Subgroups — C₄×C₇×#11744749 #38760355

Order 25284.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#11744749	C₂	1	1	yes	maximal, characteristic
2	C₄×C₇²×C₄₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×#11744749	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₇²×C₄₃	C₂×C₃	1	1	yes	characteristic
5	C₄×#11744749	C₇	1	1	yes	maximal, characteristic, direct product factor
6	C₄×C₇×C₄₃⋊C₃	—	7	1	no	maximal
7	C₇²×C₄₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₂×#11744749	C₂×C₇	1	1	yes	characteristic
9	C₂×C₇×C₄₃⋊C₃	—	7	1	no	—
10	C₄×C₇×C₄₃	—	3	2	no	—
11	C₄×C₇×C₄₃	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
12	C₄×C₇×C₄₃	C₃×C₇	1	1	yes	characteristic, complemented
13	#11744749	C₄×C₇	1	1	yes	characteristic, direct product factor
14	C₇×C₄₃⋊C₃	—	7	1	no	—
15	C₂×C₇×C₄₃	—	3	2	no	—
16	C₂×C₇×C₄₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
17	C₂×C₇×C₄₃	C₂×C₃×C₇	1	1	yes	characteristic
18	C₄×C₇×ΓL(1,𝔽₈)	—	43	1	no	maximal, Hall
19	C₄×C₄₃⋊C₃	—	7	1	no	Hall
20	C₇×C₄₃	—	3	2	no	—
21	C₇×C₄₃	C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
22	C₇×C₄₃	C₃×C₄×C₇	1	1	yes	characteristic, complemented
23	C₂×C₇×ΓL(1,𝔽₈)	—	43	1	no	—
24	C₂×C₄₃⋊C₃	—	7	1	no	—
25	C₄×C₇²	C₄₃⋊C₃	1	1	yes	characteristic, complemented, Hall
26	C₄×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	1	yes	characteristic
30	C₂×C₄₃	C₂×C₇×ΓL(1,𝔽₈)	1	1	yes	characteristic
31	C₃×C₄×C₇	—	301	1	no	—
32	C₄×ΓL(1,𝔽₈)	—	43	1	no	—
33	C₇²	C₄×C₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
34	C₄₃	C₄×C₇×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
35	C₂×C₃×C₇	—	301	1	no	—
36	C₂×ΓL(1,𝔽₈)	—	43	1	no	—
37	C₄×C₇	—	3	2	no	—
38	C₄×C₇	C₇×C₄₃⋊C₃	1	1	yes	characteristic, complemented
39	C₄×C₇	#11744749	1	1	yes	characteristic, direct product factor
40	C₃×C₇	—	301	1	no	—
41	ΓL(1,𝔽₈)	—	43	1	no	—
42	C₂×C₇	—	3	2	no	—
43	C₂×C₇	C₂×C₇×C₄₃⋊C₃	1	1	yes	characteristic
44	C₂×C₇	C₂×#11744749	1	1	yes	characteristic
45	C₃×C₄	—	301	1	no	Hall
46	C₇	—	3	2	no	—
47	C₇	C₄×C₇×C₄₃⋊C₃	1	1	yes	characteristic, complemented
48	C₇	C₄×#11744749	1	1	yes	characteristic, direct product factor
49	C₂×C₃	—	301	1	no	—
50	C₄	C₇×#11744749	1	1	yes	characteristic, direct product factor, Sylow
51	C₃	—	301	1	no	Sylow
52	C₂	C₂×C₇×#11744749	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄×C₇	#11744749
commutator, hypocenter	C₇×C₄₃	C₃×C₄×C₇
Frattini	C₂	C₂×C₇×#11744749
Fitting	C₄×C₇²×C₄₃	C₃
socle	C₂×C₇²×C₄₃	C₂×C₃
prime radical	C₂×C₇×#11744749	C₂
cosocle	C₂×C₇×C₄₃	C₂×C₃×C₇
LCS	G ▷ C₇×C₄₃
UCS	C₁ ◁ C₄×C₇

Complements

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

N	H ≅ G/N	type
2. C₄×C₇²×C₄₃	C₃	semidirect
3. C₇×#11744749	C₄	direct (N × H)
5. C₄×#11744749	C₇	direct (N × H)
7. C₇²×C₄₃	C₃×C₄	semidirect
11. C₄×C₇×C₄₃	ΓL(1,𝔽₈)	semidirect
12. C₄×C₇×C₄₃	C₃×C₇	semidirect
13. #11744749	C₄×C₇	direct (N × H)
21. C₇×C₄₃	C₄×ΓL(1,𝔽₈)	semidirect
22. C₇×C₄₃	C₃×C₄×C₇	semidirect
25. C₄×C₇²	C₄₃⋊C₃	semidirect
26. C₄×C₄₃	C₇×ΓL(1,𝔽₈)	semidirect
33. C₇²	C₄×C₄₃⋊C₃	semidirect
34. C₄₃	C₄×C₇×ΓL(1,𝔽₈)	semidirect
38. C₄×C₇	C₇×C₄₃⋊C₃	semidirect
39. C₄×C₇	#11744749	direct (N × H)
47. C₇	C₄×C₇×C₄₃⋊C₃	semidirect
48. C₇	C₄×#11744749	direct (N × H)
50. C₄	C₇×#11744749	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×#11744749	2
C₄×C₇²×C₄₃	3
C₄×#11744749	7
C₄×C₇×C₄₃⋊C₃	7
C₄×C₇×ΓL(1,𝔽₈)	43

Subgroups — C4×C7×#11744749 #38760355

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₇×#11744749 #38760355