Subgroups — Dic₁₁×#4294 #21418959

Order 7524.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#4294	C₂	1	1	yes	maximal, characteristic
2	C₃×C₁₉×Dic₁₁	C₃	1	1	yes	maximal, characteristic
3	C₁₁×#4294	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₁₁×C₁₉	C₂×C₃	1	1	yes	characteristic
5	C₁₉×Dic₁₁	C₉	1	1	yes	characteristic, complemented, Hall
6	C₄×#4294	—	11	1	no	maximal, Hall
7	C₃×C₁₁×C₁₉	C₃×C₄	1	1	yes	characteristic
8	C₂×C₁₁×C₁₉	C₂×C₉	1	1	yes	characteristic
9	C₉×Dic₁₁	—	19	1	no	maximal, Hall
10	C₂×#4294	D₁₁	1	1	yes	characteristic
11	C₃×C₄×C₁₉	—	11	1	no	—
12	C₁₁×C₁₉	C₄×C₉	1	1	yes	characteristic, complemented, Hall
13	C₂×C₉×C₁₁	—	19	1	no	—
14	#4294	Dic₁₁	1	1	yes	characteristic, direct product factor, Hall
15	C₃×Dic₁₁	C₁₉⋊C₃	1	1	yes	characteristic
16	C₂×C₃×C₁₉	C₃×D₁₁	1	1	yes	characteristic
17	C₉×C₁₁	—	19	1	no	Hall
18	C₄×C₁₉	—	11	1	no	Hall
19	C₂×C₃×C₁₁	C₂×C₁₉⋊C₃	1	1	yes	characteristic
20	C₃×C₁₉	C₃×Dic₁₁	1	1	yes	characteristic
21	Dic₁₁	#4294	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₁₉	C₉×D₁₁	1	1	yes	characteristic
23	C₄×C₉	—	209	1	no	Hall
24	C₃×C₁₁	C₄×C₁₉⋊C₃	1	1	yes	characteristic
25	C₂×C₁₁	C₂×#4294	1	1	yes	characteristic
26	C₁₉	C₉×Dic₁₁	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₉	—	19	1	no	—
28	C₃×C₄	—	11	1	no	—
29	C₁₁	C₄×#4294	1	1	yes	characteristic, complemented, Sylow
30	C₉	—	19	1	no	Sylow
31	C₂×C₃	D₁₁×C₁₉⋊C₃	1	1	yes	characteristic
32	C₄	—	11	1	no	Sylow
33	C₃	Dic₁₁×C₁₉⋊C₃	1	1	yes	characteristic
34	C₂	D₁₁×#4294	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₃	D₁₁×C₁₉⋊C₃
commutator, hypocenter	C₁₁×C₁₉	C₄×C₉
Fitting, socle	C₂×C₃×C₁₁×C₁₉	C₂×C₃
LCS	G ▷ C₁₁×C₁₉
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
3. C₁₁×#4294	C₄	semidirect
5. C₁₉×Dic₁₁	C₉	semidirect
12. C₁₁×C₁₉	C₄×C₉	semidirect
14. #4294	Dic₁₁	direct (N × H)
21. Dic₁₁	#4294	direct (N × H)
26. C₁₉	C₉×Dic₁₁	semidirect
29. C₁₁	C₄×#4294	semidirect

Subgroups — Dic11×#4294 #21418959

Conjugacy classes of subgroups

Complements

Subgroups — Dic₁₁×#4294 #21418959