Group #36443818 — subgroups

Subgroups — #36443818

Order 22784.

610 conjugacy classes of subgroups; only the 207 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 207 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×#19151649	C₂	1	3	yes	maximal
2	#26018079	C₂	1	3	yes	maximal, complemented
3	C₈₉×#1273	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄²×D₈₉	C₂²	1	1	yes	characteristic
5	#19151649	—	2	12	no	—
6	C₂×#15667941	C₄	1	6	yes	—
7	C₂×#15667924	C₄	1	6	yes	—
8	C₂×C₄×#10623494	C₂²	1	3	yes	—
9	C₂×C₄×C₈×C₈₉	C₂²	1	3	yes	—
10	C₂²×C₄×D₈₉	C₂×C₄	1	3	yes	—
11	C₂²×#10623494	C₂×C₄	1	6	yes	—
12	C₂×C₄×Dic₈₉	C₂×C₄	1	3	yes	—
13	C₄²×D₈₉	D₄	1	6	yes	—
14	C₄²×D₈₉	Q₈	1	2	yes	—
15	#15667941	—	2	12	no	—
16	#15667924	—	2	12	no	—
17	C₄×#10623494	—	2	6	no	—
18	C₂²×C₈×C₈₉	C₂×C₄	1	6	yes	—
19	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
20	C₄×C₈×C₈₉	—	2	6	no	—
21	C₂³×D₈₉	C₄²	1	1	yes	characteristic
22	C₂²×Dic₈₉	C₄²	1	3	yes	—
23	C₂×C₄×D₈₉	—	2	6	no	—
24	C₂×C₄×D₈₉	—	2	6	no	—
25	C₂×C₄×D₈₉	C₂²⋊C₄	1	6	yes	—
26	C₂×C₄×D₈₉	C₄⋊C₄	1	6	yes	—
27	C₂×#10623494	—	2	6	no	—
28	C₂×#10623494	—	2	6	no	—
29	C₂×#10623494	—	2	6	no	—
30	C₄×Dic₈₉	C₂²⋊C₄	1	6	yes	—
31	C₄×Dic₈₉	C₄⋊C₄	1	6	yes	—
32	C₂²×C₄×C₈₉	C₂²×C₄	1	3	yes	—
33	C₂×C₈×C₈₉	—	2	6	no	—
34	C₂×C₈×C₈₉	—	2	6	no	—
35	C₂×C₈×C₈₉	—	2	6	no	—
36	C₄²×C₈₉	C₂×D₄	1	3	yes	—
37	C₄²×C₈₉	C₂×Q₈	1	1	yes	characteristic
38	C₂³×C₈₉	C₂×C₄²	1	1	yes	characteristic
39	C₂²×D₈₉	—	2	3	no	—
40	C₂²×D₈₉	—	2	3	no	—
41	C₂²×D₈₉	#95	1	2	yes	—
42	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	3	yes	—
43	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	3	yes	—
44	C₂×C₄×C₈₉	#131	1	6	yes	—
45	C₂×C₄×C₈₉	#131	1	6	yes	—
46	C₂×Dic₈₉	—	2	3	no	—
47	C₂×Dic₈₉	—	2	3	no	—
48	C₂×Dic₈₉	#95	1	6	yes	—
49	C₄×D₈₉	—	2	12	no	—
50	C₄×D₈₉	—	2	12	no	—
51	C₈×C₈₉	—	4	6	no	—
52	#10623494	—	4	6	no	—
53	C₂²×C₈₉	C₂×#95	1	1	yes	characteristic
54	C₂²×C₈₉	#405	1	3	yes	—
55	C₂²×C₈₉	#405	1	3	yes	—
56	C₂×D₈₉	—	2	6	no	—
57	C₂×D₈₉	—	4	1	no	—
58	C₂×D₈₉	—	4	3	no	—
