Subgroups — Q₁₂₈×C₁₉₃ #37591048

Order 24704.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₆₄×C₁₉₃	C₂	1	2	yes	maximal
2	C₆₄×C₁₉₃	C₂	1	1	yes	maximal, characteristic
3	Q₃₂×C₁₉₃	—	2	2	no	—
4	C₃₂×C₁₉₃	C₂²	1	1	yes	characteristic
5	Q₁₆×C₁₉₃	—	4	2	no	—
6	C₁₆×C₁₉₃	D₄	1	1	yes	characteristic
7	Q₈×C₁₉₃	—	8	2	no	—
8	C₈×C₁₉₃	D₈	1	1	yes	characteristic
9	C₄×C₁₉₃	—	16	2	no	—
10	C₄×C₁₉₃	D₁₆	1	1	yes	characteristic
11	C₂×C₁₉₃	D₃₂	1	1	yes	characteristic
12	C₁₉₃	Q₁₂₈	1	1	yes	characteristic, direct product factor, Sylow
13	Q₁₂₈	C₁₉₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	Q₆₄	C₂×C₁₉₃	1	2	yes	—
15	C₆₄	C₂×C₁₉₃	1	1	yes	characteristic
16	Q₃₂	—	2	2	no	—
17	C₃₂	C₂²×C₁₉₃	1	1	yes	characteristic
18	Q₁₆	—	4	2	no	—
19	C₁₆	D₄×C₁₉₃	1	1	yes	characteristic
20	Q₈	—	8	2	no	—
21	C₈	D₈×C₁₉₃	1	1	yes	characteristic
22	C₄	—	16	2	no	—
23	C₄	D₁₆×C₁₉₃	1	1	yes	characteristic
24	C₂	D₃₂×C₁₉₃	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂×C₁₉₃	D₃₂
commutator, Frattini, cosocle	C₃₂	C₂²×C₁₉₃
LCS	G ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉₃ ◁ C₄×C₁₉₃ ◁ C₈×C₁₉₃ ◁ C₁₆×C₁₉₃ ◁ C₃₂×C₁₉₃ ◁ G

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

N	H ≅ G/N	type
12. C₁₉₃	Q₁₂₈	direct (N × H)
13. Q₁₂₈	C₁₉₃	direct (N × H)

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