

C₄²×C₉

C₂³

yes

characteristic

C₄⋊Dic₉

—

C₂×C₉⋊C₈

D₄

yes

—

#3664

—

#1708

—

Sylow

C₃×C₄⋊Q₈

C₂×D₃

yes

—

—

—

—

—

C₃×C₄×C₈

C₂×D₃

yes

characteristic

#835

—

#809

—

C₄×C₃⋊C₈

—

C₂²×D₉

—

Q₈×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

C₂×D₄

yes

—

C₂×C₄×C₉

C₂×D₄

yes

characteristic

C₂×Dic₉

—

D₃₆

—

D₃₆

—

Dic₁₈

—

C₈×C₉

SD₁₆

yes

—

C₉⋊C₈

—

#498

D₉

yes

characteristic, complemented

#492

—

#487

—

#486

—

C₈²

—

C₂×C₃×Q₈

—

C₂×D₁₂

—

C₂×D₁₂

—

C₂×Dic₆

—

C₂×C₃×C₈

#67

yes

—

C₃×C₄⋊C₄

—

C₃×C₄⋊C₄

—

C₃×C₄²

C₂²×D₃

yes

characteristic

C₄⋊Dic₃

—

C₂×C₃⋊C₈

—

#204

—

C₂²×C₉

#127

yes

characteristic

C₂×D₉

—

C₂×D₉

—

C₄×C₉

—

C₄×C₉

C₂×SD₁₆

yes

—

C₄×C₉

#135

yes

—

Dic₉

—

C₂×SD₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₉

yes

—

—

—

—

—

C₄×C₈

—

C₄×C₈

C₂×D₉

yes

characteristic

C₂²×D₃

—

C₃×Q₈

—

C₂×C₃×C₄

—

C₂×C₃×C₄

D₃×D₄

yes

—

C₂×C₃×C₄

C₂×#67

yes

characteristic

C₂×Dic₃

—

D₁₂

—

D₁₂

—

Dic₆

—

C₃×C₈

#215

yes

—

C₃⋊C₈

—

C₂×C₉

#492

yes

characteristic

C₂×C₉

#495

yes

—

D₉

—

C₂×Q₈

—

100

C₂×Q₈

—

101

C₂×D₄

—

102

C₂×D₄

—

103

SD₁₆

—

104

C₂×C₈

—

105

C₂×C₈

#611

yes

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₄⋊C₄

—

109

C₄²

C₂²×D₉

yes

characteristic

110

C₂²×C₃

#940

yes

characteristic

111

C₂×D₃

—

112

C₂×D₃

—

113

C₃×C₄

—

114

C₃×C₄

#916

yes

—

115

C₃×C₄

C₂×#215

yes

—

116

Dic₃

—

117

C₉

#1708

yes

characteristic, complemented, Sylow

118

C₂³

—

119

Q₈

—

120

Q₈

—

121

D₄

—

122

D₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

D₄×D₉

yes

—

126

C₂×C₄

C₂×#611

yes

characteristic

127

C₈

—

128

C₈

#3675

yes

—

129

C₂×C₃

#5085

yes

characteristic

130

C₂×C₃

#5168

yes

—

131

D₃

—

132

C₂²

—

133

C₂²

—

134

C₂²

#63502

yes

characteristic

135

C₄

—

136

C₄

—

137

C₄

#63478

yes

—

138

C₄

C₂×#3675

yes

—

139

C₃

#71334

yes

characteristic

140

C₂

—

144

—

141

C₂

#10588770

yes

characteristic

142

C₂

#10588848

yes

—

	subgroup	G/H
center	C₂²	#63502
commutator, cosocle	C₄²×C₉	C₂³
Frattini	C₃×C₄²	C₂²×D₃
Fitting	C₉×#498	C₂
socle	C₂²×C₃	#940
prime radical	#63436	C₂²
hypercenter	#498	D₉
hypocenter	C₉	#1708
LCS	G ▷ C₄²×C₉ ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #498

subgroup

G/H

center

C₂²

#63502

commutator, cosocle

C₄²×C₉

C₂³

Frattini

C₃×C₄²

C₂²×D₃

C₂

C₂²×C₃

C₂²

D₉

C₉

G ▷ C₄²×C₉ ▷ C₂²×C₉ ▷ C₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #498

N	H ≅ G/N	type
1. C₉×#498	C₂	semidirect
3. #10588759	C₂	semidirect
5. C₈×C₉⋊C₈	C₂	semidirect
53. #498	D₉	semidirect
117. C₉	#1708	semidirect

H ≅ G/N

type

1. C₉×#498

C₂

semidirect

3. #10588759

C₂

semidirect

5. C₈×C₉⋊C₈

C₂

semidirect

53. #498

D₉

semidirect

117. C₉

#1708

semidirect

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

subgroup	index
C₉×#498	2
#10588773	2
#10588759	2
#10588375	2
C₈×C₉⋊C₈	2
#71334	3

subgroup

index

C₈×C₉⋊C₈

Subgroups — #11782504

Conjugacy classes of subgroups

Complements

Maximal subgroups