Subgroups — D₂₀₇⋊D₄₁ #46800393

Order 33948.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×D₂₀₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×D₃₆₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×D₉₄₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₆₉⋊D₄₁	—	3	1	no	maximal
5	C₉×C₂₃×C₄₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₄₁×D₆₉	—	3	1	no	—
7	C₂₃×D₁₂₃	—	3	1	no	—
8	C₃×D₉₄₃	D₃	1	1	yes	characteristic
9	D₂₃×D₄₁	—	9	1	no	Hall
10	C₃×C₂₃×C₄₁	C₂×D₃	1	1	yes	characteristic
11	D₉₄₃	D₉	1	1	yes	characteristic, complemented
12	C₂₃×D₄₁	—	9	1	no	—
13	C₄₁×D₂₃	—	9	1	no	—
14	D₉×D₄₁	—	23	1	no	maximal, Hall
15	C₂₃×C₄₁	C₂×D₉	1	1	yes	characteristic, complemented, Hall
16	D₉×D₂₃	—	41	1	no	maximal, Hall
17	D₃₆₉	D₂₃	1	1	yes	characteristic, complemented
18	C₉×D₄₁	—	23	1	no	—
19	D₉×C₄₁	—	23	1	no	—
20	D₃×D₄₁	—	69	1	no	—
21	D₂₀₇	D₄₁	1	1	yes	characteristic, complemented
22	C₉×D₂₃	—	41	1	no	—
23	D₉×C₂₃	—	41	1	no	—
24	C₉×C₄₁	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
25	D₃×D₂₃	—	123	1	no	—
26	D₁₂₃	—	3	1	no	—
27	C₃×D₄₁	—	23	1	no	—
28	D₃×C₄₁	—	69	1	no	—
29	C₉×C₂₃	C₂×D₄₁	1	1	yes	characteristic, complemented, Hall
30	C₂×D₄₁	—	207	1	no	Hall
31	D₆₉	—	3	1	no	—
32	C₃×D₂₃	—	41	1	no	—
33	D₃×C₂₃	—	123	1	no	—
34	C₃×C₄₁	D₃×D₂₃	1	1	yes	characteristic
35	C₂×D₂₃	—	369	1	no	Hall
36	C₂×C₄₁	—	207	1	no	—
37	D₄₁	—	9	1	no	—
38	D₄₁	—	23	1	no	—
39	C₃×C₂₃	D₃×D₄₁	1	1	yes	characteristic
40	C₂×C₂₃	—	369	1	no	—
41	D₂₃	—	9	1	no	—
42	D₂₃	—	41	1	no	—
43	C₄₁	D₉×D₂₃	1	1	yes	characteristic, complemented, Sylow
44	C₂×D₉	—	943	1	no	Hall
45	C₂₃	D₉×D₄₁	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₉	—	943	1	no	—
47	D₉	—	23	1	no	—
48	D₉	—	41	1	no	—
49	C₂×D₃	—	2829	1	no	—
50	C₉	D₂₃×D₄₁	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃	—	943	1	no	—
52	D₃	—	69	1	no	—
53	D₃	—	123	1	no	—
54	C₂²	—	8487	1	no	Sylow
55	C₃	D₆₉⋊D₄₁	1	1	yes	characteristic
56	C₂	—	369	1	no	—
57	C₂	—	943	1	no	—
58	C₂	—	207	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₂₃×C₄₁	C₂²
Frattini	C₃	D₆₉⋊D₄₁
socle	C₃×C₂₃×C₄₁	C₂×D₃
LCS	G ▷ C₉×C₂₃×C₄₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₄₁×D₂₀₇	C₂	semidirect
2. C₂₃×D₃₆₉	C₂	semidirect
3. C₉×D₉₄₃	C₂	semidirect
5. C₉×C₂₃×C₄₁	C₂²	semidirect
11. D₉₄₃	D₉	semidirect
15. C₂₃×C₄₁	C₂×D₉	semidirect
17. D₃₆₉	D₂₃	semidirect
21. D₂₀₇	D₄₁	semidirect
24. C₉×C₄₁	C₂×D₂₃	semidirect
29. C₉×C₂₃	C₂×D₄₁	semidirect
43. C₄₁	D₉×D₂₃	semidirect
45. C₂₃	D₉×D₄₁	semidirect
50. C₉	D₂₃×D₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₄₁×D₂₀₇	2
C₂₃×D₃₆₉	2
C₉×D₉₄₃	2
D₆₉⋊D₄₁	3
D₉×D₄₁	23
D₉×D₂₃	41

Subgroups — D207⋊D41 #46800393

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₀₇⋊D₄₁ #46800393