Subgroups — C₃×Dic₂₂₄₇ #41004099

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	Dic₂₂₄₇	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×Dic₇₄₉	—	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	—	7	1	no	maximal, Hall
9	Dic₇₄₉	—	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	D₇	1	1	yes	characteristic
14	C₂×C₇×C₁₀₇	C₃×D₃	1	1	yes	characteristic
15	Dic₃₂₁	—	7	1	no	—
16	C₃×Dic₁₀₇	—	21	1	no	—
17	C₃²×C₁₀₇	Dic₇	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	C₃×D₇	1	1	yes	characteristic
21	C₂×C₃×C₁₀₇	D₂₁	1	1	yes	characteristic
22	Dic₁₀₇	—	21	1	no	Hall
23	C₃×C₁₀₇	—	2	1	no	—
24	C₃×C₁₀₇	C₃×Dic₇	1	1	yes	characteristic, complemented
25	C₃×C₁₀₇	Dic₂₁	1	1	yes	characteristic, complemented
26	C₃×Dic₂₁	—	107	1	no	maximal, Hall
27	C₂×C₁₀₇	C₃×D₂₁	1	1	yes	characteristic
28	C₂×C₃²×C₇	D₁₀₇	1	1	yes	characteristic
29	C₁₀₇	C₃×Dic₂₁	1	1	yes	characteristic, complemented, Sylow
30	Dic₂₁	—	107	1	no	—
31	C₃×Dic₇	—	321	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	—	749	1	no	Hall
37	Dic₇	—	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, complemented
41	C₂×C₃²	D₇₄₉	1	1	yes	characteristic
42	C₂×C₇	C₃×D₃₂₁	1	1	yes	characteristic
43	C₃×C₄	—	2247	1	no	—
44	Dic₃	—	749	1	no	—
45	C₃²	Dic₇₄₉	1	1	yes	characteristic, complemented, Sylow
46	C₇	C₃×Dic₃₂₁	1	1	yes	characteristic, complemented, Sylow
47	C₂×C₃	—	2	1	no	—
48	C₂×C₃	C₃×D₇₄₉	1	1	yes	characteristic
49	C₂×C₃	D₂₂₄₇	1	1	yes	characteristic
50	C₄	—	2247	1	no	Sylow
51	C₃	—	2	1	no	—
52	C₃	C₃×Dic₇₄₉	1	1	yes	characteristic, complemented
53	C₃	Dic₂₂₄₇	1	1	yes	characteristic, direct product factor
54	C₂	C₃×D₂₂₄₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃	D₂₂₄₇
commutator, hypocenter	C₃×C₇×C₁₀₇	C₃×C₄
Frattini	C₂	C₃×D₂₂₄₇
Fitting, socle, prime radical	C₂×C₃²×C₇×C₁₀₇	C₂
cosocle	C₂×C₃×C₇×C₁₀₇	C₂×C₃
LCS	G ▷ C₃×C₇×C₁₀₇
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
2. Dic₂₂₄₇	C₃	direct (N × H)
4. C₃²×C₇×C₁₀₇	C₄	semidirect
11. C₃×C₇×C₁₀₇	Dic₃	semidirect
12. C₃×C₇×C₁₀₇	C₃×C₄	semidirect
17. C₃²×C₁₀₇	Dic₇	semidirect
18. C₇×C₁₀₇	C₃×Dic₃	semidirect
24. C₃×C₁₀₇	C₃×Dic₇	semidirect
25. C₃×C₁₀₇	Dic₂₁	semidirect
29. C₁₀₇	C₃×Dic₂₁	semidirect
32. C₃²×C₇	Dic₁₀₇	semidirect
39. C₃×C₇	C₃×Dic₁₀₇	semidirect
40. C₃×C₇	Dic₃₂₁	semidirect
45. C₃²	Dic₇₄₉	semidirect
46. C₇	C₃×Dic₃₂₁	semidirect
52. C₃	C₃×Dic₇₄₉	semidirect
53. C₃	Dic₂₂₄₇	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
Dic₂₂₄₇	3
C₃×Dic₇₄₉	3
C₃×Dic₃₂₁	7
C₃×Dic₂₁	107

Subgroups — C3×Dic2247 #41004099

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×Dic₂₂₄₇ #41004099