Subgroups — #15750590

Order 3328.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13112972	C₂	1	1	yes	maximal, characteristic
2	#13112902	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#1369	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#364	—	2	1	no	—
5	C₁₃×#346	C₂²	1	1	yes	characteristic
6	#11718091	C₄	1	1	yes	characteristic
7	#11718091	C₄	1	1	yes	characteristic
8	#11718049	—	2	1	no	—
9	C₁₃×M₃₂	—	4	1	no	—
10	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
11	C₂×C₁₃×C₁₆	Q₈	1	1	yes	characteristic
12	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
13	C₄⋊#1055	—	4	1	no	—
14	#88034	—	2	1	no	—
15	#88034	C₈	1	2	yes	complemented
16	#7457	—	13	1	no	maximal, Sylow
17	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
18	C₂×C₈×C₁₃	SD₁₆	1	1	yes	characteristic
19	C₄²×C₁₃	SD₁₆	1	1	yes	characteristic
20	C₂×#1055	—	8	1	no	—
21	C₁₃×C₁₆	—	2	1	no	—
22	C₁₃×C₁₆	—	8	1	no	—
23	C₁₃×C₁₆	C₂×C₈	1	1	yes	characteristic
24	C₁₃×C₁₆	M₁₆	1	1	yes	characteristic
25	#1398	—	13	1	no	—
26	#1369	D₁₃	1	1	yes	characteristic
27	#1368	—	13	1	no	—
28	C₂×C₄×C₁₃	—	2	1	no	—
29	C₂×C₄×C₁₃	#106	1	1	yes	characteristic
30	C₈×C₁₃	—	2	1	no	—
31	C₈×C₁₃	C₄⋊C₈	1	1	yes	characteristic
32	C₈×C₁₃	#108	1	1	yes	characteristic
33	#1055	—	16	1	no	—
34	M₆₄	—	13	1	no	—
35	M₆₄	—	13	1	no	—
36	#364	—	2	1	no	—
37	#346	C₂×D₁₃	1	1	yes	characteristic
38	#334	—	26	1	no	—
39	C₂²×C₁₃	#365	1	1	yes	characteristic
40	C₄×C₁₃	—	4	1	no	—
41	C₄×C₁₃	#334	1	1	yes	characteristic
42	C₄×C₁₃	#365	1	1	yes	characteristic
43	M₃₂	—	4	1	no	—
44	C₂×C₁₆	Dic₂₆	1	1	yes	characteristic
45	C₂×C₁₆	C₄×D₁₃	1	1	yes	characteristic
46	C₄⋊C₈	—	52	1	no	—
47	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
48	C₃₂	—	13	2	no	—
49	C₃₂	—	26	1	no	—
50	C₂×C₁₃	—	2	1	no	—
51	C₂×C₁₃	#1368	1	1	yes	characteristic
52	C₂×C₈	—	104	1	no	—
53	C₂×C₈	#6101	1	1	yes	characteristic
54	C₂×C₈	#6105	1	1	yes	characteristic
55	C₄²	#6106	1	1	yes	characteristic
56	C₁₆	—	2	1	no	—
57	C₁₆	—	8	1	no	—
58	C₁₆	C₈×D₁₃	1	1	yes	characteristic
59	C₁₆	#6094	1	1	yes	characteristic
60	C₁₃	#7457	1	1	yes	characteristic, complemented, Sylow
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	#88048	1	1	yes	characteristic
63	C₈	—	2	1	no	—
64	C₈	—	208	1	no	—
65	C₈	#88054	1	1	yes	characteristic
66	C₈	#88062	1	1	yes	characteristic
67	C₂²	#11718086	1	1	yes	characteristic
68	C₄	—	4	1	no	—
69	C₄	#11718072	1	1	yes	characteristic
70	C₄	#11718079	1	1	yes	characteristic
71	C₂	—	2	1	no	—
72	C₂	#13112901	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#13112901
commutator	C₁₃×C₁₆	C₂×C₈
Frattini	#346	C₂×D₁₃
Fitting	C₁₃×#1369	C₂
socle	C₂×C₁₃	#1368
prime radical	C₂²×C₁₃	#365
cosocle	C₁₃×#346	C₂²
hypercenter	#1369	D₁₃
hypocenter	C₁₃	#7457
LCS	G ▷ C₁₃×C₁₆ ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #346 ◁ #1369

Complements

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

N	H ≅ G/N	type
15. #88034	C₈	semidirect
60. C₁₃	#7457	semidirect

Maximal subgroups

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

subgroup	index
#13112972	2
#13112902	2
C₁₃×#1369	2
#7457	13