Subgroups — #44505651

Order 30848.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#29507547	C₂	1	1	yes	maximal, characteristic
2	#29507545	C₂	1	1	yes	maximal, characteristic
3	M₆₄×C₂₄₁	C₂	1	1	yes	maximal, characteristic
4	#21440578	—	2	1	no	—
5	#21440576	—	2	1	no	—
6	C₂×C₁₆×C₂₄₁	C₂²	1	1	yes	characteristic
7	C₃₂×C₂₄₁	C₄	1	2	yes	complemented
8	#16838754	—	4	1	no	—
9	C₄⋊Dic₂₄₁	—	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	C₂×Dic₂₄₁	—	8	1	no	—
14	#14515349	—	8	1	no	—
15	C₂×C₄×C₂₄₁	D₈	1	1	yes	characteristic
16	C₈×C₂₄₁	C₄⋊C₄	1	1	yes	characteristic
17	C₈×C₂₄₁	Q₁₆	1	1	yes	characteristic
18	C₂²×C₂₄₁	SD₃₂	1	1	yes	characteristic
19	C₄×C₂₄₁	#107	1	1	yes	characteristic
20	C₄×C₂₄₁	SD₃₂	1	1	yes	characteristic
21	Dic₂₄₁	—	16	1	no	—
22	C₂×C₂₄₁	—	2	1	no	—
23	C₂×C₂₄₁	#367	1	1	yes	characteristic
24	C₂₄₁	#1426	1	1	yes	characteristic, complemented, Sylow
25	#1426	—	241	1	no	maximal, Sylow
26	M₆₄	D₂₄₁	1	1	yes	characteristic
27	#368	—	241	1	no	—
28	#367	—	241	1	no	—
29	C₂×C₁₆	C₂×D₂₄₁	1	1	yes	characteristic
30	#108	—	482	1	no	—
31	#107	—	482	1	no	—
32	C₃₂	Dic₂₄₁	1	2	yes	complemented
33	M₁₆	—	964	1	no	—
34	C₂×C₈	D₉₆₄	1	1	yes	characteristic
35	C₄⋊C₄	—	964	1	no	—
36	C₁₆	C₂×Dic₂₄₁	1	1	yes	characteristic
37	C₁₆	Dic₄₈₂	1	1	yes	characteristic
38	C₂×C₄	—	1928	1	no	—
39	C₂×C₄	D₁₉₂₈	1	1	yes	characteristic
40	C₈	—	1928	1	no	—
41	C₈	C₄⋊Dic₂₄₁	1	1	yes	characteristic
42	C₈	Dic₉₆₄	1	1	yes	characteristic
43	C₂²	#21440587	1	1	yes	characteristic
44	C₄	—	3856	1	no	—
45	C₄	#21440576	1	1	yes	characteristic
46	C₄	#21440587	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	#29507545	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#29507545
commutator	C₁₆×C₂₄₁	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₂₄₁
Fitting	M₆₄×C₂₄₁	C₂
socle	C₂×C₂₄₁	#367
prime radical	C₂²×C₂₄₁	SD₃₂
cosocle	C₂×C₁₆×C₂₄₁	C₂²
hypercenter	M₆₄	D₂₄₁
hypocenter	C₂₄₁	#1426
LCS	G ▷ C₁₆×C₂₄₁ ▷ C₈×C₂₄₁ ▷ C₄×C₂₄₁ ▷ C₂×C₂₄₁ ▷ C₂₄₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ M₆₄

Complements

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

N	H ≅ G/N	type
7. C₃₂×C₂₄₁	C₄	semidirect
24. C₂₄₁	#1426	semidirect
32. C₃₂	Dic₂₄₁	semidirect

Maximal subgroups

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

subgroup	index
#29507547	2
#29507545	2
M₆₄×C₂₄₁	2
#1426	241