Group #11782475 — subgroups

Subgroups — #11782475

Order 1152.

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

normal subgroups only

This group has 270 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×#500	C₂	1	1	yes	maximal, characteristic
2	#10588760	C₂	1	2	yes	maximal
3	#10588759	C₂	1	2	yes	maximal
4	#10588365	C₂	1	1	yes	maximal, characteristic
5	C₈×C₉⋊C₈	C₂	1	1	yes	maximal, characteristic
6	#71360	—	3	1	no	maximal
7	C₉×C₄⋊Q₈	C₂²	1	2	yes	—
8	C₂×Dic₃₆	—	2	2	no	—
9	#63431	C₂²	1	2	yes	—
10	C₉×#107	—	2	2	no	—
11	C₄×C₈×C₉	C₂²	1	1	yes	characteristic
12	#63395	—	2	4	no	—
13	#63367	—	2	4	no	—
14	C₄×C₉⋊C₈	C₂²	1	1	yes	characteristic
15	C₄×C₉⋊C₈	C₂²	1	1	yes	characteristic
16	C₃×#500	D₃	1	1	yes	characteristic
17	#5080	—	3	2	no	—
18	#5079	—	3	2	no	—
19	#4699	—	3	1	no	—
20	C₈×C₃⋊C₈	—	3	1	no	—
21	C₂×Q₈×C₉	—	2	2	no	—
22	C₂×Dic₁₈	—	2	2	no	—
23	C₂×C₈×C₉	D₄	1	2	yes	—
24	C₉×C₄⋊C₄	—	2	2	no	—
25	C₉×C₄⋊C₄	—	2	2	no	—
26	C₄²×C₉	C₂³	1	1	yes	characteristic
27	C₄⋊Dic₉	—	2	2	no	—
28	C₄⋊Dic₉	—	2	2	no	—
29	C₂×C₉⋊C₈	D₄	1	2	yes	—
30	C₂×C₉⋊C₈	D₄	1	2	yes	—
31	Dic₃₆	—	4	4	no	—
32	#1707	—	9	1	no	Sylow
33	C₃×C₄⋊Q₈	C₂×D₃	1	2	yes	—
34	C₂×Dic₁₂	—	6	2	no	—
35	#869	—	3	2	no	—
36	C₃×#107	—	2	2	no	—
37	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
38	#835	—	6	4	no	—
39	#808	—	6	4	no	—
40	C₄×C₃⋊C₈	—	3	1	no	—
41	C₄×C₃⋊C₈	—	3	1	no	—
42	Q₈×C₉	—	4	4	no	—
43	C₂×C₄×C₉	—	4	2	no	—
44	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
45	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
46	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
47	C₂×Dic₉	—	4	2	no	—
48	Dic₁₈	—	4	4	no	—
49	C₈×C₉	SD₁₆	1	4	yes	—
50	C₉⋊C₈	—	2	2	no	—
51	C₉⋊C₈	Q₁₆	1	4	yes	complemented
52	#500	D₉	1	1	yes	characteristic
53	#498	—	9	2	no	—
54	#494	—	9	1	no	—
55	#487	—	9	2	no	—
56	C₈²	—	9	1	no	—
57	C₂×C₃×Q₈	—	2	2	no	—
58	C₂×Dic₆	—	6	2	no	—
59	C₂×C₃×C₈	#67	1	2	yes	—
60	C₃×C₄⋊C₄	—	2	2	no	—
61	C₃×C₄⋊C₄	—	2	2	no	—
62	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
63	C₄⋊Dic₃	—	6	2	no	—
64	C₄⋊Dic₃	—	6	2	no	—
65	C₂×C₃⋊C₈	—	3	2	no	—
