Subgroups — #16778213

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	C₄×#88034	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₃×C₁₆	C₄	1	1	yes	characteristic
4	C₂×#88034	C₄	1	1	yes	characteristic
5	C₂×#88034	C₂²	1	1	yes	characteristic
6	#11718037	—	2	2	no	—
7	C₂×C₁₃×C₁₆	C₈	1	1	yes	characteristic
8	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
9	C₄×C₈×C₁₃	C₈	1	1	yes	characteristic
10	#88034	—	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	C₁₆	1	1	yes	characteristic
15	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
16	C₄²×C₁₃	C₁₆	1	1	yes	characteristic
17	C₁₃×C₁₆	—	2	1	no	—
18	C₁₃×C₁₆	C₄⋊C₄	1	1	yes	characteristic
19	C₁₃×C₁₆	M₁₆	1	1	yes	characteristic
20	M₁₂₈	—	13	2	no	—
21	C₄×C₃₂	—	13	1	no	—
22	C₂×C₄×C₁₃	—	2	1	no	—
23	C₂×C₄×C₁₃	C₂×C₁₆	1	1	yes	characteristic
24	C₈×C₁₃	C₃₂	1	2	yes	—
25	C₈×C₁₃	C₄⋊C₈	1	1	yes	characteristic
26	C₈×C₁₃	M₃₂	1	1	yes	characteristic
27	C₂×C₃₂	—	13	1	no	—
28	C₂×C₃₂	—	13	1	no	—
29	C₄×C₁₆	#261	1	1	yes	characteristic
30	C₆₄	—	26	2	no	—
31	C₂²×C₁₃	M₆₄	1	1	yes	characteristic
32	C₄×C₁₃	—	2	2	no	—
33	C₄×C₁₃	C₄⋊C₁₆	1	1	yes	characteristic
34	C₄×C₁₃	C₂×C₃₂	1	1	yes	characteristic
35	C₂×C₁₆	#1057	1	1	yes	characteristic
36	C₂×C₁₆	C₂×#261	1	1	yes	characteristic
37	C₄×C₈	#1057	1	1	yes	characteristic
38	C₃₂	—	13	1	no	—
39	C₃₂	—	13	1	no	—
40	C₃₂	—	26	1	no	—
41	C₂×C₁₃	—	2	1	no	—
42	C₂×C₁₃	C₄⋊C₃₂	1	1	yes	characteristic
43	C₂×C₈	#6092	1	1	yes	characteristic
44	C₂×C₈	C₂×#1057	1	1	yes	characteristic
45	C₄²	#6092	1	1	yes	characteristic
46	C₁₆	—	2	1	no	—
47	C₁₆	#6118	1	1	yes	characteristic
48	C₁₆	C₄⋊#261	1	1	yes	characteristic
49	C₁₃	#7544	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₄	—	2	1	no	—
51	C₂×C₄	C₂×#6092	1	1	yes	characteristic
52	C₈	#88036	1	2	yes	—
53	C₈	#88106	1	1	yes	characteristic
54	C₈	C₄⋊#1057	1	1	yes	characteristic
55	C₂²	#11718249	1	1	yes	characteristic
56	C₄	—	2	2	no	—
57	C₄	C₄⋊#6092	1	1	yes	characteristic
58	C₄	C₂×#88036	1	1	yes	characteristic
59	C₂	—	2	1	no	—
60	C₂	C₄⋊#88036	1	1	yes	characteristic

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

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
C₄×#88034	2
#7544	13