Subgroups — #19129333⋊C₂ #24925449

Order 10836.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19129339	C₂	1	1	yes	maximal, characteristic, complemented
2	#19129337	C₂	1	1	yes	maximal, characteristic, complemented
3	#19129333	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₇×D₄₃	C₃	1	1	yes	maximal, characteristic
5	#14582150	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃×D₃₀₁	C₂×C₃	1	1	yes	characteristic
7	C₃×D₇×C₄₃	C₂×C₃	1	1	yes	characteristic
8	C₃×C₇×D₄₃	C₂×C₃	1	1	yes	characteristic
9	C₂×D₄₃⋊C₉	—	7	1	no	maximal, Hall
10	D₇×D₄₃	C₉	1	1	yes	characteristic, complemented, Hall
11	C₃×C₇×C₄₃	C₂²×C₃	1	1	yes	characteristic
12	C₂×C₄₃⋊C₉	—	7	1	no	—
13	D₄₃⋊C₉	—	7	1	no	—
14	D₄₃⋊C₉	—	7	1	no	—
15	D₃₀₁	C₂×C₉	1	1	yes	characteristic, complemented
16	C₇×D₄₃	C₂×C₉	1	1	yes	characteristic, complemented
17	D₇×C₄₃	C₂×C₉	1	1	yes	characteristic, complemented
18	C₂×C₃×D₄₃	—	7	1	no	—
19	C₄₃⋊C₉	—	7	1	no	Hall
20	C₇×C₄₃	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×C₄₃	—	7	1	no	—
22	C₃×D₄₃	—	7	1	no	—
23	C₃×D₄₃	AGL(1,𝔽₇)	1	1	yes	characteristic
24	C₂×D₇⋊C₉	—	43	1	no	maximal, Hall
25	C₂×D₄₃	—	7	1	no	Hall
26	C₃×C₄₃	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
27	C₂×C₇⋊C₉	—	43	1	no	—
28	D₇⋊C₉	—	43	1	no	—
29	D₇⋊C₉	—	43	1	no	—
30	C₂×C₄₃	—	7	1	no	—
31	D₄₃	—	7	1	no	—
32	D₄₃	D₇⋊C₉	1	1	yes	characteristic, complemented
33	C₂×C₃×D₇	—	43	1	no	—
34	C₇⋊C₉	—	43	1	no	Hall
35	C₄₃	C₂×D₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₃×C₇	—	43	1	no	—
37	C₃×D₇	—	43	1	no	—
38	C₃×D₇	D₄₃⋊C₃	1	1	yes	characteristic
39	C₂²×C₉	—	301	1	no	Hall
40	C₂×D₇	—	43	1	no	Hall
41	C₃×C₇	C₂×D₄₃⋊C₃	1	1	yes	characteristic
42	C₂×C₉	—	301	1	no	—
43	C₂×C₉	—	301	1	no	—
44	C₂×C₉	—	301	1	no	—
45	C₂×C₇	—	43	1	no	—
46	D₇	—	43	1	no	—
47	D₇	D₄₃⋊C₉	1	1	yes	characteristic, complemented
48	C₂²×C₃	—	301	1	no	—
49	C₉	—	301	1	no	Sylow
50	C₇	C₂×D₄₃⋊C₉	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃	—	7	1	no	—
52	C₂×C₃	—	43	1	no	—
53	C₂×C₃	—	301	1	no	—
54	C₂²	—	301	1	no	Sylow
55	C₃	#14268587⋊C₂	1	1	yes	characteristic
56	C₂	—	7	1	no	—
57	C₂	—	43	1	no	—
58	C₂	—	301	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₃	#14268587⋊C₂
commutator, hypocenter	C₇×C₄₃	C₂²×C₉
Fitting, socle, cosocle	C₃×C₇×C₄₃	C₂²×C₃
prime radical	C₃×D₇×D₄₃	C₃
LCS	G ▷ C₇×C₄₃
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. #19129339	C₂	semidirect
2. #19129337	C₂	semidirect
3. #19129333	C₂	semidirect
5. #14582150	C₂²	semidirect
10. D₇×D₄₃	C₉	semidirect
15. D₃₀₁	C₂×C₉	semidirect
16. C₇×D₄₃	C₂×C₉	semidirect
17. D₇×C₄₃	C₂×C₉	semidirect
20. C₇×C₄₃	C₂²×C₉	semidirect
32. D₄₃	D₇⋊C₉	semidirect
35. C₄₃	C₂×D₇⋊C₉	semidirect
47. D₇	D₄₃⋊C₉	semidirect
50. C₇	C₂×D₄₃⋊C₉	semidirect

Maximal subgroups

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

subgroup	index
#19129339	2
#19129337	2
#19129333	2
C₃×D₇×D₄₃	3
C₂×D₄₃⋊C₉	7
C₂×D₇⋊C₉	43

Subgroups — #19129333⋊C2 #24925449

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #19129333⋊C₂ #24925449