Subgroups — #16777972

Order 3328.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13129995	C₂	1	2	yes	maximal
2	C₁₆×#1055	C₂	1	1	yes	maximal, characteristic
3	#11718249	—	2	2	no	—
4	C₄×C₁₃×C₁₆	C₄	1	1	yes	characteristic
5	C₄×#6090	C₂²	1	1	yes	characteristic
6	C₈×#1055	C₄	1	1	yes	characteristic
7	C₂×C₁₃×C₁₆	C₈	1	1	yes	characteristic
8	C₂×C₁₃×C₁₆	C₈	1	1	yes	characteristic
9	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
10	C₂×#6090	D₄	1	1	yes	characteristic
11	C₂×#6090	Q₈	1	1	yes	characteristic
12	C₄×#1055	—	2	1	no	—
13	#88036	—	4	2	no	—
14	#7459	—	13	1	no	maximal, Sylow
15	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
16	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
17	C₄²×C₁₃	M₁₆	1	1	yes	characteristic
18	C₂×#1055	—	2	2	no	—
19	C₁₃×C₁₆	—	2	1	no	—
20	C₁₃×C₁₆	C₁₆	1	2	yes	—
21	#6090	—	2	1	no	—
22	#6090	D₈	1	1	yes	characteristic
23	#6090	Q₁₆	1	1	yes	characteristic
24	#1422	—	13	2	no	—
25	C₈×C₁₆	—	13	1	no	—
26	C₂×C₄×C₁₃	—	2	1	no	—
27	C₂×C₄×C₁₃	C₄⋊C₈	1	1	yes	characteristic
28	C₈×C₁₃	#107	1	1	yes	characteristic
29	C₈×C₁₃	#108	1	1	yes	characteristic
30	C₈×C₁₃	C₂×C₁₆	1	1	yes	characteristic
31	C₈×C₁₃	M₃₂	1	1	yes	characteristic
32	#1055	—	2	4	no	—
33	M₆₄	—	26	2	no	—
34	C₄×C₁₆	—	13	1	no	—
35	C₄×C₁₆	#261	1	1	yes	characteristic
36	C₈²	—	13	1	no	—
37	C₂²×C₁₃	#364	1	1	yes	characteristic
38	C₄×C₁₃	—	2	2	no	—
39	C₄×C₁₃	#335	1	1	yes	characteristic
40	C₄×C₁₃	C₄⋊C₁₆	1	1	yes	characteristic
41	C₂×C₁₆	—	13	1	no	—
42	C₂×C₁₆	—	13	1	no	—
43	C₂×C₁₆	#1057	1	1	yes	characteristic
44	C₂×C₁₆	#1057	1	1	yes	characteristic
45	C₄×C₈	—	26	1	no	—
46	C₄×C₈	C₂×#261	1	1	yes	characteristic
47	C₃₂	—	52	2	no	—
48	C₂×C₁₃	—	2	1	no	—
49	C₂×C₁₃	#1370	1	1	yes	characteristic
50	C₂×C₈	—	26	2	no	—
51	C₂×C₈	C₄⋊#261	1	1	yes	characteristic
52	C₂×C₈	C₂×#1057	1	1	yes	characteristic
53	C₄²	#6118	1	1	yes	characteristic
54	C₁₆	—	2	1	no	—
55	C₁₆	—	13	1	no	—
56	C₁₆	—	13	1	no	—
57	C₁₆	—	26	1	no	—
58	C₁₆	#6092	1	2	yes	—
59	C₁₃	#7459	1	1	yes	characteristic, complemented, Sylow
60	C₂×C₄	—	2	1	no	—
61	C₂×C₄	C₄⋊#1057	1	1	yes	characteristic
62	C₈	—	26	4	no	—
63	C₈	#88102	1	1	yes	characteristic
64	C₈	#88104	1	1	yes	characteristic
65	C₈	C₂×#6092	1	1	yes	characteristic
66	C₈	#88106	1	1	yes	characteristic
67	C₂²	#11718261	1	1	yes	characteristic
68	C₄	—	2	2	no	—
69	C₄	C₄⋊#6092	1	1	yes	characteristic
70	C₄	#11718254	1	1	yes	characteristic
71	C₂	—	2	1	no	—
72	C₂	#13129865	1	1	yes	characteristic

	subgroup	G/H
center	C₈	#88102
commutator	C₈×C₁₃	C₂×C₁₆
Frattini	C₄×C₈	C₂×#261
Fitting	C₄×C₁₃×C₁₆	C₄
socle	C₂×C₁₃	#1370
prime radical	C₂²×C₁₃	#364
cosocle	C₄×#6090	C₂²
hypercenter	C₄×C₁₆	#261
hypocenter	C₁₃	#7459
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

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

Maximal subgroups

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

subgroup	index
#13129995	2
C₁₆×#1055	2
#7459	13