Group #36443771 — subgroups

Subgroups — #36443771

Order 22784.

414 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 95 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	#26021790	C₂	1	3	yes	maximal
2	#26018078	C₂	1	3	yes	maximal
3	C₈₉×#2811	C₂	1	1	yes	maximal, characteristic
4	C₂×#15667945	—	2	3	no	—
5	C₂×#15667936	—	2	3	no	—
6	#19151468	C₂²	1	1	yes	characteristic
7	#19151353	C₂²	1	3	yes	—
8	#395×C₈₉	—	2	3	no	—
9	#391×C₈₉	—	2	3	no	—
10	#391×C₈₉	C₂²	1	3	yes	—
11	C₂²×#10623494	—	2	3	no	—
12	C₂×C₄⋊Dic₈₉	—	2	3	no	—
13	#15667945	—	4	6	no	—
14	#15667936	—	4	6	no	—
15	C₂²×Q₈×C₈₉	—	2	1	no	—
16	C₂²×Q₈×C₈₉	D₄	1	3	yes	—
17	C₂×C₄⋊C₄×C₈₉	—	2	3	no	—
18	C₂×C₄⋊C₄×C₈₉	D₄	1	3	yes	—
19	C₂×C₄²×C₈₉	—	2	1	no	—
20	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
21	#95×C₈₉	—	2	3	no	—
22	#95×C₈₉	—	2	6	no	—
23	C₂²×Dic₈₉	—	4	1	no	—
24	C₂×#10623494	—	2	6	no	—
25	C₂×#10623494	—	4	3	no	—
26	C₂×#10623494	—	4	3	no	—
27	C₄⋊Dic₈₉	—	4	3	no	—
28	C₄⋊Dic₈₉	—	4	3	no	—
29	C₂×Q₈×C₈₉	—	2	3	no	—
30	C₂×Q₈×C₈₉	—	4	3	no	—
31	C₂×Q₈×C₈₉	—	4	3	no	—
32	C₂×Q₈×C₈₉	—	8	3	no	—
33	C₂×Q₈×C₈₉	Q₁₆	1	6	yes	—
34	C₂²×C₄×C₈₉	—	2	3	no	—
35	C₂²×C₄×C₈₉	—	2	3	no	—
36	C₂²×C₄×C₈₉	C₂×D₄	1	3	yes	—
37	C₄⋊C₄×C₈₉	—	4	3	no	—
38	C₄⋊C₄×C₈₉	—	8	3	no	—
39	C₄²×C₈₉	—	4	1	no	—
40	C₄²×C₈₉	—	8	1	no	—
41	C₂³×C₈₉	#120	1	1	yes	characteristic
42	Q₈×C₈₉	—	4	6	no	—
43	Q₈×C₈₉	—	8	3	no	—
44	Q₈×C₈₉	—	8	4	no	—
45	C₂×C₄×C₈₉	—	2	3	no	—
46	C₂×C₄×C₈₉	—	2	3	no	—
47	C₂×C₄×C₈₉	—	2	6	no	—
48	C₂×C₄×C₈₉	—	4	3	no	—
49	C₂×C₄×C₈₉	—	4	3	no	—
50	C₂×C₄×C₈₉	—	4	3	no	—
51	C₂×C₄×C₈₉	—	4	6	no	—
52	C₂×C₄×C₈₉	C₂×Q₁₆	1	3	yes	—
53	C₂×C₄×C₈₉	#137	1	3	yes	—
54	C₂×Dic₈₉	—	8	3	no	—
55	#10623494	—	4	6	no	—
56	C₂²×C₈₉	#451	1	3	yes	—
57	C₂²×C₈₉	#453	1	3	yes	—
58	C₂²×C₈₉	#458	1	1	yes	characteristic
59	C₄×C₈₉	—	2	3	no	—
60	C₄×C₈₉	—	2	3	no	—
61	C₄×C₈₉	—	4	6	no	—
62	C₄×C₈₉	—	8	3	no	—
