Subgroups — C₂¹¹×D₄ #72301774

Order 16384.

74629802916129 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂¹⁰×D₄	C₂	1	8188	yes	maximal, direct product factor
2	C₂⁹×D₄	C₂²	1	11168432	yes	direct product factor
3	C₂⁸×D₄	C₂³	1	3261182144	yes	direct product factor
4	C₂⁷×D₄	C₂⁴	1	221760385792	yes	direct product factor
5	C₂¹³	C₂	1	2	yes	maximal, complemented
6	C₂¹¹×C₄	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂¹⁰×C₄	C₂²	1	4094	yes	complemented
8	C₂¹²	—	2	4096	no	—
9	C₂¹²	C₂²	1	1	yes	characteristic
10	C₂¹²	C₂²	1	8188	yes	complemented
11	C₂⁹×C₄	C₂³	1	2792108	yes	complemented
12	C₂¹¹	—	2	8384512	no	—
13	C₂¹¹	D₄	1	2048	yes	direct product factor
14	C₂¹¹	C₂³	1	2047	yes	—
15	C₂¹¹	C₂³	1	5584216	yes	complemented
16	C₂¹⁰	—	2	2859118592	no	—
17	C₂¹⁰	C₂×D₄	1	2096128	yes	direct product factor
18	C₂¹⁰	C₂⁴	1	698027	yes	—
19	C₂¹⁰	C₂⁴	1	815295536	yes	complemented
20	C₂⁸×C₄	C₂⁴	1	407647768	yes	complemented
21	C₂⁹	—	2	208715657216	no	—
22	C₂⁹	C₂²×D₄	1	357389824	yes	direct product factor
23	C₂⁹	C₂⁵	1	50955971	yes	—
24	C₂⁹	C₂⁵	1	27720048224	yes	complemented
25	C₂⁶×D₄	C₂⁵	1	3634008902656	yes	direct product factor
26	C₂⁷×C₄	C₂⁵	1	13860024112	yes	complemented
27	C₂⁸	—	2	3548166172672	no	—
28	C₂⁸	C₂³×D₄	1	13044728576	yes	direct product factor
29	C₂⁸	C₂⁶	1	866251507	yes	—
30	C₂⁸	C₂⁶	1	227125556416	yes	complemented
31	C₂⁵×D₄	C₂⁶	1	14536035610624	yes	direct product factor
32	C₂⁶×C₄	C₂⁶	1	113562778208	yes	complemented
33	C₂⁷	—	2	14536035610624	no	—
34	C₂⁷	C₂⁴×D₄	1	110880192896	yes	direct product factor
35	C₂⁷	C₂⁷	1	3548836819	yes	—
36	C₂⁷	C₂⁷	1	454251112832	yes	complemented
37	C₂⁴×D₄	C₂⁷	1	14192664690688	yes	direct product factor
38	C₂⁵×C₄	C₂⁷	1	227125556416	yes	complemented
39	C₂⁶	—	2	14536035610624	no	—
40	C₂⁶	C₂⁵×D₄	1	227125556416	yes	direct product factor
41	C₂⁶	C₂⁸	1	3548836819	yes	—
42	C₂⁶	C₂⁸	1	221760385792	yes	complemented
43	C₂³×D₄	C₂⁸	1	3339450515456	yes	direct product factor
44	C₂⁴×C₄	C₂⁸	1	110880192896	yes	complemented
45	C₂⁵	—	2	3548166172672	no	—
46	C₂⁵	C₂⁶×D₄	1	113562778208	yes	direct product factor
47	C₂⁵	C₂⁹	1	866251507	yes	—
48	C₂⁵	C₂⁹	1	26089457152	yes	complemented
49	C₂²×D₄	C₂⁹	1	182983589888	yes	direct product factor
50	C₂³×C₄	C₂⁹	1	13044728576	yes	complemented
51	C₂⁴	—	2	208715657216	no	—
52	C₂⁴	C₂¹⁰	1	50955971	yes	—
53	C₂⁴	C₂¹⁰	1	714779648	yes	complemented
54	C₂⁴	C₂⁷×D₄	1	13860024112	yes	direct product factor
55	C₂×D₄	C₂¹⁰	1	2146435072	yes	direct product factor
56	C₂²×C₄	C₂¹⁰	1	357389824	yes	complemented
57	C₂³	—	2	2859118592	no	—
58	C₂³	C₂¹¹	1	698027	yes	—
59	C₂³	C₂¹¹	1	4192256	yes	complemented
60	C₂³	C₂⁸×D₄	1	407647768	yes	direct product factor
61	D₄	C₂¹¹	1	4194304	yes	direct product factor
62	C₂×C₄	C₂¹¹	1	2096128	yes	complemented
63	C₂²	—	2	8384512	no	—
64	C₂²	C₂¹²	1	2047	yes	—
65	C₂²	C₂¹²	1	4096	yes	complemented
66	C₂²	C₂⁹×D₄	1	2792108	yes	direct product factor
67	C₄	C₂¹²	1	2048	yes	complemented
68	C₂	—	2	4096	no	—
69	C₂	C₂¹³	1	1	yes	characteristic
70	C₂	C₂¹⁰×D₄	1	4094	yes	direct product factor

