Subgroups — D₇×D₃₉₇⋊C₃ #45688595

Order 33348.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	(C₃₉₇⋊C₃)⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
2	D₇×C₃₉₇⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×D₃₉₇⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₇×D₃₉₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₇×C₃₉₇⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₂₇₇₉	C₂×C₃	1	1	yes	characteristic, complemented
7	C₇×D₃₉₇	C₂×C₃	1	1	yes	characteristic, complemented
8	D₇×C₃₉₇	C₂×C₃	1	1	yes	characteristic, complemented
9	C₂×D₃₉₇⋊C₃	—	7	1	no	maximal, Hall
10	C₇×C₃₉₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃₉₇⋊C₃	—	7	1	no	—
12	D₃₉₇⋊C₃	—	7	1	no	—
13	D₃₉₇⋊C₃	D₇	1	1	yes	characteristic, direct product factor
14	C₂×D₃₉₇	—	7	1	no	Hall
15	C₃₉₇⋊C₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃₉₇	—	7	1	no	—
17	D₃₉₇	—	7	1	no	—
18	D₃₉₇	C₃×D₇	1	1	yes	characteristic, complemented
19	C₃₉₇	C₂×C₃×D₇	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₃×D₇	—	397	1	no	maximal, Hall
21	C₂×C₃×C₇	—	397	1	no	—
22	C₃×D₇	—	397	1	no	—
23	C₃×D₇	—	397	1	no	—
24	C₂×D₇	—	397	1	no	Hall
25	C₃×C₇	—	397	1	no	Hall
26	C₂×C₇	—	397	1	no	—
27	D₇	—	397	1	no	—
28	D₇	D₃₉₇⋊C₃	1	1	yes	characteristic, direct product factor
29	C₂²×C₃	—	2779	1	no	Hall
30	C₇	C₂×D₃₉₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	—	397	1	no	—
32	C₂×C₃	—	2779	1	no	—
33	C₂×C₃	—	2779	1	no	—
34	C₂²	—	2779	1	no	Sylow
35	C₃	—	397	1	no	Sylow
36	C₂	—	7	1	no	—
37	C₂	—	397	1	no	—
38	C₂	—	2779	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₃₉₇	C₂²×C₃
LCS	G ▷ C₇×C₃₉₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. (C₃₉₇⋊C₃)⋊D₇	C₂	semidirect
2. D₇×C₃₉₇⋊C₃	C₂	semidirect
3. C₇×D₃₉₇⋊C₃	C₂	semidirect
4. D₇×D₃₉₇	C₃	semidirect
5. C₇×C₃₉₇⋊C₃	C₂²	semidirect
6. D₂₇₇₉	C₂×C₃	semidirect
7. C₇×D₃₉₇	C₂×C₃	semidirect
8. D₇×C₃₉₇	C₂×C₃	semidirect
10. C₇×C₃₉₇	C₂²×C₃	semidirect
13. D₃₉₇⋊C₃	D₇	direct (N × H)
15. C₃₉₇⋊C₃	C₂×D₇	semidirect
18. D₃₉₇	C₃×D₇	semidirect
19. C₃₉₇	C₂×C₃×D₇	semidirect
28. D₇	D₃₉₇⋊C₃	direct (N × H)
30. C₇	C₂×D₃₉₇⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
(C₃₉₇⋊C₃)⋊D₇	2
D₇×C₃₉₇⋊C₃	2
C₇×D₃₉₇⋊C₃	2
D₇×D₃₉₇	3
C₂×D₃₉₇⋊C₃	7
C₂×C₃×D₇	397

Subgroups — D7×D397⋊C3 #45688595

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇×D₃₉₇⋊C₃ #45688595