Subgroups — C₃×#578 #5908

Order 192.

248 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×2₋¹⁺⁴	C₂	1	2	yes	maximal, complemented
2	C₃×#137	C₂	1	6	yes	maximal, complemented
3	C₃×#135	C₂	1	3	yes	maximal, complemented
4	C₂×C₃×Q₁₆	C₂	1	3	yes	maximal, complemented
5	C₃×#131	C₂	1	1	yes	maximal, characteristic, complemented
6	#578	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₃×#41	—	2	6	no	—
8	C₃×#41	C₂²	1	6	yes	—
9	C₃×#41	C₂²	1	1	yes	characteristic
10	C₂×C₃×Q₈	—	2	2	no	—
11	C₂×C₃×Q₈	C₂²	1	6	yes	—
12	C₃×Q₁₆	C₂²	1	3	yes	—
13	C₃×Q₁₆	C₂²	1	6	yes	—
14	C₃×SD₁₆	C₂²	1	6	yes	—
15	C₃×D₈	C₂²	1	1	yes	characteristic
16	C₃×M₁₆	C₂²	1	3	yes	—
17	C₂×C₃×C₈	C₂²	1	3	yes	—
18	2₋¹⁺⁴	C₂×C₃	1	2	yes	complemented
19	#137	C₂×C₃	1	6	yes	complemented
20	#135	C₂×C₃	1	3	yes	complemented
21	C₂×Q₁₆	C₂×C₃	1	3	yes	complemented
22	#131	C₂×C₃	1	1	yes	characteristic, complemented
23	C₃×Q₈	—	2	6	no	—
24	C₃×Q₈	D₄	1	1	yes	characteristic
25	C₃×Q₈	C₂³	1	6	yes	—
26	C₃×D₄	—	2	6	no	—
27	C₃×D₄	D₄	1	3	yes	—
28	C₃×D₄	C₂³	1	2	yes	—
29	C₂×C₃×C₄	—	2	6	no	—
30	C₂×C₃×C₄	—	2	6	no	—
31	C₂×C₃×C₄	C₂³	1	3	yes	—
32	C₃×C₈	C₂³	1	1	yes	characteristic
33	C₃×C₈	C₂³	1	3	yes	—
34	#41	—	2	6	no	—
35	#41	C₂²×C₃	1	6	yes	—
36	#41	C₂²×C₃	1	1	yes	characteristic
37	C₂×Q₈	—	2	2	no	—
38	C₂×Q₈	C₂²×C₃	1	6	yes	—
39	Q₁₆	C₂²×C₃	1	3	yes	—
40	Q₁₆	C₂²×C₃	1	6	yes	—
41	SD₁₆	C₂²×C₃	1	6	yes	—
42	D₈	C₂²×C₃	1	1	yes	characteristic
43	M₁₆	C₂²×C₃	1	3	yes	—
44	C₂×C₈	C₂²×C₃	1	3	yes	—
45	C₂²×C₃	—	2	2	no	—
46	C₂²×C₃	C₂×D₄	1	3	yes	—
47	C₃×C₄	—	2	6	no	—
48	C₃×C₄	C₂×D₄	1	3	yes	—
49	C₃×C₄	C₂⁴	1	1	yes	characteristic
50	Q₈	—	2	6	no	—
51	Q₈	C₃×D₄	1	1	yes	characteristic
52	Q₈	C₂³×C₃	1	6	yes	—
53	D₄	—	2	6	no	—
54	D₄	C₃×D₄	1	3	yes	—
55	D₄	C₂³×C₃	1	2	yes	—
56	C₂×C₄	—	2	6	no	—
57	C₂×C₄	—	2	6	no	—
58	C₂×C₄	C₂³×C₃	1	3	yes	—
59	C₈	C₂³×C₃	1	1	yes	characteristic
60	C₈	C₂³×C₃	1	3	yes	—
61	C₂×C₃	—	2	3	no	—
62	C₂×C₃	—	4	2	no	—
63	C₂×C₃	C₂²×D₄	1	1	yes	characteristic
64	C₂²	—	2	2	no	—
65	C₂²	C₂×C₃×D₄	1	3	yes	—
66	C₄	—	2	6	no	—
67	C₄	C₂×C₃×D₄	1	3	yes	—
68	C₄	C₂⁴×C₃	1	1	yes	characteristic
69	C₃	#578	1	1	yes	characteristic, direct product factor, Sylow
70	C₂	—	2	3	no	—
71	C₂	—	4	2	no	—
72	C₂	C₂²×C₃×D₄	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃	C₂²×D₄
commutator, Frattini, cosocle	C₄	C₂⁴×C₃
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃ ◁ C₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×2₋¹⁺⁴	C₂	semidirect
2. C₃×#137	C₂	semidirect
3. C₃×#135	C₂	semidirect
4. C₂×C₃×Q₁₆	C₂	semidirect
5. C₃×#131	C₂	semidirect
6. #578	C₃	direct (N × H)
18. 2₋¹⁺⁴	C₂×C₃	semidirect
19. #137	C₂×C₃	semidirect
20. #135	C₂×C₃	semidirect
21. C₂×Q₁₆	C₂×C₃	semidirect
22. #131	C₂×C₃	semidirect
69. C₃	#578	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×2₋¹⁺⁴	2
C₃×#137	2
C₃×#135	2
C₂×C₃×Q₁₆	2
C₃×#131	2
#578	3

Subgroups — C3×#578 #5908

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#578 #5908