Subgroups — D₆₉⋊D₁₂₃ #46800440

Order 33948.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₁×D₆₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₂₈₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×C₃⋊D₁₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₆₉⋊D₄₁	—	3	1	no	maximal
5	D₂₃×D₁₂₃	—	3	1	no	maximal
6	C₃²×C₂₃×C₄₁	C₂²	1	1	yes	characteristic, complemented, Hall
7	D₂₈₂₉	D₃	1	1	yes	characteristic, complemented
8	C₄₁×D₆₉	D₃	1	1	yes	characteristic, complemented
9	C₂₃×D₁₂₃	—	3	1	no	—
10	C₂₃×D₁₂₃	—	3	1	no	—
11	C₂₃×D₁₂₃	—	6	1	no	—
12	C₃×D₉₄₃	—	3	1	no	—
13	C₃×C₄₁×D₂₃	—	3	1	no	—
14	D₂₃×D₄₁	—	9	1	no	Hall
15	C₃×C₂₃×C₄₁	—	2	1	no	—
16	C₃×C₂₃×C₄₁	C₂×D₃	1	1	yes	characteristic, complemented
17	C₃×C₂₃×C₄₁	C₂×D₃	1	1	yes	characteristic, complemented
18	D₉₄₃	—	3	1	no	—
19	C₂₃×D₄₁	—	9	1	no	—
20	C₄₁×D₂₃	—	3	1	no	—
21	D₃×D₁₂₃	—	23	1	no	maximal, Hall
22	C₂₃×C₄₁	D₃²	1	1	yes	characteristic, complemented, Hall
23	(C₃⋊D₃)⋊D₂₃	—	41	1	no	maximal, Hall
24	C₃⋊D₁₂₃	D₂₃	1	1	yes	characteristic, complemented
25	C₃×D₁₂₃	—	23	1	no	—
26	C₃×D₃×C₄₁	—	23	1	no	—
27	C₂×D₁₂₃	—	69	1	no	—
28	D₃×D₄₁	—	69	1	no	—
29	C₃⋊D₃×C₂₃	—	41	1	no	—
30	C₃×D₆₉	—	41	1	no	—
31	C₃×D₆₉	D₄₁	1	1	yes	characteristic, complemented
32	C₃²×C₄₁	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
33	D₃×D₂₃	—	123	1	no	—
34	D₃×D₂₃	—	123	1	no	—
35	C₂×C₃×C₄₁	—	69	1	no	—
36	D₁₂₃	—	3	1	no	—
37	D₁₂₃	—	3	1	no	—
38	D₁₂₃	—	6	1	no	—
39	D₁₂₃	—	23	1	no	—
40	C₃×D₄₁	—	69	1	no	—
41	D₃×C₄₁	—	23	1	no	—
42	C₃²×C₂₃	C₂×D₄₁	1	1	yes	characteristic, complemented, Hall
43	C₂×D₄₁	—	207	1	no	Hall
44	D₆₉	—	41	1	no	—
45	D₆₉	D₁₂₃	1	1	yes	characteristic, complemented
46	C₃×D₂₃	—	3	1	no	—
47	C₃×D₂₃	—	123	1	no	—
48	D₃×C₂₃	—	123	1	no	—
49	D₃×C₂₃	—	123	1	no	—
50	D₃×C₂₃	—	246	1	no	—
51	C₃×C₄₁	—	2	1	no	—
52	C₃×C₄₁	D₃×D₂₃	1	1	yes	characteristic, complemented
53	C₃×C₄₁	D₃×D₂₃	1	1	yes	characteristic, complemented
54	C₂×D₂₃	—	369	1	no	Hall
55	C₂×C₄₁	—	69	1	no	—
56	D₄₁	—	9	1	no	—
57	D₄₁	—	69	1	no	—
58	C₃×C₂₃	—	2	1	no	—
59	C₃×C₂₃	D₃×D₄₁	1	1	yes	characteristic, complemented
60	C₃×C₂₃	C₂×D₁₂₃	1	1	yes	characteristic, complemented
61	C₂×C₂₃	—	369	1	no	—
62	D₂₃	—	3	1	no	—
63	D₂₃	—	123	1	no	—
64	C₄₁	(C₃⋊D₃)⋊D₂₃	1	1	yes	characteristic, complemented, Sylow
65	D₃²	—	943	1	no	Hall
66	C₂₃	D₃×D₁₂₃	1	1	yes	characteristic, complemented, Sylow
67	C₃⋊D₃	—	41	1	no	—
68	C₃×D₃	—	23	1	no	—
69	C₃×D₃	—	943	1	no	—
70	C₂×D₃	—	2829	1	no	—
71	C₂×D₃	—	2829	1	no	—
72	C₃²	D₂₃×D₄₁	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₃	—	2829	1	no	—
74	C₂×C₃	—	69	1	no	—
75	D₃	—	23	1	no	—
76	D₃	—	123	1	no	—
77	D₃	—	123	1	no	—
78	D₃	—	943	1	no	—
79	D₃	—	246	1	no	—
80	C₂²	—	8487	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	D₂₃×D₁₂₃	1	1	yes	characteristic, complemented
83	C₃	D₆₉⋊D₄₁	1	1	yes	characteristic, complemented
84	C₂	—	2829	1	no	—
85	C₂	—	69	1	no	—
86	C₂	—	369	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₂₃×C₄₁	C₂²
LCS	G ▷ C₃²×C₂₃×C₄₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₄₁×D₆₉	C₂	semidirect
2. C₃×D₂₈₂₉	C₂	semidirect
3. C₂₃×C₃⋊D₁₂₃	C₂	semidirect
6. C₃²×C₂₃×C₄₁	C₂²	semidirect
7. D₂₈₂₉	D₃	semidirect
8. C₄₁×D₆₉	D₃	semidirect
16. C₃×C₂₃×C₄₁	C₂×D₃	semidirect
17. C₃×C₂₃×C₄₁	C₂×D₃	semidirect
22. C₂₃×C₄₁	D₃²	semidirect
24. C₃⋊D₁₂₃	D₂₃	semidirect
31. C₃×D₆₉	D₄₁	semidirect
32. C₃²×C₄₁	C₂×D₂₃	semidirect
42. C₃²×C₂₃	C₂×D₄₁	semidirect
45. D₆₉	D₁₂₃	semidirect
52. C₃×C₄₁	D₃×D₂₃	semidirect
53. C₃×C₄₁	D₃×D₂₃	semidirect
59. C₃×C₂₃	D₃×D₄₁	semidirect
60. C₃×C₂₃	C₂×D₁₂₃	semidirect
64. C₄₁	(C₃⋊D₃)⋊D₂₃	semidirect
66. C₂₃	D₃×D₁₂₃	semidirect
72. C₃²	D₂₃×D₄₁	semidirect
82. C₃	D₂₃×D₁₂₃	semidirect
83. C₃	D₆₉⋊D₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄₁×D₆₉	2
C₃×D₂₈₂₉	2
C₂₃×C₃⋊D₁₂₃	2
D₆₉⋊D₄₁	3
D₂₃×D₁₂₃	3
D₃×D₁₂₃	23
(C₃⋊D₃)⋊D₂₃	41

Subgroups — D69⋊D123 #46800440

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₆₉⋊D₁₂₃ #46800440