Subgroups — C₃×C₄×C₄₉² #72205802

Order 28812.

450 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄₉²	C₂	1	1	yes	maximal, characteristic
2	C₄×C₄₉²	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₄×C₇×C₄₉	C₇	1	8	yes	maximal
4	C₂×C₃×C₇×C₄₉	C₂×C₇	1	8	yes	—
5	C₃×C₄₉²	C₄	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₄₉²	C₂×C₃	1	1	yes	characteristic
7	C₄₉²	C₃×C₄	1	1	yes	characteristic, direct product factor, Sylow
8	C₄×C₇×C₄₉	C₃×C₇	1	8	yes	—
9	C₃×C₇×C₄₉	C₄×C₇	1	8	yes	—
10	C₂×C₇×C₄₉	C₂×C₃×C₇	1	8	yes	—
11	C₃×C₄×C₇²	C₇²	1	1	yes	characteristic
12	C₃×C₄×C₄₉	C₄₉	1	56	yes	direct product factor
13	C₇×C₄₉	C₃×C₄×C₇	1	8	yes	—
14	C₂×C₃×C₇²	C₂×C₇²	1	1	yes	characteristic
15	C₂×C₃×C₄₉	C₂×C₄₉	1	56	yes	—
16	C₄×C₇²	C₃×C₇²	1	1	yes	characteristic
17	C₄×C₄₉	C₃×C₄₉	1	56	yes	direct product factor
18	C₃×C₇²	C₄×C₇²	1	1	yes	characteristic
19	C₃×C₄₉	C₄×C₄₉	1	56	yes	direct product factor
20	C₂×C₇²	C₂×C₃×C₇²	1	1	yes	characteristic
21	C₂×C₄₉	C₂×C₃×C₄₉	1	56	yes	—
22	C₃×C₄×C₇	C₇×C₄₉	1	8	yes	—
23	C₇²	C₃×C₄×C₇²	1	1	yes	characteristic
24	C₄₉	C₃×C₄×C₄₉	1	56	yes	direct product factor
25	C₂×C₃×C₇	C₂×C₇×C₄₉	1	8	yes	—
26	C₄×C₇	C₃×C₇×C₄₉	1	8	yes	—
27	C₃×C₇	C₄×C₇×C₄₉	1	8	yes	—
28	C₂×C₇	C₂×C₃×C₇×C₄₉	1	8	yes	—
29	C₃×C₄	C₄₉²	1	1	yes	characteristic, direct product factor, Hall
30	C₇	C₃×C₄×C₇×C₄₉	1	8	yes	—
31	C₂×C₃	C₂×C₄₉²	1	1	yes	characteristic
32	C₄	C₃×C₄₉²	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	C₄×C₄₉²	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	C₂×C₃×C₄₉²	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₄×C₄₉²	C₃	direct (N × H)
5. C₃×C₄₉²	C₄	direct (N × H)
7. C₄₉²	C₃×C₄	direct (N × H)
12. C₃×C₄×C₄₉	C₄₉	direct (N × H)
17. C₄×C₄₉	C₃×C₄₉	direct (N × H)
19. C₃×C₄₉	C₄×C₄₉	direct (N × H)
24. C₄₉	C₃×C₄×C₄₉	direct (N × H)
29. C₃×C₄	C₄₉²	direct (N × H)
32. C₄	C₃×C₄₉²	direct (N × H)
33. C₃	C₄×C₄₉²	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×C₄₉²	2
C₄×C₄₉²	3
C₃×C₄×C₇×C₄₉	7

Subgroups — C3×C4×C492 #72205802

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×C₄₉² #72205802