Group #11786046 — subgroups

Subgroups — #11786046

Order 1152.

324 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 142 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×#382	C₂	1	1	yes	maximal, characteristic
2	#10588616	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₉⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#10588206	C₂	1	4	yes	maximal
5	#69547	—	3	1	no	maximal
6	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
7	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊Dic₉	C₂²	1	2	yes	—
9	C₂²×C₉⋊C₈	C₂²	1	2	yes	—
10	C₉×#95	—	2	2	no	—
11	C₉⋊#95	—	2	2	no	—
12	C₄×C₉⋊C₈	C₄	1	4	yes	complemented
13	C₃×#382	D₃	1	1	yes	characteristic
14	#4936	—	3	1	no	—
15	C₂×C₄×C₃⋊C₈	—	3	1	no	—
16	#4529	—	3	4	no	—
17	C₂²×C₄×C₉	—	2	2	no	—
18	C₂²×C₄×C₉	D₄	1	2	yes	—
19	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
20	C₂²×Dic₉	—	2	2	no	—
21	C₉×C₄⋊C₄	—	2	4	no	—
22	C₄²×C₉	C₂×C₄	1	2	yes	—
23	C₄²×C₉	Q₈	1	2	yes	—
24	C₄⋊Dic₉	—	2	4	no	—
25	C₂×C₉⋊C₈	—	2	2	no	—
26	C₂×C₉⋊C₈	—	2	2	no	—
27	C₂×C₉⋊C₈	C₂×C₄	1	4	yes	—
28	#1835	—	9	1	no	Sylow
29	C₂×C₃×C₄⋊C₄	C₂×D₃	1	2	yes	—
30	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
31	C₂×C₄⋊Dic₃	—	3	2	no	—
32	C₂²×C₃⋊C₈	—	3	2	no	—
33	C₃×#95	—	2	2	no	—
34	C₃⋊#95	—	6	2	no	—
35	C₄×C₃⋊C₈	—	3	4	no	—
36	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₉	—	2	4	no	—
38	C₂×C₄×C₉	—	4	2	no	—
39	C₂×C₄×C₉	—	4	4	no	—
40	C₂×C₄×C₉	C₄⋊C₄	1	4	yes	—
41	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
42	C₂×C₄×C₉	C₂×Q₈	1	1	yes	characteristic
43	C₂×C₄×C₉	#41	1	2	yes	—
44	C₂×C₄×C₉	#41	1	2	yes	—
45	C₂×Dic₉	—	4	2	no	—
46	C₂×Dic₉	—	4	4	no	—
47	C₉⋊C₈	—	2	4	no	—
48	C₂×C₄×C₈	—	9	1	no	—
49	#382	—	9	1	no	—
50	#382	D₉	1	1	yes	characteristic
51	#340	—	9	4	no	—
52	C₂²×C₃×C₄	—	2	2	no	—
53	C₂²×C₃×C₄	#67	1	2	yes	—
54	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
55	C₂²×Dic₃	—	6	2	no	—
56	C₃×C₄⋊C₄	—	2	4	no	—
57	C₃×C₄²	Dic₆	1	2	yes	—
58	C₃×C₄²	C₄×D₃	1	2	yes	—
59	C₄⋊Dic₃	—	6	4	no	—
60	C₂×C₃⋊C₈	—	3	4	no	—
61	C₂×C₃⋊C₈	—	6	2	no	—
62	C₂×C₃⋊C₈	—	6	2	no	—
63	C₂²×C₉	C₂×C₄⋊C₄	1	1	yes	characteristic
64	C₂²×C₉	#124	1	1	yes	characteristic
65	C₂²×C₉	#124	1	1	yes	characteristic
66	C₂²×C₉	#135	1	4	yes	—
67	C₄×C₉	—	2	4	no	—
68	C₄×C₉	—	8	2	no	—
