Subgroups — #16778214

Order 3328.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13130005	C₂	1	2	yes	maximal
2	C₃₂×Dic₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×C₃₂	C₄	1	1	yes	characteristic
4	C₁₆×Dic₁₃	C₄	1	1	yes	characteristic
5	C₂×#88034	C₂²	1	1	yes	characteristic
6	#11718037	—	2	2	no	—
7	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
8	C₈×Dic₁₃	C₈	1	1	yes	characteristic
9	C₂×#6090	C₈	1	1	yes	characteristic
10	C₁₃×C₃₂	—	2	1	no	—
11	#88034	D₄	1	1	yes	characteristic
12	#88034	Q₈	1	1	yes	characteristic
13	#7544	—	13	1	no	maximal, Sylow
14	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
15	C₄×Dic₁₃	C₁₆	1	1	yes	characteristic
16	C₂×#1055	C₁₆	1	1	yes	characteristic
17	C₁₃×C₁₆	C₄⋊C₄	1	1	yes	characteristic
18	C₁₃×C₁₆	M₁₆	1	1	yes	characteristic
19	#6090	—	2	1	no	—
20	M₁₂₈	—	13	2	no	—
21	C₄×C₃₂	—	13	1	no	—
22	C₂×C₄×C₁₃	C₂×C₁₆	1	1	yes	characteristic
23	C₂×Dic₁₃	—	2	1	no	—
24	C₈×C₁₃	C₄⋊C₈	1	1	yes	characteristic
25	C₈×C₁₃	M₃₂	1	1	yes	characteristic
26	#1055	C₃₂	1	2	yes	—
27	C₂×C₃₂	—	13	1	no	—
28	C₂×C₃₂	#261	1	1	yes	characteristic
29	C₄×C₁₆	—	13	1	no	—
30	C₆₄	—	26	2	no	—
31	C₂²×C₁₃	M₆₄	1	1	yes	characteristic
32	C₄×C₁₃	C₄⋊C₁₆	1	1	yes	characteristic
33	C₄×C₁₃	C₂×C₃₂	1	1	yes	characteristic
34	Dic₁₃	—	2	2	no	—
35	C₂×C₁₆	—	13	1	no	—
36	C₂×C₁₆	C₂×#261	1	1	yes	characteristic
37	C₄×C₈	—	13	1	no	—
38	C₃₂	—	2	1	no	—
39	C₃₂	—	13	1	no	—
40	C₃₂	—	13	1	no	—
41	C₂×C₁₃	—	2	1	no	—
42	C₂×C₁₃	C₄⋊C₃₂	1	1	yes	characteristic
43	C₂×C₈	—	13	1	no	—
44	C₂×C₈	D₁₃⋊C₈	1	1	yes	characteristic
45	C₄²	—	13	1	no	—
46	C₁₆	—	26	1	no	—
47	C₁₆	C₄⋊#261	1	1	yes	characteristic
48	C₁₆	#6122	1	1	yes	characteristic
49	C₁₃	#7544	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₄	—	26	1	no	—
51	C₂×C₄	D₁₃⋊C₁₆	1	1	yes	characteristic
52	C₈	—	13	2	no	—
53	C₈	#88098	1	1	yes	characteristic
54	C₈	#88112	1	1	yes	characteristic
55	C₂²	#11718214	1	1	yes	characteristic
56	C₄	—	26	2	no	—
57	C₄	D₁₃⋊C₃₂	1	1	yes	characteristic
58	C₄	#11718260	1	1	yes	characteristic
59	C₂	—	2	1	no	—
60	C₂	#13129994	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	C₄⋊#261
commutator	C₄×C₁₃	C₂×C₃₂
Frattini	C₂×C₁₆	C₂×#261
Fitting	C₂×C₁₃×C₃₂	C₄
socle	C₂×C₁₃	C₄⋊C₃₂
prime radical	C₂²×C₁₃	M₆₄
cosocle	C₂×#88034	C₂²
hypercenter	C₂×C₃₂	#261
hypocenter	C₁₃	#7544
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
49. C₁₃	#7544	semidirect

Maximal subgroups

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

subgroup	index
#13130005	2
C₃₂×Dic₁₃	2
#7544	13