Subgroups — #16778148

Order 3328.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13130005	C₂	1	2	yes	maximal, complemented
2	C₂×#11718039	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆×D₁₃	C₄	1	1	yes	characteristic
4	C₂×C₁₃×C₃₂	C₄	1	1	yes	characteristic
5	C₂×#88034	C₂²	1	1	yes	characteristic
6	#11718039	—	2	2	no	—
7	#11718037	—	2	2	no	—
8	C₂×C₈×D₁₃	C₈	1	1	yes	characteristic
9	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
10	C₂×#6090	C₈	1	1	yes	characteristic
11	C₁₆×D₁₃	—	2	1	no	—
12	C₁₆×D₁₃	—	2	1	no	—
13	C₁₃×C₃₂	—	2	1	no	—
14	#88034	D₄	1	2	yes	—
15	#7513	—	13	1	no	maximal, Sylow
16	C₂×C₄×D₁₃	C₁₆	1	1	yes	characteristic
17	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
18	C₂×#1055	C₁₆	1	1	yes	characteristic
19	C₈×D₁₃	—	2	1	no	—
20	C₈×D₁₃	—	2	1	no	—
21	C₁₃×C₁₆	C₂²⋊C₄	1	1	yes	characteristic
22	C₁₃×C₁₆	M₁₆	1	1	yes	characteristic
23	#6090	—	2	1	no	—
24	C₂×M₆₄	—	13	1	no	—
25	M₁₂₈	—	13	2	no	—
26	C₂²×D₁₃	C₃₂	1	1	yes	characteristic
27	C₂×C₄×C₁₃	C₂×C₁₆	1	1	yes	characteristic
28	C₂×Dic₁₃	C₃₂	1	1	yes	characteristic
29	C₄×D₁₃	—	2	1	no	—
30	C₄×D₁₃	—	2	1	no	—
31	C₈×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
32	C₈×C₁₃	M₃₂	1	1	yes	characteristic
33	#1055	—	2	1	no	—
34	C₂²×C₁₆	—	13	1	no	—
35	M₆₄	—	26	2	no	—
36	C₂×C₃₂	—	13	1	no	—
37	C₂×C₃₂	#261	1	1	yes	characteristic
38	C₆₄	—	26	2	no	—
39	C₂²×C₁₃	C₂×C₃₂	1	1	yes	characteristic
40	C₂×D₁₃	—	2	1	no	—
41	C₂×D₁₃	—	4	1	no	—
42	C₄×C₁₃	C₂²⋊C₁₆	1	1	yes	characteristic
43	C₄×C₁₃	M₆₄	1	1	yes	characteristic
44	Dic₁₃	—	2	1	no	—
45	C₂²×C₈	—	13	1	no	—
46	C₂×C₁₆	—	13	1	no	—
47	C₂×C₁₆	—	26	1	no	—
48	C₂×C₁₆	—	26	1	no	—
49	C₂×C₁₆	C₂×#261	1	1	yes	characteristic
50	C₃₂	—	2	1	no	—
51	C₃₂	—	13	2	no	—
52	C₂×C₁₃	—	2	1	no	—
53	C₂×C₁₃	C₂²⋊C₃₂	1	1	yes	characteristic
54	D₁₃	—	4	1	no	—
55	C₂²×C₄	—	13	1	no	—
56	C₂×C₈	—	13	1	no	—
57	C₂×C₈	—	26	1	no	—
58	C₂×C₈	—	26	1	no	—
59	C₂×C₈	D₁₃⋊C₈	1	1	yes	characteristic
60	C₁₆	—	26	1	no	—
61	C₁₆	#6118	1	1	yes	characteristic
62	C₁₆	C₂²⋊#261	1	1	yes	characteristic
63	C₁₃	#7513	1	1	yes	characteristic, complemented, Sylow
64	C₂³	—	13	1	no	—
65	C₂×C₄	—	13	1	no	—
66	C₂×C₄	—	26	1	no	—
67	C₂×C₄	—	26	1	no	—
68	C₂×C₄	D₁₃⋊C₁₆	1	1	yes	characteristic
69	C₈	—	26	1	no	—
70	C₈	#88098	1	1	yes	characteristic
71	C₈	#88111	1	1	yes	characteristic
72	C₂²	—	26	1	no	—
73	C₂²	—	52	1	no	—
74	C₂²	D₁₃⋊C₃₂	1	1	yes	characteristic
75	C₄	—	26	1	no	—
76	C₄	#11718214	1	1	yes	characteristic
77	C₄	#11718259	1	1	yes	characteristic
78	C₂	—	2	1	no	—
79	C₂	—	52	1	no	—
80	C₂	#13129950	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	C₂²⋊#261
commutator	C₂²×C₁₃	C₂×C₃₂
Frattini	C₂×C₁₆	C₂×#261
Fitting	C₂×C₁₃×C₃₂	C₄
socle	C₂×C₁₃	C₂²⋊C₃₂
prime radical	C₂²×D₁₃	C₃₂
cosocle	C₂×#88034	C₂²
hypercenter	C₂×C₃₂	#261
hypocenter	C₁₃	#7513
LCS	G ▷ C₂²×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
1. #13130005	C₂	semidirect
63. C₁₃	#7513	semidirect

Maximal subgroups

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

subgroup	index
#13130005	2
C₂×#11718039	2
#7513	13