69	C₄×C₉	#117	1	2	yes	—
70	C₄×C₉	#125	1	2	yes	—
71	Dic₉	—	8	2	no	—
72	C₂²×C₈	—	9	2	no	—
73	C₂×C₄⋊C₄	—	9	2	no	—
74	C₂×C₄⋊C₄	C₂×D₉	1	2	yes	—
75	C₂×C₄²	C₂×D₉	1	1	yes	characteristic
76	C₄×C₈	—	9	4	no	—
77	#95	—	2	2	no	—
78	#95	—	18	2	no	—
79	C₂³×C₃	C₂×#67	1	1	yes	characteristic
80	C₂×C₃×C₄	—	2	4	no	—
81	C₂×C₃×C₄	—	4	2	no	—
82	C₂×C₃×C₄	—	4	4	no	—
83	C₂×C₃×C₄	Dic₃⋊C₄	1	4	yes	—
84	C₂×C₃×C₄	C₂×Dic₆	1	1	yes	characteristic
85	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
86	C₂×C₃×C₄	#237	1	2	yes	—
87	C₂×C₃×C₄	#239	1	2	yes	—
88	C₂×Dic₃	—	12	2	no	—
89	C₂×Dic₃	—	12	4	no	—
90	C₃⋊C₈	—	6	4	no	—
91	C₂×C₉	#382	1	1	yes	characteristic
92	C₂×C₉	#427	1	2	yes	—
93	C₂×C₉	#488	1	2	yes	—
94	C₂×C₉	#488	1	2	yes	—
95	C₂²×C₄	—	2	2	no	—
96	C₂²×C₄	—	18	2	no	—
97	C₂²×C₄	#611	1	2	yes	—
98	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
99	C₂×C₈	—	9	4	no	—
100	C₂×C₈	—	18	2	no	—
101	C₂×C₈	—	18	2	no	—
102	C₄⋊C₄	—	2	4	no	—
103	C₄⋊C₄	—	18	4	no	—
104	C₄²	Dic₁₈	1	2	yes	—
105	C₄²	C₄×D₉	1	2	yes	—
106	C₂²×C₃	C₂×Dic₃⋊C₄	1	1	yes	characteristic
107	C₂²×C₃	#936	1	1	yes	characteristic
108	C₂²×C₃	#947	1	1	yes	characteristic
109	C₂²×C₃	#950	1	4	yes	—
110	C₃×C₄	—	2	4	no	—
111	C₃×C₄	—	8	2	no	—
112	C₃×C₄	#890	1	2	yes	—
113	C₃×C₄	#892	1	2	yes	—
114	Dic₃	—	24	2	no	—
115	C₉	#1835	1	1	yes	characteristic, complemented, Sylow
116	C₂³	C₂×#611	1	1	yes	characteristic
117	C₂×C₄	—	2	4	no	—
118	C₂×C₄	—	4	2	no	—
119	C₂×C₄	—	4	4	no	—
120	C₂×C₄	—	36	2	no	—
121	C₂×C₄	—	36	4	no	—
122	C₂×C₄	Dic₉⋊C₄	1	4	yes	—
123	C₂×C₄	C₂×Dic₁₈	1	1	yes	characteristic
124	C₂×C₄	C₂×C₄×D₉	1	1	yes	characteristic
125	C₂×C₄	#3699	1	2	yes	—
126	C₂×C₄	#3701	1	2	yes	—
127	C₈	—	18	4	no	—
128	C₂×C₃	#4977	1	1	yes	characteristic
129	C₂×C₃	#4998	1	2	yes	—
130	C₂×C₃	#5056	1	2	yes	—
131	C₂×C₃	#5068	1	2	yes	—
132	C₂²	C₂×Dic₉⋊C₄	1	1	yes	characteristic
133	C₂²	#63498	1	1	yes	characteristic
134	C₂²	#63509	1	1	yes	characteristic
135	C₂²	#63513	1	4	yes	—
136	C₄	—	2	4	no	—
137	C₄	—	8	2	no	—
138	C₄	—	72	2	no	—
139	C₄	#63452	1	2	yes	—
140	C₄	#63454	1	2	yes	—
141	C₃	#69547	1	1	yes	characteristic
142	C₂	#10588657	1	1	yes	characteristic
143	C₂	#10588676	1	2	yes	—
144	C₂	#10588735	1	2	yes	—
145	C₂	#10588749	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₉×#382

