Group #36385237 — subgroups

Subgroups — C₈₉×#7389 #36385237

Order 22784.

118 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 118 conjugacy classes of subgroups — too many to draw. Only its 50 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×#2179	C₂	1	1	yes	maximal, characteristic
2	C₈₉×#1398	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#1368	C₂	1	1	yes	maximal, characteristic, complemented
4	#508×C₈₉	C₄	1	1	yes	characteristic
5	#443×C₈₉	—	2	1	no	—
6	M₆₄×C₈₉	—	2	1	no	—
7	#368×C₈₉	C₄	1	1	yes	characteristic
8	#359×C₈₉	—	2	1	no	—
9	#346×C₈₉	C₂²	1	1	yes	characteristic
10	#334×C₈₉	—	2	1	no	—
11	#135×C₈₉	—	2	1	no	—
12	#131×C₈₉	—	4	1	no	—
13	Q₃₂×C₈₉	C₈	1	1	yes	characteristic, complemented
14	SD₃₂×C₈₉	—	2	1	no	—
15	D₁₆×C₈₉	C₈	1	1	yes	characteristic, complemented
16	C₂×C₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₁₆×C₈₉	D₄	1	1	yes	characteristic
18	#108×C₈₉	—	2	1	no	—
19	C₄⋊C₈×C₈₉	—	4	1	no	—
20	#104×C₈₉	—	4	1	no	—
21	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
22	C₃₂×C₈₉	—	2	2	no	—
23	#41×C₈₉	—	4	1	no	—
24	Q₁₆×C₈₉	—	2	1	no	—
25	SD₁₆×C₈₉	—	4	1	no	—
26	D₈×C₈₉	—	2	1	no	—
27	M₁₆×C₈₉	—	4	1	no	—
28	M₁₆×C₈₉	—	8	1	no	—
29	C₂×C₈×C₈₉	—	8	1	no	—
30	C₂×C₈×C₈₉	—	8	1	no	—
31	C₂×C₈×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×C₈×C₈₉	SD₁₆	1	1	yes	characteristic
33	C₄²×C₈₉	D₈	1	1	yes	characteristic
34	C₁₆×C₈₉	—	2	1	no	—
35	C₁₆×C₈₉	C₂×C₈	1	1	yes	characteristic
36	C₁₆×C₈₉	M₁₆	1	1	yes	characteristic
37	Q₈×C₈₉	—	4	1	no	—
38	D₄×C₈₉	—	4	1	no	—
39	D₄×C₈₉	—	8	1	no	—
40	C₂×C₄×C₈₉	—	2	1	no	—
41	C₂×C₄×C₈₉	—	8	1	no	—
42	C₂×C₄×C₈₉	#102	1	1	yes	characteristic
43	C₈×C₈₉	—	2	1	no	—
44	C₈×C₈₉	—	8	1	no	—
45	C₈×C₈₉	—	16	1	no	—
46	C₈×C₈₉	C₂²⋊C₈	1	1	yes	characteristic
47	C₈×C₈₉	#104	1	1	yes	characteristic
48	C₂²×C₈₉	—	8	1	no	—
49	C₂²×C₈₉	#360	1	1	yes	characteristic
50	C₄×C₈₉	—	4	1	no	—
