Subgroups — C₂×C₃×C₇×C₃₄₃ #72192583

Order 14406.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₇×C₄₉	C₇	1	1	yes	maximal, characteristic
2	C₂×C₃×C₃₄₃	C₇	1	7	yes	maximal, direct product factor
3	C₃×C₇×C₃₄₃	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₇×C₃₄₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₇×C₃₄₃	C₂×C₃	1	1	yes	characteristic, direct product factor, Sylow
6	C₃×C₇×C₄₉	C₂×C₇	1	1	yes	characteristic
7	C₃×C₃₄₃	C₂×C₇	1	7	yes	direct product factor
8	C₂×C₇×C₄₉	C₃×C₇	1	1	yes	characteristic
9	C₂×C₃₄₃	C₃×C₇	1	7	yes	direct product factor
10	C₇×C₄₉	C₂×C₃×C₇	1	1	yes	characteristic
11	C₃₄₃	C₂×C₃×C₇	1	7	yes	direct product factor
12	C₂×C₃×C₇²	C₄₉	1	1	yes	characteristic
13	C₂×C₃×C₄₉	C₄₉	1	6	yes	—
14	C₂×C₃×C₄₉	C₇²	1	1	yes	characteristic
15	C₃×C₇²	C₂×C₄₉	1	1	yes	characteristic
16	C₃×C₄₉	C₂×C₄₉	1	6	yes	—
17	C₃×C₄₉	C₂×C₇²	1	1	yes	characteristic
18	C₂×C₇²	C₃×C₄₉	1	1	yes	characteristic
19	C₂×C₄₉	C₃×C₄₉	1	6	yes	—
20	C₂×C₄₉	C₃×C₇²	1	1	yes	characteristic
21	C₇²	C₂×C₃×C₄₉	1	1	yes	characteristic
22	C₄₉	C₂×C₃×C₄₉	1	6	yes	—
23	C₄₉	C₂×C₃×C₇²	1	1	yes	characteristic
24	C₂×C₃×C₇	C₃₄₃	1	7	yes	direct product factor
25	C₂×C₃×C₇	C₇×C₄₉	1	1	yes	characteristic
26	C₃×C₇	C₂×C₃₄₃	1	7	yes	direct product factor
27	C₃×C₇	C₂×C₇×C₄₉	1	1	yes	characteristic
28	C₂×C₇	C₃×C₃₄₃	1	7	yes	direct product factor
29	C₂×C₇	C₃×C₇×C₄₉	1	1	yes	characteristic
30	C₇	C₂×C₃×C₃₄₃	1	7	yes	direct product factor
31	C₇	C₂×C₃×C₇×C₄₉	1	1	yes	characteristic
32	C₂×C₃	C₇×C₃₄₃	1	1	yes	characteristic, direct product factor, Hall
33	C₃	C₂×C₇×C₃₄₃	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	C₃×C₇×C₃₄₃	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄₉	C₂×C₃×C₇²
socle, prime radical	C₂×C₃×C₇²	C₄₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₃₄₃	C₇	direct (N × H)
3. C₃×C₇×C₃₄₃	C₂	direct (N × H)
4. C₂×C₇×C₃₄₃	C₃	direct (N × H)
5. C₇×C₃₄₃	C₂×C₃	direct (N × H)
7. C₃×C₃₄₃	C₂×C₇	direct (N × H)
9. C₂×C₃₄₃	C₃×C₇	direct (N × H)
11. C₃₄₃	C₂×C₃×C₇	direct (N × H)
24. C₂×C₃×C₇	C₃₄₃	direct (N × H)
26. C₃×C₇	C₂×C₃₄₃	direct (N × H)
28. C₂×C₇	C₃×C₃₄₃	direct (N × H)
30. C₇	C₂×C₃×C₃₄₃	direct (N × H)
32. C₂×C₃	C₇×C₃₄₃	direct (N × H)
33. C₃	C₂×C₇×C₃₄₃	direct (N × H)
34. C₂	C₃×C₇×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
C₂×C₃×C₇×C₄₉	7
C₂×C₃×C₃₄₃	7
C₃×C₇×C₃₄₃	2
C₂×C₇×C₃₄₃	3

Subgroups — C2×C3×C7×C343 #72192583

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₇×C₃₄₃ #72192583