Subgroups — C₄₁×#1425 #19105205

Order 5248.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₂×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#368	C₂	1	2	yes	maximal
3	C₂×C₁₆×C₄₁	C₂²	1	1	yes	characteristic
4	#108×C₄₁	—	2	2	no	—
5	C₃₂×C₄₁	C₄	1	2	yes	—
6	M₁₆×C₄₁	—	4	2	no	—
7	C₂×C₈×C₄₁	D₄	1	1	yes	characteristic
8	C₁₆×C₄₁	C₂×C₄	1	1	yes	characteristic
9	C₁₆×C₄₁	Q₈	1	1	yes	characteristic
10	C₂×C₄×C₄₁	D₈	1	1	yes	characteristic
11	C₈×C₄₁	—	8	2	no	—
12	C₈×C₄₁	C₄⋊C₄	1	1	yes	characteristic
13	C₈×C₄₁	Q₁₆	1	1	yes	characteristic
14	C₂²×C₄₁	Q₃₂	1	1	yes	characteristic
15	C₄×C₄₁	#107	1	1	yes	characteristic
16	C₄×C₄₁	D₁₆	1	1	yes	characteristic
17	#1425	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
18	C₂×C₄₁	—	2	1	no	—
19	C₂×C₄₁	#366	1	1	yes	characteristic
20	C₂×C₃₂	C₂×C₄₁	1	1	yes	characteristic
21	#368	C₂×C₄₁	1	2	yes	—
22	C₄₁	#1425	1	1	yes	characteristic, direct product factor, Sylow
23	C₂×C₁₆	C₂²×C₄₁	1	1	yes	characteristic
24	#108	—	2	2	no	—
25	C₃₂	C₄×C₄₁	1	2	yes	—
26	M₁₆	—	4	2	no	—
27	C₂×C₈	D₄×C₄₁	1	1	yes	characteristic
28	C₁₆	C₂×C₄×C₄₁	1	1	yes	characteristic
29	C₁₆	Q₈×C₄₁	1	1	yes	characteristic
30	C₂×C₄	D₈×C₄₁	1	1	yes	characteristic
31	C₈	—	8	2	no	—
32	C₈	C₄⋊C₄×C₄₁	1	1	yes	characteristic
33	C₈	Q₁₆×C₄₁	1	1	yes	characteristic
34	C₂²	Q₃₂×C₄₁	1	1	yes	characteristic
35	C₄	#107×C₄₁	1	1	yes	characteristic
36	C₄	D₁₆×C₄₁	1	1	yes	characteristic
37	C₂	—	2	1	no	—
38	C₂	C₄₁×#366	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₄₁	D₁₆
commutator	C₁₆	C₂×C₄×C₄₁
Frattini, cosocle	C₂×C₁₆	C₂²×C₄₁
socle	C₂×C₄₁	#366
prime radical	C₂²×C₄₁	Q₃₂
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₄₁ ◁ C₂×C₄×C₄₁ ◁ C₂×C₈×C₄₁ ◁ C₂×C₁₆×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
17. #1425	C₄₁	direct (N × H)
22. C₄₁	#1425	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃₂×C₄₁	2
C₄₁×#368	2
#1425	41

Subgroups — C41×#1425 #19105205

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#1425 #19105205