Subgroups — C₈₉×#6896 #36342829

Order 21627.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×3₋¹⁺²×C₈₉	C₃	1	2	yes	maximal
2	C₉⋊C₉×C₈₉	C₃	1	4	yes	maximal, complemented
3	C₉⋊C₉×C₈₉	C₃	1	4	yes	maximal, complemented
4	C₃²⋊C₉×C₈₉	C₃	1	2	yes	maximal
5	C₉²×C₈₉	C₃	1	1	yes	maximal, characteristic, complemented
6	C₃³×C₈₉	C₃²	1	1	yes	characteristic
7	3₋¹⁺²×C₈₉	—	3	6	no	—
8	C₃×C₉×C₈₉	C₃²	1	2	yes	—
9	C₃×C₉×C₈₉	C₃²	1	4	yes	—
10	C₃×C₉×C₈₉	C₃²	1	4	yes	—
11	C₃×C₉×C₈₉	C₃²	1	2	yes	—
12	C₃²×C₈₉	—	3	2	no	—
13	C₃²×C₈₉	—	3	2	no	—
14	C₃²×C₈₉	C₃³	1	1	yes	characteristic
15	C₉×C₈₉	—	3	4	no	—
16	C₉×C₈₉	—	3	2	no	—
17	C₉×C₈₉	—	3	4	no	—
18	C₉×C₈₉	3₋¹⁺²	1	6	yes	complemented
19	C₃×C₈₉	—	9	1	no	—
20	C₃×C₈₉	C₃×3₋¹⁺²	1	2	yes	—
21	C₃×C₈₉	#737	1	2	yes	—
22	#6896	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
23	C₈₉	#6896	1	1	yes	characteristic, direct product factor, Sylow
24	C₃×3₋¹⁺²	C₃×C₈₉	1	2	yes	—
25	C₉⋊C₉	C₃×C₈₉	1	4	yes	complemented
26	C₉⋊C₉	C₃×C₈₉	1	4	yes	complemented
27	C₃²⋊C₉	C₃×C₈₉	1	2	yes	—
28	C₉²	C₃×C₈₉	1	1	yes	characteristic, complemented
29	C₃³	C₃²×C₈₉	1	1	yes	characteristic
30	3₋¹⁺²	—	3	6	no	—
31	C₃×C₉	C₃²×C₈₉	1	2	yes	—
32	C₃×C₉	C₃²×C₈₉	1	4	yes	—
33	C₃×C₉	C₃²×C₈₉	1	4	yes	—
34	C₃×C₉	C₃²×C₈₉	1	2	yes	—
35	C₃²	—	3	2	no	—
36	C₃²	—	3	2	no	—
37	C₃²	C₃³×C₈₉	1	1	yes	characteristic
38	C₉	—	3	4	no	—
39	C₉	—	3	2	no	—
40	C₉	—	3	4	no	—
41	C₉	3₋¹⁺²×C₈₉	1	6	yes	complemented
42	C₃	—	9	1	no	—
43	C₃	C₃×3₋¹⁺²×C₈₉	1	2	yes	—
44	C₃	#737×C₈₉	1	2	yes	—

	subgroup	G/H
center, socle	C₃²×C₈₉	C₃³
commutator, Frattini, cosocle	C₃²	C₃³×C₈₉
prime radical	C₃³×C₈₉	C₃²
LCS	G ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃²×C₈₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₉⋊C₉×C₈₉	C₃	semidirect
3. C₉⋊C₉×C₈₉	C₃	semidirect
5. C₉²×C₈₉	C₃	semidirect
18. C₉×C₈₉	3₋¹⁺²	semidirect
22. #6896	C₈₉	direct (N × H)
23. C₈₉	#6896	direct (N × H)
25. C₉⋊C₉	C₃×C₈₉	semidirect
26. C₉⋊C₉	C₃×C₈₉	semidirect
28. C₉²	C₃×C₈₉	semidirect
41. C₉	3₋¹⁺²×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₃×3₋¹⁺²×C₈₉	3
C₉⋊C₉×C₈₉	3
C₃²⋊C₉×C₈₉	3
C₉²×C₈₉	3
#6896	89

Subgroups — C89×#6896 #36342829

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#6896 #36342829