Subgroups — #13129858

Order 1664.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#6092	C₂	1	2	yes	maximal
2	C₈×#1055	C₂	1	1	yes	maximal, characteristic
3	C₂×#6092	—	2	2	no	—
4	C₄×C₈×C₁₃	C₄	1	1	yes	characteristic
5	C₄×#1055	C₄	1	1	yes	characteristic
6	C₄×#1055	C₂²	1	1	yes	characteristic
7	C₂×C₈×C₁₃	C₈	1	1	yes	characteristic
8	C₂×C₈×C₁₃	C₈	1	1	yes	characteristic
9	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
10	C₂×#1055	—	2	1	no	—
11	C₂×#1055	D₄	1	1	yes	characteristic
12	C₂×#1055	Q₈	1	1	yes	characteristic
13	#6092	—	4	2	no	—
14	#1367	—	13	1	no	maximal, Sylow
15	C₂×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
16	C₂×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
17	C₂×C₄×C₁₃	M₁₆	1	1	yes	characteristic
18	C₈×C₁₃	—	2	1	no	—
19	C₈×C₁₃	C₁₆	1	2	yes	complemented
20	#1055	—	2	2	no	—
21	#1055	—	2	1	no	—
22	#1055	SD₁₆	1	2	yes	—
23	C₄⋊C₁₆	—	13	2	no	—
24	C₈²	—	13	1	no	—
25	C₂²×C₁₃	C₄⋊C₈	1	1	yes	characteristic
26	C₄×C₁₃	—	2	1	no	—
27	C₄×C₁₃	#106	1	1	yes	characteristic
28	C₄×C₁₃	#108	1	1	yes	characteristic
29	C₄×C₁₃	C₂×C₁₆	1	1	yes	characteristic
30	C₄×C₁₃	M₃₂	1	1	yes	characteristic
31	C₂×C₁₆	—	26	2	no	—
32	C₄×C₈	—	13	1	no	—
33	C₄×C₈	—	13	1	no	—
34	C₄×C₈	#261	1	1	yes	characteristic
35	C₂×C₁₃	#334	1	1	yes	characteristic
36	C₂×C₁₃	C₄⋊C₁₆	1	1	yes	characteristic
37	C₂×C₁₃	#364	1	1	yes	characteristic
38	C₂×C₈	—	13	1	no	—
39	C₂×C₈	—	13	1	no	—
40	C₂×C₈	—	26	1	no	—
41	C₂×C₈	#1057	1	1	yes	characteristic
42	C₂×C₈	#1057	1	1	yes	characteristic
43	C₄²	C₂×#261	1	1	yes	characteristic
44	C₁₆	—	52	2	no	—
45	C₁₃	#1367	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₄	#6118	1	1	yes	characteristic
47	C₂×C₄	C₄⋊#261	1	1	yes	characteristic
48	C₂×C₄	C₂×#1057	1	1	yes	characteristic
49	C₈	—	2	1	no	—
50	C₈	—	13	2	no	—
51	C₈	—	26	2	no	—
52	C₈	—	26	1	no	—
53	C₈	#6092	1	2	yes	complemented
54	C₂²	C₄⋊#1057	1	1	yes	characteristic
55	C₄	—	2	1	no	—
56	C₄	#88101	1	1	yes	characteristic
57	C₄	#88103	1	1	yes	characteristic
58	C₄	C₂×#6092	1	1	yes	characteristic
59	C₄	#88106	1	1	yes	characteristic
60	C₂	C₄⋊#6092	1	1	yes	characteristic
61	C₂	#11718253	1	1	yes	characteristic
62	C₂	#11718261	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₄⋊#261
commutator	C₄×C₁₃	C₂×C₁₆
Frattini	C₄²	C₂×#261
Fitting	C₄×C₈×C₁₃	C₄
socle, prime radical	C₂²×C₁₃	C₄⋊C₈
cosocle	C₄×#1055	C₂²
hypercenter	C₄×C₈	#261
hypocenter	C₁₃	#1367
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
19. C₈×C₁₃	C₁₆	semidirect
45. C₁₃	#1367	semidirect
53. C₈	#6092	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊#6092	2
C₈×#1055	2
#1367	13