Group #36444885 — subgroups

Subgroups — #36444885

Order 22784.

294 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 131 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	#26018544	C₂	1	1	yes	maximal, characteristic
2	#26018535	C₂	1	1	yes	maximal, characteristic
3	#26018083	C₂	1	2	yes	maximal
4	#26018081	C₂	1	2	yes	maximal
5	C₈₉×#1746	C₂	1	1	yes	maximal, characteristic
6	#19151651	C₂²	1	2	yes	—
7	#19151651	C₂²	1	2	yes	—
8	#19151320	C₄	1	4	yes	complemented
9	#19151319	C₄	1	2	yes	complemented
10	C₈×#10623494	C₄	1	2	yes	complemented
11	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
13	#376×C₈₉	C₂²	1	1	yes	characteristic
14	#336×C₈₉	C₄	1	4	yes	—
15	C₄⋊#10623494	—	2	2	no	—
16	C₄⋊#10623494	—	2	2	no	—
17	C₂²⋊#10623494	—	2	2	no	—
18	C₂²⋊#10623494	—	2	2	no	—
19	C₄×#10623494	C₂×C₄	1	4	yes	—
20	C₄×#10623494	C₂×C₄	1	4	yes	—
21	C₂²×C₈×C₈₉	C₂×C₄	1	2	yes	—
22	C₂²×C₈×C₈₉	C₂×C₄	1	2	yes	—
23	C₂×C₄²×C₈₉	C₂×C₄	1	2	yes	—
24	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
25	#97×C₈₉	—	2	2	no	—
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	2	yes	—
29	#95×C₈₉	—	2	2	no	—
30	C₂×#10623494	—	2	4	no	—
31	C₂×#10623494	—	2	4	no	—
32	C₂²×C₄×C₈₉	—	2	2	no	—
33	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
34	C₂²×C₄×C₈₉	#41	1	2	yes	—
35	C₂×C₈×C₈₉	—	2	4	no	—
36	C₂×C₈×C₈₉	—	2	2	no	—
37	C₂×C₈×C₈₉	—	2	4	no	—
38	C₂×C₈×C₈₉	C₄²	1	2	yes	—
39	C₂×C₈×C₈₉	C₄²	1	2	yes	—
40	C₄²×C₈₉	—	2	4	no	—
41	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
42	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
43	C₄²×C₈₉	#41	1	2	yes	—
44	C₂³×C₈₉	#117	1	1	yes	characteristic
45	C₂×C₄×C₈₉	—	4	2	no	—
46	C₂×C₄×C₈₉	—	4	4	no	—
47	C₂×C₄×C₈₉	—	4	2	no	—
48	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
49	C₂×C₄×C₈₉	#117	1	2	yes	—
50	C₂×C₄×C₈₉	#117	1	2	yes	—
51	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
52	C₂×C₄×C₈₉	#131	1	4	yes	—
53	C₈×C₈₉	—	2	2	no	—
54	C₈×C₈₉	—	2	2	no	—
55	C₈×C₈₉	—	4	2	no	—
56	#10623494	—	4	4	no	—
57	#10623494	—	4	4	no	—
58	C₂²×C₈₉	—	2	2	no	—
59	C₂²×C₈₉	#376	1	1	yes	characteristic
60	C₂²×C₈₉	#433	1	2	yes	—
61	C₄×C₈₉	—	2	2	no	—
62	C₄×C₈₉	—	2	2	no	—
63	C₄×C₈₉	—	8	2	no	—
64	C₄×C₈₉	#405	1	2	yes	—
