Subgroups — #16777978

Order 3328.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13129871	C₂	1	2	yes	maximal
2	C₃₂×Dic₁₃	C₂	1	1	yes	maximal, characteristic
3	#11718261	—	2	2	no	—
4	C₂×C₁₃×C₃₂	C₄	1	1	yes	characteristic
5	C₁₆×Dic₁₃	C₂²	1	1	yes	characteristic
6	C₂×#88034	C₄	1	1	yes	characteristic
7	#88106	—	4	2	no	—
8	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
9	C₈×Dic₁₃	D₄	1	1	yes	characteristic
10	C₂×#6090	Q₈	1	1	yes	characteristic
11	C₁₃×C₃₂	C₈	1	2	yes	—
12	#88034	—	2	1	no	—
13	#7462	—	13	1	no	maximal, Sylow
14	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
15	C₄×Dic₁₃	Q₁₆	1	1	yes	characteristic
16	C₂×#1055	D₈	1	1	yes	characteristic
17	#6092	—	8	2	no	—
18	C₁₃×C₁₆	C₂×C₈	1	1	yes	characteristic
19	C₁₃×C₁₆	M₁₆	1	1	yes	characteristic
20	#6090	—	2	1	no	—
21	C₄×C₃₂	—	13	1	no	—
22	#1373	—	13	2	no	—
23	C₂×C₄×C₁₃	#107	1	1	yes	characteristic
24	C₂×Dic₁₃	—	2	1	no	—
25	C₈×C₁₃	C₄⋊C₈	1	1	yes	characteristic
26	C₈×C₁₃	#108	1	1	yes	characteristic
27	#1055	D₁₆	1	1	yes	characteristic
28	#1055	Q₃₂	1	1	yes	characteristic
29	C₂×C₃₂	—	13	1	no	—
30	C₂×C₃₂	#261	1	1	yes	characteristic
31	#364	—	26	2	no	—
32	C₄×C₁₆	—	13	1	no	—
33	C₂²×C₁₃	#368	1	1	yes	characteristic
34	C₄×C₁₃	#335	1	1	yes	characteristic
35	C₄×C₁₃	#366	1	1	yes	characteristic
36	Dic₁₃	—	2	2	no	—
37	M₃₂	—	52	2	no	—
38	C₂×C₁₆	—	13	1	no	—
39	C₂×C₁₆	C₂×#261	1	1	yes	characteristic
40	C₄×C₈	—	13	1	no	—
41	C₃₂	—	26	1	no	—
42	C₃₂	#1057	1	2	yes	—
43	C₂×C₁₃	—	2	1	no	—
44	C₂×C₁₃	#1371	1	1	yes	characteristic
45	C₂×C₈	—	13	1	no	—
46	C₂×C₈	C₄⋊#261	1	1	yes	characteristic
47	C₄²	—	13	1	no	—
48	C₁₆	—	26	1	no	—
49	C₁₆	—	104	2	no	—
50	C₁₆	#6118	1	1	yes	characteristic
51	C₁₆	C₂×#1057	1	1	yes	characteristic
52	C₁₃	#7462	1	1	yes	characteristic, complemented, Sylow
53	C₂×C₄	—	26	1	no	—
54	C₂×C₄	#88102	1	1	yes	characteristic
55	C₈	—	13	1	no	—
56	C₈	—	13	1	no	—
57	C₈	#88104	1	1	yes	characteristic
58	C₈	C₄⋊#1057	1	1	yes	characteristic
59	C₂²	#11718223	1	1	yes	characteristic
60	C₄	—	26	2	no	—
61	C₄	#11718221	1	1	yes	characteristic
62	C₄	#11718254	1	1	yes	characteristic
63	C₂	—	2	1	no	—
64	C₂	#13129867	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#11718221
commutator	C₁₃×C₁₆	C₂×C₈
Frattini	C₂×C₁₆	C₂×#261
Fitting	C₂×C₁₃×C₃₂	C₄
socle	C₂×C₁₃	#1371
prime radical	C₂²×C₁₃	#368
cosocle	C₁₆×Dic₁₃	C₂²
hypercenter	C₂×C₃₂	#261
hypocenter	C₁₃	#7462
LCS	G ▷ C₁₃×C₁₆ ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
52. C₁₃	#7462	semidirect

Maximal subgroups

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

subgroup	index
#13129871	2
C₃₂×Dic₁₃	2
#7462	13