Subgroups — C₃⋊#26015648 #46802774

Order 34164.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#15667865	C₂	1	1	yes	maximal, characteristic
2	#26015648	—	3	1	no	maximal
3	C₁₃×Dic₂₁₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×#15667865	C₄	1	1	yes	characteristic, complemented, Hall
5	C₂×#15667865	—	2	1	no	—
6	C₂×#15667865	D₃	1	1	yes	characteristic
7	C₂×C₃×C₁₃×C₇₃	C₂×C₃	1	1	yes	characteristic
8	C₁₃×Dic₇₃	—	3	1	no	Hall
9	C₃×C₁₃×C₇₃	C₃×C₄	1	1	yes	characteristic, complemented
10	#15667865	—	2	1	no	—
11	#15667865	Dic₃	1	1	yes	characteristic, complemented
12	C₃⋊(Dic₇₃⋊C₃)	—	13	1	no	maximal, Hall
13	C₂×C₁₃×C₇₃	C₃×D₃	1	1	yes	characteristic
14	C₂×C₃×C₇₃⋊C₃	—	13	1	no	—
15	C₁₃×C₇₃	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
16	Dic₂₁₉	C₁₃⋊C₃	1	1	yes	characteristic, complemented
17	Dic₇₃⋊C₃	—	39	1	no	—
18	C₃×C₇₃⋊C₃	—	13	1	no	Hall
19	Dic₃×C₁₃⋊C₃	—	73	1	no	maximal, Hall
20	C₂×C₃×C₇₃	C₂×C₁₃⋊C₃	1	1	yes	characteristic
21	C₂×C₇₃⋊C₃	—	13	1	no	—
22	C₂×C₇₃⋊C₃	—	26	1	no	—
23	Dic₇₃	—	3	1	no	Hall
24	C₂×C₃×C₁₃⋊C₃	—	73	1	no	—
25	C₃×C₇₃	C₄×C₁₃⋊C₃	1	1	yes	characteristic, complemented
26	C₇₃⋊C₃	—	13	1	no	—
27	C₇₃⋊C₃	—	26	1	no	—
28	Dic₃×C₁₃	—	73	1	no	—
29	C₄×C₁₃⋊C₃	—	219	1	no	—
30	C₂×C₇₃	D₃×C₁₃⋊C₃	1	1	yes	characteristic
31	C₃×C₁₃⋊C₃	—	73	1	no	Hall
32	C₂×C₃×C₁₃	D₇₃⋊C₃	1	1	yes	characteristic
33	C₂×C₁₃⋊C₃	—	73	1	no	—
34	C₂×C₁₃⋊C₃	—	146	1	no	—
35	C₇₃	Dic₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
36	C₄×C₁₃	—	219	1	no	Hall
37	C₃×C₁₃	Dic₇₃⋊C₃	1	1	yes	characteristic, complemented
38	C₁₃⋊C₃	—	73	1	no	—
39	C₁₃⋊C₃	—	146	1	no	—
40	C₃×Dic₃	—	949	1	no	Hall
41	C₂×C₁₃	C₃⋊(D₇₃⋊C₃)	1	1	yes	characteristic
42	C₂×C₃²	—	949	1	no	—
43	C₁₃	C₃⋊(Dic₇₃⋊C₃)	1	1	yes	characteristic, complemented, Sylow
44	C₃×C₄	—	2847	1	no	—
45	Dic₃	—	73	1	no	—
46	C₃²	—	949	1	no	Sylow
47	C₂×C₃	—	1898	1	no	—
48	C₂×C₃	—	949	1	no	—
49	C₂×C₃	#19151040	1	1	yes	characteristic
50	C₄	—	219	1	no	Sylow
51	C₃	—	1898	1	no	—
52	C₃	—	949	1	no	—
53	C₃	#26015648	1	1	yes	characteristic, complemented
54	C₂	C₃⋊#19151040	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₃⋊#19151040
commutator, hypocenter	C₃×C₁₃×C₇₃	C₃×C₄
Fitting, socle, cosocle	C₂×C₃×C₁₃×C₇₃	C₂×C₃
prime radical	C₂×C₃×#15667865	C₂
LCS	G ▷ C₃×C₁₃×C₇₃
UCS	C₁ ◁ C₂

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. C₁₃×Dic₂₁₉	C₃	semidirect
4. C₃×#15667865	C₄	semidirect
9. C₃×C₁₃×C₇₃	C₃×C₄	semidirect
11. #15667865	Dic₃	semidirect
15. C₁₃×C₇₃	C₃×Dic₃	semidirect
16. Dic₂₁₉	C₁₃⋊C₃	semidirect
25. C₃×C₇₃	C₄×C₁₃⋊C₃	semidirect
35. C₇₃	Dic₃×C₁₃⋊C₃	semidirect
37. C₃×C₁₃	Dic₇₃⋊C₃	semidirect
43. C₁₃	C₃⋊(Dic₇₃⋊C₃)	semidirect
53. C₃	#26015648	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×#15667865	2
#26015648	3
C₁₃×Dic₂₁₉	3
C₃⋊(Dic₇₃⋊C₃)	13
Dic₃×C₁₃⋊C₃	73

Subgroups — C3⋊#26015648 #46802774

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊#26015648 #46802774