Subgroups — Dic₄₃⋊#3862 #38760341

Order 25284.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃⋊#3862	C₂	1	1	yes	maximal, characteristic
2	C₇²×Dic₄₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₄₃⋊#3862	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇²×C₄₃	C₂×C₃	1	1	yes	characteristic
5	#16813401	—	7	1	no	maximal
6	#16813400	—	7	1	no	maximal
7	C₇²×C₄₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₂×#11744749	—	7	1	no	—
9	C₂×#11744748	—	7	1	no	—
10	C₇×Dic₄₃	—	3	2	no	—
11	C₇×Dic₄₃	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
12	C₇×Dic₄₃	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
13	#11744749	—	7	1	no	—
14	#11744748	—	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×ΓL(1,𝔽₈)	1	1	yes	characteristic
18	C₄×#3862	—	43	1	no	maximal, Hall
19	(C₄₃⋊C₃)⋊C₄	—	49	1	no	Hall
20	C₇×C₄₃	—	3	2	no	—
21	C₇×C₄₃	C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
22	C₇×C₄₃	C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
23	C₂×#3862	—	86	1	no	—
24	C₂×C₄₃⋊C₃	—	49	1	no	—
25	C₄×C₇²	—	43	1	no	Hall
26	Dic₄₃	#3862	1	1	yes	characteristic, complemented, Hall
27	#3862	—	86	1	no	Hall
28	C₄₃⋊C₃	—	49	1	no	Hall
29	C₂×C₇²	D₄₃⋊C₃	1	1	yes	characteristic
30	C₂×C₄₃	C₂×#3862	1	1	yes	characteristic
31	C₄×ΓL(1,𝔽₈)	—	301	1	no	—
32	C₄×ΓL(1,𝔽₈)	—	301	1	no	—
33	C₇²	(C₄₃⋊C₃)⋊C₄	1	1	yes	characteristic, complemented, Sylow
34	C₄₃	C₄×#3862	1	1	yes	characteristic, complemented, Sylow
35	C₂×ΓL(1,𝔽₈)	—	602	1	no	—
36	C₂×ΓL(1,𝔽₈)	—	602	1	no	—
37	C₄×C₇	—	43	1	no	—
38	C₄×C₇	—	43	1	no	—
39	C₄×C₇	—	129	2	no	—
40	ΓL(1,𝔽₈)	—	602	1	no	—
41	ΓL(1,𝔽₈)	—	602	1	no	—
42	C₂×C₇	—	3	2	no	—
43	C₂×C₇	#14268587	1	1	yes	characteristic
44	C₂×C₇	#14268588	1	1	yes	characteristic
45	C₃×C₄	—	2107	1	no	Hall
46	C₇	—	3	2	no	—
47	C₇	#16813400	1	1	yes	characteristic, complemented
48	C₇	#16813401	1	1	yes	characteristic, complemented
49	C₂×C₃	—	4214	1	no	—
50	C₄	—	43	1	no	Sylow
51	C₃	—	4214	1	no	Sylow
52	C₂	D₄₃⋊#3862	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₄₃⋊#3862
commutator, hypocenter	C₇²×C₄₃	C₃×C₄
Fitting, socle, cosocle	C₂×C₇²×C₄₃	C₂×C₃
prime radical	C₂×C₄₃⋊#3862	C₂
LCS	G ▷ C₇²×C₄₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
2. C₇²×Dic₄₃	C₃	semidirect
3. C₄₃⋊#3862	C₄	semidirect
7. C₇²×C₄₃	C₃×C₄	semidirect
11. C₇×Dic₄₃	ΓL(1,𝔽₈)	semidirect
12. C₇×Dic₄₃	ΓL(1,𝔽₈)	semidirect
21. C₇×C₄₃	C₄×ΓL(1,𝔽₈)	semidirect
22. C₇×C₄₃	C₄×ΓL(1,𝔽₈)	semidirect
26. Dic₄₃	#3862	semidirect
33. C₇²	(C₄₃⋊C₃)⋊C₄	semidirect
34. C₄₃	C₄×#3862	semidirect
47. C₇	#16813400	semidirect
48. C₇	#16813401	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₃⋊#3862	2
C₇²×Dic₄₃	3
#16813401	7
#16813400	7
C₄×#3862	43

Subgroups — Dic43⋊#3862 #38760341

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₄₃⋊#3862 #38760341