Subgroups — #15750593

Order 3328.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13113034	C₂	1	1	yes	maximal, characteristic
2	C₁₆×#1055	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#1422	C₂	1	1	yes	maximal, characteristic
4	C₁₃×M₆₄	—	2	1	no	—
5	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
6	#11718091	—	2	1	no	—
7	C₄×#6090	C₄	1	1	yes	characteristic
8	C₈×#1055	C₄	1	1	yes	characteristic
9	C₂×C₁₃×C₁₆	D₄	1	1	yes	characteristic
10	C₂×C₁₃×C₁₆	Q₈	1	1	yes	characteristic
11	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
12	C₂×#6090	C₈	1	1	yes	characteristic
13	C₂×#6090	C₈	1	1	yes	characteristic
14	C₄×#1055	—	2	1	no	—
15	C₁₃×C₃₂	—	4	1	no	—
16	#88034	—	4	1	no	—
17	#7459	—	13	1	no	maximal, Sylow
18	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
19	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
20	C₄²×C₁₃	M₁₆	1	1	yes	characteristic
21	C₂×#1055	—	2	2	no	—
22	C₁₃×C₁₆	—	2	1	no	—
23	C₁₃×C₁₆	D₈	1	1	yes	characteristic
24	C₁₃×C₁₆	Q₁₆	1	1	yes	characteristic
25	#6090	—	2	1	no	—
26	#6090	C₁₆	1	2	yes	—
27	#1422	—	13	1	no	—
28	#1422	D₁₃	1	1	yes	characteristic
29	C₈×C₁₆	—	13	1	no	—
30	C₂×C₄×C₁₃	—	2	1	no	—
31	C₂×C₄×C₁₃	C₄⋊C₈	1	1	yes	characteristic
32	C₈×C₁₃	#107	1	1	yes	characteristic
33	C₈×C₁₃	#108	1	1	yes	characteristic
34	C₈×C₁₃	C₂×C₁₆	1	1	yes	characteristic
35	C₈×C₁₃	M₃₂	1	1	yes	characteristic
36	#1055	—	2	4	no	—
37	M₆₄	—	2	1	no	—
38	M₆₄	—	26	1	no	—
39	C₄×C₁₆	—	13	1	no	—
40	C₄×C₁₆	C₂×D₁₃	1	1	yes	characteristic
41	C₈²	—	13	1	no	—
42	C₂²×C₁₃	#364	1	1	yes	characteristic
43	C₄×C₁₃	—	2	2	no	—
44	C₄×C₁₃	#335	1	1	yes	characteristic
45	C₄×C₁₃	C₄⋊C₁₆	1	1	yes	characteristic
46	C₂×C₁₆	—	13	1	no	—
47	C₂×C₁₆	—	13	1	no	—
48	C₂×C₁₆	Dic₂₆	1	1	yes	characteristic
49	C₂×C₁₆	C₂²⋊D₁₃	1	1	yes	characteristic
50	C₄×C₈	—	26	1	no	—
51	C₄×C₈	C₄×D₁₃	1	1	yes	characteristic
52	C₃₂	—	4	1	no	—
53	C₃₂	—	52	1	no	—
54	C₂×C₁₃	—	2	1	no	—
55	C₂×C₁₃	#1370	1	1	yes	characteristic
56	C₂×C₈	—	26	2	no	—
57	C₂×C₈	C₈×D₁₃	1	1	yes	characteristic
58	C₂×C₈	#6101	1	1	yes	characteristic
59	C₄²	#6094	1	1	yes	characteristic
60	C₁₆	—	2	1	no	—
61	C₁₆	—	13	2	no	—
62	C₁₆	—	26	1	no	—
63	C₁₆	#6104	1	1	yes	characteristic
64	C₁₆	#6107	1	1	yes	characteristic
65	C₁₃	#7459	1	1	yes	characteristic, complemented, Sylow
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	#88054	1	1	yes	characteristic
68	C₈	—	26	4	no	—
69	C₈	C₁₆×D₁₃	1	1	yes	characteristic
70	C₈	#88038	1	1	yes	characteristic
71	C₈	#88047	1	1	yes	characteristic
72	C₈	#88062	1	1	yes	characteristic
73	C₂²	#11718103	1	1	yes	characteristic
74	C₄	—	2	2	no	—
75	C₄	#11718071	1	1	yes	characteristic
76	C₄	#11718093	1	1	yes	characteristic
77	C₂	—	2	1	no	—
78	C₂	#13112905	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	#6104
commutator	C₈×C₁₃	C₂×C₁₆
Frattini	C₄×C₁₆	C₂×D₁₃
Fitting	C₁₃×#1422	C₂
socle	C₂×C₁₃	#1370
prime radical	C₂²×C₁₃	#364
cosocle	C₄×C₁₃×C₁₆	C₂²
hypercenter	#1422	D₁₃
hypocenter	C₁₃	#7459
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆ ◁ C₄×C₁₆ ◁ #1422

Complements

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

N	H ≅ G/N	type
65. C₁₃	#7459	semidirect

Maximal subgroups

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

subgroup	index
#13113034	2
C₁₆×#1055	2
C₁₃×#1422	2
#7459	13