Subgroups — D₃×D₂₂₄₉ #41008784

Order 26988.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₆₇₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₁₃×C₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₂₂₄₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₂₂₄₉	—	3	1	no	maximal, Hall
5	C₃×C₁₃×C₁₇₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₁₃×C₁₇₃	—	3	1	no	—
7	D₂₂₄₉	—	3	1	no	—
8	D₂₂₄₉	D₃	1	1	yes	characteristic, direct product factor
9	C₁₃×C₁₇₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
10	D₃×D₁₇₃	—	13	1	no	maximal, Hall
11	D₅₁₉	—	13	1	no	—
12	C₃×D₁₇₃	—	13	1	no	—
13	D₃×C₁₇₃	D₁₃	1	1	yes	characteristic, complemented
14	C₂×D₁₇₃	—	39	1	no	Hall
15	C₃×C₁₇₃	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₇₃	—	3	1	no	—
17	D₁₇₃	—	13	1	no	—
18	D₁₇₃	—	39	1	no	—
19	C₁₇₃	D₃×D₁₃	1	1	yes	characteristic, complemented, Sylow
20	D₃×D₁₃	—	173	1	no	maximal, Hall
21	D₃₉	—	173	1	no	—
22	C₃×D₁₃	—	173	1	no	—
23	D₃×C₁₃	D₁₇₃	1	1	yes	characteristic, complemented
24	C₂×D₁₃	—	519	1	no	Hall
25	C₃×C₁₃	C₂×D₁₇₃	1	1	yes	characteristic, complemented, Hall
26	C₂×C₁₃	—	3	1	no	—
27	D₁₃	—	519	1	no	—
28	D₁₃	—	173	1	no	—
29	C₁₃	D₃×D₁₇₃	1	1	yes	characteristic, complemented, Sylow
30	C₂×D₃	—	2249	1	no	Hall
31	C₂×C₃	—	2249	1	no	—
32	D₃	—	2249	1	no	—
33	D₃	D₂₂₄₉	1	1	yes	characteristic, direct product factor
34	C₂²	—	6747	1	no	Sylow
35	C₃	C₂×D₂₂₄₉	1	1	yes	characteristic, complemented, Sylow
36	C₂	—	3	1	no	—
37	C₂	—	6747	1	no	—
38	C₂	—	2249	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₃×C₁₇₃	C₂²
LCS	G ▷ C₃×C₁₃×C₁₇₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₆₇₄₇	C₂	semidirect
2. D₃×C₁₃×C₁₇₃	C₂	semidirect
3. C₃×D₂₂₄₉	C₂	semidirect
5. C₃×C₁₃×C₁₇₃	C₂²	semidirect
8. D₂₂₄₉	D₃	direct (N × H)
9. C₁₃×C₁₇₃	C₂×D₃	semidirect
13. D₃×C₁₇₃	D₁₃	semidirect
15. C₃×C₁₇₃	C₂×D₁₃	semidirect
19. C₁₇₃	D₃×D₁₃	semidirect
23. D₃×C₁₃	D₁₇₃	semidirect
25. C₃×C₁₃	C₂×D₁₇₃	semidirect
29. C₁₃	D₃×D₁₇₃	semidirect
33. D₃	D₂₂₄₉	direct (N × H)
35. C₃	C₂×D₂₂₄₉	semidirect

Maximal subgroups

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

subgroup	index
D₆₇₄₇	2
D₃×C₁₃×C₁₇₃	2
C₃×D₂₂₄₉	2
C₂×D₂₂₄₉	3
D₃×D₁₇₃	13
D₃×D₁₃	173

Subgroups — D3×D2249 #41008784

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×D₂₂₄₉ #41008784