Subgroups — C₄×C₇×C₃₁×C₁₃⋊C₃ #46799208

Order 33852.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₃₁×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₄×C₇×C₁₃×C₃₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×C₃₁×C₁₃⋊C₃	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₇×C₁₃×C₃₁	C₂×C₃	1	1	yes	characteristic
5	C₄×C₃₁×C₁₃⋊C₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×C₁₃×C₃₁	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	C₃×C₄×C₇×C₃₁	—	13	1	no	maximal, Hall
8	C₂×C₃₁×C₁₃⋊C₃	C₂×C₇	1	1	yes	characteristic
9	C₄×C₁₃×C₃₁	C₃×C₇	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃×C₇×C₃₁	—	13	1	no	—
11	C₃₁×C₁₃⋊C₃	C₄×C₇	1	1	yes	characteristic, direct product factor, Hall
12	C₄×C₇×C₁₃⋊C₃	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₄×C₇×C₃₁	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₁₃×C₃₁	C₂×C₃×C₇	1	1	yes	characteristic
15	C₃×C₇×C₃₁	—	13	1	no	Hall
16	C₂×C₇×C₁₃⋊C₃	C₂×C₃₁	1	1	yes	characteristic
17	C₂×C₇×C₃₁	C₂×C₁₃⋊C₃	1	1	yes	characteristic
18	C₁₃×C₃₁	C₃×C₄×C₇	1	1	yes	characteristic, complemented, Hall
19	C₃×C₄×C₃₁	—	13	1	no	Hall
20	C₄×C₇×C₁₃	C₃×C₃₁	1	1	yes	characteristic, complemented, Hall
21	C₇×C₁₃⋊C₃	C₄×C₃₁	1	1	yes	characteristic, direct product factor, Hall
22	C₇×C₃₁	C₄×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₃×C₃₁	—	13	1	no	—
24	C₂×C₇×C₁₃	C₂×C₃×C₃₁	1	1	yes	characteristic
25	C₄×C₁₃⋊C₃	C₇×C₃₁	1	1	yes	characteristic, direct product factor, Hall
26	C₄×C₃₁	C₇×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
27	C₃×C₃₁	—	13	1	no	Hall
28	C₇×C₁₃	C₃×C₄×C₃₁	1	1	yes	characteristic, complemented, Hall
29	C₃×C₄×C₇	—	13	1	no	Hall
30	C₂×C₁₃⋊C₃	C₂×C₇×C₃₁	1	1	yes	characteristic
31	C₂×C₃₁	C₂×C₇×C₁₃⋊C₃	1	1	yes	characteristic
32	C₄×C₁₃	C₃×C₇×C₃₁	1	1	yes	characteristic, complemented, Hall
33	C₂×C₃×C₇	—	13	1	no	—
34	C₁₃⋊C₃	C₄×C₇×C₃₁	1	1	yes	characteristic, direct product factor, Hall
35	C₃₁	C₄×C₇×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
36	C₄×C₇	C₃₁×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
37	C₂×C₁₃	C₂×C₃×C₇×C₃₁	1	1	yes	characteristic
38	C₃×C₇	—	13	1	no	Hall
39	C₂×C₇	C₂×C₃₁×C₁₃⋊C₃	1	1	yes	characteristic
40	C₁₃	C₃×C₄×C₇×C₃₁	1	1	yes	characteristic, complemented, Sylow
41	C₃×C₄	—	13	1	no	Hall
42	C₇	C₄×C₃₁×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
43	C₂×C₃	—	13	1	no	—
44	C₄	C₇×C₃₁×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	—	13	1	no	Sylow
46	C₂	C₂×C₇×C₃₁×C₁₃⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄×C₇×C₃₁	C₁₃⋊C₃
commutator, hypocenter	C₁₃	C₃×C₄×C₇×C₃₁
Frattini	C₂	C₂×C₇×C₃₁×C₁₃⋊C₃
Fitting	C₄×C₇×C₁₃×C₃₁	C₃
socle	C₂×C₇×C₁₃×C₃₁	C₂×C₃
prime radical	C₂×C₇×C₃₁×C₁₃⋊C₃	C₂
cosocle	C₂×C₁₃	C₂×C₃×C₇×C₃₁
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₄×C₇×C₃₁

Complements

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

N	H ≅ G/N	type
2. C₄×C₇×C₁₃×C₃₁	C₃	semidirect
3. C₇×C₃₁×C₁₃⋊C₃	C₄	direct (N × H)
5. C₄×C₃₁×C₁₃⋊C₃	C₇	direct (N × H)
6. C₇×C₁₃×C₃₁	C₃×C₄	semidirect
9. C₄×C₁₃×C₃₁	C₃×C₇	semidirect
11. C₃₁×C₁₃⋊C₃	C₄×C₇	direct (N × H)
12. C₄×C₇×C₁₃⋊C₃	C₃₁	direct (N × H)
13. C₄×C₇×C₃₁	C₁₃⋊C₃	direct (N × H)
18. C₁₃×C₃₁	C₃×C₄×C₇	semidirect
20. C₄×C₇×C₁₃	C₃×C₃₁	semidirect
21. C₇×C₁₃⋊C₃	C₄×C₃₁	direct (N × H)
22. C₇×C₃₁	C₄×C₁₃⋊C₃	direct (N × H)
25. C₄×C₁₃⋊C₃	C₇×C₃₁	direct (N × H)
26. C₄×C₃₁	C₇×C₁₃⋊C₃	direct (N × H)
28. C₇×C₁₃	C₃×C₄×C₃₁	semidirect
32. C₄×C₁₃	C₃×C₇×C₃₁	semidirect
34. C₁₃⋊C₃	C₄×C₇×C₃₁	direct (N × H)
35. C₃₁	C₄×C₇×C₁₃⋊C₃	direct (N × H)
36. C₄×C₇	C₃₁×C₁₃⋊C₃	direct (N × H)
40. C₁₃	C₃×C₄×C₇×C₃₁	semidirect
42. C₇	C₄×C₃₁×C₁₃⋊C₃	direct (N × H)
44. C₄	C₇×C₃₁×C₁₃⋊C₃	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×C₇×C₃₁×C₁₃⋊C₃	2
C₄×C₇×C₁₃×C₃₁	3
C₄×C₃₁×C₁₃⋊C₃	7
C₃×C₄×C₇×C₃₁	13
C₄×C₇×C₁₃⋊C₃	31

Subgroups — C4×C7×C31×C13⋊C3 #46799208

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₇×C₃₁×C₁₃⋊C₃ #46799208