Subgroups — #45691983

Order 33516.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30660650	C₂	1	1	yes	maximal, characteristic
2	(C₁₉⋊C₃)⋊#5997	C₃	1	1	yes	maximal, characteristic
3	#22552719	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₉⋊C₃×C₇⋊D₇	C₂×C₃	1	1	yes	characteristic
5	C₁₉⋊#5997	C₉	1	1	yes	characteristic, complemented, Hall
6	C₇²×C₁₉⋊C₃	C₃×C₄	1	1	yes	characteristic
7	#14558804	—	14	4	no	—
8	C₁₉×C₇⋊D₇	C₂×C₉	1	1	yes	characteristic
9	#5997⋊C₉	—	19	1	no	maximal, Hall
10	#11924781	—	14	4	no	—
11	C₇²×C₁₉	C₄×C₉	1	1	yes	characteristic, complemented, Hall
12	#11725077	—	19	1	no	—
13	D₇×C₁₉⋊C₃	—	14	4	no	—
14	#4296⋊C₄	—	49	1	no	maximal, Hall
15	C₃×#5997	—	19	1	no	—
16	#89204	—	19	1	no	Hall
17	C₇×C₁₉⋊C₃	—	2	4	no	—
18	C₂×#4296	—	49	1	no	—
19	C₃×C₇⋊D₇	—	19	1	no	—
20	D₇×C₁₉	—	14	4	no	—
21	(C₁₉⋊C₃)⋊C₄	—	49	1	no	—
22	#5997	—	19	1	no	Hall
23	#4296	—	49	1	no	Hall
24	C₃×C₇²	—	19	1	no	—
25	C₇×C₁₉	—	2	4	no	—
26	D₇⋊C₉	—	266	4	no	—
27	C₂×C₁₉⋊C₃	—	49	1	no	—
28	C₇⋊D₇	AGL(1,𝔽₁₉)	1	1	yes	characteristic
29	Dic₁₉	—	49	1	no	Hall
30	C₇⋊C₉	—	266	4	no	—
31	C₁₉⋊C₃	#5997⋊C₃	1	1	yes	characteristic
32	C₇²	#4296⋊C₄	1	1	yes	characteristic, complemented, Sylow
33	C₃×D₇	—	266	4	no	—
34	C₂×C₁₉	—	49	1	no	—
35	C₄×C₉	—	931	1	no	Hall
36	C₃×C₇	—	38	4	no	—
37	C₁₉	#5997⋊C₉	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₉	—	931	1	no	—
39	D₇	—	14	4	no	—
40	C₃×C₄	—	931	1	no	—
41	C₉	—	931	1	no	Sylow
42	C₇	—	2	4	no	—
43	C₂×C₃	—	931	1	no	—
44	C₄	—	931	1	no	Sylow
45	C₃	—	19	1	no	—
46	C₂	—	49	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₇²×C₁₉	C₄×C₉
prime radical, cosocle	C₁₉⋊C₃×C₇⋊D₇	C₂×C₃
LCS	G ▷ C₇²×C₁₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
3. #22552719	C₄	semidirect
5. C₁₉⋊#5997	C₉	semidirect
11. C₇²×C₁₉	C₄×C₉	semidirect
32. C₇²	#4296⋊C₄	semidirect
37. C₁₉	#5997⋊C₉	semidirect

Maximal subgroups

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

subgroup	index
#30660650	2
(C₁₉⋊C₃)⋊#5997	3
#5997⋊C₉	19
#4296⋊C₄	49