Subgroups — Q₁₂₈×C₁₉₁ #37568173

Order 24448.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₆₄×C₁₉₁	C₂	1	2	yes	maximal
2	C₆₄×C₁₉₁	C₂	1	1	yes	maximal, characteristic
3	Q₃₂×C₁₉₁	—	2	2	no	—
4	C₃₂×C₁₉₁	C₂²	1	1	yes	characteristic
5	Q₁₆×C₁₉₁	—	4	2	no	—
6	C₁₆×C₁₉₁	D₄	1	1	yes	characteristic
7	Q₈×C₁₉₁	—	8	2	no	—
8	C₈×C₁₉₁	D₈	1	1	yes	characteristic
9	C₄×C₁₉₁	—	16	2	no	—
10	C₄×C₁₉₁	D₁₆	1	1	yes	characteristic
11	C₂×C₁₉₁	D₃₂	1	1	yes	characteristic
12	C₁₉₁	Q₁₂₈	1	1	yes	characteristic, direct product factor, Sylow
13	Q₁₂₈	C₁₉₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	Q₆₄	C₂×C₁₉₁	1	2	yes	—
15	C₆₄	C₂×C₁₉₁	1	1	yes	characteristic
16	Q₃₂	—	2	2	no	—
17	C₃₂	C₂²×C₁₉₁	1	1	yes	characteristic
18	Q₁₆	—	4	2	no	—
19	C₁₆	D₄×C₁₉₁	1	1	yes	characteristic
20	Q₈	—	8	2	no	—
21	C₈	D₈×C₁₉₁	1	1	yes	characteristic
22	C₄	—	16	2	no	—
23	C₄	D₁₆×C₁₉₁	1	1	yes	characteristic
24	C₂	D₃₂×C₁₉₁	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂×C₁₉₁	D₃₂
commutator, Frattini, cosocle	C₃₂	C₂²×C₁₉₁
LCS	G ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉₁ ◁ C₄×C₁₉₁ ◁ C₈×C₁₉₁ ◁ C₁₆×C₁₉₁ ◁ C₃₂×C₁₉₁ ◁ G

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

N	H ≅ G/N	type
12. C₁₉₁	Q₁₂₈	direct (N × H)
13. Q₁₂₈	C₁₉₁	direct (N × H)

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