Subgroups — #16778143

Order 3328.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13130005	C₂	1	2	yes	maximal
2	#13112970	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	C₄	1	4	yes	complemented
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	C₈	1	2	yes	—
11	#88034	C₂×C₄	1	2	yes	—
12	#7511	—	13	1	no	maximal, Sylow
13	C₂×C₈×C₁₃	C₁₆	1	1	yes	characteristic
14	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
15	C₄²×C₁₃	C₁₆	1	1	yes	characteristic
16	C₁₃×C₁₆	C₁₆	1	2	yes	—
17	C₁₃×C₁₆	C₄²	1	1	yes	characteristic
18	C₁₃×C₁₆	C₂×C₈	1	1	yes	characteristic
19	M₁₂₈	—	13	2	no	—
20	#1397	—	13	1	no	—
21	C₂×C₄×C₁₃	—	2	1	no	—
22	C₂×C₄×C₁₃	C₂×C₁₆	1	1	yes	characteristic
23	C₈×C₁₃	—	2	1	no	—
24	C₈×C₁₃	C₄×C₈	1	1	yes	characteristic
25	C₈×C₁₃	C₂×C₁₆	1	1	yes	characteristic
26	C₂×C₃₂	—	13	1	no	—
27	C₂×C₃₂	—	13	1	no	—
28	C₄×C₁₆	#261	1	1	yes	characteristic
29	C₆₄	—	13	4	no	—
30	C₂²×C₁₃	M₆₄	1	1	yes	characteristic
31	C₄×C₁₃	—	4	1	no	—
32	C₄×C₁₃	C₄×C₁₆	1	1	yes	characteristic
33	C₄×C₁₃	M₆₄	1	1	yes	characteristic
34	C₂×C₁₆	#1057	1	1	yes	characteristic
35	C₂×C₁₆	C₂×#261	1	1	yes	characteristic
36	C₄×C₈	#1057	1	1	yes	characteristic
37	C₃₂	—	13	2	no	—
38	C₃₂	—	13	2	no	—
39	C₂×C₁₃	—	2	1	no	—
40	C₂×C₁₃	#1397	1	1	yes	characteristic
41	C₂×C₈	#6092	1	1	yes	characteristic
42	C₂×C₈	C₂×#1057	1	1	yes	characteristic
43	C₄²	#6092	1	1	yes	characteristic
44	C₁₆	#6092	1	2	yes	—
45	C₁₆	D₁₃⋊C₈	1	1	yes	characteristic
46	C₁₆	C₄×#261	1	1	yes	characteristic
47	C₁₃	#7511	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₄	—	2	1	no	—
49	C₂×C₄	C₂×#6092	1	1	yes	characteristic
50	C₈	—	2	1	no	—
51	C₈	C₂×#6092	1	1	yes	characteristic
52	C₈	C₄×#1057	1	1	yes	characteristic
53	C₂²	#11718249	1	1	yes	characteristic
54	C₄	—	4	1	no	—
55	C₄	C₄×#6092	1	1	yes	characteristic
56	C₄	#11718249	1	1	yes	characteristic
57	C₂	—	2	1	no	—
58	C₂	#13129943	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	C₄×#261
commutator	C₄×C₁₃	C₄×C₁₆
Frattini	C₂×C₁₆	C₂×#261
Fitting	C₄×C₁₃×C₁₆	C₄
socle	C₂×C₁₃	#1397
prime radical	C₂²×C₁₃	M₆₄
cosocle	C₂×#88034	C₂²
hypercenter	C₄×C₁₆	#261
hypocenter	C₁₃	#7511
LCS	G ▷ C₄×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₁₆ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
6. #11718037	C₄	semidirect
47. C₁₃	#7511	semidirect

Maximal subgroups

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

subgroup	index
#13130005	2
#13112970	2
#7511	13