63	Dic₈₉	—	16	1	no	—
64	#7837	—	89	1	no	maximal, Sylow
65	C₂×C₈₉	#1614	1	3	yes	—
66	C₂×C₈₉	#1633	1	3	yes	—
67	C₂×C₈₉	#1655	1	1	yes	characteristic
68	#2811	D₈₉	1	1	yes	characteristic
69	#2095	—	89	3	no	—
70	#1272	—	89	3	no	—
71	C₈₉	#7837	1	1	yes	characteristic, complemented, Sylow
72	C₂×#107	—	178	3	no	—
73	C₂×#103	—	178	3	no	—
74	#395	—	2	3	no	—
75	#391	—	2	3	no	—
76	#391	C₂×D₈₉	1	3	yes	—
77	#384	—	89	1	no	—
78	#336	—	89	3	no	—
79	C₂²×Q₈	—	2	1	no	—
80	C₂²×Q₈	C₂²⋊D₈₉	1	3	yes	—
81	C₂²×C₈	—	178	3	no	—
82	C₂×C₄⋊C₄	—	2	3	no	—
83	C₂×C₄⋊C₄	—	178	3	no	—
84	C₂×C₄⋊C₄	C₂²⋊D₈₉	1	3	yes	—
85	C₂×C₄²	—	2	1	no	—
86	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
87	#107	—	356	6	no	—
88	#103	—	356	6	no	—
89	#95	—	2	3	no	—
90	#95	—	2	6	no	—
91	C₂×Q₈	—	2	3	no	—
92	C₂×Q₈	—	4	3	no	—
93	C₂×Q₈	—	4	3	no	—
94	C₂×Q₈	—	8	3	no	—
95	C₂×Q₈	#13083564	1	6	yes	—
96	C₂²×C₄	—	2	3	no	—
97	C₂²×C₄	—	2	3	no	—
98	C₂²×C₄	—	356	1	no	—
99	C₂²×C₄	C₂×C₂²⋊D₈₉	1	3	yes	—
100	C₂×C₈	—	356	3	no	—
101	C₂×C₈	—	356	3	no	—
102	C₂×C₈	—	178	6	no	—
103	C₄⋊C₄	—	4	3	no	—
104	C₄⋊C₄	—	8	3	no	—
105	C₄⋊C₄	—	356	3	no	—
106	C₄⋊C₄	—	356	3	no	—
107	C₄²	—	4	1	no	—
108	C₄²	—	8	1	no	—
109	C₂³	#15667981	1	1	yes	characteristic
110	Q₈	—	4	6	no	—
111	Q₈	—	8	3	no	—
112	Q₈	—	8	4	no	—
113	C₂×C₄	—	2	3	no	—
114	C₂×C₄	—	2	3	no	—
115	C₂×C₄	—	2	6	no	—
116	C₂×C₄	—	4	3	no	—
117	C₂×C₄	—	4	3	no	—
118	C₂×C₄	—	4	3	no	—
119	C₂×C₄	—	4	6	no	—
120	C₂×C₄	—	712	3	no	—
121	C₂×C₄	C₂×#13083564	1	3	yes	—
122	C₂×C₄	#15668043	1	3	yes	—
123	C₈	—	356	6	no	—
124	C₂²	#19151754	1	3	yes	—
125	C₂²	#19151766	1	3	yes	—
126	C₂²	#19151788	1	1	yes	characteristic
127	C₄	—	2	3	no	—
128	C₄	—	2	3	no	—
129	C₄	—	4	6	no	—
130	C₄	—	8	3	no	—
131	C₄	—	1424	1	no	—
132	C₂	#26019277	1	3	yes	—
133	C₂	#26019392	1	3	yes	—
134	C₂	#26019541	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#26021790

