Subgroups — C₃×D₃×D₈₇₁ #44535792

Order 31356.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₈₇₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₃×C₁₃×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₂₆₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×D₈₇₁	—	3	1	no	maximal
5	D₃×D₈₇₁	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₃²×C₁₃×C₆₇	C₂²	1	1	yes	characteristic, complemented, Hall
7	D₂₆₁₃	C₂×C₃	1	1	yes	characteristic, complemented
8	D₃×C₁₃×C₆₇	C₂×C₃	1	1	yes	characteristic, complemented
9	C₃×D₈₇₁	—	2	1	no	—
10	C₃×D₈₇₁	—	3	1	no	—
11	C₃×D₈₇₁	D₃	1	1	yes	characteristic, direct product factor
12	C₃×D₈₇₁	C₂×C₃	1	1	yes	characteristic, complemented
13	C₂×C₃×C₁₃×C₆₇	—	3	1	no	—
14	C₂×D₈₇₁	—	3	1	no	Hall
15	C₃×C₁₃×C₆₇	—	2	1	no	—
16	C₃×C₁₃×C₆₇	C₂×D₃	1	1	yes	characteristic, complemented
17	C₃×C₁₃×C₆₇	C₂²×C₃	1	1	yes	characteristic, complemented
18	C₃×D₃×D₆₇	—	13	1	no	maximal, Hall
19	C₂×C₁₃×C₆₇	—	3	1	no	—
20	D₈₇₁	—	3	1	no	—
21	D₈₇₁	C₃×D₃	1	1	yes	characteristic, direct product factor
22	C₃×D₂₀₁	—	13	1	no	—
23	C₃×D₃×C₆₇	D₁₃	1	1	yes	characteristic, complemented
24	C₃²×D₆₇	—	13	1	no	—
25	C₁₃×C₆₇	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
26	C₂×C₃×D₆₇	—	39	1	no	—
27	D₃×D₆₇	—	13	1	no	—
28	C₃²×C₆₇	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
29	C₃×D₃×D₁₃	—	67	1	no	maximal, Hall
30	C₂×C₃×C₆₇	—	3	1	no	—
31	D₂₀₁	—	13	1	no	—
32	C₃×D₆₇	—	13	1	no	—
33	C₃×D₆₇	—	13	1	no	—
34	C₃×D₆₇	—	26	1	no	—
35	C₃×D₆₇	—	39	1	no	—
36	D₃×C₆₇	C₃×D₁₃	1	1	yes	characteristic, complemented
37	C₂×D₆₇	—	39	1	no	Hall
38	C₃×D₃₉	—	67	1	no	—
39	C₃×D₃×C₁₃	D₆₇	1	1	yes	characteristic, complemented
40	C₃²×D₁₃	—	67	1	no	—
41	C₃×C₆₇	—	2	1	no	—
42	C₃×C₆₇	D₃×D₁₃	1	1	yes	characteristic, complemented
43	C₃×C₆₇	C₂×C₃×D₁₃	1	1	yes	characteristic, complemented
44	C₂×C₃×D₁₃	—	201	1	no	—
45	D₃×D₁₃	—	67	1	no	—
46	C₂×C₆₇	—	3	1	no	—
47	D₆₇	—	13	1	no	—
48	D₆₇	—	39	1	no	—
49	C₃²×C₁₃	C₂×D₆₇	1	1	yes	characteristic, complemented, Hall
50	C₂×C₃×C₁₃	—	3	1	no	—
51	D₃₉	—	67	1	no	—
52	C₃×D₁₃	—	67	1	no	—
53	C₃×D₁₃	—	67	1	no	—
54	C₃×D₁₃	—	134	1	no	—
55	C₃×D₁₃	—	201	1	no	—
56	D₃×C₁₃	C₃×D₆₇	1	1	yes	characteristic, complemented
57	C₆₇	C₃×D₃×D₁₃	1	1	yes	characteristic, complemented, Sylow
58	C₂×D₁₃	—	201	1	no	Hall
59	C₃×C₁₃	—	2	1	no	—
60	C₃×C₁₃	D₃×D₆₇	1	1	yes	characteristic, complemented
