Finite Group Databasebeta

← C₃²×C₄×C₆₇₃ #37564504

Subgroups — C₃²×C₄×C₆₇₃ #37564504

Order 24228.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₆₇₃	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₆₇₃	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₆₇₃	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃×C₆₇₃	C₂×C₃	1	4	yes	—
5	C₄×C₆₇₃	C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₆₇₃	C₃×C₄	1	4	yes	direct product factor
7	C₂×C₆₇₃	C₂×C₃²	1	1	yes	characteristic
8	C₆₇₃	C₃²×C₄	1	1	yes	characteristic, direct product factor, Sylow
9	C₃²×C₄	C₆₇₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃²	C₂×C₆₇₃	1	1	yes	characteristic
11	C₃×C₄	C₃×C₆₇₃	1	4	yes	direct product factor
12	C₃²	C₄×C₆₇₃	1	1	yes	characteristic, direct product factor, Sylow
13	C₂×C₃	C₂×C₃×C₆₇₃	1	4	yes	—
14	C₄	C₃²×C₆₇₃	1	1	yes	characteristic, direct product factor, Sylow
15	C₃	C₃×C₄×C₆₇₃	1	4	yes	direct product factor
16	C₂	C₂×C₃²×C₆₇₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₃²×C₆₇₃
socle, prime radical	C₂×C₃²×C₆₇₃	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×C₆₇₃	C₃	direct (N × H)
3. C₃²×C₆₇₃	C₄	direct (N × H)
5. C₄×C₆₇₃	C₃²	direct (N × H)
6. C₃×C₆₇₃	C₃×C₄	direct (N × H)
8. C₆₇₃	C₃²×C₄	direct (N × H)
9. C₃²×C₄	C₆₇₃	direct (N × H)
11. C₃×C₄	C₃×C₆₇₃	direct (N × H)
12. C₃²	C₄×C₆₇₃	direct (N × H)
14. C₄	C₃²×C₆₇₃	direct (N × H)
15. C₃	C₃×C₄×C₆₇₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₆₇₃	2
C₃×C₄×C₆₇₃	3
C₃²×C₄	673