Subgroups — M₆₄×C₁₆₇ #24922771

Order 10688.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₆×C₁₆₇	C₂	1	1	yes	maximal, characteristic
2	C₃₂×C₁₆₇	C₂	1	2	yes	maximal, complemented
3	C₂×C₈×C₁₆₇	C₄	1	1	yes	characteristic
4	C₁₆×C₁₆₇	C₄	1	1	yes	characteristic
5	C₁₆×C₁₆₇	C₂²	1	1	yes	characteristic
6	C₂×C₄×C₁₆₇	C₈	1	1	yes	characteristic
7	C₈×C₁₆₇	C₈	1	1	yes	characteristic
8	C₈×C₁₆₇	C₂×C₄	1	1	yes	characteristic
9	C₂²×C₁₆₇	C₁₆	1	1	yes	characteristic
10	C₄×C₁₆₇	C₁₆	1	1	yes	characteristic
11	C₄×C₁₆₇	C₂×C₈	1	1	yes	characteristic
12	C₂×C₁₆₇	—	2	1	no	—
13	C₂×C₁₆₇	C₂×C₁₆	1	1	yes	characteristic
14	C₁₆₇	M₆₄	1	1	yes	characteristic, direct product factor, Sylow
15	M₆₄	C₁₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
16	C₂×C₁₆	C₂×C₁₆₇	1	1	yes	characteristic
17	C₃₂	C₂×C₁₆₇	1	2	yes	complemented
18	C₂×C₈	C₄×C₁₆₇	1	1	yes	characteristic
19	C₁₆	C₄×C₁₆₇	1	1	yes	characteristic
20	C₁₆	C₂²×C₁₆₇	1	1	yes	characteristic
21	C₂×C₄	C₈×C₁₆₇	1	1	yes	characteristic
22	C₈	C₈×C₁₆₇	1	1	yes	characteristic
23	C₈	C₂×C₄×C₁₆₇	1	1	yes	characteristic
24	C₂²	C₁₆×C₁₆₇	1	1	yes	characteristic
25	C₄	C₁₆×C₁₆₇	1	1	yes	characteristic
26	C₄	C₂×C₈×C₁₆₇	1	1	yes	characteristic
27	C₂	—	2	1	no	—
28	C₂	C₂×C₁₆×C₁₆₇	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.