Subgroups — C₂×C₃₇⋊C₃×C₄₉⋊C₃ #45657261

Order 32634.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇⋊C₃×C₄₉⋊C₃	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×#19129580	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂×#19129581	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₇×C₄₉⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₉×C₃₇⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
6	#19129581	C₂×C₃	1	1	yes	characteristic, complemented
7	#19129580	C₂×C₃	1	1	yes	characteristic, complemented
8	C₄₉×C₃₇⋊C₃	C₂×C₃	1	1	yes	characteristic, complemented
9	C₃₇×C₄₉⋊C₃	C₂×C₃	1	1	yes	characteristic, complemented
10	C₂×ΓL(1,𝔽₈)×C₃₇⋊C₃	—	7	1	no	maximal
11	C₂×C₃₇×C₄₉	C₃²	1	1	yes	characteristic, complemented, Hall
12	ΓL(1,𝔽₈)×C₃₇⋊C₃	—	7	1	no	—
13	C₃₇×C₄₉	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
14	C₂×#11715912	—	7	1	no	—
15	C₂×#11715913	—	7	1	no	—
16	C₂×ΓL(1,𝔽₈)×C₃₇	—	7	1	no	—
17	C₂×C₇×C₃₇⋊C₃	ΓL(1,𝔽₈)	1	1	yes	characteristic
18	C₂×C₃×C₄₉⋊C₃	—	37	1	no	maximal, Hall
19	#11715913	—	7	1	no	—
20	#11715912	—	7	1	no	—
21	C₇×C₃₇⋊C₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
22	ΓL(1,𝔽₈)×C₃₇	—	7	1	no	—
23	C₂×C₃×C₃₇⋊C₃	—	49	1	no	Hall
24	C₂×C₇×C₃₇	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
25	C₃×C₄₉⋊C₃	—	37	1	no	Hall
26	C₃×C₃₇⋊C₃	—	49	1	no	Hall
27	C₂×C₃×C₄₉	—	37	1	no	—
28	C₂×C₄₉⋊C₃	—	37	1	no	—
29	C₂×C₄₉⋊C₃	—	37	1	no	—
30	C₂×C₄₉⋊C₃	C₃₇⋊C₃	1	1	yes	characteristic, direct product factor
31	C₇×C₃₇	C₂×C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
32	C₂×C₃×C₃₇	—	49	1	no	—
33	C₂×C₃₇⋊C₃	—	49	1	no	—
34	C₂×C₃₇⋊C₃	—	49	1	no	—
35	C₂×C₃₇⋊C₃	C₄₉⋊C₃	1	1	yes	characteristic, direct product factor
36	C₃×C₄₉	—	37	1	no	—
37	C₄₉⋊C₃	—	37	1	no	—
38	C₄₉⋊C₃	—	37	1	no	—
39	C₄₉⋊C₃	C₂×C₃₇⋊C₃	1	1	yes	characteristic, direct product factor
40	C₂×C₃×ΓL(1,𝔽₈)	—	259	1	no	—
41	C₃×C₃₇	—	49	1	no	—
42	C₃₇⋊C₃	—	49	1	no	—
43	C₃₇⋊C₃	—	49	1	no	—
44	C₃₇⋊C₃	C₂×C₄₉⋊C₃	1	1	yes	characteristic, direct product factor
45	C₂×C₄₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic, complemented, Hall
46	C₂×C₃₇	C₃×C₄₉⋊C₃	1	1	yes	characteristic, complemented, Hall
47	C₃×ΓL(1,𝔽₈)	—	259	1	no	—
48	C₄₉	C₂×C₃×C₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
49	C₂×C₃×C₇	—	37	1	no	—
50	C₂×ΓL(1,𝔽₈)	—	259	1	no	—
51	C₂×ΓL(1,𝔽₈)	—	259	1	no	—
52	C₂×ΓL(1,𝔽₈)	—	7	1	no	—
53	C₃₇	C₂×C₃×C₄₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
54	C₃×C₇	—	37	1	no	—
55	ΓL(1,𝔽₈)	—	259	1	no	—
56	ΓL(1,𝔽₈)	—	259	1	no	—
57	ΓL(1,𝔽₈)	—	7	1	no	—
58	C₂×C₃²	—	1813	1	no	Hall
59	C₂×C₇	ΓL(1,𝔽₈)×C₃₇⋊C₃	1	1	yes	characteristic
60	C₃²	—	1813	1	no	Sylow
61	C₇	C₂×ΓL(1,𝔽₈)×C₃₇⋊C₃	1	1	yes	characteristic
62	C₂×C₃	—	1813	1	no	—
63	C₂×C₃	—	1813	1	no	—
64	C₂×C₃	—	37	1	no	—
65	C₂×C₃	—	49	1	no	—
66	C₃	—	1813	1	no	—
67	C₃	—	1813	1	no	—
68	C₃	—	37	1	no	—
69	C₃	—	49	1	no	—
70	C₂	C₃₇⋊C₃×C₄₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂	C₃₇⋊C₃×C₄₉⋊C₃
commutator, cosocle, hypocenter	C₃₇×C₄₉	C₂×C₃²
Frattini	C₇	C₂×ΓL(1,𝔽₈)×C₃₇⋊C₃
Fitting	C₂×C₃₇×C₄₉	C₃²
socle	C₂×C₇×C₃₇	C₃×ΓL(1,𝔽₈)
LCS	G ▷ C₃₇×C₄₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₃₇⋊C₃×C₄₉⋊C₃	C₂	direct (N × H)
2. C₂×#19129580	C₃	semidirect
3. C₂×#19129581	C₃	semidirect
4. C₂×C₃₇×C₄₉⋊C₃	C₃	semidirect
5. C₂×C₄₉×C₃₇⋊C₃	C₃	semidirect
6. #19129581	C₂×C₃	semidirect
7. #19129580	C₂×C₃	semidirect
8. C₄₉×C₃₇⋊C₃	C₂×C₃	semidirect
9. C₃₇×C₄₉⋊C₃	C₂×C₃	semidirect
11. C₂×C₃₇×C₄₉	C₃²	semidirect
13. C₃₇×C₄₉	C₂×C₃²	semidirect
30. C₂×C₄₉⋊C₃	C₃₇⋊C₃	direct (N × H)
35. C₂×C₃₇⋊C₃	C₄₉⋊C₃	direct (N × H)
39. C₄₉⋊C₃	C₂×C₃₇⋊C₃	direct (N × H)
44. C₃₇⋊C₃	C₂×C₄₉⋊C₃	direct (N × H)
45. C₂×C₄₉	C₃×C₃₇⋊C₃	semidirect
46. C₂×C₃₇	C₃×C₄₉⋊C₃	semidirect
48. C₄₉	C₂×C₃×C₃₇⋊C₃	semidirect
53. C₃₇	C₂×C₃×C₄₉⋊C₃	semidirect
70. C₂	C₃₇⋊C₃×C₄₉⋊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
C₃₇⋊C₃×C₄₉⋊C₃	2
C₂×#19129580	3
C₂×#19129581	3
C₂×C₃₇×C₄₉⋊C₃	3
C₂×C₄₉×C₃₇⋊C₃	3
C₂×ΓL(1,𝔽₈)×C₃₇⋊C₃	7
C₂×C₃×C₄₉⋊C₃	37

Subgroups — C2×C37⋊C3×C49⋊C3 #45657261

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₇⋊C₃×C₄₉⋊C₃ #45657261