Finite Group Databasebeta

← C₄×C₁₁²×C₇₁ #46805366

Subgroups — C₄×C₁₁²×C₇₁ #46805366

Order 34364.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁²×C₇₁	C₂	1	1	yes	maximal, characteristic
2	C₁₁²×C₇₁	C₄	1	1	yes	characteristic, direct product factor, Hall
3	C₄×C₁₁×C₇₁	C₁₁	1	12	yes	maximal, direct product factor
4	C₂×C₁₁×C₇₁	C₂×C₁₁	1	12	yes	—
5	C₁₁×C₇₁	C₄×C₁₁	1	12	yes	direct product factor
6	C₄×C₁₁²	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₄×C₇₁	C₁₁²	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₁₁²	C₂×C₇₁	1	1	yes	characteristic
9	C₂×C₇₁	C₂×C₁₁²	1	1	yes	characteristic
10	C₁₁²	C₄×C₇₁	1	1	yes	characteristic, direct product factor, Sylow
11	C₇₁	C₄×C₁₁²	1	1	yes	characteristic, direct product factor, Sylow
12	C₄×C₁₁	C₁₁×C₇₁	1	12	yes	direct product factor
13	C₂×C₁₁	C₂×C₁₁×C₇₁	1	12	yes	—
14	C₁₁	C₄×C₁₁×C₇₁	1	12	yes	direct product factor
15	C₄	C₁₁²×C₇₁	1	1	yes	characteristic, direct product factor, Sylow
16	C₂	C₂×C₁₁²×C₇₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₁₁²×C₇₁
socle, prime radical	C₂×C₁₁²×C₇₁	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁²×C₇₁	C₄	direct (N × H)
3. C₄×C₁₁×C₇₁	C₁₁	direct (N × H)
5. C₁₁×C₇₁	C₄×C₁₁	direct (N × H)
6. C₄×C₁₁²	C₇₁	direct (N × H)
7. C₄×C₇₁	C₁₁²	direct (N × H)
10. C₁₁²	C₄×C₇₁	direct (N × H)
11. C₇₁	C₄×C₁₁²	direct (N × H)
12. C₄×C₁₁	C₁₁×C₇₁	direct (N × H)
14. C₁₁	C₄×C₁₁×C₇₁	direct (N × H)
15. C₄	C₁₁²×C₇₁	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×C₁₁²×C₇₁	2
C₄×C₁₁×C₇₁	11
C₄×C₁₁²	71