Subgroups — C₃⋊(C₃⋊#16838294) #46803000

Order 34164.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃×D₇₃	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#16838294	—	3	4	no	maximal
3	C₃²×C₁₃×C₇₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₃×D₇₃	D₃	1	4	yes	—
5	#16838294	—	9	1	no	Hall
6	C₃×C₁₃×C₇₃	Dic₃	1	4	yes	complemented
7	C₃⋊(C₃⋊#64408)	—	13	1	no	maximal, Hall
8	C₁₃×D₇₃	C₃⋊D₃	1	1	yes	characteristic
9	C₃²×D₇₃	D₁₃	1	1	yes	characteristic
10	C₁₃×C₇₃	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
11	C₃⋊#64408	—	39	4	no	—
12	C₃²×C₇₃	Dic₁₃	1	1	yes	characteristic, complemented, Hall
13	C₃⋊Dic₃₉	—	73	1	no	maximal, Hall
14	C₃×D₇₃	D₃₉	1	4	yes	—
15	#64408	—	117	1	no	Hall
16	C₂×C₃²×C₁₃	—	73	1	no	—
17	C₃×C₇₃	Dic₃₉	1	4	yes	complemented
18	Dic₃₉	—	219	4	no	—
19	D₇₃	C₃⋊D₃₉	1	1	yes	characteristic
20	C₃²×C₁₃	#64408	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×C₁₃	—	73	4	no	—
22	C₇₃	C₃⋊Dic₃₉	1	1	yes	characteristic, complemented, Sylow
23	Dic₁₃	—	657	1	no	Hall
24	C₃×C₁₃	C₃⋊#64408	1	4	yes	complemented
25	C₃⋊Dic₃	—	949	1	no	Hall
26	C₂×C₁₃	—	73	1	no	—
27	C₂×C₃²	—	73	1	no	—
28	C₁₃	C₃⋊(C₃⋊#64408)	1	1	yes	characteristic, complemented, Sylow
29	Dic₃	—	2847	4	no	—
30	C₃²	#16838294	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	—	73	4	no	—
32	C₄	—	8541	1	no	Sylow
33	C₃	C₃⋊#16838294	1	4	yes	complemented
34	C₂	—	73	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₁₃×C₇₃	C₄
prime radical, cosocle	C₃²×C₁₃×D₇₃	C₂
LCS	G ▷ C₃²×C₁₃×C₇₃
UCS	C₁

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.