Subgroups — C₂×C₄₁×D₁₇₇ #44395083

Order 29028.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×D₁₇₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₄₁×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×D₅₉	—	3	1	no	maximal, Hall
4	C₃×C₄₁×C₅₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₄₁×C₅₉	D₃	1	1	yes	characteristic, complemented
6	C₄₁×D₅₉	—	3	2	no	—
7	C₄₁×C₅₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
8	C₂×D₁₇₇	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×D₃×C₄₁	—	59	1	no	maximal, Hall
10	C₂×C₃×C₅₉	C₂×C₄₁	1	1	yes	characteristic, complemented
11	D₁₇₇	C₂×C₄₁	1	2	yes	direct product factor
12	C₂×C₃×C₄₁	D₅₉	1	1	yes	characteristic, complemented
13	D₃×C₄₁	—	59	2	no	—
14	C₂×D₅₉	—	3	1	no	Hall
15	C₃×C₅₉	C₂²×C₄₁	1	1	yes	characteristic, complemented, Hall
16	C₂²×C₄₁	—	177	1	no	Hall
17	C₃×C₄₁	C₂×D₅₉	1	1	yes	characteristic, complemented, Hall
18	C₂×C₅₉	D₃×C₄₁	1	1	yes	characteristic, complemented
19	D₅₉	—	3	2	no	—
20	C₂×C₄₁	—	177	2	no	—
21	C₂×C₄₁	D₁₇₇	1	1	yes	characteristic, direct product factor
22	C₅₉	C₂×D₃×C₄₁	1	1	yes	characteristic, complemented, Sylow
23	C₄₁	C₂×D₁₇₇	1	1	yes	characteristic, direct product factor, Sylow
24	C₂×D₃	—	59	1	no	Hall
25	C₂×C₃	C₄₁×D₅₉	1	1	yes	characteristic, complemented
26	D₃	—	59	2	no	—
27	C₂²	—	177	1	no	Sylow
28	C₃	C₂×C₄₁×D₅₉	1	1	yes	characteristic, complemented, Sylow
29	C₂	—	177	2	no	—
30	C₂	C₄₁×D₁₇₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₄₁	D₁₇₇
commutator, cosocle, hypocenter	C₃×C₅₉	C₂²×C₄₁
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₄₁×C₅₉	C₂
LCS	G ▷ C₃×C₅₉
UCS	C₁ ◁ C₂×C₄₁

Complements

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

N	H ≅ G/N	type
1. C₄₁×D₁₇₇	C₂	direct (N × H)
2. C₂×C₃×C₄₁×C₅₉	C₂	semidirect
4. C₃×C₄₁×C₅₉	C₂²	semidirect
5. C₂×C₄₁×C₅₉	D₃	semidirect
7. C₄₁×C₅₉	C₂×D₃	semidirect
8. C₂×D₁₇₇	C₄₁	direct (N × H)
10. C₂×C₃×C₅₉	C₂×C₄₁	semidirect
11. D₁₇₇	C₂×C₄₁	direct (N × H)
12. C₂×C₃×C₄₁	D₅₉	semidirect
15. C₃×C₅₉	C₂²×C₄₁	semidirect
17. C₃×C₄₁	C₂×D₅₉	semidirect
18. C₂×C₅₉	D₃×C₄₁	semidirect
21. C₂×C₄₁	D₁₇₇	direct (N × H)
22. C₅₉	C₂×D₃×C₄₁	semidirect
23. C₄₁	C₂×D₁₇₇	direct (N × H)
25. C₂×C₃	C₄₁×D₅₉	semidirect
28. C₃	C₂×C₄₁×D₅₉	semidirect
30. C₂	C₄₁×D₁₇₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₁×D₁₇₇	2
C₂×C₃×C₄₁×C₅₉	2
C₂×C₄₁×D₅₉	3
C₂×D₁₇₇	41
C₂×D₃×C₄₁	59

Subgroups — C2×C41×D177 #44395083

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×D₁₇₇ #44395083