Subgroups — C₇×#13181892⋊C₂ #37566217

Order 24276.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×(C₁₇⋊D₁₇)⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#13181892	C₂	1	2	yes	maximal, complemented
3	C₇×D₁₇²	—	3	1	no	maximal, Hall
4	C₇×C₁₇²⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₇×C₁₇⋊D₁₇	D₃	1	1	yes	characteristic, complemented
6	C₇×C₁₇×D₁₇	—	3	2	no	—
7	#13181892⋊C₂	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₇×C₁₇²	C₂×D₃	1	1	yes	characteristic, complemented, Hall
9	(C₁₇⋊D₁₇)⋊C₃	C₂×C₇	1	1	yes	characteristic, complemented
10	#13181892	C₂×C₇	1	2	yes	complemented
11	D₁₇²	—	3	1	no	Hall
12	C₁₇²⋊C₃	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
13	C₁₇⋊D₁₇	D₃×C₇	1	1	yes	characteristic, complemented
14	C₁₇×D₁₇	—	3	2	no	—
15	C₂×C₇×D₁₇	—	51	2	no	—
16	C₁₇²	C₂×D₃×C₇	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₇×C₁₇	—	51	2	no	—
18	C₇×D₁₇	—	3	2	no	—
19	C₇×D₁₇	—	51	2	no	—
20	C₇×D₁₇	—	102	2	no	—
21	C₇×C₁₇	—	3	2	no	—
22	C₇×C₁₇	—	6	2	no	—
23	C₂×D₃×C₇	—	289	1	no	maximal, Hall
24	C₂×D₁₇	—	51	2	no	—
25	C₂×C₃×C₇	—	289	1	no	—
26	D₃×C₇	—	289	2	no	—
27	C₂×C₁₇	—	51	2	no	—
28	D₁₇	—	3	2	no	—
29	D₁₇	—	51	2	no	—
30	D₁₇	—	102	2	no	—
31	C₂²×C₇	—	867	1	no	Hall
32	C₃×C₇	—	289	1	no	Hall
33	C₁₇	—	3	2	no	—
34	C₁₇	—	6	2	no	—
35	C₂×C₇	—	289	1	no	—
36	C₂×C₇	—	51	2	no	—
37	C₂×D₃	—	289	1	no	Hall
38	C₇	#13181892⋊C₂	1	1	yes	characteristic, direct product factor, Sylow
39	C₂×C₃	—	289	1	no	—
40	D₃	—	289	2	no	—
41	C₂²	—	867	1	no	Sylow
42	C₃	—	289	1	no	Sylow
43	C₂	—	289	1	no	—
44	C₂	—	51	2	no	—

	subgroup	G/H
center, hypercenter	C₇	#13181892⋊C₂
commutator, cosocle, hypocenter	C₁₇²⋊C₃	C₂²×C₇
Frattini	C₁	G
Fitting, socle	C₇×C₁₇²	C₂×D₃
LCS	G ▷ C₁₇²⋊C₃
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
1. C₇×(C₁₇⋊D₁₇)⋊C₃	C₂	semidirect
2. C₇×#13181892	C₂	semidirect
4. C₇×C₁₇²⋊C₃	C₂²	semidirect
5. C₇×C₁₇⋊D₁₇	D₃	semidirect
7. #13181892⋊C₂	C₇	direct (N × H)
8. C₇×C₁₇²	C₂×D₃	semidirect
9. (C₁₇⋊D₁₇)⋊C₃	C₂×C₇	semidirect
10. #13181892	C₂×C₇	semidirect
12. C₁₇²⋊C₃	C₂²×C₇	semidirect
13. C₁₇⋊D₁₇	D₃×C₇	semidirect
16. C₁₇²	C₂×D₃×C₇	semidirect
38. C₇	#13181892⋊C₂	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×(C₁₇⋊D₁₇)⋊C₃	2
C₇×#13181892	2
C₇×D₁₇²	3
#13181892⋊C₂	7
C₂×D₃×C₇	289

Subgroups — C7×#13181892⋊C2 #37566217

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#13181892⋊C₂ #37566217