Subgroups — C₇²×C₈×C₆₁ #72201192

Order 23912.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₈×C₆₁	C₇	1	8	yes	maximal, direct product factor
2	C₄×C₇²×C₆₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₇²×C₆₁	C₄	1	1	yes	characteristic
4	C₇²×C₆₁	C₈	1	1	yes	characteristic, direct product factor, Hall
5	C₄×C₇×C₆₁	C₂×C₇	1	8	yes	—
6	C₂×C₇×C₆₁	C₄×C₇	1	8	yes	—
7	C₈×C₆₁	C₇²	1	1	yes	characteristic, direct product factor, Hall
8	C₇×C₆₁	C₇×C₈	1	8	yes	direct product factor
9	C₇²×C₈	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₄×C₆₁	C₂×C₇²	1	1	yes	characteristic
11	C₄×C₇²	C₂×C₆₁	1	1	yes	characteristic
12	C₂×C₆₁	C₄×C₇²	1	1	yes	characteristic
13	C₂×C₇²	C₄×C₆₁	1	1	yes	characteristic
14	C₆₁	C₇²×C₈	1	1	yes	characteristic, direct product factor, Sylow
15	C₇×C₈	C₇×C₆₁	1	8	yes	direct product factor
16	C₇²	C₈×C₆₁	1	1	yes	characteristic, direct product factor, Sylow
17	C₄×C₇	C₂×C₇×C₆₁	1	8	yes	—
18	C₂×C₇	C₄×C₇×C₆₁	1	8	yes	—
19	C₈	C₇²×C₆₁	1	1	yes	characteristic, direct product factor, Sylow
20	C₇	C₇×C₈×C₆₁	1	8	yes	direct product factor
21	C₄	C₂×C₇²×C₆₁	1	1	yes	characteristic
22	C₂	C₄×C₇²×C₆₁	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.