Subgroups — C₁₇×C₃⋊(C₁₁⋊Dic₁₁) #37590591

Order 24684.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₁²×C₁₇	C₂	1	1	yes	maximal, characteristic
2	C₁₇×C₁₁⋊Dic₁₁	—	3	1	no	maximal, Hall
3	C₃×C₁₁²×C₁₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₁²×C₁₇	D₃	1	1	yes	characteristic
5	C₁₇×Dic₃₃	—	11	12	no	maximal
6	C₁₁²×C₁₇	Dic₃	1	1	yes	characteristic, complemented, Hall
7	C₃⋊(C₁₁⋊Dic₁₁)	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₃×C₁₁×C₁₇	D₁₁	1	12	yes	—
9	C₁₇×Dic₁₁	—	33	12	no	—
10	C₂×C₃×C₁₁²	C₂×C₁₇	1	1	yes	characteristic
11	C₃×C₁₁×C₁₇	Dic₁₁	1	12	yes	complemented
12	C₁₁⋊Dic₁₁	—	3	1	no	Hall
13	C₂×C₁₁×C₁₇	D₃₃	1	12	yes	—
14	C₃×C₁₁²	C₄×C₁₇	1	1	yes	characteristic, complemented, Hall
15	C₂×C₁₁²	D₃×C₁₇	1	1	yes	characteristic
16	Dic₃×C₁₇	—	121	1	no	Hall
17	C₁₁×C₁₇	Dic₃₃	1	12	yes	complemented
18	Dic₃₃	—	11	12	no	—
19	C₁₁²	Dic₃×C₁₇	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₃×C₁₇	C₁₁⋊D₁₁	1	1	yes	characteristic
21	C₄×C₁₇	—	363	1	no	Hall
22	C₂×C₃×C₁₁	C₁₇×D₁₁	1	12	yes	—
23	C₃×C₁₇	C₁₁⋊Dic₁₁	1	1	yes	characteristic, complemented, Hall
24	Dic₁₁	—	33	12	no	—
25	C₂×C₁₇	C₃⋊(C₁₁⋊D₁₁)	1	1	yes	characteristic
26	C₃×C₁₁	C₁₇×Dic₁₁	1	12	yes	complemented
27	C₂×C₁₁	C₁₇×D₃₃	1	12	yes	—
28	C₁₇	C₃⋊(C₁₁⋊Dic₁₁)	1	1	yes	characteristic, direct product factor, Sylow
29	Dic₃	—	121	1	no	Hall
30	C₁₁	C₁₇×Dic₃₃	1	12	yes	complemented
31	C₂×C₃	C₁₇×C₁₁⋊D₁₁	1	1	yes	characteristic
32	C₄	—	363	1	no	Sylow
33	C₃	C₁₇×C₁₁⋊Dic₁₁	1	1	yes	characteristic, complemented, Sylow
34	C₂	C₁₇×C₃⋊(C₁₁⋊D₁₁)	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₁₇	C₃⋊(C₁₁⋊D₁₁)
commutator, hypocenter	C₃×C₁₁²	C₄×C₁₇
Frattini	C₂	C₁₇×C₃⋊(C₁₁⋊D₁₁)
Fitting, socle, prime radical	C₂×C₃×C₁₁²×C₁₇	C₂
cosocle	C₂×C₃×C₁₁²	C₂×C₁₇
LCS	G ▷ C₃×C₁₁²
UCS	C₁ ◁ C₂×C₁₇

Complements

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

N	H ≅ G/N	type
3. C₃×C₁₁²×C₁₇	C₄	semidirect
6. C₁₁²×C₁₇	Dic₃	semidirect
7. C₃⋊(C₁₁⋊Dic₁₁)	C₁₇	direct (N × H)
11. C₃×C₁₁×C₁₇	Dic₁₁	semidirect
14. C₃×C₁₁²	C₄×C₁₇	semidirect
17. C₁₁×C₁₇	Dic₃₃	semidirect
19. C₁₁²	Dic₃×C₁₇	semidirect
23. C₃×C₁₇	C₁₁⋊Dic₁₁	semidirect
26. C₃×C₁₁	C₁₇×Dic₁₁	semidirect
28. C₁₇	C₃⋊(C₁₁⋊Dic₁₁)	direct (N × H)
30. C₁₁	C₁₇×Dic₃₃	semidirect
33. C₃	C₁₇×C₁₁⋊Dic₁₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₁₁²×C₁₇	2
C₁₇×C₁₁⋊Dic₁₁	3
C₁₇×Dic₃₃	11
C₃⋊(C₁₁⋊Dic₁₁)	17

Subgroups — C17×C3⋊(C11⋊Dic11) #37590591

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×C₃⋊(C₁₁⋊Dic₁₁) #37590591