Subgroups — C₇²×C₃⋊(C₃⋊#261) #37525629

Order 22932.

360 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇²×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₇²×C₃⋊#261	—	3	4	no	maximal
3	C₃²×C₇²×C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₇²×D₁₃	D₃	1	4	yes	—
5	C₇×C₃⋊(C₃⋊#261)	C₇	1	8	yes	maximal, direct product factor
6	C₇²×#261	—	9	1	no	Hall
7	C₃×C₇²×C₁₃	Dic₃	1	4	yes	complemented
8	C₇²×C₃⋊Dic₃	—	13	1	no	maximal, Hall
9	C₃²×C₇×D₁₃	C₂×C₇	1	8	yes	—
10	C₇²×D₁₃	C₃⋊D₃	1	1	yes	characteristic
11	C₇×C₃⋊#261	—	3	32	no	—
12	C₂×C₃²×C₇²	—	13	1	no	—
13	C₃²×C₇×C₁₃	C₄×C₇	1	8	yes	complemented
14	C₇²×C₁₃	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
15	C₇²×Dic₃	—	39	4	no	—
16	C₃×C₇×D₁₃	D₃×C₇	1	32	yes	—
17	C₃⋊(C₃⋊#261)	C₇²	1	1	yes	characteristic, direct product factor, Hall
18	C₃²×C₇²	#261	1	1	yes	characteristic, complemented, Hall
19	C₇×#261	—	9	8	no	—
20	C₂×C₃×C₇²	—	13	4	no	—
21	C₃×C₇×C₁₃	C₇×Dic₃	1	32	yes	complemented
22	C₇×C₃⋊Dic₃	—	13	8	no	—
23	C₃²×D₁₃	C₂×C₇²	1	1	yes	characteristic
24	C₄×C₇²	—	117	1	no	Hall
25	C₇×D₁₃	C₇×C₃⋊D₃	1	8	yes	—
26	C₃⋊#261	—	3	4	no	—
27	C₃×C₇²	C₃⋊#261	1	4	yes	complemented
28	C₂×C₃²×C₇	—	13	8	no	—
29	C₃²×C₁₃	C₄×C₇²	1	1	yes	characteristic, complemented, Hall
30	C₂×C₇²	—	13	1	no	—
31	C₇×C₁₃	C₇×C₃⋊Dic₃	1	8	yes	complemented
32	C₇×Dic₃	—	39	32	no	—
33	C₃×D₁₃	D₃×C₇²	1	4	yes	—
34	C₃²×C₇	C₇×#261	1	8	yes	complemented
35	#261	—	9	1	no	Hall
36	C₇²	C₃⋊(C₃⋊#261)	1	1	yes	characteristic, direct product factor, Sylow
37	C₂×C₃×C₇	—	13	32	no	—
38	C₃×C₁₃	C₇²×Dic₃	1	4	yes	complemented
39	C₃⋊Dic₃	—	13	1	no	Hall
40	C₄×C₇	—	117	8	no	—
41	D₁₃	C₇²×C₃⋊D₃	1	1	yes	characteristic
42	C₃×C₇	C₇×C₃⋊#261	1	32	yes	complemented
43	C₂×C₃²	—	13	1	no	—
44	C₂×C₇	—	13	8	no	—
45	C₁₃	C₇²×C₃⋊Dic₃	1	1	yes	characteristic, complemented, Sylow
46	Dic₃	—	39	4	no	—
47	C₃²	C₇²×#261	1	1	yes	characteristic, complemented, Sylow
48	C₇	C₇×C₃⋊(C₃⋊#261)	1	8	yes	direct product factor
49	C₂×C₃	—	13	4	no	—
50	C₄	—	117	1	no	Sylow
51	C₃	C₇²×C₃⋊#261	1	4	yes	complemented
52	C₂	—	13	1	no	—

	subgroup	G/H
center, hypercenter	C₇²	C₃⋊(C₃⋊#261)
commutator, hypocenter	C₃²×C₁₃	C₄×C₇²
Frattini	C₁	G
Fitting, socle	C₃²×C₇²×C₁₃	C₄
prime radical	C₃²×C₇²×D₁₃	C₂
cosocle	C₃²×D₁₃	C₂×C₇²
LCS	G ▷ C₃²×C₁₃
UCS	C₁ ◁ C₇²

Complements

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

N	H ≅ G/N	type
3. C₃²×C₇²×C₁₃	C₄	semidirect
5. C₇×C₃⋊(C₃⋊#261)	C₇	direct (N × H)
7. C₃×C₇²×C₁₃	Dic₃	semidirect
13. C₃²×C₇×C₁₃	C₄×C₇	semidirect
14. C₇²×C₁₃	C₃⋊Dic₃	semidirect
17. C₃⋊(C₃⋊#261)	C₇²	direct (N × H)
18. C₃²×C₇²	#261	semidirect
21. C₃×C₇×C₁₃	C₇×Dic₃	semidirect
27. C₃×C₇²	C₃⋊#261	semidirect
29. C₃²×C₁₃	C₄×C₇²	semidirect
31. C₇×C₁₃	C₇×C₃⋊Dic₃	semidirect
34. C₃²×C₇	C₇×#261	semidirect
36. C₇²	C₃⋊(C₃⋊#261)	direct (N × H)
38. C₃×C₁₃	C₇²×Dic₃	semidirect
42. C₃×C₇	C₇×C₃⋊#261	semidirect
45. C₁₃	C₇²×C₃⋊Dic₃	semidirect
47. C₃²	C₇²×#261	semidirect
48. C₇	C₇×C₃⋊(C₃⋊#261)	direct (N × H)
51. C₃	C₇²×C₃⋊#261	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₇²×D₁₃	2
C₇²×C₃⋊#261	3
C₇×C₃⋊(C₃⋊#261)	7
C₇²×C₃⋊Dic₃	13

Subgroups — C72×C3⋊(C3⋊#261) #37525629

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇²×C₃⋊(C₃⋊#261) #37525629