Subgroups — C₄³×#261 #16791502

Order 3328.

3966 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×#261	C₂	1	14	yes	maximal
2	C₄³×D₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄×#261	C₂²	1	28	yes	—
4	C₂×C₄²×D₁₃	C₂²	1	7	yes	—
5	C₄²×#261	C₄	1	112	yes	direct product factor
6	C₄³×C₁₃	C₄	1	1	yes	characteristic, complemented
7	C₄²×Dic₁₃	C₄	1	7	yes	complemented
8	C₂³×#261	C₂³	1	8	yes	—
9	C₂²×C₄×D₁₃	C₂³	1	7	yes	—
10	C₂×C₄×#261	C₂×C₄	1	336	yes	—
11	C₂×C₄²×C₁₃	C₂×C₄	1	7	yes	—
12	C₂×C₄×Dic₁₃	C₂×C₄	1	21	yes	—
13	C₄²×D₁₃	C₂×C₄	1	56	yes	—
14	C₄⁴	—	13	1	no	maximal, Sylow
15	C₂³×D₁₃	C₂⁴	1	1	yes	characteristic
16	C₂²×#261	C₂²×C₄	1	112	yes	—
17	C₂²×C₄×C₁₃	C₂²×C₄	1	7	yes	—
18	C₂²×Dic₁₃	C₂²×C₄	1	7	yes	—
19	C₂×C₄×D₁₃	C₂²×C₄	1	84	yes	—
20	C₄×#261	C₄²	1	448	yes	direct product factor
21	C₄²×C₁₃	C₄²	1	28	yes	complemented
22	C₄×Dic₁₃	C₄²	1	84	yes	complemented
23	C₂×C₄³	—	13	14	no	—
24	C₂×C₄³	—	13	1	no	—
25	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
26	C₂²×D₁₃	C₂³×C₄	1	14	yes	—
27	C₂×#261	C₂×C₄²	1	224	yes	—
28	C₂×C₄×C₁₃	C₂×C₄²	1	42	yes	—
29	C₂×Dic₁₃	C₂×C₄²	1	42	yes	—
30	C₄×D₁₃	C₂×C₄²	1	112	yes	—
31	C₂²×C₄²	—	13	28	no	—
32	C₂²×C₄²	—	13	7	no	—
33	C₄³	—	13	112	no	—
34	C₄³	—	13	7	no	—
35	C₄³	#261	1	1	yes	characteristic, direct product factor
36	C₂²×C₁₃	C₂²×C₄²	1	7	yes	—
37	C₂×D₁₃	C₂²×C₄²	1	28	yes	—
38	#261	C₄³	1	64	yes	direct product factor
39	C₄×C₁₃	C₄³	1	28	yes	complemented
40	Dic₁₃	C₄³	1	28	yes	complemented
41	C₂³×C₄	—	13	8	no	—
42	C₂³×C₄	—	13	7	no	—
43	C₂×C₄²	—	13	336	no	—
44	C₂×C₄²	—	13	21	no	—
45	C₂×C₄²	—	13	56	no	—
46	C₂×C₄²	C₂×#261	1	7	yes	—
47	C₂×C₁₃	C₂×C₄³	1	7	yes	—
48	D₁₃	C₂×C₄³	1	8	yes	—
49	C₂⁴	—	13	1	no	—
50	C₂²×C₄	—	13	112	no	—
51	C₂²×C₄	—	13	7	no	—
52	C₂²×C₄	—	13	84	no	—
53	C₂²×C₄	C₂²×#261	1	7	yes	—
54	C₄²	—	13	448	no	—
55	C₄²	—	13	84	no	—
56	C₄²	C₄×#261	1	28	yes	direct product factor
57	C₁₃	C₄⁴	1	1	yes	characteristic, complemented, Sylow
58	C₂³	—	13	14	no	—
59	C₂³	C₂³×#261	1	1	yes	characteristic
60	C₂×C₄	—	13	224	no	—
61	C₂×C₄	—	13	42	no	—
62	C₂×C₄	—	13	112	no	—
63	C₂×C₄	C₂×C₄×#261	1	42	yes	—
64	C₂²	—	13	28	no	—
65	C₂²	C₂²×C₄×#261	1	7	yes	—
66	C₄	—	13	64	no	—
67	C₄	—	13	28	no	—
68	C₄	C₄²×#261	1	28	yes	direct product factor
69	C₂	—	13	8	no	—
70	C₂	C₂×C₄²×#261	1	7	yes	—

	subgroup	G/H
center, hypercenter	C₄³	#261
commutator, hypocenter	C₁₃	C₄⁴
Frattini	C₂³	C₂³×#261
Fitting	C₄³×C₁₃	C₄
socle	C₂³×C₁₃	C₂³×C₄
prime radical, cosocle	C₂³×D₁₃	C₂⁴
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₄³

Complements

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

N	H ≅ G/N	type
5. C₄²×#261	C₄	direct (N × H)
6. C₄³×C₁₃	C₄	semidirect
7. C₄²×Dic₁₃	C₄	semidirect
20. C₄×#261	C₄²	direct (N × H)
21. C₄²×C₁₃	C₄²	semidirect
22. C₄×Dic₁₃	C₄²	semidirect
35. C₄³	#261	direct (N × H)
38. #261	C₄³	direct (N × H)
39. C₄×C₁₃	C₄³	semidirect
40. Dic₁₃	C₄³	semidirect
56. C₄²	C₄×#261	direct (N × H)
57. C₁₃	C₄⁴	semidirect
68. C₄	C₄²×#261	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×C₄²×#261	2
C₄³×D₁₃	2
C₄⁴	13

Subgroups — C43×#261 #16791502

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄³×#261 #16791502