Group #36441830 — subgroups

Subgroups — #36441830

Order 22784.

126 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 45 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	#26022007	C₂	1	1	yes	maximal, characteristic
2	#26018392	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#1400	C₂	1	1	yes	maximal, characteristic
4	C₂×#15667952	C₄	1	1	yes	characteristic
5	C₂×C₈×Dic₈₉	C₄	1	1	yes	characteristic
6	#19151432	—	2	1	no	—
7	#19151416	—	2	1	no	—
8	#19151416	—	2	1	no	—
9	C₂×M₃₂×C₈₉	C₂²	1	1	yes	characteristic
10	M₆₄×C₈₉	—	2	1	no	—
11	C₂²×#10623494	C₈	1	1	yes	characteristic
12	C₂×C₄×Dic₈₉	C₈	1	1	yes	characteristic
13	#15667952	—	4	1	no	—
14	C₂×#13083549	—	2	1	no	—
15	C₈×Dic₈₉	—	2	1	no	—
16	C₈×Dic₈₉	—	2	1	no	—
17	#15667918	—	4	1	no	—
18	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
19	M₃₂×C₈₉	—	4	1	no	—
20	C₂×C₁₆×C₈₉	D₄	1	1	yes	characteristic
21	C₂×C₁₆×C₈₉	D₄	1	1	yes	characteristic
22	C₃₂×C₈₉	—	4	1	no	—
23	C₂²×Dic₈₉	—	2	1	no	—
24	C₂×#10623494	—	2	1	no	—
25	C₂×#10623494	—	4	1	no	—
26	C₄×Dic₈₉	—	2	1	no	—
27	C₄×Dic₈₉	C₁₆	1	1	yes	characteristic
28	C₄×Dic₈₉	C₁₆	1	1	yes	characteristic
29	#13083549	—	4	1	no	—
30	C₂²×C₄×C₈₉	C₂×C₈	1	1	yes	characteristic
31	C₂×C₈×C₈₉	—	2	1	no	—
32	C₂×C₈×C₈₉	—	2	1	no	—
33	C₂×C₈×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×C₈×C₈₉	M₁₆	1	1	yes	characteristic
35	C₁₆×C₈₉	—	2	1	no	—
36	C₁₆×C₈₉	—	2	1	no	—
37	C₂³×C₈₉	M₃₂	1	1	yes	characteristic
38	C₂×C₄×C₈₉	—	2	1	no	—
39	C₂×C₄×C₈₉	—	2	1	no	—
40	C₂×C₄×C₈₉	C₂²⋊C₈	1	1	yes	characteristic
41	C₂×C₄×C₈₉	C₂×C₁₆	1	1	yes	characteristic
42	C₂×Dic₈₉	—	2	1	no	—
43	C₂×Dic₈₉	—	2	1	no	—
44	C₂×Dic₈₉	—	4	2	no	—
45	C₈×C₈₉	—	2	1	no	—
46	C₈×C₈₉	#99	1	1	yes	characteristic
47	C₈×C₈₉	#101	1	1	yes	characteristic
48	#10623494	—	4	1	no	—
49	C₂²×C₈₉	—	2	1	no	—
50	C₂²×C₈₉	—	4	1	no	—
51	C₂²×C₈₉	C₂²⋊C₁₆	1	1	yes	characteristic
52	C₄×C₈₉	—	2	1	no	—
53	C₄×C₈₉	#324	1	1	yes	characteristic
