Subgroups — #14558781⋊C₂ #18012113

Order 4788.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14558787	C₂	1	1	yes	maximal, characteristic, complemented
2	#14558785	C₂	1	1	yes	maximal, characteristic, complemented
3	#14558781	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₇×D₁₉	C₃	1	1	yes	maximal, characteristic
5	#11924777	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃×D₁₃₃	C₂×C₃	1	1	yes	characteristic
7	C₃×D₇×C₁₉	C₂×C₃	1	1	yes	characteristic
8	C₃×C₇×D₁₉	C₂×C₃	1	1	yes	characteristic
9	C₂×#4294⋊C₂	—	7	1	no	maximal, Hall
10	D₇×D₁₉	C₉	1	1	yes	characteristic, complemented, Hall
11	C₃×C₇×C₁₉	C₂²×C₃	1	1	yes	characteristic
12	C₂×#4294	—	7	1	no	—
13	#4294⋊C₂	—	7	1	no	—
14	#4294⋊C₂	—	7	1	no	—
15	D₁₃₃	C₂×C₉	1	1	yes	characteristic, complemented
16	C₇×D₁₉	C₂×C₉	1	1	yes	characteristic, complemented
17	D₇×C₁₉	C₂×C₉	1	1	yes	characteristic, complemented
18	C₂×D₇⋊C₉	—	19	1	no	maximal, Hall
19	C₂×C₃×D₁₉	—	7	1	no	—
20	#4294	—	7	1	no	Hall
21	C₇×C₁₉	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
22	C₂×C₇⋊C₉	—	19	1	no	—
23	D₇⋊C₉	—	19	1	no	—
24	D₇⋊C₉	—	19	1	no	—
25	C₂×C₃×C₁₉	—	7	1	no	—
26	C₃×D₁₉	—	7	1	no	—
27	C₃×D₁₉	AGL(1,𝔽₇)	1	1	yes	characteristic
28	C₂×C₃×D₇	—	19	1	no	—
29	C₂×D₁₉	—	7	1	no	Hall
30	C₇⋊C₉	—	19	1	no	Hall
31	C₃×C₁₉	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
32	C₂×C₃×C₇	—	19	1	no	—
33	C₃×D₇	—	19	1	no	—
34	C₃×D₇	D₁₉⋊C₃	1	1	yes	characteristic
35	C₂×C₁₉	—	7	1	no	—
36	D₁₉	—	7	1	no	—
37	D₁₉	D₇⋊C₉	1	1	yes	characteristic, complemented
38	C₂²×C₉	—	133	1	no	Hall
39	C₂×D₇	—	19	1	no	Hall
40	C₃×C₇	C₂×D₁₉⋊C₃	1	1	yes	characteristic
41	C₁₉	C₂×D₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₉	—	133	1	no	—
43	C₂×C₉	—	133	1	no	—
44	C₂×C₉	—	133	1	no	—
45	C₂×C₇	—	19	1	no	—
46	D₇	—	19	1	no	—
47	D₇	#4294⋊C₂	1	1	yes	characteristic, complemented
48	C₂²×C₃	—	133	1	no	—
49	C₉	—	133	1	no	Sylow
50	C₇	C₂×#4294⋊C₂	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃	—	7	1	no	—
52	C₂×C₃	—	19	1	no	—
53	C₂×C₃	—	133	1	no	—
54	C₂²	—	133	1	no	Sylow
55	C₃	#11716322⋊C₂	1	1	yes	characteristic
56	C₂	—	7	1	no	—
57	C₂	—	19	1	no	—
58	C₂	—	133	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₃	#11716322⋊C₂
commutator, hypocenter	C₇×C₁₉	C₂²×C₉
Fitting, socle, cosocle	C₃×C₇×C₁₉	C₂²×C₃
prime radical	C₃×D₇×D₁₉	C₃
LCS	G ▷ C₇×C₁₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. #14558787	C₂	semidirect
2. #14558785	C₂	semidirect
3. #14558781	C₂	semidirect
5. #11924777	C₂²	semidirect
10. D₇×D₁₉	C₉	semidirect
15. D₁₃₃	C₂×C₉	semidirect
16. C₇×D₁₉	C₂×C₉	semidirect
17. D₇×C₁₉	C₂×C₉	semidirect
21. C₇×C₁₉	C₂²×C₉	semidirect
37. D₁₉	D₇⋊C₉	semidirect
41. C₁₉	C₂×D₇⋊C₉	semidirect
47. D₇	#4294⋊C₂	semidirect
50. C₇	C₂×#4294⋊C₂	semidirect

Maximal subgroups

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

subgroup	index
#14558787	2
#14558785	2
#14558781	2
C₃×D₇×D₁₉	3
C₂×#4294⋊C₂	7
C₂×D₇⋊C₉	19

Subgroups — #14558781⋊C2 #18012113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #14558781⋊C₂ #18012113