Subgroups — C₈×C₉×C₃₄₃ #72201990

Order 24696.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₉×C₃₄₃	C₂	1	1	yes	maximal, characteristic
2	C₃×C₈×C₃₄₃	C₃	1	1	yes	maximal, characteristic
3	C₂×C₉×C₃₄₃	C₄	1	1	yes	characteristic
4	C₃×C₄×C₃₄₃	C₂×C₃	1	1	yes	characteristic
5	C₈×C₉×C₄₉	C₇	1	1	yes	maximal, characteristic
6	C₉×C₃₄₃	C₈	1	1	yes	characteristic, direct product factor, Hall
7	C₈×C₃₄₃	C₉	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₃×C₃₄₃	C₃×C₄	1	1	yes	characteristic
9	C₄×C₉×C₄₉	C₂×C₇	1	1	yes	characteristic
10	C₄×C₃₄₃	C₂×C₉	1	1	yes	characteristic
11	C₃×C₈×C₄₉	C₃×C₇	1	1	yes	characteristic
12	C₃×C₃₄₃	C₃×C₈	1	1	yes	characteristic
13	C₂×C₉×C₄₉	C₄×C₇	1	1	yes	characteristic
14	C₂×C₃₄₃	C₄×C₉	1	1	yes	characteristic
15	C₃×C₄×C₄₉	C₂×C₃×C₇	1	1	yes	characteristic
16	C₇×C₈×C₉	C₄₉	1	1	yes	characteristic
17	C₉×C₄₉	C₇×C₈	1	1	yes	characteristic
18	C₈×C₄₉	C₇×C₉	1	1	yes	characteristic
19	C₃₄₃	C₈×C₉	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₃×C₄₉	C₃×C₄×C₇	1	1	yes	characteristic
21	C₄×C₇×C₉	C₂×C₄₉	1	1	yes	characteristic
22	C₄×C₄₉	C₂×C₇×C₉	1	1	yes	characteristic
23	C₃×C₇×C₈	C₃×C₄₉	1	1	yes	characteristic
24	C₃×C₄₉	C₃×C₇×C₈	1	1	yes	characteristic
25	C₂×C₇×C₉	C₄×C₄₉	1	1	yes	characteristic
26	C₂×C₄₉	C₄×C₇×C₉	1	1	yes	characteristic
27	C₃×C₄×C₇	C₂×C₃×C₄₉	1	1	yes	characteristic
28	C₈×C₉	C₃₄₃	1	1	yes	characteristic, direct product factor, Hall
29	C₇×C₉	C₈×C₄₉	1	1	yes	characteristic
30	C₇×C₈	C₉×C₄₉	1	1	yes	characteristic
31	C₄₉	C₇×C₈×C₉	1	1	yes	characteristic
32	C₂×C₃×C₇	C₃×C₄×C₄₉	1	1	yes	characteristic
33	C₄×C₉	C₂×C₃₄₃	1	1	yes	characteristic
34	C₄×C₇	C₂×C₉×C₄₉	1	1	yes	characteristic
35	C₃×C₈	C₃×C₃₄₃	1	1	yes	characteristic
36	C₃×C₇	C₃×C₈×C₄₉	1	1	yes	characteristic
37	C₂×C₉	C₄×C₃₄₃	1	1	yes	characteristic
38	C₂×C₇	C₄×C₉×C₄₉	1	1	yes	characteristic
39	C₃×C₄	C₂×C₃×C₃₄₃	1	1	yes	characteristic
40	C₉	C₈×C₃₄₃	1	1	yes	characteristic, direct product factor, Sylow
41	C₈	C₉×C₃₄₃	1	1	yes	characteristic, direct product factor, Sylow
42	C₇	C₈×C₉×C₄₉	1	1	yes	characteristic
43	C₂×C₃	C₃×C₄×C₃₄₃	1	1	yes	characteristic
44	C₄	C₂×C₉×C₃₄₃	1	1	yes	characteristic
45	C₃	C₃×C₈×C₃₄₃	1	1	yes	characteristic
46	C₂	C₄×C₉×C₃₄₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₄×C₄₉	C₂×C₃×C₇
socle, prime radical	C₂×C₃×C₇	C₃×C₄×C₄₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₉×C₃₄₃	C₈	direct (N × H)
7. C₈×C₃₄₃	C₉	direct (N × H)
19. C₃₄₃	C₈×C₉	direct (N × H)
28. C₈×C₉	C₃₄₃	direct (N × H)
40. C₉	C₈×C₃₄₃	direct (N × H)
41. C₈	C₉×C₃₄₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₉×C₃₄₃	2
C₃×C₈×C₃₄₃	3
C₈×C₉×C₄₉	7

Subgroups — C8×C9×C343 #72201990

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×C₉×C₃₄₃ #72201990