Subgroups — C₂²×C₇×#11744748 #38760576

Order 25284.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#11744748	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₇²×C₄₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×#11744748	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₇²×C₄₃	C₂×C₃	1	3	yes	complemented
5	C₂²×#11744748	C₇	1	1	yes	maximal, characteristic, direct product factor
6	C₂²×C₇×C₄₃⋊C₃	—	7	1	no	maximal
7	C₇²×C₄₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂×#11744748	C₂×C₇	1	3	yes	direct product factor
9	C₂×C₇×C₄₃⋊C₃	—	7	3	no	—
10	C₂²×C₇×C₄₃	—	3	2	no	—
11	C₂²×C₇×C₄₃	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
12	C₂²×C₇×C₄₃	C₃×C₇	1	1	yes	characteristic, complemented
13	#11744748	C₂²×C₇	1	1	yes	characteristic, direct product factor
14	C₇×C₄₃⋊C₃	—	7	1	no	—
15	C₂×C₇×C₄₃	—	3	6	no	—
16	C₂×C₇×C₄₃	C₂×ΓL(1,𝔽₈)	1	3	yes	complemented
17	C₂×C₇×C₄₃	C₂×C₃×C₇	1	3	yes	complemented
18	C₂²×C₇×ΓL(1,𝔽₈)	—	43	1	no	maximal, Hall
19	C₂²×C₄₃⋊C₃	—	7	1	no	Hall
20	C₇×C₄₃	—	3	2	no	—
21	C₇×C₄₃	C₂²×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
22	C₇×C₄₃	C₂²×C₃×C₇	1	1	yes	characteristic, complemented
23	C₂×C₇×ΓL(1,𝔽₈)	—	43	3	no	—
24	C₂×C₄₃⋊C₃	—	7	3	no	—
25	C₂²×C₇²	C₄₃⋊C₃	1	1	yes	characteristic, complemented, Hall
26	C₂²×C₄₃	C₇×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
27	C₇×ΓL(1,𝔽₈)	—	43	1	no	Hall
28	C₄₃⋊C₃	—	7	1	no	Hall
29	C₂×C₇²	C₂×C₄₃⋊C₃	1	3	yes	complemented
30	C₂×C₄₃	C₂×C₇×ΓL(1,𝔽₈)	1	3	yes	complemented
31	C₂²×C₃×C₇	—	301	1	no	—
32	C₂²×ΓL(1,𝔽₈)	—	43	1	no	—
33	C₇²	C₂²×C₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
34	C₄₃	C₂²×C₇×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
35	C₂×C₃×C₇	—	301	3	no	—
36	C₂×ΓL(1,𝔽₈)	—	43	3	no	—
37	C₂²×C₇	—	3	2	no	—
38	C₂²×C₇	C₇×C₄₃⋊C₃	1	1	yes	characteristic, complemented
39	C₂²×C₇	#11744748	1	1	yes	characteristic, direct product factor
40	C₃×C₇	—	301	1	no	—
41	ΓL(1,𝔽₈)	—	43	1	no	—
42	C₂×C₇	—	3	6	no	—
43	C₂×C₇	C₂×C₇×C₄₃⋊C₃	1	3	yes	complemented
44	C₂×C₇	C₂×#11744748	1	3	yes	direct product factor
45	C₂²×C₃	—	301	1	no	Hall
46	C₇	—	3	2	no	—
47	C₇	C₂²×C₇×C₄₃⋊C₃	1	1	yes	characteristic, complemented
48	C₇	C₂²×#11744748	1	1	yes	characteristic, direct product factor
49	C₂×C₃	—	301	3	no	—
50	C₂²	C₇×#11744748	1	1	yes	characteristic, direct product factor, Sylow
51	C₃	—	301	1	no	Sylow
52	C₂	C₂×C₇×#11744748	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₇	#11744748
commutator, cosocle, hypocenter	C₇×C₄₃	C₂²×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₂²×C₇²×C₄₃	C₃
LCS	G ▷ C₇×C₄₃
UCS	C₁ ◁ C₂²×C₇

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#11744748	C₂	direct (N × H)
2. C₂²×C₇²×C₄₃	C₃	semidirect
3. C₇×#11744748	C₂²	direct (N × H)
4. C₂×C₇²×C₄₃	C₂×C₃	semidirect
5. C₂²×#11744748	C₇	direct (N × H)
7. C₇²×C₄₃	C₂²×C₃	semidirect
8. C₂×#11744748	C₂×C₇	direct (N × H)
11. C₂²×C₇×C₄₃	ΓL(1,𝔽₈)	semidirect
12. C₂²×C₇×C₄₃	C₃×C₇	semidirect
13. #11744748	C₂²×C₇	direct (N × H)
16. C₂×C₇×C₄₃	C₂×ΓL(1,𝔽₈)	semidirect
17. C₂×C₇×C₄₃	C₂×C₃×C₇	semidirect
21. C₇×C₄₃	C₂²×ΓL(1,𝔽₈)	semidirect
22. C₇×C₄₃	C₂²×C₃×C₇	semidirect
25. C₂²×C₇²	C₄₃⋊C₃	semidirect
26. C₂²×C₄₃	C₇×ΓL(1,𝔽₈)	semidirect
29. C₂×C₇²	C₂×C₄₃⋊C₃	semidirect
30. C₂×C₄₃	C₂×C₇×ΓL(1,𝔽₈)	semidirect
33. C₇²	C₂²×C₄₃⋊C₃	semidirect
34. C₄₃	C₂²×C₇×ΓL(1,𝔽₈)	semidirect
38. C₂²×C₇	C₇×C₄₃⋊C₃	semidirect
39. C₂²×C₇	#11744748	direct (N × H)
43. C₂×C₇	C₂×C₇×C₄₃⋊C₃	semidirect
44. C₂×C₇	C₂×#11744748	direct (N × H)
47. C₇	C₂²×C₇×C₄₃⋊C₃	semidirect
48. C₇	C₂²×#11744748	direct (N × H)
50. C₂²	C₇×#11744748	direct (N × H)
52. C₂	C₂×C₇×#11744748	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×C₇×#11744748	2
C₂²×C₇²×C₄₃	3
C₂²×#11744748	7
C₂²×C₇×C₄₃⋊C₃	7
C₂²×C₇×ΓL(1,𝔽₈)	43

Subgroups — C22×C7×#11744748 #38760576

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₇×#11744748 #38760576