Subgroups — D₁₁×D₇₄₁ #45656804

Order 32604.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₈₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×D₇₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₃×C₁₉×D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₁×D₂₄₇	—	3	1	no	maximal, Hall
5	C₃×C₁₁×C₁₃×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₂₇₁₇	—	3	1	no	—
7	C₁₃×C₁₉×D₁₁	D₃	1	1	yes	characteristic, complemented
8	C₁₁×D₂₄₇	—	3	1	no	—
9	C₂×D₇₄₁	—	11	1	no	maximal, Hall
10	C₁₁×C₁₃×C₁₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	D₁₁×D₅₇	—	13	1	no	maximal, Hall
12	D₁₁×D₃₉	—	19	1	no	maximal, Hall
13	C₂×C₃×C₁₃×C₁₉	—	11	1	no	—
14	D₇₄₁	—	11	1	no	—
15	D₇₄₁	D₁₁	1	1	yes	characteristic, direct product factor
16	D₆₂₇	—	13	1	no	—
17	C₁₁×D₅₇	—	13	1	no	—
18	C₃×C₁₉×D₁₁	D₁₃	1	1	yes	characteristic, complemented
19	C₂×D₂₄₇	—	33	1	no	Hall
20	D₄₂₉	—	19	1	no	—
21	C₁₁×D₃₉	—	19	1	no	—
22	C₃×C₁₃×D₁₁	D₁₉	1	1	yes	characteristic, complemented
23	D₁₁×D₁₉	—	39	1	no	Hall
24	C₃×C₁₃×C₁₉	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
25	C₃×C₁₁×C₁₉	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
26	D₁₁×D₁₃	—	57	1	no	Hall
27	C₂×C₁₃×C₁₉	—	11	1	no	—
28	D₂₄₇	—	3	1	no	—
29	D₂₄₇	—	33	1	no	—
30	C₃×C₁₁×C₁₃	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
31	D₂₀₉	—	39	1	no	—
32	C₁₁×D₁₉	—	39	1	no	—
33	C₁₉×D₁₁	D₃₉	1	1	yes	characteristic, complemented
34	D₁₄₃	—	57	1	no	—
35	C₁₁×D₁₃	—	57	1	no	—
36	C₁₃×D₁₁	D₅₇	1	1	yes	characteristic, complemented
37	C₁₃×C₁₉	D₃×D₁₁	1	1	yes	characteristic, complemented, Hall
38	C₂×D₅₇	—	143	1	no	Hall
39	C₁₁×C₁₉	C₂×D₃₉	1	1	yes	characteristic, complemented, Hall
40	C₂×D₃₉	—	209	1	no	Hall
41	C₁₁×C₁₃	C₂×D₅₇	1	1	yes	characteristic, complemented, Hall
42	D₃×D₁₁	—	247	1	no	Hall
43	C₂×C₃×C₁₉	—	11	1	no	—
44	D₅₇	—	13	1	no	—
45	D₅₇	—	143	1	no	—
46	C₂×C₃×C₁₃	—	11	1	no	—
47	D₃₉	—	19	1	no	—
48	D₃₉	—	209	1	no	—
49	C₂×D₁₉	—	429	1	no	Hall
50	D₃₃	—	247	1	no	—
51	C₃×D₁₁	D₂₄₇	1	1	yes	characteristic, complemented
52	D₃×C₁₁	—	247	1	no	—
53	C₃×C₁₉	D₁₁×D₁₃	1	1	yes	characteristic, complemented, Hall
54	C₂×D₁₃	—	627	1	no	Hall
55	C₂×D₁₁	—	741	1	no	Hall
56	C₃×C₁₃	D₁₁×D₁₉	1	1	yes	characteristic, complemented, Hall
57	C₂×C₁₉	—	11	1	no	—
58	D₁₉	—	39	1	no	—
59	D₁₉	—	429	1	no	—
60	C₃×C₁₁	C₂×D₂₄₇	1	1	yes	characteristic, complemented, Hall
61	C₂×C₁₃	—	11	1	no	—
62	D₁₃	—	57	1	no	—
63	D₁₃	—	627	1	no	—
64	C₂×C₁₁	—	741	1	no	—
65	D₁₁	—	741	1	no	—
66	D₁₁	D₇₄₁	1	1	yes	characteristic, direct product factor
67	C₁₉	D₁₁×D₃₉	1	1	yes	characteristic, complemented, Sylow
68	C₁₃	D₁₁×D₅₇	1	1	yes	characteristic, complemented, Sylow
69	C₂×D₃	—	2717	1	no	Hall
70	C₁₁	C₂×D₇₄₁	1	1	yes	characteristic, complemented, Sylow
71	C₂×C₃	—	11	1	no	—
72	D₃	—	2717	1	no	—
73	D₃	—	247	1	no	—
74	C₂²	—	8151	1	no	Sylow
75	C₃	D₁₁×D₂₄₇	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	11	1	no	—
77	C₂	—	8151	1	no	—
78	C₂	—	741	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₁×C₁₃×C₁₉	C₂²
LCS	G ▷ C₃×C₁₁×C₁₃×C₁₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₈₁₅₁	C₂	semidirect
2. C₁₁×D₇₄₁	C₂	semidirect
3. C₃×C₁₃×C₁₉×D₁₁	C₂	semidirect
5. C₃×C₁₁×C₁₃×C₁₉	C₂²	semidirect
7. C₁₃×C₁₉×D₁₁	D₃	semidirect
10. C₁₁×C₁₃×C₁₉	C₂×D₃	semidirect
15. D₇₄₁	D₁₁	direct (N × H)
18. C₃×C₁₉×D₁₁	D₁₃	semidirect
22. C₃×C₁₃×D₁₁	D₁₉	semidirect
24. C₃×C₁₃×C₁₉	C₂×D₁₁	semidirect
25. C₃×C₁₁×C₁₉	C₂×D₁₃	semidirect
30. C₃×C₁₁×C₁₃	C₂×D₁₉	semidirect
33. C₁₉×D₁₁	D₃₉	semidirect
36. C₁₃×D₁₁	D₅₇	semidirect
37. C₁₃×C₁₉	D₃×D₁₁	semidirect
39. C₁₁×C₁₉	C₂×D₃₉	semidirect
41. C₁₁×C₁₃	C₂×D₅₇	semidirect
51. C₃×D₁₁	D₂₄₇	semidirect
53. C₃×C₁₉	D₁₁×D₁₃	semidirect
56. C₃×C₁₃	D₁₁×D₁₉	semidirect
60. C₃×C₁₁	C₂×D₂₄₇	semidirect
66. D₁₁	D₇₄₁	direct (N × H)
67. C₁₉	D₁₁×D₃₉	semidirect
68. C₁₃	D₁₁×D₅₇	semidirect
70. C₁₁	C₂×D₇₄₁	semidirect
75. C₃	D₁₁×D₂₄₇	semidirect

Maximal subgroups

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

subgroup	index
D₈₁₅₁	2
C₁₁×D₇₄₁	2
C₃×C₁₃×C₁₉×D₁₁	2
D₁₁×D₂₄₇	3
C₂×D₇₄₁	11
D₁₁×D₅₇	13
D₁₁×D₃₉	19

Subgroups — D11×D741 #45656804

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₁×D₇₄₁ #45656804