Subgroups — #15749533

Order 3328.

150 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×#6090	C₂	1	2	yes	maximal
2	C₈×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₃×C₁₆	C₄	1	2	yes	—
4	C₈²×C₁₃	C₂²	1	1	yes	characteristic
5	C₄×#6090	C₄	1	4	yes	—
6	C₂×C₁₃×C₁₆	C₈	1	4	yes	—
7	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
8	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
9	C₂×#6090	C₈	1	8	yes	—
10	#7052	—	13	1	no	maximal, Sylow
11	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
12	C₂×C₈×C₁₃	C₂×C₈	1	4	yes	—
13	C₄²×C₁₃	C₄²	1	1	yes	characteristic
14	C₁₃×C₁₆	C₁₆	1	8	yes	complemented
15	#6090	—	2	8	no	—
16	C₈×C₁₆	—	13	2	no	—
17	C₈×C₁₆	D₁₃	1	1	yes	characteristic
18	C₂×C₄×C₁₃	C₄×C₈	1	1	yes	characteristic
19	C₂×C₄×C₁₃	C₄×C₈	1	2	yes	—
20	C₈×C₁₃	C₂×C₁₆	1	4	yes	—
21	C₈×C₁₃	M₃₂	1	8	yes	—
22	C₄×C₁₆	—	13	4	no	—
23	C₄×C₁₆	Dic₁₃	1	2	yes	—
24	C₈²	C₂×D₁₃	1	1	yes	characteristic
25	C₂²×C₁₃	C₈²	1	1	yes	characteristic
26	C₄×C₁₃	C₄×C₁₆	1	2	yes	—
27	C₄×C₁₃	#346	1	4	yes	—
28	C₂×C₁₆	—	13	8	no	—
29	C₂×C₁₆	#1055	1	4	yes	—
30	C₄×C₈	C₄×D₁₃	1	2	yes	—
31	C₄×C₈	C₂×Dic₁₃	1	1	yes	characteristic
32	C₂×C₁₃	C₈×C₁₆	1	1	yes	characteristic
33	C₂×C₁₃	#1311	1	2	yes	—
34	C₂×C₈	C₈×D₁₃	1	4	yes	—
35	C₂×C₈	C₂×#1055	1	2	yes	—
36	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
37	C₁₆	—	26	8	no	—
38	C₁₆	#6090	1	8	yes	complemented
39	C₁₃	#7052	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₄	C₄×#1055	1	1	yes	characteristic
41	C₂×C₄	C₈×Dic₁₃	1	2	yes	—
42	C₈	#88038	1	8	yes	—
43	C₈	C₂×#6090	1	4	yes	—
44	C₂²	C₈×#1055	1	1	yes	characteristic
45	C₄	C₄×#6090	1	2	yes	—
46	C₄	#11718094	1	4	yes	—
47	C₂	C₈×#6090	1	1	yes	characteristic
48	C₂	#13112752	1	2	yes	—

	subgroup	G/H
center, Frattini	C₈²	C₂×D₁₃
commutator	C₂×C₁₃	C₈×C₁₆
Fitting	C₈×C₁₃×C₁₆	C₂
socle, prime radical	C₂²×C₁₃	C₈²
cosocle	C₈²×C₁₃	C₂²
hypercenter	C₈×C₁₆	D₁₃
hypocenter	C₁₃	#7052
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₈² ◁ C₈×C₁₆

Complements

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

N	H ≅ G/N	type
14. C₁₃×C₁₆	C₁₆	semidirect
38. C₁₆	#6090	semidirect
39. C₁₃	#7052	semidirect

Maximal subgroups

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

subgroup	index
C₈×#6090	2
C₈×C₁₃×C₁₆	2
#7052	13