Subgroups — C₁₁×Q₁₂₈ #13064269

Order 1408.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, socle, prime radical	C₂×C₁₁	D₃₂
commutator, Frattini, cosocle	C₃₂	C₂²×C₁₁
LCS	G ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₄×C₁₁ ◁ C₈×C₁₁ ◁ C₁₁×C₁₆ ◁ C₁₁×C₃₂ ◁ G

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

N	H ≅ G/N	type
7. Q₁₂₈	C₁₁	direct (N × H)
19. C₁₁	Q₁₂₈	direct (N × H)

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