Subgroups — #41005078

Order 26973.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22582510	C₃	1	1	yes	maximal, characteristic, complemented
2	#22582507	C₃	1	1	yes	maximal, characteristic, complemented
3	#22582464	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃₇×#6879	C₃	1	1	yes	maximal, characteristic, complemented
5	#15688521	—	3	1	no	—
6	#15688519	—	3	1	no	—
7	C₃×#11758601	—	3	1	no	—
8	C₃₇×#732	—	3	1	no	—
9	C₉²×C₃₇	C₃²	1	1	yes	characteristic
10	H(3,𝔽₃)×C₃₇	—	9	1	no	—
11	C₃×C₉×C₃₇	—	3	1	no	—
12	C₃×C₉×C₃₇	H(3,𝔽₃)	1	1	yes	characteristic
13	C₃²⋊(C₃₇⋊C₃)	—	9	1	no	—
14	#11758608	—	9	1	no	—
15	#11758601	—	3	3	no	—
16	#10624540	—	37	1	no	maximal, Sylow
17	C₃²×C₃₇	—	27	1	no	—
18	C₃²×C₃₇	#732	1	1	yes	characteristic
19	C₃×C₃₇⋊C₃	—	27	1	no	—
20	C₉×C₃₇	—	3	1	no	—
21	C₉×C₃₇	—	9	1	no	—
22	#66524	—	27	1	no	—
23	#6880	—	37	1	no	—
24	#6879	—	37	1	no	—
25	#6879	C₃₇⋊C₃	1	1	yes	characteristic, complemented
26	#6864	—	37	1	no	—
27	C₃×C₃₇	—	3	1	no	—
28	C₃×C₃₇	—	81	1	no	—
29	C₃×C₃₇	#6879	1	1	yes	characteristic
30	C₃₇⋊C₃	—	81	1	no	—
31	#733	—	111	1	no	—
32	#732	—	3	1	no	—
33	#732	—	111	1	no	—
34	C₃×C₂₇	—	111	1	no	—
35	C₉²	C₃×C₃₇⋊C₃	1	1	yes	characteristic
36	C₃₇	#10624540	1	1	yes	characteristic, complemented, Sylow
37	3₋¹⁺²	—	333	1	no	—
38	H(3,𝔽₃)	—	9	1	no	—
39	H(3,𝔽₃)	—	333	1	no	—
40	C₃×C₉	—	3	1	no	—
41	C₃×C₉	C₃²⋊(C₃₇⋊C₃)	1	1	yes	characteristic
42	C₂₇	—	111	3	no	—
43	C₃²	—	27	1	no	—
44	C₃²	—	999	1	no	—
45	C₃²	#15688518	1	1	yes	characteristic
46	C₉	—	3	1	no	—
47	C₉	—	9	1	no	—
48	C₉	—	999	1	no	—
49	C₃	—	3	1	no	—
50	C₃	—	81	1	no	—
51	C₃	—	2997	1	no	—
52	C₃	#22582506	1	1	yes	characteristic

	subgroup	G/H
center	C₃	#22582506
commutator, cosocle	C₉²×C₃₇	C₃²
Frattini	C₉²	C₃×C₃₇⋊C₃
Fitting	C₃₇×#6879	C₃
socle	C₃×C₃₇	#6879
hypercenter	#6879	C₃₇⋊C₃
hypocenter	C₃₇	#10624540
LCS	G ▷ C₉²×C₃₇ ▷ C₃×C₉×C₃₇ ▷ C₃²×C₃₇ ▷ C₃×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃ ◁ C₃² ◁ C₃×C₉ ◁ C₉² ◁ #6879

Complements

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

N	H ≅ G/N	type
1. #22582510	C₃	semidirect
2. #22582507	C₃	semidirect
3. #22582464	C₃	semidirect
4. C₃₇×#6879	C₃	semidirect
25. #6879	C₃₇⋊C₃	semidirect
36. C₃₇	#10624540	semidirect

Maximal subgroups

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

subgroup	index
#22582510	3
#22582507	3
#22582464	3
C₃₇×#6879	3
#10624540	37