Subgroups — C₂×C₄₁×Q₆₄ #19106041

Order 5248.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₃₂×C₄₁	C₂	1	2	yes	maximal
2	C₄₁×Q₆₄	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₃₂×C₄₁	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₁₆×C₄₁	—	2	2	no	—
5	Q₃₂×C₄₁	—	2	2	no	—
6	Q₃₂×C₄₁	C₂²	1	4	yes	—
7	C₂×C₁₆×C₄₁	C₂²	1	1	yes	characteristic
8	C₃₂×C₄₁	C₂²	1	2	yes	—
9	C₂×Q₈×C₄₁	—	4	2	no	—
10	Q₁₆×C₄₁	—	2	4	no	—
11	Q₁₆×C₄₁	—	4	2	no	—
12	C₂×C₈×C₄₁	D₄	1	1	yes	characteristic
13	C₁₆×C₄₁	D₄	1	1	yes	characteristic
14	C₁₆×C₄₁	C₂³	1	1	yes	characteristic
15	Q₈×C₄₁	—	4	4	no	—
16	Q₈×C₄₁	—	8	2	no	—
17	C₂×C₄×C₄₁	—	8	2	no	—
18	C₂×C₄×C₄₁	D₈	1	1	yes	characteristic
19	C₈×C₄₁	D₈	1	1	yes	characteristic
20	C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
21	C₂²×C₄₁	D₁₆	1	1	yes	characteristic
22	C₄×C₄₁	—	8	4	no	—
23	C₄×C₄₁	D₁₆	1	1	yes	characteristic
24	C₄×C₄₁	C₂×D₈	1	1	yes	characteristic
25	C₂×Q₆₄	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
26	C₂×C₄₁	Q₆₄	1	2	yes	direct product factor
27	C₂×C₄₁	C₂×D₁₆	1	1	yes	characteristic
28	C₂×Q₃₂	C₂×C₄₁	1	2	yes	—
29	Q₆₄	C₂×C₄₁	1	4	yes	direct product factor
30	C₂×C₃₂	C₂×C₄₁	1	1	yes	characteristic
31	C₄₁	C₂×Q₆₄	1	1	yes	characteristic, direct product factor, Sylow
32	C₂×Q₁₆	—	2	2	no	—
33	Q₃₂	—	2	2	no	—
34	Q₃₂	C₂²×C₄₁	1	4	yes	—
35	C₂×C₁₆	C₂²×C₄₁	1	1	yes	characteristic
36	C₃₂	C₂²×C₄₁	1	2	yes	—
37	C₂×Q₈	—	4	2	no	—
38	Q₁₆	—	2	4	no	—
39	Q₁₆	—	4	2	no	—
40	C₂×C₈	D₄×C₄₁	1	1	yes	characteristic
41	C₁₆	D₄×C₄₁	1	1	yes	characteristic
42	C₁₆	C₂³×C₄₁	1	1	yes	characteristic
43	Q₈	—	4	4	no	—
44	Q₈	—	8	2	no	—
45	C₂×C₄	—	8	2	no	—
46	C₂×C₄	D₈×C₄₁	1	1	yes	characteristic
47	C₈	D₈×C₄₁	1	1	yes	characteristic
48	C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
49	C₂²	D₁₆×C₄₁	1	1	yes	characteristic
50	C₄	—	8	4	no	—
51	C₄	D₁₆×C₄₁	1	1	yes	characteristic
52	C₄	C₂×D₈×C₄₁	1	1	yes	characteristic
53	C₂	C₄₁×Q₆₄	1	2	yes	direct product factor
54	C₂	C₂×D₁₆×C₄₁	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₄₁	D₁₆
commutator, Frattini, cosocle	C₁₆	C₂³×C₄₁
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×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×Q₆₄	C₂	direct (N × H)
25. C₂×Q₆₄	C₄₁	direct (N × H)
26. C₂×C₄₁	Q₆₄	direct (N × H)
29. Q₆₄	C₂×C₄₁	direct (N × H)
31. C₄₁	C₂×Q₆₄	direct (N × H)
53. C₂	C₄₁×Q₆₄	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×Q₃₂×C₄₁	2
C₄₁×Q₆₄	2
C₂×C₃₂×C₄₁	2
C₂×Q₆₄	41

Subgroups — C2×C41×Q64 #19106041

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×Q₆₄ #19106041