Subgroups — C₃²×C₇×#1181 #20300642

Order 7308.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×D₂₉	C₂	1	1	yes	maximal, characteristic
2	C₃×C₇×#1181	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₇×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₇×D₂₉	C₂×C₃	1	4	yes	—
5	C₃²×#1181	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×#1181	C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₃×C₇×C₂₉	C₃×C₄	1	4	yes	complemented
8	C₃²×D₂₉	C₂×C₇	1	1	yes	characteristic
9	C₇×D₂₉	C₂×C₃²	1	1	yes	characteristic
10	C₃×#1181	C₃×C₇	1	4	yes	direct product factor
11	C₃²×C₂₉	C₄×C₇	1	1	yes	characteristic, complemented, Hall
12	C₃²×C₄×C₇	—	29	1	no	maximal, Hall
13	C₇×C₂₉	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
14	C₃×D₂₉	C₂×C₃×C₇	1	4	yes	—
15	C₂×C₃²×C₇	—	29	1	no	—
16	#1181	C₃²×C₇	1	1	yes	characteristic, direct product factor, Hall
17	C₃×C₂₉	C₃×C₄×C₇	1	4	yes	complemented
18	C₃×C₄×C₇	—	29	4	no	—
19	C₃²×C₇	#1181	1	1	yes	characteristic, direct product factor, Hall
20	D₂₉	C₂×C₃²×C₇	1	1	yes	characteristic
21	C₂×C₃×C₇	—	29	4	no	—
22	C₃²×C₄	—	29	1	no	Hall
23	C₂₉	C₃²×C₄×C₇	1	1	yes	characteristic, complemented, Sylow
24	C₄×C₇	—	29	1	no	Hall
25	C₃×C₇	C₃×#1181	1	4	yes	direct product factor
26	C₂×C₃²	—	29	1	no	—
27	C₂×C₇	—	29	1	no	—
28	C₃×C₄	—	29	4	no	—
29	C₃²	C₇×#1181	1	1	yes	characteristic, direct product factor, Sylow
30	C₇	C₃²×#1181	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	—	29	4	no	—
32	C₄	—	29	1	no	Sylow
33	C₃	C₃×C₇×#1181	1	4	yes	direct product factor
34	C₂	—	29	1	no	—

	subgroup	G/H
center, hypercenter	C₃²×C₇	#1181
commutator, hypocenter	C₂₉	C₃²×C₄×C₇
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₂₉	C₄
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₃²×C₇

Complements

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

N	H ≅ G/N	type
2. C₃×C₇×#1181	C₃	direct (N × H)
3. C₃²×C₇×C₂₉	C₄	semidirect
5. C₃²×#1181	C₇	direct (N × H)
6. C₇×#1181	C₃²	direct (N × H)
7. C₃×C₇×C₂₉	C₃×C₄	semidirect
10. C₃×#1181	C₃×C₇	direct (N × H)
11. C₃²×C₂₉	C₄×C₇	semidirect
13. C₇×C₂₉	C₃²×C₄	semidirect
16. #1181	C₃²×C₇	direct (N × H)
17. C₃×C₂₉	C₃×C₄×C₇	semidirect
19. C₃²×C₇	#1181	direct (N × H)
23. C₂₉	C₃²×C₄×C₇	semidirect
25. C₃×C₇	C₃×#1181	direct (N × H)
29. C₃²	C₇×#1181	direct (N × H)
30. C₇	C₃²×#1181	direct (N × H)
33. C₃	C₃×C₇×#1181	direct (N × H)

Subgroups — C32×C7×#1181 #20300642

Conjugacy classes of subgroups

Complements

Subgroups — C₃²×C₇×#1181 #20300642