Subgroups — #64604⋊C₃ #11745486

Order 936.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃⋊(D₁₃⋊C₃)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₃×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×Dic₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#64604	C₃	1	1	yes	maximal, characteristic, complemented
5	(C₂²⋊D₁₃)⋊C₃	—	3	1	no	maximal
6	C₂×C₃×C₁₃⋊C₃	C₂²	1	1	yes	characteristic
7	C₃⋊(D₁₃⋊C₃)	—	2	1	no	—
8	D₃×C₁₃⋊C₃	—	2	1	no	—
9	C₂×D₃₉	C₂×C₃	1	1	yes	characteristic, complemented
10	C₂×D₃×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
11	C₂²×C₁₃⋊C₃	—	3	1	no	—
12	C₂×D₁₃⋊C₃	—	3	1	no	—
13	C₃×Dic₁₃	C₂×C₃	1	1	yes	characteristic, complemented
14	Dic₁₃⋊C₃	—	2	1	no	—
15	Dic₁₃⋊C₃	D₃	1	1	yes	characteristic, complemented
16	C₃×C₁₃⋊C₃	D₄	1	1	yes	characteristic, complemented, Hall
17	C₂²⋊D₁₃	—	3	1	no	Hall
18	C₂×C₃×C₁₃	C₂²×C₃	1	1	yes	characteristic
19	D₃₉	—	2	1	no	—
20	D₃×C₁₃	—	2	1	no	—
21	C₂×C₁₃⋊C₃	—	2	1	no	—
22	C₂×C₁₃⋊C₃	—	6	1	no	—
23	C₂×C₁₃⋊C₃	C₂×D₃	1	1	yes	characteristic
24	D₁₃⋊C₃	—	6	1	no	—
25	C₃×D₁₂	—	13	1	no	maximal, Hall
26	C₂²×C₁₃	—	3	1	no	—
27	C₂×D₁₃	—	3	1	no	—
28	Dic₁₃	C₃×D₃	1	1	yes	characteristic, complemented
29	C₃×C₁₃	C₃×D₄	1	1	yes	characteristic, complemented
30	C₁₃⋊C₃	—	2	1	no	—
31	C₁₃⋊C₃	D₁₂	1	1	yes	characteristic, complemented
32	C₂×C₃×D₃	—	13	1	no	—
33	C₂×C₃×D₃	—	13	1	no	—
34	C₃²×C₄	—	13	1	no	—
35	C₂×C₁₃	—	6	1	no	—
36	C₂×C₁₃	C₂×C₃×D₃	1	1	yes	characteristic
37	D₁₃	—	6	1	no	—
38	C₃×D₄	—	39	1	no	—
39	D₁₂	—	13	1	no	—
40	C₂×C₃²	—	13	1	no	—
41	C₃×D₃	—	26	1	no	—
42	C₃×D₃	—	26	1	no	—
43	C₁₃	C₃×D₁₂	1	1	yes	characteristic, complemented, Sylow
44	C₂²×C₃	—	39	1	no	—
45	C₂²×C₃	—	39	1	no	—
46	C₂×D₃	—	13	1	no	—
47	C₂×D₃	D₁₃⋊C₃	1	1	yes	characteristic, complemented
48	C₃×C₄	—	13	1	no	—
49	C₃×C₄	—	13	1	no	—
50	C₃×C₄	—	26	1	no	—
51	C₃²	—	13	1	no	Sylow
52	D₄	—	39	1	no	Sylow
53	C₂×C₃	—	13	1	no	—
54	C₂×C₃	—	26	1	no	—
55	C₂×C₃	—	78	1	no	—
56	C₂×C₃	—	78	1	no	—
57	C₂×C₃	C₂×D₁₃⋊C₃	1	1	yes	characteristic
58	D₃	—	2	1	no	—
59	D₃	—	26	1	no	—
60	C₂²	—	3	1	no	—
61	C₂²	—	39	1	no	—
62	C₄	—	13	1	no	—
63	C₃	—	13	1	no	—
64	C₃	—	26	1	no	—
65	C₃	(C₂²⋊D₁₃)⋊C₃	1	1	yes	characteristic, complemented
66	C₂	—	6	1	no	—
67	C₂	—	78	1	no	—
68	C₂	D₃×D₁₃⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃×D₁₃⋊C₃
commutator, Fitting, socle, cosocle	C₂×C₃×C₁₃	C₂²×C₃
hypocenter	C₃×C₁₃	C₃×D₄
LCS	G ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₃⋊(D₁₃⋊C₃)	C₂	semidirect
2. C₂×D₃×C₁₃⋊C₃	C₂	semidirect
3. C₃×Dic₁₃⋊C₃	C₂	semidirect
4. #64604	C₃	semidirect
9. C₂×D₃₉	C₂×C₃	semidirect
10. C₂×D₃×C₁₃	C₂×C₃	semidirect
13. C₃×Dic₁₃	C₂×C₃	semidirect
15. Dic₁₃⋊C₃	D₃	semidirect
16. C₃×C₁₃⋊C₃	D₄	semidirect
28. Dic₁₃	C₃×D₃	semidirect
29. C₃×C₁₃	C₃×D₄	semidirect
31. C₁₃⋊C₃	D₁₂	semidirect
43. C₁₃	C₃×D₁₂	semidirect
47. C₂×D₃	D₁₃⋊C₃	semidirect
65. C₃	(C₂²⋊D₁₃)⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃⋊(D₁₃⋊C₃)	2
C₂×D₃×C₁₃⋊C₃	2
C₃×Dic₁₃⋊C₃	2
#64604	3
(C₂²⋊D₁₃)⋊C₃	3
C₃×D₁₂	13

Subgroups — #64604⋊C3 #11745486

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #64604⋊C₃ #11745486