Subgroups — C₇×C₈×C₂₇ #13094109

Order 1512.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₇×C₂₇	C₂	1	1	yes	maximal, characteristic
2	C₇×C₈×C₉	C₃	1	1	yes	maximal, characteristic
3	C₂×C₇×C₂₇	C₄	1	1	yes	characteristic
4	C₄×C₇×C₉	C₂×C₃	1	1	yes	characteristic
5	C₈×C₂₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×C₂₇	C₈	1	1	yes	characteristic, direct product factor, Hall
7	C₃×C₇×C₈	C₉	1	1	yes	characteristic
8	C₂×C₇×C₉	C₃×C₄	1	1	yes	characteristic
9	C₄×C₂₇	C₂×C₇	1	1	yes	characteristic
10	C₃×C₄×C₇	C₂×C₉	1	1	yes	characteristic
11	C₈×C₉	C₃×C₇	1	1	yes	characteristic
12	C₇×C₉	C₃×C₈	1	1	yes	characteristic
13	C₇×C₈	C₂₇	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₂₇	C₄×C₇	1	1	yes	characteristic
15	C₂×C₃×C₇	C₄×C₉	1	1	yes	characteristic
16	C₄×C₉	C₂×C₃×C₇	1	1	yes	characteristic
17	C₄×C₇	C₂×C₂₇	1	1	yes	characteristic
18	C₂₇	C₇×C₈	1	1	yes	characteristic, direct product factor, Sylow
19	C₃×C₈	C₇×C₉	1	1	yes	characteristic
20	C₃×C₇	C₈×C₉	1	1	yes	characteristic
21	C₂×C₉	C₃×C₄×C₇	1	1	yes	characteristic
22	C₂×C₇	C₄×C₂₇	1	1	yes	characteristic
23	C₃×C₄	C₂×C₇×C₉	1	1	yes	characteristic
24	C₉	C₃×C₇×C₈	1	1	yes	characteristic
25	C₈	C₇×C₂₇	1	1	yes	characteristic, direct product factor, Sylow
26	C₇	C₈×C₂₇	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₃	C₄×C₇×C₉	1	1	yes	characteristic
28	C₄	C₂×C₇×C₂₇	1	1	yes	characteristic
29	C₃	C₇×C₈×C₉	1	1	yes	characteristic
30	C₂	C₄×C₇×C₂₇	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄×C₉	C₂×C₃×C₇
socle, prime radical	C₂×C₃×C₇	C₄×C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₈×C₂₇	C₇	direct (N × H)
6. C₇×C₂₇	C₈	direct (N × H)
13. C₇×C₈	C₂₇	direct (N × H)
18. C₂₇	C₇×C₈	direct (N × H)
25. C₈	C₇×C₂₇	direct (N × H)
26. C₇	C₈×C₂₇	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×C₇×C₂₇	2
C₇×C₈×C₉	3
C₈×C₂₇	7

Subgroups — C7×C8×C27 #13094109

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₈×C₂₇ #13094109