Subgroups — C₂×#30654571 #45657366

Order 32634.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30654571	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃×C₇²×C₃₇	C₃	1	1	yes	maximal, characteristic
3	C₃×C₇²×C₃₇	C₂×C₃	1	1	yes	characteristic
4	C₂×#14556418	—	7	8	no	maximal
5	C₂×C₇²×C₃₇	C₉	1	1	yes	characteristic, complemented, Hall
6	#14556418	—	7	8	no	—
7	C₇²×C₃₇	C₂×C₉	1	1	yes	characteristic, complemented, Hall
8	C₂×C₃×C₇×C₃₇	ΓL(1,𝔽₈)	1	8	yes	—
9	C₂×#89204	—	37	1	no	maximal, Hall
10	C₃×C₇×C₃₇	C₂×ΓL(1,𝔽₈)	1	8	yes	—
11	C₂×#66524	—	49	1	no	Hall
12	C₂×C₇×C₃₇	C₇⋊C₉	1	8	yes	complemented
13	#89204	—	37	1	no	Hall
14	#66524	—	49	1	no	Hall
15	C₂×C₃×C₇²	C₃₇⋊C₃	1	1	yes	characteristic
16	C₇×C₃₇	C₂×C₇⋊C₉	1	8	yes	complemented
17	C₂×C₃×C₃₇	#3861	1	1	yes	characteristic
18	C₃×C₇²	C₂×C₃₇⋊C₃	1	1	yes	characteristic
19	C₂×C₇⋊C₉	—	259	8	no	—
20	C₃×C₃₇	C₂×#3861	1	1	yes	characteristic
21	C₂×C₇²	#66524	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃₇	#89204	1	1	yes	characteristic, complemented, Hall
23	C₇⋊C₉	—	259	8	no	—
24	C₇²	C₂×#66524	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₃×C₇	#11715912	1	8	yes	—
26	C₃₇	C₂×#89204	1	1	yes	characteristic, complemented, Sylow
27	C₃×C₇	C₂×#11715912	1	8	yes	—
28	C₂×C₉	—	1813	1	no	Hall
29	C₂×C₇	#14556418	1	8	yes	complemented
30	C₉	—	1813	1	no	Sylow
31	C₇	C₂×#14556418	1	8	yes	complemented
32	C₂×C₃	#19129589	1	1	yes	characteristic
33	C₃	C₂×#19129589	1	1	yes	characteristic
34	C₂	#30654571	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₃	#19129589
commutator, hypocenter	C₇²×C₃₇	C₂×C₉
Frattini	C₃	C₂×#19129589
Fitting, socle, prime radical	C₂×C₃×C₇²×C₃₇	C₃
cosocle	C₃×C₇²×C₃₇	C₂×C₃
LCS	G ▷ C₇²×C₃₇
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. #30654571	C₂	direct (N × H)
5. C₂×C₇²×C₃₇	C₉	semidirect
7. C₇²×C₃₇	C₂×C₉	semidirect
12. C₂×C₇×C₃₇	C₇⋊C₉	semidirect
16. C₇×C₃₇	C₂×C₇⋊C₉	semidirect
21. C₂×C₇²	#66524	semidirect
22. C₂×C₃₇	#89204	semidirect
24. C₇²	C₂×#66524	semidirect
26. C₃₇	C₂×#89204	semidirect
29. C₂×C₇	#14556418	semidirect
31. C₇	C₂×#14556418	semidirect
34. C₂	#30654571	direct (N × H)

Maximal subgroups

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

subgroup	index
#30654571	2
C₂×C₃×C₇²×C₃₇	3
C₂×#14556418	7
C₂×#89204	37

Subgroups — C2×#30654571 #45657366

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#30654571 #45657366