Subgroups — #16778142

Order 3328.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13130006	C₂	1	1	yes	maximal, characteristic
2	#13129942	C₂	1	1	yes	maximal, characteristic
3	#13113046	C₂	1	1	yes	maximal, characteristic
4	C₁₆×#261	C₄	1	1	yes	characteristic
5	D₁₃⋊C₃₂	C₄	1	1	yes	characteristic
6	D₁₃×C₃₂	C₂²	1	1	yes	characteristic
7	#11718037	C₄	1	2	yes	complemented
8	C₁₃×C₆₄	C₄	1	1	yes	characteristic, complemented
9	#11718035	C₄	1	1	yes	characteristic, complemented
10	C₈×#261	C₈	1	1	yes	characteristic
11	D₁₃⋊C₁₆	C₈	1	1	yes	characteristic
12	C₁₆×D₁₃	C₂×C₄	1	1	yes	characteristic
13	#88036	C₈	1	2	yes	—
14	C₁₃×C₃₂	C₂×C₄	1	1	yes	characteristic
15	#88034	C₂×C₄	1	1	yes	characteristic
16	#7511	—	13	1	no	maximal, Sylow
17	C₄×#261	C₁₆	1	1	yes	characteristic
18	D₁₃⋊C₈	C₁₆	1	1	yes	characteristic
19	C₈×D₁₃	C₂×C₈	1	1	yes	characteristic
20	#6092	C₁₆	1	2	yes	—
21	C₁₃×C₁₆	C₄²	1	1	yes	characteristic
22	#6090	C₂×C₈	1	1	yes	characteristic
23	M₁₂₈	—	13	1	no	—
24	M₁₂₈	—	13	1	no	—
25	#1397	—	13	1	no	—
26	C₂×#261	—	2	1	no	—
27	C₄×D₁₃	C₂×C₁₆	1	1	yes	characteristic
28	#1057	—	2	1	no	—
29	C₈×C₁₃	C₄×C₈	1	1	yes	characteristic
30	#1055	C₂×C₁₆	1	1	yes	characteristic
31	C₂×C₃₂	—	13	1	no	—
32	C₂×C₃₂	—	13	1	no	—
33	C₄×C₁₆	—	13	1	no	—
34	C₆₄	—	13	2	no	—
35	C₆₄	—	13	1	no	—
36	C₆₄	#261	1	1	yes	characteristic, complemented
37	C₂×D₁₃	M₆₄	1	1	yes	characteristic
38	#261	—	4	1	no	—
39	C₄×C₁₃	C₄×C₁₆	1	1	yes	characteristic
40	Dic₁₃	M₆₄	1	1	yes	characteristic
41	C₂×C₁₆	—	13	1	no	—
42	C₂×C₁₆	—	13	1	no	—
43	C₄×C₈	—	13	1	no	—
44	C₃₂	—	13	2	no	—
45	C₃₂	—	13	1	no	—
46	C₃₂	C₂×#261	1	1	yes	characteristic
47	C₂×C₁₃	#1397	1	1	yes	characteristic
48	D₁₃	—	2	1	no	—
49	C₂×C₈	—	13	1	no	—
50	C₂×C₈	—	13	1	no	—
51	C₄²	—	13	1	no	—
52	C₁₆	—	13	2	no	—
53	C₁₆	—	13	1	no	—
54	C₁₆	C₄×#261	1	1	yes	characteristic
55	C₁₃	#7511	1	1	yes	characteristic, complemented, Sylow
56	C₂×C₄	—	13	1	no	—
57	C₂×C₄	—	26	1	no	—
58	C₈	—	13	1	no	—
59	C₈	—	26	1	no	—
60	C₈	C₈×#261	1	1	yes	characteristic
61	C₂²	—	13	1	no	—
62	C₄	—	13	1	no	—
63	C₄	—	52	1	no	—
64	C₄	C₁₆×#261	1	1	yes	characteristic
65	C₂	—	26	1	no	—
66	C₂	#13129942	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	C₄×#261
commutator	C₄×C₁₃	C₄×C₁₆
Frattini	C₃₂	C₂×#261
Fitting	C₁₃×C₆₄	C₄
socle	C₂×C₁₃	#1397
prime radical	C₂×D₁₃	M₆₄
cosocle	D₁₃×C₃₂	C₂²
hypercenter	C₆₄	#261
hypocenter	C₁₃	#7511
LCS	G ▷ C₄×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₁₆ ◁ C₆₄

Complements

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

N	H ≅ G/N	type
7. #11718037	C₄	semidirect
8. C₁₃×C₆₄	C₄	semidirect
9. #11718035	C₄	semidirect
36. C₆₄	#261	semidirect
55. C₁₃	#7511	semidirect

Maximal subgroups

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

subgroup	index
#13130006	2
#13129942	2
#13113046	2
#7511	13