C₂

yes

maximal

#26018078

C₂

yes

maximal

C₈₉×#2811

C₂

yes

maximal, characteristic

C₂×#15667945

—

C₂×#15667936

—

#19151468

C₂²

yes

characteristic

#19151353

C₂²

yes

—

#395×C₈₉

—

#391×C₈₉

—

#391×C₈₉

C₂²

yes

—

C₂²×#10623494

—

C₂×C₄⋊Dic₈₉

—

#15667945

—

#15667936

—

C₂²×Q₈×C₈₉

—

C₂²×Q₈×C₈₉

D₄

yes

—

C₂×C₄⋊C₄×C₈₉

—

C₂×C₄⋊C₄×C₈₉

D₄

yes

—

C₂×C₄²×C₈₉

—

C₂×C₄²×C₈₉

C₂³

yes

characteristic

#95×C₈₉

—

#95×C₈₉

—

C₂²×Dic₈₉

—

C₂×#10623494

—

C₂×#10623494

—

C₂×#10623494

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

C₂×Q₈×C₈₉

—

C₂×Q₈×C₈₉

—

C₂×Q₈×C₈₉

—

C₂×Q₈×C₈₉

—

C₂×Q₈×C₈₉

Q₁₆

yes

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

C₂×D₄

yes

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄²×C₈₉

—

C₄²×C₈₉

—

C₂³×C₈₉

#120

yes

characteristic

Q₈×C₈₉

—

Q₈×C₈₉

—

Q₈×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

C₂×Q₁₆

yes

—

C₂×C₄×C₈₉

#137

yes

—

C₂×Dic₈₉

—

#10623494

—

C₂²×C₈₉

#451

yes

—

C₂²×C₈₉

#453

yes

—

C₂²×C₈₉

#458

yes

characteristic

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

—

Dic₈₉

—

#7837

—

maximal, Sylow

C₂×C₈₉

#1614

yes

—

C₂×C₈₉

#1633

yes

—

C₂×C₈₉

#1655

yes

characteristic

#2811

D₈₉

yes

characteristic

#2095

—

#1272

—

C₈₉

#7837

yes

characteristic, complemented, Sylow

C₂×#107

—

178

—

C₂×#103

—

178

—

#395

—

#391

—

#391

C₂×D₈₉

yes

—

#384

—

#336

—

C₂²×Q₈

—

C₂²×Q₈

C₂²⋊D₈₉

yes

—

C₂²×C₈

—

178

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

178

—

C₂×C₄⋊C₄

C₂²⋊D₈₉

yes

—

C₂×C₄²

—

C₂×C₄²

C₂²×D₈₉

yes

characteristic

#107

—

356

—

#103

—

356

—

#95

—

#95

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

#13083564

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

356

—

C₂²×C₄

C₂×C₂²⋊D₈₉

yes

—

100

C₂×C₈

—

356

—

101

C₂×C₈

—

356

—

102

C₂×C₈

—

178

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

356

—

106

C₄⋊C₄

—

356

—

107

C₄²

—

108

C₄²

—

109

C₂³

#15667981

yes

characteristic

110

Q₈

—

111

Q₈

—

112

Q₈

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

712

—

121

C₂×C₄

C₂×#13083564

yes

—

122

C₂×C₄

#15668043

yes

—

123

C₈

—

356

—

124

C₂²

#19151754

yes

—

125

C₂²

#19151766

yes

—

126

C₂²

#19151788

yes

characteristic

127

C₄

—

128

C₄

—

129

C₄

—

130

C₄

—

131

C₄

—

1424

—

132

C₂

#26019277

yes

—

133

C₂

#26019392

yes

—

134

C₂

#26019541

yes

characteristic

	subgroup	G/H
center	C₂³	#15667981
commutator, cosocle	C₂×C₄²×C₈₉	C₂³
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₈₉×#2811	C₂
socle, prime radical	C₂³×C₈₉	#120
hypercenter	#2811	D₈₉
hypocenter	C₈₉	#7837
LCS	G ▷ C₂×C₄²×C₈₉ ▷ C₂³×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2811

subgroup

G/H

center

C₂³

#15667981

commutator, cosocle

C₂×C₄²×C₈₉

C₂³

Frattini

C₂×C₄²

C₂²×D₈₉

Fitting

C₈₉×#2811

C₂

C₂³×C₈₉

D₈₉

C₈₉

G ▷ C₂×C₄²×C₈₉ ▷ C₂³×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2811

N	H ≅ G/N	type
71. C₈₉	#7837	semidirect

H ≅ G/N

type

71. C₈₉

#7837

semidirect

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

subgroup	index
#26021790	2
#26018078	2
C₈₉×#2811	2
#7837	89

subgroup

index

#26021790

#26018078

C₈₉×#2811

#7837

Subgroups — #36443771

Conjugacy classes of subgroups

Complements

Maximal subgroups