Subgroups — C₃×#443 #5317

Order 192.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#135	C₂	1	1	yes	maximal, characteristic
2	C₃×#131	C₂	1	2	yes	maximal, complemented
3	C₃×#108	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#104	C₂	1	2	yes	maximal, complemented
5	C₃×C₄×C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	#443	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₃×#41	C₂²	1	2	yes	—
8	C₃×Q₁₆	C₄	1	1	yes	characteristic, complemented
9	C₃×SD₁₆	C₄	1	2	yes	complemented
10	C₃×D₈	C₄	1	1	yes	characteristic, complemented
11	C₃×M₁₆	—	2	2	no	—
12	C₃×M₁₆	C₂²	1	2	yes	—
13	C₂×C₃×C₈	—	2	2	no	—
14	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
16	C₃×C₄²	C₂²	1	1	yes	characteristic
17	#135	C₂×C₃	1	1	yes	characteristic
18	#131	C₂×C₃	1	2	yes	complemented
19	#108	C₂×C₃	1	1	yes	characteristic, complemented
20	#104	C₂×C₃	1	2	yes	complemented
21	C₄×C₈	C₂×C₃	1	1	yes	characteristic, complemented
22	C₃×Q₈	C₂×C₄	1	2	yes	—
23	C₃×D₄	—	2	2	no	—
24	C₃×D₄	C₂×C₄	1	2	yes	—
25	C₂×C₃×C₄	—	2	1	no	—
26	C₂×C₃×C₄	—	2	2	no	—
27	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
28	C₃×C₈	—	2	2	no	—
29	C₃×C₈	C₂×C₄	1	1	yes	characteristic
30	C₃×C₈	C₂×C₄	1	1	yes	characteristic
31	C₃×C₈	D₄	1	1	yes	characteristic
32	C₃×C₈	D₄	1	1	yes	characteristic
33	#41	C₂²×C₃	1	2	yes	—
34	Q₁₆	C₃×C₄	1	1	yes	characteristic, complemented
35	SD₁₆	C₃×C₄	1	2	yes	complemented
36	D₈	C₃×C₄	1	1	yes	characteristic, complemented
37	M₁₆	—	2	2	no	—
38	M₁₆	C₂²×C₃	1	2	yes	—
39	C₂×C₈	—	2	2	no	—
40	C₂×C₈	C₂²×C₃	1	1	yes	characteristic
41	C₂×C₈	C₂²×C₃	1	1	yes	characteristic
42	C₄²	C₂²×C₃	1	1	yes	characteristic
43	C₂²×C₃	—	2	2	no	—
44	C₂²×C₃	#41	1	1	yes	characteristic
45	C₃×C₄	—	2	2	no	—
46	C₃×C₄	—	2	2	no	—
47	C₃×C₄	C₂²×C₄	1	1	yes	characteristic
48	C₃×C₄	C₂×D₄	1	1	yes	characteristic
49	Q₈	C₂×C₃×C₄	1	2	yes	—
50	D₄	—	2	2	no	—
51	D₄	C₂×C₃×C₄	1	2	yes	—
52	C₂×C₄	—	2	1	no	—
53	C₂×C₄	—	2	2	no	—
54	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
55	C₈	—	2	2	no	—
56	C₈	C₂×C₃×C₄	1	1	yes	characteristic
57	C₈	C₂×C₃×C₄	1	1	yes	characteristic
58	C₈	C₃×D₄	1	1	yes	characteristic
59	C₈	C₃×D₄	1	1	yes	characteristic
60	C₂×C₃	—	2	1	no	—
61	C₂×C₃	—	4	2	no	—
62	C₂×C₃	C₄×D₄	1	1	yes	characteristic
63	C₂²	—	2	2	no	—
64	C₂²	C₃×#41	1	1	yes	characteristic
65	C₄	—	2	2	no	—
66	C₄	—	2	2	no	—
67	C₄	C₂²×C₃×C₄	1	1	yes	characteristic
68	C₄	C₂×C₃×D₄	1	1	yes	characteristic
69	C₃	#443	1	1	yes	characteristic, direct product factor, Sylow
70	C₂	—	2	1	no	—
71	C₂	—	4	2	no	—
72	C₂	C₃×C₄×D₄	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₈	D₄
commutator	C₄	C₂²×C₃×C₄
Frattini, cosocle	C₂×C₄	C₂³×C₃
socle	C₂×C₃	C₄×D₄
prime radical	C₃×#135	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₃×C₈ ◁ C₂×C₃×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×#131	C₂	semidirect
3. C₃×#108	C₂	semidirect
4. C₃×#104	C₂	semidirect
5. C₃×C₄×C₈	C₂	semidirect
6. #443	C₃	direct (N × H)
8. C₃×Q₁₆	C₄	semidirect
9. C₃×SD₁₆	C₄	semidirect
10. C₃×D₈	C₄	semidirect
18. #131	C₂×C₃	semidirect
19. #108	C₂×C₃	semidirect
20. #104	C₂×C₃	semidirect
21. C₄×C₈	C₂×C₃	semidirect
34. Q₁₆	C₃×C₄	semidirect
35. SD₁₆	C₃×C₄	semidirect
36. D₈	C₃×C₄	semidirect
69. C₃	#443	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×#135	2
C₃×#131	2
C₃×#108	2
C₃×#104	2
C₃×C₄×C₈	2
#443	3

Subgroups — C3×#443 #5317

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#443 #5317