Subgroups — C₃×C₃⋊(C₇⋊#67063) #36375910

Order 22428.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×D₈₉	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₇⋊#67063)	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₇⋊#67063	—	3	1	no	maximal
4	C₃²×C₇×C₈₉	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×C₇×D₈₉	—	2	1	no	—
6	C₃×C₇×D₈₉	D₃	1	1	yes	characteristic
7	C₃×C₇×D₈₉	C₂×C₃	1	1	yes	characteristic
8	C₃×C₃⋊#67063	—	7	1	no	maximal, Hall
9	C₇⋊#67063	—	3	1	no	Hall
10	C₃×C₇×C₈₉	—	2	1	no	—
11	C₃×C₇×C₈₉	Dic₃	1	1	yes	characteristic, complemented
12	C₃×C₇×C₈₉	C₃×C₄	1	1	yes	characteristic, complemented
13	C₃²×D₈₉	D₇	1	1	yes	characteristic
14	C₇×D₈₉	C₃×D₃	1	1	yes	characteristic
15	C₃⋊#67063	—	7	1	no	—
16	C₃×#67063	—	21	1	no	—
17	C₃²×C₈₉	Dic₇	1	1	yes	characteristic, complemented, Hall
18	C₇×C₈₉	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
19	C₃×D₈₉	—	2	1	no	—
20	C₃×D₈₉	C₃×D₇	1	1	yes	characteristic
21	C₃×D₈₉	D₂₁	1	1	yes	characteristic
22	#67063	—	21	1	no	Hall
23	C₃×C₈₉	—	2	1	no	—
24	C₃×C₈₉	C₃×Dic₇	1	1	yes	characteristic, complemented
25	C₃×C₈₉	Dic₂₁	1	1	yes	characteristic, complemented
26	C₃×Dic₂₁	—	89	1	no	maximal, Hall
27	D₈₉	C₃×D₂₁	1	1	yes	characteristic
28	C₂×C₃²×C₇	—	89	1	no	—
29	C₈₉	C₃×Dic₂₁	1	1	yes	characteristic, complemented, Sylow
30	Dic₂₁	—	89	1	no	—
31	C₃×Dic₇	—	267	1	no	—
32	C₃²×C₇	#67063	1	1	yes	characteristic, complemented, Hall
33	C₂×C₃×C₇	—	89	1	no	—
34	C₂×C₃×C₇	—	89	1	no	—
35	C₂×C₃×C₇	—	178	1	no	—
36	C₃×Dic₃	—	623	1	no	Hall
37	Dic₇	—	267	1	no	Hall
38	C₃×C₇	—	2	1	no	—
39	C₃×C₇	C₃×#67063	1	1	yes	characteristic, complemented
40	C₃×C₇	C₃⋊#67063	1	1	yes	characteristic, complemented
41	C₂×C₃²	—	89	1	no	—
42	C₂×C₇	—	89	1	no	—
43	C₃×C₄	—	1869	1	no	—
44	Dic₃	—	623	1	no	—
45	C₃²	C₇⋊#67063	1	1	yes	characteristic, complemented, Sylow
46	C₇	C₃×C₃⋊#67063	1	1	yes	characteristic, complemented, Sylow
47	C₂×C₃	—	89	1	no	—
48	C₂×C₃	—	89	1	no	—
49	C₂×C₃	—	178	1	no	—
50	C₄	—	1869	1	no	Sylow
51	C₃	—	2	1	no	—
52	C₃	C₃×C₇⋊#67063	1	1	yes	characteristic, complemented
53	C₃	C₃⋊(C₇⋊#67063)	1	1	yes	characteristic, direct product factor
54	C₂	—	89	1	no	—

	subgroup	G/H
center, hypercenter	C₃	C₃⋊(C₇⋊#67063)
commutator, hypocenter	C₃×C₇×C₈₉	C₃×C₄
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₈₉	C₄
prime radical	C₃²×C₇×D₈₉	C₂
cosocle	C₃×C₇×D₈₉	C₂×C₃
LCS	G ▷ C₃×C₇×C₈₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
2. C₃⋊(C₇⋊#67063)	C₃	direct (N × H)
4. C₃²×C₇×C₈₉	C₄	semidirect
11. C₃×C₇×C₈₉	Dic₃	semidirect
12. C₃×C₇×C₈₉	C₃×C₄	semidirect
17. C₃²×C₈₉	Dic₇	semidirect
18. C₇×C₈₉	C₃×Dic₃	semidirect
24. C₃×C₈₉	C₃×Dic₇	semidirect
25. C₃×C₈₉	Dic₂₁	semidirect
29. C₈₉	C₃×Dic₂₁	semidirect
32. C₃²×C₇	#67063	semidirect
39. C₃×C₇	C₃×#67063	semidirect
40. C₃×C₇	C₃⋊#67063	semidirect
45. C₃²	C₇⋊#67063	semidirect
46. C₇	C₃×C₃⋊#67063	semidirect
52. C₃	C₃×C₇⋊#67063	semidirect
53. C₃	C₃⋊(C₇⋊#67063)	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×D₈₉	2
C₃⋊(C₇⋊#67063)	3
C₃×C₇⋊#67063	3
C₃×C₃⋊#67063	7
C₃×Dic₂₁	89

Subgroups — C3×C3⋊(C7⋊#67063) #36375910

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₃⋊(C₇⋊#67063) #36375910