51	C₄×C₈₉	—	8	1	no	—
52	C₄×C₈₉	D₄⋊C₈	1	1	yes	characteristic
53	C₄×C₈₉	#361	1	1	yes	characteristic
54	#7389	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
55	C₂×C₈₉	—	2	1	no	—
56	C₂×C₈₉	—	16	1	no	—
57	C₂×C₈₉	#1333	1	1	yes	characteristic
58	#2179	C₂×C₈₉	1	1	yes	characteristic
59	#1398	C₂×C₈₉	1	1	yes	characteristic, complemented
60	#1368	C₂×C₈₉	1	1	yes	characteristic, complemented
61	C₈₉	#7389	1	1	yes	characteristic, direct product factor, Sylow
62	#508	C₄×C₈₉	1	1	yes	characteristic
63	#443	—	2	1	no	—
64	M₆₄	—	2	1	no	—
65	#368	C₄×C₈₉	1	1	yes	characteristic
66	#359	—	2	1	no	—
67	#346	C₂²×C₈₉	1	1	yes	characteristic
68	#334	—	2	1	no	—
69	#135	—	2	1	no	—
70	#131	—	4	1	no	—
71	Q₃₂	C₈×C₈₉	1	1	yes	characteristic, complemented
72	SD₃₂	—	2	1	no	—
73	D₁₆	C₈×C₈₉	1	1	yes	characteristic, complemented
74	C₂×C₁₆	C₂×C₄×C₈₉	1	1	yes	characteristic
75	C₂×C₁₆	D₄×C₈₉	1	1	yes	characteristic
76	#108	—	2	1	no	—
77	C₄⋊C₈	—	4	1	no	—
78	#104	—	4	1	no	—
79	C₄×C₈	D₄×C₈₉	1	1	yes	characteristic
80	C₃₂	—	2	2	no	—
81	#41	—	4	1	no	—
82	Q₁₆	—	2	1	no	—
83	SD₁₆	—	4	1	no	—
84	D₈	—	2	1	no	—
85	M₁₆	—	4	1	no	—
86	M₁₆	—	8	1	no	—
87	C₂×C₈	—	8	1	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	C₂×C₈×C₈₉	1	1	yes	characteristic
94	C₁₆	M₁₆×C₈₉	1	1	yes	characteristic
95	Q₈	—	4	1	no	—
96	D₄	—	4	1	no	—
97	D₄	—	8	1	no	—
98	C₂×C₄	—	2	1	no	—
99	C₂×C₄	—	8	1	no	—
100	C₂×C₄	#102×C₈₉	1	1	yes	characteristic
101	C₈	—	2	1	no	—
102	C₈	—	8	1	no	—
103	C₈	—	16	1	no	—
104	C₈	C₂²⋊C₈×C₈₉	1	1	yes	characteristic
105	C₈	#104×C₈₉	1	1	yes	characteristic
106	C₂²	—	8	1	no	—
107	C₂²	#360×C₈₉	1	1	yes	characteristic
108	C₄	—	4	1	no	—
109	C₄	—	8	1	no	—
110	C₄	D₄⋊C₈×C₈₉	1	1	yes	characteristic
111	C₄	#361×C₈₉	1	1	yes	characteristic
112	C₂	—	2	1	no	—
113	C₂	—	16	1	no	—
114	C₂	C₈₉×#1333	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₈₉×#2179

