Subgroups — C₄₁×Q₂₅₆ #23783754

Order 10496.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×Q₁₂₈	C₂	1	2	yes	maximal
2	C₄₁×C₁₂₈	C₂	1	1	yes	maximal, characteristic
3	C₄₁×Q₆₄	—	2	2	no	—
4	C₄₁×C₆₄	C₂²	1	1	yes	characteristic
5	Q₃₂×C₄₁	—	4	2	no	—
6	C₃₂×C₄₁	D₄	1	1	yes	characteristic
7	Q₁₆×C₄₁	—	8	2	no	—
8	C₁₆×C₄₁	D₈	1	1	yes	characteristic
9	Q₈×C₄₁	—	16	2	no	—
10	C₈×C₄₁	D₁₆	1	1	yes	characteristic
11	Q₂₅₆	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₄×C₄₁	—	32	2	no	—
13	C₄×C₄₁	D₃₂	1	1	yes	characteristic
14	Q₁₂₈	C₂×C₄₁	1	2	yes	—
15	C₁₂₈	C₂×C₄₁	1	1	yes	characteristic
16	C₂×C₄₁	D₆₄	1	1	yes	characteristic
17	Q₆₄	—	2	2	no	—
18	C₆₄	C₂²×C₄₁	1	1	yes	characteristic
19	C₄₁	Q₂₅₆	1	1	yes	characteristic, direct product factor, Sylow
20	Q₃₂	—	4	2	no	—
21	C₃₂	D₄×C₄₁	1	1	yes	characteristic
22	Q₁₆	—	8	2	no	—
23	C₁₆	D₈×C₄₁	1	1	yes	characteristic
24	Q₈	—	16	2	no	—
25	C₈	D₁₆×C₄₁	1	1	yes	characteristic
26	C₄	—	32	2	no	—
27	C₄	C₄₁×D₃₂	1	1	yes	characteristic
28	C₂	C₄₁×D₆₄	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂×C₄₁	D₆₄
commutator, Frattini, cosocle	C₆₄	C₂²×C₄₁
LCS	G ▷ C₆₄ ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄₁ ◁ C₄×C₄₁ ◁ C₈×C₄₁ ◁ C₁₆×C₄₁ ◁ C₃₂×C₄₁ ◁ C₄₁×C₆₄ ◁ G

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

N	H ≅ G/N	type
11. Q₂₅₆	C₄₁	direct (N × H)
19. C₄₁	Q₂₅₆	direct (N × H)

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