Subgroups — C₁₁×Q₂₅₆ #14584746

Order 2816.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×Q₁₂₈	C₂	1	2	yes	maximal
2	C₁₁×C₁₂₈	C₂	1	1	yes	maximal, characteristic
3	C₁₁×Q₆₄	—	2	2	no	—
4	C₁₁×C₆₄	C₂²	1	1	yes	characteristic
5	C₁₁×Q₃₂	—	4	2	no	—
6	C₁₁×C₃₂	D₄	1	1	yes	characteristic
7	Q₂₅₆	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
8	C₁₁×Q₁₆	—	8	2	no	—
9	C₁₁×C₁₆	D₈	1	1	yes	characteristic
10	Q₁₂₈	C₂×C₁₁	1	2	yes	—
11	C₁₂₈	C₂×C₁₁	1	1	yes	characteristic
12	Q₈×C₁₁	—	16	2	no	—
13	C₈×C₁₁	D₁₆	1	1	yes	characteristic
14	Q₆₄	—	2	2	no	—
15	C₆₄	C₂²×C₁₁	1	1	yes	characteristic
16	C₄×C₁₁	—	32	2	no	—
17	C₄×C₁₁	D₃₂	1	1	yes	characteristic
18	Q₃₂	—	4	2	no	—
19	C₃₂	D₄×C₁₁	1	1	yes	characteristic
20	C₂×C₁₁	D₆₄	1	1	yes	characteristic
21	Q₁₆	—	8	2	no	—
22	C₁₆	C₁₁×D₈	1	1	yes	characteristic
23	C₁₁	Q₂₅₆	1	1	yes	characteristic, direct product factor, Sylow
24	Q₈	—	16	2	no	—
25	C₈	C₁₁×D₁₆	1	1	yes	characteristic
26	C₄	—	32	2	no	—
27	C₄	C₁₁×D₃₂	1	1	yes	characteristic
28	C₂	C₁₁×D₆₄	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂×C₁₁	D₆₄
commutator, Frattini, cosocle	C₆₄	C₂²×C₁₁
LCS	G ▷ C₆₄ ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₄×C₁₁ ◁ C₈×C₁₁ ◁ C₁₁×C₁₆ ◁ C₁₁×C₃₂ ◁ C₁₁×C₆₄ ◁ G

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

N	H ≅ G/N	type
7. Q₂₅₆	C₁₁	direct (N × H)
23. C₁₁	Q₂₅₆	direct (N × H)

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