66	C₂×C₃⋊C₈	—	3	2	no	—
67	Dic₁₂	—	12	4	no	—
68	C₂²×C₉	#127	1	1	yes	characteristic
69	C₄×C₉	—	8	2	no	—
70	C₄×C₉	C₂×SD₁₆	1	2	yes	—
71	C₄×C₉	C₂×Q₁₆	1	2	yes	—
72	C₄×C₉	#135	1	2	yes	—
73	Dic₉	—	8	2	no	—
74	C₂×Q₁₆	—	18	2	no	—
75	C₄⋊Q₈	—	9	2	no	—
76	C₄⋊Q₈	C₂×D₉	1	2	yes	—
77	#107	—	2	2	no	—
78	#106	—	18	4	no	—
79	#103	—	18	4	no	—
80	C₄×C₈	—	9	1	no	—
81	C₄×C₈	—	9	1	no	—
82	C₄×C₈	C₂×D₉	1	1	yes	characteristic
83	C₃×Q₈	—	4	4	no	—
84	C₂×C₃×C₄	—	4	2	no	—
85	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
86	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
87	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
88	C₂×Dic₃	—	12	2	no	—
89	Dic₆	—	12	4	no	—
90	C₃×C₈	#215	1	4	yes	—
91	C₃⋊C₈	—	3	4	no	—
92	C₃⋊C₈	—	6	2	no	—
93	C₂×C₉	#492	1	1	yes	characteristic
94	C₂×C₉	#494	1	1	yes	characteristic
95	C₂×C₉	#495	1	1	yes	characteristic
96	C₂×Q₈	—	2	2	no	—
97	C₂×Q₈	—	18	2	no	—
98	Q₁₆	—	36	4	no	—
99	C₂×C₈	—	9	2	no	—
100	C₂×C₈	—	9	2	no	—
101	C₂×C₈	#611	1	2	yes	—
102	C₄⋊C₄	—	2	2	no	—
103	C₄⋊C₄	—	2	2	no	—
104	C₄⋊C₄	—	18	2	no	—
105	C₄⋊C₄	—	18	2	no	—
106	C₄²	C₂²×D₉	1	1	yes	characteristic
107	C₂²×C₃	#940	1	1	yes	characteristic
108	C₃×C₄	—	8	2	no	—
109	C₃×C₄	#912	1	2	yes	—
110	C₃×C₄	D₃×Q₁₆	1	2	yes	—
111	C₃×C₄	C₂×#215	1	2	yes	—
112	Dic₃	—	24	2	no	—
113	C₉	#1707	1	1	yes	characteristic, complemented, Sylow
114	Q₈	—	4	4	no	—
115	Q₈	—	36	4	no	—
116	C₂×C₄	—	4	2	no	—
117	C₂×C₄	—	36	2	no	—
118	C₂×C₄	D₄×D₉	1	1	yes	characteristic
119	C₂×C₄	D₄×D₉	1	1	yes	characteristic
120	C₂×C₄	C₂×#611	1	1	yes	characteristic
121	C₈	—	9	4	no	—
122	C₈	—	18	2	no	—
123	C₈	#3675	1	4	yes	—
124	C₂×C₃	#5085	1	1	yes	characteristic
125	C₂×C₃	#5155	1	1	yes	characteristic
126	C₂×C₃	#5183	1	1	yes	characteristic
127	C₂²	#63502	1	1	yes	characteristic
128	C₄	—	8	2	no	—
129	C₄	—	72	2	no	—
130	C₄	#63474	1	2	yes	—
131	C₄	Q₁₆×D₉	1	2	yes	—
132	C₄	C₂×#3675	1	2	yes	—
133	C₃	#71360	1	1	yes	characteristic
134	C₂	#10588770	1	1	yes	characteristic
135	C₂	#10588835	1	1	yes	characteristic
136	C₂	#10588863	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₉×#500

