Subgroups — C₃²×Dic₇₄₉ #41004103

Order 26964.

72 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	C₃×Dic₇₄₉	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₇×C₁₀₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₇×C₁₀₇	C₂×C₃	1	4	yes	—
5	C₃²×Dic₁₀₇	—	7	1	no	maximal, Hall
6	Dic₇₄₉	C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₃×C₇×C₁₀₇	C₃×C₄	1	4	yes	complemented
8	C₂×C₃²×C₁₀₇	D₇	1	1	yes	characteristic
9	C₂×C₇×C₁₀₇	C₂×C₃²	1	1	yes	characteristic
10	C₃×Dic₁₀₇	—	7	4	no	—
11	C₃²×C₁₀₇	Dic₇	1	1	yes	characteristic, complemented, Hall
12	C₇×C₁₀₇	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃×C₁₀₇	C₃×D₇	1	4	yes	—
14	Dic₁₀₇	—	7	1	no	Hall
15	C₃×C₁₀₇	C₃×Dic₇	1	4	yes	complemented
16	C₃²×Dic₇	—	107	1	no	maximal, Hall
17	C₂×C₁₀₇	C₃²×D₇	1	1	yes	characteristic
18	C₂×C₃²×C₇	D₁₀₇	1	1	yes	characteristic
19	C₁₀₇	C₃²×Dic₇	1	1	yes	characteristic, complemented, Sylow
20	C₃×Dic₇	—	107	4	no	—
21	C₃²×C₇	Dic₁₀₇	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₇	C₃×D₁₀₇	1	4	yes	—
23	C₃²×C₄	—	749	1	no	Hall
24	Dic₇	—	107	1	no	Hall
25	C₃×C₇	C₃×Dic₁₀₇	1	4	yes	complemented
26	C₂×C₃²	D₇₄₉	1	1	yes	characteristic
27	C₂×C₇	C₃²×D₁₀₇	1	1	yes	characteristic
28	C₃×C₄	—	749	4	no	—
29	C₃²	Dic₇₄₉	1	1	yes	characteristic, direct product factor, Sylow
30	C₇	C₃²×Dic₁₀₇	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	C₃×D₇₄₉	1	4	yes	—
32	C₄	—	749	1	no	Sylow
33	C₃	C₃×Dic₇₄₉	1	4	yes	direct product factor
34	C₂	C₃²×D₇₄₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃²	D₇₄₉
commutator, hypocenter	C₇×C₁₀₇	C₃²×C₄
Frattini	C₂	C₃²×D₇₄₉
Fitting, socle, prime radical	C₂×C₃²×C₇×C₁₀₇	C₂
cosocle	C₂×C₇×C₁₀₇	C₂×C₃²
LCS	G ▷ C₇×C₁₀₇
UCS	C₁ ◁ C₂×C₃²

Complements

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

N	H ≅ G/N	type
2. C₃×Dic₇₄₉	C₃	direct (N × H)
3. C₃²×C₇×C₁₀₇	C₄	semidirect
6. Dic₇₄₉	C₃²	direct (N × H)
7. C₃×C₇×C₁₀₇	C₃×C₄	semidirect
11. C₃²×C₁₀₇	Dic₇	semidirect
12. C₇×C₁₀₇	C₃²×C₄	semidirect
15. C₃×C₁₀₇	C₃×Dic₇	semidirect
19. C₁₀₇	C₃²×Dic₇	semidirect
21. C₃²×C₇	Dic₁₀₇	semidirect
25. C₃×C₇	C₃×Dic₁₀₇	semidirect
29. C₃²	Dic₇₄₉	direct (N × H)
30. C₇	C₃²×Dic₁₀₇	semidirect
33. C₃	C₃×Dic₇₄₉	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
C₃×Dic₇₄₉	3
C₃²×Dic₁₀₇	7
C₃²×Dic₇	107

Subgroups — C32×Dic749 #41004103

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×Dic₇₄₉ #41004103