Subgroups — C₂×#22604108 #32913839

Order 18396.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17987163	C₂	1	1	yes	maximal, characteristic, complemented
2	#22604108	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₇×D₇₃⋊C₃	C₃	1	1	yes	maximal, characteristic
4	#17987163	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₇×D₇₃⋊C₃	C₂×C₃	1	2	yes	—
6	C₂×C₇×C₇₃⋊C₃	C₂×C₃	1	1	yes	characteristic
7	C₂×#10620323⋊C₂	—	7	1	no	maximal, Hall
8	C₂×C₇×D₇₃	C₉	1	1	yes	characteristic, complemented, Hall
9	C₇×C₇₃⋊C₃	C₂²×C₃	1	1	yes	characteristic
10	C₂×#10620323	—	7	1	no	—
11	#10620323⋊C₂	—	7	2	no	—
12	C₂×C₇×C₇₃	C₂×C₉	1	1	yes	characteristic, complemented
13	C₇×D₇₃	C₂×C₉	1	2	yes	complemented
14	C₂×D₇₃⋊C₃	ΓL(1,𝔽₈)	1	1	yes	characteristic
15	#10620323	—	7	1	no	Hall
16	C₇×C₇₃	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
17	C₂×C₇₃⋊C₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
18	D₇₃⋊C₃	C₂×ΓL(1,𝔽₈)	1	2	yes	—
19	C₂×D₇₃	C₇⋊C₉	1	1	yes	characteristic, complemented, Hall
20	C₂²×C₇⋊C₉	—	73	1	no	maximal, Hall
21	C₇₃⋊C₃	C₂²×ΓL(1,𝔽₈)	1	1	yes	characteristic
22	C₂×C₇₃	C₂×C₇⋊C₉	1	1	yes	characteristic, complemented
23	D₇₃	C₂×C₇⋊C₉	1	2	yes	complemented
24	C₂×C₇⋊C₉	—	73	2	no	—
25	C₂×C₇⋊C₉	—	73	1	no	—
26	C₂²×C₃×C₇	—	73	1	no	—
27	C₇₃	C₂²×C₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
28	C₇⋊C₉	—	73	1	no	Hall
29	C₂×C₃×C₇	—	73	2	no	—
30	C₂×C₃×C₇	—	73	1	no	—
31	C₂²×C₉	—	511	1	no	Hall
32	C₂²×C₇	—	657	1	no	Hall
33	C₃×C₇	—	73	1	no	—
34	C₂×C₉	—	511	2	no	—
35	C₂×C₉	—	511	1	no	—
36	C₂×C₇	—	657	2	no	—
37	C₂×C₇	#10620323⋊C₂	1	1	yes	characteristic, complemented
38	C₂²×C₃	—	73	1	no	—
39	C₉	—	511	1	no	Sylow
40	C₇	C₂×#10620323⋊C₂	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	—	73	2	no	—
42	C₂×C₃	—	73	1	no	—
43	C₂²	—	657	1	no	Sylow
44	C₃	—	73	1	no	—
45	C₂	—	657	2	no	—
46	C₂	#22604108	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	#22604108
commutator, hypocenter	C₇×C₇₃	C₂²×C₉
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₇₃	C₂×C₉
prime radical	C₂×C₇×D₇₃⋊C₃	C₃
cosocle	C₇×C₇₃⋊C₃	C₂²×C₃
LCS	G ▷ C₇×C₇₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×#17987163	C₂	semidirect
2. #22604108	C₂	direct (N × H)
4. #17987163	C₂²	semidirect
8. C₂×C₇×D₇₃	C₉	semidirect
12. C₂×C₇×C₇₃	C₂×C₉	semidirect
13. C₇×D₇₃	C₂×C₉	semidirect
16. C₇×C₇₃	C₂²×C₉	semidirect
19. C₂×D₇₃	C₇⋊C₉	semidirect
22. C₂×C₇₃	C₂×C₇⋊C₉	semidirect
23. D₇₃	C₂×C₇⋊C₉	semidirect
27. C₇₃	C₂²×C₇⋊C₉	semidirect
37. C₂×C₇	#10620323⋊C₂	semidirect
40. C₇	C₂×#10620323⋊C₂	semidirect
46. C₂	#22604108	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#17987163	2
#22604108	2
C₂×C₇×D₇₃⋊C₃	3
C₂×#10620323⋊C₂	7
C₂²×C₇⋊C₉	73

Subgroups — C2×#22604108 #32913839

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22604108 #32913839