Subgroups — C₃⋊#15688286 #22580207

Order 8892.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#10625203	C₂	1	1	yes	maximal, characteristic
2	Dic₇₄₁	C₃	1	1	yes	maximal, characteristic, complemented
3	#15688286	—	3	1	no	maximal
4	C₃×#10625203	C₄	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic
6	C₂×#10625203	—	2	1	no	—
7	C₂×#10625203	D₃	1	1	yes	characteristic
8	Dic₂₄₇	—	3	1	no	Hall
9	C₃×C₁₃×C₁₉	C₃×C₄	1	1	yes	characteristic, complemented
10	#10625203	—	2	1	no	—
11	#10625203	Dic₃	1	1	yes	characteristic, complemented
12	C₃⋊((C₁₉⋊C₃)⋊C₄)	—	13	1	no	maximal, Hall
13	C₂×C₁₃×C₁₉	C₃×D₃	1	1	yes	characteristic
14	C₃⋊(Dic₁₃⋊C₃)	—	19	1	no	maximal, Hall
15	C₂×C₃×C₁₉⋊C₃	—	13	1	no	—
16	C₁₃×C₁₉	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₁₃⋊C₃	—	19	1	no	—
18	Dic₅₇	—	13	1	no	—
19	(C₁₉⋊C₃)⋊C₄	—	39	1	no	—
20	C₃×C₁₉⋊C₃	—	13	1	no	Hall
21	Dic₃₉	—	19	1	no	—
22	Dic₁₃⋊C₃	—	57	1	no	—
23	C₃×C₁₃⋊C₃	—	19	1	no	Hall
24	C₂×C₃×C₁₉	D₁₃⋊C₃	1	1	yes	characteristic
25	C₂×C₁₉⋊C₃	—	13	1	no	—
26	C₂×C₁₉⋊C₃	—	26	1	no	—
27	C₂×C₃×C₁₃	D₁₉⋊C₃	1	1	yes	characteristic
28	C₂×C₁₃⋊C₃	—	19	1	no	—
29	C₂×C₁₃⋊C₃	—	38	1	no	—
30	Dic₁₉	—	39	1	no	Hall
31	C₃×C₁₉	Dic₁₃⋊C₃	1	1	yes	characteristic, complemented
32	C₁₉⋊C₃	—	13	1	no	—
33	C₁₉⋊C₃	—	26	1	no	—
34	Dic₁₃	—	57	1	no	Hall
35	C₃×C₁₃	(C₁₉⋊C₃)⋊C₄	1	1	yes	characteristic, complemented
36	C₁₃⋊C₃	—	19	1	no	—
37	C₁₃⋊C₃	—	38	1	no	—
38	C₂×C₁₉	C₃⋊(D₁₃⋊C₃)	1	1	yes	characteristic
39	C₃×Dic₃	—	247	1	no	Hall
40	C₂×C₁₃	C₃⋊(D₁₉⋊C₃)	1	1	yes	characteristic
41	C₁₉	C₃⋊(Dic₁₃⋊C₃)	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₃²	—	247	1	no	—
43	C₁₃	C₃⋊((C₁₉⋊C₃)⋊C₄)	1	1	yes	characteristic, complemented, Sylow
44	C₃×C₄	—	741	1	no	—
45	Dic₃	—	247	1	no	—
46	C₃²	—	247	1	no	Sylow
47	C₂×C₃	—	494	1	no	—
48	C₂×C₃	—	247	1	no	—
49	C₂×C₃	#13093367	1	1	yes	characteristic
50	C₄	—	741	1	no	Sylow
51	C₃	—	494	1	no	—
52	C₃	—	247	1	no	—
53	C₃	#15688286	1	1	yes	characteristic, complemented
54	C₂	C₃⋊#13093367	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₃⋊#13093367
commutator, hypocenter	C₃×C₁₃×C₁₉	C₃×C₄
Fitting, socle	C₂×C₃×C₁₃×C₁₉	C₂×C₃
LCS	G ▷ C₃×C₁₃×C₁₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
2. Dic₇₄₁	C₃	semidirect
4. C₃×#10625203	C₄	semidirect
9. C₃×C₁₃×C₁₉	C₃×C₄	semidirect
11. #10625203	Dic₃	semidirect
16. C₁₃×C₁₉	C₃×Dic₃	semidirect
31. C₃×C₁₉	Dic₁₃⋊C₃	semidirect
35. C₃×C₁₃	(C₁₉⋊C₃)⋊C₄	semidirect
41. C₁₉	C₃⋊(Dic₁₃⋊C₃)	semidirect
43. C₁₃	C₃⋊((C₁₉⋊C₃)⋊C₄)	semidirect
53. C₃	#15688286	semidirect

Subgroups — C3⋊#15688286 #22580207

Conjugacy classes of subgroups

Complements

Subgroups — C₃⋊#15688286 #22580207