Subgroups — #44505648

Order 30848.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#21440548	C₂	1	1	yes	maximal, characteristic
2	#29507547	C₂	1	1	yes	maximal, characteristic
3	#368×C₂₄₁	C₂	1	1	yes	maximal, characteristic
4	#21440578	—	2	1	no	—
5	#21440548	C₄	1	2	yes	—
6	C₂×C₁₆×C₂₄₁	C₂²	1	1	yes	characteristic
7	#108×C₂₄₁	—	2	1	no	—
8	#16838754	—	4	1	no	—
9	M₁₆×C₂₄₁	—	4	1	no	—
10	C₂×C₈×C₂₄₁	D₄	1	1	yes	characteristic
11	C₁₆×C₂₄₁	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₂₄₁	Q₈	1	1	yes	characteristic
13	#14515349	—	8	1	no	—
14	C₂×C₄×C₂₄₁	D₈	1	1	yes	characteristic
15	C₈×C₂₄₁	—	8	1	no	—
16	C₈×C₂₄₁	C₄⋊C₄	1	1	yes	characteristic
17	C₈×C₂₄₁	Q₁₆	1	1	yes	characteristic
18	C₂²×C₂₄₁	Q₃₂	1	1	yes	characteristic
19	C₄×C₂₄₁	#107	1	1	yes	characteristic
20	C₄×C₂₄₁	D₁₆	1	1	yes	characteristic
21	C₂×C₂₄₁	—	2	1	no	—
22	C₂×C₂₄₁	#366	1	1	yes	characteristic
23	C₂₄₁	#1425	1	1	yes	characteristic, complemented, Sylow
24	#1425	—	241	1	no	maximal, Sylow
25	C₂×C₃₂	—	241	1	no	—
26	#368	—	241	1	no	—
27	#368	D₂₄₁	1	1	yes	characteristic
28	C₂×C₁₆	C₂×D₂₄₁	1	1	yes	characteristic
29	#108	—	2	1	no	—
30	#108	—	482	1	no	—
31	C₃₂	—	241	2	no	—
32	M₁₆	—	4	1	no	—
33	M₁₆	—	964	1	no	—
34	C₂×C₈	C₂²⋊D₂₄₁	1	1	yes	characteristic
35	C₁₆	C₄×D₂₄₁	1	1	yes	characteristic
36	C₁₆	Dic₄₈₂	1	1	yes	characteristic
37	C₂×C₄	#16838755	1	1	yes	characteristic
38	C₈	—	8	1	no	—
39	C₈	—	1928	1	no	—
40	C₈	#16838749	1	1	yes	characteristic
41	C₈	#16838760	1	1	yes	characteristic
42	C₂²	#21440588	1	1	yes	characteristic
43	C₄	#21440575	1	1	yes	characteristic
44	C₄	#21440583	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	C₂	#29507542	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#21440583
commutator	C₁₆×C₂₄₁	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₂₄₁
Fitting	#368×C₂₄₁	C₂
socle	C₂×C₂₄₁	#366
prime radical	C₂²×C₂₄₁	Q₃₂
cosocle	C₂×C₁₆×C₂₄₁	C₂²
hypercenter	#368	D₂₄₁
hypocenter	C₂₄₁	#1425
LCS	G ▷ C₁₆×C₂₄₁ ▷ C₈×C₂₄₁ ▷ C₄×C₂₄₁ ▷ C₂×C₂₄₁ ▷ C₂₄₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #368

Complements

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

N	H ≅ G/N	type
23. C₂₄₁	#1425	semidirect

Maximal subgroups

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

subgroup	index
C₂×#21440548	2
#29507547	2
#368×C₂₄₁	2
#1425	241