Subgroups — C₂×C₁₁²×C₃⋊D₂₁ #44479271

Order 30492.

840 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁²×C₃⋊D₂₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₇×C₁₁²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₁²×D₂₁	—	3	4	no	maximal
4	C₃²×C₇×C₁₁²	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₁₁²×D₂₁	—	3	8	no	—
6	C₂×C₃×C₇×C₁₁²	D₃	1	4	yes	complemented
7	C₂×C₁₁²×C₃⋊D₃	—	7	1	no	maximal, Hall
8	C₂×C₁₁²×D₇	—	9	1	no	Hall
9	C₂×C₁₁×C₃⋊D₂₁	C₁₁	1	12	yes	maximal, direct product factor
10	C₃×C₇×C₁₁²	C₂×D₃	1	4	yes	complemented
11	C₁₁²×C₃⋊D₃	—	7	2	no	—
12	C₂×C₃²×C₁₁²	D₇	1	1	yes	characteristic, complemented
13	C₂×C₇×C₁₁²	C₃⋊D₃	1	1	yes	characteristic, complemented
14	C₁₁²×D₇	—	9	2	no	—
15	C₂×D₃×C₁₁²	—	21	4	no	—
16	C₂×C₃²×C₇×C₁₁	C₂×C₁₁	1	12	yes	complemented
17	C₁₁×C₃⋊D₂₁	C₂×C₁₁	1	24	yes	direct product factor
18	C₃²×C₁₁²	C₂×D₇	1	1	yes	characteristic, complemented, Hall
19	C₂×C₁₁×D₂₁	—	3	48	no	—
20	C₇×C₁₁²	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×C₁₁²	D₂₁	1	4	yes	complemented
22	D₃×C₁₁²	—	21	8	no	—
23	C₃²×C₇×C₁₁	C₂²×C₁₁	1	12	yes	complemented
24	C₂²×C₁₁²	—	63	1	no	Hall
25	C₂×C₃×C₇×C₁₁	D₃×C₁₁	1	48	yes	complemented
26	C₁₁×D₂₁	—	3	96	no	—
27	C₂×C₁₁×C₃⋊D₃	—	7	12	no	—
28	C₃×C₁₁²	C₂×D₂₁	1	4	yes	complemented
29	C₂×C₁₁×D₇	—	9	12	no	—
30	C₂×C₃⋊D₂₁	C₁₁²	1	1	yes	characteristic, direct product factor, Hall
31	C₂×C₁₁²	—	63	2	no	—
32	C₂×C₁₁²	C₃⋊D₂₁	1	1	yes	characteristic, direct product factor
33	C₃×C₇×C₁₁	C₂×D₃×C₁₁	1	48	yes	complemented
34	C₂×C₃²×C₁₁	C₁₁×D₇	1	12	yes	complemented
35	C₁₁×C₃⋊D₃	—	7	24	no	—
36	C₂×C₇×C₁₁	C₁₁×C₃⋊D₃	1	12	yes	complemented
37	C₁₁×D₇	—	9	24	no	—
38	C₂×D₃×C₁₁	—	21	48	no	—
39	C₂×C₃²×C₇	C₂×C₁₁²	1	1	yes	characteristic, complemented
40	C₃⋊D₂₁	C₂×C₁₁²	1	2	yes	direct product factor
41	C₁₁²	C₂×C₃⋊D₂₁	1	1	yes	characteristic, direct product factor, Sylow
42	C₃²×C₁₁	C₂×C₁₁×D₇	1	12	yes	complemented
43	C₂×D₂₁	—	3	4	no	—
44	C₇×C₁₁	C₂×C₁₁×C₃⋊D₃	1	12	yes	complemented
45	C₂×C₃×C₁₁	C₁₁×D₂₁	1	48	yes	complemented
46	D₃×C₁₁	—	21	96	no	—
47	C₃²×C₇	C₂²×C₁₁²	1	1	yes	characteristic, complemented, Hall
48	C₂²×C₁₁	—	63	12	no	—
49	C₂×C₃×C₇	D₃×C₁₁²	1	4	yes	complemented
50	D₂₁	—	3	8	no	—
51	C₂×C₃⋊D₃	—	7	1	no	Hall
52	C₃×C₁₁	C₂×C₁₁×D₂₁	1	48	yes	complemented
53	C₂×D₇	—	9	1	no	Hall
54	C₂×C₁₁	—	63	24	no	—
55	C₂×C₁₁	C₁₁×C₃⋊D₂₁	1	12	yes	direct product factor
56	C₃×C₇	C₂×D₃×C₁₁²	1	4	yes	complemented
57	C₂×C₃²	C₁₁²×D₇	1	1	yes	characteristic, complemented
58	C₃⋊D₃	—	7	2	no	—
59	C₂×C₇	C₁₁²×C₃⋊D₃	1	1	yes	characteristic, complemented
60	D₇	—	9	2	no	—
61	C₂×D₃	—	21	4	no	—
62	C₁₁	C₂×C₁₁×C₃⋊D₂₁	1	12	yes	direct product factor
63	C₃²	C₂×C₁₁²×D₇	1	1	yes	characteristic, complemented, Sylow
64	C₇	C₂×C₁₁²×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
65	C₂×C₃	C₁₁²×D₂₁	1	4	yes	complemented
66	D₃	—	21	8	no	—
67	C₂²	—	63	1	no	Sylow
68	C₃	C₂×C₁₁²×D₂₁	1	4	yes	complemented
69	C₂	—	63	2	no	—
70	C₂	C₁₁²×C₃⋊D₂₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₁²	C₃⋊D₂₁
commutator, cosocle, hypocenter	C₃²×C₇	C₂²×C₁₁²
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₇×C₁₁²	C₂
LCS	G ▷ C₃²×C₇
UCS	C₁ ◁ C₂×C₁₁²

