Subgroups — #15750603

Order 3328.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13112970	C₂	1	1	yes	maximal, characteristic
2	#13112912	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#1373	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#364	—	2	1	no	—
5	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
6	C₂×#88034	C₄	1	1	yes	characteristic
7	C₂×#88034	C₄	1	1	yes	characteristic
8	#11718055	—	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	#88052	—	4	1	no	—
14	#88034	—	2	1	no	—
15	#88034	C₈	1	2	yes	—
16	#7464	—	13	1	no	maximal, Sylow
17	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
18	C₂×C₈×C₁₃	D₈	1	1	yes	characteristic
19	C₄²×C₁₃	Q₁₆	1	1	yes	characteristic
20	C₁₃×C₁₆	—	2	1	no	—
21	C₁₃×C₁₆	—	8	1	no	—
22	C₁₃×C₁₆	C₂×C₈	1	1	yes	characteristic
23	C₁₃×C₁₆	M₁₆	1	1	yes	characteristic
24	#6090	—	8	1	no	—
25	#1397	—	13	1	no	—
26	#1373	—	13	1	no	—
27	#1373	D₁₃	1	1	yes	characteristic
28	C₂×C₄×C₁₃	—	2	1	no	—
29	C₂×C₄×C₁₃	#107	1	1	yes	characteristic
30	C₈×C₁₃	C₄⋊C₈	1	1	yes	characteristic
31	C₈×C₁₃	#108	1	1	yes	characteristic
32	C₈×C₁₃	SD₃₂	1	1	yes	characteristic
33	C₈×C₁₃	SD₃₂	1	1	yes	characteristic
34	C₂×C₃₂	—	13	1	no	—
35	C₂×C₃₂	—	13	1	no	—
36	#364	—	2	1	no	—
37	#364	—	26	1	no	—
38	C₄×C₁₆	C₂×D₁₃	1	1	yes	characteristic
39	C₂²×C₁₃	#368	1	1	yes	characteristic
40	C₄×C₁₃	—	4	1	no	—
41	C₄×C₁₃	#335	1	1	yes	characteristic
42	C₄×C₁₃	#367	1	1	yes	characteristic
43	M₃₂	—	4	1	no	—
44	M₃₂	—	52	1	no	—
45	C₂×C₁₆	Dic₂₆	1	1	yes	characteristic
46	C₂×C₁₆	C₄×D₁₃	1	1	yes	characteristic
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	#1372	1	1	yes	characteristic
52	C₂×C₈	#6101	1	1	yes	characteristic
53	C₂×C₈	#6104	1	1	yes	characteristic
54	C₄²	#6107	1	1	yes	characteristic
55	C₁₆	—	2	1	no	—
56	C₁₆	—	8	1	no	—
57	C₁₆	—	104	1	no	—
58	C₁₆	C₈×D₁₃	1	1	yes	characteristic
59	C₁₆	#6094	1	1	yes	characteristic
60	C₁₃	#7464	1	1	yes	characteristic, complemented, Sylow
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	#88047	1	1	yes	characteristic
63	C₈	#88054	1	1	yes	characteristic
64	C₈	#88062	1	1	yes	characteristic
65	C₈	#88067	1	1	yes	characteristic
66	C₈	#88068	1	1	yes	characteristic
67	C₂²	#11718085	1	1	yes	characteristic
68	C₄	—	4	1	no	—
69	C₄	#11718071	1	1	yes	characteristic
70	C₄	#11718082	1	1	yes	characteristic
71	C₂	—	2	1	no	—
72	C₂	#13112909	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#11718082
commutator	C₁₃×C₁₆	C₂×C₈
Frattini	C₄×C₁₆	C₂×D₁₃
Fitting	C₁₃×#1373	C₂
socle	C₂×C₁₃	#1372
prime radical	C₂²×C₁₃	#368
cosocle	C₄×C₁₃×C₁₆	C₂²
hypercenter	#1373	D₁₃
hypocenter	C₁₃	#7464
LCS	G ▷ C₁₃×C₁₆ ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #1373

Complements

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

N	H ≅ G/N	type
60. C₁₃	#7464	semidirect

Maximal subgroups

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

subgroup	index
#13112970	2
#13112912	2
C₁₃×#1373	2
#7464	13