Subgroups — C₃×#444 #5318

Order 192.

104 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×#97	C₂	1	1	yes	maximal, characteristic, complemented
6	#444	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	#97	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	2	no	—
26	C₂×C₃×C₄	—	2	1	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	2	yes	—
32	#41	C₂²×C₃	1	2	yes	—
33	Q₁₆	C₃×C₄	1	1	yes	characteristic, complemented
34	SD₁₆	C₃×C₄	1	2	yes	complemented
35	D₈	C₃×C₄	1	1	yes	characteristic, complemented
36	M₁₆	—	2	2	no	—
37	M₁₆	C₂²×C₃	1	2	yes	—
38	C₂×C₈	—	2	2	no	—
39	C₂×C₈	C₂²×C₃	1	1	yes	characteristic
40	C₂×C₈	C₂²×C₃	1	1	yes	characteristic
41	C₄²	C₂²×C₃	1	1	yes	characteristic
42	C₂²×C₃	—	2	2	no	—
43	C₂²×C₃	#41	1	1	yes	characteristic
44	C₃×C₄	—	2	2	no	—
45	C₃×C₄	—	4	1	no	—
46	C₃×C₄	C₂²×C₄	1	1	yes	characteristic
47	C₃×C₄	C₂×D₄	1	1	yes	characteristic
48	Q₈	C₂×C₃×C₄	1	2	yes	—
49	D₄	—	2	2	no	—
50	D₄	C₂×C₃×C₄	1	2	yes	—
51	C₂×C₄	—	2	2	no	—
52	C₂×C₄	—	2	1	no	—
53	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
54	C₈	—	2	2	no	—
55	C₈	C₂×C₃×C₄	1	1	yes	characteristic
56	C₈	C₂×C₃×C₄	1	1	yes	characteristic
57	C₈	C₃×D₄	1	2	yes	—
58	C₂×C₃	—	2	1	no	—
59	C₂×C₃	—	4	2	no	—
60	C₂×C₃	C₄×D₄	1	1	yes	characteristic
61	C₂²	—	2	2	no	—
62	C₂²	C₃×#41	1	1	yes	characteristic
63	C₄	—	2	2	no	—
64	C₄	—	4	1	no	—
65	C₄	C₂²×C₃×C₄	1	1	yes	characteristic
66	C₄	C₂×C₃×D₄	1	1	yes	characteristic
67	C₃	#444	1	1	yes	characteristic, direct product factor, Sylow
68	C₂	—	2	1	no	—
69	C₂	—	4	2	no	—
70	C₂	C₃×C₄×D₄	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	C₂×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×C₄ ◁ 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×#97	C₂	semidirect
6. #444	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. #97	C₂×C₃	semidirect
33. Q₁₆	C₃×C₄	semidirect
34. SD₁₆	C₃×C₄	semidirect
35. D₈	C₃×C₄	semidirect
67. C₃	#444	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×#97	2
#444	3

Subgroups — C3×#444 #5318

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#444 #5318