Subgroups — C₃×#3573 #87457

Order 384.

1424 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#585	C₂	1	1	yes	maximal, characteristic
2	C₃×#568	C₂	1	15	yes	maximal, complemented
3	C₂×C₃×#131	C₂	1	15	yes	maximal, complemented
4	#3573	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₃×2₋¹⁺⁴	C₄	1	6	yes	—
6	C₃×H(5,𝔽₂)	C₄	1	10	yes	—
7	C₂×C₃×#41	C₂²	1	15	yes	—
8	C₃×#131	C₂²	1	20	yes	complemented
9	C₃×#131	C₂²	1	60	yes	complemented
10	C₂×C₃×M₁₆	C₂²	1	45	yes	complemented
11	C₂²×C₃×C₈	C₂²	1	15	yes	complemented
12	#585	C₂×C₃	1	1	yes	characteristic
13	#568	C₂×C₃	1	15	yes	complemented
14	C₂×#131	C₂×C₃	1	15	yes	complemented
15	C₃×#41	C₂×C₄	1	60	yes	—
16	C₃×#41	C₂³	1	20	yes	—
17	C₂×C₃×Q₈	C₂×C₄	1	15	yes	—
18	C₂×C₃×D₄	C₂×C₄	1	45	yes	—
19	C₂²×C₃×C₄	C₂³	1	15	yes	—
20	C₃×M₁₆	C₂³	1	60	yes	—
21	C₂×C₃×C₈	C₂³	1	45	yes	—
22	C₂×C₃×C₈	C₂³	1	15	yes	—
23	2₋¹⁺⁴	C₃×C₄	1	6	yes	—
24	H(5,𝔽₂)	C₃×C₄	1	10	yes	—
25	C₂×#41	C₂²×C₃	1	15	yes	—
26	#131	C₂²×C₃	1	20	yes	complemented
27	#131	C₂²×C₃	1	60	yes	complemented
28	C₂×M₁₆	C₂²×C₃	1	45	yes	complemented
29	C₂²×C₈	C₂²×C₃	1	15	yes	complemented
30	C₂³×C₃	C₂²×C₄	1	15	yes	—
31	C₃×Q₈	C₂²×C₄	1	20	yes	—
32	C₃×D₄	C₂²×C₄	1	60	yes	—
33	C₂×C₃×C₄	C₂²×C₄	1	45	yes	—
34	C₂×C₃×C₄	C₂⁴	1	15	yes	—
35	C₃×C₈	C₂⁴	1	15	yes	—
36	C₃×C₈	C₂⁴	1	1	yes	characteristic
37	#41	C₂×C₃×C₄	1	60	yes	—
38	#41	C₂³×C₃	1	20	yes	—
39	C₂×Q₈	C₂×C₃×C₄	1	15	yes	—
40	C₂×D₄	C₂×C₃×C₄	1	45	yes	—
41	C₂²×C₄	C₂³×C₃	1	15	yes	—
42	M₁₆	C₂³×C₃	1	60	yes	—
43	C₂×C₈	C₂³×C₃	1	15	yes	—
44	C₂×C₈	C₂³×C₃	1	45	yes	—
45	C₂²×C₃	—	4	15	no	—
46	C₂²×C₃	C₂³×C₄	1	15	yes	—
47	C₃×C₄	C₂³×C₄	1	15	yes	—
48	C₃×C₄	C₂⁵	1	1	yes	characteristic
49	C₂³	C₂²×C₃×C₄	1	15	yes	—
50	Q₈	C₂²×C₃×C₄	1	20	yes	—
51	D₄	C₂²×C₃×C₄	1	60	yes	—
52	C₂×C₄	C₂²×C₃×C₄	1	45	yes	—
53	C₂×C₄	C₂⁴×C₃	1	15	yes	—
54	C₈	C₂⁴×C₃	1	1	yes	characteristic
55	C₈	C₂⁴×C₃	1	15	yes	—
56	C₂×C₃	—	2	15	no	—
57	C₂×C₃	C₂⁴×C₄	1	1	yes	characteristic
58	C₂²	—	4	15	no	—
59	C₂²	C₂³×C₃×C₄	1	15	yes	—
60	C₄	C₂³×C₃×C₄	1	15	yes	—
61	C₄	C₂⁵×C₃	1	1	yes	characteristic
62	C₃	#3573	1	1	yes	characteristic, direct product factor, Sylow
63	C₂	—	2	15	no	—
64	C₂	C₂⁴×C₃×C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₈	C₂⁴
commutator	C₂	C₂⁴×C₃×C₄
Frattini, cosocle	C₄	C₂⁵×C₃
socle	C₂×C₃	C₂⁴×C₄
prime radical	C₃×#585	C₂
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₃×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×#568	C₂	semidirect
3. C₂×C₃×#131	C₂	semidirect
4. #3573	C₃	direct (N × H)
8. C₃×#131	C₂²	semidirect
9. C₃×#131	C₂²	semidirect
10. C₂×C₃×M₁₆	C₂²	semidirect
11. C₂²×C₃×C₈	C₂²	semidirect
13. #568	C₂×C₃	semidirect
14. C₂×#131	C₂×C₃	semidirect
26. #131	C₂²×C₃	semidirect
27. #131	C₂²×C₃	semidirect
28. C₂×M₁₆	C₂²×C₃	semidirect
29. C₂²×C₈	C₂²×C₃	semidirect
62. C₃	#3573	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#585	2
C₃×#568	2
C₂×C₃×#131	2
#3573	3

Subgroups — C3×#3573 #87457

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3573 #87457