Subgroups — C₃⋊#22550921 #37567907

Order 24444.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×D₉₇⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₇⋊#87604)	C₃	1	1	yes	maximal, characteristic, complemented
3	#22550921	—	3	1	no	maximal
4	C₃×C₇×C₉₇⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
5	C₇×D₉₇⋊C₃	—	2	1	no	—
6	C₇×D₉₇⋊C₃	D₃	1	1	yes	characteristic
7	C₃×C₇×D₉₇	C₂×C₃	1	1	yes	characteristic
8	C₃⋊(#87604⋊C₃)	—	7	1	no	maximal, Hall
9	C₇⋊#87604	—	3	1	no	Hall
10	C₃×C₇×C₉₇	C₃×C₄	1	1	yes	characteristic, complemented
11	C₇×C₉₇⋊C₃	—	2	1	no	—
12	C₇×C₉₇⋊C₃	Dic₃	1	1	yes	characteristic, complemented
13	C₃×D₉₇⋊C₃	D₇	1	1	yes	characteristic
14	C₇×D₉₇	C₃×D₃	1	1	yes	characteristic
15	C₃⋊#87604	—	7	1	no	—
16	#87604⋊C₃	—	21	1	no	—
17	C₃×C₉₇⋊C₃	Dic₇	1	1	yes	characteristic, complemented, Hall
18	C₇×C₉₇	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
19	C₃×D₉₇	C₃×D₇	1	1	yes	characteristic
20	D₉₇⋊C₃	—	2	1	no	—
21	D₉₇⋊C₃	D₂₁	1	1	yes	characteristic
22	#87604	—	21	1	no	Hall
23	C₃×C₉₇	C₃×Dic₇	1	1	yes	characteristic, complemented
24	C₉₇⋊C₃	—	2	1	no	—
25	C₉₇⋊C₃	Dic₂₁	1	1	yes	characteristic, complemented
26	C₃×Dic₂₁	—	97	1	no	maximal, Hall
27	D₉₇	C₃×D₂₁	1	1	yes	characteristic
28	C₂×C₃²×C₇	—	97	1	no	—
29	C₉₇	C₃×Dic₂₁	1	1	yes	characteristic, complemented, Sylow
30	Dic₂₁	—	97	1	no	—
31	C₃×Dic₇	—	291	1	no	—
32	C₃²×C₇	—	388	1	no	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	—	679	1	no	Hall
37	Dic₇	—	291	1	no	Hall
38	C₃×C₇	—	388	1	no	—
39	C₃×C₇	—	388	1	no	—
40	C₃×C₇	#87604⋊C₃	1	1	yes	characteristic, complemented
41	C₂×C₃²	—	97	1	no	—
42	C₂×C₇	—	97	1	no	—
43	C₃×C₄	—	2037	1	no	—
44	Dic₃	—	679	1	no	—
45	C₃²	—	388	1	no	Sylow
46	C₇	C₃⋊(#87604⋊C₃)	1	1	yes	characteristic, complemented, Sylow
47	C₂×C₃	—	97	1	no	—
48	C₂×C₃	—	97	1	no	—
49	C₂×C₃	—	194	1	no	—
50	C₄	—	2037	1	no	Sylow
51	C₃	—	388	1	no	—
52	C₃	—	388	1	no	—
53	C₃	#22550921	1	1	yes	characteristic, complemented
54	C₂	—	97	1	no	—

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

Complements

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

N	H ≅ G/N	type
2. C₃⋊(C₇⋊#87604)	C₃	semidirect
4. C₃×C₇×C₉₇⋊C₃	C₄	semidirect
10. C₃×C₇×C₉₇	C₃×C₄	semidirect
12. C₇×C₉₇⋊C₃	Dic₃	semidirect
17. C₃×C₉₇⋊C₃	Dic₇	semidirect
18. C₇×C₉₇	C₃×Dic₃	semidirect
23. C₃×C₉₇	C₃×Dic₇	semidirect
25. C₉₇⋊C₃	Dic₂₁	semidirect
29. C₉₇	C₃×Dic₂₁	semidirect
40. C₃×C₇	#87604⋊C₃	semidirect
46. C₇	C₃⋊(#87604⋊C₃)	semidirect
53. C₃	#22550921	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₇×D₉₇⋊C₃	2
C₃⋊(C₇⋊#87604)	3
#22550921	3
C₃⋊(#87604⋊C₃)	7
C₃×Dic₂₁	97

Subgroups — C3⋊#22550921 #37567907

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊#22550921 #37567907