Finite Group Databasebeta

← C₂²×C₄×C₁₄₅₁ #37551017

Subgroups — C₂²×C₄×C₁₄₅₁ #37551017

Order 23216.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₁₄₅₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₁₄₅₁	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₁₄₅₁	C₄	1	4	yes	direct product factor
4	C₂²×C₁₄₅₁	C₂²	1	3	yes	—
5	C₄×C₁₄₅₁	C₂²	1	4	yes	direct product factor
6	C₂×C₁₄₅₁	C₂×C₄	1	6	yes	direct product factor
7	C₂×C₁₄₅₁	C₂³	1	1	yes	characteristic
8	C₁₄₅₁	C₂²×C₄	1	1	yes	characteristic, direct product factor, Sylow
9	C₂²×C₄	C₁₄₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₂³	C₂×C₁₄₅₁	1	1	yes	characteristic
11	C₂×C₄	C₂×C₁₄₅₁	1	6	yes	direct product factor
12	C₂²	C₄×C₁₄₅₁	1	4	yes	direct product factor
13	C₂²	C₂²×C₁₄₅₁	1	3	yes	—
14	C₄	C₂²×C₁₄₅₁	1	4	yes	direct product factor
15	C₂	C₂×C₄×C₁₄₅₁	1	6	yes	direct product factor
16	C₂	C₂³×C₁₄₅₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂³×C₁₄₅₁
socle, prime radical	C₂³×C₁₄₅₁	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₁₄₅₁	C₂	direct (N × H)
3. C₂²×C₁₄₅₁	C₄	direct (N × H)
5. C₄×C₁₄₅₁	C₂²	direct (N × H)
6. C₂×C₁₄₅₁	C₂×C₄	direct (N × H)
8. C₁₄₅₁	C₂²×C₄	direct (N × H)
9. C₂²×C₄	C₁₄₅₁	direct (N × H)
11. C₂×C₄	C₂×C₁₄₅₁	direct (N × H)
12. C₂²	C₄×C₁₄₅₁	direct (N × H)
14. C₄	C₂²×C₁₄₅₁	direct (N × H)
15. C₂	C₂×C₄×C₁₄₅₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₁₄₅₁	2
C₂×C₄×C₁₄₅₁	2
C₂²×C₄	1451