Subgroups — D₂₁×D₁₂₃ #23780224

Order 10332.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₈₆₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₄₁×D₂₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇×D₁₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₇×D₁₂₃	—	3	1	no	maximal
5	D₂₁×D₄₁	—	3	1	no	maximal
6	C₃²×C₇×C₄₁	C₂²	1	1	yes	characteristic, complemented, Hall
7	D₈₆₁	—	3	1	no	—
8	D₈₆₁	—	3	1	no	—
9	D₈₆₁	—	6	1	no	—
10	C₄₁×D₂₁	D₃	1	1	yes	characteristic, complemented
11	C₇×D₁₂₃	D₃	1	1	yes	characteristic, complemented
12	C₃×D₇×C₄₁	—	3	1	no	—
13	C₃×C₇×D₄₁	—	3	1	no	—
14	D₃×D₁₂₃	—	7	1	no	maximal, Hall
15	D₇×D₄₁	—	9	1	no	Hall
16	C₃×C₇×C₄₁	—	2	1	no	—
17	C₃×C₇×C₄₁	C₂×D₃	1	1	yes	characteristic, complemented
18	C₃×C₇×C₄₁	C₂×D₃	1	1	yes	characteristic, complemented
19	C₃⋊D₁₂₃	—	7	1	no	—
20	C₃×D₁₂₃	D₇	1	1	yes	characteristic, complemented
21	C₃×D₃×C₄₁	—	7	1	no	—
22	D₂₈₇	—	9	1	no	—
23	C₇×D₄₁	—	3	1	no	—
24	D₇×C₄₁	—	3	1	no	—
25	C₂×D₁₂₃	—	21	1	no	—
26	D₃×D₄₁	—	21	1	no	—
27	C₃²×C₄₁	C₂×D₇	1	1	yes	characteristic, complemented, Hall
28	C₇×C₄₁	D₃²	1	1	yes	characteristic, complemented, Hall
29	D₃×D₂₁	—	41	1	no	maximal, Hall
30	C₂×C₃×C₄₁	—	21	1	no	—
31	D₁₂₃	—	21	1	no	—
32	D₁₂₃	—	21	1	no	—
33	D₁₂₃	—	42	1	no	—
34	D₁₂₃	D₂₁	1	1	yes	characteristic, direct product factor
35	C₃×D₄₁	—	3	1	no	—
36	D₃×C₄₁	—	7	1	no	—
37	C₂×D₄₁	—	63	1	no	Hall
38	C₃⋊D₂₁	—	41	1	no	—
39	C₃×D₂₁	D₄₁	1	1	yes	characteristic, complemented
40	C₃×D₃×C₇	—	41	1	no	—
41	C₃×C₄₁	—	2	1	no	—
42	C₃×C₄₁	D₃×D₇	1	1	yes	characteristic, complemented
43	C₃×C₄₁	C₂×D₂₁	1	1	yes	characteristic, complemented
44	C₂×D₂₁	—	123	1	no	—
45	D₃×D₇	—	123	1	no	—
46	C₂×C₄₁	—	21	1	no	—
47	D₄₁	—	3	1	no	—
48	D₄₁	—	63	1	no	—
49	C₃²×C₇	C₂×D₄₁	1	1	yes	characteristic, complemented, Hall
50	C₂×C₃×C₇	—	123	1	no	—
51	D₂₁	—	123	1	no	—
52	D₂₁	—	123	1	no	—
53	D₂₁	—	246	1	no	—
54	D₂₁	D₁₂₃	1	1	yes	characteristic, direct product factor
55	C₃×D₇	—	3	1	no	—
56	D₃×C₇	—	41	1	no	—
57	C₄₁	D₃×D₂₁	1	1	yes	characteristic, complemented, Sylow
58	D₃²	—	287	1	no	Hall
59	C₂×D₇	—	369	1	no	Hall
60	C₃×C₇	—	2	1	no	—
61	C₃×C₇	D₃×D₄₁	1	1	yes	characteristic, complemented
62	C₃×C₇	C₂×D₁₂₃	1	1	yes	characteristic, complemented
63	C₃⋊D₃	—	287	1	no	—
64	C₃×D₃	—	7	1	no	—
65	C₃×D₃	—	41	1	no	—
66	C₂×C₇	—	123	1	no	—
67	D₇	—	3	1	no	—
68	D₇	—	369	1	no	—
69	C₂×D₃	—	861	1	no	—
70	C₂×D₃	—	861	1	no	—
71	C₃²	D₇×D₄₁	1	1	yes	characteristic, complemented, Sylow
72	C₇	D₃×D₁₂₃	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₃	—	21	1	no	—
74	C₂×C₃	—	123	1	no	—
75	D₃	—	7	1	no	—
76	D₃	—	41	1	no	—
77	D₃	—	861	1	no	—
78	D₃	—	861	1	no	—
79	D₃	—	1722	1	no	—
80	C₂²	—	2583	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	D₂₁×D₄₁	1	1	yes	characteristic, complemented
83	C₃	D₇×D₁₂₃	1	1	yes	characteristic, complemented
84	C₂	—	21	1	no	—
85	C₂	—	2583	1	no	—
86	C₂	—	123	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₇×C₄₁	C₂²
LCS	G ▷ C₃²×C₇×C₄₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃⋊D₈₆₁	C₂	semidirect
2. C₃×C₄₁×D₂₁	C₂	semidirect
3. C₃×C₇×D₁₂₃	C₂	semidirect
6. C₃²×C₇×C₄₁	C₂²	semidirect
10. C₄₁×D₂₁	D₃	semidirect
11. C₇×D₁₂₃	D₃	semidirect
17. C₃×C₇×C₄₁	C₂×D₃	semidirect
18. C₃×C₇×C₄₁	C₂×D₃	semidirect
20. C₃×D₁₂₃	D₇	semidirect
27. C₃²×C₄₁	C₂×D₇	semidirect
28. C₇×C₄₁	D₃²	semidirect
34. D₁₂₃	D₂₁	direct (N × H)
39. C₃×D₂₁	D₄₁	semidirect
42. C₃×C₄₁	D₃×D₇	semidirect
43. C₃×C₄₁	C₂×D₂₁	semidirect
49. C₃²×C₇	C₂×D₄₁	semidirect
54. D₂₁	D₁₂₃	direct (N × H)
57. C₄₁	D₃×D₂₁	semidirect
61. C₃×C₇	D₃×D₄₁	semidirect
62. C₃×C₇	C₂×D₁₂₃	semidirect
71. C₃²	D₇×D₄₁	semidirect
72. C₇	D₃×D₁₂₃	semidirect
82. C₃	D₂₁×D₄₁	semidirect
83. C₃	D₇×D₁₂₃	semidirect

Subgroups — D21×D123 #23780224

Conjugacy classes of subgroups

Complements

Subgroups — D₂₁×D₁₂₃ #23780224