Subgroups — #13129954

Order 1664.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11718568	C₂	1	1	yes	maximal, characteristic
2	#11718249	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#88036	C₂	1	1	yes	maximal, characteristic, complemented
4	#88155	C₄	1	1	yes	characteristic
5	C₁₃×M₃₂	C₄	1	1	yes	characteristic
6	C₂×#6090	C₂²	1	1	yes	characteristic
7	#88038	—	2	1	no	—
8	C₁₆×D₁₃	—	2	1	no	—
9	#88036	—	2	1	no	—
10	#88036	—	2	1	no	—
11	#6127	C₈	1	1	yes	characteristic
12	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
13	#6099	C₈	1	1	yes	characteristic
14	#6094	—	2	1	no	—
15	C₈×D₁₃	—	2	1	no	—
16	C₁₃×C₁₆	—	2	1	no	—
17	#6090	D₄	1	1	yes	characteristic
18	#6090	D₄	1	1	yes	characteristic
19	#1401	—	13	1	no	maximal, Sylow
20	C₂×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
21	C₂²⋊D₁₃	—	2	1	no	—
22	D₅₂	C₁₆	1	1	yes	characteristic
23	C₄×D₁₃	—	2	1	no	—
24	Dic₂₆	C₁₆	1	1	yes	characteristic
25	C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₈×C₁₃	M₁₆	1	1	yes	characteristic
27	#1055	—	2	1	no	—
28	#504	—	13	1	no	—
29	M₆₄	—	13	1	no	—
30	C₂×C₃₂	—	13	1	no	—
31	C₂²×C₁₃	M₃₂	1	1	yes	characteristic
32	C₂×D₁₃	—	2	1	no	—
33	C₄×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
34	C₄×C₁₃	C₂×C₁₆	1	1	yes	characteristic
35	Dic₁₃	—	2	1	no	—
36	#131	—	13	1	no	—
37	M₃₂	—	26	1	no	—
38	M₃₂	#261	1	1	yes	characteristic
39	C₂×C₁₆	—	13	1	no	—
40	C₂×C₁₆	—	26	1	no	—
41	C₃₂	—	26	1	no	—
42	C₃₂	—	26	1	no	—
43	C₂×C₁₃	—	2	1	no	—
44	C₂×C₁₃	C₂²⋊C₁₆	1	1	yes	characteristic
45	D₁₃	—	4	1	no	—
46	#41	—	13	1	no	—
47	M₁₆	—	13	1	no	—
48	M₁₆	—	26	1	no	—
49	C₂×C₈	—	26	1	no	—
50	C₂×C₈	C₂×#261	1	1	yes	characteristic
51	C₁₆	—	2	1	no	—
52	C₁₆	—	13	1	no	—
53	C₁₆	—	13	1	no	—
54	C₁₃	#1401	1	1	yes	characteristic, complemented, Sylow
55	Q₈	—	13	1	no	—
56	D₄	—	13	1	no	—
57	D₄	—	26	1	no	—
58	C₂×C₄	—	26	1	no	—
59	C₂×C₄	D₁₃⋊C₈	1	1	yes	characteristic
60	C₈	—	26	1	no	—
61	C₈	#6118	1	1	yes	characteristic
62	C₈	C₂²⋊#261	1	1	yes	characteristic
63	C₂²	—	26	1	no	—
64	C₂²	#88098	1	1	yes	characteristic
65	C₄	—	26	1	no	—
66	C₄	D₁₃⋊C₁₆	1	1	yes	characteristic
67	C₄	#88111	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	52	1	no	—
70	C₂	#11718259	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂²⋊#261
commutator	C₄×C₁₃	C₂×C₁₆
Frattini	C₂×C₈	C₂×#261
Fitting	C₁₃×M₃₂	C₄
socle	C₂×C₁₃	C₂²⋊C₁₆
prime radical	#6127	C₈
cosocle	C₂×#6090	C₂²
hypercenter	M₃₂	#261
hypocenter	C₁₃	#1401
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ M₃₂

Complements

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

N	H ≅ G/N	type
2. #11718249	C₂	semidirect
3. C₂×#88036	C₂	semidirect
54. C₁₃	#1401	semidirect

Maximal subgroups

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

subgroup	index
#11718568	2
#11718249	2
C₂×#88036	2
#1401	13