Subgroups — C₃×C₇×Dic₃₂₁ #41004101

Order 26964.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₇×C₁₀₇	C₂	1	1	yes	maximal, characteristic
2	C₇×Dic₃₂₁	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₇×Dic₁₀₇	—	3	1	no	maximal
4	C₃²×C₇×C₁₀₇	C₄	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₇×C₁₀₇	—	2	1	no	—
6	C₂×C₃×C₇×C₁₀₇	D₃	1	1	yes	characteristic
7	C₂×C₃×C₇×C₁₀₇	C₂×C₃	1	1	yes	characteristic
8	C₃×Dic₃₂₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₇×Dic₁₀₇	—	3	1	no	Hall
10	C₃×C₇×C₁₀₇	—	2	1	no	—
11	C₃×C₇×C₁₀₇	Dic₃	1	1	yes	characteristic, complemented
12	C₃×C₇×C₁₀₇	C₃×C₄	1	1	yes	characteristic, complemented
13	C₂×C₃²×C₁₀₇	C₂×C₇	1	1	yes	characteristic
14	C₂×C₇×C₁₀₇	C₃×D₃	1	1	yes	characteristic
15	Dic₃₂₁	C₃×C₇	1	1	yes	characteristic, direct product factor
16	C₃×Dic₁₀₇	—	3	1	no	—
17	C₃²×C₁₀₇	C₄×C₇	1	1	yes	characteristic, complemented, Hall
18	C₇×C₁₀₇	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
19	C₂×C₃×C₁₀₇	—	2	1	no	—
20	C₂×C₃×C₁₀₇	D₃×C₇	1	1	yes	characteristic
21	C₂×C₃×C₁₀₇	C₂×C₃×C₇	1	1	yes	characteristic
22	Dic₁₀₇	—	3	1	no	Hall
23	C₃×C₁₀₇	—	2	1	no	—
24	C₃×C₁₀₇	C₇×Dic₃	1	1	yes	characteristic, complemented
25	C₃×C₁₀₇	C₃×C₄×C₇	1	1	yes	characteristic, complemented
26	C₃×C₇×Dic₃	—	107	1	no	maximal, Hall
27	C₂×C₁₀₇	C₃×D₃×C₇	1	1	yes	characteristic
28	C₂×C₃²×C₇	D₁₀₇	1	1	yes	characteristic
29	C₁₀₇	C₃×C₇×Dic₃	1	1	yes	characteristic, complemented, Sylow
30	C₃×C₄×C₇	—	321	1	no	—
31	C₇×Dic₃	—	107	1	no	—
32	C₃²×C₇	Dic₁₀₇	1	1	yes	characteristic, complemented, Hall
33	C₂×C₃×C₇	—	2	1	no	—
34	C₂×C₃×C₇	C₃×D₁₀₇	1	1	yes	characteristic
35	C₂×C₃×C₇	D₃₂₁	1	1	yes	characteristic
36	C₃×Dic₃	—	107	1	no	Hall
37	C₄×C₇	—	321	1	no	Hall
38	C₃×C₇	—	2	1	no	—
39	C₃×C₇	C₃×Dic₁₀₇	1	1	yes	characteristic, complemented
40	C₃×C₇	Dic₃₂₁	1	1	yes	characteristic, direct product factor
41	C₂×C₃²	C₇×D₁₀₇	1	1	yes	characteristic
42	C₂×C₇	C₃×D₃₂₁	1	1	yes	characteristic
43	C₃×C₄	—	321	1	no	—
44	Dic₃	—	107	1	no	—
45	C₃²	C₇×Dic₁₀₇	1	1	yes	characteristic, complemented, Sylow
46	C₇	C₃×Dic₃₂₁	1	1	yes	characteristic, direct product factor, Sylow
47	C₂×C₃	—	2	1	no	—
48	C₂×C₃	C₃×C₇×D₁₀₇	1	1	yes	characteristic
49	C₂×C₃	C₇×D₃₂₁	1	1	yes	characteristic
50	C₄	—	321	1	no	Sylow
51	C₃	—	2	1	no	—
52	C₃	C₃×C₇×Dic₁₀₇	1	1	yes	characteristic, complemented
53	C₃	C₇×Dic₃₂₁	1	1	yes	characteristic, direct product factor
54	C₂	C₃×C₇×D₃₂₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₇	D₃₂₁
commutator, hypocenter	C₃×C₁₀₇	C₃×C₄×C₇
Frattini	C₂	C₃×C₇×D₃₂₁
Fitting, socle, prime radical	C₂×C₃²×C₇×C₁₀₇	C₂
cosocle	C₂×C₃×C₁₀₇	C₂×C₃×C₇
LCS	G ▷ C₃×C₁₀₇
UCS	C₁ ◁ C₂×C₃×C₇

Complements

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

N	H ≅ G/N	type
2. C₇×Dic₃₂₁	C₃	direct (N × H)
4. C₃²×C₇×C₁₀₇	C₄	semidirect
8. C₃×Dic₃₂₁	C₇	direct (N × H)
11. C₃×C₇×C₁₀₇	Dic₃	semidirect
12. C₃×C₇×C₁₀₇	C₃×C₄	semidirect
15. Dic₃₂₁	C₃×C₇	direct (N × H)
17. C₃²×C₁₀₇	C₄×C₇	semidirect
18. C₇×C₁₀₇	C₃×Dic₃	semidirect
24. C₃×C₁₀₇	C₇×Dic₃	semidirect
25. C₃×C₁₀₇	C₃×C₄×C₇	semidirect
29. C₁₀₇	C₃×C₇×Dic₃	semidirect
32. C₃²×C₇	Dic₁₀₇	semidirect
39. C₃×C₇	C₃×Dic₁₀₇	semidirect
40. C₃×C₇	Dic₃₂₁	direct (N × H)
45. C₃²	C₇×Dic₁₀₇	semidirect
46. C₇	C₃×Dic₃₂₁	direct (N × H)
52. C₃	C₃×C₇×Dic₁₀₇	semidirect
53. C₃	C₇×Dic₃₂₁	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×C₇×C₁₀₇	2
C₇×Dic₃₂₁	3
C₃×C₇×Dic₁₀₇	3
C₃×Dic₃₂₁	7
C₃×C₇×Dic₃	107

Subgroups — C3×C7×Dic321 #41004101

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇×Dic₃₂₁ #41004101