Subgroups — C₃⋊((C₄₃⋊C₃)⋊Dic₇) #24925529

Order 10836.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₇×C₄₃⋊C₃	C₂	1	1	yes	maximal, characteristic
2	Dic₉₀₃	C₃	1	1	yes	maximal, characteristic, complemented
3	(C₄₃⋊C₃)⋊Dic₇	—	3	1	no	maximal
4	C₃×C₇×C₄₃⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₇×C₄₃	C₂×C₃	1	1	yes	characteristic
6	C₂×C₇×C₄₃⋊C₃	—	2	1	no	—
7	C₂×C₇×C₄₃⋊C₃	D₃	1	1	yes	characteristic
8	C₃⋊((C₄₃⋊C₃)⋊C₄)	—	7	1	no	maximal, Hall
9	Dic₃₀₁	—	3	1	no	Hall
10	C₃×C₇×C₄₃	C₃×C₄	1	1	yes	characteristic, complemented
11	C₇×C₄₃⋊C₃	—	2	1	no	—
12	C₇×C₄₃⋊C₃	Dic₃	1	1	yes	characteristic, complemented
13	C₂×C₃×C₄₃⋊C₃	D₇	1	1	yes	characteristic
14	C₂×C₇×C₄₃	C₃×D₃	1	1	yes	characteristic
15	Dic₁₂₉	—	7	1	no	—
16	(C₄₃⋊C₃)⋊C₄	—	21	1	no	—
17	C₃×C₄₃⋊C₃	Dic₇	1	1	yes	characteristic, complemented, Hall
18	C₇×C₄₃	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
19	C₂×C₃×C₄₃	C₃×D₇	1	1	yes	characteristic
20	C₂×C₄₃⋊C₃	—	2	1	no	—
21	C₂×C₄₃⋊C₃	D₂₁	1	1	yes	characteristic
22	C₃×Dic₂₁	—	43	1	no	maximal, Hall
23	Dic₄₃	—	21	1	no	Hall
24	C₃×C₄₃	C₃×Dic₇	1	1	yes	characteristic, complemented
25	C₄₃⋊C₃	—	2	1	no	—
26	C₄₃⋊C₃	Dic₂₁	1	1	yes	characteristic, complemented
27	C₂×C₃²×C₇	—	43	1	no	—
28	C₂×C₄₃	C₃×D₂₁	1	1	yes	characteristic
29	Dic₂₁	—	43	1	no	—
30	C₃×Dic₇	—	129	1	no	—
31	C₃²×C₇	—	43	1	no	Hall
32	C₄₃	C₃×Dic₂₁	1	1	yes	characteristic, complemented, Sylow
33	C₂×C₃×C₇	—	43	1	no	—
34	C₂×C₃×C₇	—	86	1	no	—
35	C₂×C₃×C₇	D₄₃⋊C₃	1	1	yes	characteristic
36	C₃×Dic₃	—	301	1	no	Hall
37	Dic₇	—	129	1	no	Hall
38	C₃×C₇	—	43	1	no	—
39	C₃×C₇	—	86	1	no	—
40	C₃×C₇	(C₄₃⋊C₃)⋊C₄	1	1	yes	characteristic, complemented
41	C₂×C₃²	—	43	1	no	—
42	C₂×C₇	C₃⋊(D₄₃⋊C₃)	1	1	yes	characteristic
43	C₃×C₄	—	903	1	no	—
44	Dic₃	—	301	1	no	—
45	C₃²	—	43	1	no	Sylow
46	C₇	C₃⋊((C₄₃⋊C₃)⋊C₄)	1	1	yes	characteristic, complemented, Sylow
47	C₂×C₃	—	43	1	no	—
48	C₂×C₃	—	86	1	no	—
49	C₂×C₃	(C₄₃⋊C₃)⋊D₇	1	1	yes	characteristic
50	C₄	—	903	1	no	Sylow
51	C₃	—	43	1	no	—
52	C₃	—	86	1	no	—
53	C₃	(C₄₃⋊C₃)⋊Dic₇	1	1	yes	characteristic, complemented
54	C₂	C₃⋊((C₄₃⋊C₃)⋊D₇)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₃⋊((C₄₃⋊C₃)⋊D₇)
commutator, hypocenter	C₃×C₇×C₄₃	C₃×C₄
Fitting, socle, cosocle	C₂×C₃×C₇×C₄₃	C₂×C₃
prime radical	C₂×C₃×C₇×C₄₃⋊C₃	C₂
LCS	G ▷ C₃×C₇×C₄₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
2. Dic₉₀₃	C₃	semidirect
4. C₃×C₇×C₄₃⋊C₃	C₄	semidirect
10. C₃×C₇×C₄₃	C₃×C₄	semidirect
12. C₇×C₄₃⋊C₃	Dic₃	semidirect
17. C₃×C₄₃⋊C₃	Dic₇	semidirect
18. C₇×C₄₃	C₃×Dic₃	semidirect
24. C₃×C₄₃	C₃×Dic₇	semidirect
26. C₄₃⋊C₃	Dic₂₁	semidirect
32. C₄₃	C₃×Dic₂₁	semidirect
40. C₃×C₇	(C₄₃⋊C₃)⋊C₄	semidirect
46. C₇	C₃⋊((C₄₃⋊C₃)⋊C₄)	semidirect
53. C₃	(C₄₃⋊C₃)⋊Dic₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₇×C₄₃⋊C₃	2
Dic₉₀₃	3
(C₄₃⋊C₃)⋊Dic₇	3
C₃⋊((C₄₃⋊C₃)⋊C₄)	7
C₃×Dic₂₁	43

Subgroups — C3⋊((C43⋊C3)⋊Dic7) #24925529

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊((C₄₃⋊C₃)⋊Dic₇) #24925529