Group #36385978 — subgroups

Subgroups — C₈₉×#8130 #36385978

Order 22784.

520 conjugacy classes of subgroups; only the 230 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 230 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×#2920	C₂	1	3	yes	maximal
2	C₈₉×#1309	C₂	1	4	yes	maximal, complemented
3	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
4	#432×C₈₉	—	2	6	no	—
5	#431×C₈₉	—	2	6	no	—
6	#423×C₈₉	C₂²	1	6	yes	—
7	#407×C₈₉	C₄	1	6	yes	—
8	C₄×M₁₆×C₈₉	C₄	1	6	yes	—
9	C₂³×C₄×C₈₉	C₂×C₄	1	3	yes	—
10	C₂×M₁₆×C₈₉	C₂×C₄	1	12	yes	—
11	C₂×C₄²×C₈₉	C₂×C₄	1	3	yes	—
12	C₂×C₄²×C₈₉	D₄	1	6	yes	—
13	C₂×C₄²×C₈₉	Q₈	1	2	yes	—
14	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
15	C₄⋊C₈×C₈₉	—	2	12	no	—
16	C₂²⋊C₈×C₈₉	—	2	12	no	—
17	#97×C₈₉	—	2	6	no	—
18	C₄×C₈×C₈₉	—	2	6	no	—
19	C₂⁴×C₈₉	C₄²	1	1	yes	characteristic
20	C₂²×C₄×C₈₉	—	4	6	no	—
21	C₂²×C₄×C₈₉	C₄²	1	3	yes	—
22	C₂²×C₄×C₈₉	C₂²⋊C₄	1	6	yes	—
23	C₂²×C₄×C₈₉	C₄⋊C₄	1	6	yes	—
24	C₂²×C₄×C₈₉	C₂²×C₄	1	3	yes	—
25	M₁₆×C₈₉	—	4	12	no	—
26	C₂×C₈×C₈₉	—	2	12	no	—
27	C₄²×C₈₉	C₂²⋊C₄	1	3	yes	—
28	C₄²×C₈₉	C₂²⋊C₄	1	3	yes	—
29	C₄²×C₈₉	C₄⋊C₄	1	6	yes	—
30	C₄²×C₈₉	C₂×D₄	1	3	yes	—
31	C₄²×C₈₉	C₂×Q₈	1	1	yes	characteristic
32	C₂³×C₈₉	—	4	3	no	—
33	C₂³×C₈₉	#95	1	2	yes	—
34	C₂³×C₈₉	C₂×C₄²	1	1	yes	characteristic
35	C₂×C₄×C₈₉	—	2	6	no	—
36	C₂×C₄×C₈₉	—	2	12	no	—
37	C₂×C₄×C₈₉	—	4	3	no	—
38	C₂×C₄×C₈₉	—	4	6	no	—
39	C₂×C₄×C₈₉	#95	1	6	yes	—
40	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	3	yes	—
41	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	3	yes	—
42	C₈×C₈₉	—	4	12	no	—
43	C₂²×C₈₉	—	2	6	no	—
44	C₂²×C₈₉	—	2	3	no	—
45	C₂²×C₈₉	—	4	4	no	—
46	C₂²×C₈₉	C₂×#95	1	1	yes	characteristic
47	C₄×C₈₉	—	2	6	no	—
48	C₄×C₈₉	—	2	3	no	—
