Subgroups — C₄₉×C₂₅₆ #72190880

Order 12544.

27 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₉×C₁₂₈	C₂	1	1	yes	maximal, characteristic
2	C₄₉×C₆₄	C₄	1	1	yes	characteristic
3	C₇×C₂₅₆	C₇	1	1	yes	maximal, characteristic
4	C₃₂×C₄₉	C₈	1	1	yes	characteristic
5	C₇×C₁₂₈	C₂×C₇	1	1	yes	characteristic
6	C₁₆×C₄₉	C₁₆	1	1	yes	characteristic
7	C₇×C₆₄	C₄×C₇	1	1	yes	characteristic
8	C₈×C₄₉	C₃₂	1	1	yes	characteristic
9	C₂₅₆	C₄₉	1	1	yes	characteristic, direct product factor, Sylow
10	C₇×C₃₂	C₇×C₈	1	1	yes	characteristic
11	C₄×C₄₉	C₆₄	1	1	yes	characteristic
12	C₁₂₈	C₂×C₄₉	1	1	yes	characteristic
13	C₇×C₁₆	C₇×C₁₆	1	1	yes	characteristic
14	C₂×C₄₉	C₁₂₈	1	1	yes	characteristic
15	C₆₄	C₄×C₄₉	1	1	yes	characteristic
16	C₇×C₈	C₇×C₃₂	1	1	yes	characteristic
17	C₄₉	C₂₅₆	1	1	yes	characteristic, direct product factor, Sylow
18	C₃₂	C₈×C₄₉	1	1	yes	characteristic
19	C₄×C₇	C₇×C₆₄	1	1	yes	characteristic
20	C₁₆	C₁₆×C₄₉	1	1	yes	characteristic
21	C₂×C₇	C₇×C₁₂₈	1	1	yes	characteristic
22	C₈	C₃₂×C₄₉	1	1	yes	characteristic
23	C₇	C₇×C₂₅₆	1	1	yes	characteristic
24	C₄	C₄₉×C₆₄	1	1	yes	characteristic
25	C₂	C₄₉×C₁₂₈	1	1	yes	characteristic

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

N	H ≅ G/N	type
9. C₂₅₆	C₄₉	direct (N × H)
17. C₄₉	C₂₅₆	direct (N × H)

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

subgroup	index
C₄₉×C₁₂₈	2
C₇×C₂₅₆	7