Group #11785738 — subgroups

Subgroups — #11785738

Order 1152.

408 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 134 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	C₂×C₉×#117	C₂	1	1	yes	maximal, characteristic
2	#10588887	C₂	1	2	yes	maximal
3	#10588207	C₂	1	4	yes	maximal, complemented
4	#71589	—	3	1	no	maximal
5	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
6	C₉×#117	—	2	4	no	—
7	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
8	C₂×C₉×C₂²⋊C₄	C₄	1	2	yes	—
9	C₂×C₄²×C₉	C₄	1	2	yes	—
10	C₂×#3667	C₂²	1	4	yes	—
11	#63389	—	2	4	no	—
12	C₂×C₃×#117	D₃	1	1	yes	characteristic
13	#5207	—	3	2	no	—
14	#4530	—	3	4	no	—
15	C₂⁴×C₉	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₄×C₉	—	2	4	no	—
17	C₂²×C₄×C₉	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₄×C₉	C₂×C₄	1	4	yes	—
19	C₂²×C₄×C₉	D₄	1	4	yes	—
20	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
21	C₉×C₄⋊C₄	—	2	4	no	—
22	C₉×C₂²⋊C₄	—	2	4	no	—
23	C₄²×C₉	—	2	4	no	—
24	#3667	—	2	8	no	—
25	C₂×C₉⋊C₈	—	2	4	no	—
26	#1822	—	9	1	no	Sylow
27	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
28	C₃×#117	—	2	4	no	—
29	C₂×C₃×C₄⋊C₄	C₂×D₃	1	2	yes	—
30	C₂×C₃×C₂²⋊C₄	Dic₃	1	2	yes	—
31	C₂×C₃×C₄²	Dic₃	1	2	yes	—
32	C₂×#208	—	3	4	no	—
33	#830	—	6	4	no	—
34	C₂³×C₉	—	2	2	no	—
35	C₂³×C₉	—	4	2	no	—
36	C₂³×C₉	C₂²⋊C₄	1	2	yes	—
37	C₂³×C₉	C₂²×C₄	1	1	yes	characteristic
38	C₂×C₄×C₉	—	2	2	no	—
39	C₂×C₄×C₉	—	2	8	no	—
40	C₂×C₄×C₉	—	2	4	no	—
41	C₂×C₄×C₉	—	4	4	no	—
42	C₂×C₄×C₉	C₂²⋊C₄	1	2	yes	—
43	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
44	C₂×C₄×C₉	#41	1	4	yes	—
45	C₉⋊C₈	—	4	4	no	—
46	C₂×#117	D₉	1	1	yes	characteristic
47	#407	—	9	2	no	—
48	#343	—	9	4	no	—
49	C₂⁴×C₃	C₂×Dic₃	1	1	yes	characteristic
50	C₂²×C₃×C₄	—	2	4	no	—
51	C₂²×C₃×C₄	C₂×Dic₃	1	1	yes	characteristic
52	C₂²×C₃×C₄	C₂×Dic₃	1	4	yes	—
53	C₂²×C₃×C₄	#67	1	4	yes	—
54	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
55	C₃×C₄⋊C₄	—	2	4	no	—
56	C₃×C₂²⋊C₄	—	2	4	no	—
57	C₃×C₄²	—	2	4	no	—
58	#208	—	6	8	no	—
59	C₂×C₃⋊C₈	—	6	4	no	—
60	C₂²×C₉	—	2	2	no	—
61	C₂²×C₉	—	2	2	no	—
62	C₂²×C₉	—	2	4	no	—
63	C₂²×C₉	—	4	4	no	—