C₂

yes

maximal, characteristic

C₈₉×#1398

C₂

yes

maximal, characteristic, complemented

C₈₉×#1368

C₂

yes

maximal, characteristic, complemented

#508×C₈₉

C₄

yes

characteristic

#443×C₈₉

—

M₆₄×C₈₉

—

#368×C₈₉

C₄

yes

characteristic

#359×C₈₉

—

#346×C₈₉

C₂²

yes

characteristic

#334×C₈₉

—

#135×C₈₉

—

#131×C₈₉

—

Q₃₂×C₈₉

C₈

yes

characteristic, complemented

SD₃₂×C₈₉

—

D₁₆×C₈₉

C₈

yes

characteristic, complemented

C₂×C₁₆×C₈₉

C₂×C₄

yes

characteristic

C₂×C₁₆×C₈₉

D₄

yes

characteristic

#108×C₈₉

—

C₄⋊C₈×C₈₉

—

#104×C₈₉

—

C₄×C₈×C₈₉

D₄

yes

characteristic

C₃₂×C₈₉

—

#41×C₈₉

—

Q₁₆×C₈₉

—

SD₁₆×C₈₉

—

D₈×C₈₉

—

M₁₆×C₈₉

—

M₁₆×C₈₉

—

C₂×C₈×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

C₂×C₈

yes

characteristic

C₁₆×C₈₉

M₁₆

yes

characteristic

Q₈×C₈₉

—

D₄×C₈₉

—

D₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

#102

yes

characteristic

C₈×C₈₉

—

C₈×C₈₉

—

C₈×C₈₉

—

C₈×C₈₉

C₂²⋊C₈

yes

characteristic

C₈×C₈₉

#104

yes

characteristic

C₂²×C₈₉

—

C₂²×C₈₉

#360

yes

characteristic

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

D₄⋊C₈

yes

C₄×C₈₉

yes

C₈₉

yes

maximal, characteristic, direct product factor, Sylow

C₂×C₈₉

—

C₂×C₈₉

—

C₂×C₈₉

#1333

yes

characteristic

#2179

C₂×C₈₉

yes

characteristic

#1398

C₂×C₈₉

yes

characteristic, complemented

#1368

C₂×C₈₉

yes

characteristic, complemented

C₈₉

#7389

yes

characteristic, direct product factor, Sylow

#508

C₄×C₈₉

yes

characteristic

#443

—

M₆₄

—

#368

C₄×C₈₉

yes

characteristic

#359

—

#346

C₂²×C₈₉

yes

—

—

—

Q₃₂

C₈×C₈₉

yes

characteristic, complemented

SD₃₂

—

D₁₆

C₈×C₈₉

yes

characteristic, complemented

C₂×C₁₆

C₂×C₄×C₈₉

yes

characteristic

C₂×C₁₆

D₄×C₈₉

yes

characteristic

#108

—

C₄⋊C₈

—

#104

—

C₄×C₈

D₄×C₈₉

yes

characteristic

C₃₂

—

#41

—

Q₁₆

—

SD₁₆

—

D₈

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊C₄×C₈₉

yes

characteristic

C₂×C₈

SD₁₆×C₈₉

yes

characteristic

C₄²

D₈×C₈₉

yes

characteristic

C₁₆

—

C₁₆

C₂×C₈×C₈₉

yes

characteristic

C₁₆

M₁₆×C₈₉

yes

characteristic

Q₈

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

#102×C₈₉

yes

characteristic

101

C₈

—

102

C₈

—

103

C₈

—

104

C₈

C₂²⋊C₈×C₈₉

yes

characteristic

105

C₈

#104×C₈₉

yes

characteristic

106

C₂²

—

107

C₂²

#360×C₈₉

yes

characteristic

108

C₄

—

109

C₄

—

110

C₄

D₄⋊C₈×C₈₉

yes

characteristic

111

C₄

#361×C₈₉

yes

characteristic

112

C₂

—

113

C₂

—

114

C₂

C₈₉×#1333

yes

characteristic

	subgroup	G/H
center, socle	C₂×C₈₉	#1333
commutator	C₁₆	C₂×C₈×C₈₉
Frattini, cosocle	#346	C₂²×C₈₉
prime radical	#508×C₈₉	C₄
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈₉ ◁ C₂×C₄×C₈₉ ◁ C₄×C₈×C₈₉ ◁ #346×C₈₉ ◁ G

subgroup

G/H

center, socle

C₂×C₈₉

#1333

commutator

C₁₆

C₂×C₈×C₈₉

Frattini, cosocle

#346

C₂²×C₈₉

prime radical

#508×C₈₉

C₄

LCS

G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂×C₈₉ ◁ C₂×C₄×C₈₉ ◁ C₄×C₈×C₈₉ ◁ #346×C₈₉ ◁ G

N	H ≅ G/N	type
2. C₈₉×#1398	C₂	semidirect
3. C₈₉×#1368	C₂	semidirect
13. Q₃₂×C₈₉	C₈	semidirect
15. D₁₆×C₈₉	C₈	semidirect
54. #7389	C₈₉	direct (N × H)
59. #1398	C₂×C₈₉	semidirect
60. #1368	C₂×C₈₉	semidirect
61. C₈₉	#7389	direct (N × H)
71. Q₃₂	C₈×C₈₉	semidirect
73. D₁₆	C₈×C₈₉	semidirect

H ≅ G/N

type

2. C₈₉×#1398

C₂

semidirect

3. C₈₉×#1368

C₂

semidirect

13. Q₃₂×C₈₉

C₈

semidirect

15. D₁₆×C₈₉

C₈

semidirect

54. #7389

C₈₉

direct (N × H)

59. #1398

C₂×C₈₉

semidirect

60. #1368

C₂×C₈₉

semidirect

61. C₈₉

#7389

direct (N × H)

71. Q₃₂

C₈×C₈₉

semidirect

73. D₁₆

C₈×C₈₉

semidirect

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

subgroup	index
C₈₉×#2179	2
C₈₉×#1398	2
C₈₉×#1368	2
#7389	89

subgroup

index

C₈₉×#2179

C₈₉×#1398

C₈₉×#1368

#7389

Subgroups — C₈₉×#7389 #36385237

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C89×#7389 #36385237

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#7389 #36385237