Group #11777918 — subgroups

Subgroups — #11777918

Order 1152.

222 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 84 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	#10588509	C₂	1	2	yes	maximal
2	C₄×Dic₃₆	C₂	1	1	yes	maximal, characteristic
3	C₉×#334	C₂	1	1	yes	maximal, characteristic
4	#10588160	C₂	1	2	yes	maximal
5	#10588132	C₂	1	1	yes	maximal, characteristic
6	#68524	—	3	1	no	maximal
7	C₂×Dic₃₆	C₄	1	1	yes	characteristic
8	C₄×Dic₁₈	C₂²	1	2	yes	—
9	C₉×C₄⋊C₈	C₂²	1	2	yes	—
10	C₄×C₈×C₉	C₂²	1	1	yes	characteristic
11	#63378	C₄	1	1	yes	characteristic
12	#63376	C₄	1	2	yes	—
13	#63375	—	2	2	no	—
14	Dic₉⋊C₈	—	2	2	no	—
15	C₄×C₉⋊C₈	C₂²	1	1	yes	characteristic
16	C₄×C₉⋊C₈	C₂²	1	1	yes	characteristic
17	#4831	—	3	2	no	—
18	C₄×Dic₁₂	—	3	1	no	—
19	C₃×#334	D₃	1	1	yes	characteristic
20	#4484	—	3	2	no	—
21	#4455	—	3	1	no	—
22	C₂×Dic₁₈	C₂×C₄	1	2	yes	—
23	C₂×C₈×C₉	—	2	2	no	—
24	C₂×C₈×C₉	C₂×C₄	1	1	yes	characteristic
25	C₂×C₈×C₉	C₂×C₄	1	1	yes	characteristic
26	C₄²×C₉	C₂³	1	1	yes	characteristic
27	C₄⋊Dic₉	C₂×C₄	1	2	yes	—
28	Dic₉⋊C₄	—	2	2	no	—
29	C₄×Dic₉	—	2	2	no	—
30	C₂×C₉⋊C₈	—	2	1	no	—
31	C₂×C₉⋊C₈	D₄	1	2	yes	—
32	Dic₃₆	—	2	2	no	—
33	#1593	—	9	1	no	Sylow
34	C₂×Dic₁₂	—	3	1	no	—
35	C₄×Dic₆	—	3	2	no	—
36	C₃×C₄⋊C₈	C₂×D₃	1	2	yes	—
37	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
38	#818	—	3	1	no	—
39	#816	—	3	2	no	—
40	#815	—	6	2	no	—
41	Dic₃⋊C₈	—	6	2	no	—
42	C₄×C₃⋊C₈	—	3	1	no	—
43	C₄×C₃⋊C₈	—	3	1	no	—
44	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
45	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
46	C₂×C₄×C₉	#41	1	1	yes	characteristic
47	C₂×Dic₉	—	2	2	no	—
48	C₂×Dic₉	—	2	2	no	—
49	Dic₁₈	—	2	2	no	—
50	Dic₁₈	—	2	2	no	—
51	C₈×C₉	—	2	1	no	—
52	C₈×C₉	—	4	2	no	—
53	C₈×C₉	M₁₆	1	2	yes	—
54	C₉⋊C₈	—	2	2	no	—
55	C₉⋊C₈	—	4	1	no	—
56	#446	—	9	2	no	—
57	C₄×Q₁₆	—	9	1	no	—
58	#334	D₉	1	1	yes	characteristic
59	Q₈⋊C₈	—	9	2	no	—
60	#322	—	9	1	no	—
61	C₂×Dic₆	—	3	2	no	—
62	C₂×C₃×C₈	—	2	2	no	—
63	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
64	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
65	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
66	C₄⋊Dic₃	—	3	2	no	—
67	Dic₃⋊C₄	—	6	2	no	—
68	C₄×Dic₃	—	6	2	no	—
69	C₂×C₃⋊C₈	—	3	2	no	—
70	C₂×C₃⋊C₈	—	6	1	no	—
71	Dic₁₂	—	6	2	no	—
72	C₂²×C₉	C₄×D₄	1	1	yes	characteristic
