Subgroups — C₂×C₄×C₄₉×C₆₁ #72201193

Order 23912.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₇×C₆₁	C₇	1	1	yes	maximal, characteristic
2	C₂²×C₄₉×C₆₁	C₂	1	1	yes	maximal, characteristic
3	C₄×C₄₉×C₆₁	C₂	1	2	yes	maximal, direct product factor
4	C₂×C₄₉×C₆₁	C₄	1	2	yes	direct product factor
5	C₂×C₄₉×C₆₁	C₂²	1	1	yes	characteristic
6	C₄₉×C₆₁	C₂×C₄	1	1	yes	characteristic, direct product factor, Hall
7	C₂²×C₇×C₆₁	C₂×C₇	1	1	yes	characteristic
8	C₄×C₇×C₆₁	C₂×C₇	1	2	yes	—
9	C₂×C₇×C₆₁	C₄×C₇	1	2	yes	—
10	C₂×C₇×C₆₁	C₂²×C₇	1	1	yes	characteristic
11	C₂×C₄×C₆₁	C₄₉	1	1	yes	characteristic, direct product factor, Hall
12	C₇×C₆₁	C₂×C₄×C₇	1	1	yes	characteristic
13	C₂×C₄×C₄₉	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂²×C₆₁	C₂×C₄₉	1	1	yes	characteristic
15	C₄×C₆₁	C₂×C₄₉	1	2	yes	direct product factor
16	C₂²×C₄₉	C₂×C₆₁	1	1	yes	characteristic
17	C₄×C₄₉	C₂×C₆₁	1	2	yes	direct product factor
18	C₂×C₆₁	C₄×C₄₉	1	2	yes	direct product factor
19	C₂×C₆₁	C₂²×C₄₉	1	1	yes	characteristic
20	C₂×C₄₉	C₄×C₆₁	1	2	yes	direct product factor
21	C₂×C₄₉	C₂²×C₆₁	1	1	yes	characteristic
22	C₆₁	C₂×C₄×C₄₉	1	1	yes	characteristic, direct product factor, Sylow
23	C₂×C₄×C₇	C₇×C₆₁	1	1	yes	characteristic
24	C₄₉	C₂×C₄×C₆₁	1	1	yes	characteristic, direct product factor, Sylow
25	C₂²×C₇	C₂×C₇×C₆₁	1	1	yes	characteristic
26	C₄×C₇	C₂×C₇×C₆₁	1	2	yes	—
27	C₂×C₇	C₄×C₇×C₆₁	1	2	yes	—
28	C₂×C₇	C₂²×C₇×C₆₁	1	1	yes	characteristic
29	C₂×C₄	C₄₉×C₆₁	1	1	yes	characteristic, direct product factor, Sylow
30	C₇	C₂×C₄×C₇×C₆₁	1	1	yes	characteristic
31	C₂²	C₂×C₄₉×C₆₁	1	1	yes	characteristic
32	C₄	C₂×C₄₉×C₆₁	1	2	yes	direct product factor
33	C₂	C₄×C₄₉×C₆₁	1	2	yes	direct product factor
34	C₂	C₂²×C₄₉×C₆₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₇	C₂²×C₇×C₆₁
socle, prime radical	C₂²×C₇×C₆₁	C₂×C₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₄×C₄₉×C₆₁	C₂	direct (N × H)
4. C₂×C₄₉×C₆₁	C₄	direct (N × H)
6. C₄₉×C₆₁	C₂×C₄	direct (N × H)
11. C₂×C₄×C₆₁	C₄₉	direct (N × H)
13. C₂×C₄×C₄₉	C₆₁	direct (N × H)
15. C₄×C₆₁	C₂×C₄₉	direct (N × H)
17. C₄×C₄₉	C₂×C₆₁	direct (N × H)
18. C₂×C₆₁	C₄×C₄₉	direct (N × H)
20. C₂×C₄₉	C₄×C₆₁	direct (N × H)
22. C₆₁	C₂×C₄×C₄₉	direct (N × H)
24. C₄₉	C₂×C₄×C₆₁	direct (N × H)
29. C₂×C₄	C₄₉×C₆₁	direct (N × H)
32. C₄	C₂×C₄₉×C₆₁	direct (N × H)
33. C₂	C₄×C₄₉×C₆₁	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×C₄×C₇×C₆₁	7
C₂²×C₄₉×C₆₁	2
C₄×C₄₉×C₆₁	2
C₂×C₄×C₄₉	61

Subgroups — C2×C4×C49×C61 #72201193

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×C₄₉×C₆₁ #72201193