Subgroups — C₂×C₇×#14582151 #49181598

Order 37926.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#14582151	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃×C₇²×C₄₃	C₃	1	1	yes	maximal, characteristic
3	C₃×C₇²×C₄₃	C₂×C₃	1	1	yes	characteristic
4	C₂×#14582151	C₇	1	1	yes	maximal, characteristic, direct product factor
5	C₂×C₇×C₄₃⋊C₉	—	7	1	no	maximal
6	C₂×C₇²×C₄₃	C₉	1	1	yes	characteristic, complemented, Hall
7	#14582151	C₂×C₇	1	1	yes	characteristic, direct product factor
8	C₇×C₄₃⋊C₉	—	7	1	no	—
9	C₇²×C₄₃	C₂×C₉	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃×C₇×C₄₃	—	3	2	no	—
11	C₂×C₃×C₇×C₄₃	ΓL(1,𝔽₈)	1	1	yes	characteristic
12	C₂×C₃×C₇×C₄₃	C₃×C₇	1	1	yes	characteristic
13	C₃×C₇×C₄₃	—	3	2	no	—
14	C₃×C₇×C₄₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
15	C₃×C₇×C₄₃	C₂×C₃×C₇	1	1	yes	characteristic
16	C₂×C₇×C₇⋊C₉	—	43	1	no	maximal, Hall
17	C₂×C₄₃⋊C₉	—	7	1	no	Hall
18	C₂×C₇×C₄₃	—	3	2	no	—
19	C₂×C₇×C₄₃	C₇⋊C₉	1	1	yes	characteristic, complemented
20	C₂×C₇×C₄₃	C₇×C₉	1	1	yes	characteristic, complemented
21	C₇×C₇⋊C₉	—	43	1	no	Hall
22	C₄₃⋊C₉	—	7	1	no	Hall
23	C₇×C₄₃	—	3	2	no	—
24	C₇×C₄₃	C₂×C₇⋊C₉	1	1	yes	characteristic, complemented
25	C₇×C₄₃	C₂×C₇×C₉	1	1	yes	characteristic, complemented
26	C₂×C₃×C₇²	C₄₃⋊C₃	1	1	yes	characteristic
27	C₂×C₃×C₄₃	C₇×ΓL(1,𝔽₈)	1	1	yes	characteristic
28	C₃×C₇²	C₂×C₄₃⋊C₃	1	1	yes	characteristic
29	C₃×C₄₃	C₂×C₇×ΓL(1,𝔽₈)	1	1	yes	characteristic
30	C₂×C₇×C₉	—	301	1	no	—
31	C₂×C₇⋊C₉	—	43	1	no	—
32	C₂×C₇²	C₄₃⋊C₉	1	1	yes	characteristic, complemented, Hall
33	C₂×C₄₃	C₇×C₇⋊C₉	1	1	yes	characteristic, complemented, Hall
34	C₇×C₉	—	301	1	no	—
35	C₇⋊C₉	—	43	1	no	—
36	C₇²	C₂×C₄₃⋊C₉	1	1	yes	characteristic, complemented, Sylow
37	C₄₃	C₂×C₇×C₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₃×C₇	—	3	2	no	—
39	C₂×C₃×C₇	C₇×C₄₃⋊C₃	1	1	yes	characteristic
40	C₂×C₃×C₇	#11744749	1	1	yes	characteristic
41	C₃×C₇	—	3	2	no	—
42	C₃×C₇	C₂×C₇×C₄₃⋊C₃	1	1	yes	characteristic
43	C₃×C₇	C₂×#11744749	1	1	yes	characteristic
44	C₂×C₉	—	301	1	no	Hall
45	C₂×C₇	—	3	2	no	—
46	C₂×C₇	C₇×C₄₃⋊C₉	1	1	yes	characteristic, complemented
47	C₂×C₇	#14582151	1	1	yes	characteristic, direct product factor
48	C₉	—	301	1	no	Sylow
49	C₇	—	3	2	no	—
50	C₇	C₂×C₇×C₄₃⋊C₉	1	1	yes	characteristic, complemented
51	C₇	C₂×#14582151	1	1	yes	characteristic, direct product factor
52	C₂×C₃	C₇×#11744749	1	1	yes	characteristic
53	C₃	C₂×C₇×#11744749	1	1	yes	characteristic
54	C₂	C₇×#14582151	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₃×C₇	#11744749
commutator, hypocenter	C₇×C₄₃	C₂×C₇×C₉
Frattini	C₃	C₂×C₇×#11744749
Fitting, socle, prime radical	C₂×C₃×C₇²×C₄₃	C₃
cosocle	C₃×C₇×C₄₃	C₂×C₃×C₇
LCS	G ▷ C₇×C₄₃
UCS	C₁ ◁ C₂×C₃×C₇

Complements

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

N	H ≅ G/N	type
1. C₇×#14582151	C₂	direct (N × H)
4. C₂×#14582151	C₇	direct (N × H)
6. C₂×C₇²×C₄₃	C₉	semidirect
7. #14582151	C₂×C₇	direct (N × H)
9. C₇²×C₄₃	C₂×C₉	semidirect
19. C₂×C₇×C₄₃	C₇⋊C₉	semidirect
20. C₂×C₇×C₄₃	C₇×C₉	semidirect
24. C₇×C₄₃	C₂×C₇⋊C₉	semidirect
25. C₇×C₄₃	C₂×C₇×C₉	semidirect
32. C₂×C₇²	C₄₃⋊C₉	semidirect
33. C₂×C₄₃	C₇×C₇⋊C₉	semidirect
36. C₇²	C₂×C₄₃⋊C₉	semidirect
37. C₄₃	C₂×C₇×C₇⋊C₉	semidirect
46. C₂×C₇	C₇×C₄₃⋊C₉	semidirect
47. C₂×C₇	#14582151	direct (N × H)
50. C₇	C₂×C₇×C₄₃⋊C₉	semidirect
51. C₇	C₂×#14582151	direct (N × H)
54. C₂	C₇×#14582151	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×#14582151	2
C₂×C₃×C₇²×C₄₃	3
C₂×#14582151	7
C₂×C₇×C₄₃⋊C₉	7
C₂×C₇×C₇⋊C₉	43

Subgroups — C2×C7×#14582151 #49181598

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#14582151 #49181598