Subgroups — #564×D₈₉ #26034394

Order 11392.

896 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉⋊#564	C₂	1	15	yes	maximal, complemented
2	#125×D₈₉	C₂	1	15	yes	maximal
3	#564×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#15668004	C₂²	1	15	yes	—
5	#15668003	C₂²	1	30	yes	—
6	#15668002	C₂²	1	60	yes	—
7	C₄⋊C₄×D₈₉	C₂²	1	30	yes	—
8	C₄²×D₈₉	C₂²	1	5	yes	—
9	#125×C₈₉	C₂²	1	15	yes	—
10	C₂×C₄×D₈₉	C₂³	1	15	yes	—
11	C₄⋊Dic₈₉	C₂³	1	30	yes	—
12	#13083553	C₂³	1	60	yes	—
13	C₄×Dic₈₉	C₂³	1	15	yes	—
14	C₄⋊C₄×C₈₉	C₂³	1	30	yes	—
15	C₄²×C₈₉	C₂³	1	5	yes	—
16	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
17	C₂×C₄×C₈₉	C₂⁴	1	15	yes	—
18	C₂×Dic₈₉	C₂⁴	1	15	yes	—
19	C₄×D₈₉	—	2	30	no	—
20	C₂²×C₈₉	C₂⁵	1	1	yes	characteristic
21	C₂×D₈₉	2₋¹⁺⁴	1	6	yes	—
22	C₄×C₈₉	—	2	15	no	—
23	Dic₈₉	—	2	15	no	—
24	C₂×C₈₉	C₂×2₋¹⁺⁴	1	3	yes	—
25	D₈₉	#564	1	4	yes	direct product factor
26	C₂×#564	—	89	1	no	maximal, Sylow
27	C₈₉	C₂×#564	1	1	yes	characteristic, complemented, Sylow
28	#564	—	89	15	no	—
29	#564	D₈₉	1	1	yes	characteristic, direct product factor
30	C₂×#125	—	89	15	no	—
31	#125	—	89	60	no	—
32	#125	—	89	30	no	—
33	#125	—	89	15	no	—
34	#125	C₂×D₈₉	1	15	yes	—
35	C₂×C₄⋊C₄	—	89	30	no	—
36	C₂×C₄²	—	89	5	no	—
37	C₂²×C₄	—	89	15	no	—
38	C₄⋊C₄	—	89	60	no	—
39	C₄⋊C₄	—	89	30	no	—
40	C₄⋊C₄	C₂²×D₈₉	1	30	yes	—
41	C₄²	—	89	15	no	—
42	C₄²	C₂²×D₈₉	1	5	yes	—
43	C₂³	—	89	1	no	—
44	C₂×C₄	—	89	15	no	—
45	C₂×C₄	—	178	30	no	—
46	C₂×C₄	C₂³×D₈₉	1	15	yes	—
47	C₂²	—	89	6	no	—
48	C₂²	C₂⁴×D₈₉	1	1	yes	characteristic
49	C₄	—	2	15	no	—
50	C₄	—	178	15	no	—
51	C₂	—	89	4	no	—
52	C₂	2₋¹⁺⁴×D₈₉	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₉
commutator, socle, cosocle	C₂²×C₈₉	C₂⁵
Fitting	#564×C₈₉	C₂
prime radical	C₂²×D₈₉	C₂⁴
hypercenter	#564	D₈₉
hypocenter	C₈₉	C₂×#564
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ #564

Complements

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

N	H ≅ G/N	type
1. C₈₉⋊#564	C₂	semidirect
3. #564×C₈₉	C₂	semidirect
25. D₈₉	#564	direct (N × H)
27. C₈₉	C₂×#564	semidirect
29. #564	D₈₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈₉⋊#564	2
#125×D₈₉	2
#564×C₈₉	2
C₂×#564	89

Subgroups — #564×D89 #26034394

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #564×D₈₉ #26034394