Group #36448079 — subgroups

Subgroups — #36448079

Order 22784.

262 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 99 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	#26020005	C₂	1	1	yes	maximal, characteristic
2	#26018998	C₂	1	2	yes	maximal
3	#26018097	C₂	1	1	yes	maximal, characteristic
4	#26018080	C₂	1	2	yes	maximal
5	C₈₉×#1281	C₂	1	1	yes	maximal, characteristic
6	#19151651	C₂²	1	2	yes	—
7	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
8	#19151444	C₂²	1	1	yes	characteristic
9	#19151352	C₄	1	2	yes	—
10	#19151352	C₄	1	2	yes	—
11	#19151350	—	2	2	no	—
12	#19151348	—	2	2	no	—
13	#431×C₈₉	C₂²	1	2	yes	—
14	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
15	C₂²×#10623494	C₂×C₄	1	2	yes	—
16	C₂×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
18	C₄⋊#10623494	—	2	2	no	—
19	C₂²⋊#10623494	—	2	2	no	—
20	C₄×#10623494	—	2	2	no	—
21	C₄×#10623494	D₄	1	1	yes	characteristic
22	C₄×#10623494	D₄	1	1	yes	characteristic
23	C₄×#10623494	Q₈	1	2	yes	—
24	#15667919	—	2	2	no	—
25	C₂²×C₈×C₈₉	C₂×C₄	1	2	yes	—
26	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
27	C₄⋊C₈×C₈₉	—	2	2	no	—
28	C₂²⋊C₈×C₈₉	—	2	2	no	—
29	#97×C₈₉	—	2	2	no	—
30	C₄×C₈×C₈₉	—	2	2	no	—
31	C₂²×Dic₈₉	—	2	1	no	—
32	C₂²×Dic₈₉	—	2	1	no	—
33	C₂×#10623494	—	2	2	no	—
34	C₂×#10623494	—	2	2	no	—
35	C₂×#10623494	—	4	2	no	—
36	C₂×#10623494	C₄⋊C₄	1	2	yes	—
37	C₂×#10623494	C₄⋊C₄	1	2	yes	—
38	C₄×Dic₈₉	—	2	2	no	—
39	C₄×Dic₈₉	—	2	2	no	—
40	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
41	C₂²×C₄×C₈₉	#41	1	2	yes	—
42	C₂×C₈×C₈₉	—	2	2	no	—
43	C₂×C₈×C₈₉	—	2	2	no	—
44	C₂×C₈×C₈₉	—	2	2	no	—
45	C₂×C₈×C₈₉	—	4	2	no	—
46	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
47	C₄²×C₈₉	C₂×Q₈	1	1	yes	characteristic
48	C₄²×C₈₉	#41	1	2	yes	—
49	C₂³×C₈₉	#117	1	1	yes	characteristic
50	C₂×C₄×C₈₉	—	4	2	no	—
51	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
52	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
53	C₂×C₄×C₈₉	#124	1	2	yes	—
54	C₂×C₄×C₈₉	#125	1	2	yes	—
55	C₂×C₄×C₈₉	#131	1	2	yes	—
56	C₂×C₄×C₈₉	#131	1	2	yes	—
57	C₂×Dic₈₉	—	4	2	no	—
58	C₂×Dic₈₉	—	4	2	no	—
59	C₂×Dic₈₉	—	4	1	no	—
60	C₂×Dic₈₉	—	4	1	no	—
61	C₈×C₈₉	—	4	2	no	—
62	C₈×C₈₉	—	8	2	no	—
63	#10623494	—	2	2	no	—
64	#10623494	—	2	2	no	—
65	#10623494	—	8	2	no	—
66	C₂²×C₈₉	—	2	2	no	—
67	C₂²×C₈₉	#382	1	1	yes	characteristic
68	C₂²×C₈₉	#433	1	1	yes	characteristic
69	C₂²×C₈₉	#433	1	1	yes	characteristic
70	C₄×C₈₉	—	2	2	no	—
71	C₄×C₈₉	—	2	2	no	—