49	C₄×C₈₉	#413	1	6	yes	—
50	#8130	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
51	C₂×C₈₉	—	4	2	no	—
52	C₂×C₈₉	—	4	1	no	—
53	C₂×C₈₉	#1742	1	3	yes	—
54	#2920	C₂×C₈₉	1	3	yes	—
55	#1309	C₂×C₈₉	1	4	yes	complemented
56	C₈₉	#8130	1	1	yes	characteristic, direct product factor, Sylow
57	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
58	#432	—	2	6	no	—
59	#431	—	2	6	no	—
60	#423	C₂²×C₈₉	1	6	yes	—
61	#407	C₄×C₈₉	1	6	yes	—
62	C₄×M₁₆	C₄×C₈₉	1	6	yes	—
63	C₂³×C₄	C₂×C₄×C₈₉	1	3	yes	—
64	C₂×M₁₆	C₂×C₄×C₈₉	1	12	yes	—
65	C₂×C₄²	C₂×C₄×C₈₉	1	3	yes	—
66	C₂×C₄²	D₄×C₈₉	1	6	yes	—
67	C₂×C₄²	Q₈×C₈₉	1	2	yes	—
68	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
69	C₄⋊C₈	—	2	12	no	—
70	C₂²⋊C₈	—	2	12	no	—
71	#97	—	2	6	no	—
72	C₄×C₈	—	2	6	no	—
73	C₂⁴	C₄²×C₈₉	1	1	yes	characteristic
74	C₂²×C₄	—	4	6	no	—
75	C₂²×C₄	C₄²×C₈₉	1	3	yes	—
76	C₂²×C₄	C₂²⋊C₄×C₈₉	1	6	yes	—
77	C₂²×C₄	C₄⋊C₄×C₈₉	1	6	yes	—
78	C₂²×C₄	C₂²×C₄×C₈₉	1	3	yes	—
79	M₁₆	—	4	12	no	—
80	C₂×C₈	—	2	12	no	—
81	C₄²	C₂²⋊C₄×C₈₉	1	3	yes	—
82	C₄²	C₂²⋊C₄×C₈₉	1	3	yes	—
83	C₄²	C₄⋊C₄×C₈₉	1	6	yes	—
84	C₄²	C₂×D₄×C₈₉	1	3	yes	—
85	C₄²	C₂×Q₈×C₈₉	1	1	yes	characteristic
86	C₂³	—	4	3	no	—
87	C₂³	#95×C₈₉	1	2	yes	—
88	C₂³	C₂×C₄²×C₈₉	1	1	yes	characteristic
89	C₂×C₄	—	2	6	no	—
90	C₂×C₄	—	2	12	no	—
91	C₂×C₄	—	4	3	no	—
92	C₂×C₄	—	4	6	no	—
93	C₂×C₄	#95×C₈₉	1	6	yes	—
94	C₂×C₄	C₂×C₂²⋊C₄×C₈₉	1	3	yes	—
95	C₂×C₄	C₂×C₄⋊C₄×C₈₉	1	3	yes	—
96	C₈	—	4	12	no	—
97	C₂²	—	2	6	no	—
98	C₂²	—	2	3	no	—
99	C₂²	—	4	4	no	—
100	C₂²	C₂×#95×C₈₉	1	1	yes	characteristic
101	C₄	—	2	6	no	—
102	C₄	—	2	3	no	—
103	C₄	#413×C₈₉	1	6	yes	—
104	C₂	—	4	2	no	—
105	C₂	—	4	1	no	—
106	C₂	C₈₉×#1742	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₈₉×#2920

