Subgroups — C₂×C₃×D₆₇₃⋊C₃ #37564519

Order 24228.

60 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×C₃×D₆₇₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×D₆₇₃⋊C₃	C₃	1	3	yes	maximal, direct product factor
5	C₃×C₆₇₃⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×C₆₇₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₃×D₆₇₃	C₂×C₃	1	2	yes	complemented
8	C₂×C₆₇₃⋊C₃	C₂×C₃	1	3	yes	complemented
9	D₆₇₃⋊C₃	C₂×C₃	1	6	yes	direct product factor
10	C₂×D₆₇₃	C₃²	1	1	yes	characteristic, complemented, Hall
11	C₃×C₆₇₃	C₂²×C₃	1	1	yes	characteristic, complemented
12	C₆₇₃⋊C₃	C₂²×C₃	1	3	yes	complemented
13	C₂×C₆₇₃	C₂×C₃²	1	1	yes	characteristic, complemented
14	D₆₇₃	C₂×C₃²	1	2	yes	complemented
15	C₆₇₃	C₂²×C₃²	1	1	yes	characteristic, complemented, Sylow
16	C₂²×C₃²	—	673	1	no	maximal, Hall
17	C₂×C₃²	—	673	2	no	—
18	C₂×C₃²	—	673	1	no	—
19	C₂²×C₃	—	673	3	no	—
20	C₂²×C₃	—	2019	1	no	—
21	C₃²	—	673	1	no	Sylow
22	C₂×C₃	—	673	6	no	—
23	C₂×C₃	—	673	3	no	—
24	C₂×C₃	—	2019	2	no	—
25	C₂×C₃	D₆₇₃⋊C₃	1	1	yes	characteristic, direct product factor
26	C₂²	—	2019	1	no	Sylow
27	C₃	—	673	3	no	—
28	C₃	C₂×D₆₇₃⋊C₃	1	1	yes	characteristic, direct product factor
29	C₂	—	2019	2	no	—
30	C₂	C₃×D₆₇₃⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	D₆₇₃⋊C₃
commutator, cosocle, hypocenter	C₆₇₃	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₆₇₃	C₂×C₃
LCS	G ▷ C₆₇₃
UCS	C₁ ◁ C₂×C₃

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.