Subgroups — #16778223

Order 3328.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13129651	C₂	1	2	yes	maximal, complemented
2	C₂×#11718035	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×C₃₂	C₄	1	1	yes	characteristic
4	#11718035	C₄	1	1	yes	characteristic
5	#11718035	C₂²	1	1	yes	characteristic
6	C₂×C₁₃×C₁₆	C₈	1	1	yes	characteristic
7	C₁₃×C₃₂	C₈	1	1	yes	characteristic
8	C₁₃×C₃₂	C₂×C₄	1	1	yes	characteristic
9	M₂₅₆	—	13	1	no	maximal, Sylow
10	C₂×C₈×C₁₃	C₁₆	1	1	yes	characteristic
11	C₁₃×C₁₆	C₁₆	1	1	yes	characteristic
12	C₁₃×C₁₆	C₂×C₈	1	1	yes	characteristic
13	C₂×C₆₄	—	13	1	no	—
14	C₁₂₈	—	13	2	no	—
15	C₂×C₄×C₁₃	C₃₂	1	1	yes	characteristic
16	C₈×C₁₃	C₃₂	1	1	yes	characteristic
17	C₈×C₁₃	C₂×C₁₆	1	1	yes	characteristic
18	C₂×C₃₂	#261	1	1	yes	characteristic
19	C₆₄	—	13	1	no	—
20	C₆₄	—	13	1	no	—
21	C₂²×C₁₃	C₆₄	1	1	yes	characteristic
22	C₄×C₁₃	C₆₄	1	1	yes	characteristic
23	C₄×C₁₃	C₂×C₃₂	1	1	yes	characteristic
24	C₂×C₁₆	#1057	1	1	yes	characteristic
25	C₃₂	#1057	1	1	yes	characteristic
26	C₃₂	C₂×#261	1	1	yes	characteristic
27	C₂×C₁₃	—	2	1	no	—
28	C₂×C₁₃	C₂×C₆₄	1	1	yes	characteristic
29	C₂×C₈	#6092	1	1	yes	characteristic
30	C₁₆	#6092	1	1	yes	characteristic
31	C₁₆	C₂×#1057	1	1	yes	characteristic
32	C₁₃	M₂₅₆	1	1	yes	characteristic, complemented, Sylow
33	C₂×C₄	#88036	1	1	yes	characteristic
34	C₈	#88036	1	1	yes	characteristic
35	C₈	C₂×#6092	1	1	yes	characteristic
36	C₂²	#11718037	1	1	yes	characteristic
37	C₄	#11718037	1	1	yes	characteristic
38	C₄	C₂×#88036	1	1	yes	characteristic
39	C₂	—	2	1	no	—
40	C₂	C₂×#11718037	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₃₂	C₂×#261
commutator, socle	C₂×C₁₃	C₂×C₆₄
Fitting	C₂×C₁₃×C₃₂	C₄
prime radical	C₂²×C₁₃	C₆₄
cosocle	#11718035	C₂²
hypercenter	C₂×C₃₂	#261
hypocenter	C₁₃	M₂₅₆
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₃₂ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
1. #13129651	C₂	semidirect
32. C₁₃	M₂₅₆	semidirect

Maximal subgroups

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

subgroup	index
#13129651	2
C₂×#11718035	2
M₂₅₆	13