Subgroups — C₄×C₁₃²×C₃₂ #72199146

Order 21632.

576 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₃²×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃²×C₃₂	C₂	1	2	yes	maximal
3	C₄×C₈×C₁₃²	C₄	1	1	yes	characteristic
4	C₂×C₁₃²×C₁₆	C₄	1	1	yes	characteristic
5	C₂×C₁₃²×C₁₆	C₂²	1	1	yes	characteristic
6	C₁₃²×C₃₂	C₄	1	4	yes	direct product factor
7	C₄²×C₁₃²	C₈	1	1	yes	characteristic
8	C₂×C₈×C₁₃²	C₈	1	1	yes	characteristic
9	C₂×C₈×C₁₃²	C₂×C₄	1	1	yes	characteristic
10	C₁₃²×C₁₆	C₈	1	2	yes	—
11	C₁₃²×C₁₆	C₂×C₄	1	2	yes	—
12	C₄×C₁₃×C₃₂	C₁₃	1	14	yes	maximal, direct product factor
13	C₂×C₄×C₁₃²	C₁₆	1	2	yes	—
14	C₂×C₄×C₁₃²	C₂×C₈	1	1	yes	characteristic
15	C₈×C₁₃²	C₁₆	1	2	yes	—
16	C₈×C₁₃²	C₄²	1	1	yes	characteristic
17	C₈×C₁₃²	C₂×C₈	1	1	yes	characteristic
18	C₂×C₁₃×C₃₂	C₂×C₁₃	1	28	yes	—
19	C₄×C₁₃×C₁₆	C₂×C₁₃	1	14	yes	—
20	C₂²×C₁₃²	C₂×C₁₆	1	1	yes	characteristic
21	C₄×C₁₃²	C₃₂	1	4	yes	direct product factor
22	C₄×C₁₃²	C₄×C₈	1	1	yes	characteristic
23	C₄×C₁₃²	C₂×C₁₆	1	1	yes	characteristic
24	C₂×C₁₃×C₁₆	C₄×C₁₃	1	14	yes	—
25	C₂×C₁₃×C₁₆	C₂²×C₁₃	1	14	yes	—
26	C₄×C₈×C₁₃	C₄×C₁₃	1	14	yes	—
27	C₁₃×C₃₂	C₄×C₁₃	1	56	yes	direct product factor
28	C₂×C₁₃²	C₄×C₁₆	1	1	yes	characteristic
29	C₂×C₁₃²	C₂×C₃₂	1	2	yes	—
30	C₂×C₈×C₁₃	C₈×C₁₃	1	14	yes	—
31	C₂×C₈×C₁₃	C₂×C₄×C₁₃	1	14	yes	—
32	C₄²×C₁₃	C₈×C₁₃	1	14	yes	—
33	C₁₃×C₁₆	C₈×C₁₃	1	28	yes	—
34	C₁₃×C₁₆	C₂×C₄×C₁₃	1	28	yes	—
35	C₁₃²	C₄×C₃₂	1	1	yes	characteristic, direct product factor, Sylow
36	C₄×C₃₂	C₁₃²	1	1	yes	characteristic, direct product factor, Sylow
37	C₂×C₄×C₁₃	C₁₃×C₁₆	1	28	yes	—
38	C₂×C₄×C₁₃	C₂×C₈×C₁₃	1	14	yes	—
39	C₈×C₁₃	C₁₃×C₁₆	1	28	yes	—
40	C₈×C₁₃	C₄²×C₁₃	1	14	yes	—
41	C₈×C₁₃	C₂×C₈×C₁₃	1	14	yes	—
42	C₂×C₃₂	C₂×C₁₃²	1	2	yes	—
43	C₄×C₁₆	C₂×C₁₃²	1	1	yes	characteristic
44	C₂²×C₁₃	C₂×C₁₃×C₁₆	1	14	yes	—
45	C₄×C₁₃	C₁₃×C₃₂	1	56	yes	direct product factor
46	C₄×C₁₃	C₄×C₈×C₁₃	1	14	yes	—
47	C₄×C₁₃	C₂×C₁₃×C₁₆	1	14	yes	—
48	C₂×C₁₆	C₄×C₁₃²	1	1	yes	characteristic
49	C₂×C₁₆	C₂²×C₁₃²	1	1	yes	characteristic
50	C₄×C₈	C₄×C₁₃²	1	1	yes	characteristic
51	C₃₂	C₄×C₁₃²	1	4	yes	direct product factor
52	C₂×C₁₃	C₄×C₁₃×C₁₆	1	14	yes	—
53	C₂×C₁₃	C₂×C₁₃×C₃₂	1	28	yes	—
54	C₂×C₈	C₈×C₁₃²	1	1	yes	characteristic
55	C₂×C₈	C₂×C₄×C₁₃²	1	1	yes	characteristic
56	C₄²	C₈×C₁₃²	1	1	yes	characteristic
57	C₁₆	C₈×C₁₃²	1	2	yes	—
58	C₁₆	C₂×C₄×C₁₃²	1	2	yes	—
59	C₁₃	C₄×C₁₃×C₃₂	1	14	yes	direct product factor
60	C₂×C₄	C₁₃²×C₁₆	1	2	yes	—
61	C₂×C₄	C₂×C₈×C₁₃²	1	1	yes	characteristic
62	C₈	C₁₃²×C₁₆	1	2	yes	—
63	C₈	C₂×C₈×C₁₃²	1	1	yes	characteristic
64	C₈	C₄²×C₁₃²	1	1	yes	characteristic
65	C₂²	C₂×C₁₃²×C₁₆	1	1	yes	characteristic
66	C₄	C₁₃²×C₃₂	1	4	yes	direct product factor
67	C₄	C₂×C₁₃²×C₁₆	1	1	yes	characteristic
68	C₄	C₄×C₈×C₁₃²	1	1	yes	characteristic
69	C₂	C₂×C₁₃²×C₃₂	1	2	yes	—
70	C₂	C₄×C₁₃²×C₁₆	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₁₆	C₂²×C₁₃²
socle, prime radical	C₂²×C₁₃²	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. C₁₃²×C₃₂	C₄	direct (N × H)
12. C₄×C₁₃×C₃₂	C₁₃	direct (N × H)
21. C₄×C₁₃²	C₃₂	direct (N × H)
27. C₁₃×C₃₂	C₄×C₁₃	direct (N × H)
35. C₁₃²	C₄×C₃₂	direct (N × H)
36. C₄×C₃₂	C₁₃²	direct (N × H)
45. C₄×C₁₃	C₁₃×C₃₂	direct (N × H)
51. C₃₂	C₄×C₁₃²	direct (N × H)
59. C₁₃	C₄×C₁₃×C₃₂	direct (N × H)
66. C₄	C₁₃²×C₃₂	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₁₃²×C₁₆	2
C₂×C₁₃²×C₃₂	2
C₄×C₁₃×C₃₂	13

Subgroups — C4×C132×C32 #72199146

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₃²×C₃₂ #72199146