64	C₂²×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
65	C₂²×C₉	#117	1	2	yes	—
66	C₄×C₉	—	2	2	no	—
67	C₄×C₉	—	4	4	no	—
68	C₄×C₉	#123	1	4	yes	—
69	C₂³×C₄	C₂×D₉	1	1	yes	characteristic
70	C₂×M₁₆	—	9	4	no	—
71	#117	—	2	4	no	—
72	C₂×C₄⋊C₄	C₂×D₉	1	2	yes	—
73	C₂×C₂²⋊C₄	Dic₉	1	2	yes	—
74	C₂×C₄²	Dic₉	1	2	yes	—
75	C₂²⋊C₈	—	18	4	no	—
76	C₂³×C₃	—	2	2	no	—
77	C₂³×C₃	—	4	2	no	—
78	C₂³×C₃	#217	1	2	yes	—
79	C₂³×C₃	C₂²×Dic₃	1	1	yes	characteristic
80	C₂×C₃×C₄	—	2	2	no	—
81	C₂×C₃×C₄	—	2	8	no	—
82	C₂×C₃×C₄	—	2	4	no	—
83	C₂×C₃×C₄	—	4	4	no	—
84	C₂×C₃×C₄	#217	1	2	yes	—
85	C₂×C₃×C₄	#235	1	4	yes	—
86	C₂×C₃×C₄	C₂×#67	1	2	yes	—
87	C₃⋊C₈	—	12	4	no	—
88	C₂×C₉	—	2	2	no	—
89	C₂×C₉	—	4	2	no	—
90	C₂×C₉	#381	1	1	yes	characteristic
91	C₂×C₉	#413	1	2	yes	—
92	C₂⁴	C₂×Dic₉	1	1	yes	characteristic
93	C₂²×C₄	—	2	4	no	—
94	C₂²×C₄	C₂×Dic₉	1	1	yes	characteristic
95	C₂²×C₄	C₂×Dic₉	1	4	yes	—
96	C₂²×C₄	#611	1	4	yes	—
97	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
98	M₁₆	—	18	8	no	—
99	C₂×C₈	—	18	4	no	—
100	C₄⋊C₄	—	2	4	no	—
101	C₂²⋊C₄	—	2	4	no	—
102	C₄²	—	2	4	no	—
103	C₂²×C₃	—	2	2	no	—
104	C₂²×C₃	—	2	2	no	—
105	C₂²×C₃	—	2	4	no	—
106	C₂²×C₃	—	4	4	no	—
107	C₂²×C₃	#926	1	2	yes	—
108	C₂²×C₃	C₂×#217	1	1	yes	characteristic
109	C₃×C₄	—	2	2	no	—
110	C₃×C₄	—	4	4	no	—
111	C₃×C₄	#929	1	4	yes	—
112	C₉	#1822	1	1	yes	characteristic, complemented, Sylow
113	C₂³	—	2	2	no	—
114	C₂³	—	4	2	no	—
115	C₂³	#3676	1	2	yes	—
116	C₂³	C₂²×Dic₉	1	1	yes	characteristic
117	C₂×C₄	—	2	2	no	—
118	C₂×C₄	—	2	8	no	—
119	C₂×C₄	—	2	4	no	—
120	C₂×C₄	—	4	4	no	—
121	C₂×C₄	#3676	1	2	yes	—
122	C₂×C₄	#3697	1	4	yes	—
123	C₂×C₄	C₂×#611	1	2	yes	—
124	C₈	—	36	4	no	—
125	C₂×C₃	—	2	2	no	—
126	C₂×C₃	—	4	2	no	—
127	C₂×C₃	#5211	1	1	yes	characteristic
128	C₂×C₃	#5237	1	2	yes	—
129	C₂²	—	2	2	no	—
130	C₂²	—	2	2	no	—
131	C₂²	—	2	4	no	—
132	C₂²	—	4	4	no	—
133	C₂²	#63488	1	2	yes	—
134	C₂²	C₂×#3676	1	1	yes	characteristic
135	C₄	—	2	2	no	—
136	C₄	—	4	4	no	—
137	C₄	#63491	1	4	yes	—
138	C₃	#71589	1	1	yes	characteristic
139	C₂	—	2	2	no	—
140	C₂	—	4	2	no	—
141	C₂	#10588891	1	1	yes	characteristic
142	C₂	#10588915	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₉×#117

