Group #36469432 — subgroups

Subgroups — #36469432

Order 22784.

358 conjugacy classes of subgroups; only the 195 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 195 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×#19151374	C₂	1	1	yes	maximal, characteristic
2	#26019938	C₂	1	1	yes	maximal, characteristic
3	#26018329	C₂	1	4	yes	maximal
4	C₂×C₄×C₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic
5	C₂²×#13083549	C₂²	1	2	yes	—
6	C₂×#15667923	C₄	1	1	yes	characteristic
7	C₂×#15667922	C₄	1	2	yes	—
8	C₂×C₈×Dic₈₉	C₂²	1	2	yes	—
9	#19151444	C₄	1	1	yes	characteristic
10	#19151374	C₄	1	4	yes	complemented
11	C₂²×C₁₆×C₈₉	C₂²	1	2	yes	—
12	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
13	C₄×C₁₆×C₈₉	C₄	1	4	yes	complemented
14	C₂²×#10623494	C₂×C₄	1	2	yes	—
15	C₂×C₄×Dic₈₉	C₂×C₄	1	2	yes	—
16	C₂×#13083549	—	2	4	no	—
17	C₂×#13083549	C₂×C₄	1	4	yes	—
18	#15667923	C₈	1	4	yes	—
19	#15667922	—	2	4	no	—
20	C₈×Dic₈₉	—	2	4	no	—
21	#15667919	C₈	1	4	yes	—
22	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
24	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
25	C₂×C₁₆×C₈₉	—	2	4	no	—
26	C₂×C₁₆×C₈₉	C₂×C₄	1	4	yes	—
27	C₄×C₈×C₈₉	C₂×C₄	1	2	yes	—
28	C₄×C₈×C₈₉	C₂×C₄	1	2	yes	—
29	C₂²×Dic₈₉	C₂×C₈	1	4	yes	—
30	C₂×#10623494	—	2	2	no	—
31	C₂×#10623494	—	2	2	no	—
32	C₂×#10623494	C₂×C₈	1	4	yes	—
33	C₄×Dic₈₉	—	2	2	no	—
34	C₄×Dic₈₉	—	2	2	no	—
35	#13083549	—	2	4	no	—
36	C₂²×C₄×C₈₉	C₂×C₈	1	2	yes	—
37	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
38	C₂×C₈×C₈₉	C₄²	1	2	yes	—
39	C₂×C₈×C₈₉	M₁₆	1	4	yes	—
40	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
41	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
42	C₂×C₈×C₈₉	#41	1	4	yes	—
43	C₄²×C₈₉	C₄²	1	2	yes	—
44	C₄²×C₈₉	C₂×C₈	1	2	yes	—
45	C₁₆×C₈₉	—	2	4	no	—
46	C₂³×C₈₉	C₂²×C₈	1	1	yes	characteristic
47	C₂×C₄×C₈₉	—	2	4	no	—
48	C₂×C₄×C₈₉	C₄×C₈	1	4	yes	—
49	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
50	C₂×C₄×C₈₉	#117	1	2	yes	—
51	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
52	C₂×C₄×C₈₉	C₂×M₁₆	1	2	yes	—
53	C₂×Dic₈₉	—	2	4	no	—
54	C₂×Dic₈₉	—	2	8	no	—
55	C₈×C₈₉	#97	1	4	yes	—
56	C₈×C₈₉	#117	1	2	yes	—
57	C₈×C₈₉	#117	1	2	yes	—
58	#10623494	—	2	4	no	—
59	C₂²×C₈₉	C₂×C₄×C₈	1	1	yes	characteristic
60	C₂²×C₈₉	#431	1	2	yes	—
61	C₂²×C₈₉	#504	1	4	yes	—
62	C₄×C₈₉	—	2	4	no	—
63	C₄×C₈₉	#376	1	1	yes	characteristic
64	C₄×C₈₉	C₂×#97	1	1	yes	characteristic
