Subgroups — C₃⋊D₃×D₁₁×C₆₇ #40997709

Order 26532.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₁₁×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×C₃⋊D₃×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×C₃⋊D₃₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×D₁₁×C₆₇	—	3	4	no	maximal
5	C₃²×C₁₁×C₆₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃₃×C₆₇	—	3	4	no	—
7	D₃×C₁₁×C₆₇	—	3	4	no	—
8	C₃×D₁₁×C₆₇	D₃	1	4	yes	complemented
9	C₂×D₁₁×C₆₇	—	9	1	no	Hall
10	C₂×C₃⋊D₃×C₆₇	—	11	1	no	maximal, Hall
11	C₃×C₁₁×C₆₇	C₂×D₃	1	4	yes	complemented
12	C₂×C₁₁×C₆₇	—	9	1	no	—
13	D₁₁×C₆₇	—	9	1	no	—
14	D₁₁×C₆₇	C₃⋊D₃	1	1	yes	characteristic, direct product factor
15	C₂×C₃²×C₆₇	—	11	1	no	—
16	C₃⋊D₃×C₆₇	—	11	1	no	—
17	C₃⋊D₃×C₆₇	D₁₁	1	1	yes	characteristic, direct product factor
18	C₂×D₃×C₆₇	—	33	4	no	—
19	C₁₁×C₆₇	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
20	C₃²×C₆₇	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×C₆₇	—	11	4	no	—
22	D₃×C₆₇	—	3	4	no	—
23	D₃×C₆₇	—	33	4	no	—
24	C₃⋊D₃×D₁₁	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₂²×C₆₇	—	99	1	no	Hall
26	C₃×C₆₇	D₃×D₁₁	1	4	yes	complemented
27	C₃⋊D₃₃	C₂×C₆₇	1	1	yes	characteristic, complemented
28	C₁₁×C₃⋊D₃	C₂×C₆₇	1	1	yes	characteristic, complemented
29	C₃²×D₁₁	C₂×C₆₇	1	1	yes	characteristic, complemented
30	C₂×C₆₇	—	9	1	no	—
31	C₂×C₆₇	—	11	1	no	—
32	C₂×C₆₇	—	99	1	no	—
33	D₃×D₁₁	—	3	4	no	—
34	C₃²×C₁₁	C₂²×C₆₇	1	1	yes	characteristic, complemented, Hall
35	C₆₇	C₃⋊D₃×D₁₁	1	1	yes	characteristic, direct product factor, Sylow
36	D₃₃	—	3	4	no	—
37	C₃×D₁₁	D₃×C₆₇	1	4	yes	complemented
38	D₃×C₁₁	—	3	4	no	—
39	C₂×D₁₁	—	9	1	no	Hall
40	C₂×C₃⋊D₃	—	11	1	no	Hall
41	C₃×C₁₁	C₂×D₃×C₆₇	1	4	yes	complemented
42	C₂×C₁₁	—	9	1	no	—
43	D₁₁	—	9	1	no	—
44	D₁₁	C₃⋊D₃×C₆₇	1	1	yes	characteristic, direct product factor
45	C₂×C₃²	—	11	1	no	—
46	C₃⋊D₃	—	11	1	no	—
47	C₃⋊D₃	D₁₁×C₆₇	1	1	yes	characteristic, direct product factor
48	C₂×D₃	—	33	4	no	—
49	C₁₁	C₂×C₃⋊D₃×C₆₇	1	1	yes	characteristic, complemented, Sylow
50	C₃²	C₂×D₁₁×C₆₇	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃	—	11	4	no	—
52	D₃	—	3	4	no	—
53	D₃	—	33	4	no	—
54	C₂²	—	99	1	no	Sylow
55	C₃	D₃×D₁₁×C₆₇	1	4	yes	complemented
56	C₂	—	9	1	no	—
57	C₂	—	11	1	no	—
58	C₂	—	99	1	no	—

	subgroup	G/H
center, hypercenter	C₆₇	C₃⋊D₃×D₁₁
commutator, cosocle, hypocenter	C₃²×C₁₁	C₂²×C₆₇
Frattini	C₁	G
Fitting, socle	C₃²×C₁₁×C₆₇	C₂²
LCS	G ▷ C₃²×C₁₁
UCS	C₁ ◁ C₆₇

Complements

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

N	H ≅ G/N	type
1. C₃²×D₁₁×C₆₇	C₂	semidirect
2. C₁₁×C₃⋊D₃×C₆₇	C₂	semidirect
3. C₆₇×C₃⋊D₃₃	C₂	semidirect
5. C₃²×C₁₁×C₆₇	C₂²	semidirect
8. C₃×D₁₁×C₆₇	D₃	semidirect
11. C₃×C₁₁×C₆₇	C₂×D₃	semidirect
14. D₁₁×C₆₇	C₃⋊D₃	direct (N × H)
17. C₃⋊D₃×C₆₇	D₁₁	direct (N × H)
19. C₁₁×C₆₇	C₂×C₃⋊D₃	semidirect
20. C₃²×C₆₇	C₂×D₁₁	semidirect
24. C₃⋊D₃×D₁₁	C₆₇	direct (N × H)
26. C₃×C₆₇	D₃×D₁₁	semidirect
27. C₃⋊D₃₃	C₂×C₆₇	semidirect
28. C₁₁×C₃⋊D₃	C₂×C₆₇	semidirect
29. C₃²×D₁₁	C₂×C₆₇	semidirect
34. C₃²×C₁₁	C₂²×C₆₇	semidirect
35. C₆₇	C₃⋊D₃×D₁₁	direct (N × H)
37. C₃×D₁₁	D₃×C₆₇	semidirect
41. C₃×C₁₁	C₂×D₃×C₆₇	semidirect
44. D₁₁	C₃⋊D₃×C₆₇	direct (N × H)
47. C₃⋊D₃	D₁₁×C₆₇	direct (N × H)
49. C₁₁	C₂×C₃⋊D₃×C₆₇	semidirect
50. C₃²	C₂×D₁₁×C₆₇	semidirect
55. C₃	D₃×D₁₁×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₃²×D₁₁×C₆₇	2
C₁₁×C₃⋊D₃×C₆₇	2
C₆₇×C₃⋊D₃₃	2
D₃×D₁₁×C₆₇	3
C₂×C₃⋊D₃×C₆₇	11
C₃⋊D₃×D₁₁	67

Subgroups — C3⋊D3×D11×C67 #40997709

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊D₃×D₁₁×C₆₇ #40997709