Subgroups — C₁₆²×C₈₃ #35234875

Order 21248.

166 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×C₁₆×C₈₃	C₂	1	3	yes	maximal
2	C₄×C₁₆×C₈₃	C₄	1	6	yes	—
3	C₈²×C₈₃	C₂²	1	1	yes	characteristic
4	C₂×C₁₆×C₈₃	C₈	1	12	yes	—
5	C₄×C₈×C₈₃	C₂×C₄	1	3	yes	—
6	C₂×C₈×C₈₃	C₂×C₈	1	6	yes	—
7	C₄²×C₈₃	C₄²	1	1	yes	characteristic
8	C₁₆×C₈₃	C₁₆	1	24	yes	direct product factor
9	C₂×C₄×C₈₃	C₄×C₈	1	3	yes	—
10	C₈×C₈₃	C₂×C₁₆	1	12	yes	—
11	C₂²×C₈₃	C₈²	1	1	yes	characteristic
12	C₄×C₈₃	C₄×C₁₆	1	6	yes	—
13	C₁₆²	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₂×C₈₃	C₈×C₁₆	1	3	yes	—
15	C₈×C₁₆	C₂×C₈₃	1	3	yes	—
16	C₈₃	C₁₆²	1	1	yes	characteristic, direct product factor, Sylow
17	C₄×C₁₆	C₄×C₈₃	1	6	yes	—
18	C₈²	C₂²×C₈₃	1	1	yes	characteristic
19	C₂×C₁₆	C₈×C₈₃	1	12	yes	—
20	C₄×C₈	C₂×C₄×C₈₃	1	3	yes	—
21	C₂×C₈	C₂×C₈×C₈₃	1	6	yes	—
22	C₄²	C₄²×C₈₃	1	1	yes	characteristic
23	C₁₆	C₁₆×C₈₃	1	24	yes	direct product factor
24	C₂×C₄	C₄×C₈×C₈₃	1	3	yes	—
25	C₈	C₂×C₁₆×C₈₃	1	12	yes	—
26	C₂²	C₈²×C₈₃	1	1	yes	characteristic
27	C₄	C₄×C₁₆×C₈₃	1	6	yes	—
28	C₂	C₈×C₁₆×C₈₃	1	3	yes	—

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.

subgroup	index
C₈×C₁₆×C₈₃	2
C₁₆²	83