Finite Group Databasebeta

← C₃⁴×C₁₉² #72206178

Subgroups — C₃⁴×C₁₉² #72206178

Order 29241.

4664 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₁₉²	C₃	1	40	yes	maximal, direct product factor
2	C₃²×C₁₉²	C₃²	1	130	yes	direct product factor
3	C₃⁴×C₁₉	C₁₉	1	20	yes	maximal, direct product factor
4	C₃×C₁₉²	C₃³	1	40	yes	direct product factor
5	C₃³×C₁₉	C₃×C₁₉	1	800	yes	direct product factor
6	C₁₉²	C₃⁴	1	1	yes	characteristic, direct product factor, Sylow
7	C₃²×C₁₉	C₃²×C₁₉	1	2600	yes	direct product factor
8	C₃⁴	C₁₉²	1	1	yes	characteristic, direct product factor, Sylow
9	C₃×C₁₉	C₃³×C₁₉	1	800	yes	direct product factor
10	C₃³	C₃×C₁₉²	1	40	yes	direct product factor
11	C₁₉	C₃⁴×C₁₉	1	20	yes	direct product factor
12	C₃²	C₃²×C₁₉²	1	130	yes	direct product factor
13	C₃	C₃³×C₁₉²	1	40	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃³×C₁₉²	C₃	direct (N × H)
2. C₃²×C₁₉²	C₃²	direct (N × H)
3. C₃⁴×C₁₉	C₁₉	direct (N × H)
4. C₃×C₁₉²	C₃³	direct (N × H)
5. C₃³×C₁₉	C₃×C₁₉	direct (N × H)
6. C₁₉²	C₃⁴	direct (N × H)
7. C₃²×C₁₉	C₃²×C₁₉	direct (N × H)
8. C₃⁴	C₁₉²	direct (N × H)
9. C₃×C₁₉	C₃³×C₁₉	direct (N × H)
10. C₃³	C₃×C₁₉²	direct (N × H)
11. C₁₉	C₃⁴×C₁₉	direct (N × H)
12. C₃²	C₃²×C₁₉²	direct (N × H)
13. C₃	C₃³×C₁₉²	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃³×C₁₉²	3
C₃⁴×C₁₉	19