Subgroups — #16778219

Order 3328.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13130000	C₂	1	1	yes	maximal, characteristic
2	#13129998	C₂	1	1	yes	maximal, characteristic
3	#13113046	C₂	1	1	yes	maximal, characteristic
4	#11718223	—	2	1	no	—
5	#11718221	—	2	1	no	—
6	D₁₃×C₃₂	C₂²	1	1	yes	characteristic
7	C₁₃×C₆₄	C₄	1	1	yes	characteristic, complemented
8	#11718035	C₄	1	1	yes	characteristic, complemented
9	#88104	—	4	1	no	—
10	#88102	—	4	1	no	—
11	C₁₆×D₁₃	D₄	1	1	yes	characteristic
12	C₁₃×C₃₂	C₂×C₄	1	1	yes	characteristic
13	#88034	Q₈	1	1	yes	characteristic
14	#7548	—	13	1	no	maximal, Sylow
15	C₄⋊#261	—	8	1	no	—
16	#6118	—	8	1	no	—
17	C₈×D₁₃	D₈	1	1	yes	characteristic
18	C₁₃×C₁₆	C₄⋊C₄	1	1	yes	characteristic
19	#6090	Q₁₆	1	1	yes	characteristic
20	M₁₂₈	—	13	1	no	—
21	#1425	—	13	1	no	—
22	#1424	—	13	1	no	—
23	C₂×#261	—	16	1	no	—
24	C₄×D₁₃	D₁₆	1	1	yes	characteristic
25	#1057	—	16	1	no	—
26	C₈×C₁₃	#107	1	1	yes	characteristic
27	#1055	Q₃₂	1	1	yes	characteristic
28	C₂×C₃₂	—	13	1	no	—
29	#368	—	26	1	no	—
30	#366	—	26	1	no	—
31	C₆₄	—	13	1	no	—
32	C₆₄	#261	1	1	yes	characteristic, complemented
33	C₂×D₁₃	SD₆₄	1	1	yes	characteristic
34	#261	—	32	1	no	—
35	C₄×C₁₃	#366	1	1	yes	characteristic
36	Dic₁₃	SD₆₄	1	1	yes	characteristic
37	C₂×C₁₆	—	13	1	no	—
38	#108	—	52	1	no	—
39	#107	—	52	1	no	—
40	C₃₂	—	13	1	no	—
41	C₃₂	C₂×#261	1	1	yes	characteristic
42	C₂×C₁₃	#1424	1	1	yes	characteristic
43	D₁₃	—	2	1	no	—
44	M₁₆	—	104	1	no	—
45	C₂×C₈	—	13	1	no	—
46	C₄⋊C₄	—	104	1	no	—
47	C₁₆	—	13	1	no	—
48	C₁₆	C₄⋊#261	1	1	yes	characteristic
49	C₁₃	#7548	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₄	—	13	1	no	—
51	C₂×C₄	—	208	1	no	—
52	C₈	—	13	1	no	—
53	C₈	—	208	1	no	—
54	C₈	#88102	1	1	yes	characteristic
55	C₂²	—	13	1	no	—
56	C₄	—	13	1	no	—
57	C₄	—	416	1	no	—
58	C₄	#11718221	1	1	yes	characteristic
59	C₂	—	26	1	no	—
60	C₂	#13129998	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#13129998
commutator	C₁₃×C₃₂	C₂×C₄
Frattini	C₃₂	C₂×#261
Fitting	C₁₃×C₆₄	C₄
socle	C₂×C₁₃	#1424
prime radical	C₂×D₁₃	SD₆₄
cosocle	D₁₃×C₃₂	C₂²
hypercenter	C₆₄	#261
hypocenter	C₁₃	#7548
LCS	G ▷ C₁₃×C₃₂ ▷ C₁₃×C₁₆ ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ C₃₂ ◁ C₆₄

Complements

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

N	H ≅ G/N	type
7. C₁₃×C₆₄	C₄	semidirect
8. #11718035	C₄	semidirect
32. C₆₄	#261	semidirect
49. C₁₃	#7548	semidirect

Maximal subgroups

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

subgroup	index
#13130000	2
#13129998	2
#13113046	2
#7548	13