Subgroups — C₅₉×Q₁₂₈ #21419749

Order 7552.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×Q₆₄	C₂	1	2	yes	maximal
2	C₅₉×C₆₄	C₂	1	1	yes	maximal, characteristic
3	Q₃₂×C₅₉	—	2	2	no	—
4	C₃₂×C₅₉	C₂²	1	1	yes	characteristic
5	Q₁₆×C₅₉	—	4	2	no	—
6	C₁₆×C₅₉	D₄	1	1	yes	characteristic
7	Q₈×C₅₉	—	8	2	no	—
8	C₈×C₅₉	D₈	1	1	yes	characteristic
9	C₄×C₅₉	—	16	2	no	—
10	C₄×C₅₉	D₁₆	1	1	yes	characteristic
11	Q₁₂₈	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₂×C₅₉	D₃₂	1	1	yes	characteristic
13	Q₆₄	C₂×C₅₉	1	2	yes	—
14	C₆₄	C₂×C₅₉	1	1	yes	characteristic
15	C₅₉	Q₁₂₈	1	1	yes	characteristic, direct product factor, Sylow
16	Q₃₂	—	2	2	no	—
17	C₃₂	C₂²×C₅₉	1	1	yes	characteristic
18	Q₁₆	—	4	2	no	—
19	C₁₆	D₄×C₅₉	1	1	yes	characteristic
20	Q₈	—	8	2	no	—
21	C₈	D₈×C₅₉	1	1	yes	characteristic
22	C₄	—	16	2	no	—
23	C₄	D₁₆×C₅₉	1	1	yes	characteristic
24	C₂	C₅₉×D₃₂	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂×C₅₉	D₃₂
commutator, Frattini, cosocle	C₃₂	C₂²×C₅₉
LCS	G ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅₉ ◁ C₄×C₅₉ ◁ C₈×C₅₉ ◁ C₁₆×C₅₉ ◁ C₃₂×C₅₉ ◁ G

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

N	H ≅ G/N	type
11. Q₁₂₈	C₅₉	direct (N × H)
15. C₅₉	Q₁₂₈	direct (N × H)

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