Subgroups — D₉×D₇₃₇ #40997607

Order 26532.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₆₆₃₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×D₉×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×D₇₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×D₇₃₇	—	3	1	no	maximal
5	C₉×C₁₁×C₆₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₂₂₁₁	—	3	1	no	—
7	D₃×C₁₁×C₆₇	—	3	1	no	—
8	C₃×D₇₃₇	D₃	1	1	yes	characteristic
9	C₂×D₇₃₇	—	9	1	no	Hall
10	D₉×D₆₇	—	11	1	no	maximal, Hall
11	C₃×C₁₁×C₆₇	C₂×D₃	1	1	yes	characteristic
12	C₂×C₁₁×C₆₇	—	9	1	no	—
13	D₇₃₇	—	9	1	no	—
14	D₇₃₇	D₉	1	1	yes	characteristic, direct product factor
15	D₆₀₃	—	11	1	no	—
16	C₉×D₆₇	—	11	1	no	—
17	D₉×C₆₇	D₁₁	1	1	yes	characteristic, complemented
18	D₃×D₆₇	—	33	1	no	—
19	C₁₁×C₆₇	C₂×D₉	1	1	yes	characteristic, complemented, Hall
20	C₉×C₆₇	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
21	D₂₀₁	—	33	1	no	—
22	C₃×D₆₇	—	11	1	no	—
23	D₃×C₆₇	—	3	1	no	—
24	D₉×D₁₁	—	67	1	no	maximal, Hall
25	C₂×D₆₇	—	99	1	no	Hall
26	C₃×C₆₇	D₃×D₁₁	1	1	yes	characteristic
27	D₉₉	—	67	1	no	—
28	C₉×D₁₁	—	67	1	no	—
29	C₁₁×D₉	D₆₇	1	1	yes	characteristic, complemented
30	C₂×C₆₇	—	9	1	no	—
31	D₆₇	—	11	1	no	—
32	D₆₇	—	99	1	no	—
33	D₃×D₁₁	—	201	1	no	—
34	C₉×C₁₁	C₂×D₆₇	1	1	yes	characteristic, complemented, Hall
35	C₆₇	D₉×D₁₁	1	1	yes	characteristic, complemented, Sylow
36	D₃₃	—	201	1	no	—
37	C₃×D₁₁	—	67	1	no	—
38	D₃×C₁₁	—	3	1	no	—
39	C₂×D₁₁	—	603	1	no	Hall
40	C₂×D₉	—	737	1	no	Hall
41	C₃×C₁₁	D₃×D₆₇	1	1	yes	characteristic
42	C₂×C₁₁	—	9	1	no	—
43	D₁₁	—	67	1	no	—
44	D₁₁	—	603	1	no	—
45	C₂×C₉	—	737	1	no	—
46	D₉	—	737	1	no	—
47	D₉	D₇₃₇	1	1	yes	characteristic, direct product factor
48	C₂×D₃	—	2211	1	no	—
49	C₁₁	D₉×D₆₇	1	1	yes	characteristic, complemented, Sylow
50	C₉	C₂×D₇₃₇	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃	—	737	1	no	—
52	D₃	—	3	1	no	—
53	D₃	—	2211	1	no	—
54	C₂²	—	6633	1	no	Sylow
55	C₃	D₃×D₇₃₇	1	1	yes	characteristic
56	C₂	—	9	1	no	—
57	C₂	—	737	1	no	—
58	C₂	—	6633	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₁₁×C₆₇	C₂²
Frattini	C₃	D₃×D₇₃₇
socle	C₃×C₁₁×C₆₇	C₂×D₃
LCS	G ▷ C₉×C₁₁×C₆₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₆₆₃₃	C₂	semidirect
2. C₁₁×D₉×C₆₇	C₂	semidirect
3. C₉×D₇₃₇	C₂	semidirect
5. C₉×C₁₁×C₆₇	C₂²	semidirect
14. D₇₃₇	D₉	direct (N × H)
17. D₉×C₆₇	D₁₁	semidirect
19. C₁₁×C₆₇	C₂×D₉	semidirect
20. C₉×C₆₇	C₂×D₁₁	semidirect
29. C₁₁×D₉	D₆₇	semidirect
34. C₉×C₁₁	C₂×D₆₇	semidirect
35. C₆₇	D₉×D₁₁	semidirect
47. D₉	D₇₃₇	direct (N × H)
49. C₁₁	D₉×D₆₇	semidirect
50. C₉	C₂×D₇₃₇	semidirect

Maximal subgroups

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

subgroup	index
D₆₆₃₃	2
C₁₁×D₉×C₆₇	2
C₉×D₇₃₇	2
D₃×D₇₃₇	3
D₉×D₆₇	11
D₉×D₁₁	67

Subgroups — D9×D737 #40997607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₉×D₇₃₇ #40997607