54	C₄×C₈₉	#349	1	1	yes	characteristic
55	Dic₈₉	—	2	2	no	—
56	Dic₈₉	—	4	1	no	—
57	#7364	—	89	1	no	maximal, Sylow
58	C₂×C₈₉	—	2	1	no	—
59	C₂×C₈₉	—	4	1	no	—
60	C₂×C₈₉	#1322	1	1	yes	characteristic
61	#2150	—	89	1	no	—
62	#1400	—	89	1	no	—
63	#1400	D₈₉	1	1	yes	characteristic
64	C₈₉	#7364	1	1	yes	characteristic, complemented, Sylow
65	C₂×M₃₂	—	89	1	no	—
66	C₂×M₃₂	C₂×D₈₉	1	1	yes	characteristic
67	C₂×C₄×C₈	—	89	1	no	—
68	M₆₄	—	2	1	no	—
69	M₆₄	—	178	1	no	—
70	C₄⋊C₁₆	—	178	1	no	—
71	C₄⋊C₁₆	—	178	1	no	—
72	C₂²×C₈	—	89	1	no	—
73	C₂²×C₈	C₄×D₈₉	1	1	yes	characteristic
74	C₂×C₄²	—	89	1	no	—
75	M₃₂	—	4	1	no	—
76	M₃₂	—	356	1	no	—
77	C₂×C₁₆	—	178	1	no	—
78	C₂×C₁₆	D₃₅₆	1	1	yes	characteristic
79	C₂×C₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
80	C₄×C₈	—	178	1	no	—
81	C₄×C₈	—	178	1	no	—
82	C₃₂	—	4	1	no	—
83	C₃₂	—	356	1	no	—
84	C₂²×C₄	—	178	1	no	—
85	C₂²×C₄	C₈×D₈₉	1	1	yes	characteristic
86	C₂×C₈	—	2	1	no	—
87	C₂×C₈	—	2	1	no	—
88	C₂×C₈	—	356	1	no	—
89	C₂×C₈	—	178	1	no	—
90	C₂×C₈	#13083551	1	1	yes	characteristic
91	C₂×C₈	#13083557	1	1	yes	characteristic
92	C₄²	—	89	1	no	—
93	C₄²	—	89	1	no	—
94	C₄²	—	178	1	no	—
95	C₁₆	—	2	1	no	—
96	C₁₆	—	2	1	no	—
97	C₁₆	—	356	1	no	—
98	C₂³	#15667951	1	1	yes	characteristic
99	C₂×C₄	—	2	1	no	—
100	C₂×C₄	—	2	1	no	—
101	C₂×C₄	—	356	2	no	—
102	C₂×C₄	—	178	1	no	—
103	C₂×C₄	—	178	1	no	—
104	C₂×C₄	#15667924	1	1	yes	characteristic
105	C₂×C₄	C₁₆×D₈₉	1	1	yes	characteristic
106	C₈	—	2	1	no	—
107	C₈	—	356	1	no	—
108	C₈	#15667926	1	1	yes	characteristic
109	C₈	#15667930	1	1	yes	characteristic
110	C₂²	—	2	1	no	—
111	C₂²	—	4	1	no	—
112	C₂²	#19151377	1	1	yes	characteristic
113	C₄	—	2	1	no	—
114	C₄	—	356	1	no	—
115	C₄	—	178	2	no	—
116	C₄	#19151323	1	1	yes	characteristic
117	C₄	#19151379	1	1	yes	characteristic
118	C₂	—	2	1	no	—
119	C₂	—	4	1	no	—
120	C₂	#26018191	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#26022007

