Subgroups — C₃×#21439406 #37523864

Order 22914.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16838389	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	#21439406	C₃	1	3	yes	maximal, direct product factor
3	C₃×C₁₉×D₆₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₁₉×C₆₇	C₂×C₃	1	1	yes	characteristic, complemented
5	#16838389	C₂×C₃	1	3	yes	complemented
6	C₁₉×D₆₇	C₃²	1	1	yes	characteristic, complemented, Hall
7	C₁₉×C₆₇	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×D₆₇⋊C₃	—	19	1	no	maximal, Hall
9	C₃×C₆₇⋊C₃	—	19	1	no	Hall
10	C₃×D₆₇	C₁₉⋊C₃	1	1	yes	characteristic, complemented
11	D₆₇⋊C₃	—	19	3	no	—
12	C₂×C₃×C₁₉⋊C₃	—	67	1	no	maximal, Hall
13	C₃×C₆₇	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented
14	C₆₇⋊C₃	—	19	3	no	—
15	C₃×C₁₉⋊C₃	—	67	1	no	Hall
16	D₆₇	C₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₁₉	—	201	1	no	—
18	C₂×C₁₉⋊C₃	—	67	3	no	—
19	C₆₇	C₂×C₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
20	C₃×C₁₉	D₆₇⋊C₃	1	1	yes	characteristic, complemented
21	C₁₉⋊C₃	—	67	3	no	—
22	C₂×C₁₉	—	201	1	no	Hall
23	C₁₉	C₃×D₆₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₃²	—	1273	1	no	Hall
25	C₃²	—	1273	1	no	Sylow
26	C₂×C₃	—	201	1	no	—
27	C₂×C₃	—	1273	3	no	—
28	C₃	—	1273	3	no	—
29	C₃	#21439406	1	1	yes	characteristic, direct product factor
30	C₂	—	201	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	#21439406
commutator, cosocle, hypocenter	C₁₉×C₆₇	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₁₉×C₆₇	C₂×C₃
LCS	G ▷ C₁₉×C₆₇
UCS	C₁ ◁ 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.