Finite Group Databasebeta

← C₈×C₁₉×C₇₃ #72189607

Subgroups — C₈×C₁₉×C₇₃ #72189607

Order 11096.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₉×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×C₇₃	C₄	1	1	yes	characteristic
3	C₁₉×C₇₃	C₈	1	1	yes	characteristic, direct product factor, Hall
4	C₈×C₇₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₄×C₇₃	C₂×C₁₉	1	1	yes	characteristic
6	C₈×C₁₉	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₇₃	C₄×C₁₉	1	1	yes	characteristic
8	C₄×C₁₉	C₂×C₇₃	1	1	yes	characteristic
9	C₇₃	C₈×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
10	C₂×C₁₉	C₄×C₇₃	1	1	yes	characteristic
11	C₁₉	C₈×C₇₃	1	1	yes	characteristic, direct product factor, Sylow
12	C₈	C₁₉×C₇₃	1	1	yes	characteristic, direct product factor, Sylow
13	C₄	C₂×C₁₉×C₇₃	1	1	yes	characteristic
14	C₂	C₄×C₁₉×C₇₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₁₉×C₇₃
socle, prime radical	C₂×C₁₉×C₇₃	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₉×C₇₃	C₈	direct (N × H)
4. C₈×C₇₃	C₁₉	direct (N × H)
6. C₈×C₁₉	C₇₃	direct (N × H)
9. C₇₃	C₈×C₁₉	direct (N × H)
11. C₁₉	C₈×C₇₃	direct (N × H)
12. C₈	C₁₉×C₇₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₁₉×C₇₃	2
C₈×C₇₃	19
C₈×C₁₉	73