Subgroups — #16778140

Order 3328.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718037	C₂	1	2	yes	maximal
2	C₃₂×Dic₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×C₃₂	C₄	1	1	yes	characteristic
4	C₁₆×Dic₁₃	C₄	1	1	yes	characteristic
5	C₂×#88034	C₂²	1	1	yes	characteristic
6	#11718037	C₄	1	4	yes	complemented
7	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
8	C₈×Dic₁₃	C₈	1	1	yes	characteristic
9	C₂×#6090	C₈	1	1	yes	characteristic
10	C₁₃×C₃₂	C₈	1	2	yes	—
11	#88034	C₂×C₄	1	2	yes	—
12	#7510	—	13	1	no	maximal, Sylow
13	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
14	C₄×Dic₁₃	C₁₆	1	1	yes	characteristic
15	C₂×#1055	C₁₆	1	1	yes	characteristic
16	C₁₃×C₁₆	C₄²	1	1	yes	characteristic
17	C₁₃×C₁₆	C₂×C₈	1	1	yes	characteristic
18	#6090	C₁₆	1	2	yes	—
19	C₂×C₆₄	—	13	2	no	—
20	C₄×C₃₂	—	13	1	no	—
21	C₂×C₄×C₁₃	C₂×C₁₆	1	1	yes	characteristic
22	C₂×Dic₁₃	C₃₂	1	2	yes	—
23	C₈×C₁₃	C₄×C₈	1	1	yes	characteristic
24	C₈×C₁₃	C₂×C₁₆	1	1	yes	characteristic
25	#1055	C₃₂	1	2	yes	—
26	C₂×C₃₂	—	13	1	no	—
27	C₂×C₃₂	#261	1	1	yes	characteristic
28	C₄×C₁₆	—	13	1	no	—
29	C₆₄	—	13	4	no	—
30	C₂²×C₁₃	C₂×C₃₂	1	1	yes	characteristic
31	C₄×C₁₃	C₄×C₁₆	1	1	yes	characteristic
32	C₄×C₁₃	C₂×C₃₂	1	1	yes	characteristic
33	Dic₁₃	—	2	2	no	—
34	C₂×C₁₆	—	13	1	no	—
35	C₂×C₁₆	C₂×#261	1	1	yes	characteristic
36	C₄×C₈	—	13	1	no	—
37	C₃₂	—	13	2	no	—
38	C₃₂	#1057	1	2	yes	—
39	C₂×C₁₃	C₄×C₃₂	1	1	yes	characteristic
40	C₂×C₁₃	M₁₂₈	1	2	yes	—
41	C₂×C₈	—	13	1	no	—
42	C₂×C₈	D₁₃⋊C₈	1	1	yes	characteristic
43	C₄²	—	13	1	no	—
44	C₁₆	—	13	2	no	—
45	C₁₆	C₄×#261	1	1	yes	characteristic
46	C₁₆	C₂×#1057	1	1	yes	characteristic
47	C₁₃	#7510	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₄	—	13	2	no	—
49	C₂×C₄	D₁₃⋊C₁₆	1	1	yes	characteristic
50	C₈	—	13	2	no	—
51	C₈	D₁₃⋊C₁₆	1	1	yes	characteristic
52	C₈	C₄×#1057	1	1	yes	characteristic
53	C₂²	D₁₃⋊C₃₂	1	1	yes	characteristic
54	C₄	—	26	2	no	—
55	C₄	D₁₃⋊C₃₂	1	1	yes	characteristic
56	C₄	#11718257	1	1	yes	characteristic
57	C₂	#13129941	1	1	yes	characteristic
58	C₂	#13130006	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₁₆	C₂×#261
commutator	C₂×C₁₃	C₄×C₃₂
Fitting	C₂×C₁₃×C₃₂	C₄
socle, prime radical	C₂²×C₁₃	C₂×C₃₂
cosocle	C₂×#88034	C₂²
hypercenter	C₂×C₃₂	#261
hypocenter	C₁₃	#7510
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
6. #11718037	C₄	semidirect
47. C₁₃	#7510	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718037	2
C₃₂×Dic₁₃	2
#7510	13