Subgroups — C₃×#510 #5384

Order 192.

82 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	C₂×C₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×Q₃₂	C₂	1	2	yes	maximal, complemented
4	C₃×SD₃₂	C₂	1	2	yes	maximal, complemented
5	C₃×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
6	#510	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₃×#41	—	2	1	no	—
8	C₂×C₃×Q₈	—	2	1	no	—
9	C₃×Q₁₆	—	2	1	no	—
10	C₃×Q₁₆	C₂²	1	2	yes	—
11	C₃×Q₁₆	C₂²	1	1	yes	characteristic
12	C₃×SD₁₆	—	2	1	no	—
13	C₃×D₈	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
15	C₃×C₁₆	C₂²	1	2	yes	—
16	#135	C₂×C₃	1	1	yes	characteristic
17	C₂×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
18	Q₃₂	C₂×C₃	1	2	yes	complemented
19	SD₃₂	C₂×C₃	1	2	yes	complemented
20	M₃₂	C₂×C₃	1	1	yes	characteristic, complemented
21	C₃×Q₈	—	2	1	no	—
22	C₃×Q₈	—	2	2	no	—
23	C₃×Q₈	—	4	1	no	—
24	C₃×D₄	—	2	1	no	—
25	C₃×D₄	—	4	1	no	—
26	C₂×C₃×C₄	—	4	1	no	—
27	C₂×C₃×C₄	—	4	1	no	—
28	C₂×C₃×C₄	D₄	1	1	yes	characteristic
29	C₃×C₈	D₄	1	1	yes	characteristic
30	C₃×C₈	C₂³	1	1	yes	characteristic
31	#41	—	2	1	no	—
32	C₂×Q₈	—	2	1	no	—
33	Q₁₆	—	2	1	no	—
34	Q₁₆	C₂²×C₃	1	2	yes	—
35	Q₁₆	C₂²×C₃	1	1	yes	characteristic
36	SD₁₆	—	2	1	no	—
37	D₈	C₂²×C₃	1	1	yes	characteristic
38	C₂×C₈	C₂²×C₃	1	1	yes	characteristic
39	C₁₆	C₂²×C₃	1	2	yes	—
40	C₂²×C₃	—	4	1	no	—
41	C₂²×C₃	D₈	1	1	yes	characteristic
42	C₃×C₄	—	4	1	no	—
43	C₃×C₄	—	4	2	no	—
44	C₃×C₄	D₈	1	1	yes	characteristic
45	C₃×C₄	C₂×D₄	1	1	yes	characteristic
46	Q₈	—	2	1	no	—
47	Q₈	—	2	2	no	—
48	Q₈	—	4	1	no	—
49	D₄	—	2	1	no	—
50	D₄	—	4	1	no	—
51	C₂×C₄	—	4	1	no	—
52	C₂×C₄	—	4	1	no	—
53	C₂×C₄	C₃×D₄	1	1	yes	characteristic
54	C₈	C₃×D₄	1	1	yes	characteristic
55	C₈	C₂³×C₃	1	1	yes	characteristic
56	C₂×C₃	—	2	1	no	—
57	C₂×C₃	—	8	1	no	—
58	C₂×C₃	C₂×D₈	1	1	yes	characteristic
59	C₂²	—	4	1	no	—
60	C₂²	C₃×D₈	1	1	yes	characteristic
61	C₄	—	4	1	no	—
62	C₄	—	4	2	no	—
63	C₄	C₃×D₈	1	1	yes	characteristic
64	C₄	C₂×C₃×D₄	1	1	yes	characteristic
65	C₃	#510	1	1	yes	characteristic, direct product factor, Sylow
66	C₂	—	2	1	no	—
67	C₂	—	8	1	no	—
68	C₂	C₂×C₃×D₈	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃	C₂×D₈
commutator, Frattini, cosocle	C₈	C₂³×C₃
prime radical	C₃×#135	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×Q₁₆	C₂	semidirect
3. C₃×Q₃₂	C₂	semidirect
4. C₃×SD₃₂	C₂	semidirect
5. C₃×M₃₂	C₂	semidirect
6. #510	C₃	direct (N × H)
17. C₂×Q₁₆	C₂×C₃	semidirect
18. Q₃₂	C₂×C₃	semidirect
19. SD₃₂	C₂×C₃	semidirect
20. M₃₂	C₂×C₃	semidirect
65. C₃	#510	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
C₂×C₃×Q₁₆	2
C₃×Q₃₂	2
C₃×SD₃₂	2
C₃×M₃₂	2
#510	3

Subgroups — C3×#510 #5384

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#510 #5384