Subgroups — C₄×C₃₂×C₂₁₁ #41009016

Order 27008.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₂×C₂₁₁	C₂	1	2	yes	maximal
2	C₄×C₁₆×C₂₁₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆×C₂₁₁	C₄	1	1	yes	characteristic
4	C₂×C₁₆×C₂₁₁	C₂²	1	1	yes	characteristic
5	C₄×C₈×C₂₁₁	C₄	1	1	yes	characteristic
6	C₃₂×C₂₁₁	C₄	1	4	yes	direct product factor
7	C₂×C₈×C₂₁₁	C₈	1	1	yes	characteristic
8	C₂×C₈×C₂₁₁	C₂×C₄	1	1	yes	characteristic
9	C₄²×C₂₁₁	C₈	1	1	yes	characteristic
10	C₁₆×C₂₁₁	C₈	1	2	yes	—
11	C₁₆×C₂₁₁	C₂×C₄	1	2	yes	—
12	C₂×C₄×C₂₁₁	C₁₆	1	2	yes	—
13	C₂×C₄×C₂₁₁	C₂×C₈	1	1	yes	characteristic
14	C₈×C₂₁₁	C₁₆	1	2	yes	—
15	C₈×C₂₁₁	C₄²	1	1	yes	characteristic
16	C₈×C₂₁₁	C₂×C₈	1	1	yes	characteristic
17	C₂²×C₂₁₁	C₂×C₁₆	1	1	yes	characteristic
18	C₄×C₂₁₁	C₃₂	1	4	yes	direct product factor
19	C₄×C₂₁₁	C₄×C₈	1	1	yes	characteristic
20	C₄×C₂₁₁	C₂×C₁₆	1	1	yes	characteristic
21	C₂×C₂₁₁	C₄×C₁₆	1	1	yes	characteristic
22	C₂×C₂₁₁	C₂×C₃₂	1	2	yes	—
23	C₂₁₁	C₄×C₃₂	1	1	yes	characteristic, direct product factor, Sylow
24	C₄×C₃₂	C₂₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂×C₃₂	C₂×C₂₁₁	1	2	yes	—
26	C₄×C₁₆	C₂×C₂₁₁	1	1	yes	characteristic
27	C₂×C₁₆	C₄×C₂₁₁	1	1	yes	characteristic
28	C₂×C₁₆	C₂²×C₂₁₁	1	1	yes	characteristic
29	C₄×C₈	C₄×C₂₁₁	1	1	yes	characteristic
30	C₃₂	C₄×C₂₁₁	1	4	yes	direct product factor
31	C₂×C₈	C₈×C₂₁₁	1	1	yes	characteristic
32	C₂×C₈	C₂×C₄×C₂₁₁	1	1	yes	characteristic
33	C₄²	C₈×C₂₁₁	1	1	yes	characteristic
34	C₁₆	C₈×C₂₁₁	1	2	yes	—
35	C₁₆	C₂×C₄×C₂₁₁	1	2	yes	—
36	C₂×C₄	C₁₆×C₂₁₁	1	2	yes	—
37	C₂×C₄	C₂×C₈×C₂₁₁	1	1	yes	characteristic
38	C₈	C₁₆×C₂₁₁	1	2	yes	—
39	C₈	C₄²×C₂₁₁	1	1	yes	characteristic
40	C₈	C₂×C₈×C₂₁₁	1	1	yes	characteristic
41	C₂²	C₂×C₁₆×C₂₁₁	1	1	yes	characteristic
42	C₄	C₃₂×C₂₁₁	1	4	yes	direct product factor
43	C₄	C₄×C₈×C₂₁₁	1	1	yes	characteristic
44	C₄	C₂×C₁₆×C₂₁₁	1	1	yes	characteristic
45	C₂	C₄×C₁₆×C₂₁₁	1	1	yes	characteristic
46	C₂	C₂×C₃₂×C₂₁₁	1	2	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₁₆	C₂²×C₂₁₁
socle, prime radical	C₂²×C₂₁₁	C₂×C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₃₂×C₂₁₁	C₄	direct (N × H)
18. C₄×C₂₁₁	C₃₂	direct (N × H)
23. C₂₁₁	C₄×C₃₂	direct (N × H)
24. C₄×C₃₂	C₂₁₁	direct (N × H)
30. C₃₂	C₄×C₂₁₁	direct (N × H)
42. C₄	C₃₂×C₂₁₁	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×C₂₁₁	2
C₄×C₁₆×C₂₁₁	2
C₄×C₃₂	211

Subgroups — C4×C32×C211 #41009016

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₃₂×C₂₁₁ #41009016