Subgroups — #16813401⋊C₇ #38760281

Order 25284.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11744749⋊C₇	C₂	1	1	yes	maximal, characteristic
2	C₇×Dic₄₃⋊C₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	#11744749⋊C₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇×C₄₃⋊C₇	C₂×C₃	1	1	yes	characteristic
5	#16813401	C₇	1	1	yes	maximal, characteristic, complemented
6	((C₄₃⋊C₃)⋊C₄)⋊C₇	—	7	1	no	maximal
7	C₇×C₄₃⋊C₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₂×#11744749	C₂×C₇	1	1	yes	characteristic
9	C₂×(C₄₃⋊C₃)⋊C₇	—	7	1	no	—
10	C₇×Dic₄₃	C₃×C₇	1	1	yes	characteristic, complemented
11	Dic₄₃⋊C₇	—	3	2	no	—
12	Dic₄₃⋊C₇	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
13	#11744749	C₄×C₇	1	1	yes	characteristic, complemented
14	(C₄₃⋊C₃)⋊C₇	—	7	1	no	—
15	C₂×C₇×C₄₃	C₂×C₃×C₇	1	1	yes	characteristic
16	C₂×C₄₃⋊C₇	—	3	2	no	—
17	C₂×C₄₃⋊C₇	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
18	C₄×C₇×ΓL(1,𝔽₈)	—	43	1	no	maximal, Hall
19	(C₄₃⋊C₃)⋊C₄	—	7	1	no	Hall
20	C₇×C₄₃	C₃×C₄×C₇	1	1	yes	characteristic, complemented
21	C₄₃⋊C₇	—	3	2	no	—
22	C₄₃⋊C₇	C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
23	C₂×C₇×ΓL(1,𝔽₈)	—	86	1	no	—
24	C₂×C₄₃⋊C₃	—	7	1	no	—
25	C₄×C₇²	—	43	1	no	Hall
26	Dic₄₃	C₇×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
27	C₇×ΓL(1,𝔽₈)	—	86	1	no	Hall
28	C₄₃⋊C₃	—	7	1	no	Hall
29	C₂×C₇²	—	86	1	no	—
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	—	86	1	no	Sylow
34	C₄₃	C₄×C₇×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
35	C₂×C₃×C₇	—	602	1	no	—
36	C₂×ΓL(1,𝔽₈)	—	43	1	no	—
37	C₄×C₇	—	43	1	no	—
38	C₄×C₇	—	43	1	no	—
39	C₄×C₇	—	129	2	no	—
40	C₃×C₇	—	602	1	no	—
41	ΓL(1,𝔽₈)	—	43	1	no	—
42	C₂×C₇	—	258	2	no	—
43	C₂×C₇	—	86	1	no	—
44	C₂×C₇	AGL(1,𝔽₄₃)	1	1	yes	characteristic
45	C₃×C₄	—	301	1	no	Hall
46	C₇	—	258	2	no	—
47	C₇	—	86	1	no	—
48	C₇	((C₄₃⋊C₃)⋊C₄)⋊C₇	1	1	yes	characteristic, complemented
49	C₂×C₃	—	602	1	no	—
50	C₄	—	43	1	no	Sylow
51	C₃	—	602	1	no	Sylow
52	C₂	#14268588⋊C₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	#14268588⋊C₇
commutator, hypocenter	C₇×C₄₃	C₃×C₄×C₇
Fitting, socle, cosocle	C₂×C₇×C₄₃	C₂×C₃×C₇
prime radical	C₂×#11744749⋊C₇	C₂
LCS	G ▷ C₇×C₄₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
2. C₇×Dic₄₃⋊C₇	C₃	semidirect
3. #11744749⋊C₇	C₄	semidirect
5. #16813401	C₇	semidirect
7. C₇×C₄₃⋊C₇	C₃×C₄	semidirect
10. C₇×Dic₄₃	C₃×C₇	semidirect
12. Dic₄₃⋊C₇	ΓL(1,𝔽₈)	semidirect
13. #11744749	C₄×C₇	semidirect
20. C₇×C₄₃	C₃×C₄×C₇	semidirect
22. C₄₃⋊C₇	C₄×ΓL(1,𝔽₈)	semidirect
26. Dic₄₃	C₇×ΓL(1,𝔽₈)	semidirect
34. C₄₃	C₄×C₇×ΓL(1,𝔽₈)	semidirect
48. C₇	((C₄₃⋊C₃)⋊C₄)⋊C₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11744749⋊C₇	2
C₇×Dic₄₃⋊C₇	3
#16813401	7
((C₄₃⋊C₃)⋊C₄)⋊C₇	7
C₄×C₇×ΓL(1,𝔽₈)	43

Subgroups — #16813401⋊C7 #38760281

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #16813401⋊C₇ #38760281