Subgroups — C₃⋊#564 #5686

Order 192.

172 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#125	C₂	1	1	yes	maximal, characteristic
2	#890	C₂	1	4	yes	maximal
3	#889	C₂	1	4	yes	maximal
4	#889	C₂	1	4	yes	maximal
5	#870	C₂	1	2	yes	maximal
6	#564	—	3	1	no	maximal, Sylow
7	C₃×C₄⋊C₄	C₂²	1	2	yes	—
8	C₃×C₄⋊C₄	C₂²	1	4	yes	—
9	C₃×C₄²	C₂²	1	1	yes	characteristic
10	C₄⋊Dic₃	C₂²	1	2	yes	—
11	C₄⋊Dic₃	C₂²	1	2	yes	—
12	C₄⋊Dic₃	C₂²	1	4	yes	—
13	Dic₃⋊C₄	C₂²	1	4	yes	—
14	Dic₃⋊C₄	C₂²	1	4	yes	—
15	Dic₃⋊C₄	C₂²	1	4	yes	—
16	Dic₃⋊C₄	C₂²	1	4	yes	—
17	C₄×Dic₃	C₂²	1	4	yes	—
18	#125	—	3	4	no	—
19	#125	—	3	4	no	—
20	#125	—	3	4	no	—
21	#125	—	3	2	no	—
22	#125	D₃	1	1	yes	characteristic
23	C₂×C₃×C₄	C₂³	1	4	yes	—
24	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
25	C₂×C₃×C₄	C₂³	1	2	yes	—
26	C₂×Dic₃	C₂³	1	4	yes	—
27	C₂×Dic₃	C₂³	1	4	yes	—
28	C₄⋊C₄	—	3	4	no	—
29	C₄⋊C₄	—	3	4	no	—
30	C₄⋊C₄	—	3	4	no	—
31	C₄⋊C₄	—	3	4	no	—
32	C₄⋊C₄	—	3	4	no	—
33	C₄⋊C₄	—	3	2	no	—
34	C₄⋊C₄	—	3	2	no	—
35	C₄⋊C₄	C₂×D₃	1	2	yes	—
36	C₄⋊C₄	C₂×D₃	1	4	yes	—
37	C₄²	—	3	4	no	—
38	C₄²	C₂×D₃	1	1	yes	characteristic
39	C₂²×C₃	C₂⁴	1	1	yes	characteristic
40	C₃×C₄	—	2	1	no	—
41	C₃×C₄	—	2	4	no	—
42	C₃×C₄	—	2	2	no	—
43	Dic₃	—	2	4	no	—
44	Dic₃	—	2	4	no	—
45	C₂×C₄	—	3	4	no	—
46	C₂×C₄	—	3	4	no	—
47	C₂×C₄	C₂²×D₃	1	4	yes	—
48	C₂×C₄	C₂²×D₃	1	1	yes	characteristic
49	C₂×C₄	C₂²×D₃	1	2	yes	—
50	C₂×C₃	2₋¹⁺⁴	1	1	yes	characteristic
51	C₂×C₃	2₋¹⁺⁴	1	2	yes	—
52	C₂²	C₂³×D₃	1	1	yes	characteristic
53	C₄	—	2	1	no	—
54	C₄	—	2	4	no	—
55	C₄	—	2	2	no	—
56	C₄	—	6	4	no	—
57	C₄	—	6	4	no	—
58	C₃	#564	1	1	yes	characteristic, complemented, Sylow
59	C₂	#1007	1	1	yes	characteristic
60	C₂	#1010	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₃
commutator, socle, prime radical, cosocle	C₂²×C₃	C₂⁴
Fitting	C₃×#125	C₂
hypercenter	#125	D₃
hypocenter	C₃	#564
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ #125

Complements

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

N	H ≅ G/N	type
58. C₃	#564	semidirect

Maximal subgroups

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

subgroup	index
C₃×#125	2
#890	2
#889	2
#870	2
#564	3

Subgroups — C3⋊#564 #5686

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊#564 #5686