Subgroups — #30633765⋊C₂ #44569439

Order 32412.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30633773	C₂	1	1	yes	maximal, characteristic, complemented
2	#30633769	C₂	1	1	yes	maximal, characteristic, complemented
3	#30633765	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃₇×D₇₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	#22549193	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₂₇₀₁	C₂×C₃	1	1	yes	characteristic, complemented
7	C₃₇×D₇₃	C₂×C₃	1	1	yes	characteristic, complemented
8	C₇₃×D₃₇	C₂×C₃	1	1	yes	characteristic, complemented
9	C₃₇×C₇₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
10	C₂×D₇₃⋊C₃	—	37	1	no	maximal, Hall
11	C₂×D₃₇⋊C₃	—	73	1	no	maximal, Hall
12	C₂×C₇₃⋊C₃	—	37	1	no	—
13	D₇₃⋊C₃	—	37	1	no	—
14	D₇₃⋊C₃	—	37	1	no	—
15	C₂×D₇₃	—	37	1	no	Hall
16	C₂×C₃₇⋊C₃	—	73	1	no	—
17	D₃₇⋊C₃	—	73	1	no	—
18	D₃₇⋊C₃	—	73	1	no	—
19	C₇₃⋊C₃	—	37	1	no	Hall
20	C₂×D₃₇	—	73	1	no	Hall
21	C₂×C₇₃	—	37	1	no	—
22	D₇₃	—	37	1	no	—
23	D₇₃	D₃₇⋊C₃	1	1	yes	characteristic, complemented
24	C₃₇⋊C₃	—	73	1	no	Hall
25	C₂×C₃₇	—	73	1	no	—
26	D₃₇	—	73	1	no	—
27	D₃₇	D₇₃⋊C₃	1	1	yes	characteristic, complemented
28	C₇₃	C₂×D₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
29	C₃₇	C₂×D₇₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
30	C₂²×C₃	—	2701	1	no	Hall
31	C₂×C₃	—	2701	1	no	—
32	C₂×C₃	—	2701	1	no	—
33	C₂×C₃	—	2701	1	no	—
34	C₂²	—	2701	1	no	Sylow
35	C₃	—	2701	1	no	Sylow
36	C₂	—	37	1	no	—
37	C₂	—	73	1	no	—
38	C₂	—	2701	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃₇×C₇₃	C₂²×C₃
LCS	G ▷ C₃₇×C₇₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. #30633773	C₂	semidirect
2. #30633769	C₂	semidirect
3. #30633765	C₂	semidirect
4. D₃₇×D₇₃	C₃	semidirect
5. #22549193	C₂²	semidirect
6. D₂₇₀₁	C₂×C₃	semidirect
7. C₃₇×D₇₃	C₂×C₃	semidirect
8. C₇₃×D₃₇	C₂×C₃	semidirect
9. C₃₇×C₇₃	C₂²×C₃	semidirect
23. D₇₃	D₃₇⋊C₃	semidirect
27. D₃₇	D₇₃⋊C₃	semidirect
28. C₇₃	C₂×D₃₇⋊C₃	semidirect
29. C₃₇	C₂×D₇₃⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
#30633773	2
#30633769	2
#30633765	2
D₃₇×D₇₃	3
C₂×D₇₃⋊C₃	37
C₂×D₃₇⋊C₃	73

Subgroups — #30633765⋊C2 #44569439

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #30633765⋊C₂ #44569439