Subgroups — C₂×C₃×D₂₁₇₃ #39907702

Order 26076.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₂₁₇₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₄₁×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₂₁₇₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₄₁×C₅₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₄₁×C₅₃	C₂×C₃	1	1	yes	characteristic, complemented
6	D₂₁₇₃	C₂×C₃	1	2	yes	direct product factor
7	C₄₁×C₅₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂×C₃×D₅₃	—	41	1	no	maximal, Hall
9	C₂×C₃×D₄₁	—	53	1	no	maximal, Hall
10	C₂×C₃×C₅₃	D₄₁	1	1	yes	characteristic, complemented
11	C₃×D₅₃	—	41	2	no	—
12	C₂×C₃×C₄₁	D₅₃	1	1	yes	characteristic, complemented
13	C₃×D₄₁	—	53	2	no	—
14	C₂×D₅₃	—	41	1	no	Hall
15	C₂×D₄₁	—	53	1	no	Hall
16	C₃×C₅₃	C₂×D₄₁	1	1	yes	characteristic, complemented, Hall
17	C₃×C₄₁	C₂×D₅₃	1	1	yes	characteristic, complemented, Hall
18	C₂×C₅₃	C₃×D₄₁	1	1	yes	characteristic, complemented
19	D₅₃	—	41	2	no	—
20	C₂×C₄₁	C₃×D₅₃	1	1	yes	characteristic, complemented
21	D₄₁	—	53	2	no	—
22	C₅₃	C₂×C₃×D₄₁	1	1	yes	characteristic, complemented, Sylow
23	C₄₁	C₂×C₃×D₅₃	1	1	yes	characteristic, complemented, Sylow
24	C₂²×C₃	—	2173	1	no	Hall
25	C₂×C₃	—	2173	2	no	—
26	C₂×C₃	D₂₁₇₃	1	1	yes	characteristic, direct product factor
27	C₂²	—	2173	1	no	Sylow
28	C₃	C₂×D₂₁₇₃	1	1	yes	characteristic, direct product factor, Sylow
29	C₂	—	2173	2	no	—
30	C₂	C₃×D₂₁₇₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	D₂₁₇₃
commutator, cosocle, hypocenter	C₄₁×C₅₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₄₁×C₅₃	C₂
LCS	G ▷ C₄₁×C₅₃
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₂₁₇₃	C₂	direct (N × H)
2. C₂×C₃×C₄₁×C₅₃	C₂	semidirect
3. C₂×D₂₁₇₃	C₃	direct (N × H)
4. C₃×C₄₁×C₅₃	C₂²	semidirect
5. C₂×C₄₁×C₅₃	C₂×C₃	semidirect
6. D₂₁₇₃	C₂×C₃	direct (N × H)
7. C₄₁×C₅₃	C₂²×C₃	semidirect
10. C₂×C₃×C₅₃	D₄₁	semidirect
12. C₂×C₃×C₄₁	D₅₃	semidirect
16. C₃×C₅₃	C₂×D₄₁	semidirect
17. C₃×C₄₁	C₂×D₅₃	semidirect
18. C₂×C₅₃	C₃×D₄₁	semidirect
20. C₂×C₄₁	C₃×D₅₃	semidirect
22. C₅₃	C₂×C₃×D₄₁	semidirect
23. C₄₁	C₂×C₃×D₅₃	semidirect
26. C₂×C₃	D₂₁₇₃	direct (N × H)
28. C₃	C₂×D₂₁₇₃	direct (N × H)
30. C₂	C₃×D₂₁₇₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×D₂₁₇₃	2
C₂×C₃×C₄₁×C₅₃	2
C₂×D₂₁₇₃	3
C₂×C₃×D₅₃	41
C₂×C₃×D₄₁	53

Subgroups — C2×C3×D2173 #39907702

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×D₂₁₇₃ #39907702