Subgroups — C₃×C₇⋊#11923884 #37566267

Order 24276.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₇⋊D₁₇	C₂	1	1	yes	maximal, characteristic
2	C₇⋊#11923884	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₇×C₁₇²	C₄	1	1	yes	characteristic, complemented, Hall
4	C₇×C₁₇⋊D₁₇	C₂×C₃	1	1	yes	characteristic
5	C₃×#11923884	—	7	1	no	maximal, Hall
6	C₇×C₁₇²	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	C₃×C₁₇⋊D₁₇	D₇	1	1	yes	characteristic
8	C₃×C₇⋊#595	—	17	2	no	maximal
9	#11923884	—	7	1	no	Hall
10	C₃×C₁₇²	Dic₇	1	1	yes	characteristic, complemented, Hall
11	C₃×C₇×D₁₇	—	17	2	no	—
12	C₃×C₇×D₁₇	—	34	8	no	—
13	C₁₇⋊D₁₇	C₃×D₇	1	1	yes	characteristic
14	C₇⋊#595	—	17	2	no	—
15	C₃×C₇×C₁₇	—	2	8	no	—
16	C₃×C₇×C₁₇	#595	1	2	yes	complemented
17	C₁₇²	C₃×Dic₇	1	1	yes	characteristic, complemented, Sylow
18	C₇×D₁₇	—	17	2	no	—
19	C₇×D₁₇	—	34	8	no	—
20	C₃×#595	—	119	2	no	—
21	C₇×C₁₇	—	2	8	no	—
22	C₇×C₁₇	C₃×#595	1	2	yes	complemented
23	C₃×D₁₇	—	17	2	no	—
24	C₃×D₁₇	—	34	8	no	—
25	C₃×Dic₇	—	289	1	no	Hall
26	#595	—	119	2	no	—
27	C₃×C₁₇	—	2	8	no	—
28	C₃×C₁₇	C₇⋊#595	1	2	yes	complemented
29	C₂×C₃×C₇	—	289	1	no	—
30	D₁₇	—	17	2	no	—
31	D₁₇	—	34	8	no	—
32	Dic₇	—	289	1	no	Hall
33	C₃×C₇	#11923884	1	1	yes	characteristic, complemented, Hall
34	C₁₇	—	2	8	no	—
35	C₁₇	C₃×C₇⋊#595	1	2	yes	complemented
36	C₂×C₇	—	289	1	no	—
37	C₃×C₄	—	2023	1	no	Hall
38	C₇	C₃×#11923884	1	1	yes	characteristic, complemented, Sylow
39	C₂×C₃	—	289	1	no	—
40	C₄	—	2023	1	no	Sylow
41	C₃	C₇⋊#11923884	1	1	yes	characteristic, direct product factor, Sylow
42	C₂	—	289	1	no	—

	subgroup	G/H
center, hypercenter	C₃	C₇⋊#11923884
commutator, hypocenter	C₇×C₁₇²	C₃×C₄
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₇²	C₄
prime radical	C₃×C₇×C₁₇⋊D₁₇	C₂
cosocle	C₇×C₁₇⋊D₁₇	C₂×C₃
LCS	G ▷ C₇×C₁₇²
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
2. C₇⋊#11923884	C₃	direct (N × H)
3. C₃×C₇×C₁₇²	C₄	semidirect
6. C₇×C₁₇²	C₃×C₄	semidirect
10. C₃×C₁₇²	Dic₇	semidirect
16. C₃×C₇×C₁₇	#595	semidirect
17. C₁₇²	C₃×Dic₇	semidirect
22. C₇×C₁₇	C₃×#595	semidirect
28. C₃×C₁₇	C₇⋊#595	semidirect
33. C₃×C₇	#11923884	semidirect
35. C₁₇	C₃×C₇⋊#595	semidirect
38. C₇	C₃×#11923884	semidirect
41. C₃	C₇⋊#11923884	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₇×C₁₇⋊D₁₇	2
C₇⋊#11923884	3
C₃×#11923884	7
C₃×C₇⋊#595	17

Subgroups — C3×C7⋊#11923884 #37566267

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇⋊#11923884 #37566267