Subgroups — C₂×C₇²×#66526 #45657479

Order 32634.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×#66526	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₇²×C₃₇⋊C₃	C₃	1	1	yes	maximal, characteristic
3	C₇²×C₃₇⋊C₃	C₂×C₃	1	1	yes	characteristic
4	C₂×C₇×#66526	C₇	1	8	yes	maximal, direct product factor
5	C₂×C₇²×C₃₇	C₉	1	1	yes	characteristic, complemented, Hall
6	C₇×#66526	C₂×C₇	1	8	yes	direct product factor
7	C₇²×C₃₇	C₂×C₉	1	1	yes	characteristic, complemented, Hall
8	C₂×C₇×C₃₇⋊C₃	C₃×C₇	1	8	yes	—
9	C₂×C₇²×C₉	—	37	1	no	maximal, Hall
10	C₇×C₃₇⋊C₃	C₂×C₃×C₇	1	8	yes	—
11	C₂×#66526	C₇²	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₇×C₃₇	C₇×C₉	1	8	yes	complemented
13	C₇²×C₉	—	37	1	no	Hall
14	#66526	C₂×C₇²	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₃×C₇²	—	37	1	no	—
16	C₇×C₃₇	C₂×C₇×C₉	1	8	yes	complemented
17	C₂×C₃₇⋊C₃	C₃×C₇²	1	1	yes	characteristic
18	C₃×C₇²	—	37	1	no	—
19	C₂×C₇×C₉	—	37	8	no	—
20	C₃₇⋊C₃	C₂×C₃×C₇²	1	1	yes	characteristic
21	C₂×C₇²	#66526	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₃₇	C₇²×C₉	1	1	yes	characteristic, complemented, Hall
23	C₇×C₉	—	37	8	no	—
24	C₇²	C₂×#66526	1	1	yes	characteristic, direct product factor, Sylow
25	C₂×C₃×C₇	—	37	8	no	—
26	C₃₇	C₂×C₇²×C₉	1	1	yes	characteristic, complemented, Sylow
27	C₃×C₇	—	37	8	no	—
28	C₂×C₉	—	37	1	no	Hall
29	C₂×C₇	C₇×#66526	1	8	yes	direct product factor
30	C₉	—	37	1	no	Sylow
31	C₇	C₂×C₇×#66526	1	8	yes	direct product factor
32	C₂×C₃	—	37	1	no	—
33	C₃	—	37	1	no	—
34	C₂	C₇²×#66526	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₇²	#66526
commutator, hypocenter	C₃₇	C₂×C₇²×C₉
Frattini	C₁	G
Fitting, socle	C₂×C₇²×C₃₇	C₉
prime radical	C₂×C₇²×C₃₇⋊C₃	C₃
cosocle	C₃₇⋊C₃	C₂×C₃×C₇²
LCS	G ▷ C₃₇
UCS	C₁ ◁ C₂×C₇²

Complements

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

N	H ≅ G/N	type
1. C₇²×#66526	C₂	direct (N × H)
4. C₂×C₇×#66526	C₇	direct (N × H)
5. C₂×C₇²×C₃₇	C₉	semidirect
6. C₇×#66526	C₂×C₇	direct (N × H)
7. C₇²×C₃₇	C₂×C₉	semidirect
11. C₂×#66526	C₇²	direct (N × H)
12. C₂×C₇×C₃₇	C₇×C₉	semidirect
14. #66526	C₂×C₇²	direct (N × H)
16. C₇×C₃₇	C₂×C₇×C₉	semidirect
21. C₂×C₇²	#66526	direct (N × H)
22. C₂×C₃₇	C₇²×C₉	semidirect
24. C₇²	C₂×#66526	direct (N × H)
26. C₃₇	C₂×C₇²×C₉	semidirect
29. C₂×C₇	C₇×#66526	direct (N × H)
31. C₇	C₂×C₇×#66526	direct (N × H)
34. C₂	C₇²×#66526	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇²×#66526	2
C₂×C₇²×C₃₇⋊C₃	3
C₂×C₇×#66526	7
C₂×C₇²×C₉	37

Subgroups — C2×C72×#66526 #45657479

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇²×#66526 #45657479