C₂

yes

maximal, characteristic

#10588760

C₂

yes

maximal

#10588759

C₂

yes

maximal

#10588365

C₂

yes

maximal, characteristic

C₈×C₉⋊C₈

C₂

yes

maximal, characteristic

#71360

—

maximal

C₉×C₄⋊Q₈

C₂²

yes

—

C₂×Dic₃₆

—

#63431

C₂²

yes

—

C₉×#107

—

C₄×C₈×C₉

C₂²

yes

characteristic

#63395

—

#63367

—

C₄×C₉⋊C₈

C₂²

yes

characteristic

C₄×C₉⋊C₈

C₂²

yes

characteristic

C₃×#500

D₃

yes

—

—

—

C₈×C₃⋊C₈

—

C₂×Q₈×C₉

—

C₂×Dic₁₈

—

C₂×C₈×C₉

D₄

yes

—

C₉×C₄⋊C₄

—

C₉×C₄⋊C₄

—

C₄²×C₉

C₂³

yes

characteristic

C₄⋊Dic₉

—

C₄⋊Dic₉

—

C₂×C₉⋊C₈

D₄

yes

—

C₂×C₉⋊C₈

D₄

yes

—

Dic₃₆

—

#1707

—

Sylow

C₃×C₄⋊Q₈

C₂×D₃

yes

—

C₂×Dic₁₂

—

#869

—

C₃×#107

—

C₃×C₄×C₈

C₂×D₃

yes

characteristic

#835

—

#808

—

C₄×C₃⋊C₈

—

C₄×C₃⋊C₈

—

Q₈×C₉

—

C₂×C₄×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

—

C₉⋊C₈

—

C₉⋊C₈

Q₁₆

yes

complemented

#500

D₉

yes

—

—

—

C₈²

—

C₂×C₃×Q₈

—

C₂×Dic₆

—

C₂×C₃×C₈

#67

yes

—

C₃×C₄⋊C₄

—

C₃×C₄⋊C₄

—

C₃×C₄²

C₂²×D₃

yes

characteristic

C₄⋊Dic₃

—

C₄⋊Dic₃

—

C₂×C₃⋊C₈

—

C₂×C₃⋊C₈

—

Dic₁₂

—

C₂²×C₉

#127

yes

characteristic

C₄×C₉

—

C₄×C₉

C₂×SD₁₆

yes

—

C₄×C₉

C₂×Q₁₆

yes

—

C₄×C₉

#135

yes

—

Dic₉

—

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₉

yes

—

#107

—

#106

—

#103

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₉

yes

characteristic

C₃×Q₈

—

C₂×C₃×C₄

—

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

#215

yes

—

C₃⋊C₈

—

C₃⋊C₈

—

C₂×C₉

yes

C₂×C₉

yes

C₂×C₉

yes

C₂×Q₈

—

C₂×Q₈

—

Q₁₆

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

#611

yes

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄²

C₂²×D₉

yes

characteristic

107

C₂²×C₃

#940

yes

characteristic

108

C₃×C₄

—

109

C₃×C₄

#912

yes

—

110

C₃×C₄

D₃×Q₁₆

yes

—

111

C₃×C₄

C₂×#215

yes

—

112

Dic₃

—

113

C₉

#1707

yes

characteristic, complemented, Sylow

114

Q₈

—

115

Q₈

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

D₄×D₉

yes

characteristic

119

C₂×C₄

D₄×D₉

yes

characteristic

120

C₂×C₄

C₂×#611

yes

characteristic

121

C₈

—

122

C₈

—

123

C₈

#3675

yes

—

124

C₂×C₃

#5085

yes

characteristic

125

C₂×C₃

#5155

yes

characteristic

126

C₂×C₃

#5183

yes

characteristic

127

C₂²

#63502

yes

characteristic

128

C₄

—

129

C₄

—

130

C₄

#63474

yes

—

131

C₄

Q₁₆×D₉

yes

—

132

C₄

C₂×#3675

yes

—

133

C₃

#71360

yes

characteristic

134

C₂

#10588770

yes

characteristic

135

C₂

#10588835

yes

characteristic

136

C₂

#10588863

yes

characteristic

	subgroup	G/H
center	C₂²	#63502
commutator, cosocle	C₄²×C₉	C₂³
Frattini	C₃×C₄²	C₂²×D₃
Fitting	C₉×#500	C₂
socle, prime radical	C₂²×C₃	#940
hypercenter	#500	D₉
hypocenter	C₉	#1707
LCS	G ▷ C₄²×C₉ ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #500

subgroup

G/H

center

C₂²

#63502

commutator, cosocle

C₄²×C₉

C₂³

Frattini

C₃×C₄²

C₂²×D₃

C₂

C₂²×C₃

D₉

C₉

G ▷ C₄²×C₉ ▷ C₂²×C₉ ▷ C₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #500

N	H ≅ G/N	type
51. C₉⋊C₈	Q₁₆	semidirect
113. C₉	#1707	semidirect

H ≅ G/N

type

51. C₉⋊C₈

Q₁₆

semidirect

113. C₉

#1707

semidirect

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

subgroup	index
C₉×#500	2
#10588760	2
#10588759	2
#10588365	2
C₈×C₉⋊C₈	2
#71360	3

subgroup

index

C₈×C₉⋊C₈

Subgroups — #11782475

Conjugacy classes of subgroups

Complements

Maximal subgroups