Subgroups — C₄₁×#215 #14520139

Order 1968.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×Q₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
2	D₁₂×C₄₁	C₂	1	1	yes	maximal, characteristic
3	C₃⋊C₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	SD₁₆×C₄₁	—	3	1	no	maximal, Hall
5	C₂×D₃×C₄₁	—	2	1	no	—
6	C₃×C₄×C₄₁	—	2	1	no	—
7	C₃×C₄×C₄₁	C₂²	1	1	yes	characteristic
8	Q₈×C₄₁	D₃	1	1	yes	characteristic, complemented
9	D₄×C₄₁	—	3	1	no	—
10	C₈×C₄₁	—	3	1	no	—
11	C₂×C₃×C₄₁	D₄	1	1	yes	characteristic
12	D₃×C₄₁	—	4	1	no	—
13	C₂²×C₄₁	—	6	1	no	—
14	C₄×C₄₁	—	2	1	no	—
15	C₄×C₄₁	C₂×D₃	1	1	yes	characteristic
16	C₃×C₄₁	SD₁₆	1	1	yes	characteristic, complemented, Hall
17	C₂×C₄₁	—	12	1	no	—
18	C₂×C₄₁	#67	1	1	yes	characteristic
19	#215	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₄₁	#215	1	1	yes	characteristic, direct product factor, Sylow
21	C₃×Q₈	C₂×C₄₁	1	1	yes	characteristic, complemented
22	D₁₂	C₂×C₄₁	1	1	yes	characteristic
23	C₃⋊C₈	C₂×C₄₁	1	1	yes	characteristic, complemented
24	SD₁₆	—	3	1	no	Sylow
25	C₂×D₃	—	2	1	no	—
26	C₃×C₄	—	2	1	no	—
27	C₃×C₄	C₂²×C₄₁	1	1	yes	characteristic
28	Q₈	D₃×C₄₁	1	1	yes	characteristic, complemented
29	D₄	—	3	1	no	—
30	C₈	—	3	1	no	—
31	C₂×C₃	D₄×C₄₁	1	1	yes	characteristic
32	D₃	—	4	1	no	—
33	C₂²	—	6	1	no	—
34	C₄	—	2	1	no	—
35	C₄	C₂×D₃×C₄₁	1	1	yes	characteristic
36	C₃	SD₁₆×C₄₁	1	1	yes	characteristic, complemented, Sylow
37	C₂	—	12	1	no	—
38	C₂	#67×C₄₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄₁	#67
commutator, cosocle	C₃×C₄	C₂²×C₄₁
Frattini	C₄	C₂×D₃×C₄₁
Fitting	C₃×Q₈×C₄₁	C₂
socle	C₂×C₃×C₄₁	D₄
prime radical	D₁₂×C₄₁	C₂
hypercenter	Q₈×C₄₁	D₃
hypocenter	C₃	SD₁₆×C₄₁
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄₁ ◁ C₄×C₄₁ ◁ Q₈×C₄₁

Complements

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

N	H ≅ G/N	type
1. C₃×Q₈×C₄₁	C₂	semidirect
3. C₃⋊C₈×C₄₁	C₂	semidirect
8. Q₈×C₄₁	D₃	semidirect
16. C₃×C₄₁	SD₁₆	semidirect
19. #215	C₄₁	direct (N × H)
20. C₄₁	#215	direct (N × H)
21. C₃×Q₈	C₂×C₄₁	semidirect
23. C₃⋊C₈	C₂×C₄₁	semidirect
28. Q₈	D₃×C₄₁	semidirect
36. C₃	SD₁₆×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₃×Q₈×C₄₁	2
D₁₂×C₄₁	2
C₃⋊C₈×C₄₁	2
SD₁₆×C₄₁	3
#215	41

Subgroups — C41×#215 #14520139

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#215 #14520139