Subgroups — C₂×#29509854 #44527800

Order 31122.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#29509854	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₇×C₁₃×C₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic
3	C₇×C₁₃×C₁₉⋊C₃	C₂×C₃	1	1	yes	characteristic
4	C₂×#14555739	—	7	1	no	maximal, Hall
5	C₂×C₇×C₁₃×C₁₉	C₉	1	1	yes	characteristic, complemented, Hall
6	C₂×#11924780	—	13	1	no	maximal, Hall
7	#14555739	—	7	1	no	Hall
8	C₇×C₁₃×C₁₉	C₂×C₉	1	1	yes	characteristic, complemented, Hall
9	C₂×#11717941	—	19	1	no	maximal, Hall
10	C₂×C₁₃×C₁₉⋊C₃	ΓL(1,𝔽₈)	1	1	yes	characteristic
11	#11924780	—	13	1	no	Hall
12	#11717941	—	19	1	no	Hall
13	C₂×C₇×C₁₉⋊C₃	C₁₃⋊C₃	1	1	yes	characteristic
14	C₁₃×C₁₉⋊C₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
15	C₂×C₃×C₇×C₁₃	—	19	1	no	—
16	C₂×C₁₃×C₁₉	C₇⋊C₉	1	1	yes	characteristic, complemented, Hall
17	C₇×C₁₉⋊C₃	C₂×C₁₃⋊C₃	1	1	yes	characteristic
18	C₂×#4296	—	91	1	no	Hall
19	C₃×C₇×C₁₃	—	19	1	no	—
20	C₂×C₇×C₁₉	C₁₃⋊C₉	1	1	yes	characteristic, complemented, Hall
21	C₁₃×C₁₉	C₂×C₇⋊C₉	1	1	yes	characteristic, complemented, Hall
22	C₂×C₁₃⋊C₉	—	133	1	no	Hall
23	C₂×C₇×C₁₃	#4296	1	1	yes	characteristic, complemented, Hall
24	#4296	—	91	1	no	Hall
25	C₇×C₁₉	C₂×C₁₃⋊C₉	1	1	yes	characteristic, complemented, Hall
26	C₂×C₇⋊C₉	—	247	1	no	Hall
27	C₁₃⋊C₉	—	133	1	no	Hall
28	C₂×C₁₉⋊C₃	#63270	1	1	yes	characteristic
29	C₇×C₁₃	C₂×#4296	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃×C₁₃	—	19	1	no	—
31	C₇⋊C₉	—	247	1	no	Hall
32	C₁₉⋊C₃	C₂×#63270	1	1	yes	characteristic
33	C₂×C₃×C₇	—	19	1	no	—
34	C₃×C₁₃	—	19	1	no	—
35	C₂×C₁₉	#11717941	1	1	yes	characteristic, complemented, Hall
36	C₂×C₁₃	#11924780	1	1	yes	characteristic, complemented, Hall
37	C₃×C₇	—	19	1	no	—
38	C₁₉	C₂×#11717941	1	1	yes	characteristic, complemented, Sylow
39	C₂×C₉	—	1729	1	no	Hall
40	C₂×C₇	#14555739	1	1	yes	characteristic, complemented, Hall
41	C₁₃	C₂×#11924780	1	1	yes	characteristic, complemented, Sylow
42	C₉	—	1729	1	no	Sylow
43	C₇	C₂×#14555739	1	1	yes	characteristic, complemented, Sylow
44	C₂×C₃	—	19	1	no	—
45	C₃	—	19	1	no	—
46	C₂	#29509854	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂	#29509854
commutator, hypocenter	C₇×C₁₃×C₁₉	C₂×C₉
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₁₃×C₁₉	C₉
prime radical	C₂×C₇×C₁₃×C₁₉⋊C₃	C₃
cosocle	C₇×C₁₃×C₁₉⋊C₃	C₂×C₃
LCS	G ▷ C₇×C₁₃×C₁₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. #29509854	C₂	direct (N × H)
5. C₂×C₇×C₁₃×C₁₉	C₉	semidirect
8. C₇×C₁₃×C₁₉	C₂×C₉	semidirect
16. C₂×C₁₃×C₁₉	C₇⋊C₉	semidirect
20. C₂×C₇×C₁₉	C₁₃⋊C₉	semidirect
21. C₁₃×C₁₉	C₂×C₇⋊C₉	semidirect
23. C₂×C₇×C₁₃	#4296	semidirect
25. C₇×C₁₉	C₂×C₁₃⋊C₉	semidirect
29. C₇×C₁₃	C₂×#4296	semidirect
35. C₂×C₁₉	#11717941	semidirect
36. C₂×C₁₃	#11924780	semidirect
38. C₁₉	C₂×#11717941	semidirect
40. C₂×C₇	#14555739	semidirect
41. C₁₃	C₂×#11924780	semidirect
43. C₇	C₂×#14555739	semidirect
46. C₂	#29509854	direct (N × H)

Maximal subgroups

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

subgroup	index
#29509854	2
C₂×C₇×C₁₃×C₁₉⋊C₃	3
C₂×#14555739	7
C₂×#11924780	13
C₂×#11717941	19

Subgroups — C2×#29509854 #44527800

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#29509854 #44527800