Subgroups — D₄₃×D₆₇⋊C₃ #46828987

Order 34572.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	(C₆₇⋊C₃)⋊D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄₃×C₆₇⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×D₆₇⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄₃×D₆₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₄₃×C₆₇⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₂₈₈₁	C₂×C₃	1	1	yes	characteristic, complemented
7	C₄₃×D₆₇	C₂×C₃	1	1	yes	characteristic, complemented
8	C₆₇×D₄₃	C₂×C₃	1	1	yes	characteristic, complemented
9	C₄₃×C₆₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
10	C₂×D₆₇⋊C₃	—	43	1	no	maximal, Hall
11	C₂×C₃×D₄₃	—	67	1	no	maximal, Hall
12	C₂×C₆₇⋊C₃	—	43	1	no	—
13	D₆₇⋊C₃	—	43	1	no	—
14	D₆₇⋊C₃	D₄₃	1	1	yes	characteristic, direct product factor
15	C₂×D₆₇	—	43	1	no	Hall
16	C₂×C₃×C₄₃	—	67	1	no	—
17	C₃×D₄₃	—	67	1	no	—
18	C₃×D₄₃	—	67	1	no	—
19	C₆₇⋊C₃	C₂×D₄₃	1	1	yes	characteristic, complemented, Hall
20	C₂×D₄₃	—	67	1	no	Hall
21	C₂×C₆₇	—	43	1	no	—
22	D₆₇	—	43	1	no	—
23	D₆₇	C₃×D₄₃	1	1	yes	characteristic, complemented
24	C₃×C₄₃	—	67	1	no	Hall
25	C₂×C₄₃	—	67	1	no	—
26	D₄₃	—	67	1	no	—
27	D₄₃	D₆₇⋊C₃	1	1	yes	characteristic, direct product factor
28	C₆₇	C₂×C₃×D₄₃	1	1	yes	characteristic, complemented, Sylow
29	C₄₃	C₂×D₆₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
30	C₂²×C₃	—	2881	1	no	Hall
31	C₂×C₃	—	2881	1	no	—
32	C₂×C₃	—	2881	1	no	—
33	C₂×C₃	—	67	1	no	—
34	C₂²	—	2881	1	no	Sylow
35	C₃	—	67	1	no	Sylow
36	C₂	—	43	1	no	—
37	C₂	—	2881	1	no	—
38	C₂	—	67	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₄₃×C₆₇	C₂²×C₃
LCS	G ▷ C₄₃×C₆₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. (C₆₇⋊C₃)⋊D₄₃	C₂	semidirect
2. D₄₃×C₆₇⋊C₃	C₂	semidirect
3. C₄₃×D₆₇⋊C₃	C₂	semidirect
4. D₄₃×D₆₇	C₃	semidirect
5. C₄₃×C₆₇⋊C₃	C₂²	semidirect
6. D₂₈₈₁	C₂×C₃	semidirect
7. C₄₃×D₆₇	C₂×C₃	semidirect
8. C₆₇×D₄₃	C₂×C₃	semidirect
9. C₄₃×C₆₇	C₂²×C₃	semidirect
14. D₆₇⋊C₃	D₄₃	direct (N × H)
19. C₆₇⋊C₃	C₂×D₄₃	semidirect
23. D₆₇	C₃×D₄₃	semidirect
27. D₄₃	D₆₇⋊C₃	direct (N × H)
28. C₆₇	C₂×C₃×D₄₃	semidirect
29. C₄₃	C₂×D₆₇⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
(C₆₇⋊C₃)⋊D₄₃	2
D₄₃×C₆₇⋊C₃	2
C₄₃×D₆₇⋊C₃	2
D₄₃×D₆₇	3
C₂×D₆₇⋊C₃	43
C₂×C₃×D₄₃	67

Subgroups — D43×D67⋊C3 #46828987

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₃×D₆₇⋊C₃ #46828987