	subgroup	G/H
center, socle	C₂¹²	C₂²
commutator, Frattini, cosocle	C₂	C₂¹³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂¹² ◁ G
LECS	G ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂¹⁰×D₄	C₂	direct (N × H)
2. C₂⁹×D₄	C₂²	direct (N × H)
3. C₂⁸×D₄	C₂³	direct (N × H)
4. C₂⁷×D₄	C₂⁴	direct (N × H)
5. C₂¹³	C₂	semidirect
6. C₂¹¹×C₄	C₂	semidirect
7. C₂¹⁰×C₄	C₂²	semidirect
10. C₂¹²	C₂²	semidirect
11. C₂⁹×C₄	C₂³	semidirect
13. C₂¹¹	D₄	direct (N × H)
15. C₂¹¹	C₂³	semidirect
17. C₂¹⁰	C₂×D₄	direct (N × H)
19. C₂¹⁰	C₂⁴	semidirect
20. C₂⁸×C₄	C₂⁴	semidirect
22. C₂⁹	C₂²×D₄	direct (N × H)
24. C₂⁹	C₂⁵	semidirect
25. C₂⁶×D₄	C₂⁵	direct (N × H)
26. C₂⁷×C₄	C₂⁵	semidirect
28. C₂⁸	C₂³×D₄	direct (N × H)
30. C₂⁸	C₂⁶	semidirect
31. C₂⁵×D₄	C₂⁶	direct (N × H)
32. C₂⁶×C₄	C₂⁶	semidirect
34. C₂⁷	C₂⁴×D₄	direct (N × H)
36. C₂⁷	C₂⁷	semidirect
37. C₂⁴×D₄	C₂⁷	direct (N × H)
38. C₂⁵×C₄	C₂⁷	semidirect
40. C₂⁶	C₂⁵×D₄	direct (N × H)
42. C₂⁶	C₂⁸	semidirect
43. C₂³×D₄	C₂⁸	direct (N × H)
44. C₂⁴×C₄	C₂⁸	semidirect
46. C₂⁵	C₂⁶×D₄	direct (N × H)
48. C₂⁵	C₂⁹	semidirect
49. C₂²×D₄	C₂⁹	direct (N × H)
50. C₂³×C₄	C₂⁹	semidirect
53. C₂⁴	C₂¹⁰	semidirect
54. C₂⁴	C₂⁷×D₄	direct (N × H)
55. C₂×D₄	C₂¹⁰	direct (N × H)
56. C₂²×C₄	C₂¹⁰	semidirect
59. C₂³	C₂¹¹	semidirect
60. C₂³	C₂⁸×D₄	direct (N × H)
61. D₄	C₂¹¹	direct (N × H)
62. C₂×C₄	C₂¹¹	semidirect
65. C₂²	C₂¹²	semidirect
66. C₂²	C₂⁹×D₄	direct (N × H)
67. C₄	C₂¹²	semidirect
70. C₂	C₂¹⁰×D₄	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂¹⁰×D₄	2
C₂¹³	2
C₂¹¹×C₄	2

Subgroups — C211×D4 #72301774

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂¹¹×D₄ #72301774