Subgroups — C₃×C₆₇×Dic₃₃ #40997643

Order 26532.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₁₁×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₆₇×Dic₃₃	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×Dic₁₁×C₆₇	—	3	1	no	maximal
4	C₃²×C₁₁×C₆₇	C₄	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₁₁×C₆₇	—	2	1	no	—
6	C₂×C₃×C₁₁×C₆₇	D₃	1	1	yes	characteristic
7	C₂×C₃×C₁₁×C₆₇	C₂×C₃	1	1	yes	characteristic
8	Dic₁₁×C₆₇	—	3	1	no	Hall
9	C₃×Dic₃×C₆₇	—	11	1	no	maximal, Hall
10	C₃×C₁₁×C₆₇	—	2	1	no	—
11	C₃×C₁₁×C₆₇	Dic₃	1	1	yes	characteristic, complemented
12	C₃×C₁₁×C₆₇	C₃×C₄	1	1	yes	characteristic, complemented
13	C₂×C₁₁×C₆₇	C₃×D₃	1	1	yes	characteristic
14	C₂×C₃²×C₆₇	D₁₁	1	1	yes	characteristic
15	C₃×C₄×C₆₇	—	33	1	no	—
16	Dic₃×C₆₇	—	11	1	no	—
17	C₁₁×C₆₇	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
18	C₃²×C₆₇	Dic₁₁	1	1	yes	characteristic, complemented, Hall
19	C₂×C₃×C₆₇	—	2	1	no	—
20	C₂×C₃×C₆₇	C₃×D₁₁	1	1	yes	characteristic
21	C₂×C₃×C₆₇	D₃₃	1	1	yes	characteristic
22	C₃×Dic₃₃	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
23	C₄×C₆₇	—	33	1	no	Hall
24	C₃×C₆₇	—	2	1	no	—
25	C₃×C₆₇	C₃×Dic₁₁	1	1	yes	characteristic, complemented
26	C₃×C₆₇	Dic₃₃	1	1	yes	characteristic, direct product factor
27	C₂×C₃²×C₁₁	C₂×C₆₇	1	1	yes	characteristic
28	C₂×C₆₇	C₃×D₃₃	1	1	yes	characteristic
29	Dic₃₃	C₃×C₆₇	1	1	yes	characteristic, direct product factor
30	C₃×Dic₁₁	—	3	1	no	—
31	C₃²×C₁₁	C₄×C₆₇	1	1	yes	characteristic, complemented, Hall
32	C₆₇	C₃×Dic₃₃	1	1	yes	characteristic, direct product factor, Sylow
33	C₂×C₃×C₁₁	—	2	1	no	—
34	C₂×C₃×C₁₁	D₃×C₆₇	1	1	yes	characteristic
35	C₂×C₃×C₁₁	C₂×C₃×C₆₇	1	1	yes	characteristic
36	Dic₁₁	—	3	1	no	Hall
37	C₃×Dic₃	—	11	1	no	Hall
38	C₃×C₁₁	—	2	1	no	—
39	C₃×C₁₁	Dic₃×C₆₇	1	1	yes	characteristic, complemented
40	C₃×C₁₁	C₃×C₄×C₆₇	1	1	yes	characteristic, complemented
41	C₂×C₁₁	C₃×D₃×C₆₇	1	1	yes	characteristic
42	C₂×C₃²	D₁₁×C₆₇	1	1	yes	characteristic
43	C₃×C₄	—	33	1	no	—
44	Dic₃	—	11	1	no	—
45	C₁₁	C₃×Dic₃×C₆₇	1	1	yes	characteristic, complemented, Sylow
46	C₃²	Dic₁₁×C₆₇	1	1	yes	characteristic, complemented, Sylow
47	C₂×C₃	—	2	1	no	—
48	C₂×C₃	C₃×D₁₁×C₆₇	1	1	yes	characteristic
49	C₂×C₃	D₃₃×C₆₇	1	1	yes	characteristic
50	C₄	—	33	1	no	Sylow
51	C₃	—	2	1	no	—
52	C₃	C₃×Dic₁₁×C₆₇	1	1	yes	characteristic, complemented
53	C₃	C₆₇×Dic₃₃	1	1	yes	characteristic, direct product factor
54	C₂	C₃×D₃₃×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₆₇	D₃₃
commutator, hypocenter	C₃×C₁₁	C₃×C₄×C₆₇
Frattini	C₂	C₃×D₃₃×C₆₇
Fitting, socle, prime radical	C₂×C₃²×C₁₁×C₆₇	C₂
cosocle	C₂×C₃×C₁₁	C₂×C₃×C₆₇
LCS	G ▷ C₃×C₁₁
UCS	C₁ ◁ C₂×C₃×C₆₇

Complements

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

N	H ≅ G/N	type
2. C₆₇×Dic₃₃	C₃	direct (N × H)
4. C₃²×C₁₁×C₆₇	C₄	semidirect
11. C₃×C₁₁×C₆₇	Dic₃	semidirect
12. C₃×C₁₁×C₆₇	C₃×C₄	semidirect
17. C₁₁×C₆₇	C₃×Dic₃	semidirect
18. C₃²×C₆₇	Dic₁₁	semidirect
22. C₃×Dic₃₃	C₆₇	direct (N × H)
25. C₃×C₆₇	C₃×Dic₁₁	semidirect
26. C₃×C₆₇	Dic₃₃	direct (N × H)
29. Dic₃₃	C₃×C₆₇	direct (N × H)
31. C₃²×C₁₁	C₄×C₆₇	semidirect
32. C₆₇	C₃×Dic₃₃	direct (N × H)
39. C₃×C₁₁	Dic₃×C₆₇	semidirect
40. C₃×C₁₁	C₃×C₄×C₆₇	semidirect
45. C₁₁	C₃×Dic₃×C₆₇	semidirect
46. C₃²	Dic₁₁×C₆₇	semidirect
52. C₃	C₃×Dic₁₁×C₆₇	semidirect
53. C₃	C₆₇×Dic₃₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₁₁×C₆₇	2
C₆₇×Dic₃₃	3
C₃×Dic₁₁×C₆₇	3
C₃×Dic₃×C₆₇	11
C₃×Dic₃₃	67

Subgroups — C3×C67×Dic33 #40997643

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₆₇×Dic₃₃ #40997643