C₂

yes

maximal, characteristic

#26018392

C₂

yes

maximal, characteristic

C₈₉×#1400

C₂

yes

maximal, characteristic

C₂×#15667952

C₄

yes

characteristic

C₂×C₈×Dic₈₉

C₄

yes

—

—

—

C₂×M₃₂×C₈₉

C₂²

yes

characteristic

M₆₄×C₈₉

—

C₂²×#10623494

C₈

yes

characteristic

C₂×C₄×Dic₈₉

C₈

yes

characteristic

#15667952

—

C₂×#13083549

—

C₈×Dic₈₉

—

C₈×Dic₈₉

—

#15667918

—

C₂²×C₈×C₈₉

C₂×C₄

yes

characteristic

M₃₂×C₈₉

—

C₂×C₁₆×C₈₉

D₄

yes

characteristic

C₂×C₁₆×C₈₉

D₄

yes

characteristic

C₃₂×C₈₉

—

C₂²×Dic₈₉

—

C₂×#10623494

—

C₂×#10623494

—

C₄×Dic₈₉

—

C₄×Dic₈₉

C₁₆

yes

characteristic

C₄×Dic₈₉

C₁₆

yes

characteristic

#13083549

—

C₂²×C₄×C₈₉

C₂×C₈

yes

characteristic

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₈₉

M₁₆

yes

characteristic

C₁₆×C₈₉

—

C₁₆×C₈₉

—

C₂³×C₈₉

M₃₂

yes

characteristic

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₈₉

C₂×C₁₆

yes

characteristic

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₈×C₈₉

—

C₈×C₈₉

yes

C₈×C₈₉

yes

—

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

C₂²⋊C₁₆

yes

characteristic

C₄×C₈₉

—

C₄×C₈₉

yes

C₄×C₈₉

yes

Dic₈₉

—

Dic₈₉

—

#7364

—

maximal, Sylow

C₂×C₈₉

—

C₂×C₈₉

—

C₂×C₈₉

yes

—

—

D₈₉

yes

characteristic

C₈₉

#7364

yes

characteristic, complemented, Sylow

C₂×M₃₂

—

C₂×M₃₂

C₂×D₈₉

yes

characteristic

C₂×C₄×C₈

—

M₆₄

—

M₆₄

—

178

—

C₄⋊C₁₆

—

178

—

C₄⋊C₁₆

—

178

—

C₂²×C₈

—

C₂²×C₈

C₄×D₈₉

yes

characteristic

C₂×C₄²

—

M₃₂

—

M₃₂

—

356

—

C₂×C₁₆

—

178

—

C₂×C₁₆

D₃₅₆

yes

characteristic

C₂×C₁₆

C₂²⋊D₈₉

yes

characteristic

C₄×C₈

—

178

—

C₄×C₈

—

178

—

C₃₂

—

C₃₂

—

356

—

C₂²×C₄

—

178

—

C₂²×C₄

C₈×D₈₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

356

—

C₂×C₈

—

178

—

C₂×C₈

yes

C₂×C₈

yes

C₄²

—

C₄²

—

C₄²

—

178

—

C₁₆

—

C₁₆

—

C₁₆

—

356

—

C₂³

#15667951

yes

characteristic

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

356

—

102

C₂×C₄

—

178

—

103

C₂×C₄

—

178

—

104

C₂×C₄

#15667924

yes

characteristic

105

C₂×C₄

C₁₆×D₈₉

yes

characteristic

106

C₈

—

107

C₈

—

356

—

108

C₈

#15667926

yes

characteristic

109

C₈

#15667930

yes

characteristic

110

C₂²

—

111

C₂²

—

112

C₂²

#19151377

yes

characteristic

113

C₄

—

114

C₄

—

356

—

115

C₄

—

178

—

116

C₄

#19151323

yes

characteristic

117

C₄

#19151379

yes

characteristic

118

C₂

—

119

C₂

—

120

C₂

#26018191

yes

characteristic

	subgroup	G/H
center	C₈	#15667926
commutator	C₂×C₄×C₈₉	C₂×C₁₆
Frattini	C₂×M₃₂	C₂×D₈₉
Fitting	C₈₉×#1400	C₂
socle	C₂×C₈₉	#1322
prime radical	C₂³×C₈₉	M₃₂
cosocle	C₂×M₃₂×C₈₉	C₂²
hypercenter	#1400	D₈₉
hypocenter	C₈₉	#7364
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂²×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₂×M₃₂ ◁ #1400

subgroup

G/H

center

C₈

#15667926

commutator

C₂×C₄×C₈₉

C₂×C₁₆

Frattini

C₂×M₃₂

C₂×D₈₉

Fitting

C₈₉×#1400

C₂

socle

C₂×C₈₉

#1322

prime radical

C₂³×C₈₉

M₃₂

cosocle

C₂×M₃₂×C₈₉

C₂²

D₈₉

C₈₉

G ▷ C₂×C₄×C₈₉ ▷ C₂²×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₂×M₃₂ ◁ #1400

N	H ≅ G/N	type
64. C₈₉	#7364	semidirect

H ≅ G/N

type

64. C₈₉

#7364

semidirect

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

subgroup	index
#26022007	2
#26018392	2
C₈₉×#1400	2
#7364	89

subgroup

index

#26022007

#26018392

C₈₉×#1400

#7364

Subgroups — #36441830

Conjugacy classes of subgroups

Complements

Maximal subgroups