59	C₄×C₈₉	#408	1	6	yes	—
60	C₄×C₈₉	#424	1	6	yes	—
61	Dic₈₉	—	2	6	no	—
62	#7851	—	89	1	no	maximal, Sylow
63	C₂×C₈₉	#1454	1	1	yes	characteristic
64	C₂×C₈₉	#1454	1	3	yes	—
65	C₂×C₈₉	#1729	1	3	yes	—
66	D₈₉	—	4	2	no	—
67	C₂×#431	—	89	3	no	—
68	#1273	—	89	3	no	—
69	#1273	D₈₉	1	1	yes	characteristic, complemented
70	C₈₉	#7851	1	1	yes	characteristic, complemented, Sylow
71	C₂²×C₄²	—	89	1	no	—
72	#431	—	178	12	no	—
73	C₂×C₄⋊C₈	—	89	6	no	—
74	C₂×C₂²⋊C₈	—	89	6	no	—
75	C₂×C₄×C₈	—	89	3	no	—
76	C₂×C₄×C₈	C₂×D₈₉	1	3	yes	—
77	C₂³×C₄	—	89	3	no	—
78	C₂²×C₈	—	89	6	no	—
79	C₂²×C₈	C₄×D₈₉	1	6	yes	—
80	C₂×C₄²	—	89	3	no	—
81	C₂×C₄²	—	89	6	no	—
82	C₂×C₄²	—	89	2	no	—
83	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
84	C₄⋊C₈	—	178	12	no	—
85	C₂²⋊C₈	—	178	12	no	—
86	C₄×C₈	—	2	6	no	—
87	C₄×C₈	—	178	6	no	—
88	C₂⁴	—	89	1	no	—
89	C₂²×C₄	—	89	3	no	—
90	C₂²×C₄	—	89	6	no	—
91	C₂²×C₄	—	89	6	no	—
92	C₂²×C₄	—	178	6	no	—
93	C₂²×C₄	—	178	6	no	—
94	C₂²×C₄	C₂×C₄×D₈₉	1	3	yes	—
95	C₂×C₈	—	2	6	no	—
96	C₂×C₈	—	2	6	no	—
97	C₂×C₈	—	2	6	no	—
98	C₂×C₈	—	178	6	no	—
99	C₂×C₈	—	178	6	no	—
100	C₂×C₈	—	178	6	no	—
101	C₄²	—	89	6	no	—
102	C₄²	—	89	6	no	—
103	C₄²	D₄×D₈₉	1	3	yes	—
104	C₄²	Q₈×D₈₉	1	1	yes	characteristic
105	C₂³	—	89	2	no	—
106	C₂³	—	178	3	no	—
107	C₂³	—	178	3	no	—
108	C₂³	C₄²×D₈₉	1	1	yes	characteristic
109	C₂×C₄	—	89	6	no	—
110	C₂×C₄	—	178	3	no	—
111	C₂×C₄	—	178	3	no	—
112	C₂×C₄	—	178	12	no	—
113	C₂×C₄	—	178	12	no	—
114	C₂×C₄	C₂²⋊C₄×D₈₉	1	3	yes	—
115	C₂×C₄	C₄⋊C₄×D₈₉	1	3	yes	—
116	C₂×C₄	#15668018	1	6	yes	—
117	C₂×C₄	#15668020	1	6	yes	—
118	C₈	—	4	6	no	—
119	C₈	—	356	6	no	—
120	C₂²	—	356	1	no	—
121	C₂²	—	356	3	no	—
122	C₂²	—	178	6	no	—
123	C₂²	#95×D₈₉	1	1	yes	characteristic
124	C₂²	#19151552	1	3	yes	—
125	C₂²	#19151555	1	3	yes	—
126	C₄	—	178	6	no	—
127	C₄	#19151563	1	6	yes	—
128	C₄	#19151623	1	6	yes	—
129	C₂	—	356	2	no	—
130	C₂	#26018551	1	1	yes	characteristic
131	C₂	#26018553	1	3	yes	—
132	C₂	#26019947	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19151649

