Subgroups — C₄²×C₇×C₁₉₉ #72199733

Order 22288.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₇×C₁₉₉	C₂	1	3	yes	maximal
2	C₂²×C₇×C₁₉₉	C₂²	1	1	yes	characteristic
3	C₄×C₇×C₁₉₉	C₄	1	6	yes	direct product factor
4	C₄²×C₁₉₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₇×C₁₉₉	C₂×C₄	1	3	yes	—
6	C₂×C₄×C₁₉₉	C₂×C₇	1	3	yes	—
7	C₇×C₁₉₉	C₄²	1	1	yes	characteristic, direct product factor, Hall
8	C₂²×C₁₉₉	C₂²×C₇	1	1	yes	characteristic
9	C₄×C₁₉₉	C₄×C₇	1	6	yes	direct product factor
10	C₂×C₁₉₉	C₂×C₄×C₇	1	3	yes	—
11	C₁₉₉	C₄²×C₇	1	1	yes	characteristic, direct product factor, Sylow
12	C₄²×C₇	C₁₉₉	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₄×C₇	C₂×C₁₉₉	1	3	yes	—
14	C₂²×C₇	C₂²×C₁₉₉	1	1	yes	characteristic
15	C₄×C₇	C₄×C₁₉₉	1	6	yes	direct product factor
16	C₄²	C₇×C₁₉₉	1	1	yes	characteristic, direct product factor, Sylow
17	C₂×C₇	C₂×C₄×C₁₉₉	1	3	yes	—
18	C₂×C₄	C₂×C₇×C₁₉₉	1	3	yes	—
19	C₇	C₄²×C₁₉₉	1	1	yes	characteristic, direct product factor, Sylow
20	C₂²	C₂²×C₇×C₁₉₉	1	1	yes	characteristic
21	C₄	C₄×C₇×C₁₉₉	1	6	yes	direct product factor
22	C₂	C₂×C₄×C₇×C₁₉₉	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.