Subgroups — #30660728

Order 16758.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22552728	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₉×#64418	C₃	1	1	yes	maximal, characteristic, complemented
3	#19150296	—	3	1	no	maximal
4	C₁₉×#3862	C₂×C₃	1	1	yes	characteristic, complemented
5	#14584115	D₃	1	1	yes	characteristic, complemented
6	C₇×#87705	—	2	1	no	—
7	C₇×D₇×C₁₉	—	3	1	no	Hall
8	ΓL(1,𝔽₈)×C₁₉⋊C₃	—	14	1	no	—
9	C₇²×C₁₉	C₃×D₃	1	1	yes	characteristic, complemented, Hall
10	#64418⋊C₃	—	19	1	no	maximal, Hall
11	C₂×#87704	—	21	1	no	—
12	#11716325	—	21	1	no	—
13	ΓL(1,𝔽₈)²	—	19	1	no	Hall
14	#87705	—	2	1	no	—
15	#87704	—	14	1	no	—
16	#87704	—	21	1	no	—
17	#87704	—	21	1	no	—
18	C₇×C₁₉⋊C₃	—	14	1	no	—
19	C₁₉×ΓL(1,𝔽₈)	—	14	1	no	—
20	D₃×C₁₉⋊C₃	—	49	1	no	maximal, Hall
21	#64423	—	57	1	no	—
22	#64418	C₁₉⋊C₃	1	1	yes	characteristic, complemented
23	C₂×C₇×C₁₉	—	21	1	no	—
24	D₇×C₁₉	—	3	1	no	—
25	C₃×C₁₉⋊C₃	—	49	1	no	Hall
26	#3862	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented
27	#3861	—	19	1	no	—
28	C₇×ΓL(1,𝔽₈)	—	38	1	no	—
29	C₇×C₁₉	—	2	1	no	—
30	C₇×C₁₉	—	3	1	no	—
31	C₇×C₁₉	—	3	1	no	—
32	D₃×C₁₉	—	49	1	no	—
33	C₂×C₁₉⋊C₃	—	147	1	no	—
34	C₇×D₇	—	3	1	no	Hall
35	C₃×ΓL(1,𝔽₈)	—	266	1	no	—
36	C₃×C₁₉	—	49	1	no	—
37	C₁₉⋊C₃	—	14	1	no	—
38	C₁₉⋊C₃	—	49	1	no	—
39	C₇²	D₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
40	C₂×ΓL(1,𝔽₈)	—	399	1	no	—
41	AGL(1,𝔽₇)	—	399	1	no	—
42	C₂×C₁₉	—	21	1	no	Hall
43	C₃×C₇	—	266	1	no	—
44	ΓL(1,𝔽₈)	—	266	1	no	—
45	ΓL(1,𝔽₈)	—	14	1	no	—
46	ΓL(1,𝔽₈)	—	38	1	no	—
47	ΓL(1,𝔽₈)	—	399	1	no	—
48	ΓL(1,𝔽₈)	—	399	1	no	—
49	C₁₉	#64418⋊C₃	1	1	yes	characteristic, complemented, Sylow
50	C₃×D₃	—	931	1	no	Hall
51	C₂×C₇	—	21	1	no	—
52	D₇	—	3	1	no	—
53	C₃²	—	931	1	no	Sylow
54	C₇	—	2	1	no	—
55	C₇	—	3	1	no	—
56	C₇	—	3	1	no	—
57	C₂×C₃	—	2793	1	no	—
58	D₃	—	49	1	no	—
59	C₃	—	266	1	no	—
60	C₃	—	49	1	no	—
61	C₃	—	931	1	no	—
62	C₂	—	21	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₁₉×#3862	C₂×C₃
Fitting, socle	C₇²×C₁₉	C₃×D₃
LCS	G ▷ C₁₉×#3862
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. #22552728	C₂	semidirect
2. C₁₉×#64418	C₃	semidirect
4. C₁₉×#3862	C₂×C₃	semidirect
5. #14584115	D₃	semidirect
9. C₇²×C₁₉	C₃×D₃	semidirect
22. #64418	C₁₉⋊C₃	semidirect
26. #3862	C₂×C₁₉⋊C₃	semidirect
39. C₇²	D₃×C₁₉⋊C₃	semidirect
49. C₁₉	#64418⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
#22552728	2
C₁₉×#64418	3
#19150296	3
#64418⋊C₃	19
D₃×C₁₉⋊C₃	49