72	C₄×C₈₉	#424	1	2	yes	—
73	C₄×C₈₉	#433	1	2	yes	—
74	Dic₈₉	—	8	1	no	—
75	Dic₈₉	—	8	1	no	—
76	#8782	—	89	1	no	maximal, Sylow
77	C₂×C₈₉	—	2	1	no	—
78	C₂×C₈₉	—	2	1	no	—
79	C₂×C₈₉	#1832	1	1	yes	characteristic
80	C₂×C₈₉	#1833	1	2	yes	—
81	#1746	—	89	1	no	—
82	#1564	—	89	2	no	—
83	#1281	—	89	1	no	—
84	#1281	D₈₉	1	1	yes	characteristic
85	#1274	—	89	2	no	—
86	C₈₉	#8782	1	1	yes	characteristic, complemented, Sylow
87	#431	—	89	2	no	—
88	#431	C₂×D₈₉	1	2	yes	—
89	C₂×#97	C₂×D₈₉	1	1	yes	characteristic
90	C₂×C₄×C₈	—	89	1	no	—
91	#376	—	89	1	no	—
92	#336	—	89	2	no	—
93	#336	—	89	2	no	—
94	#335	—	178	2	no	—
95	#334	—	178	2	no	—
96	C₂²×C₈	—	89	2	no	—
97	C₂²×C₈	C₄×D₈₉	1	2	yes	—
98	C₂×C₄²	—	89	1	no	—
99	C₂×C₄²	—	89	1	no	—
100	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
101	C₄⋊C₈	—	2	2	no	—
102	C₄⋊C₈	—	178	2	no	—
103	C₂²⋊C₈	—	2	2	no	—
104	C₂²⋊C₈	—	178	2	no	—
105	#97	—	2	2	no	—
106	C₄×C₈	—	2	2	no	—
107	C₄×C₈	—	89	1	no	—
108	C₄×C₈	—	89	1	no	—
109	C₄×C₈	—	89	2	no	—
110	C₄×C₈	—	178	2	no	—
111	#95	—	178	2	no	—
112	C₂²×C₄	—	178	1	no	—
113	C₂²×C₄	—	178	1	no	—
114	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
115	C₂²×C₄	#13083574	1	2	yes	—
116	C₂×C₈	—	2	2	no	—
117	C₂×C₈	—	2	2	no	—
118	C₂×C₈	—	2	2	no	—
119	C₂×C₈	—	4	2	no	—
120	C₂×C₈	—	89	2	no	—
121	C₂×C₈	—	89	2	no	—
122	C₂×C₈	—	356	2	no	—
123	C₂×C₈	—	178	2	no	—
124	C₂×C₈	—	178	2	no	—
125	C₄²	—	178	2	no	—
126	C₄²	—	178	2	no	—
127	C₄²	D₄×D₈₉	1	1	yes	characteristic
128	C₄²	Q₈×D₈₉	1	1	yes	characteristic
129	C₄²	#13083573	1	2	yes	—
130	C₂³	#15667969	1	1	yes	characteristic
131	C₂×C₄	—	4	2	no	—
132	C₂×C₄	—	356	2	no	—
133	C₂×C₄	—	356	2	no	—
134	C₂×C₄	—	356	1	no	—
135	C₂×C₄	—	356	1	no	—
136	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
137	C₂×C₄	#15667968	1	1	yes	characteristic
138	C₂×C₄	#15667998	1	2	yes	—
139	C₂×C₄	#15668002	1	2	yes	—
140	C₂×C₄	#15668018	1	2	yes	—
141	C₂×C₄	#15668020	1	2	yes	—
142	C₈	—	4	2	no	—
143	C₈	—	8	2	no	—
144	C₈	—	178	2	no	—
145	C₈	—	178	2	no	—
146	C₈	—	712	2	no	—
147	C₂²	—	2	2	no	—
148	C₂²	#19151462	1	1	yes	characteristic
149	C₂²	#19151657	1	1	yes	characteristic
150	C₂²	#19151660	1	1	yes	characteristic
151	C₄	—	2	2	no	—
152	C₄	—	2	2	no	—
153	C₄	—	712	1	no	—
154	C₄	—	712	1	no	—
155	C₄	#19151623	1	2	yes	—
156	C₄	#19151656	1	2	yes	—
157	C₂	—	2	1	no	—
158	C₂	—	2	1	no	—
159	C₂	#26020370	1	1	yes	characteristic
160	C₂	#26020373	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#26020005

