Subgroups — C₇×C₁₁²×C₃⋊Dic₃ #44479039

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

	subgroup	G/H
center, hypercenter	C₂×C₇×C₁₁²	C₃⋊D₃
commutator, hypocenter	C₃²	C₄×C₇×C₁₁²
Frattini	C₂	C₇×C₁₁²×C₃⋊D₃
Fitting, socle, prime radical	C₂×C₃²×C₇×C₁₁²	C₂
cosocle	C₂×C₃²	C₂×C₇×C₁₁²
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂×C₇×C₁₁²

Complements

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

N	H ≅ G/N	type
3. C₃²×C₇×C₁₁²	C₄	semidirect
5. C₁₁²×C₃⋊Dic₃	C₇	direct (N × H)
7. C₇×C₁₁×C₃⋊Dic₃	C₁₁	direct (N × H)
8. C₃×C₇×C₁₁²	Dic₃	semidirect
13. C₃²×C₁₁²	C₄×C₇	semidirect
15. C₇×C₁₁²	C₃⋊Dic₃	direct (N × H)
17. C₃²×C₇×C₁₁	C₄×C₁₁	semidirect
20. C₁₁×C₃⋊Dic₃	C₇×C₁₁	direct (N × H)
21. C₃×C₁₁²	C₇×Dic₃	semidirect
23. C₇×C₃⋊Dic₃	C₁₁²	direct (N × H)
25. C₃×C₇×C₁₁	C₁₁×Dic₃	semidirect
30. C₁₁²	C₇×C₃⋊Dic₃	direct (N × H)
31. C₃²×C₁₁	C₄×C₇×C₁₁	semidirect
33. C₇×C₁₁	C₁₁×C₃⋊Dic₃	direct (N × H)
35. C₃²×C₇	C₄×C₁₁²	semidirect
38. C₃⋊Dic₃	C₇×C₁₁²	direct (N × H)
39. C₃×C₁₁	C₇×C₁₁×Dic₃	semidirect
42. C₃×C₇	C₁₁²×Dic₃	semidirect
46. C₁₁	C₇×C₁₁×C₃⋊Dic₃	direct (N × H)
47. C₃²	C₄×C₇×C₁₁²	semidirect
48. C₇	C₁₁²×C₃⋊Dic₃	direct (N × H)
51. C₃	C₇×C₁₁²×Dic₃	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
C₇×C₁₁²×Dic₃	3
C₁₁²×C₃⋊Dic₃	7
C₇×C₁₁×C₃⋊Dic₃	11

Subgroups — C7×C112×C3⋊Dic3 #44479039

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₁₁²×C₃⋊Dic₃ #44479039