65	C₄×C₈₉	#433	1	2	yes	—
66	#8141	—	89	1	no	maximal, Sylow
67	C₂×C₈₉	—	2	2	no	—
68	C₂×C₈₉	#1746	1	1	yes	characteristic
69	C₂×C₈₉	#1747	1	2	yes	—
70	#1746	D₈₉	1	1	yes	characteristic
71	#1452	—	89	1	no	—
72	#1450	—	89	1	no	—
73	#1275	—	89	2	no	—
74	#1274	—	89	2	no	—
75	C₈₉	#8141	1	1	yes	characteristic, complemented, Sylow
76	#431	—	89	2	no	—
77	#431	—	89	2	no	—
78	C₂×#97	C₂×D₈₉	1	1	yes	characteristic
79	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
80	#376	C₂×D₈₉	1	1	yes	characteristic
81	#336	Dic₈₉	1	4	yes	—
82	#322	—	89	2	no	—
83	#322	—	89	4	no	—
84	C₈²	—	89	2	no	—
85	C₂²×C₈	C₂×Dic₈₉	1	2	yes	—
86	C₂²×C₈	C₂×Dic₈₉	1	2	yes	—
87	C₂×C₄²	C₂×Dic₈₉	1	2	yes	—
88	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
89	C₄⋊C₈	—	178	2	no	—
90	C₄⋊C₈	—	178	2	no	—
91	C₂²⋊C₈	—	178	2	no	—
92	C₂²⋊C₈	—	178	2	no	—
93	#97	—	2	2	no	—
94	C₄×C₈	—	89	4	no	—
95	C₄×C₈	—	89	4	no	—
96	C₄×C₈	C₄×D₈₉	1	1	yes	characteristic
97	C₄×C₈	C₄×D₈₉	1	1	yes	characteristic
98	C₄×C₈	C₄×D₈₉	1	2	yes	—
99	#95	—	2	2	no	—
100	C₂²×C₄	—	2	2	no	—
101	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
102	C₂²×C₄	#13083574	1	2	yes	—
103	C₂×C₈	—	2	4	no	—
104	C₂×C₈	—	2	2	no	—
105	C₂×C₈	—	2	4	no	—
106	C₂×C₈	—	178	4	no	—
107	C₂×C₈	—	178	4	no	—
108	C₂×C₈	C₄×Dic₈₉	1	2	yes	—
109	C₂×C₈	C₄×Dic₈₉	1	2	yes	—
110	C₄²	—	2	4	no	—
111	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
112	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
113	C₄²	#13083574	1	2	yes	—
114	C₂³	#15667971	1	1	yes	characteristic
115	C₂×C₄	—	4	2	no	—
116	C₂×C₄	—	4	4	no	—
117	C₂×C₄	—	4	2	no	—
118	C₂×C₄	C₂×C₄×Dic₈₉	1	1	yes	characteristic
119	C₂×C₄	#15667969	1	2	yes	—
120	C₂×C₄	#15667969	1	2	yes	—
121	C₂×C₄	#15667971	1	1	yes	characteristic
122	C₂×C₄	#15668019	1	4	yes	—
123	C₈	—	2	2	no	—
124	C₈	—	2	2	no	—
125	C₈	—	4	2	no	—
126	C₈	—	356	4	no	—
127	C₈	—	356	4	no	—
128	C₂²	—	2	2	no	—
129	C₂²	#19151444	1	1	yes	characteristic
130	C₂²	#19151659	1	2	yes	—
131	C₄	—	2	2	no	—
132	C₄	—	2	2	no	—
133	C₄	—	8	2	no	—
134	C₄	#19151554	1	2	yes	—
135	C₄	#19151659	1	2	yes	—
136	C₂	—	2	2	no	—
137	C₂	#26020004	1	1	yes	characteristic
138	C₂	#26020007	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#26018544

