Subgroups — C₃×C₄×C₁₁²×C₁₇ #37590583

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	C₄×C₁₁²×C₁₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₁²×C₁₇	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₁₁²×C₁₇	C₂×C₃	1	1	yes	characteristic
5	C₃×C₄×C₁₁×C₁₇	C₁₁	1	12	yes	maximal, direct product factor
6	C₁₁²×C₁₇	C₃×C₄	1	1	yes	characteristic, direct product factor, Hall
7	C₃×C₄×C₁₁²	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₃×C₁₁×C₁₇	C₂×C₁₁	1	12	yes	—
9	C₄×C₁₁×C₁₇	C₃×C₁₁	1	12	yes	direct product factor
10	C₂×C₃×C₁₁²	C₂×C₁₇	1	1	yes	characteristic
11	C₃×C₁₁×C₁₇	C₄×C₁₁	1	12	yes	direct product factor
12	C₄×C₁₁²	C₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₁₁×C₁₇	C₂×C₃×C₁₁	1	12	yes	—
14	C₃×C₁₁²	C₄×C₁₇	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₁₁²	C₂×C₃×C₁₇	1	1	yes	characteristic
16	C₃×C₄×C₁₇	C₁₁²	1	1	yes	characteristic, direct product factor, Hall
17	C₁₁×C₁₇	C₃×C₄×C₁₁	1	12	yes	direct product factor
18	C₃×C₄×C₁₁	C₁₁×C₁₇	1	12	yes	direct product factor
19	C₁₁²	C₃×C₄×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₃×C₁₇	C₂×C₁₁²	1	1	yes	characteristic
21	C₄×C₁₇	C₃×C₁₁²	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₃×C₁₁	C₂×C₁₁×C₁₇	1	12	yes	—
23	C₃×C₁₇	C₄×C₁₁²	1	1	yes	characteristic, direct product factor, Hall
24	C₄×C₁₁	C₃×C₁₁×C₁₇	1	12	yes	direct product factor
25	C₂×C₁₇	C₂×C₃×C₁₁²	1	1	yes	characteristic
26	C₃×C₁₁	C₄×C₁₁×C₁₇	1	12	yes	direct product factor
27	C₂×C₁₁	C₂×C₃×C₁₁×C₁₇	1	12	yes	—
28	C₁₇	C₃×C₄×C₁₁²	1	1	yes	characteristic, direct product factor, Sylow
29	C₃×C₄	C₁₁²×C₁₇	1	1	yes	characteristic, direct product factor, Hall
30	C₁₁	C₃×C₄×C₁₁×C₁₇	1	12	yes	direct product factor
31	C₂×C₃	C₂×C₁₁²×C₁₇	1	1	yes	characteristic
32	C₄	C₃×C₁₁²×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	C₄×C₁₁²×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	C₂×C₃×C₁₁²×C₁₇	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₃×C₁₁²×C₁₇
socle, prime radical	C₂×C₃×C₁₁²×C₁₇	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×C₁₁²×C₁₇	C₃	direct (N × H)
3. C₃×C₁₁²×C₁₇	C₄	direct (N × H)
5. C₃×C₄×C₁₁×C₁₇	C₁₁	direct (N × H)
6. C₁₁²×C₁₇	C₃×C₄	direct (N × H)
7. C₃×C₄×C₁₁²	C₁₇	direct (N × H)
9. C₄×C₁₁×C₁₇	C₃×C₁₁	direct (N × H)
11. C₃×C₁₁×C₁₇	C₄×C₁₁	direct (N × H)
12. C₄×C₁₁²	C₃×C₁₇	direct (N × H)
14. C₃×C₁₁²	C₄×C₁₇	direct (N × H)
16. C₃×C₄×C₁₇	C₁₁²	direct (N × H)
17. C₁₁×C₁₇	C₃×C₄×C₁₁	direct (N × H)
18. C₃×C₄×C₁₁	C₁₁×C₁₇	direct (N × H)
19. C₁₁²	C₃×C₄×C₁₇	direct (N × H)
21. C₄×C₁₇	C₃×C₁₁²	direct (N × H)
23. C₃×C₁₇	C₄×C₁₁²	direct (N × H)
24. C₄×C₁₁	C₃×C₁₁×C₁₇	direct (N × H)
26. C₃×C₁₁	C₄×C₁₁×C₁₇	direct (N × H)
28. C₁₇	C₃×C₄×C₁₁²	direct (N × H)
29. C₃×C₄	C₁₁²×C₁₇	direct (N × H)
30. C₁₁	C₃×C₄×C₁₁×C₁₇	direct (N × H)
32. C₄	C₃×C₁₁²×C₁₇	direct (N × H)
33. C₃	C₄×C₁₁²×C₁₇	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×C₁₁²×C₁₇	2
C₄×C₁₁²×C₁₇	3
C₃×C₄×C₁₁×C₁₇	11
C₃×C₄×C₁₁²	17

Subgroups — C3×C4×C112×C17 #37590583

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×C₁₁²×C₁₇ #37590583