Group #36463484 — subgroups

Subgroups — #36463484

Order 22784.

228 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 123 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	#26022055	C₂	1	1	yes	maximal, characteristic
2	#26018535	C₂	1	1	yes	maximal, characteristic
3	#26018174	C₂	1	2	yes	maximal, complemented
4	#26018172	C₂	1	2	yes	maximal, complemented
5	C₈₉×#2163	C₂	1	1	yes	maximal, characteristic
6	#19151651	C₄	1	2	yes	—
7	C₄⋊#13083549	C₄	1	2	yes	—
8	C₂²⋊#13083549	C₄	1	2	yes	—
9	#19151374	C₂²	1	2	yes	—
10	#19151319	C₂²	1	1	yes	characteristic
11	#19151319	C₂²	1	1	yes	characteristic
12	C₈×#10623494	C₄	1	2	yes	—
13	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
14	C₄⋊C₁₆×C₈₉	C₄	1	2	yes	—
15	C₂²⋊C₁₆×C₈₉	C₄	1	2	yes	—
16	#346×C₈₉	C₂²	1	2	yes	—
17	C₂×#13083549	C₂×C₄	1	4	yes	—
18	C₄⋊#10623494	—	2	2	no	—
19	C₂²⋊#10623494	—	2	2	no	—
20	C₄×#10623494	C₂×C₄	1	2	yes	—
21	C₄×#10623494	C₂×C₄	1	2	yes	—
22	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
25	C₂×C₁₆×C₈₉	C₂×C₄	1	4	yes	—
26	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
27	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
28	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
29	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
30	C₂×#10623494	—	2	2	no	—
31	C₂×#10623494	—	2	2	no	—
32	#13083549	—	2	4	no	—
33	C₂²×C₄×C₈₉	C₄²	1	1	yes	characteristic
34	C₂²×C₄×C₈₉	M₁₆	1	2	yes	—
35	C₂×C₈×C₈₉	—	2	2	no	—
36	C₂×C₈×C₈₉	—	2	2	no	—
37	C₂×C₈×C₈₉	C₄²	1	1	yes	characteristic
38	C₂×C₈×C₈₉	C₄²	1	1	yes	characteristic
39	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
40	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
41	C₄²×C₈₉	C₄²	1	1	yes	characteristic
42	C₄²×C₈₉	M₁₆	1	2	yes	—
43	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
44	C₁₆×C₈₉	—	2	4	no	—
45	C₂³×C₈₉	#97	1	1	yes	characteristic
46	C₂×C₄×C₈₉	—	2	1	no	—
47	C₂×C₄×C₈₉	—	2	1	no	—
48	C₂×C₄×C₈₉	—	4	2	no	—
49	C₂×C₄×C₈₉	#97	1	2	yes	—
50	C₂×C₄×C₈₉	#97	1	1	yes	characteristic
51	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
52	C₂×C₄×C₈₉	C₂×M₁₆	1	2	yes	—
53	C₈×C₈₉	—	2	1	no	—
54	C₈×C₈₉	—	2	1	no	—
55	C₈×C₈₉	#131	1	2	yes	—
56	C₈×C₈₉	#131	1	2	yes	—
57	#10623494	—	4	2	no	—
58	#10623494	—	4	2	no	—
59	C₂²×C₈₉	—	2	2	no	—
60	C₂²×C₈₉	—	2	1	no	—
61	C₂²×C₈₉	C₂×#97	1	1	yes	characteristic
62	C₄×C₈₉	—	2	2	no	—
63	C₄×C₈₉	—	2	2	no	—
64	C₄×C₈₉	—	2	1	no	—
65	C₄×C₈₉	#405	1	1	yes	characteristic