73	C₄×C₉	—	2	1	no	—
74	C₄×C₉	C₂×M₁₆	1	1	yes	characteristic
75	C₄×C₉	#131	1	1	yes	characteristic
76	C₄×C₉	#137	1	2	yes	—
77	Dic₉	—	4	2	no	—
78	Dic₉	—	4	2	no	—
79	C₂×Q₁₆	—	9	1	no	—
80	C₄×Q₈	—	9	2	no	—
81	#107	—	9	1	no	—
82	C₄⋊C₈	—	18	2	no	—
83	C₄⋊C₈	C₂×D₉	1	2	yes	—
84	#103	—	9	2	no	—
85	#97	—	18	2	no	—
86	C₄×C₈	—	9	1	no	—
87	C₄×C₈	—	9	1	no	—
88	C₄×C₈	C₂×D₉	1	1	yes	characteristic
89	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
90	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
91	C₂×C₃×C₄	#239	1	1	yes	characteristic
92	C₂×Dic₃	—	6	2	no	—
93	C₂×Dic₃	—	6	2	no	—
94	Dic₆	—	6	2	no	—
95	Dic₆	—	6	2	no	—
96	C₃×C₈	—	2	1	no	—
97	C₃×C₈	—	4	2	no	—
98	C₃×C₈	ΓL(1,𝔽₂₅)	1	2	yes	—
99	C₃⋊C₈	—	6	2	no	—
100	C₃⋊C₈	—	12	1	no	—
101	C₂×C₉	#436	1	1	yes	characteristic
102	C₂×C₉	#441	1	1	yes	characteristic
103	C₂×C₉	#444	1	1	yes	characteristic
104	C₂×Q₈	—	9	2	no	—
105	Q₁₆	—	18	2	no	—
106	C₂×C₈	—	2	2	no	—
107	C₂×C₈	—	9	2	no	—
108	C₂×C₈	—	18	1	no	—
109	C₂×C₈	C₄×D₉	1	1	yes	characteristic
110	C₂×C₈	C₄×D₉	1	1	yes	characteristic
111	C₄⋊C₄	—	9	2	no	—
112	C₄⋊C₄	—	18	2	no	—
113	C₄²	—	18	2	no	—
114	C₄²	C₂²×D₉	1	1	yes	characteristic
115	C₂²×C₃	#893	1	1	yes	characteristic
116	C₃×C₄	—	2	1	no	—
117	C₃×C₄	C₂×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
118	C₃×C₄	#907	1	1	yes	characteristic
119	C₃×C₄	#915	1	2	yes	—
120	Dic₃	—	12	2	no	—
121	Dic₃	—	12	2	no	—
122	C₉	#1593	1	1	yes	characteristic, complemented, Sylow
123	Q₈	—	18	2	no	—
124	Q₈	—	18	2	no	—
125	C₂×C₄	—	18	2	no	—
126	C₂×C₄	—	18	2	no	—
127	C₂×C₄	C₂×C₄×D₉	1	1	yes	characteristic
128	C₂×C₄	D₄×D₉	1	1	yes	characteristic
129	C₂×C₄	#3701	1	1	yes	characteristic
130	C₈	—	2	1	no	—
131	C₈	—	4	2	no	—
132	C₈	—	18	2	no	—
133	C₈	—	36	1	no	—
134	C₈	#3663	1	2	yes	—
135	C₂×C₃	#4838	1	1	yes	characteristic
136	C₂×C₃	#4853	1	1	yes	characteristic
137	C₂×C₃	#4894	1	1	yes	characteristic
138	C₂²	#63455	1	1	yes	characteristic
139	C₄	—	2	1	no	—
140	C₄	—	36	2	no	—
141	C₄	—	36	2	no	—
142	C₄	C₂×#3663	1	1	yes	characteristic
143	C₄	#63469	1	1	yes	characteristic
144	C₄	#63477	1	2	yes	—
145	C₃	#68524	1	1	yes	characteristic
146	C₂	#10588522	1	1	yes	characteristic
147	C₂	#10588533	1	1	yes	characteristic
148	C₂	#10588574	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#10588509

