Subgroups — Q₁₆×D₃₁₁ #23755724

Order 9952.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×D₃₁₁	C₂	1	2	yes	maximal
2	Dic₁₂₄₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#19097305	C₂	1	2	yes	maximal, complemented
4	C₈×D₃₁₁	C₂	1	1	yes	maximal, characteristic
5	Q₁₆×C₃₁₁	C₂	1	1	yes	maximal, characteristic, complemented
6	Dic₆₂₂	—	2	2	no	—
7	Dic₆₂₂	C₂²	1	2	yes	—
8	C₄×D₃₁₁	—	2	2	no	—
9	C₄×D₃₁₁	C₂²	1	1	yes	characteristic
10	C₃₁₁⋊C₈	C₂²	1	1	yes	characteristic
11	Q₈×C₃₁₁	C₂²	1	2	yes	—
12	C₈×C₃₁₁	C₂²	1	1	yes	characteristic
13	C₂×D₃₁₁	D₄	1	1	yes	characteristic
14	C₄×C₃₁₁	—	2	2	no	—
15	C₄×C₃₁₁	C₂³	1	1	yes	characteristic
16	Dic₃₁₁	—	2	2	no	—
17	Dic₃₁₁	D₄	1	1	yes	characteristic
18	C₂×C₃₁₁	C₂×D₄	1	1	yes	characteristic
19	D₃₁₁	Q₁₆	1	2	yes	direct product factor
20	C₃₁₁	C₂×Q₁₆	1	1	yes	characteristic, complemented, Sylow
21	C₂×Q₁₆	—	311	1	no	maximal, Sylow
22	C₂×Q₈	—	311	2	no	—
23	Q₁₆	—	311	2	no	—
24	Q₁₆	—	311	1	no	—
25	Q₁₆	D₃₁₁	1	1	yes	characteristic, direct product factor
26	C₂×C₈	—	311	1	no	—
27	Q₈	—	311	2	no	—
28	Q₈	—	622	2	no	—
29	Q₈	C₂×D₃₁₁	1	2	yes	—
30	C₂×C₄	—	311	1	no	—
31	C₂×C₄	—	622	2	no	—
32	C₈	—	311	1	no	—
33	C₈	C₂×D₃₁₁	1	1	yes	characteristic
34	C₂²	—	311	1	no	—
35	C₄	—	2	2	no	—
36	C₄	—	311	1	no	—
37	C₄	—	622	2	no	—
38	C₄	C₂²×D₃₁₁	1	1	yes	characteristic
39	C₂	—	311	2	no	—
40	C₂	D₄×D₃₁₁	1	1	yes	characteristic

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