Subgroups — C₂×C₃₁⋊C₃×D₉₃ #46829424

Order 34596.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₃₁×C₃₁⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁⋊C₃×D₉₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃₁×D₉₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×D₃₁×C₃₁⋊C₃	—	3	1	no	maximal
5	C₃×C₃₁×C₃₁⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃₁×D₉₃	C₂×C₃	1	2	yes	complemented
7	C₂×C₃₁×C₃₁⋊C₃	—	2	1	no	—
8	C₂×C₃₁×C₃₁⋊C₃	D₃	1	1	yes	characteristic, complemented
9	D₃₁×C₃₁⋊C₃	—	3	2	no	—
10	C₂×C₃×C₃₁²	C₂×C₃	1	1	yes	characteristic, complemented
11	C₂×C₃₁×D₃₁	—	3	1	no	Hall
12	C₃×C₃₁²	C₂²×C₃	1	1	yes	characteristic, complemented
13	C₃₁×C₃₁⋊C₃	—	2	1	no	—
14	C₃₁×C₃₁⋊C₃	C₂×D₃	1	1	yes	characteristic, complemented
15	C₂×C₃₁²	C₃×D₃	1	1	yes	characteristic, complemented
16	C₃₁×D₃₁	—	3	2	no	—
17	C₂×C₃×D₉₃	—	31	1	no	maximal
18	C₂×D₃×C₃₁⋊C₃	—	31	1	no	maximal
19	C₃₁²	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₃²×C₃₁	—	31	1	no	—
21	C₃×D₉₃	—	31	2	no	—
22	C₂×C₃×C₃₁⋊C₃	D₃₁	1	1	yes	characteristic, complemented
23	D₃×C₃₁⋊C₃	—	31	2	no	—
24	C₂×D₉₃	C₃₁⋊C₃	1	1	yes	characteristic, direct product factor
25	C₂×D₃×C₃₁	—	31	1	no	—
26	C₂×C₃×D₃₁	—	93	1	no	—
27	C₂²×C₃₁⋊C₃	—	93	1	no	—
28	C₃²×C₃₁	—	31	1	no	—
29	C₃×C₃₁⋊C₃	C₂×D₃₁	1	1	yes	characteristic, complemented
30	C₂×C₃×C₃₁	—	6	5	no	—
31	C₂×C₃×C₃₁	—	31	1	no	—
32	C₂×C₃×C₃₁	—	62	1	no	—
33	C₂×C₃×C₃₁	C₂×C₃₁⋊C₃	1	1	yes	characteristic, complemented
34	C₂×C₃×C₃₁	C₃×D₃₁	1	1	yes	characteristic, complemented
35	D₉₃	C₂×C₃₁⋊C₃	1	2	yes	direct product factor
36	C₃×D₃₁	—	93	2	no	—
37	D₃×C₃₁	—	31	2	no	—
38	C₂×C₃₁⋊C₃	—	2	1	no	—
39	C₂×C₃₁⋊C₃	—	93	2	no	—
40	C₂×C₃₁⋊C₃	D₉₃	1	1	yes	characteristic, direct product factor
41	C₂²×C₃₁	—	93	1	no	—
42	C₂×D₃₁	—	3	1	no	—
43	C₃×C₃₁	—	6	5	no	—
44	C₃×C₃₁	—	31	1	no	—
45	C₃×C₃₁	—	62	1	no	—
46	C₃×C₃₁	C₂²×C₃₁⋊C₃	1	1	yes	characteristic, complemented
47	C₃×C₃₁	C₂×C₃×D₃₁	1	1	yes	characteristic, complemented
48	C₃₁⋊C₃	—	2	1	no	—
49	C₃₁⋊C₃	C₂×D₉₃	1	1	yes	characteristic, direct product factor
50	C₂×C₃₁	—	6	5	no	—
51	C₂×C₃₁	—	93	2	no	—
52	C₂×C₃₁	D₃×C₃₁⋊C₃	1	1	yes	characteristic, complemented
53	C₂×C₃₁	C₃×D₉₃	1	1	yes	characteristic, complemented
54	D₃₁	—	3	2	no	—
55	C₂×C₃×D₃	—	961	1	no	Hall
56	C₃₁	—	6	5	no	—
57	C₃₁	C₂×D₃×C₃₁⋊C₃	1	1	yes	characteristic, complemented
58	C₃₁	C₂×C₃×D₉₃	1	1	yes	characteristic, complemented
59	C₂×C₃²	—	31	1	no	—
60	C₃×D₃	—	961	2	no	—
61	C₂²×C₃	—	2883	1	no	—
62	C₂×D₃	—	31	1	no	—
63	C₃²	—	31	1	no	Sylow
64	C₂×C₃	—	31	1	no	—
65	C₂×C₃	—	62	1	no	—
66	C₂×C₃	—	2883	2	no	—
67	C₂×C₃	D₃₁×C₃₁⋊C₃	1	1	yes	characteristic, complemented
68	D₃	—	31	2	no	—
69	C₂²	—	93	1	no	Sylow
70	C₃	—	31	1	no	—
71	C₃	—	62	1	no	—
72	C₃	C₂×D₃₁×C₃₁⋊C₃	1	1	yes	characteristic, complemented
73	C₂	—	93	2	no	—
74	C₂	C₃₁⋊C₃×D₉₃	1	1	yes	characteristic, direct product factor

