Subgroups — #16777969

Order 3328.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13129863	C₂	1	1	yes	maximal, characteristic
2	#13129861	C₂	1	1	yes	maximal, characteristic
3	#13112971	C₂	1	1	yes	maximal, characteristic
4	#11718261	—	2	1	no	—
5	#11718253	—	2	1	no	—
6	C₁₃×M₆₄	C₄	1	1	yes	characteristic
7	#11718094	C₂²	1	1	yes	characteristic
8	#11718091	C₄	1	1	yes	characteristic
9	C₄⋊#1057	—	4	1	no	—
10	#88106	—	4	1	no	—
11	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
12	C₈×Dic₁₃	D₄	1	1	yes	characteristic
13	C₂×#6090	Q₈	1	1	yes	characteristic
14	C₁₃×C₃₂	—	2	1	no	—
15	#88034	C₈	1	2	yes	complemented
16	#7457	—	13	1	no	maximal, Sylow
17	C₂×#1057	—	8	1	no	—
18	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
19	C₄×Dic₁₃	SD₁₆	1	1	yes	characteristic
20	C₂×#1055	SD₁₆	1	1	yes	characteristic
21	#6092	—	8	1	no	—
22	C₁₃×C₁₆	C₂×C₈	1	1	yes	characteristic
23	C₁₃×C₁₆	M₁₆	1	1	yes	characteristic
24	#6090	—	2	1	no	—
25	#1398	—	13	1	no	—
26	#1369	—	13	1	no	—
27	#1368	—	13	1	no	—
28	C₂×C₄×C₁₃	#106	1	1	yes	characteristic
29	C₂×Dic₁₃	—	2	1	no	—
30	#1057	—	16	1	no	—
31	C₈×C₁₃	C₄⋊C₈	1	1	yes	characteristic
32	C₈×C₁₃	#108	1	1	yes	characteristic
33	#1055	—	2	1	no	—
34	M₆₄	—	13	1	no	—
35	M₆₄	#261	1	1	yes	characteristic
36	#364	—	26	1	no	—
37	#346	—	13	1	no	—
38	#334	—	26	1	no	—
39	C₂²×C₁₃	#365	1	1	yes	characteristic
40	C₄×C₁₃	#334	1	1	yes	characteristic
41	C₄×C₁₃	#365	1	1	yes	characteristic
42	Dic₁₃	—	4	1	no	—
43	M₃₂	—	52	1	no	—
44	C₂×C₁₆	—	13	1	no	—
45	C₂×C₁₆	C₂×#261	1	1	yes	characteristic
46	C₄⋊C₈	—	52	1	no	—
47	C₄×C₈	—	13	1	no	—
48	C₃₂	—	2	1	no	—
49	C₃₂	—	13	2	no	—
50	C₂×C₁₃	—	2	1	no	—
51	C₂×C₁₃	#1368	1	1	yes	characteristic
52	C₂×C₈	—	13	1	no	—
53	C₂×C₈	—	104	1	no	—
54	C₂×C₈	C₄⋊#261	1	1	yes	characteristic
55	C₄²	—	13	1	no	—
56	C₁₆	—	26	1	no	—
57	C₁₆	—	104	1	no	—
58	C₁₆	D₁₃⋊C₈	1	1	yes	characteristic
59	C₁₆	#6122	1	1	yes	characteristic
60	C₁₃	#7457	1	1	yes	characteristic, complemented, Sylow
61	C₂×C₄	—	26	1	no	—
62	C₂×C₄	#88101	1	1	yes	characteristic
63	C₈	—	26	1	no	—
64	C₈	—	208	1	no	—
65	C₈	#88104	1	1	yes	characteristic
66	C₈	#88112	1	1	yes	characteristic
67	C₂²	#11718219	1	1	yes	characteristic
68	C₄	—	52	1	no	—
69	C₄	#11718220	1	1	yes	characteristic
70	C₄	#11718255	1	1	yes	characteristic
71	C₂	—	2	1	no	—
72	C₂	#13129862	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#13129862
commutator	C₁₃×C₁₆	C₂×C₈
Frattini	C₂×C₁₆	C₂×#261
Fitting	C₁₃×M₆₄	C₄
socle	C₂×C₁₃	#1368
prime radical	C₂²×C₁₃	#365
cosocle	#11718094	C₂²
hypercenter	M₆₄	#261
hypocenter	C₁₃	#7457
LCS	G ▷ C₁₃×C₁₆ ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ M₆₄

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
#13129863	2
#13129861	2
#13112971	2
#7457	13