Subgroups — M₃₂×C₅₄₇ #31775873

Order 17504.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×C₅₄₇	C₂	1	1	yes	maximal, characteristic
2	C₁₆×C₅₄₇	C₂	1	2	yes	maximal, complemented
3	C₂×C₄×C₅₄₇	C₄	1	1	yes	characteristic
4	C₈×C₅₄₇	C₄	1	1	yes	characteristic
5	C₈×C₅₄₇	C₂²	1	1	yes	characteristic
6	C₂²×C₅₄₇	C₈	1	1	yes	characteristic
7	C₄×C₅₄₇	C₈	1	1	yes	characteristic
8	C₄×C₅₄₇	C₂×C₄	1	1	yes	characteristic
9	C₂×C₅₄₇	—	2	1	no	—
10	C₂×C₅₄₇	C₂×C₈	1	1	yes	characteristic
11	C₅₄₇	M₃₂	1	1	yes	characteristic, direct product factor, Sylow
12	M₃₂	C₅₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₂×C₈	C₂×C₅₄₇	1	1	yes	characteristic
14	C₁₆	C₂×C₅₄₇	1	2	yes	complemented
15	C₂×C₄	C₄×C₅₄₇	1	1	yes	characteristic
16	C₈	C₄×C₅₄₇	1	1	yes	characteristic
17	C₈	C₂²×C₅₄₇	1	1	yes	characteristic
18	C₂²	C₈×C₅₄₇	1	1	yes	characteristic
19	C₄	C₈×C₅₄₇	1	1	yes	characteristic
20	C₄	C₂×C₄×C₅₄₇	1	1	yes	characteristic
21	C₂	—	2	1	no	—
22	C₂	C₂×C₈×C₅₄₇	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.