Subgroups — C₁₁²×C₃⋊Dic₂₁ #44479036

Order 30492.

504 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₇×C₁₁²	C₂	1	1	yes	maximal, characteristic
2	C₁₁²×Dic₂₁	—	3	4	no	maximal
3	C₃²×C₇×C₁₁²	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₇×C₁₁²	D₃	1	4	yes	—
5	C₁₁²×C₃⋊Dic₃	—	7	1	no	maximal, Hall
6	C₁₁²×Dic₇	—	9	1	no	Hall
7	C₁₁×C₃⋊Dic₂₁	C₁₁	1	12	yes	maximal, direct product factor
8	C₃×C₇×C₁₁²	Dic₃	1	4	yes	complemented
9	C₂×C₃²×C₁₁²	D₇	1	1	yes	characteristic
10	C₂×C₇×C₁₁²	C₃⋊D₃	1	1	yes	characteristic
11	C₁₁²×Dic₃	—	21	4	no	—
12	C₂×C₃²×C₇×C₁₁	C₂×C₁₁	1	12	yes	—
13	C₃²×C₁₁²	Dic₇	1	1	yes	characteristic, complemented, Hall
14	C₁₁×Dic₂₁	—	3	48	no	—
15	C₇×C₁₁²	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃×C₁₁²	D₂₁	1	4	yes	—
17	C₃²×C₇×C₁₁	C₄×C₁₁	1	12	yes	complemented
18	C₄×C₁₁²	—	63	1	no	Hall
19	C₂×C₃×C₇×C₁₁	D₃×C₁₁	1	48	yes	—
20	C₁₁×C₃⋊Dic₃	—	7	12	no	—
21	C₃×C₁₁²	Dic₂₁	1	4	yes	complemented
22	C₁₁×Dic₇	—	9	12	no	—
23	C₃⋊Dic₂₁	C₁₁²	1	1	yes	characteristic, direct product factor, Hall
24	C₂×C₁₁²	C₃⋊D₂₁	1	1	yes	characteristic
25	C₃×C₇×C₁₁	C₁₁×Dic₃	1	48	yes	complemented
26	C₂×C₃²×C₁₁	C₁₁×D₇	1	12	yes	—
27	C₂×C₇×C₁₁	C₁₁×C₃⋊D₃	1	12	yes	—
28	C₁₁×Dic₃	—	21	48	no	—
29	C₂×C₃²×C₇	C₂×C₁₁²	1	1	yes	characteristic
30	C₁₁²	C₃⋊Dic₂₁	1	1	yes	characteristic, direct product factor, Sylow
31	C₃²×C₁₁	C₁₁×Dic₇	1	12	yes	complemented
32	Dic₂₁	—	3	4	no	—
33	C₇×C₁₁	C₁₁×C₃⋊Dic₃	1	12	yes	complemented
34	C₂×C₃×C₁₁	C₁₁×D₂₁	1	48	yes	—
35	C₃²×C₇	C₄×C₁₁²	1	1	yes	characteristic, complemented, Hall
36	C₄×C₁₁	—	63	12	no	—
37	C₂×C₃×C₇	D₃×C₁₁²	1	4	yes	—
38	C₃⋊Dic₃	—	7	1	no	Hall
39	C₃×C₁₁	C₁₁×Dic₂₁	1	48	yes	complemented
40	Dic₇	—	9	1	no	Hall
41	C₂×C₁₁	C₁₁×C₃⋊D₂₁	1	12	yes	—
42	C₃×C₇	C₁₁²×Dic₃	1	4	yes	complemented
43	C₂×C₃²	C₁₁²×D₇	1	1	yes	characteristic
44	C₂×C₇	C₁₁²×C₃⋊D₃	1	1	yes	characteristic
45	Dic₃	—	21	4	no	—
46	C₁₁	C₁₁×C₃⋊Dic₂₁	1	12	yes	direct product factor
47	C₃²	C₁₁²×Dic₇	1	1	yes	characteristic, complemented, Sylow
48	C₇	C₁₁²×C₃⋊Dic₃	1	1	yes	characteristic, complemented, Sylow
49	C₂×C₃	C₁₁²×D₂₁	1	4	yes	—
50	C₄	—	63	1	no	Sylow
51	C₃	C₁₁²×Dic₂₁	1	4	yes	complemented
52	C₂	C₁₁²×C₃⋊D₂₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₁₁²	C₃⋊D₂₁
commutator, hypocenter	C₃²×C₇	C₄×C₁₁²
Frattini	C₂	C₁₁²×C₃⋊D₂₁
Fitting, socle, prime radical	C₂×C₃²×C₇×C₁₁²	C₂
cosocle	C₂×C₃²×C₇	C₂×C₁₁²
LCS	G ▷ C₃²×C₇
UCS	C₁ ◁ C₂×C₁₁²

Complements

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

N	H ≅ G/N	type
3. C₃²×C₇×C₁₁²	C₄	semidirect
7. C₁₁×C₃⋊Dic₂₁	C₁₁	direct (N × H)
8. C₃×C₇×C₁₁²	Dic₃	semidirect
13. C₃²×C₁₁²	Dic₇	semidirect
15. C₇×C₁₁²	C₃⋊Dic₃	semidirect
17. C₃²×C₇×C₁₁	C₄×C₁₁	semidirect
21. C₃×C₁₁²	Dic₂₁	semidirect
23. C₃⋊Dic₂₁	C₁₁²	direct (N × H)
25. C₃×C₇×C₁₁	C₁₁×Dic₃	semidirect
30. C₁₁²	C₃⋊Dic₂₁	direct (N × H)
31. C₃²×C₁₁	C₁₁×Dic₇	semidirect
33. C₇×C₁₁	C₁₁×C₃⋊Dic₃	semidirect
35. C₃²×C₇	C₄×C₁₁²	semidirect
39. C₃×C₁₁	C₁₁×Dic₂₁	semidirect
42. C₃×C₇	C₁₁²×Dic₃	semidirect
46. C₁₁	C₁₁×C₃⋊Dic₂₁	direct (N × H)
47. C₃²	C₁₁²×Dic₇	semidirect
48. C₇	C₁₁²×C₃⋊Dic₃	semidirect
51. C₃	C₁₁²×Dic₂₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₇×C₁₁²	2
C₁₁²×Dic₂₁	3
C₁₁²×C₃⋊Dic₃	7
C₁₁×C₃⋊Dic₂₁	11

Subgroups — C112×C3⋊Dic21 #44479036

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁²×C₃⋊Dic₂₁ #44479036