Subgroups — #44527719

Order 31122.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#11924780	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₉⋊C₃×D₉₁	C₃	1	1	yes	maximal, characteristic
3	C₇×C₁₃×C₁₉⋊C₃	C₂×C₃	1	1	yes	characteristic
4	D₁₃×#4296	—	7	1	no	maximal, Hall
5	C₁₉×D₉₁	C₉	1	1	yes	characteristic, complemented, Hall
6	#14558803	—	13	1	no	maximal, Hall
7	C₁₃×#4296	—	7	1	no	Hall
8	C₇×C₁₃×C₁₉	C₂×C₉	1	1	yes	characteristic, complemented, Hall
9	(C₇⋊C₉)⋊D₁₃	—	19	1	no	maximal, Hall
10	D₁₃×C₁₉⋊C₃	—	7	1	no	—
11	#11924780	D₁₃	1	1	yes	characteristic, complemented, Hall
12	C₁₃×C₇⋊C₉	—	19	1	no	Hall
13	D₇×C₁₉⋊C₃	—	13	1	no	—
14	C₁₃×C₁₉⋊C₃	AGL(1,𝔽₇)	1	1	yes	characteristic
15	C₃×D₉₁	—	19	1	no	—
16	C₁₉×D₁₃	—	7	1	no	Hall
17	C₇×C₁₉⋊C₃	C₃×D₁₃	1	1	yes	characteristic
18	C₂×#4296	—	91	1	no	Hall
19	C₃×C₇×C₁₃	—	19	1	no	—
20	D₇×C₁₉	—	13	1	no	Hall
21	C₁₃×C₁₉	D₇⋊C₉	1	1	yes	characteristic, complemented, Hall
22	C₉×D₁₃	—	133	1	no	Hall
23	D₉₁	#4296	1	1	yes	characteristic, complemented, Hall
24	#4296	—	7	1	no	Hall
25	C₇×C₁₉	C₉×D₁₃	1	1	yes	characteristic, complemented, Hall
26	D₇⋊C₉	—	247	1	no	Hall
27	C₉×C₁₃	—	133	1	no	Hall
28	C₂×C₁₉⋊C₃	—	91	1	no	—
29	C₇×C₁₃	C₂×#4296	1	1	yes	characteristic, complemented, Hall
30	C₃×D₁₃	—	133	1	no	—
31	C₇⋊C₉	—	19	1	no	Hall
32	C₁₉⋊C₃	ΓL(1,𝔽₈)⋊D₁₃	1	1	yes	characteristic
33	C₃×D₇	—	247	1	no	—
34	C₃×C₁₃	—	19	1	no	—
35	C₂×C₁₉	—	91	1	no	Hall
36	D₁₃	—	7	1	no	Hall
37	C₃×C₇	—	19	1	no	—
38	C₁₉	(C₇⋊C₉)⋊D₁₃	1	1	yes	characteristic, complemented, Sylow
39	C₂×C₉	—	1729	1	no	Hall
40	D₇	—	13	1	no	Hall
41	C₁₃	#14558803	1	1	yes	characteristic, complemented, Sylow
42	C₉	—	133	1	no	Sylow
43	C₇	D₁₃×#4296	1	1	yes	characteristic, complemented, Sylow
44	C₂×C₃	—	1729	1	no	—
45	C₃	—	19	1	no	—
46	C₂	—	91	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₇×C₁₃×C₁₉	C₂×C₉
prime radical	C₁₉⋊C₃×D₉₁	C₃
cosocle	C₇×C₁₃×C₁₉⋊C₃	C₂×C₃
LCS	G ▷ C₇×C₁₃×C₁₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₁₃×#11924780	C₂	semidirect
5. C₁₉×D₉₁	C₉	semidirect
8. C₇×C₁₃×C₁₉	C₂×C₉	semidirect
11. #11924780	D₁₃	semidirect
21. C₁₃×C₁₉	D₇⋊C₉	semidirect
23. D₉₁	#4296	semidirect
25. C₇×C₁₉	C₉×D₁₃	semidirect
29. C₇×C₁₃	C₂×#4296	semidirect
38. C₁₉	(C₇⋊C₉)⋊D₁₃	semidirect
41. C₁₃	#14558803	semidirect
43. C₇	D₁₃×#4296	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#11924780	2
C₁₉⋊C₃×D₉₁	3
D₁₃×#4296	7
#14558803	13
(C₇⋊C₉)⋊D₁₃	19