Subgroups — C₇×C₉×#87604 #37567787

Order 24444.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₉×D₉₇	C₂	1	1	yes	maximal, characteristic
2	C₃×C₇×#87604	C₃	1	1	yes	maximal, characteristic
3	C₇×C₉×C₉₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₇×D₉₇	C₂×C₃	1	1	yes	characteristic
5	C₉×#87604	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×#87604	C₉	1	1	yes	characteristic, direct product factor, Hall
7	C₃×C₇×C₉₇	C₃×C₄	1	1	yes	characteristic
8	C₉×D₉₇	C₂×C₇	1	1	yes	characteristic
9	C₇×D₉₇	C₂×C₉	1	1	yes	characteristic
10	C₃×#87604	C₃×C₇	1	1	yes	characteristic
11	C₉×C₉₇	C₄×C₇	1	1	yes	characteristic, complemented, Hall
12	C₇×C₉₇	C₄×C₉	1	1	yes	characteristic, complemented, Hall
13	C₃×D₉₇	C₂×C₃×C₇	1	1	yes	characteristic
14	#87604	C₇×C₉	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₉₇	C₃×C₄×C₇	1	1	yes	characteristic
16	C₄×C₇×C₉	—	97	1	no	maximal, Hall
17	D₉₇	C₂×C₇×C₉	1	1	yes	characteristic
18	C₂×C₇×C₉	—	97	1	no	—
19	C₉₇	C₄×C₇×C₉	1	1	yes	characteristic, complemented, Sylow
20	C₃×C₄×C₇	—	97	1	no	—
21	C₇×C₉	#87604	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₃×C₇	—	97	1	no	—
23	C₄×C₉	—	97	1	no	Hall
24	C₄×C₇	—	97	1	no	Hall
25	C₃×C₇	C₃×#87604	1	1	yes	characteristic
26	C₂×C₉	—	97	1	no	—
27	C₂×C₇	—	97	1	no	—
28	C₃×C₄	—	97	1	no	—
29	C₉	C₇×#87604	1	1	yes	characteristic, direct product factor, Sylow
30	C₇	C₉×#87604	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	—	97	1	no	—
32	C₄	—	97	1	no	Sylow
33	C₃	C₃×C₇×#87604	1	1	yes	characteristic
34	C₂	—	97	1	no	—

	subgroup	G/H
center, hypercenter	C₇×C₉	#87604
commutator, hypocenter	C₉₇	C₄×C₇×C₉
Frattini	C₃	C₃×C₇×#87604
Fitting	C₇×C₉×C₉₇	C₄
socle	C₃×C₇×C₉₇	C₃×C₄
prime radical	C₃×C₇×D₉₇	C₂×C₃
cosocle	C₃×D₉₇	C₂×C₃×C₇
LCS	G ▷ C₉₇
UCS	C₁ ◁ C₇×C₉

Complements

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

N	H ≅ G/N	type
3. C₇×C₉×C₉₇	C₄	semidirect
5. C₉×#87604	C₇	direct (N × H)
6. C₇×#87604	C₉	direct (N × H)
11. C₉×C₉₇	C₄×C₇	semidirect
12. C₇×C₉₇	C₄×C₉	semidirect
14. #87604	C₇×C₉	direct (N × H)
19. C₉₇	C₄×C₇×C₉	semidirect
21. C₇×C₉	#87604	direct (N × H)
29. C₉	C₇×#87604	direct (N × H)
30. C₇	C₉×#87604	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×C₉×D₉₇	2
C₃×C₇×#87604	3
C₉×#87604	7
C₄×C₇×C₉	97

Subgroups — C7×C9×#87604 #37567787

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₉×#87604 #37567787