65	C₄×C₈₉	#431	1	2	yes	—
66	Dic₈₉	—	4	4	no	—
67	#12592	—	89	1	no	maximal, Sylow
68	C₂×C₈₉	#1744	1	1	yes	characteristic
69	C₂×C₈₉	#2108	1	2	yes	—
70	C₂×C₈₉	#2164	1	4	yes	—
71	C₂×#346	—	89	1	no	—
72	C₂×C₄×C₁₆	D₈₉	1	1	yes	characteristic
73	#1726	—	89	1	no	—
74	#1374	—	89	4	no	—
75	C₈₉	#12592	1	1	yes	characteristic, complemented, Sylow
76	C₂²×C₁₆	—	89	2	no	—
77	C₂²×C₁₆	C₂×D₈₉	1	2	yes	—
78	C₂×#97	—	89	1	no	—
79	C₂×#97	—	89	2	no	—
80	C₂×C₄×C₈	—	89	2	no	—
81	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
82	#376	—	89	1	no	—
83	#346	—	89	4	no	—
84	C₄×C₁₆	Dic₈₉	1	4	yes	complemented
85	C₂²×C₈	—	89	2	no	—
86	C₂²×C₈	C₄×D₈₉	1	1	yes	characteristic
87	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
88	C₂×C₄²	—	89	2	no	—
89	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
90	C₂×C₁₆	—	2	4	no	—
91	C₂×C₁₆	—	89	4	no	—
92	C₂×C₁₆	—	178	4	no	—
93	C₂×C₁₆	C₂×Dic₈₉	1	4	yes	—
94	#97	—	89	4	no	—
95	#97	—	178	4	no	—
96	C₄×C₈	—	178	4	no	—
97	C₄×C₈	C₄×D₈₉	1	2	yes	—
98	C₄×C₈	C₂×Dic₈₉	1	2	yes	—
99	#95	—	89	4	no	—
100	C₂²×C₄	—	89	4	no	—
101	C₂²×C₄	C₈×D₈₉	1	2	yes	—
102	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
103	C₂×C₈	—	89	4	no	—
104	C₂×C₈	—	178	2	no	—
105	C₂×C₈	—	178	2	no	—
106	C₂×C₈	C₄×Dic₈₉	1	2	yes	—
107	C₂×C₈	#13083557	1	4	yes	—
108	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
109	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
110	C₂×C₈	#13083574	1	4	yes	—
111	C₄²	—	178	2	no	—
112	C₄²	—	178	2	no	—
113	C₄²	C₄×Dic₈₉	1	2	yes	—
114	C₄²	C₈×D₈₉	1	2	yes	—
115	C₁₆	—	2	4	no	—
116	C₁₆	—	178	4	no	—
117	C₂³	C₂×C₈×D₈₉	1	1	yes	characteristic
118	C₂×C₄	—	2	4	no	—
119	C₂×C₄	—	178	4	no	—
120	C₂×C₄	—	178	8	no	—
121	C₂×C₄	C₈×Dic₈₉	1	4	yes	—
122	C₂×C₄	C₂×C₄×Dic₈₉	1	1	yes	characteristic
123	C₂×C₄	#15667969	1	2	yes	—
124	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
125	C₂×C₄	C₂×#13083557	1	2	yes	—
126	C₈	—	178	4	no	—
127	C₈	#15667922	1	4	yes	—
128	C₈	#15667969	1	2	yes	—
129	C₈	#15667971	1	2	yes	—
130	C₂²	C₂×C₈×Dic₈₉	1	1	yes	characteristic
131	C₂²	#19151649	1	2	yes	—
132	C₂²	#19152014	1	4	yes	—
133	C₄	—	2	4	no	—
134	C₄	—	356	4	no	—
135	C₄	#19151444	1	1	yes	characteristic
136	C₄	C₂×#15667922	1	1	yes	characteristic
137	C₄	#19151649	1	2	yes	—
138	C₂	#26019997	1	1	yes	characteristic
139	C₂	#26021848	1	2	yes	—
140	C₂	#26022057	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19151374

