Subgroups — #13129953

Order 1664.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11718801	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	C₁₃×#131	C₄	1	1	yes	characteristic
5	#88052	—	2	1	no	—
6	#88052	C₄	1	1	yes	characteristic
7	C₂×#6090	—	2	1	no	—
8	C₂×#6090	C₂²	1	1	yes	characteristic
9	#88036	—	2	1	no	—
10	#88036	—	2	1	no	—
11	C₁₃×#41	C₈	1	1	yes	characteristic
12	C₁₃×M₁₆	—	2	1	no	—
13	C₁₃×M₁₆	C₈	1	1	yes	characteristic
14	C₂×C₈×C₁₃	—	2	1	no	—
15	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
16	#6090	—	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	Q₈×C₁₃	C₁₆	1	1	yes	characteristic
21	D₄×C₁₃	—	2	1	no	—
22	D₄×C₁₃	C₁₆	1	1	yes	characteristic
23	C₂×C₄×C₁₃	—	2	1	no	—
24	C₂×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
25	C₈×C₁₃	—	2	1	no	—
26	C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
27	C₈×C₁₃	M₁₆	1	1	yes	characteristic
28	#504	—	13	1	no	—
29	M₆₄	—	13	1	no	—
30	C₂×C₃₂	—	13	1	no	—
31	C₂²×C₁₃	—	2	1	no	—
32	C₂²×C₁₃	M₃₂	1	1	yes	characteristic
33	C₄×C₁₃	—	2	1	no	—
34	C₄×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
35	C₄×C₁₃	C₂×C₁₆	1	1	yes	characteristic
36	#131	#261	1	1	yes	characteristic
37	M₃₂	—	13	1	no	—
38	M₃₂	—	26	1	no	—
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	—	4	1	no	—
45	C₂×C₁₃	C₂²⋊C₁₆	1	1	yes	characteristic
46	#41	#1057	1	1	yes	characteristic
47	M₁₆	—	2	1	no	—
48	M₁₆	#1057	1	1	yes	characteristic
49	C₂×C₈	—	2	1	no	—
50	C₂×C₈	C₂×#261	1	1	yes	characteristic
51	C₁₆	—	13	1	no	—
52	C₁₆	—	13	1	no	—
53	C₁₆	—	26	1	no	—
54	C₁₃	#1401	1	1	yes	characteristic, complemented, Sylow
55	Q₈	#6092	1	1	yes	characteristic
56	D₄	—	2	1	no	—
57	D₄	#6092	1	1	yes	characteristic
58	C₂×C₄	—	2	1	no	—
59	C₂×C₄	C₂×#1057	1	1	yes	characteristic
60	C₈	—	2	1	no	—
61	C₈	#6122	1	1	yes	characteristic
62	C₈	C₂²⋊#261	1	1	yes	characteristic
63	C₂²	—	2	1	no	—
64	C₂²	#88106	1	1	yes	characteristic
65	C₄	—	2	1	no	—
66	C₄	C₂×#6092	1	1	yes	characteristic
67	C₄	C₂²⋊#1057	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	4	1	no	—
70	C₂	C₂²⋊#6092	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂²⋊#261
commutator	C₄×C₁₃	C₂×C₁₆
Frattini	C₂×C₈	C₂×#261
Fitting	C₁₃×#131	C₄
socle	C₂×C₁₃	C₂²⋊C₁₆
prime radical	C₁₃×#41	C₈
cosocle	C₂×#6090	C₂²
hypercenter	#131	#261
hypocenter	C₁₃	#1401
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ #131

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
#11718801	2
#11718249	2
C₂×#88036	2
#1401	13