61	C₃×C₁₃	C₂×C₃×D₆₇	1	1	yes	characteristic, complemented
62	C₂×C₃×D₃	—	871	1	no	Hall
63	C₂×C₁₃	—	3	1	no	—
64	D₁₃	—	67	1	no	—
65	D₁₃	—	201	1	no	—
66	C₂×C₃²	—	871	1	no	—
67	C₃×D₃	—	871	1	no	—
68	C₃×D₃	D₈₇₁	1	1	yes	characteristic, direct product factor
69	C₁₃	C₃×D₃×D₆₇	1	1	yes	characteristic, complemented, Sylow
70	C₂²×C₃	—	2613	1	no	—
71	C₂×D₃	—	871	1	no	—
72	C₃²	C₂×D₈₇₁	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₃	—	3	1	no	—
74	C₂×C₃	—	2613	1	no	—
75	C₂×C₃	—	871	1	no	—
76	C₂×C₃	—	871	1	no	—
77	C₂×C₃	—	1742	1	no	—
78	D₃	—	871	1	no	—
79	D₃	C₃×D₈₇₁	1	1	yes	characteristic, direct product factor
80	C₂²	—	2613	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	D₃×D₈₇₁	1	1	yes	characteristic, direct product factor
83	C₃	C₂×C₃×D₈₇₁	1	1	yes	characteristic, complemented
84	C₂	—	3	1	no	—
85	C₂	—	2613	1	no	—
86	C₂	—	871	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₃×D₈₇₁
commutator, cosocle, hypocenter	C₃×C₁₃×C₆₇	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃²×C₁₃×C₆₇	C₂²
LCS	G ▷ C₃×C₁₃×C₆₇
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃²×D₈₇₁	C₂	semidirect
2. C₃×D₃×C₁₃×C₆₇	C₂	semidirect
3. C₃×D₂₆₁₃	C₂	semidirect
5. D₃×D₈₇₁	C₃	direct (N × H)
6. C₃²×C₁₃×C₆₇	C₂²	semidirect
7. D₂₆₁₃	C₂×C₃	semidirect
8. D₃×C₁₃×C₆₇	C₂×C₃	semidirect
11. C₃×D₈₇₁	D₃	direct (N × H)
12. C₃×D₈₇₁	C₂×C₃	semidirect
16. C₃×C₁₃×C₆₇	C₂×D₃	semidirect
17. C₃×C₁₃×C₆₇	C₂²×C₃	semidirect
21. D₈₇₁	C₃×D₃	direct (N × H)
23. C₃×D₃×C₆₇	D₁₃	semidirect
25. C₁₃×C₆₇	C₂×C₃×D₃	semidirect
28. C₃²×C₆₇	C₂×D₁₃	semidirect
36. D₃×C₆₇	C₃×D₁₃	semidirect
39. C₃×D₃×C₁₃	D₆₇	semidirect
42. C₃×C₆₇	D₃×D₁₃	semidirect
43. C₃×C₆₇	C₂×C₃×D₁₃	semidirect
49. C₃²×C₁₃	C₂×D₆₇	semidirect
56. D₃×C₁₃	C₃×D₆₇	semidirect
57. C₆₇	C₃×D₃×D₁₃	semidirect
60. C₃×C₁₃	D₃×D₆₇	semidirect
61. C₃×C₁₃	C₂×C₃×D₆₇	semidirect
68. C₃×D₃	D₈₇₁	direct (N × H)
69. C₁₃	C₃×D₃×D₆₇	semidirect
72. C₃²	C₂×D₈₇₁	semidirect
79. D₃	C₃×D₈₇₁	direct (N × H)
82. C₃	D₃×D₈₇₁	direct (N × H)
83. C₃	C₂×C₃×D₈₇₁	semidirect

Maximal subgroups

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

subgroup	index
C₃²×D₈₇₁	2
C₃×D₃×C₁₃×C₆₇	2
C₃×D₂₆₁₃	2
C₂×C₃×D₈₇₁	3
D₃×D₈₇₁	3
C₃×D₃×D₆₇	13
C₃×D₃×D₁₃	67

Subgroups — C3×D3×D871 #44535792

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃×D₈₇₁ #44535792