Group #36385292 — subgroups

Subgroups — C₈₉×#7444 #36385292

Order 22784.

152 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 58 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	C₈₉×#2246	C₂	1	1	yes	maximal, characteristic
2	C₈₉×C₄⋊C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#1371	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₆×C₈₉	—	2	1	no	—
5	C₂×D₁₆×C₈₉	C₄	1	2	yes	—
6	#493×C₈₉	—	2	1	no	—
7	C₂×C₃₂×C₈₉	—	2	1	no	—
8	C₄×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
9	#335×C₈₉	—	2	1	no	—
10	C₂×D₈×C₈₉	—	2	2	no	—
11	C₂×D₈×C₈₉	—	4	1	no	—
12	#127×C₈₉	—	4	1	no	—
13	D₁₆×C₈₉	—	4	2	no	—
14	D₁₆×C₈₉	—	4	1	no	—
15	D₁₆×C₈₉	—	4	1	no	—
16	C₂×C₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₁₆×C₈₉	D₄	1	1	yes	characteristic
18	C₄⋊C₈×C₈₉	—	4	1	no	—
19	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
20	C₃₂×C₈₉	—	4	1	no	—
21	C₂×D₄×C₈₉	—	4	2	no	—
22	C₂×D₄×C₈₉	—	8	1	no	—
23	C₂×D₄×C₈₉	—	8	1	no	—
24	D₈×C₈₉	—	4	2	no	—
25	D₈×C₈₉	—	4	2	no	—
26	D₈×C₈₉	—	8	2	no	—
27	C₂×C₈×C₈₉	—	8	1	no	—
28	C₂×C₈×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×C₈×C₈₉	SD₁₆	1	1	yes	characteristic
30	C₄²×C₈₉	D₈	1	1	yes	characteristic
31	C₁₆×C₈₉	—	2	1	no	—
32	C₁₆×C₈₉	D₈	1	1	yes	characteristic
33	C₁₆×C₈₉	SD₁₆	1	1	yes	characteristic
34	C₂³×C₈₉	—	8	2	no	—
35	D₄×C₈₉	—	8	2	no	—
36	D₄×C₈₉	—	8	2	no	—
37	D₄×C₈₉	—	16	2	no	—
38	D₄×C₈₉	—	16	1	no	—
39	D₄×C₈₉	—	16	1	no	—
40	C₂×C₄×C₈₉	#102	1	1	yes	characteristic
41	C₂×C₄×C₈₉	D₁₆	1	1	yes	characteristic
42	C₂×C₄×C₈₉	SD₃₂	1	1	yes	characteristic
43	C₈×C₈₉	—	2	1	no	—
44	C₈×C₈₉	—	16	1	no	—
45	C₈×C₈₉	#100	1	1	yes	characteristic
46	C₈×C₈₉	#102	1	1	yes	characteristic
47	C₂²×C₈₉	—	16	2	no	—
48	C₂²×C₈₉	—	16	2	no	—
49	C₂²×C₈₉	—	16	2	no	—
50	C₂²×C₈₉	#357	1	1	yes	characteristic
51	C₄×C₈₉	—	2	1	no	—
52	C₄×C₈₉	#331	1	1	yes	characteristic
53	C₄×C₈₉	#361	1	1	yes	characteristic
54	C₄×C₈₉	D₃₂	1	1	yes	characteristic
55	C₄×C₈₉	SD₆₄	1	1	yes	characteristic
56	#7444	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