C₂

yes

maximal, characteristic

#26018998

C₂

yes

maximal

#26018097

C₂

yes

maximal, characteristic

#26018080

C₂

yes

maximal

C₈₉×#1281

C₂

yes

maximal, characteristic

#19151651

C₂²

yes

—

C₂×C₄×#10623494

C₂²

yes

characteristic

#19151444

C₂²

yes

characteristic

#19151352

C₄

yes

—

#19151352

C₄

yes

—

#19151350

—

#19151348

—

#431×C₈₉

C₂²

yes

—

C₂×#97×C₈₉

C₂²

yes

characteristic

C₂²×#10623494

C₂×C₄

yes

—

C₂×C₄×Dic₈₉

C₂×C₄

yes

characteristic

C₂×C₄×Dic₈₉

C₂×C₄

yes

—

—

—

D₄

yes

characteristic

C₄×#10623494

D₄

yes

characteristic

C₄×#10623494

Q₈

yes

—

#15667919

—

C₂²×C₈×C₈₉

C₂×C₄

yes

—

C₂×C₄²×C₈₉

C₂³

yes

characteristic

C₄⋊C₈×C₈₉

—

C₂²⋊C₈×C₈₉

—

#97×C₈₉

—

C₄×C₈×C₈₉

—

C₂²×Dic₈₉

—

C₂²×Dic₈₉

—

—

—

—

C₄⋊C₄

yes

—

C₂×#10623494

C₄⋊C₄

yes

—

C₄×Dic₈₉

—

C₄×Dic₈₉

—

C₂²×C₄×C₈₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₈₉

#41

yes

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₄²×C₈₉

C₂×D₄

yes

characteristic

C₄²×C₈₉

C₂×Q₈

yes

characteristic

C₄²×C₈₉

#41

yes

—

C₂³×C₈₉

#117

yes

characteristic

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

C₂×C₄⋊C₄

yes

C₂×C₄×C₈₉

yes

C₂×C₄×C₈₉

yes

—

C₂×C₄×C₈₉

#125

yes

—

C₂×C₄×C₈₉

#131

yes

—

C₂×C₄×C₈₉

#131

yes

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₈×C₈₉

—

C₈×C₈₉

—

#10623494

—

#10623494

—

#10623494

—

C₂²×C₈₉

—

C₂²×C₈₉

yes

C₂²×C₈₉

yes

C₂²×C₈₉

yes

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

#424

yes

—

C₄×C₈₉

#433

yes

—

Dic₈₉

—

Dic₈₉

—

#8782

—

maximal, Sylow

C₂×C₈₉

—

C₂×C₈₉

—

C₂×C₈₉

#1832

yes

characteristic

C₂×C₈₉

#1833

yes

—

—

—

—

D₈₉

yes

characteristic

#1274

—

C₈₉

#8782

yes

characteristic, complemented, Sylow

#431

—

#431

C₂×D₈₉

yes

—

C₂×#97

C₂×D₈₉

yes

characteristic

C₂×C₄×C₈

—

—

—

—

—

178

—

#334

—

178

—

C₂²×C₈

—

C₂²×C₈

C₄×D₈₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

100

C₂×C₄²

C₂²×D₈₉

yes

characteristic

101

C₄⋊C₈

—

102

C₄⋊C₈

—

178

—

103

C₂²⋊C₈

—

104

C₂²⋊C₈

—

178

—

105

#97

—

106

C₄×C₈

—

107

C₄×C₈

—

108

C₄×C₈

—

109

C₄×C₈

—

110

C₄×C₈

—

178

—

111

#95

—

178

—

112

C₂²×C₄

—

178

—

113

C₂²×C₄

—

178

—

114

C₂²×C₄

C₂×C₄×D₈₉

yes

characteristic

115

C₂²×C₄

#13083574

yes

—

116

C₂×C₈

—

117

C₂×C₈

—

118

C₂×C₈

—

119

C₂×C₈

—

120

C₂×C₈

—

121

C₂×C₈

—

122

C₂×C₈

—

356

—

123

C₂×C₈

—

178

—

124

C₂×C₈

—

178

—

125

C₄²

—

178

—

126

C₄²

—

178

—

127

C₄²

D₄×D₈₉

yes

characteristic

128

C₄²

Q₈×D₈₉

yes

characteristic

129

C₄²

#13083573

yes

—

130

C₂³

#15667969

yes

characteristic

131

C₂×C₄

—

132

C₂×C₄

—

356

—

133

C₂×C₄

—

356

—

134

C₂×C₄

—

356

—

135

C₂×C₄

—

356

—

136

C₂×C₄

C₄⋊C₄×D₈₉

yes

characteristic

137

C₂×C₄

#15667968

yes

characteristic

138

C₂×C₄

#15667998

yes

—

139

C₂×C₄

#15668002

yes

—

140

C₂×C₄

#15668018

yes

—

141

C₂×C₄

#15668020

yes

—

142

C₈

—

143

C₈

—

144

C₈

—

178

—

145

C₈

—

178

—

146

C₈

—

712

—

147

C₂²

—

148

C₂²

#19151462

yes

characteristic

149

C₂²

#19151657

yes

characteristic

150

C₂²

#19151660

yes

characteristic

151

C₄

—

152

C₄

—

153

C₄

—

712

—

154

C₄

—

712

—

155

C₄

#19151623

yes

—

156

C₄

#19151656

yes

—

157

C₂

—

158

C₂

—

159

C₂

#26020370

yes

characteristic

160

C₂

#26020373

yes

—

	subgroup	G/H
center	C₂×C₄	#15667968
commutator	C₂²×C₄×C₈₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₈₉×#1281	C₂
socle	C₂²×C₈₉	#382
prime radical	C₂³×C₈₉	#117
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	#1281	D₈₉
hypocenter	C₈₉	#8782
LCS	G ▷ C₂²×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1281

subgroup

G/H

center

C₂×C₄

#15667968

commutator

C₂²×C₄×C₈₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₈₉

Fitting

C₈₉×#1281

C₂

C₂²×C₈₉

C₂³×C₈₉

C₂×C₄²×C₈₉

C₂³

D₈₉

C₈₉

G ▷ C₂²×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1281

N	H ≅ G/N	type
86. C₈₉	#8782	semidirect

H ≅ G/N

type

86. C₈₉

#8782

semidirect

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

subgroup	index
#26020005	2
#26018998	2
#26018097	2
#26018080	2
C₈₉×#1281	2
#8782	89

subgroup

index

C₈₉×#1281

Subgroups — #36448079

Conjugacy classes of subgroups

Complements

Maximal subgroups