C₂

yes

maximal, characteristic

#26019938

C₂

yes

maximal, characteristic

#26018329

C₂

yes

maximal

C₂×C₄×C₁₆×C₈₉

C₂

yes

maximal, characteristic

C₂²×#13083549

C₂²

yes

—

C₂×#15667923

C₄

yes

characteristic

C₂×#15667922

C₄

yes

—

C₂×C₈×Dic₈₉

C₂²

yes

—

#19151444

C₄

yes

characteristic

#19151374

C₄

yes

complemented

C₂²×C₁₆×C₈₉

C₂²

yes

—

C₂×C₄×C₈×C₈₉

C₂²

yes

characteristic

C₄×C₁₆×C₈₉

C₄

yes

complemented

C₂²×#10623494

C₂×C₄

yes

—

C₂×C₄×Dic₈₉

C₂×C₄

yes

—

C₂×#13083549

—

C₂×#13083549

C₂×C₄

yes

—

#15667923

C₈

yes

—

#15667922

—

C₈×Dic₈₉

—

#15667919

C₈

yes

—

C₂²×C₈×C₈₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₈₉

C₂³

yes

characteristic

C₂×C₄²×C₈₉

C₂×C₄

yes

characteristic

C₂×C₁₆×C₈₉

—

C₂×C₁₆×C₈₉

C₂×C₄

yes

—

C₄×C₈×C₈₉

C₂×C₄

yes

—

C₄×C₈×C₈₉

C₂×C₄

yes

—

C₂²×Dic₈₉

C₂×C₈

yes

—

C₂×#10623494

—

C₂×#10623494

—

C₂×#10623494

C₂×C₈

yes

—

C₄×Dic₈₉

—

C₄×Dic₈₉

—

#13083549

—

C₂²×C₄×C₈₉

C₂×C₈

yes

—

C₂²×C₄×C₈₉

C₂²×C₄

yes

characteristic

C₂×C₈×C₈₉

C₄²

yes

—

C₂×C₈×C₈₉

M₁₆

yes

—

C₂×C₈×C₈₉

C₂²×C₄

yes

characteristic

C₂×C₈×C₈₉

C₂²×C₄

yes

characteristic

C₂×C₈×C₈₉

#41

yes

—

C₄²×C₈₉

C₄²

yes

—

C₄²×C₈₉

C₂×C₈

yes

—

C₁₆×C₈₉

—

C₂³×C₈₉

C₂²×C₈

yes

characteristic

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

C₄×C₈

yes

—

C₂×C₄×C₈₉

C₂×C₄²

yes

characteristic

C₂×C₄×C₈₉

#117

yes

—

C₂×C₄×C₈₉

C₂²×C₈

yes

characteristic

C₂×C₄×C₈₉

C₂×M₁₆

yes

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₈×C₈₉

#97

yes

—

C₈×C₈₉

#117

yes

—

C₈×C₈₉

#117

yes

—

#10623494

—

C₂²×C₈₉

C₂×C₄×C₈

yes

characteristic

C₂²×C₈₉

#431

yes

—

C₂²×C₈₉

#504

yes

—

C₄×C₈₉

—

C₄×C₈₉

#376

yes

characteristic

C₄×C₈₉

C₂×#97

yes

characteristic

C₄×C₈₉

#431

yes

—

Dic₈₉

—

—

C₂×C₈₉

yes

C₂×C₈₉

yes

—

C₂×C₈₉

#2164

yes

—

C₂×#346

—

C₂×C₄×C₁₆

D₈₉

yes

characteristic

#1726

—

#1374

—

C₈₉

#12592

yes

characteristic, complemented, Sylow

C₂²×C₁₆

—

C₂²×C₁₆

C₂×D₈₉

yes

—

C₂×#97

—

C₂×#97

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₈₉

yes

characteristic

#376

—

#346

—

C₄×C₁₆

Dic₈₉

yes

complemented

C₂²×C₈

—

C₂²×C₈

C₄×D₈₉

yes

characteristic

C₂²×C₈

C₂²×D₈₉

yes

characteristic

C₂×C₄²

—

C₂×C₄²

C₄×D₈₉

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

178

—

C₂×C₁₆