C₂

yes

maximal

#26018079

C₂

yes

maximal, complemented

C₈₉×#1273

C₂

yes

maximal, characteristic, complemented

C₂×C₄²×D₈₉

C₂²

yes

characteristic

#19151649

—

C₂×#15667941

C₄

yes

—

C₂×#15667924

C₄

yes

—

C₂×C₄×#10623494

C₂²

yes

—

C₂×C₄×C₈×C₈₉

C₂²

yes

—

C₂²×C₄×D₈₉

C₂×C₄

yes

—

C₂²×#10623494

C₂×C₄

yes

—

C₂×C₄×Dic₈₉

C₂×C₄

yes

—

C₄²×D₈₉

D₄

yes

—

C₄²×D₈₉

Q₈

yes

—

#15667941

—

#15667924

—

C₄×#10623494

—

C₂²×C₈×C₈₉

C₂×C₄

yes

—

C₂×C₄²×C₈₉

C₂³

yes

characteristic

C₄×C₈×C₈₉

—

C₂³×D₈₉

C₄²

yes

characteristic

C₂²×Dic₈₉

C₄²

yes

—

C₂×C₄×D₈₉

—

C₂×C₄×D₈₉

—

C₂×C₄×D₈₉

C₂²⋊C₄

yes

—

C₂×C₄×D₈₉

C₄⋊C₄

yes

—

C₂×#10623494

—

C₂×#10623494

—

C₂×#10623494

—

C₄×Dic₈₉

C₂²⋊C₄

yes

—

C₄×Dic₈₉

C₄⋊C₄

yes

—

C₂²×C₄×C₈₉

C₂²×C₄

yes

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₄²×C₈₉

C₂×D₄

yes

—

C₄²×C₈₉

C₂×Q₈

yes

characteristic

C₂³×C₈₉

C₂×C₄²

yes

characteristic

C₂²×D₈₉

—

C₂²×D₈₉

—

C₂²×D₈₉

#95

yes

—

C₂×C₄×C₈₉

C₂×C₂²⋊C₄

yes

—

C₂×C₄×C₈₉

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₈₉

#131

yes

—

C₂×C₄×C₈₉

#131

yes

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

#95

yes

—

C₄×D₈₉

—

C₄×D₈₉

—

C₈×C₈₉

—

#10623494

—

C₂²×C₈₉

C₂×#95

yes

characteristic

C₂²×C₈₉

#405

yes

—

C₂²×C₈₉

#405

yes

—

C₂×D₈₉

—

C₂×D₈₉

—

C₂×D₈₉

—

C₄×C₈₉

#408

yes

—

C₄×C₈₉

#424

yes

—

Dic₈₉

—

—

C₂×C₈₉

yes

C₂×C₈₉

yes

—

C₂×C₈₉

#1729

yes

—

D₈₉

—

C₂×#431

—

#1273

—

#1273

D₈₉

yes

characteristic, complemented

C₈₉

#7851

yes

characteristic, complemented, Sylow

C₂²×C₄²

—

#431

—

178

—

C₂×C₄⋊C₈

—

C₂×C₂²⋊C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₈₉

yes

—

C₂³×C₄

—

C₂²×C₈

—

C₂²×C₈

C₄×D₈₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂²×D₈₉

yes

characteristic

C₄⋊C₈

—

178

—

C₂²⋊C₈

—

178

—

C₄×C₈

—

C₄×C₈

—

178

—

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

178

—

C₂²×C₄

—

178

—

C₂²×C₄

C₂×C₄×D₈₉

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

178

—

C₂×C₈

—

178

—

100

C₂×C₈

—

178

—

101

C₄²

—

102

C₄²

—

103

C₄²

D₄×D₈₉

yes

—

104

C₄²

Q₈×D₈₉

yes

characteristic

105

C₂³

—

106

C₂³

—

178

—

107

C₂³

—

178

—

108

C₂³

C₄²×D₈₉

yes

characteristic

109

C₂×C₄

—

110

C₂×C₄

—

178

—

111

C₂×C₄

—

178

—

112

C₂×C₄

—

178

—

113

C₂×C₄

—

178

—

114

C₂×C₄

C₂²⋊C₄×D₈₉

yes

—

115

C₂×C₄

C₄⋊C₄×D₈₉

yes

—

116

C₂×C₄

#15668018

yes

—

117

C₂×C₄

#15668020

yes

—

118

C₈

—

119

C₈

—

356

—

120

C₂²

—

356

—

121

C₂²

—

356

—

122

C₂²

—

178

—

123

C₂²

#95×D₈₉

yes

characteristic

124

C₂²

#19151552

yes

—

125

C₂²

#19151555

yes

—

126

C₄

—

178

—

127

C₄

#19151563

yes

—

128

C₄

#19151623

yes

—

129

C₂

—

356

—

130

C₂

#26018551

yes

characteristic

131

C₂

#26018553

yes

—

132

C₂

#26019947

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₈₉
commutator, socle	C₂³×C₈₉	C₂×C₄²
Fitting	C₈₉×#1273	C₂
prime radical	C₂³×D₈₉	C₄²
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	#1273	D₈₉
hypocenter	C₈₉	#7851
LCS	G ▷ C₂³×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄² ◁ #1273

subgroup

G/H

center, Frattini

C₂×C₄²

C₂²×D₈₉

commutator, socle

C₂³×C₈₉

C₂×C₄²

Fitting

C₈₉×#1273

C₂

prime radical

C₂³×D₈₉

C₄²

cosocle

C₂×C₄²×C₈₉

C₂³

D₈₉

C₈₉

G ▷ C₂³×C₈₉ ▷ C₈₉

C₁ ◁ C₂×C₄² ◁ #1273

N	H ≅ G/N	type
2. #26018079	C₂	semidirect
3. C₈₉×#1273	C₂	semidirect
69. #1273	D₈₉	semidirect
70. C₈₉	#7851	semidirect

H ≅ G/N

type

2. #26018079

C₂

semidirect

3. C₈₉×#1273

C₂

semidirect

69. #1273

D₈₉

semidirect

70. C₈₉

#7851

semidirect

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

subgroup	index
C₂×#19151649	2
#26018079	2
C₈₉×#1273	2
#7851	89

subgroup

index

C₂×#19151649

#26018079

C₈₉×#1273

#7851

Subgroups — #36443818

Conjugacy classes of subgroups

Complements

Maximal subgroups