Subgroups — C₄×C₁₁×#87705 #31798190

Order 17556.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#87705	C₂	1	1	yes	maximal, characteristic
2	C₄×C₇×C₁₁×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₁×#87705	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₇×C₁₁×C₁₉	C₂×C₃	1	1	yes	characteristic
5	C₄×C₁₁×C₁₉⋊C₃	—	7	1	no	maximal, Hall
6	C₄×#87705	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₇×C₁₁×C₁₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₂×C₁₁×C₁₉⋊C₃	—	7	1	no	—
9	C₄×C₁₁×ΓL(1,𝔽₈)	—	19	1	no	maximal, Hall
10	C₄×C₁₁×C₁₉	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
11	C₂×#87705	C₂×C₁₁	1	1	yes	characteristic
12	C₁₁×C₁₉⋊C₃	—	7	1	no	Hall
13	C₄×C₇×C₁₉	C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
14	C₂×C₁₁×ΓL(1,𝔽₈)	—	19	1	no	—
15	C₂×C₁₁×C₁₉	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
16	#87705	C₄×C₁₁	1	1	yes	characteristic, direct product factor, Hall
17	C₄×C₇×C₁₁	C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
18	C₂×C₇×C₁₉	C₂×C₃×C₁₁	1	1	yes	characteristic
19	C₁₁×ΓL(1,𝔽₈)	—	19	1	no	Hall
20	C₄×C₁₉⋊C₃	—	7	1	no	Hall
21	C₁₁×C₁₉	C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
22	C₂×C₇×C₁₁	C₂×C₁₉⋊C₃	1	1	yes	characteristic
23	C₇×C₁₉	C₃×C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
24	C₃×C₄×C₁₁	—	133	1	no	Hall
25	C₂×C₁₉⋊C₃	—	7	1	no	—
26	C₄×ΓL(1,𝔽₈)	—	19	1	no	Hall
27	C₇×C₁₁	C₄×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
28	C₄×C₁₉	C₁₁×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
29	C₂×C₃×C₁₁	—	133	1	no	—
30	C₁₉⋊C₃	—	7	1	no	Hall
31	C₄×C₁₁	#87705	1	1	yes	characteristic, direct product factor, Hall
32	C₂×ΓL(1,𝔽₈)	—	19	1	no	—
33	C₂×C₁₉	C₂×C₁₁×ΓL(1,𝔽₈)	1	1	yes	characteristic
34	C₃×C₁₁	—	133	1	no	Hall
35	C₄×C₇	C₁₁×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
36	C₂×C₁₁	C₂×#87705	1	1	yes	characteristic
37	ΓL(1,𝔽₈)	—	19	1	no	Hall
38	C₁₉	C₄×C₁₁×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
39	C₂×C₇	C₂×C₁₁×C₁₉⋊C₃	1	1	yes	characteristic
40	C₃×C₄	—	133	1	no	Hall
41	C₁₁	C₄×#87705	1	1	yes	characteristic, direct product factor, Sylow
42	C₇	C₄×C₁₁×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₃	—	133	1	no	—
44	C₄	C₁₁×#87705	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	—	133	1	no	Sylow
46	C₂	C₂×C₁₁×#87705	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄×C₁₁	#87705
commutator, hypocenter	C₇×C₁₉	C₃×C₄×C₁₁
Frattini	C₂	C₂×C₁₁×#87705
Fitting	C₄×C₇×C₁₁×C₁₉	C₃
socle	C₂×C₇×C₁₁×C₁₉	C₂×C₃
prime radical	C₂×C₁₁×#87705	C₂
cosocle	C₂×C₇×C₁₉	C₂×C₃×C₁₁
LCS	G ▷ C₇×C₁₉
UCS	C₁ ◁ C₄×C₁₁

Complements

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

N	H ≅ G/N	type
2. C₄×C₇×C₁₁×C₁₉	C₃	semidirect
3. C₁₁×#87705	C₄	direct (N × H)
6. C₄×#87705	C₁₁	direct (N × H)
7. C₇×C₁₁×C₁₉	C₃×C₄	semidirect
10. C₄×C₁₁×C₁₉	ΓL(1,𝔽₈)	semidirect
13. C₄×C₇×C₁₉	C₃×C₁₁	semidirect
16. #87705	C₄×C₁₁	direct (N × H)
17. C₄×C₇×C₁₁	C₁₉⋊C₃	semidirect
21. C₁₁×C₁₉	C₄×ΓL(1,𝔽₈)	semidirect
23. C₇×C₁₉	C₃×C₄×C₁₁	semidirect
27. C₇×C₁₁	C₄×C₁₉⋊C₃	semidirect
28. C₄×C₁₉	C₁₁×ΓL(1,𝔽₈)	semidirect
31. C₄×C₁₁	#87705	direct (N × H)
35. C₄×C₇	C₁₁×C₁₉⋊C₃	semidirect
38. C₁₉	C₄×C₁₁×ΓL(1,𝔽₈)	semidirect
41. C₁₁	C₄×#87705	direct (N × H)
42. C₇	C₄×C₁₁×C₁₉⋊C₃	semidirect
44. C₄	C₁₁×#87705	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×C₁₁×#87705	2
C₄×C₇×C₁₁×C₁₉	3
C₄×C₁₁×C₁₉⋊C₃	7
C₄×#87705	11
C₄×C₁₁×ΓL(1,𝔽₈)	19

Subgroups — C4×C11×#87705 #31798190

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₁×#87705 #31798190