Subgroups — D₄₃×#89205 #49181585

Order 37926.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×#89205	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₇²×D₄₃	C₃	1	1	yes	maximal, characteristic
3	C₃×C₇²×C₄₃	C₂×C₃	1	1	yes	characteristic
4	C₇⋊C₉×D₄₃	—	7	2	no	maximal
5	C₇²×D₄₃	C₉	1	1	yes	characteristic, complemented, Hall
6	C₄₃×C₇⋊C₉	—	7	2	no	—
7	C₇²×C₄₃	C₂×C₉	1	1	yes	characteristic, complemented, Hall
8	C₃×C₇×D₄₃	—	3	2	no	—
9	C₃×C₇×D₄₃	ΓL(1,𝔽₈)	1	2	yes	—
10	C₃×C₇×C₄₃	—	3	2	no	—
11	C₃×C₇×C₄₃	C₂×ΓL(1,𝔽₈)	1	2	yes	—
12	C₂×#89205	—	43	1	no	maximal, Hall
13	C₉×D₄₃	—	49	1	no	Hall
14	C₇×D₄₃	—	3	2	no	—
15	C₇×D₄₃	C₇⋊C₉	1	2	yes	complemented
16	#89205	D₄₃	1	1	yes	characteristic, direct product factor, Hall
17	C₉×C₄₃	—	49	1	no	Hall
18	C₇×C₄₃	—	3	2	no	—
19	C₇×C₄₃	C₂×C₇⋊C₉	1	2	yes	complemented
20	C₂×C₃×C₇²	—	43	1	no	—
21	C₃×D₄₃	#3862	1	1	yes	characteristic
22	C₃×C₇²	C₃×D₄₃	1	1	yes	characteristic
23	C₃×C₄₃	C₂×#3862	1	1	yes	characteristic
24	C₂×C₇⋊C₉	—	301	2	no	—
25	C₂×C₇²	—	43	1	no	Hall
26	D₄₃	#89205	1	1	yes	characteristic, direct product factor, Hall
27	C₇⋊C₉	—	7	2	no	—
28	C₇²	C₉×D₄₃	1	1	yes	characteristic, complemented, Sylow
29	C₄₃	C₂×#89205	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₃×C₇	—	43	2	no	—
31	C₂×C₃×C₇	—	129	2	no	—
32	C₃×C₇	—	3	2	no	—
33	C₃×C₇	ΓL(1,𝔽₈)×D₄₃	1	2	yes	—
34	C₂×C₉	—	2107	1	no	Hall
35	C₂×C₇	—	43	2	no	—
36	C₂×C₇	—	129	2	no	—
37	C₉	—	49	1	no	Sylow
38	C₇	—	3	2	no	—
39	C₇	C₇⋊C₉×D₄₃	1	2	yes	complemented
40	C₂×C₃	—	43	1	no	—
41	C₃	D₄₃×#3862	1	1	yes	characteristic
42	C₂	—	43	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₃	D₄₃×#3862
commutator, hypocenter	C₇²×C₄₃	C₂×C₉
Fitting, socle, cosocle	C₃×C₇²×C₄₃	C₂×C₃
prime radical	C₃×C₇²×D₄₃	C₃
LCS	G ▷ C₇²×C₄₃
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₄₃×#89205	C₂	semidirect
5. C₇²×D₄₃	C₉	semidirect
7. C₇²×C₄₃	C₂×C₉	semidirect
15. C₇×D₄₃	C₇⋊C₉	semidirect
16. #89205	D₄₃	direct (N × H)
19. C₇×C₄₃	C₂×C₇⋊C₉	semidirect
26. D₄₃	#89205	direct (N × H)
28. C₇²	C₉×D₄₃	semidirect
29. C₄₃	C₂×#89205	semidirect
39. C₇	C₇⋊C₉×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₄₃×#89205	2
C₃×C₇²×D₄₃	3
C₇⋊C₉×D₄₃	7
C₂×#89205	43

Subgroups — D43×#89205 #49181585

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₃×#89205 #49181585