Subgroups — C₈²×C₁₇² #72196296

Order 18496.

740 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₈×C₁₇²	C₂	1	3	yes	maximal
2	C₄²×C₁₇²	C₂²	1	1	yes	characteristic
3	C₂×C₈×C₁₇²	C₄	1	6	yes	—
4	C₂×C₄×C₁₇²	C₂×C₄	1	3	yes	—
5	C₈×C₁₇²	C₈	1	12	yes	direct product factor
6	C₂²×C₁₇²	C₄²	1	1	yes	characteristic
7	C₄×C₁₇²	C₂×C₈	1	6	yes	—
8	C₈²×C₁₇	C₁₇	1	18	yes	maximal, direct product factor
9	C₂×C₁₇²	C₄×C₈	1	3	yes	—
10	C₄×C₈×C₁₇	C₂×C₁₇	1	54	yes	—
11	C₁₇²	C₈²	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₈×C₁₇	C₄×C₁₇	1	108	yes	—
13	C₄²×C₁₇	C₂²×C₁₇	1	18	yes	—
14	C₂×C₄×C₁₇	C₂×C₄×C₁₇	1	54	yes	—
15	C₈×C₁₇	C₈×C₁₇	1	216	yes	direct product factor
16	C₂²×C₁₇	C₄²×C₁₇	1	18	yes	—
17	C₄×C₁₇	C₂×C₈×C₁₇	1	108	yes	—
18	C₈²	C₁₇²	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₁₇	C₄×C₈×C₁₇	1	54	yes	—
20	C₄×C₈	C₂×C₁₇²	1	3	yes	—
21	C₁₇	C₈²×C₁₇	1	18	yes	direct product factor
22	C₂×C₈	C₄×C₁₇²	1	6	yes	—
23	C₄²	C₂²×C₁₇²	1	1	yes	characteristic
24	C₂×C₄	C₂×C₄×C₁₇²	1	3	yes	—
25	C₈	C₈×C₁₇²	1	12	yes	direct product factor
26	C₂²	C₄²×C₁₇²	1	1	yes	characteristic
27	C₄	C₂×C₈×C₁₇²	1	6	yes	—
28	C₂	C₄×C₈×C₁₇²	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
C₄×C₈×C₁₇²	2
C₈²×C₁₇	17