66	C₄×C₈₉	#405	1	1	yes	characteristic
67	#11416	—	89	1	no	maximal, Sylow
68	C₂×C₈₉	—	4	1	no	—
69	C₂×C₈₉	#1452	1	1	yes	characteristic
70	C₂×C₈₉	#2110	1	2	yes	—
71	#2163	—	89	1	no	—
72	#2163	D₈₉	1	1	yes	characteristic
73	#1450	—	89	1	no	—
74	#1313	—	89	2	no	—
75	#1313	—	89	2	no	—
76	C₈₉	#11416	1	1	yes	characteristic, complemented, Sylow
77	#431	—	89	2	no	—
78	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
79	C₄⋊C₁₆	—	89	2	no	—
80	C₄⋊C₁₆	Dic₈₉	1	2	yes	—
81	C₂²⋊C₁₆	—	89	2	no	—
82	C₂²⋊C₁₆	Dic₈₉	1	2	yes	—
83	#346	—	89	2	no	—
84	#346	C₂×D₈₉	1	2	yes	—
85	#322	—	89	1	no	—
86	#322	—	89	1	no	—
87	C₈²	—	89	2	no	—
88	C₂²×C₈	C₄×D₈₉	1	1	yes	characteristic
89	C₂²×C₈	C₂×Dic₈₉	1	1	yes	characteristic
90	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
91	C₂×C₁₆	—	89	4	no	—
92	C₂×C₁₆	C₂×Dic₈₉	1	4	yes	—
93	C₄⋊C₈	—	178	2	no	—
94	C₂²⋊C₈	—	178	2	no	—
95	C₄×C₈	—	89	2	no	—
96	C₄×C₈	—	89	2	no	—
97	C₄×C₈	C₄×D₈₉	1	1	yes	characteristic
98	C₄×C₈	C₄×D₈₉	1	1	yes	characteristic
99	C₄×C₈	C₂×Dic₈₉	1	1	yes	characteristic
100	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
101	C₂²×C₄	C₄×Dic₈₉	1	1	yes	characteristic
102	C₂²×C₄	#13083557	1	2	yes	—
103	C₂×C₈	—	2	2	no	—
104	C₂×C₈	—	2	2	no	—
105	C₂×C₈	—	178	2	no	—
106	C₂×C₈	—	178	2	no	—
107	C₂×C₈	C₄×Dic₈₉	1	1	yes	characteristic
108	C₂×C₈	C₄×Dic₈₉	1	1	yes	characteristic
109	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
110	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
111	C₄²	C₄×Dic₈₉	1	1	yes	characteristic
112	C₄²	#13083557	1	2	yes	—
113	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
114	C₁₆	—	2	4	no	—
115	C₁₆	—	178	4	no	—
116	C₂³	#15667922	1	1	yes	characteristic
117	C₂×C₄	—	2	1	no	—
118	C₂×C₄	—	2	1	no	—
119	C₂×C₄	—	4	2	no	—
120	C₂×C₄	#15667922	1	2	yes	—
121	C₂×C₄	#15667922	1	1	yes	characteristic
122	C₂×C₄	C₂×C₄×Dic₈₉	1	1	yes	characteristic
123	C₂×C₄	C₂×#13083557	1	2	yes	—
124	C₈	—	2	1	no	—
125	C₈	—	2	1	no	—
126	C₈	—	356	2	no	—
127	C₈	—	356	2	no	—
128	C₈	#15668019	1	2	yes	—
129	C₈	#15668020	1	2	yes	—
130	C₂²	—	2	2	no	—
131	C₂²	—	2	1	no	—
132	C₂²	C₂×#15667922	1	1	yes	characteristic
133	C₄	—	2	2	no	—
134	C₄	—	2	2	no	—
135	C₄	—	2	1	no	—
136	C₄	#19151554	1	1	yes	characteristic
137	C₄	#19151556	1	1	yes	characteristic
138	C₂	—	4	1	no	—
139	C₂	#26018545	1	1	yes	characteristic
140	C₂	#26021856	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#26022055

