Subgroups — C₃²×C₈×C₃₄₃ #72201992

Order 24696.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₄×C₃₄₃	C₂	1	1	yes	maximal, characteristic
2	C₃×C₈×C₃₄₃	C₃	1	4	yes	maximal, direct product factor
3	C₂×C₃²×C₃₄₃	C₄	1	1	yes	characteristic
4	C₃×C₄×C₃₄₃	C₂×C₃	1	4	yes	—
5	C₃²×C₈×C₄₉	C₇	1	1	yes	maximal, characteristic
6	C₃²×C₃₄₃	C₈	1	1	yes	characteristic, direct product factor, Hall
7	C₈×C₃₄₃	C₃²	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₃×C₃₄₃	C₃×C₄	1	4	yes	—
9	C₃²×C₄×C₄₉	C₂×C₇	1	1	yes	characteristic
10	C₄×C₃₄₃	C₂×C₃²	1	1	yes	characteristic
11	C₃×C₈×C₄₉	C₃×C₇	1	4	yes	—
12	C₃×C₃₄₃	C₃×C₈	1	4	yes	direct product factor
13	C₂×C₃²×C₄₉	C₄×C₇	1	1	yes	characteristic
14	C₂×C₃₄₃	C₃²×C₄	1	1	yes	characteristic
15	C₃×C₄×C₄₉	C₂×C₃×C₇	1	4	yes	—
16	C₃²×C₇×C₈	C₄₉	1	1	yes	characteristic
17	C₃²×C₄₉	C₇×C₈	1	1	yes	characteristic
18	C₈×C₄₉	C₃²×C₇	1	1	yes	characteristic
19	C₃₄₃	C₃²×C₈	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₃×C₄₉	C₃×C₄×C₇	1	4	yes	—
21	C₃²×C₄×C₇	C₂×C₄₉	1	1	yes	characteristic
22	C₄×C₄₉	C₂×C₃²×C₇	1	1	yes	characteristic
23	C₃×C₇×C₈	C₃×C₄₉	1	4	yes	—
24	C₃×C₄₉	C₃×C₇×C₈	1	4	yes	—
25	C₂×C₃²×C₇	C₄×C₄₉	1	1	yes	characteristic
26	C₂×C₄₉	C₃²×C₄×C₇	1	1	yes	characteristic
27	C₃×C₄×C₇	C₂×C₃×C₄₉	1	4	yes	—
28	C₃²×C₈	C₃₄₃	1	1	yes	characteristic, direct product factor, Hall
29	C₃²×C₇	C₈×C₄₉	1	1	yes	characteristic
30	C₇×C₈	C₃²×C₄₉	1	1	yes	characteristic
31	C₄₉	C₃²×C₇×C₈	1	1	yes	characteristic
32	C₂×C₃×C₇	C₃×C₄×C₄₉	1	4	yes	—
33	C₃²×C₄	C₂×C₃₄₃	1	1	yes	characteristic
34	C₄×C₇	C₂×C₃²×C₄₉	1	1	yes	characteristic
35	C₃×C₈	C₃×C₃₄₃	1	4	yes	direct product factor
36	C₃×C₇	C₃×C₈×C₄₉	1	4	yes	—
37	C₂×C₃²	C₄×C₃₄₃	1	1	yes	characteristic
38	C₂×C₇	C₃²×C₄×C₄₉	1	1	yes	characteristic
39	C₃×C₄	C₂×C₃×C₃₄₃	1	4	yes	—
40	C₃²	C₈×C₃₄₃	1	1	yes	characteristic, direct product factor, Sylow
41	C₈	C₃²×C₃₄₃	1	1	yes	characteristic, direct product factor, Sylow
42	C₇	C₃²×C₈×C₄₉	1	1	yes	characteristic
43	C₂×C₃	C₃×C₄×C₃₄₃	1	4	yes	—
44	C₄	C₂×C₃²×C₃₄₃	1	1	yes	characteristic
45	C₃	C₃×C₈×C₃₄₃	1	4	yes	direct product factor
46	C₂	C₃²×C₄×C₃₄₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄×C₄₉	C₂×C₃²×C₇
socle, prime radical	C₂×C₃²×C₇	C₄×C₄₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₈×C₃₄₃	C₃	direct (N × H)
6. C₃²×C₃₄₃	C₈	direct (N × H)
7. C₈×C₃₄₃	C₃²	direct (N × H)
12. C₃×C₃₄₃	C₃×C₈	direct (N × H)
19. C₃₄₃	C₃²×C₈	direct (N × H)
28. C₃²×C₈	C₃₄₃	direct (N × H)
35. C₃×C₈	C₃×C₃₄₃	direct (N × H)
40. C₃²	C₈×C₃₄₃	direct (N × H)
41. C₈	C₃²×C₃₄₃	direct (N × H)
45. C₃	C₃×C₈×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
C₃²×C₄×C₃₄₃	2
C₃×C₈×C₃₄₃	3
C₃²×C₈×C₄₉	7

Subgroups — C32×C8×C343 #72201992

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₈×C₃₄₃ #72201992