C₂

yes

maximal, characteristic

#10588616

C₂

yes

maximal, characteristic

C₂×C₄×C₉⋊C₈

C₂

yes

maximal, characteristic

#10588206

C₂

yes

maximal

#69547

—

maximal

C₂×C₉×C₄⋊C₄

C₂²

yes

—

C₂×C₄²×C₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₉

C₂²

yes

—

C₂²×C₉⋊C₈

C₂²

yes

—

C₉×#95

—

C₉⋊#95

—

C₄×C₉⋊C₈

C₄

yes

complemented

C₃×#382

D₃

yes

characteristic

#4936

—

C₂×C₄×C₃⋊C₈

—

#4529

—

C₂²×C₄×C₉

—

C₂²×C₄×C₉

D₄

yes

—

C₂²×C₄×C₉

C₂³

yes

characteristic

C₂²×Dic₉

—

C₉×C₄⋊C₄

—

C₄²×C₉

C₂×C₄

yes

—

C₄²×C₉

Q₈

yes

—

C₄⋊Dic₉

—

C₂×C₉⋊C₈

—

C₂×C₉⋊C₈

—

C₂×C₉⋊C₈

C₂×C₄

yes

—

#1835

—

Sylow

C₂×C₃×C₄⋊C₄

C₂×D₃

yes

—

C₂×C₃×C₄²

C₂×D₃

yes

characteristic

C₂×C₄⋊Dic₃

—

C₂²×C₃⋊C₈

—

C₃×#95

—

C₃⋊#95

—

C₄×C₃⋊C₈

—

C₂³×C₉

C₂×D₄

yes

characteristic

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

C₄⋊C₄

yes

—

C₂×C₄×C₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₉

#41

yes

—

C₂×C₄×C₉

#41

yes

—

C₂×Dic₉

—

C₂×Dic₉

—

C₉⋊C₈

—

C₂×C₄×C₈

—

#382

—

#382

D₉

yes

characteristic

#340

—

C₂²×C₃×C₄

—

C₂²×C₃×C₄

#67

yes

—

C₂²×C₃×C₄

C₂²×D₃

yes

characteristic

C₂²×Dic₃

—

C₃×C₄⋊C₄

—

C₃×C₄²

Dic₆

yes

—

C₃×C₄²

C₄×D₃

yes

—

C₄⋊Dic₃

—

C₂×C₃⋊C₈

—

C₂×C₃⋊C₈

—

C₂×C₃⋊C₈

—

C₂²×C₉

C₂×C₄⋊C₄

yes

C₂²×C₉

yes

C₂²×C₉

yes

C₂²×C₉

yes

—

C₄×C₉

—

C₄×C₉

—

C₄×C₉

#117

yes

—

C₄×C₉

#125

yes

—

Dic₉

—

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₉

yes

—

C₂×C₄²

C₂×D₉

yes

characteristic

C₄×C₈

—

#95

—

#95

—

C₂³×C₃

C₂×#67

yes

characteristic

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

Dic₃⋊C₄

yes

—

C₂×C₃×C₄

C₂×Dic₆

yes

characteristic

C₂×C₃×C₄

C₂×C₄×D₃

yes

characteristic

C₂×C₃×C₄

#237

yes

—

C₂×C₃×C₄

#239

yes

—

C₂×Dic₃

—

C₂×Dic₃

—

C₃⋊C₈

—

C₂×C₉

#382

yes

characteristic

C₂×C₉

#427

yes

—

C₂×C₉

#488

yes

—

C₂×C₉

#488

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

#611

yes

—

C₂²×C₄

C₂²×D₉

yes

characteristic

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄²

Dic₁₈

yes

—

105

C₄²

C₄×D₉

yes

—

106

C₂²×C₃

C₂×Dic₃⋊C₄

yes

characteristic

107

C₂²×C₃

#936

yes

characteristic

108

C₂²×C₃

#947

yes

characteristic

109

C₂²×C₃

#950

yes

—

110

C₃×C₄

—

111

C₃×C₄

—

112

C₃×C₄

#890

yes

—

113

C₃×C₄

#892

yes

—

114

Dic₃

—

115

C₉

#1835

yes

characteristic, complemented, Sylow

116

C₂³

C₂×#611

yes

characteristic

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

Dic₉⋊C₄

yes

—

123

C₂×C₄

C₂×Dic₁₈

yes

characteristic

124

C₂×C₄

C₂×C₄×D₉

yes

characteristic

125

C₂×C₄

#3699

yes

—

126

C₂×C₄

#3701

yes

—

127

C₈

—

128

C₂×C₃

#4977

yes

characteristic

129

C₂×C₃

#4998

yes

—

130

C₂×C₃

#5056

yes

—

131

C₂×C₃

#5068

yes

—

132

C₂²

C₂×Dic₉⋊C₄

yes

characteristic

133

C₂²

#63498

yes

characteristic

134

C₂²

#63509

yes

characteristic

135

C₂²

#63513

yes

—

136

C₄

—

137

C₄

—

138

C₄

—

139

C₄

#63452

yes

—

140

C₄

#63454

yes

—

141

C₃

#69547

yes

characteristic

142

C₂

#10588657

yes

characteristic

143

C₂

#10588676

yes

—

144

C₂

#10588735

yes

—

145

C₂

#10588749

yes

—

	subgroup	G/H
center	C₂³	C₂×#611
commutator	C₂×C₄×C₉	C₂²×C₄
Frattini	C₂²×C₃×C₄	C₂²×D₃
Fitting	C₉×#382	C₂
socle, prime radical	C₂³×C₃	C₂×#67
cosocle	C₂²×C₄×C₉	C₂³
hypercenter	#382	D₉
hypocenter	C₉	#1835
LCS	G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #382

subgroup

G/H

center

C₂³

C₂×#611

commutator

C₂×C₄×C₉

C₂²×C₄

Frattini

C₂²×C₃×C₄

C₂²×D₃

Fitting

C₉×#382

C₂

socle, prime radical

C₂³×C₃

C₂×#67

cosocle

C₂²×C₄×C₉

C₂³

D₉

C₉

G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #382

N	H ≅ G/N	type
12. C₄×C₉⋊C₈	C₄	semidirect
115. C₉	#1835	semidirect

H ≅ G/N

type

12. C₄×C₉⋊C₈

C₄

semidirect

115. C₉

#1835

semidirect

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

subgroup	index
C₉×#382	2
#10588616	2
C₂×C₄×C₉⋊C₈	2
#10588206	2
#69547	3

subgroup

index

C₂×C₄×C₉⋊C₈

Subgroups — #11786046

Conjugacy classes of subgroups

Complements

Maximal subgroups