Subgroups — D₄₁×D₂₀₃ #45685641

Order 33292.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₈₃₂₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×D₂₀₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₂₉×D₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×C₂₉×C₄₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₂₉×D₄₁	—	7	1	no	maximal, Hall
6	D₁₁₈₉	—	7	1	no	—
7	C₂₉×D₄₁	D₇	1	1	yes	characteristic, complemented
8	C₄₁×D₂₉	—	7	1	no	—
9	C₂₉×C₄₁	C₂×D₇	1	1	yes	characteristic, complemented, Hall
10	D₇×D₄₁	—	29	1	no	maximal, Hall
11	C₂×D₂₀₃	—	41	1	no	maximal, Hall
12	D₂₈₇	—	29	1	no	—
13	C₇×D₄₁	D₂₉	1	1	yes	characteristic, complemented
14	D₇×C₄₁	—	29	1	no	—
15	C₂×C₇×C₂₉	—	41	1	no	—
16	D₂₀₃	—	41	1	no	—
17	D₂₀₃	D₄₁	1	1	yes	characteristic, direct product factor
18	C₇×C₄₁	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
19	C₇×C₂₉	C₂×D₄₁	1	1	yes	characteristic, complemented, Hall
20	C₂×D₄₁	—	203	1	no	Hall
21	C₂×D₂₉	—	287	1	no	Hall
22	C₂×C₄₁	—	203	1	no	—
23	D₄₁	—	203	1	no	—
24	D₄₁	D₂₀₃	1	1	yes	characteristic, direct product factor
25	C₂×C₂₉	—	41	1	no	—
26	D₂₉	—	7	1	no	—
27	D₂₉	—	287	1	no	—
28	C₄₁	C₂×D₂₀₃	1	1	yes	characteristic, complemented, Sylow
29	C₂₉	D₇×D₄₁	1	1	yes	characteristic, complemented, Sylow
30	C₂×D₇	—	1189	1	no	Hall
31	C₂×C₇	—	41	1	no	—
32	D₇	—	29	1	no	—
33	D₇	—	1189	1	no	—
34	C₇	D₂₉×D₄₁	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	8323	1	no	Sylow
36	C₂	—	41	1	no	—
37	C₂	—	8323	1	no	—
38	C₂	—	203	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₂₉×C₄₁	C₂²
LCS	G ▷ C₇×C₂₉×C₄₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₈₃₂₃	C₂	semidirect
2. C₄₁×D₂₀₃	C₂	semidirect
3. C₇×C₂₉×D₄₁	C₂	semidirect
4. C₇×C₂₉×C₄₁	C₂²	semidirect
7. C₂₉×D₄₁	D₇	semidirect
9. C₂₉×C₄₁	C₂×D₇	semidirect
13. C₇×D₄₁	D₂₉	semidirect
17. D₂₀₃	D₄₁	direct (N × H)
18. C₇×C₄₁	C₂×D₂₉	semidirect
19. C₇×C₂₉	C₂×D₄₁	semidirect
24. D₄₁	D₂₀₃	direct (N × H)
28. C₄₁	C₂×D₂₀₃	semidirect
29. C₂₉	D₇×D₄₁	semidirect
34. C₇	D₂₉×D₄₁	semidirect

Maximal subgroups

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

subgroup	index
D₈₃₂₃	2
C₄₁×D₂₀₃	2
C₇×C₂₉×D₄₁	2
D₂₉×D₄₁	7
D₇×D₄₁	29
C₂×D₂₀₃	41

Subgroups — D41×D203 #45685641

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₁×D₂₀₃ #45685641