Subgroups — C₇×C₂₉×C₁₂₈ #72203142

Order 25984.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₂₉×C₆₄	C₂	1	1	yes	maximal, characteristic
2	C₇×C₂₉×C₃₂	C₄	1	1	yes	characteristic
3	C₇×C₁₆×C₂₉	C₈	1	1	yes	characteristic
4	C₂₉×C₁₂₈	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂₉×C₆₄	C₂×C₇	1	1	yes	characteristic
6	C₇×C₈×C₂₉	C₁₆	1	1	yes	characteristic
7	C₂₉×C₃₂	C₄×C₇	1	1	yes	characteristic
8	C₇×C₁₂₈	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₄×C₇×C₂₉	C₃₂	1	1	yes	characteristic
10	C₁₆×C₂₉	C₇×C₈	1	1	yes	characteristic
11	C₇×C₆₄	C₂×C₂₉	1	1	yes	characteristic
12	C₂×C₇×C₂₉	C₆₄	1	1	yes	characteristic
13	C₈×C₂₉	C₇×C₁₆	1	1	yes	characteristic
14	C₇×C₃₂	C₄×C₂₉	1	1	yes	characteristic
15	C₇×C₂₉	C₁₂₈	1	1	yes	characteristic, direct product factor, Hall
16	C₁₂₈	C₇×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
17	C₄×C₂₉	C₇×C₃₂	1	1	yes	characteristic
18	C₇×C₁₆	C₈×C₂₉	1	1	yes	characteristic
19	C₆₄	C₂×C₇×C₂₉	1	1	yes	characteristic
20	C₂×C₂₉	C₇×C₆₄	1	1	yes	characteristic
21	C₇×C₈	C₁₆×C₂₉	1	1	yes	characteristic
22	C₃₂	C₄×C₇×C₂₉	1	1	yes	characteristic
23	C₂₉	C₇×C₁₂₈	1	1	yes	characteristic, direct product factor, Sylow
24	C₄×C₇	C₂₉×C₃₂	1	1	yes	characteristic
25	C₁₆	C₇×C₈×C₂₉	1	1	yes	characteristic
26	C₂×C₇	C₂₉×C₆₄	1	1	yes	characteristic
27	C₈	C₇×C₁₆×C₂₉	1	1	yes	characteristic
28	C₇	C₂₉×C₁₂₈	1	1	yes	characteristic, direct product factor, Sylow
29	C₄	C₇×C₂₉×C₃₂	1	1	yes	characteristic
30	C₂	C₇×C₂₉×C₆₄	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₆₄	C₂×C₇×C₂₉
socle, prime radical	C₂×C₇×C₂₉	C₆₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂₉×C₁₂₈	C₇	direct (N × H)
8. C₇×C₁₂₈	C₂₉	direct (N × H)
15. C₇×C₂₉	C₁₂₈	direct (N × H)
16. C₁₂₈	C₇×C₂₉	direct (N × H)
23. C₂₉	C₇×C₁₂₈	direct (N × H)
28. C₇	C₂₉×C₁₂₈	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×C₂₉×C₆₄	2
C₂₉×C₁₂₈	7
C₇×C₁₂₈	29

Subgroups — C7×C29×C128 #72203142

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₂₉×C₁₂₈ #72203142