Complements

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

N	H ≅ G/N	type
1. C₁₁²×C₃⋊D₂₁	C₂	direct (N × H)
2. C₂×C₃²×C₇×C₁₁²	C₂	semidirect
4. C₃²×C₇×C₁₁²	C₂²	semidirect
6. C₂×C₃×C₇×C₁₁²	D₃	semidirect
9. C₂×C₁₁×C₃⋊D₂₁	C₁₁	direct (N × H)
10. C₃×C₇×C₁₁²	C₂×D₃	semidirect
12. C₂×C₃²×C₁₁²	D₇	semidirect
13. C₂×C₇×C₁₁²	C₃⋊D₃	semidirect
16. C₂×C₃²×C₇×C₁₁	C₂×C₁₁	semidirect
17. C₁₁×C₃⋊D₂₁	C₂×C₁₁	direct (N × H)
18. C₃²×C₁₁²	C₂×D₇	semidirect
20. C₇×C₁₁²	C₂×C₃⋊D₃	semidirect
21. C₂×C₃×C₁₁²	D₂₁	semidirect
23. C₃²×C₇×C₁₁	C₂²×C₁₁	semidirect
25. C₂×C₃×C₇×C₁₁	D₃×C₁₁	semidirect
28. C₃×C₁₁²	C₂×D₂₁	semidirect
30. C₂×C₃⋊D₂₁	C₁₁²	direct (N × H)
32. C₂×C₁₁²	C₃⋊D₂₁	direct (N × H)
33. C₃×C₇×C₁₁	C₂×D₃×C₁₁	semidirect
34. C₂×C₃²×C₁₁	C₁₁×D₇	semidirect
36. C₂×C₇×C₁₁	C₁₁×C₃⋊D₃	semidirect
39. C₂×C₃²×C₇	C₂×C₁₁²	semidirect
40. C₃⋊D₂₁	C₂×C₁₁²	direct (N × H)
41. C₁₁²	C₂×C₃⋊D₂₁	direct (N × H)
42. C₃²×C₁₁	C₂×C₁₁×D₇	semidirect
44. C₇×C₁₁	C₂×C₁₁×C₃⋊D₃	semidirect
45. C₂×C₃×C₁₁	C₁₁×D₂₁	semidirect
47. C₃²×C₇	C₂²×C₁₁²	semidirect
49. C₂×C₃×C₇	D₃×C₁₁²	semidirect
52. C₃×C₁₁	C₂×C₁₁×D₂₁	semidirect
55. C₂×C₁₁	C₁₁×C₃⋊D₂₁	direct (N × H)
56. C₃×C₇	C₂×D₃×C₁₁²	semidirect
57. C₂×C₃²	C₁₁²×D₇	semidirect
59. C₂×C₇	C₁₁²×C₃⋊D₃	semidirect
62. C₁₁	C₂×C₁₁×C₃⋊D₂₁	direct (N × H)
63. C₃²	C₂×C₁₁²×D₇	semidirect
64. C₇	C₂×C₁₁²×C₃⋊D₃	semidirect
65. C₂×C₃	C₁₁²×D₂₁	semidirect
68. C₃	C₂×C₁₁²×D₂₁	semidirect
70. C₂	C₁₁²×C₃⋊D₂₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁²×C₃⋊D₂₁	2
C₂×C₃²×C₇×C₁₁²	2
C₂×C₁₁²×D₂₁	3
C₂×C₁₁²×C₃⋊D₃	7
C₂×C₁₁×C₃⋊D₂₁	11

Subgroups — C2×C112×C3⋊D21 #44479271

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁²×C₃⋊D₂₁ #44479271