C₂×Dic₈₉

yes

—

#97

—

#97

—

178

—

C₄×C₈

—

178

—

C₄×C₈

C₄×D₈₉

yes

—

C₄×C₈

C₂×Dic₈₉

yes

—

#95

—

100

C₂²×C₄

—

101

C₂²×C₄

C₈×D₈₉

yes

—

102

C₂²×C₄

C₂×C₄×D₈₉

yes

characteristic

103

C₂×C₈

—

104

C₂×C₈

—

178

—

105

C₂×C₈

—

178

—

106

C₂×C₈

C₄×Dic₈₉

yes

—

107

C₂×C₈

#13083557

yes

—

108

C₂×C₈

C₂×C₄×D₈₉

yes

characteristic

109

C₂×C₈

C₂²×Dic₈₉

yes

characteristic

110

C₂×C₈

#13083574

yes

—

111

C₄²

—

178

—

112

C₄²

—

178

—

113

C₄²

C₄×Dic₈₉

yes

—

114

C₄²

C₈×D₈₉

yes

—

115

C₁₆

—

116

C₁₆

—

178

—

117

C₂³

C₂×C₈×D₈₉

yes

characteristic

118

C₂×C₄

—

119

C₂×C₄

—

178

—

120

C₂×C₄

—

178

—

121

C₂×C₄

C₈×Dic₈₉

yes

—

122

C₂×C₄

C₂×C₄×Dic₈₉

yes

characteristic

123

C₂×C₄

#15667969

yes

—

124

C₂×C₄

C₂×C₈×D₈₉

yes

characteristic

125

C₂×C₄

C₂×#13083557

yes

—

126

C₈

—

178

—

127

C₈

#15667922

yes

—

128

C₈

#15667969

yes

—

129

C₈

#15667971

yes

—

130

C₂²

C₂×C₈×Dic₈₉

yes

characteristic

131

C₂²

#19151649

yes

—

132

C₂²

#19152014

yes

—

133

C₄

—

134

C₄

—

356

—

135

C₄

#19151444

yes

characteristic

136

C₄

C₂×#15667922

yes

characteristic

137

C₄

#19151649

yes

—

138

C₂

#26019997

yes

characteristic

139

C₂

#26021848

yes

—

140

C₂

#26022057

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₈	C₂²×D₈₉
commutator	C₂²×C₈₉	C₂×C₄×C₈
Fitting	C₂×C₄×C₁₆×C₈₉	C₂
socle, prime radical	C₂³×C₈₉	C₂²×C₈
cosocle	C₂²×C₈×C₈₉	C₂³
hypercenter	C₂×C₄×C₁₆	D₈₉
hypocenter	C₈₉	#12592
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂²×C₈ ◁ C₂×C₄×C₁₆

subgroup

G/H

center, Frattini

C₂²×C₈

C₂²×D₈₉

commutator

C₂²×C₈₉

C₂×C₄×C₈

Fitting

C₂×C₄×C₁₆×C₈₉

C₂

socle, prime radical

C₂³×C₈₉

C₂²×C₈

cosocle

C₂²×C₈×C₈₉

C₂³

hypercenter

C₂×C₄×C₁₆

D₈₉

C₈₉

G ▷ C₂²×C₈₉ ▷ C₈₉

C₁ ◁ C₂²×C₈ ◁ C₂×C₄×C₁₆

N	H ≅ G/N	type
10. #19151374	C₄	semidirect
13. C₄×C₁₆×C₈₉	C₄	semidirect
75. C₈₉	#12592	semidirect
84. C₄×C₁₆	Dic₈₉	semidirect

H ≅ G/N

type

10. #19151374

C₄

semidirect

13. C₄×C₁₆×C₈₉

C₄

semidirect

75. C₈₉

#12592

semidirect

84. C₄×C₁₆

Dic₈₉

semidirect

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

subgroup	index
C₂×#19151374	2
#26019938	2
#26018329	2
C₂×C₄×C₁₆×C₈₉	2
#12592	89

subgroup

index

C₂×C₄×C₁₆×C₈₉

Subgroups — #36469432

Conjugacy classes of subgroups

Complements

Maximal subgroups