Subgroups — C₄₁×#1419 #19105199

Order 5248.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₆×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₄₁×M₆₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#368	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₈×C₄₁	—	2	1	no	—
5	D₁₆×C₄₁	—	2	1	no	—
6	D₁₆×C₄₁	C₄	1	2	yes	—
7	C₂×C₁₆×C₄₁	C₂²	1	1	yes	characteristic
8	#108×C₄₁	—	2	1	no	—
9	C₃₂×C₄₁	—	2	1	no	—
10	C₂×D₄×C₄₁	—	4	1	no	—
11	D₈×C₄₁	—	2	2	no	—
12	D₈×C₄₁	—	4	1	no	—
13	M₁₆×C₄₁	—	4	1	no	—
14	C₂×C₈×C₄₁	D₄	1	1	yes	characteristic
15	C₁₆×C₄₁	C₂×C₄	1	1	yes	characteristic
16	C₁₆×C₄₁	D₄	1	1	yes	characteristic
17	C₂³×C₄₁	—	8	1	no	—
18	D₄×C₄₁	—	4	2	no	—
19	D₄×C₄₁	—	8	1	no	—
20	C₂×C₄×C₄₁	D₈	1	1	yes	characteristic
21	C₈×C₄₁	—	8	1	no	—
22	C₈×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
23	C₈×C₄₁	SD₁₆	1	1	yes	characteristic
24	C₂²×C₄₁	—	8	2	no	—
25	C₂²×C₄₁	—	16	2	no	—
26	C₂²×C₄₁	SD₃₂	1	1	yes	characteristic
27	C₄×C₄₁	#102	1	1	yes	characteristic
28	C₄×C₄₁	D₁₆	1	1	yes	characteristic
29	#1419	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
30	C₂×C₄₁	—	2	1	no	—
31	C₂×C₄₁	—	16	2	no	—
32	C₂×C₄₁	#357	1	1	yes	characteristic
33	C₂×D₁₆	C₂×C₄₁	1	1	yes	characteristic
34	M₆₄	C₂×C₄₁	1	1	yes	characteristic, complemented
35	#368	C₂×C₄₁	1	1	yes	characteristic, complemented
36	C₄₁	#1419	1	1	yes	characteristic, direct product factor, Sylow
37	C₂×D₈	—	2	1	no	—
38	D₁₆	—	2	1	no	—
39	D₁₆	C₄×C₄₁	1	2	yes	—
40	C₂×C₁₆	C₂²×C₄₁	1	1	yes	characteristic
41	#108	—	2	1	no	—
42	C₃₂	—	2	1	no	—
43	C₂×D₄	—	4	1	no	—
44	D₈	—	2	2	no	—
45	D₈	—	4	1	no	—
46	M₁₆	—	4	1	no	—
47	C₂×C₈	D₄×C₄₁	1	1	yes	characteristic
48	C₁₆	C₂×C₄×C₄₁	1	1	yes	characteristic
49	C₁₆	D₄×C₄₁	1	1	yes	characteristic
50	C₂³	—	8	1	no	—
51	D₄	—	4	2	no	—
52	D₄	—	8	1	no	—
53	C₂×C₄	D₈×C₄₁	1	1	yes	characteristic
54	C₈	—	8	1	no	—
55	C₈	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
56	C₈	SD₁₆×C₄₁	1	1	yes	characteristic
57	C₂²	—	8	2	no	—
58	C₂²	—	16	2	no	—
59	C₂²	SD₃₂×C₄₁	1	1	yes	characteristic
60	C₄	#102×C₄₁	1	1	yes	characteristic
61	C₄	D₁₆×C₄₁	1	1	yes	characteristic
62	C₂	—	2	1	no	—
63	C₂	—	16	2	no	—
64	C₂	C₄₁×#357	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₄₁	#357
commutator	C₁₆	C₂×C₄×C₄₁
Frattini, cosocle	C₂×C₁₆	C₂²×C₄₁
prime radical	C₂×D₁₆×C₄₁	C₂
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×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
2. C₄₁×M₆₄	C₂	semidirect
3. C₄₁×#368	C₂	semidirect
29. #1419	C₄₁	direct (N × H)
34. M₆₄	C₂×C₄₁	semidirect
35. #368	C₂×C₄₁	semidirect
36. C₄₁	#1419	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×D₁₆×C₄₁	2
C₄₁×M₆₄	2
C₄₁×#368	2
#1419	41

Subgroups — C41×#1419 #19105199

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#1419 #19105199