C₂

yes

maximal

C₈₉×#1309

C₂

yes

maximal, complemented

C₂²×C₄²×C₈₉

C₂²

yes

characteristic

#432×C₈₉

—

#431×C₈₉

—

#423×C₈₉

C₂²

yes

—

#407×C₈₉

C₄

yes

—

C₄×M₁₆×C₈₉

C₄

yes

—

C₂³×C₄×C₈₉

C₂×C₄

yes

—

C₂×M₁₆×C₈₉

C₂×C₄

yes

—

C₂×C₄²×C₈₉

C₂×C₄

yes

—

C₂×C₄²×C₈₉

D₄

yes

—

C₂×C₄²×C₈₉

Q₈

yes

—

C₂×C₄²×C₈₉

C₂³

yes

characteristic

C₄⋊C₈×C₈₉

—

C₂²⋊C₈×C₈₉

—

#97×C₈₉

—

C₄×C₈×C₈₉

—

C₂⁴×C₈₉

C₄²

yes

characteristic

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

C₄²

yes

—

C₂²×C₄×C₈₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₈₉

C₄⋊C₄

yes

—

C₂²×C₄×C₈₉

C₂²×C₄

yes

—

M₁₆×C₈₉

—

C₂×C₈×C₈₉

—

C₄²×C₈₉

C₂²⋊C₄

yes

—

C₄²×C₈₉

C₂²⋊C₄

yes

—

C₄²×C₈₉

C₄⋊C₄

yes

—

C₄²×C₈₉

C₂×D₄

yes

—

C₄²×C₈₉

C₂×Q₈

yes

characteristic

C₂³×C₈₉

—

C₂³×C₈₉

#95

yes

—

C₂³×C₈₉

C₂×C₄²

yes

characteristic

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

#95

yes

—

C₂×C₄×C₈₉

C₂×C₂²⋊C₄

yes

—

C₂×C₄×C₈₉

C₂×C₄⋊C₄

yes

—

C₈×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

C₂×#95

yes

characteristic

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

#413

yes

—

#8130

C₈₉

yes

maximal, characteristic, direct product factor, Sylow

C₂×C₈₉

—

C₂×C₈₉

—

C₂×C₈₉

#1742

yes

—

#2920

C₂×C₈₉

yes

—

#1309

C₂×C₈₉

yes

complemented

C₈₉

#8130

yes

characteristic, direct product factor, Sylow

C₂²×C₄²

C₂²×C₈₉

yes

—

—

C₂²×C₈₉

yes

—

#407

C₄×C₈₉

yes

—

C₄×M₁₆

C₄×C₈₉

yes

—

C₂³×C₄

C₂×C₄×C₈₉

yes

—

C₂×M₁₆

C₂×C₄×C₈₉

yes

—

C₂×C₄²

C₂×C₄×C₈₉

yes

—

C₂×C₄²

D₄×C₈₉

yes

—

C₂×C₄²

Q₈×C₈₉

yes

—

C₂×C₄²

C₂³×C₈₉

yes

characteristic

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

C₄×C₈

—

C₂⁴

C₄²×C₈₉

yes

characteristic

C₂²×C₄

—

C₂²×C₄

C₄²×C₈₉

yes

—

C₂²×C₄

C₂²⋊C₄×C₈₉

yes

—

C₂²×C₄

C₄⋊C₄×C₈₉

yes

—

C₂²×C₄

C₂²×C₄×C₈₉

yes

—

M₁₆

—

C₂×C₈

—

C₄²

C₂²⋊C₄×C₈₉

yes

—

C₄²

C₂²⋊C₄×C₈₉

yes

—

C₄²

C₄⋊C₄×C₈₉

yes

—

C₄²

C₂×D₄×C₈₉

yes

—

C₄²

C₂×Q₈×C₈₉

yes

characteristic

C₂³

—

C₂³

#95×C₈₉

yes

—

C₂³

C₂×C₄²×C₈₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#95×C₈₉

yes

—

C₂×C₄

C₂×C₂²⋊C₄×C₈₉

yes

—

C₂×C₄

C₂×C₄⋊C₄×C₈₉

yes

—

C₈

—

C₂²

—

C₂²

—

C₂²

—

100

C₂²

C₂×#95×C₈₉

yes

characteristic

101

C₄

—

102

C₄

—

103

C₄

#413×C₈₉

yes

—

104

C₂

—

105

C₂

—

106

C₂

C₈₉×#1742

yes

—

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂×#95
commutator	C₂³	C₂×C₄²×C₈₉
Frattini, cosocle	C₂×C₄²	C₂³×C₈₉
prime radical	C₂⁴×C₈₉	C₄²
LCS	G ▷ C₂³ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₂²×C₄²×C₈₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₈₉

C₂×#95

commutator

C₂³

C₂×C₄²×C₈₉

Frattini, cosocle

C₂×C₄²

C₂³×C₈₉

prime radical

C₂⁴×C₈₉

C₄²

LCS

G ▷ C₂³ ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₈₉ ◁ C₂²×C₄²×C₈₉ ◁ G

N	H ≅ G/N	type
2. C₈₉×#1309	C₂	semidirect
50. #8130	C₈₉	direct (N × H)
55. #1309	C₂×C₈₉	semidirect
56. C₈₉	#8130	direct (N × H)

H ≅ G/N

type

2. C₈₉×#1309

C₂

semidirect

50. #8130

C₈₉

direct (N × H)

55. #1309

C₂×C₈₉

semidirect

56. C₈₉

#8130

direct (N × H)

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

subgroup	index
C₈₉×#2920	2
C₈₉×#1309	2
#8130	89

subgroup

index

C₈₉×#2920

C₈₉×#1309

#8130

Subgroups — C₈₉×#8130 #36385978

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C89×#8130 #36385978

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#8130 #36385978