Subgroups — D₃₁×D₂₇₃ #46799583

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

Maximal subgroups

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

subgroup	index
D₈₄₆₃	2
C₃₁×D₂₇₃	2
C₃×C₇×C₁₃×D₃₁	2
D₃₁×D₉₁	3
D₃₁×D₃₉	7
D₂₁×D₃₁	13
C₂×D₂₇₃	31

Subgroups — D31×D273 #46799583

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃₁×D₂₇₃ #46799583