Subgroups — C₃×C₇×C₃⋊#87604 #37567959

Order 24444.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×D₉₇	C₂	1	1	yes	maximal, characteristic
2	C₇×C₃⋊#87604	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₇×#87604	—	3	1	no	maximal
4	C₃²×C₇×C₉₇	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×C₇×D₉₇	—	2	1	no	—
6	C₃×C₇×D₉₇	D₃	1	1	yes	characteristic
7	C₃×C₇×D₉₇	C₂×C₃	1	1	yes	characteristic
8	C₃×C₃⋊#87604	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₇×#87604	—	3	1	no	Hall
10	C₃×C₇×C₉₇	—	2	1	no	—
11	C₃×C₇×C₉₇	Dic₃	1	1	yes	characteristic, complemented
12	C₃×C₇×C₉₇	C₃×C₄	1	1	yes	characteristic, complemented
13	C₃²×D₉₇	C₂×C₇	1	1	yes	characteristic
14	C₇×D₉₇	C₃×D₃	1	1	yes	characteristic
15	C₃⋊#87604	C₃×C₇	1	1	yes	characteristic, direct product factor
16	C₃×#87604	—	3	1	no	—
17	C₃²×C₉₇	C₄×C₇	1	1	yes	characteristic, complemented, Hall
18	C₇×C₉₇	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
19	C₃×D₉₇	—	2	1	no	—
20	C₃×D₉₇	D₃×C₇	1	1	yes	characteristic
21	C₃×D₉₇	C₂×C₃×C₇	1	1	yes	characteristic
22	#87604	—	3	1	no	Hall
23	C₃×C₉₇	—	2	1	no	—
24	C₃×C₉₇	C₇×Dic₃	1	1	yes	characteristic, complemented
25	C₃×C₉₇	C₃×C₄×C₇	1	1	yes	characteristic, complemented
26	C₃×C₇×Dic₃	—	97	1	no	maximal, Hall
27	D₉₇	C₃×D₃×C₇	1	1	yes	characteristic
28	C₂×C₃²×C₇	—	97	1	no	—
29	C₉₇	C₃×C₇×Dic₃	1	1	yes	characteristic, complemented, Sylow
30	C₃×C₄×C₇	—	291	1	no	—
31	C₇×Dic₃	—	97	1	no	—
32	C₃²×C₇	#87604	1	1	yes	characteristic, complemented, Hall
33	C₂×C₃×C₇	—	97	1	no	—
34	C₂×C₃×C₇	—	97	1	no	—
35	C₂×C₃×C₇	—	194	1	no	—
36	C₃×Dic₃	—	97	1	no	Hall
37	C₄×C₇	—	291	1	no	Hall
38	C₃×C₇	—	2	1	no	—
39	C₃×C₇	C₃×#87604	1	1	yes	characteristic, complemented
40	C₃×C₇	C₃⋊#87604	1	1	yes	characteristic, direct product factor
41	C₂×C₃²	—	97	1	no	—
42	C₂×C₇	—	97	1	no	—
43	C₃×C₄	—	291	1	no	—
44	Dic₃	—	97	1	no	—
45	C₃²	C₇×#87604	1	1	yes	characteristic, complemented, Sylow
46	C₇	C₃×C₃⋊#87604	1	1	yes	characteristic, direct product factor, Sylow
47	C₂×C₃	—	97	1	no	—
48	C₂×C₃	—	97	1	no	—
49	C₂×C₃	—	194	1	no	—
50	C₄	—	291	1	no	Sylow
51	C₃	—	2	1	no	—
52	C₃	C₃×C₇×#87604	1	1	yes	characteristic, complemented
53	C₃	C₇×C₃⋊#87604	1	1	yes	characteristic, direct product factor
54	C₂	—	97	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₇	C₃⋊#87604
commutator, hypocenter	C₃×C₉₇	C₃×C₄×C₇
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₉₇	C₄
prime radical	C₃²×C₇×D₉₇	C₂
cosocle	C₃×D₉₇	C₂×C₃×C₇
LCS	G ▷ C₃×C₉₇
UCS	C₁ ◁ C₃×C₇

Complements

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

N	H ≅ G/N	type
2. C₇×C₃⋊#87604	C₃	direct (N × H)
4. C₃²×C₇×C₉₇	C₄	semidirect
8. C₃×C₃⋊#87604	C₇	direct (N × H)
11. C₃×C₇×C₉₇	Dic₃	semidirect
12. C₃×C₇×C₉₇	C₃×C₄	semidirect
15. C₃⋊#87604	C₃×C₇	direct (N × H)
17. C₃²×C₉₇	C₄×C₇	semidirect
18. C₇×C₉₇	C₃×Dic₃	semidirect
24. C₃×C₉₇	C₇×Dic₃	semidirect
25. C₃×C₉₇	C₃×C₄×C₇	semidirect
29. C₉₇	C₃×C₇×Dic₃	semidirect
32. C₃²×C₇	#87604	semidirect
39. C₃×C₇	C₃×#87604	semidirect
40. C₃×C₇	C₃⋊#87604	direct (N × H)
45. C₃²	C₇×#87604	semidirect
46. C₇	C₃×C₃⋊#87604	direct (N × H)
52. C₃	C₃×C₇×#87604	semidirect
53. C₃	C₇×C₃⋊#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
C₃²×C₇×D₉₇	2
C₇×C₃⋊#87604	3
C₃×C₇×#87604	3
C₃×C₃⋊#87604	7
C₃×C₇×Dic₃	97

Subgroups — C3×C7×C3⋊#87604 #37567959

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇×C₃⋊#87604 #37567959