Subgroups — C₂×C₃⋊#19153446 #46829425

Order 34596.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#15668333	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃⋊#19153446	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃₁×D₉₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×#19153446	—	3	1	no	maximal
5	C₃×#15668333	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃₁×D₉₃	C₂×C₃	1	2	yes	complemented
7	C₂×#15668333	—	2	1	no	—
8	C₂×#15668333	D₃	1	1	yes	characteristic, complemented
9	#19153446	—	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	#15668333	—	2	1	no	—
14	#15668333	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⋊(D₃₁⋊C₃)	—	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×C₃×C₃₁⋊C₃	—	31	1	no	—
21	C₂×C₃×C₃₁⋊C₃	—	31	1	no	—
22	C₃⋊(D₃₁⋊C₃)	—	31	2	no	—
23	D₃×C₃₁⋊C₃	—	31	2	no	—
24	C₂×D₉₃	C₃₁⋊C₃	1	1	yes	characteristic, complemented
25	C₂×D₃×C₃₁	—	31	1	no	—
26	C₂²×C₃₁⋊C₃	—	93	1	no	—
27	C₂×D₃₁⋊C₃	—	93	1	no	—
28	C₃×C₃₁⋊C₃	—	31	1	no	—
29	C₃×C₃₁⋊C₃	—	31	1	no	—
30	C₂×C₃×C₃₁	—	6	5	no	—
31	C₂×C₃×C₃₁	D₃₁⋊C₃	1	1	yes	characteristic, complemented
32	C₂×C₃×C₃₁	C₂×C₃₁⋊C₃	1	1	yes	characteristic, complemented
33	D₉₃	C₂×C₃₁⋊C₃	1	2	yes	complemented
34	D₃×C₃₁	—	31	2	no	—
35	C₂×C₃₁⋊C₃	—	31	1	no	—
36	C₂×C₃₁⋊C₃	—	31	1	no	—
37	C₂×C₃₁⋊C₃	—	62	1	no	—
38	C₂×C₃₁⋊C₃	—	62	1	no	—
39	C₂×C₃₁⋊C₃	—	93	2	no	—
40	D₃₁⋊C₃	—	93	2	no	—
41	C₂²×C₃₁	—	93	1	no	—
42	C₂×D₃₁	—	3	1	no	—
43	C₃×C₃₁	—	6	5	no	—
44	C₃×C₃₁	C₂×D₃₁⋊C₃	1	1	yes	characteristic, complemented
45	C₃×C₃₁	C₂²×C₃₁⋊C₃	1	1	yes	characteristic, complemented
46	C₃₁⋊C₃	—	31	1	no	—
47	C₃₁⋊C₃	—	31	1	no	—
48	C₃₁⋊C₃	—	62	1	no	—
49	C₃₁⋊C₃	—	62	1	no	—
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⋊(D₃₁⋊C₃)	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⋊(D₃₁⋊C₃)	1	1	yes	characteristic, complemented
59	C₂×C₃²	—	961	1	no	—
60	C₃×D₃	—	961	2	no	—
61	C₂²×C₃	—	2883	1	no	—
62	C₂×D₃	—	31	1	no	—
63	C₃²	—	961	1	no	Sylow
64	C₂×C₃	—	2883	2	no	—
65	C₂×C₃	—	1922	1	no	—
66	C₂×C₃	—	961	1	no	—
67	C₂×C₃	#19153446	1	1	yes	characteristic, complemented
68	D₃	—	31	2	no	—
69	C₂²	—	93	1	no	Sylow
70	C₃	—	1922	1	no	—
71	C₃	—	961	1	no	—
72	C₃	C₂×#19153446	1	1	yes	characteristic, complemented
73	C₂	—	93	2	no	—
74	C₂	C₃⋊#19153446	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₃⋊#19153446
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×#15668333	C₂	semidirect
2. C₃⋊#19153446	C₂	direct (N × H)
3. C₂×C₃₁×D₉₃	C₃	semidirect
5. C₃×#15668333	C₂²	semidirect
6. C₃₁×D₉₃	C₂×C₃	semidirect
8. C₂×#15668333	D₃	semidirect
10. C₂×C₃×C₃₁²	C₂×C₃	semidirect
12. C₃×C₃₁²	C₂²×C₃	semidirect
14. #15668333	C₂×D₃	semidirect
15. C₂×C₃₁²	C₃×D₃	semidirect
19. C₃₁²	C₂×C₃×D₃	semidirect
24. C₂×D₉₃	C₃₁⋊C₃	semidirect
31. C₂×C₃×C₃₁	D₃₁⋊C₃	semidirect
32. C₂×C₃×C₃₁	C₂×C₃₁⋊C₃	semidirect
33. D₉₃	C₂×C₃₁⋊C₃	semidirect
44. C₃×C₃₁	C₂×D₃₁⋊C₃	semidirect
45. C₃×C₃₁	C₂²×C₃₁⋊C₃	semidirect
52. C₂×C₃₁	D₃×C₃₁⋊C₃	semidirect
53. C₂×C₃₁	C₃⋊(D₃₁⋊C₃)	semidirect
57. C₃₁	C₂×D₃×C₃₁⋊C₃	semidirect
58. C₃₁	C₂×C₃⋊(D₃₁⋊C₃)	semidirect
67. C₂×C₃	#19153446	semidirect
72. C₃	C₂×#19153446	semidirect
74. C₂	C₃⋊#19153446	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×#15668333	2
C₃⋊#19153446	2
C₂×C₃₁×D₉₃	3
C₂×#19153446	3
C₂×C₃⋊(D₃₁⋊C₃)	31
C₂×D₃×C₃₁⋊C₃	31

Subgroups — C2×C3⋊#19153446 #46829425

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃⋊#19153446 #46829425