Subgroups — D₃×D₁₉₃₇ #37551290

Order 23244.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅₈₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₁₃×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₁₉₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₉₃₇	—	3	1	no	maximal, Hall
5	C₃×C₁₃×C₁₄₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₁₃×C₁₄₉	—	3	1	no	—
7	D₁₉₃₇	—	3	1	no	—
8	D₁₉₃₇	D₃	1	1	yes	characteristic, direct product factor
9	C₁₃×C₁₄₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
10	D₃×D₁₄₉	—	13	1	no	maximal, Hall
11	D₄₄₇	—	13	1	no	—
12	C₃×D₁₄₉	—	13	1	no	—
13	D₃×C₁₄₉	D₁₃	1	1	yes	characteristic, complemented
14	C₂×D₁₄₉	—	39	1	no	Hall
15	C₃×C₁₄₉	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₄₉	—	3	1	no	—
17	D₁₄₉	—	13	1	no	—
18	D₁₄₉	—	39	1	no	—
19	D₃×D₁₃	—	149	1	no	maximal, Hall
20	C₁₄₉	D₃×D₁₃	1	1	yes	characteristic, complemented, Sylow
21	D₃₉	—	149	1	no	—
22	C₃×D₁₃	—	149	1	no	—
23	D₃×C₁₃	D₁₄₉	1	1	yes	characteristic, complemented
24	C₂×D₁₃	—	447	1	no	Hall
25	C₃×C₁₃	C₂×D₁₄₉	1	1	yes	characteristic, complemented, Hall
26	C₂×C₁₃	—	3	1	no	—
27	D₁₃	—	149	1	no	—
28	D₁₃	—	447	1	no	—
29	C₁₃	D₃×D₁₄₉	1	1	yes	characteristic, complemented, Sylow
30	C₂×D₃	—	1937	1	no	Hall
31	C₂×C₃	—	1937	1	no	—
32	D₃	—	1937	1	no	—
33	D₃	D₁₉₃₇	1	1	yes	characteristic, direct product factor
34	C₂²	—	5811	1	no	Sylow
35	C₃	C₂×D₁₉₃₇	1	1	yes	characteristic, complemented, Sylow
36	C₂	—	3	1	no	—
37	C₂	—	1937	1	no	—
38	C₂	—	5811	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₃×C₁₄₉	C₂²
LCS	G ▷ C₃×C₁₃×C₁₄₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₅₈₁₁	C₂	semidirect
2. D₃×C₁₃×C₁₄₉	C₂	semidirect
3. C₃×D₁₉₃₇	C₂	semidirect
5. C₃×C₁₃×C₁₄₉	C₂²	semidirect
8. D₁₉₃₇	D₃	direct (N × H)
9. C₁₃×C₁₄₉	C₂×D₃	semidirect
13. D₃×C₁₄₉	D₁₃	semidirect
15. C₃×C₁₄₉	C₂×D₁₃	semidirect
20. C₁₄₉	D₃×D₁₃	semidirect
23. D₃×C₁₃	D₁₄₉	semidirect
25. C₃×C₁₃	C₂×D₁₄₉	semidirect
29. C₁₃	D₃×D₁₄₉	semidirect
33. D₃	D₁₉₃₇	direct (N × H)
35. C₃	C₂×D₁₉₃₇	semidirect

Maximal subgroups

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

subgroup	index
D₅₈₁₁	2
D₃×C₁₃×C₁₄₉	2
C₃×D₁₉₃₇	2
C₂×D₁₉₃₇	3
D₃×D₁₄₉	13
D₃×D₁₃	149

Subgroups — D3×D1937 #37551290

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×D₁₉₃₇ #37551290