Finite Group Databasebeta

← C₂⁶×C₂₈₉ #72196307

Subgroups — C₂⁶×C₂₈₉ #72196307

Order 18496.

8475 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₂₈₉	C₂	1	63	yes	maximal, direct product factor
2	C₂⁴×C₂₈₉	C₂²	1	651	yes	direct product factor
3	C₂³×C₂₈₉	C₂³	1	1395	yes	direct product factor
4	C₂²×C₂₈₉	C₂⁴	1	651	yes	direct product factor
5	C₂⁶×C₁₇	C₁₇	1	1	yes	maximal, characteristic
6	C₂×C₂₈₉	C₂⁵	1	63	yes	direct product factor
7	C₂⁵×C₁₇	C₂×C₁₇	1	63	yes	—
8	C₂₈₉	C₂⁶	1	1	yes	characteristic, direct product factor, Sylow
9	C₂⁴×C₁₇	C₂²×C₁₇	1	651	yes	—
10	C₂³×C₁₇	C₂³×C₁₇	1	1395	yes	—
11	C₂²×C₁₇	C₂⁴×C₁₇	1	651	yes	—
12	C₂⁶	C₂₈₉	1	1	yes	characteristic, direct product factor, Sylow
13	C₂×C₁₇	C₂⁵×C₁₇	1	63	yes	—
14	C₂⁵	C₂×C₂₈₉	1	63	yes	direct product factor
15	C₁₇	C₂⁶×C₁₇	1	1	yes	characteristic
16	C₂⁴	C₂²×C₂₈₉	1	651	yes	direct product factor
17	C₂³	C₂³×C₂₈₉	1	1395	yes	direct product factor
18	C₂²	C₂⁴×C₂₈₉	1	651	yes	direct product factor
19	C₂	C₂⁵×C₂₈₉	1	63	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₁₇	C₂⁶×C₁₇
socle, prime radical	C₂⁶×C₁₇	C₁₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂⁵×C₂₈₉	C₂	direct (N × H)
2. C₂⁴×C₂₈₉	C₂²	direct (N × H)
3. C₂³×C₂₈₉	C₂³	direct (N × H)
4. C₂²×C₂₈₉	C₂⁴	direct (N × H)
6. C₂×C₂₈₉	C₂⁵	direct (N × H)
8. C₂₈₉	C₂⁶	direct (N × H)
12. C₂⁶	C₂₈₉	direct (N × H)
14. C₂⁵	C₂×C₂₈₉	direct (N × H)
16. C₂⁴	C₂²×C₂₈₉	direct (N × H)
17. C₂³	C₂³×C₂₈₉	direct (N × H)
18. C₂²	C₂⁴×C₂₈₉	direct (N × H)
19. C₂	C₂⁵×C₂₈₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁵×C₂₈₉	2
C₂⁶×C₁₇	17