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₃₁×C₃₁⋊C₃	C₂	semidirect
2. C₃₁⋊C₃×D₉₃	C₂	direct (N × H)
3. C₂×C₃₁×D₉₃	C₃	semidirect
5. C₃×C₃₁×C₃₁⋊C₃	C₂²	semidirect
6. C₃₁×D₉₃	C₂×C₃	semidirect
8. C₂×C₃₁×C₃₁⋊C₃	D₃	semidirect
10. C₂×C₃×C₃₁²	C₂×C₃	semidirect
12. C₃×C₃₁²	C₂²×C₃	semidirect
14. C₃₁×C₃₁⋊C₃	C₂×D₃	semidirect
15. C₂×C₃₁²	C₃×D₃	semidirect
19. C₃₁²	C₂×C₃×D₃	semidirect
22. C₂×C₃×C₃₁⋊C₃	D₃₁	semidirect
24. C₂×D₉₃	C₃₁⋊C₃	direct (N × H)
29. C₃×C₃₁⋊C₃	C₂×D₃₁	semidirect
33. C₂×C₃×C₃₁	C₂×C₃₁⋊C₃	semidirect
34. C₂×C₃×C₃₁	C₃×D₃₁	semidirect
35. D₉₃	C₂×C₃₁⋊C₃	direct (N × H)
40. C₂×C₃₁⋊C₃	D₉₃	direct (N × H)
46. C₃×C₃₁	C₂²×C₃₁⋊C₃	semidirect
47. C₃×C₃₁	C₂×C₃×D₃₁	semidirect
49. C₃₁⋊C₃	C₂×D₉₃	direct (N × H)
52. C₂×C₃₁	D₃×C₃₁⋊C₃	semidirect
53. C₂×C₃₁	C₃×D₉₃	semidirect
57. C₃₁	C₂×D₃×C₃₁⋊C₃	semidirect
58. C₃₁	C₂×C₃×D₉₃	semidirect
67. C₂×C₃	D₃₁×C₃₁⋊C₃	semidirect
72. C₃	C₂×D₃₁×C₃₁⋊C₃	semidirect
74. 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
C₂×C₃×C₃₁×C₃₁⋊C₃	2
C₃₁⋊C₃×D₉₃	2
C₂×C₃₁×D₉₃	3
C₂×D₃₁×C₃₁⋊C₃	3
C₂×C₃×D₉₃	31
C₂×D₃×C₃₁⋊C₃	31

Subgroups — C2×C31⋊C3×D93 #46829424

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁⋊C₃×D₉₃ #46829424