C₂

yes

maximal, characteristic

#10588887

C₂

yes

maximal

#10588207

C₂

yes

maximal, complemented

#71589

—

maximal

C₂³×C₄×C₉

C₂²

yes

characteristic

C₉×#117

—

C₂×C₉×C₄⋊C₄

C₂²

yes

—

C₂×C₉×C₂²⋊C₄

C₄

yes

—

C₂×C₄²×C₉

C₄

yes

—

C₂×#3667

C₂²

yes

—

#63389

—

C₂×C₃×#117

D₃

yes

characteristic

#5207

—

#4530

—

C₂⁴×C₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₉

—

C₂²×C₄×C₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₉

C₂×C₄

yes

—

C₂²×C₄×C₉

D₄

yes

—

C₂²×C₄×C₉

C₂³

yes

characteristic

C₉×C₄⋊C₄

—

C₉×C₂²⋊C₄

—

C₄²×C₉

—

#3667

—

C₂×C₉⋊C₈

—

#1822

—

Sylow

C₂³×C₃×C₄

C₂×D₃

yes

characteristic

C₃×#117

—

C₂×C₃×C₄⋊C₄

C₂×D₃

yes

—

C₂×C₃×C₂²⋊C₄

Dic₃

yes

—

C₂×C₃×C₄²

Dic₃

yes

—

C₂×#208

—

#830

—

C₂³×C₉

—

C₂³×C₉

—

C₂³×C₉

C₂²⋊C₄

yes

—

C₂³×C₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

C₂²⋊C₄

yes

—

C₂×C₄×C₉

C₂×D₄

yes

—

C₂×C₄×C₉

#41

yes

—

C₉⋊C₈

—

C₂×#117

D₉

yes

characteristic

#407

—

#343

—

C₂⁴×C₃

C₂×Dic₃

yes

characteristic

C₂²×C₃×C₄

—

C₂²×C₃×C₄

C₂×Dic₃

yes

characteristic

C₂²×C₃×C₄

C₂×Dic₃

yes

—

C₂²×C₃×C₄

#67

yes

—

C₂²×C₃×C₄

C₂²×D₃

yes

characteristic

C₃×C₄⋊C₄

—

C₃×C₂²⋊C₄

—

C₃×C₄²

—

#208

—

C₂×C₃⋊C₈

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₉

#117

yes

—

C₄×C₉

—

C₄×C₉

—

C₄×C₉

#123

yes

—

C₂³×C₄

C₂×D₉

yes

characteristic

C₂×M₁₆

—

#117

—

C₂×C₄⋊C₄

C₂×D₉

yes

—

C₂×C₂²⋊C₄

Dic₉

yes

—

C₂×C₄²

Dic₉

yes

—

C₂²⋊C₈

—

C₂³×C₃

—

C₂³×C₃

—

C₂³×C₃

#217

yes

—

C₂³×C₃

C₂²×Dic₃

yes

characteristic

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

#217

yes

—

C₂×C₃×C₄

#235

yes

—

C₂×C₃×C₄

C₂×#67

yes

—

C₃⋊C₈

—

C₂×C₉

—

C₂×C₉

—

C₂×C₉

#381

yes

characteristic

C₂×C₉

#413

yes

—

C₂⁴

C₂×Dic₉

yes

characteristic

C₂²×C₄

—

C₂²×C₄

C₂×Dic₉

yes

characteristic

C₂²×C₄

C₂×Dic₉

yes

—

C₂²×C₄

#611

yes

—

C₂²×C₄

C₂²×D₉

yes

characteristic

M₁₆

—

C₂×C₈

—

100

C₄⋊C₄

—

101

C₂²⋊C₄

—

102

C₄²

—

103

C₂²×C₃

—

104

C₂²×C₃

—

105

C₂²×C₃

—

106

C₂²×C₃

—

107

C₂²×C₃

#926

yes

—

108

C₂²×C₃

C₂×#217

yes

characteristic

109

C₃×C₄

—

110

C₃×C₄

—

111

C₃×C₄

#929

yes

—

112

C₉

#1822

yes

characteristic, complemented, Sylow

113

C₂³

—

114

C₂³

—

115

C₂³

#3676

yes

—

116

C₂³

C₂²×Dic₉

yes

characteristic

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

#3676

yes

—

122

C₂×C₄

#3697

yes

—

123

C₂×C₄

C₂×#611

yes

—

124

C₈

—

125

C₂×C₃

—

126

C₂×C₃

—

127

C₂×C₃

#5211

yes

characteristic

128

C₂×C₃

#5237

yes

—

129

C₂²

—

130

C₂²

—

131

C₂²

—

132

C₂²

—

133

C₂²

#63488

yes

—

134

C₂²

C₂×#3676

yes

characteristic

135

C₄

—

136

C₄

—

137

C₄

#63491

yes

—

138

C₃

#71589

yes

characteristic

139

C₂

—

140

C₂

—

141

C₂

#10588891

yes

characteristic

142

C₂

#10588915

yes

—

	subgroup	G/H
center	C₂²	C₂×#3676
commutator	C₂³×C₉	C₂²×C₄
Frattini	C₂²×C₃×C₄	C₂²×D₃
Fitting	C₂×C₉×#117	C₂
socle	C₂²×C₃	C₂×#217
prime radical	C₂⁴×C₃	C₂×Dic₃
cosocle	C₂²×C₄×C₉	C₂³
hypercenter	C₂×#117	D₉
hypocenter	C₉	#1822
LCS	G ▷ C₂³×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂×#117

subgroup

G/H

center

C₂²

C₂×#3676

commutator

C₂³×C₉

C₂²×C₄

Frattini

C₂²×C₃×C₄

C₂²×D₃

Fitting

C₂×C₉×#117

C₂

socle

C₂²×C₃

C₂×#217

prime radical

C₂⁴×C₃

C₂×Dic₃

cosocle

C₂²×C₄×C₉

C₂³

D₉

C₉

G ▷ C₂³×C₉ ▷ C₂×C₉ ▷ C₉

UCS

C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂×#117

N	H ≅ G/N	type
3. #10588207	C₂	semidirect
112. C₉	#1822	semidirect

H ≅ G/N

type

3. #10588207

C₂

semidirect

112. C₉

#1822

semidirect

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

subgroup	index
C₂×C₉×#117	2
#10588887	2
#10588207	2
#71589	3

subgroup

index

C₂×C₉×#117

#10588887

#10588207

#71589

Subgroups — #11785738

Conjugacy classes of subgroups

Complements

Maximal subgroups