Subgroups — D₃×D₂₈₂₁ #46799598

Order 33852.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₈₄₆₃	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₇×C₁₃×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₂₈₂₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₂₈₂₁	—	3	1	no	maximal, Hall
5	C₃×C₇×C₁₃×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₂₈₂₁	—	3	1	no	—
7	D₂₈₂₁	D₃	1	1	yes	characteristic, direct product factor
8	C₂×C₇×C₁₃×C₃₁	—	3	1	no	—
9	D₃×D₄₀₃	—	7	1	no	maximal, Hall
10	C₇×C₁₃×C₃₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	D₃×D₂₁₇	—	13	1	no	maximal, Hall
12	D₁₂₀₉	—	7	1	no	—
13	D₃×C₁₃×C₃₁	D₇	1	1	yes	characteristic, complemented
14	C₃×D₄₀₃	—	7	1	no	—
15	C₂×D₄₀₃	—	21	1	no	Hall
16	D₆₅₁	—	13	1	no	—
17	D₃×C₇×C₃₁	D₁₃	1	1	yes	characteristic, complemented
18	C₃×D₂₁₇	—	13	1	no	—
19	C₃×C₁₃×C₃₁	C₂×D₇	1	1	yes	characteristic, complemented, Hall
20	D₃×D₉₁	—	31	1	no	maximal, Hall
21	C₂×D₂₁₇	—	39	1	no	Hall
22	C₂×C₁₃×C₃₁	—	3	1	no	—
23	D₄₀₃	—	7	1	no	—
24	D₄₀₃	—	21	1	no	—
25	C₃×C₇×C₃₁	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
26	D₂₇₃	—	31	1	no	—
27	D₃×C₇×C₁₃	D₃₁	1	1	yes	characteristic, complemented
28	C₃×D₉₁	—	31	1	no	—
29	C₂×C₇×C₃₁	—	3	1	no	—
30	D₂₁₇	—	13	1	no	—
31	D₂₁₇	—	39	1	no	—
32	C₁₃×C₃₁	D₃×D₇	1	1	yes	characteristic, complemented, Hall
33	D₃×D₃₁	—	91	1	no	Hall
34	C₂×D₉₁	—	93	1	no	Hall
35	C₃×C₇×C₁₃	C₂×D₃₁	1	1	yes	characteristic, complemented, Hall
36	C₇×C₃₁	D₃×D₁₃	1	1	yes	characteristic, complemented, Hall
37	D₉₃	—	91	1	no	—
38	C₃×D₃₁	—	91	1	no	—
39	D₃×C₃₁	D₉₁	1	1	yes	characteristic, complemented
40	C₂×C₇×C₁₃	—	3	1	no	—
41	D₉₁	—	31	1	no	—
42	D₉₁	—	93	1	no	—
43	D₃×D₁₃	—	217	1	no	Hall
44	C₂×D₃₁	—	273	1	no	Hall
45	C₃×C₃₁	C₂×D₉₁	1	1	yes	characteristic, complemented, Hall
46	C₇×C₁₃	D₃×D₃₁	1	1	yes	characteristic, complemented, Hall
47	D₃×D₇	—	403	1	no	Hall
48	D₃₉	—	217	1	no	—
49	C₃×D₁₃	—	217	1	no	—
50	D₃×C₁₃	D₂₁₇	1	1	yes	characteristic, complemented
51	C₂×C₃₁	—	3	1	no	—
52	D₃₁	—	273	1	no	—
53	D₃₁	—	91	1	no	—
54	C₂×D₁₃	—	651	1	no	Hall
55	D₂₁	—	403	1	no	—
56	C₃×D₇	—	403	1	no	—
57	D₃×C₇	D₄₀₃	1	1	yes	characteristic, complemented
58	C₃×C₁₃	C₂×D₂₁₇	1	1	yes	characteristic, complemented, Hall
59	C₃₁	D₃×D₉₁	1	1	yes	characteristic, complemented, Sylow
60	C₂×D₇	—	1209	1	no	Hall
61	C₂×C₁₃	—	3	1	no	—
62	D₁₃	—	651	1	no	—
63	D₁₃	—	217	1	no	—
64	C₃×C₇	C₂×D₄₀₃	1	1	yes	characteristic, complemented, Hall
65	C₂×C₇	—	3	1	no	—
66	D₇	—	403	1	no	—
67	D₇	—	1209	1	no	—
68	C₁₃	D₃×D₂₁₇	1	1	yes	characteristic, complemented, Sylow
69	C₂×D₃	—	2821	1	no	Hall
70	C₇	D₃×D₄₀₃	1	1	yes	characteristic, complemented, Sylow
71	C₂×C₃	—	2821	1	no	—
72	D₃	—	2821	1	no	—
73	D₃	D₂₈₂₁	1	1	yes	characteristic, direct product factor
74	C₂²	—	8463	1	no	Sylow
75	C₃	C₂×D₂₈₂₁	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	3	1	no	—
77	C₂	—	2821	1	no	—
78	C₂	—	8463	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₇×C₁₃×C₃₁	C₂²
LCS	G ▷ C₃×C₇×C₁₃×C₃₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₈₄₆₃	C₂	semidirect
2. D₃×C₇×C₁₃×C₃₁	C₂	semidirect
3. C₃×D₂₈₂₁	C₂	semidirect
5. C₃×C₇×C₁₃×C₃₁	C₂²	semidirect
7. D₂₈₂₁	D₃	direct (N × H)
10. C₇×C₁₃×C₃₁	C₂×D₃	semidirect
13. D₃×C₁₃×C₃₁	D₇	semidirect
17. D₃×C₇×C₃₁	D₁₃	semidirect
19. C₃×C₁₃×C₃₁	C₂×D₇	semidirect
25. C₃×C₇×C₃₁	C₂×D₁₃	semidirect
27. D₃×C₇×C₁₃	D₃₁	semidirect
32. C₁₃×C₃₁	D₃×D₇	semidirect
35. C₃×C₇×C₁₃	C₂×D₃₁	semidirect
36. C₇×C₃₁	D₃×D₁₃	semidirect
39. D₃×C₃₁	D₉₁	semidirect
45. C₃×C₃₁	C₂×D₉₁	semidirect
46. C₇×C₁₃	D₃×D₃₁	semidirect
50. D₃×C₁₃	D₂₁₇	semidirect
57. D₃×C₇	D₄₀₃	semidirect
58. C₃×C₁₃	C₂×D₂₁₇	semidirect
59. C₃₁	D₃×D₉₁	semidirect
64. C₃×C₇	C₂×D₄₀₃	semidirect
68. C₁₃	D₃×D₂₁₇	semidirect
70. C₇	D₃×D₄₀₃	semidirect
73. D₃	D₂₈₂₁	direct (N × H)
75. C₃	C₂×D₂₈₂₁	semidirect

Maximal subgroups

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

subgroup	index
D₈₄₆₃	2
D₃×C₇×C₁₃×C₃₁	2
C₃×D₂₈₂₁	2
C₂×D₂₈₂₁	3
D₃×D₄₀₃	7
D₃×D₂₁₇	13
D₃×D₉₁	31

Subgroups — D3×D2821 #46799598

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×D₂₈₂₁ #46799598