Subgroups — #44527618

Order 31122.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#11924777	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₁₉×D₉₁	C₃	1	1	yes	maximal, characteristic
3	C₃×C₇×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic
4	D₁₃×#4294	—	7	1	no	maximal, Hall
5	C₁₉×D₉₁	C₉	1	1	yes	characteristic, complemented, Hall
6	#14558785	—	13	1	no	maximal, Hall
7	C₁₃×#4294	—	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	C₃×C₁₉×D₁₃	—	7	1	no	—
11	#11924777	D₁₃	1	1	yes	characteristic, complemented, Hall
12	C₁₃×C₇⋊C₉	—	19	1	no	Hall
13	C₃×D₇×C₁₉	—	13	1	no	—
14	C₃×C₁₃×C₁₉	AGL(1,𝔽₇)	1	1	yes	characteristic
15	C₃×D₉₁	C₁₉⋊C₃	1	1	yes	characteristic
16	C₁₉×D₁₃	—	7	1	no	Hall
17	C₃×C₇×C₁₉	C₃×D₁₃	1	1	yes	characteristic
18	C₂×#4294	—	91	1	no	Hall
19	C₃×C₇×C₁₃	C₂×C₁₉⋊C₃	1	1	yes	characteristic
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	#4294	1	1	yes	characteristic, complemented, Hall
24	#4294	—	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×C₃×C₁₉	—	91	1	no	—
29	C₇×C₁₃	C₂×#4294	1	1	yes	characteristic, complemented, Hall
30	C₃×D₁₃	—	7	1	no	—
31	C₇⋊C₉	—	19	1	no	Hall
32	C₃×C₁₉	ΓL(1,𝔽₈)⋊D₁₃	1	1	yes	characteristic
33	C₃×D₇	—	13	1	no	—
34	C₃×C₁₃	#11716326	1	1	yes	characteristic
35	C₂×C₁₉	—	91	1	no	Hall
36	D₁₃	—	7	1	no	Hall
37	C₃×C₇	D₁₃×C₁₉⋊C₃	1	1	yes	characteristic
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	#14558785	1	1	yes	characteristic, complemented, Sylow
42	C₉	—	133	1	no	Sylow
43	C₇	D₁₃×#4294	1	1	yes	characteristic, complemented, Sylow
44	C₂×C₃	—	91	1	no	—
45	C₃	#23780610	1	1	yes	characteristic
46	C₂	—	91	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₃	#23780610
commutator, hypocenter	C₇×C₁₃×C₁₉	C₂×C₉
Fitting, socle, cosocle	C₃×C₇×C₁₃×C₁₉	C₂×C₃
prime radical	C₃×C₁₉×D₉₁	C₃
LCS	G ▷ C₇×C₁₃×C₁₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₁₃×#11924777	C₂	semidirect
5. C₁₉×D₉₁	C₉	semidirect
8. C₇×C₁₃×C₁₉	C₂×C₉	semidirect
11. #11924777	D₁₃	semidirect
21. C₁₃×C₁₉	D₇⋊C₉	semidirect
23. D₉₁	#4294	semidirect
25. C₇×C₁₉	C₉×D₁₃	semidirect
29. C₇×C₁₃	C₂×#4294	semidirect
38. C₁₉	(C₇⋊C₉)⋊D₁₃	semidirect
41. C₁₃	#14558785	semidirect
43. C₇	D₁₃×#4294	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#11924777	2
C₃×C₁₉×D₉₁	3
D₁₃×#4294	7
#14558785	13
(C₇⋊C₉)⋊D₁₃	19