Subgroups — D₉×D₁₃×C₆₇ #44535621

Order 31356.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×D₁₁₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×D₉×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×D₁₃×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×D₁₃×C₆₇	—	3	1	no	maximal
5	C₉×C₁₃×C₆₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₆₇×D₃₉	—	3	1	no	—
7	D₃×C₁₃×C₆₇	—	3	1	no	—
8	C₃×D₁₃×C₆₇	D₃	1	1	yes	characteristic
9	C₂×D₁₃×C₆₇	—	9	1	no	Hall
10	C₃×C₁₃×C₆₇	C₂×D₃	1	1	yes	characteristic
11	C₂×D₉×C₆₇	—	13	1	no	maximal, Hall
12	C₂×C₁₃×C₆₇	—	9	1	no	—
13	D₁₃×C₆₇	—	9	1	no	—
14	D₁₃×C₆₇	D₉	1	1	yes	characteristic, direct product factor
15	C₂×C₉×C₆₇	—	13	1	no	—
16	D₉×C₆₇	—	13	1	no	—
17	D₉×C₆₇	D₁₃	1	1	yes	characteristic, direct product factor
18	C₁₃×C₆₇	C₂×D₉	1	1	yes	characteristic, complemented, Hall
19	C₂×D₃×C₆₇	—	39	1	no	—
20	C₉×C₆₇	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
21	D₉×D₁₃	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂×C₃×C₆₇	—	13	1	no	—
23	D₃×C₆₇	—	3	1	no	—
24	D₃×C₆₇	—	39	1	no	—
25	C₂²×C₆₇	—	117	1	no	Hall
26	D₁₁₇	C₂×C₆₇	1	1	yes	characteristic, complemented
27	C₉×D₁₃	C₂×C₆₇	1	1	yes	characteristic, complemented
28	C₁₃×D₉	C₂×C₆₇	1	1	yes	characteristic, complemented
29	C₃×C₆₇	D₃×D₁₃	1	1	yes	characteristic
30	D₃×D₁₃	—	3	1	no	—
31	C₂×C₆₇	—	9	1	no	—
32	C₂×C₆₇	—	13	1	no	—
33	C₂×C₆₇	—	117	1	no	—
34	C₉×C₁₃	C₂²×C₆₇	1	1	yes	characteristic, complemented, Hall
35	D₃₉	—	3	1	no	—
36	C₃×D₁₃	D₃×C₆₇	1	1	yes	characteristic
37	D₃×C₁₃	—	3	1	no	—
38	C₆₇	D₉×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
39	C₂×D₁₃	—	9	1	no	Hall
40	C₃×C₁₃	C₂×D₃×C₆₇	1	1	yes	characteristic
41	C₂×D₉	—	13	1	no	Hall
42	C₂×C₁₃	—	9	1	no	—
43	D₁₃	—	9	1	no	—
44	D₁₃	D₉×C₆₇	1	1	yes	characteristic, direct product factor
45	C₂×C₉	—	13	1	no	—
46	D₉	—	13	1	no	—
47	D₉	D₁₃×C₆₇	1	1	yes	characteristic, direct product factor
48	C₁₃	C₂×D₉×C₆₇	1	1	yes	characteristic, complemented, Sylow
49	C₂×D₃	—	39	1	no	—
50	C₉	C₂×D₁₃×C₆₇	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃	—	13	1	no	—
52	D₃	—	3	1	no	—
53	D₃	—	39	1	no	—
54	C₂²	—	117	1	no	Sylow
55	C₃	D₃×D₁₃×C₆₇	1	1	yes	characteristic
56	C₂	—	9	1	no	—
57	C₂	—	13	1	no	—
58	C₂	—	117	1	no	—

	subgroup	G/H
center, hypercenter	C₆₇	D₉×D₁₃
commutator, cosocle, hypocenter	C₉×C₁₃	C₂²×C₆₇
Frattini	C₃	D₃×D₁₃×C₆₇
Fitting	C₉×C₁₃×C₆₇	C₂²
socle	C₃×C₁₃×C₆₇	C₂×D₃
LCS	G ▷ C₉×C₁₃
UCS	C₁ ◁ C₆₇

Complements

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

N	H ≅ G/N	type
1. C₆₇×D₁₁₇	C₂	semidirect
2. C₁₃×D₉×C₆₇	C₂	semidirect
3. C₉×D₁₃×C₆₇	C₂	semidirect
5. C₉×C₁₃×C₆₇	C₂²	semidirect
14. D₁₃×C₆₇	D₉	direct (N × H)
17. D₉×C₆₇	D₁₃	direct (N × H)
18. C₁₃×C₆₇	C₂×D₉	semidirect
20. C₉×C₆₇	C₂×D₁₃	semidirect
21. D₉×D₁₃	C₆₇	direct (N × H)
26. D₁₁₇	C₂×C₆₇	semidirect
27. C₉×D₁₃	C₂×C₆₇	semidirect
28. C₁₃×D₉	C₂×C₆₇	semidirect
34. C₉×C₁₃	C₂²×C₆₇	semidirect
38. C₆₇	D₉×D₁₃	direct (N × H)
44. D₁₃	D₉×C₆₇	direct (N × H)
47. D₉	D₁₃×C₆₇	direct (N × H)
48. C₁₃	C₂×D₉×C₆₇	semidirect
50. C₉	C₂×D₁₃×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×D₁₁₇	2
C₁₃×D₉×C₆₇	2
C₉×D₁₃×C₆₇	2
D₃×D₁₃×C₆₇	3
C₂×D₉×C₆₇	13
D₉×D₁₃	67

Subgroups — D9×D13×C67 #44535621

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₉×D₁₃×C₆₇ #44535621