Subgroups — C₂×C₄₃×#89205 #49181597

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, direct product factor, Hall
2	C₂×C₃×C₇²×C₄₃	C₃	1	1	yes	maximal, characteristic
3	C₃×C₇²×C₄₃	C₂×C₃	1	1	yes	characteristic
4	C₂×C₄₃×C₇⋊C₉	—	7	2	no	maximal
5	C₂×C₇²×C₄₃	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	C₂×C₃×C₇×C₄₃	—	3	2	no	—
9	C₂×C₃×C₇×C₄₃	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	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₉×C₄₃	—	49	1	no	Hall
14	C₂×C₇×C₄₃	—	3	2	no	—
15	C₂×C₇×C₄₃	C₇⋊C₉	1	2	yes	complemented
16	#89205	C₂×C₄₃	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	C₃×C₄₃	1	1	yes	characteristic
21	C₂×C₃×C₄₃	#3862	1	1	yes	characteristic
22	C₃×C₇²	C₂×C₃×C₄₃	1	1	yes	characteristic
23	C₃×C₄₃	C₂×#3862	1	1	yes	characteristic
24	C₂×C₇⋊C₉	—	7	2	no	—
25	C₂×C₇²	C₉×C₄₃	1	1	yes	characteristic, complemented, Hall
26	C₂×C₄₃	#89205	1	1	yes	characteristic, direct product factor, Hall
27	C₇⋊C₉	—	7	2	no	—
28	C₇²	C₂×C₉×C₄₃	1	1	yes	characteristic, complemented, Sylow
29	C₄₃	C₂×#89205	1	1	yes	characteristic, direct product factor, Sylow
30	C₂×C₃×C₇	—	3	2	no	—
31	C₂×C₃×C₇	ΓL(1,𝔽₈)×C₄₃	1	2	yes	—
32	C₃×C₇	—	3	2	no	—
33	C₃×C₇	C₂×ΓL(1,𝔽₈)×C₄₃	1	2	yes	—
34	C₂×C₉	—	49	1	no	Hall
35	C₂×C₇	—	3	2	no	—
36	C₂×C₇	C₄₃×C₇⋊C₉	1	2	yes	complemented
37	C₉	—	49	1	no	Sylow
38	C₇	—	3	2	no	—
39	C₇	C₂×C₄₃×C₇⋊C₉	1	2	yes	complemented
40	C₂×C₃	C₄₃×#3862	1	1	yes	characteristic
41	C₃	C₂×C₄₃×#3862	1	1	yes	characteristic
42	C₂	C₄₃×#89205	1	1	yes	characteristic, direct product factor, Sylow

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

Complements

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

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

Maximal subgroups

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

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

Subgroups — C2×C43×#89205 #49181597

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₃×#89205 #49181597