Subgroups — C₂×C₃₁×C₃⋊D₉₃ #46829467

Order 34596.

300 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×C₃⋊D₉₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₃₁²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₁×D₉₃	—	3	4	no	maximal
4	C₃²×C₃₁²	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃₁×D₉₃	—	3	8	no	—
6	C₂×C₃×C₃₁²	D₃	1	4	yes	complemented
7	C₂×C₃₁×D₃₁	—	9	1	no	Hall
8	C₃×C₃₁²	C₂×D₃	1	4	yes	complemented
9	C₂×C₃₁²	C₃⋊D₃	1	1	yes	characteristic, complemented
10	C₃₁×D₃₁	—	9	2	no	—
11	C₂×C₃⋊D₉₃	C₃₁	1	1	yes	maximal, characteristic, direct product factor
12	C₂×C₃⋊D₃×C₃₁	—	31	1	no	maximal
13	C₃₁²	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
14	C₂×C₃²×C₃₁	—	2	15	no	—
15	C₂×C₃²×C₃₁	D₃₁	1	1	yes	characteristic, complemented
16	C₂×C₃²×C₃₁	C₂×C₃₁	1	1	yes	characteristic, complemented
17	C₃⋊D₉₃	C₂×C₃₁	1	2	yes	direct product factor
18	C₃⋊D₃×C₃₁	—	31	2	no	—
19	C₂×D₉₃	—	3	4	no	—
20	C₂×D₃×C₃₁	—	93	4	no	—
21	C₃²×C₃₁	—	2	15	no	—
22	C₃²×C₃₁	C₂×D₃₁	1	1	yes	characteristic, complemented
23	C₃²×C₃₁	C₂²×C₃₁	1	1	yes	characteristic, complemented
24	C₂×C₃×C₃₁	—	2	60	no	—
25	C₂×C₃×C₃₁	D₃×C₃₁	1	4	yes	complemented
26	C₂×C₃×C₃₁	D₉₃	1	4	yes	complemented
27	D₉₃	—	3	8	no	—
28	D₃×C₃₁	—	93	8	no	—
29	C₂²×C₃₁	—	279	1	no	—
30	C₂×D₃₁	—	9	1	no	—
31	C₃×C₃₁	—	2	60	no	—
32	C₃×C₃₁	C₂×D₃×C₃₁	1	4	yes	complemented
33	C₃×C₃₁	C₂×D₉₃	1	4	yes	complemented
34	C₂×C₃₁	—	2	15	no	—
35	C₂×C₃₁	—	279	2	no	—
36	C₂×C₃₁	C₃⋊D₃×C₃₁	1	1	yes	characteristic, complemented
37	C₂×C₃₁	C₃⋊D₉₃	1	1	yes	characteristic, direct product factor
38	D₃₁	—	9	2	no	—
39	C₂×C₃⋊D₃	—	31	1	no	Hall
40	C₃₁	—	2	15	no	—
41	C₃₁	C₂×C₃⋊D₃×C₃₁	1	1	yes	characteristic, complemented
42	C₃₁	C₂×C₃⋊D₉₃	1	1	yes	characteristic, direct product factor
43	C₂×C₃²	C₃₁×D₃₁	1	1	yes	characteristic, complemented
44	C₃⋊D₃	—	31	2	no	—
45	C₂×D₃	—	93	4	no	—
46	C₃²	C₂×C₃₁×D₃₁	1	1	yes	characteristic, complemented, Sylow
47	C₂×C₃	C₃₁×D₉₃	1	4	yes	complemented
48	D₃	—	93	8	no	—
49	C₂²	—	279	1	no	Sylow
50	C₃	C₂×C₃₁×D₉₃	1	4	yes	complemented
51	C₂	—	279	2	no	—
52	C₂	C₃₁×C₃⋊D₉₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃₁	C₃⋊D₉₃
commutator, cosocle, hypocenter	C₃²×C₃₁	C₂²×C₃₁
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₃₁²	C₂
LCS	G ▷ C₃²×C₃₁
UCS	C₁ ◁ C₂×C₃₁

Complements

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

N	H ≅ G/N	type
1. C₃₁×C₃⋊D₉₃	C₂	direct (N × H)
2. C₂×C₃²×C₃₁²	C₂	semidirect
4. C₃²×C₃₁²	C₂²	semidirect
6. C₂×C₃×C₃₁²	D₃	semidirect
8. C₃×C₃₁²	C₂×D₃	semidirect
9. C₂×C₃₁²	C₃⋊D₃	semidirect
11. C₂×C₃⋊D₉₃	C₃₁	direct (N × H)
13. C₃₁²	C₂×C₃⋊D₃	semidirect
15. C₂×C₃²×C₃₁	D₃₁	semidirect
16. C₂×C₃²×C₃₁	C₂×C₃₁	semidirect
17. C₃⋊D₉₃	C₂×C₃₁	direct (N × H)
22. C₃²×C₃₁	C₂×D₃₁	semidirect
23. C₃²×C₃₁	C₂²×C₃₁	semidirect
25. C₂×C₃×C₃₁	D₃×C₃₁	semidirect
26. C₂×C₃×C₃₁	D₉₃	semidirect
32. C₃×C₃₁	C₂×D₃×C₃₁	semidirect
33. C₃×C₃₁	C₂×D₉₃	semidirect
36. C₂×C₃₁	C₃⋊D₃×C₃₁	semidirect
37. C₂×C₃₁	C₃⋊D₉₃	direct (N × H)
41. C₃₁	C₂×C₃⋊D₃×C₃₁	semidirect
42. C₃₁	C₂×C₃⋊D₉₃	direct (N × H)
43. C₂×C₃²	C₃₁×D₃₁	semidirect
46. C₃²	C₂×C₃₁×D₃₁	semidirect
47. C₂×C₃	C₃₁×D₉₃	semidirect
50. C₃	C₂×C₃₁×D₉₃	semidirect
52. C₂	C₃₁×C₃⋊D₉₃	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃₁×C₃⋊D₉₃	2
C₂×C₃²×C₃₁²	2
C₂×C₃₁×D₉₃	3
C₂×C₃⋊D₉₃	31
C₂×C₃⋊D₃×C₃₁	31

Subgroups — C2×C31×C3⋊D93 #46829467

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×C₃⋊D₉₃ #46829467