C₂

yes

maximal, characteristic

#26018535

C₂

yes

maximal, characteristic

#26018174

C₂

yes

maximal, complemented

#26018172

C₂

yes

maximal, complemented

C₈₉×#2163

C₂

yes

maximal, characteristic

#19151651

C₄

yes

—

C₄⋊#13083549

C₄

yes

—

C₂²⋊#13083549

C₄

yes

—

#19151374

C₂²

yes

—

#19151319

C₂²

yes

characteristic

#19151319

C₂²

yes

characteristic

C₈×#10623494

C₄

yes

—

C₂×C₄×C₈×C₈₉

C₂²

yes

characteristic

C₄⋊C₁₆×C₈₉

C₄

yes

—

C₂²⋊C₁₆×C₈₉

C₄

yes

—

#346×C₈₉

C₂²

yes

—

C₂×#13083549

C₂×C₄

yes

—

C₄⋊#10623494

—

C₂²⋊#10623494

—

C₄×#10623494

C₂×C₄

yes

—

C₄×#10623494

C₂×C₄

yes

—

C₂²×C₈×C₈₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₈₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₈₉

C₂×C₄

yes

characteristic

C₂×C₁₆×C₈₉

C₂×C₄

yes

—

C₄×C₈×C₈₉

C₂×C₄

yes

characteristic

C₄×C₈×C₈₉

C₂×C₄

yes

characteristic

C₄×C₈×C₈₉

C₂×C₄

yes

characteristic

C₄×C₈×C₈₉

C₂³

yes

—

—

—

C₂²×C₄×C₈₉

C₄²

yes

characteristic

C₂²×C₄×C₈₉

M₁₆

yes

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

C₄²

yes

characteristic

C₂×C₈×C₈₉

C₄²

yes

characteristic

C₂×C₈×C₈₉

C₂²×C₄

yes

characteristic

C₂×C₈×C₈₉

C₂²×C₄

yes

characteristic

C₄²×C₈₉

C₄²

yes

characteristic

C₄²×C₈₉

M₁₆

yes

—

C₄²×C₈₉

C₂²×C₄

yes

characteristic

C₁₆×C₈₉

—

C₂³×C₈₉

#97

yes

characteristic

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

#97

yes

—

C₂×C₄×C₈₉

#97

yes

characteristic

C₂×C₄×C₈₉

C₂×C₄²

yes

characteristic

C₂×C₄×C₈₉

C₂×M₁₆

yes

—

C₈×C₈₉

—

C₈×C₈₉

—

C₈×C₈₉

#131

yes

—

C₈×C₈₉

#131

yes

—

#10623494

—

#10623494

—

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

C₂×#97

yes

characteristic

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

yes

C₄×C₈₉

yes

—

C₂×C₈₉

—

C₂×C₈₉

#1452

yes

characteristic

C₂×C₈₉

#2110

yes

—

#2163

—

#2163

D₈₉

yes

—

—

—

C₈₉

#11416

yes

characteristic, complemented, Sylow

#431

—

C₂×C₄×C₈

C₂×D₈₉

yes

characteristic

C₄⋊C₁₆

—

C₄⋊C₁₆

Dic₈₉

yes

—

C₂²⋊C₁₆

—

C₂²⋊C₁₆

Dic₈₉

yes

—

#346

—

#346

C₂×D₈₉

yes

—

#322

—

#322

—

C₈²

—

C₂²×C₈

C₄×D₈₉

yes

characteristic

C₂²×C₈

C₂×Dic₈₉

yes

characteristic

C₂×C₄²

C₄×D₈₉

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

C₂×Dic₈₉

yes

—

C₄⋊C₈

—

178

—

C₂²⋊C₈

—

178

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₄×D₈₉

yes

characteristic

C₄×C₈

C₄×D₈₉

yes

characteristic

C₄×C₈

C₂×Dic₈₉

yes

characteristic

100

C₄×C₈

C₂²×D₈₉

yes

characteristic

101

C₂²×C₄

C₄×Dic₈₉

yes

characteristic

102

C₂²×C₄

#13083557

yes

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

—

178

—

106

C₂×C₈

—

178

—

107

C₂×C₈

C₄×Dic₈₉

yes

characteristic

108

C₂×C₈

C₄×Dic₈₉

yes

characteristic

109

C₂×C₈

C₂×C₄×D₈₉

yes

characteristic

110

C₂×C₈

C₂²×Dic₈₉

yes

characteristic

111

C₄²

C₄×Dic₈₉

yes

characteristic

112

C₄²

#13083557

yes

—

113

C₄²

C₂×C₄×D₈₉

yes

characteristic

114

C₁₆

—

115

C₁₆

—

178

—

116

C₂³

#15667922

yes

characteristic

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

#15667922

yes

—

121

C₂×C₄

#15667922

yes

characteristic

122

C₂×C₄

C₂×C₄×Dic₈₉

yes

characteristic

123

C₂×C₄

C₂×#13083557

yes

—

124

C₈

—

125

C₈

—

126

C₈

—

356

—

127

C₈

—

356

—

128

C₈

#15668019

yes

—

129

C₈

#15668020

yes

—

130

C₂²

—

131

C₂²

—

132

C₂²

C₂×#15667922

yes

characteristic

133

C₄

—

134

C₄

—

135

C₄

—

136

C₄

#19151554

yes

characteristic

137

C₄

#19151556

yes

characteristic

138

C₂

—

139

C₂

#26018545

yes

characteristic

140

C₂

#26021856

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×C₄×Dic₈₉
commutator	C₂×C₄×C₈₉	C₂×C₄²
Frattini	C₄×C₈	C₂²×D₈₉
Fitting	C₈₉×#2163	C₂
socle	C₂²×C₈₉	C₂×#97
prime radical	C₂³×C₈₉	#97
cosocle	C₄×C₈×C₈₉	C₂³
hypercenter	#2163	D₈₉
hypocenter	C₈₉	#11416
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ #2163

subgroup

G/H

center

C₂×C₄

C₂×C₄×Dic₈₉

commutator

C₂×C₄×C₈₉

C₂×C₄²

Frattini

C₄×C₈

C₂²×D₈₉

Fitting

C₈₉×#2163

C₂

socle

C₂²×C₈₉

C₂×#97

prime radical

C₂³×C₈₉

#97

cosocle

C₄×C₈×C₈₉

C₂³

D₈₉

C₈₉

G ▷ C₂×C₄×C₈₉ ▷ C₈₉

C₁ ◁ C₂×C₄ ◁ #2163

N	H ≅ G/N	type
3. #26018174	C₂	semidirect
4. #26018172	C₂	semidirect
76. C₈₉	#11416	semidirect

H ≅ G/N

type

3. #26018174

C₂

semidirect

4. #26018172

C₂

semidirect

76. C₈₉

#11416

semidirect

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

subgroup	index
#26022055	2
#26018535	2
#26018174	2
#26018172	2
C₈₉×#2163	2
#11416	89

subgroup

index

C₈₉×#2163

Subgroups — #36463484

Conjugacy classes of subgroups

Complements

Maximal subgroups