C₂

yes

maximal

C₄×Dic₃₆

C₂

yes

maximal, characteristic

C₉×#334

C₂

yes

maximal, characteristic

#10588160

C₂

yes

maximal

#10588132

C₂

yes

maximal, characteristic

#68524

—

maximal

C₂×Dic₃₆

C₄

yes

characteristic

C₄×Dic₁₈

C₂²

yes

—

C₉×C₄⋊C₈

C₂²

yes

—

C₄×C₈×C₉

C₂²

yes

characteristic

#63378

C₄

yes

characteristic

#63376

C₄

yes

—

#63375

—

Dic₉⋊C₈

—

C₄×C₉⋊C₈

C₂²

yes

characteristic

C₄×C₉⋊C₈

C₂²

yes

characteristic

#4831

—

C₄×Dic₁₂

—

C₃×#334

D₃

yes

characteristic

#4484

—

#4455

—

C₂×Dic₁₈

C₂×C₄

yes

—

C₂×C₈×C₉

—

C₂×C₈×C₉

C₂×C₄

yes

characteristic

C₂×C₈×C₉

C₂×C₄

yes

characteristic

C₄²×C₉

C₂³

yes

characteristic

C₄⋊Dic₉

C₂×C₄

yes

—

Dic₉⋊C₄

—

C₄×Dic₉

—

C₂×C₉⋊C₈

—

C₂×C₉⋊C₈

D₄

yes

—

Dic₃₆

—

#1593

—

Sylow

C₂×Dic₁₂

—

C₄×Dic₆

—

C₃×C₄⋊C₈

C₂×D₃

yes

—

C₃×C₄×C₈

C₂×D₃

yes

—

—

—

Dic₃⋊C₈

—

C₄×C₃⋊C₈

—

C₄×C₃⋊C₈

—

C₂×C₄×C₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₉

C₂×D₄

yes

characteristic

C₂×C₄×C₉

#41

yes

characteristic

C₂×Dic₉

—

C₂×Dic₉

—

Dic₁₈

—

Dic₁₈

—

C₈×C₉

—

C₈×C₉

—

C₈×C₉

M₁₆

yes

—

C₉⋊C₈

—

C₉⋊C₈

—

#446

—

C₄×Q₁₆

—

#334

D₉

yes

characteristic

Q₈⋊C₈

—

#322

—

C₂×Dic₆

—

C₂×C₃×C₈

—

C₂×C₃×C₈

C₄×D₃

yes

characteristic

C₂×C₃×C₈

C₄×D₃

yes

characteristic

C₃×C₄²

C₂²×D₃

yes

characteristic

C₄⋊Dic₃

—

Dic₃⋊C₄

—

C₄×Dic₃

—

C₂×C₃⋊C₈

—

C₂×C₃⋊C₈

—

Dic₁₂

—

C₂²×C₉

C₄×D₄

yes

characteristic

C₄×C₉

—

C₄×C₉

C₂×M₁₆

yes

C₄×C₉

yes

C₄×C₉

yes

—

Dic₉

—

Dic₉

—

C₂×Q₁₆

—

C₄×Q₈

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₉

yes

—

#103

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₉

yes

characteristic

C₂×C₃×C₄

C₂×C₄×D₃

yes

characteristic

C₂×C₃×C₄

D₃×D₄

yes

characteristic

C₂×C₃×C₄

#239

yes

characteristic

C₂×Dic₃

—

C₂×Dic₃

—

Dic₆

—

Dic₆

—

C₃×C₈

—

C₃×C₈

—

C₃×C₈

ΓL(1,𝔽₂₅)

yes

—

C₃⋊C₈

—

100

C₃⋊C₈

—

101

C₂×C₉

#436

yes

characteristic

102

C₂×C₉

#441

yes

characteristic

103

C₂×C₉

#444

yes

characteristic

104

C₂×Q₈

—

105

Q₁₆

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

C₄×D₉

yes

characteristic

110

C₂×C₈

C₄×D₉

yes

characteristic

111

C₄⋊C₄

—

112

C₄⋊C₄

—

113

C₄²

—

114

C₄²

C₂²×D₉

yes

characteristic

115

C₂²×C₃

#893

yes

characteristic

116

C₃×C₄

—

117

C₃×C₄

C₂×ΓL(1,𝔽₂₅)

yes

characteristic

118

C₃×C₄

#907

yes

characteristic

119

C₃×C₄

#915

yes

—

120

Dic₃

—

121

Dic₃

—

122

C₉

#1593

yes

characteristic, complemented, Sylow

123

Q₈

—

124

Q₈

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

C₂×C₄×D₉

yes

characteristic

128

C₂×C₄

D₄×D₉

yes

characteristic

129

C₂×C₄

#3701

yes

characteristic

130

C₈

—

131

C₈

—

132

C₈

—

133

C₈

—

134

C₈

#3663

yes

—

135

C₂×C₃

#4838

yes

characteristic

136

C₂×C₃

#4853

yes

characteristic

137

C₂×C₃

#4894

yes

characteristic

138

C₂²

#63455

yes

characteristic

139

C₄

—

140

C₄

—

141

C₄

—

142

C₄

C₂×#3663

yes

characteristic

143

C₄

#63469

yes

characteristic

144

C₄

#63477

yes

—

145

C₃

#68524

yes

characteristic

146

C₂

#10588522

yes

characteristic

147

C₂

#10588533

yes

characteristic

148

C₂

#10588574

yes

characteristic

	subgroup	G/H
center	C₂×C₄	D₄×D₉
commutator	C₂×C₄×C₉	C₂²×C₄
Frattini	C₃×C₄²	C₂²×D₃
Fitting	C₉×#334	C₂
socle, prime radical	C₂²×C₃	#893
cosocle	C₄²×C₉	C₂³
hypercenter	#334	D₉
hypocenter	C₉	#1593
LCS	G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ #334

subgroup

G/H

center

C₂×C₄

D₄×D₉

commutator

C₂×C₄×C₉

C₂²×C₄

Frattini

C₃×C₄²

C₂²×D₃

C₂

C₂²×C₃

C₄²×C₉

C₂³

D₉

C₉

G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉

UCS

C₁ ◁ C₂×C₄ ◁ C₄² ◁ #334

N	H ≅ G/N	type
122. C₉	#1593	semidirect

H ≅ G/N

type

122. C₉

#1593

semidirect

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

subgroup	index
#10588509	2
C₄×Dic₃₆	2
C₉×#334	2
#10588160	2
#10588132	2
#68524	3

subgroup

index

C₄×Dic₃₆

Subgroups — #11777918

Conjugacy classes of subgroups

Complements

Maximal subgroups