Subgroups — C₄×C₁₆×C₃₆₁ #72200451

Order 23104.

87 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₈×C₃₆₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₆×C₃₆₁	C₂	1	2	yes	maximal
3	C₄²×C₃₆₁	C₄	1	1	yes	characteristic
4	C₂×C₈×C₃₆₁	C₄	1	1	yes	characteristic
5	C₂×C₈×C₃₆₁	C₂²	1	1	yes	characteristic
6	C₁₆×C₃₆₁	C₄	1	4	yes	direct product factor
7	C₂×C₄×C₃₆₁	C₈	1	2	yes	—
8	C₂×C₄×C₃₆₁	C₂×C₄	1	1	yes	characteristic
9	C₈×C₃₆₁	C₈	1	2	yes	—
10	C₈×C₃₆₁	C₂×C₄	1	2	yes	—
11	C₂²×C₃₆₁	C₂×C₈	1	1	yes	characteristic
12	C₄×C₃₆₁	C₁₆	1	4	yes	direct product factor
13	C₄×C₃₆₁	C₄²	1	1	yes	characteristic
14	C₄×C₃₆₁	C₂×C₈	1	1	yes	characteristic
15	C₄×C₁₆×C₁₉	C₁₉	1	1	yes	maximal, characteristic
16	C₂×C₃₆₁	C₄×C₈	1	1	yes	characteristic
17	C₂×C₃₆₁	C₂×C₁₆	1	2	yes	—
18	C₂×C₁₆×C₁₉	C₂×C₁₉	1	2	yes	—
19	C₄×C₈×C₁₉	C₂×C₁₉	1	1	yes	characteristic
20	C₃₆₁	C₄×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
21	C₂×C₈×C₁₉	C₄×C₁₉	1	1	yes	characteristic
22	C₂×C₈×C₁₉	C₂²×C₁₉	1	1	yes	characteristic
23	C₄²×C₁₉	C₄×C₁₉	1	1	yes	characteristic
24	C₁₆×C₁₉	C₄×C₁₉	1	4	yes	—
25	C₂×C₄×C₁₉	C₈×C₁₉	1	2	yes	—
26	C₂×C₄×C₁₉	C₂×C₄×C₁₉	1	1	yes	characteristic
27	C₈×C₁₉	C₈×C₁₉	1	2	yes	—
28	C₈×C₁₉	C₂×C₄×C₁₉	1	2	yes	—
29	C₂²×C₁₉	C₂×C₈×C₁₉	1	1	yes	characteristic
30	C₄×C₁₉	C₁₆×C₁₉	1	4	yes	—
31	C₄×C₁₉	C₄²×C₁₉	1	1	yes	characteristic
32	C₄×C₁₉	C₂×C₈×C₁₉	1	1	yes	characteristic
33	C₄×C₁₆	C₃₆₁	1	1	yes	characteristic, direct product factor, Sylow
34	C₂×C₁₉	C₄×C₈×C₁₉	1	1	yes	characteristic
35	C₂×C₁₉	C₂×C₁₆×C₁₉	1	2	yes	—
36	C₂×C₁₆	C₂×C₃₆₁	1	2	yes	—
37	C₄×C₈	C₂×C₃₆₁	1	1	yes	characteristic
38	C₁₉	C₄×C₁₆×C₁₉	1	1	yes	characteristic
39	C₂×C₈	C₄×C₃₆₁	1	1	yes	characteristic
40	C₂×C₈	C₂²×C₃₆₁	1	1	yes	characteristic
41	C₄²	C₄×C₃₆₁	1	1	yes	characteristic
42	C₁₆	C₄×C₃₆₁	1	4	yes	direct product factor
43	C₂×C₄	C₈×C₃₆₁	1	2	yes	—
44	C₂×C₄	C₂×C₄×C₃₆₁	1	1	yes	characteristic
45	C₈	C₈×C₃₆₁	1	2	yes	—
46	C₈	C₂×C₄×C₃₆₁	1	2	yes	—
47	C₂²	C₂×C₈×C₃₆₁	1	1	yes	characteristic
48	C₄	C₁₆×C₃₆₁	1	4	yes	direct product factor
49	C₄	C₂×C₈×C₃₆₁	1	1	yes	characteristic
50	C₄	C₄²×C₃₆₁	1	1	yes	characteristic
51	C₂	C₂×C₁₆×C₃₆₁	1	2	yes	—
52	C₂	C₄×C₈×C₃₆₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₈×C₁₉	C₂²×C₁₉
socle, prime radical	C₂²×C₁₉	C₂×C₈×C₁₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₁₆×C₃₆₁	C₄	direct (N × H)
12. C₄×C₃₆₁	C₁₆	direct (N × H)
20. C₃₆₁	C₄×C₁₆	direct (N × H)
33. C₄×C₁₆	C₃₆₁	direct (N × H)
42. C₁₆	C₄×C₃₆₁	direct (N × H)
48. C₄	C₁₆×C₃₆₁	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×C₈×C₃₆₁	2
C₂×C₁₆×C₃₆₁	2
C₄×C₁₆×C₁₉	19

Subgroups — C4×C16×C361 #72200451

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₆×C₃₆₁ #72200451