Subgroups — C₃²×C₇×D₁₉₉ #38736992

Order 25074.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×C₁₉₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₇×D₁₉₉	C₃	1	4	yes	maximal, direct product factor
3	C₃×C₇×C₁₉₉	C₂×C₃	1	4	yes	complemented
4	C₃²×D₁₉₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₇×D₁₉₉	C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₃²×C₁₉₉	C₂×C₇	1	1	yes	characteristic, complemented, Hall
7	C₇×C₁₉₉	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×D₁₉₉	C₃×C₇	1	4	yes	direct product factor
9	C₃×C₁₉₉	C₂×C₃×C₇	1	4	yes	complemented
10	D₁₉₉	C₃²×C₇	1	1	yes	characteristic, direct product factor, Hall
11	C₁₉₉	C₂×C₃²×C₇	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₃²×C₇	—	199	1	no	maximal, Hall
13	C₃²×C₇	D₁₉₉	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₃×C₇	—	199	4	no	—
15	C₃×C₇	C₃×D₁₉₉	1	4	yes	direct product factor
16	C₂×C₃²	—	199	1	no	Hall
17	C₂×C₇	—	199	1	no	Hall
18	C₃²	C₇×D₁₉₉	1	1	yes	characteristic, direct product factor, Sylow
19	C₇	C₃²×D₁₉₉	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₃	—	199	4	no	—
21	C₃	C₃×C₇×D₁₉₉	1	4	yes	direct product factor
22	C₂	—	199	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²×C₇	D₁₉₉
commutator, cosocle, hypocenter	C₁₉₉	C₂×C₃²×C₇
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₁₉₉	C₂
LCS	G ▷ C₁₉₉
UCS	C₁ ◁ C₃²×C₇

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.