Subgroups — Q₁₆×C₃₁⋊C₃ #13093459

Order 1488.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×C₃₁⋊C₃	C₂	1	2	yes	maximal
2	C₈×C₃₁⋊C₃	C₂	1	1	yes	maximal, characteristic
3	Q₁₆×C₃₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₄×C₃₁⋊C₃	—	2	2	no	—
5	C₄×C₃₁⋊C₃	C₂²	1	1	yes	characteristic
6	Q₈×C₃₁	C₂×C₃	1	2	yes	—
7	C₈×C₃₁	C₂×C₃	1	1	yes	characteristic
8	C₂×C₃₁⋊C₃	D₄	1	1	yes	characteristic
9	C₄×C₃₁	—	2	2	no	—
10	C₄×C₃₁	C₂²×C₃	1	1	yes	characteristic
11	C₃₁⋊C₃	Q₁₆	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₃₁	C₃×D₄	1	1	yes	characteristic
13	C₃×Q₁₆	—	31	1	no	maximal, Hall
14	C₃₁	C₃×Q₁₆	1	1	yes	characteristic, complemented, Sylow
15	C₃×Q₈	—	31	2	no	—
16	C₃×C₈	—	31	1	no	—
17	Q₁₆	C₃₁⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
18	C₃×C₄	—	31	1	no	—
19	C₃×C₄	—	62	2	no	—
20	Q₈	C₂×C₃₁⋊C₃	1	2	yes	—
21	C₈	C₂×C₃₁⋊C₃	1	1	yes	characteristic
22	C₂×C₃	—	31	1	no	—
23	C₄	—	2	2	no	—
24	C₄	C₂²×C₃₁⋊C₃	1	1	yes	characteristic
25	C₃	—	31	1	no	Sylow
26	C₂	D₄×C₃₁⋊C₃	1	1	yes	characteristic

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

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