57	C₂×C₈₉	—	32	2	no	—
58	C₂×C₈₉	#1361	1	1	yes	characteristic
59	C₂×C₈₉	#1415	1	1	yes	characteristic
60	C₂×C₈₉	#1419	1	1	yes	characteristic
61	#2246	C₂×C₈₉	1	1	yes	characteristic
62	C₄⋊C₃₂	C₂×C₈₉	1	1	yes	characteristic, complemented
63	#1371	C₂×C₈₉	1	1	yes	characteristic, complemented
64	C₈₉	#7444	1	1	yes	characteristic, direct product factor, Sylow
65	C₂×D₁₆	—	2	1	no	—
66	C₂×D₁₆	C₄×C₈₉	1	2	yes	—
67	#493	—	2	1	no	—
68	C₂×C₃₂	—	2	1	no	—
69	C₄×C₁₆	C₂²×C₈₉	1	1	yes	characteristic
70	#335	—	2	1	no	—
71	C₂×D₈	—	2	2	no	—
72	C₂×D₈	—	4	1	no	—
73	#127	—	4	1	no	—
74	D₁₆	—	4	2	no	—
75	D₁₆	—	4	1	no	—
76	D₁₆	—	4	1	no	—
77	C₂×C₁₆	C₂×C₄×C₈₉	1	1	yes	characteristic
78	C₂×C₁₆	D₄×C₈₉	1	1	yes	characteristic
79	C₄⋊C₈	—	4	1	no	—
80	C₄×C₈	D₄×C₈₉	1	1	yes	characteristic
81	C₃₂	—	4	1	no	—
82	C₂×D₄	—	4	2	no	—
83	C₂×D₄	—	8	1	no	—
84	C₂×D₄	—	8	1	no	—
85	D₈	—	4	2	no	—
86	D₈	—	4	2	no	—
87	D₈	—	8	2	no	—
88	C₂×C₈	—	8	1	no	—
89	C₂×C₈	C₂²⋊C₄×C₈₉	1	1	yes	characteristic
90	C₂×C₈	SD₁₆×C₈₉	1	1	yes	characteristic
91	C₄²	D₈×C₈₉	1	1	yes	characteristic
92	C₁₆	—	2	1	no	—
93	C₁₆	D₈×C₈₉	1	1	yes	characteristic
94	C₁₆	SD₁₆×C₈₉	1	1	yes	characteristic
95	C₂³	—	8	2	no	—
96	D₄	—	8	2	no	—
97	D₄	—	8	2	no	—
98	D₄	—	16	2	no	—
99	D₄	—	16	1	no	—
100	D₄	—	16	1	no	—
101	C₂×C₄	#102×C₈₉	1	1	yes	characteristic
102	C₂×C₄	D₁₆×C₈₉	1	1	yes	characteristic
103	C₂×C₄	SD₃₂×C₈₉	1	1	yes	characteristic
104	C₈	—	2	1	no	—
105	C₈	—	16	1	no	—
106	C₈	#100×C₈₉	1	1	yes	characteristic
107	C₈	#102×C₈₉	1	1	yes	characteristic
108	C₂²	—	16	2	no	—
109	C₂²	—	16	2	no	—
110	C₂²	—	16	2	no	—
111	C₂²	#357×C₈₉	1	1	yes	characteristic
112	C₄	—	2	1	no	—
113	C₄	#331×C₈₉	1	1	yes	characteristic
114	C₄	#361×C₈₉	1	1	yes	characteristic
115	C₄	D₃₂×C₈₉	1	1	yes	characteristic
116	C₄	SD₆₄×C₈₉	1	1	yes	characteristic
117	C₂	—	32	2	no	—
118	C₂	C₈₉×#1361	1	1	yes	characteristic
119	C₂	C₈₉×#1415	1	1	yes	characteristic
120	C₂	C₈₉×#1419	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₈₉×#2246

