Subgroups — D₄₃×#64425 #38760478

Order 25284.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄₃×#3862	C₂	1	1	yes	maximal, characteristic, complemented
2	#27162412	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#64425	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄₃×C₇⋊D₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₄₃×#3862	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₇⋊D₃₀₁	C₂×C₃	1	1	yes	characteristic, complemented
7	C₄₃×C₇⋊D₇	C₂×C₃	1	1	yes	characteristic, complemented
8	C₇²×D₄₃	C₂×C₃	1	1	yes	characteristic, complemented
9	AGL(1,𝔽₇)×D₄₃	—	7	2	no	maximal
10	C₇²×C₄₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	ΓL(1,𝔽₈)⋊D₄₃	—	7	2	no	—
12	AGL(1,𝔽₇)×C₄₃	—	7	2	no	—
13	ΓL(1,𝔽₈)×D₄₃	—	14	2	no	—
14	D₇×D₄₃	—	7	2	no	—
15	D₇×D₄₃	—	21	2	no	—
16	ΓL(1,𝔽₈)×C₄₃	—	14	2	no	—
17	D₃₀₁	—	7	2	no	—
18	D₃₀₁	—	21	2	no	—
19	C₇×D₄₃	—	3	2	no	—
20	C₇×D₄₃	AGL(1,𝔽₇)	1	2	yes	complemented
21	D₇×C₄₃	—	7	2	no	—
22	D₇×C₄₃	—	21	2	no	—
23	C₂×#64425	—	43	1	no	maximal, Hall
24	C₂×C₃×D₄₃	—	49	1	no	Hall
25	C₇×C₄₃	—	3	2	no	—
26	C₇×C₄₃	C₂×AGL(1,𝔽₇)	1	2	yes	complemented
27	C₂×#3862	—	43	1	no	—
28	#64425	—	43	1	no	—
29	#64425	D₄₃	1	1	yes	characteristic, direct product factor
30	C₂×C₃×C₄₃	—	49	1	no	—
31	C₃×D₄₃	—	49	1	no	—
32	C₃×D₄₃	—	98	1	no	—
33	C₂×C₇⋊D₇	—	43	1	no	Hall
34	C₂×D₄₃	—	49	1	no	Hall
35	#3862	C₂×D₄₃	1	1	yes	characteristic, complemented, Hall
36	C₃×C₄₃	—	98	1	no	Hall
37	C₂×C₇²	—	43	1	no	—
38	C₇⋊D₇	—	43	1	no	—
39	C₇⋊D₇	C₃×D₄₃	1	1	yes	characteristic, complemented
40	C₂×C₄₃	—	49	1	no	—
41	D₄₃	—	49	1	no	—
42	D₄₃	#64425	1	1	yes	characteristic, direct product factor
43	C₂×AGL(1,𝔽₇)	—	301	2	no	—
44	C₇²	C₂×C₃×D₄₃	1	1	yes	characteristic, complemented, Sylow
45	C₄₃	C₂×#64425	1	1	yes	characteristic, complemented, Sylow
46	C₂×ΓL(1,𝔽₈)	—	602	2	no	—
47	AGL(1,𝔽₇)	—	7	2	no	—
48	AGL(1,𝔽₇)	—	301	2	no	—
49	C₂×D₇	—	301	2	no	—
50	C₂×D₇	—	903	2	no	—
51	ΓL(1,𝔽₈)	—	14	2	no	—
52	C₂×C₇	—	43	2	no	—
53	C₂×C₇	—	129	2	no	—
54	D₇	—	7	2	no	—
55	D₇	—	21	2	no	—
56	D₇	—	301	2	no	—
57	D₇	—	903	2	no	—
58	C₂²×C₃	—	2107	1	no	Hall
59	C₇	—	3	2	no	—
60	C₇	AGL(1,𝔽₇)×D₄₃	1	2	yes	complemented
61	C₂×C₃	—	49	1	no	—
62	C₂×C₃	—	2107	1	no	—
63	C₂×C₃	—	4214	1	no	—
64	C₂²	—	2107	1	no	Sylow
65	C₃	—	98	1	no	Sylow
66	C₂	—	43	1	no	—
67	C₂	—	49	1	no	—
68	C₂	—	2107	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. D₄₃×#3862	C₂	semidirect
2. #27162412	C₂	semidirect
3. C₄₃×#64425	C₂	semidirect
4. D₄₃×C₇⋊D₇	C₃	semidirect
5. C₄₃×#3862	C₂²	semidirect
6. C₇⋊D₃₀₁	C₂×C₃	semidirect
7. C₄₃×C₇⋊D₇	C₂×C₃	semidirect
8. C₇²×D₄₃	C₂×C₃	semidirect
10. C₇²×C₄₃	C₂²×C₃	semidirect
20. C₇×D₄₃	AGL(1,𝔽₇)	semidirect
26. C₇×C₄₃	C₂×AGL(1,𝔽₇)	semidirect
29. #64425	D₄₃	direct (N × H)
35. #3862	C₂×D₄₃	semidirect
39. C₇⋊D₇	C₃×D₄₃	semidirect
42. D₄₃	#64425	direct (N × H)
44. C₇²	C₂×C₃×D₄₃	semidirect
45. C₄₃	C₂×#64425	semidirect
60. C₇	AGL(1,𝔽₇)×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
D₄₃×#3862	2
#27162412	2
C₄₃×#64425	2
D₄₃×C₇⋊D₇	3
AGL(1,𝔽₇)×D₄₃	7
C₂×#64425	43

Subgroups — D43×#64425 #38760478

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₃×#64425 #38760478