C₂

yes

maximal, characteristic

#26018535

C₂

yes

maximal, characteristic

#26018083

C₂

yes

maximal

#26018081

C₂

yes

maximal

C₈₉×#1746

C₂

yes

maximal, characteristic

#19151651

C₂²

yes

—

#19151651

C₂²

yes

—

#19151320

C₄

yes

complemented

#19151319

C₄

yes

complemented

C₈×#10623494

C₄

yes

complemented

C₂×#97×C₈₉

C₂²

yes

characteristic

C₂×C₄×C₈×C₈₉

C₂²

yes

characteristic

#376×C₈₉

C₂²

yes

characteristic

#336×C₈₉

C₄

yes

—

—

—

—

—

C₂×C₄

yes

—

C₄×#10623494

C₂×C₄

yes

—

C₂²×C₈×C₈₉

C₂×C₄

yes

—

C₂²×C₈×C₈₉

C₂×C₄

yes

—

C₂×C₄²×C₈₉

C₂×C₄

yes

—

C₂×C₄²×C₈₉

C₂³

yes

characteristic

#97×C₈₉

—

C₄×C₈×C₈₉

C₂×C₄

yes

characteristic

C₄×C₈×C₈₉

C₂×C₄

yes

characteristic

C₄×C₈×C₈₉

C₂×C₄

yes

—

#95×C₈₉

—

C₂×#10623494

—

C₂×#10623494

—

C₂²×C₄×C₈₉

—

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

yes

—

C₂×C₈×C₈₉

C₄²

yes

—

C₄²×C₈₉

—

C₄²×C₈₉

C₂²×C₄

yes

characteristic

C₄²×C₈₉

C₂²×C₄

yes

characteristic

C₄²×C₈₉

#41

yes

—

C₂³×C₈₉

#117

yes

characteristic

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

C₂×C₄²

yes

characteristic

C₂×C₄×C₈₉

#117

yes

—

C₂×C₄×C₈₉

#117

yes

—

C₂×C₄×C₈₉

#117

yes

characteristic

C₂×C₄×C₈₉

#131

yes

—

C₈×C₈₉

—

C₈×C₈₉

—

C₈×C₈₉

—

#10623494

—

#10623494

—

C₂²×C₈₉

—

C₂²×C₈₉

#376

yes

characteristic

C₂²×C₈₉

#433

yes

—

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

#405

yes

—

C₄×C₈₉

#433

yes

—

#8141

—

maximal, Sylow

C₂×C₈₉

—

C₂×C₈₉

#1746

yes

characteristic

C₂×C₈₉

#1747

yes

—

#1746

D₈₉

yes

—

—

—

—

C₈₉

#8141

yes

characteristic, complemented, Sylow

#431

—

#431

—

C₂×#97

C₂×D₈₉

yes

characteristic

C₂×C₄×C₈

C₂×D₈₉

yes

characteristic

#376

C₂×D₈₉

yes

characteristic

#336

Dic₈₉

yes

—

#322

—

#322

—

C₈²

—

C₂²×C₈

C₂×Dic₈₉

yes

—

C₂²×C₈

C₂×Dic₈₉

yes

—

C₂×C₄²

C₂×Dic₈₉

yes

—

C₂×C₄²

C₂²×D₈₉

yes

characteristic

C₄⋊C₈

—

178

—

C₄⋊C₈

—

178

—

C₂²⋊C₈

—

178

—

C₂²⋊C₈

—

178

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₄×D₈₉

yes

characteristic

C₄×C₈

C₄×D₈₉

yes

characteristic

C₄×C₈

C₄×D₈₉

yes

—

#95

—

100

C₂²×C₄

—

101

C₂²×C₄

C₂²×Dic₈₉

yes

characteristic

102

C₂²×C₄

#13083574

yes

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₂×C₈

—

178

—

107

C₂×C₈

—

178

—

108

C₂×C₈

C₄×Dic₈₉

yes

—

109

C₂×C₈

C₄×Dic₈₉

yes

—

110

C₄²

—

111

C₄²

C₂×C₄×D₈₉

yes

characteristic

112

C₄²

C₂×C₄×D₈₉

yes

characteristic

113

C₄²

#13083574

yes

—

114

C₂³

#15667971

yes

characteristic

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

C₂×C₄×Dic₈₉

yes

characteristic

119

C₂×C₄

#15667969

yes

—

120

C₂×C₄

#15667969

yes

—

121

C₂×C₄

#15667971

yes

characteristic

122

C₂×C₄

#15668019

yes

—

123

C₈

—

124

C₈

—

125

C₈

—

126

C₈

—

356

—

127

C₈

—

356

—

128

C₂²

—

129

C₂²

#19151444

yes

characteristic

130

C₂²

#19151659

yes

—

131

C₄

—

132

C₄

—

133

C₄

—

134

C₄

#19151554

yes

—

135

C₄

#19151659

yes

—

136

C₂

—

137

C₂

#26020004

yes

characteristic

138

C₂

#26020007

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×C₄×Dic₈₉
commutator	C₂×C₄×C₈₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₈₉×#1746	C₂
socle	C₂²×C₈₉	#376
prime radical	C₂³×C₈₉	#117
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	#1746	D₈₉
hypocenter	C₈₉	#8141
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ #1746

subgroup

G/H

center

C₂×C₄

C₂×C₄×Dic₈₉

commutator

C₂×C₄×C₈₉

C₂×C₄²

Frattini

C₂×C₄²

C₂²×D₈₉

Fitting

C₈₉×#1746

C₂

C₂²×C₈₉

C₂³×C₈₉

C₂×C₄²×C₈₉

C₂³

D₈₉

C₈₉

G ▷ C₂×C₄×C₈₉ ▷ C₈₉

C₁ ◁ C₂×C₄ ◁ #1746

N	H ≅ G/N	type
8. #19151320	C₄	semidirect
9. #19151319	C₄	semidirect
10. C₈×#10623494	C₄	semidirect
75. C₈₉	#8141	semidirect

H ≅ G/N

type

8. #19151320

C₄

semidirect

9. #19151319

C₄

semidirect

10. C₈×#10623494

C₄

semidirect

75. C₈₉

#8141

semidirect

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

subgroup	index
#26018544	2
#26018535	2
#26018083	2
#26018081	2
C₈₉×#1746	2
#8141	89

subgroup

index

C₈₉×#1746

Subgroups — #36444885

Conjugacy classes of subgroups

Complements

Maximal subgroups