Subgroups — #45657029

Order 32608.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30654503	C₂	1	1	yes	maximal, characteristic
2	Q₈×D₁₀₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	Dic₄₀₇₆	C₂	1	1	yes	maximal, characteristic, complemented
4	#30654494	C₂	1	1	yes	maximal, characteristic, complemented
5	#30654492	C₂	1	1	yes	maximal, characteristic, complemented
6	#30654487	C₂	1	1	yes	maximal, characteristic, complemented
7	SD₁₆×C₁₀₁₉	C₂	1	1	yes	maximal, characteristic, complemented
8	Dic₂₀₃₈	—	2	1	no	—
9	Dic₂₀₃₈	C₂²	1	1	yes	characteristic
10	Dic₂₀₃₈	C₂²	1	1	yes	characteristic
11	C₂²⋊D₁₀₁₉	—	2	1	no	—
12	C₂×Dic₁₀₁₉	—	2	1	no	—
13	C₄×D₁₀₁₉	—	2	1	no	—
14	C₄×D₁₀₁₉	C₂²	1	1	yes	characteristic
15	C₁₀₁₉⋊C₈	C₂²	1	1	yes	characteristic
16	Q₈×C₁₀₁₉	C₂²	1	1	yes	characteristic
17	D₄×C₁₀₁₉	C₂²	1	1	yes	characteristic
18	C₈×C₁₀₁₉	C₂²	1	1	yes	characteristic
19	C₂²×C₁₀₁₉	—	2	1	no	—
20	C₂×D₁₀₁₉	D₄	1	1	yes	characteristic
21	C₄×C₁₀₁₉	—	2	1	no	—
22	C₄×C₁₀₁₉	C₂³	1	1	yes	characteristic
23	Dic₁₀₁₉	—	2	1	no	—
24	Dic₁₀₁₉	—	2	1	no	—
25	Dic₁₀₁₉	D₄	1	1	yes	characteristic
26	C₂×C₁₀₁₉	—	4	1	no	—
27	C₂×C₁₀₁₉	C₂×D₄	1	1	yes	characteristic
28	D₁₀₁₉	—	2	1	no	—
29	C₁₀₁₉	#137	1	1	yes	characteristic, complemented, Sylow
30	#137	—	1019	1	no	maximal, Sylow
31	#41	—	1019	1	no	—
32	C₂×Q₈	—	1019	1	no	—
33	Q₁₆	—	1019	1	no	—
34	Q₁₆	—	1019	1	no	—
35	SD₁₆	—	1019	1	no	—
36	SD₁₆	D₁₀₁₉	1	1	yes	characteristic, complemented
37	M₁₆	—	1019	1	no	—
38	Q₈	—	2038	1	no	—
39	Q₈	—	1019	1	no	—
40	Q₈	—	1019	1	no	—
41	Q₈	C₂×D₁₀₁₉	1	1	yes	characteristic
42	D₄	—	2038	1	no	—
43	D₄	C₂×D₁₀₁₉	1	1	yes	characteristic
44	C₂×C₄	—	2038	1	no	—
45	C₂×C₄	—	2038	1	no	—
46	C₂×C₄	—	1019	1	no	—
47	C₈	—	1019	1	no	—
48	C₈	C₂×D₁₀₁₉	1	1	yes	characteristic
49	C₂²	—	2	1	no	—
50	C₂²	—	1019	1	no	—
51	C₄	—	2	1	no	—
52	C₄	—	2038	1	no	—
53	C₄	—	2038	1	no	—
54	C₄	—	1019	1	no	—
55	C₄	C₂²×D₁₀₁₉	1	1	yes	characteristic
56	C₂	—	4	1	no	—
57	C₂	—	2038	1	no	—
58	C₂	D₄×D₁₀₁₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×D₁₀₁₉
commutator, cosocle	C₄×C₁₀₁₉	C₂³
Frattini	C₄	C₂²×D₁₀₁₉
Fitting	SD₁₆×C₁₀₁₉	C₂
socle	C₂×C₁₀₁₉	C₂×D₄
prime radical	#30654503	C₂
hypercenter	SD₁₆	D₁₀₁₉
hypocenter	C₁₀₁₉	#137
LCS	G ▷ C₄×C₁₀₁₉ ▷ C₂×C₁₀₁₉ ▷ C₁₀₁₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ SD₁₆

Complements

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

N	H ≅ G/N	type
2. Q₈×D₁₀₁₉	C₂	semidirect
3. Dic₄₀₇₆	C₂	semidirect
4. #30654494	C₂	semidirect
5. #30654492	C₂	semidirect
6. #30654487	C₂	semidirect
7. SD₁₆×C₁₀₁₉	C₂	semidirect
29. C₁₀₁₉	#137	semidirect
36. SD₁₆	D₁₀₁₉	semidirect

Maximal subgroups

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

subgroup	index
#30654503	2
Q₈×D₁₀₁₉	2
Dic₄₀₇₆	2
#30654494	2
#30654492	2
#30654487	2
SD₁₆×C₁₀₁₉	2
#137	1019