Subgroups — C₂×C₃⋊(D₆₇₃⋊C₃) #37564520

Order 24228.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₆₇₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃⋊(D₆₇₃⋊C₃)	C₂	1	2	yes	maximal, direct product factor
3	C₂×D₂₀₁₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×D₆₇₃⋊C₃	—	3	1	no	maximal
5	C₃×C₆₇₃⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×C₆₇₃	C₂×C₃	1	1	yes	characteristic, complemented
7	D₂₀₁₉	C₂×C₃	1	2	yes	complemented
8	C₂×C₆₇₃⋊C₃	—	2	1	no	—
9	C₂×C₆₇₃⋊C₃	D₃	1	1	yes	characteristic, complemented
10	D₆₇₃⋊C₃	—	3	2	no	—
11	C₂×D₆₇₃	—	3	1	no	Hall
12	C₃×C₆₇₃	C₂²×C₃	1	1	yes	characteristic, complemented
13	C₆₇₃⋊C₃	—	2	1	no	—
14	C₆₇₃⋊C₃	C₂×D₃	1	1	yes	characteristic, complemented
15	C₂×C₆₇₃	C₃×D₃	1	1	yes	characteristic, complemented
16	D₆₇₃	—	3	2	no	—
17	C₆₇₃	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₃×D₃	—	673	1	no	maximal, Hall
19	C₂×C₃²	—	1346	1	no	—
20	C₃×D₃	—	673	2	no	—
21	C₂²×C₃	—	2019	1	no	—
22	C₂×D₃	—	673	1	no	—
23	C₃²	—	1346	1	no	Sylow
24	C₂×C₃	—	1346	1	no	—
25	C₂×C₃	—	1346	1	no	—
26	C₂×C₃	—	2019	2	no	—
27	C₂×C₃	D₆₇₃⋊C₃	1	1	yes	characteristic, complemented
28	D₃	—	673	2	no	—
29	C₂²	—	2019	1	no	Sylow
30	C₃	—	1346	1	no	—
31	C₃	—	1346	1	no	—
32	C₃	C₂×D₆₇₃⋊C₃	1	1	yes	characteristic, complemented
33	C₂	—	2019	2	no	—
34	C₂	C₃⋊(D₆₇₃⋊C₃)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₃⋊(D₆₇₃⋊C₃)
commutator, cosocle, hypocenter	C₃×C₆₇₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₆₇₃	C₂×C₃
LCS	G ▷ C₃×C₆₇₃
UCS	C₁ ◁ C₂

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.