Subgroups — C₃×C₇⋊#11923880 #37566211

Order 24276.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₇×C₁₇²	C₂	1	1	yes	maximal, characteristic
2	C₇⋊#11923880	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₇×C₁₇²	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇×C₁₇²	C₂×C₃	1	1	yes	characteristic
5	C₃×#11923880	—	7	1	no	maximal, Hall
6	C₇×C₁₇²	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×C₁₇²	D₇	1	1	yes	characteristic
8	C₃×Dic₁₁₉	—	17	18	no	maximal
9	#11923880	—	7	1	no	Hall
10	C₃×C₁₇²	Dic₇	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₇×C₁₇	D₁₇	1	18	yes	—
12	C₂×C₁₇²	C₃×D₇	1	1	yes	characteristic
13	Dic₁₁₉	—	17	18	no	—
14	C₃×C₇×C₁₇	Dic₁₇	1	18	yes	complemented
15	C₁₇²	C₃×Dic₇	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₇×C₁₇	C₃×D₁₇	1	18	yes	—
17	C₃×Dic₁₇	—	119	18	no	—
18	C₇×C₁₇	C₃×Dic₁₇	1	18	yes	complemented
19	C₂×C₃×C₁₇	D₁₁₉	1	18	yes	—
20	C₃×Dic₇	—	289	1	no	Hall
21	Dic₁₇	—	119	18	no	—
22	C₃×C₁₇	Dic₁₁₉	1	18	yes	complemented
23	C₂×C₃×C₇	C₁₇⋊D₁₇	1	1	yes	characteristic
24	C₂×C₁₇	C₃×D₁₁₉	1	18	yes	—
25	Dic₇	—	289	1	no	Hall
26	C₃×C₇	#11923880	1	1	yes	characteristic, complemented, Hall
27	C₁₇	C₃×Dic₁₁₉	1	18	yes	complemented
28	C₂×C₇	C₃×C₁₇⋊D₁₇	1	1	yes	characteristic
29	C₃×C₄	—	2023	1	no	Hall
30	C₇	C₃×#11923880	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	C₇⋊(C₁₇⋊D₁₇)	1	1	yes	characteristic
32	C₄	—	2023	1	no	Sylow
33	C₃	C₇⋊#11923880	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	C₃×C₇⋊(C₁₇⋊D₁₇)	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₇⋊#11923880	C₃	direct (N × H)
3. C₃×C₇×C₁₇²	C₄	semidirect
6. C₇×C₁₇²	C₃×C₄	semidirect
10. C₃×C₁₇²	Dic₇	semidirect
14. C₃×C₇×C₁₇	Dic₁₇	semidirect
15. C₁₇²	C₃×Dic₇	semidirect
18. C₇×C₁₇	C₃×Dic₁₇	semidirect
22. C₃×C₁₇	Dic₁₁₉	semidirect
26. C₃×C₇	#11923880	semidirect
27. C₁₇	C₃×Dic₁₁₉	semidirect
30. C₇	C₃×#11923880	semidirect
33. C₃	C₇⋊#11923880	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₇×C₁₇²	2
C₇⋊#11923880	3
C₃×#11923880	7
C₃×Dic₁₁₉	17

Subgroups — C3×C7⋊#11923880 #37566211

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇⋊#11923880 #37566211