C₂

yes

maximal, characteristic

C₈₉×C₄⋊C₃₂

C₂

yes

maximal, characteristic, complemented

C₈₉×#1371

C₂

yes

maximal, characteristic, complemented

C₂×D₁₆×C₈₉

—

C₂×D₁₆×C₈₉

C₄

yes

—

#493×C₈₉

—

C₂×C₃₂×C₈₉

—

C₄×C₁₆×C₈₉

C₂²

yes

characteristic

#335×C₈₉

—

C₂×D₈×C₈₉

—

C₂×D₈×C₈₉

—

#127×C₈₉

—

D₁₆×C₈₉

—

D₁₆×C₈₉

—

D₁₆×C₈₉

—

C₂×C₁₆×C₈₉

C₂×C₄

yes

characteristic

C₂×C₁₆×C₈₉

D₄

yes

characteristic

C₄⋊C₈×C₈₉

—

C₄×C₈×C₈₉

D₄

yes

characteristic

C₃₂×C₈₉

—

C₂×D₄×C₈₉

—

C₂×D₄×C₈₉

—

C₂×D₄×C₈₉

—

D₈×C₈₉

—

D₈×C₈₉

—

D₈×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₈₉

SD₁₆

yes

characteristic

C₄²×C₈₉

D₈

yes

characteristic

C₁₆×C₈₉

—

C₁₆×C₈₉

D₈

yes

characteristic

C₁₆×C₈₉

SD₁₆

yes

characteristic

C₂³×C₈₉

—

D₄×C₈₉

—

D₄×C₈₉

—

D₄×C₈₉

—

D₄×C₈₉

—

D₄×C₈₉

—

C₂×C₄×C₈₉

#102

yes

characteristic

C₂×C₄×C₈₉

D₁₆

yes

characteristic

C₂×C₄×C₈₉

SD₃₂

yes

characteristic

C₈×C₈₉

—

C₈×C₈₉

—

C₈×C₈₉

yes

C₈×C₈₉

yes

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

#357

yes

characteristic

C₄×C₈₉

—

C₄×C₈₉

yes

C₄×C₈₉

yes

C₄×C₈₉

D₃₂

yes

characteristic

C₄×C₈₉

SD₆₄

yes

characteristic

#7444

C₈₉

yes

maximal, characteristic, direct product factor, Sylow

C₂×C₈₉

—

C₂×C₈₉

yes

C₂×C₈₉

yes

C₂×C₈₉

yes

C₂×C₈₉

yes

characteristic

C₄⋊C₃₂

C₂×C₈₉

yes

characteristic, complemented

#1371

C₂×C₈₉

yes

characteristic, complemented

C₈₉

#7444

yes

characteristic, direct product factor, Sylow

C₂×D₁₆

—

C₂×D₁₆

C₄×C₈₉

yes

—

#493

—

C₂×C₃₂

—

C₄×C₁₆

C₂²×C₈₉

yes

characteristic

#335

—

C₂×D₈

—

C₂×D₈

—

#127

—

D₁₆

—

D₁₆

—

D₁₆

—

C₂×C₁₆

C₂×C₄×C₈₉

yes

characteristic

C₂×C₁₆

D₄×C₈₉

yes

characteristic

C₄⋊C₈

—

C₄×C₈

D₄×C₈₉

yes

characteristic

C₃₂

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

D₈

—

D₈

—

D₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊C₄×C₈₉

yes

characteristic

C₂×C₈

SD₁₆×C₈₉

yes

characteristic

C₄²

D₈×C₈₉

yes

characteristic

C₁₆

—

C₁₆

D₈×C₈₉

yes

characteristic

C₁₆

SD₁₆×C₈₉

yes

characteristic

C₂³

—

D₄

—

D₄

—

D₄

—

D₄

—

100

D₄

—

101

C₂×C₄

#102×C₈₉

yes

characteristic

102

C₂×C₄

D₁₆×C₈₉

yes

characteristic

103

C₂×C₄

SD₃₂×C₈₉

yes

characteristic

104

C₈

—

105

C₈

—

106

C₈

#100×C₈₉

yes

characteristic

107

C₈

#102×C₈₉

yes

characteristic

108

C₂²

—

109

C₂²

—

110

C₂²

—

111

C₂²

#357×C₈₉

yes

characteristic

112

C₄

—

113

C₄

#331×C₈₉

yes

characteristic

114

C₄

#361×C₈₉

yes

characteristic

115

C₄

D₃₂×C₈₉

yes

characteristic

116

C₄

SD₆₄×C₈₉

yes

characteristic

117

C₂

—

118

C₂

C₈₉×#1361

yes

characteristic

119

C₂

C₈₉×#1415

yes

characteristic

120

C₂

C₈₉×#1419

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	#357
commutator	C₂×C₁₆	C₂×C₄×C₈₉
Frattini, cosocle	C₄×C₁₆	C₂²×C₈₉
prime radical	C₈₉×#2246	C₂
LCS	G ▷ C₂×C₁₆ ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₄²×C₈₉ ◁ C₄×C₈×C₈₉ ◁ C₄×C₁₆×C₈₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₈₉

#357

commutator

C₂×C₁₆

C₂×C₄×C₈₉

Frattini, cosocle

C₄×C₁₆

C₂²×C₈₉

prime radical

C₈₉×#2246

C₂

LCS

G ▷ C₂×C₁₆ ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₈₉ ◁ C₄²×C₈₉ ◁ C₄×C₈×C₈₉ ◁ C₄×C₁₆×C₈₉ ◁ G

N	H ≅ G/N	type
2. C₈₉×C₄⋊C₃₂	C₂	semidirect
3. C₈₉×#1371	C₂	semidirect
56. #7444	C₈₉	direct (N × H)
62. C₄⋊C₃₂	C₂×C₈₉	semidirect
63. #1371	C₂×C₈₉	semidirect
64. C₈₉	#7444	direct (N × H)

H ≅ G/N

type

2. C₈₉×C₄⋊C₃₂

C₂

semidirect

3. C₈₉×#1371

C₂

semidirect

56. #7444

C₈₉

direct (N × H)

62. C₄⋊C₃₂

C₂×C₈₉

semidirect

63. #1371

C₂×C₈₉

semidirect

64. C₈₉

#7444

direct (N × H)

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

subgroup	index
C₈₉×#2246	2
C₈₉×C₄⋊C₃₂	2
C₈₉×#1371	2
#7444	89

subgroup

index

C₈₉×#2246

C₈₉×C₄⋊C₃₂

C₈₉×#1371

#7444

Subgroups — C₈₉×#7444 #36385292

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C89×#7444 #36385292

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#7444 #36385292