Subgroups — #13113138

Order 1664.

214 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#6094	C₂	1	3	yes	maximal
2	C₈²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#11718047	C₂	1	3	yes	maximal, complemented
4	C₂×#6094	C₄	1	6	yes	—
5	C₄²×D₁₃	C₂²	1	1	yes	characteristic
6	C₄×C₈×C₁₃	C₂²	1	3	yes	—
7	#88055	C₄	1	6	yes	—
8	C₄×#1055	C₂²	1	3	yes	—
9	C₂×C₄×D₁₃	C₂×C₄	1	3	yes	—
10	C₂×C₈×C₁₃	C₂×C₄	1	6	yes	—
11	C₄²×C₁₃	C₂³	1	1	yes	characteristic
12	C₄×Dic₁₃	C₂×C₄	1	3	yes	—
13	C₂×#1055	C₂×C₄	1	6	yes	—
14	#6094	—	2	12	no	—
15	#1455	—	13	1	no	maximal, Sylow
16	C₂²×D₁₃	C₄²	1	1	yes	characteristic
17	C₂×C₄×C₁₃	C₂²×C₄	1	3	yes	—
18	C₂×Dic₁₃	C₄²	1	3	yes	—
19	C₄×D₁₃	—	2	6	no	—
20	C₈×C₁₃	M₁₆	1	12	yes	complemented
21	#1055	—	2	6	no	—
22	C₄×M₁₆	—	13	3	no	—
23	#322	—	13	3	no	—
24	C₈²	D₁₃	1	1	yes	characteristic, complemented
25	C₂²×C₁₃	C₂×C₄²	1	1	yes	characteristic
26	C₂×D₁₃	—	2	3	no	—
27	C₄×C₁₃	C₂×M₁₆	1	6	yes	—
28	Dic₁₃	—	2	3	no	—
29	C₂×M₁₆	—	13	6	no	—
30	C₂×C₄²	—	13	1	no	—
31	#97	—	13	6	no	—
32	C₄×C₈	—	13	3	no	—
33	C₄×C₈	C₂×D₁₃	1	3	yes	—
34	C₂×C₁₃	C₄×M₁₆	1	3	yes	—
35	D₁₃	—	4	1	no	—
36	C₂²×C₄	—	13	3	no	—
37	M₁₆	—	26	12	no	—
38	C₂×C₈	—	13	6	no	—
39	C₂×C₈	C₄×D₁₃	1	6	yes	—
40	C₄²	—	13	3	no	—
41	C₄²	C₂²×D₁₃	1	1	yes	characteristic
42	C₁₃	#1455	1	1	yes	characteristic, complemented, Sylow
43	C₂³	—	13	1	no	—
44	C₂×C₄	—	13	3	no	—
45	C₂×C₄	—	26	6	no	—
46	C₂×C₄	C₂×C₄×D₁₃	1	3	yes	—
47	C₈	—	26	6	no	—
48	C₈	#6094	1	12	yes	complemented
49	C₂²	—	26	3	no	—
50	C₂²	C₄²×D₁₃	1	1	yes	characteristic
51	C₄	—	26	3	no	—
52	C₄	C₂×#6094	1	6	yes	—
53	C₂	—	52	1	no	—
54	C₂	C₄×#6094	1	3	yes	—

	subgroup	G/H
center, Frattini	C₄²	C₂²×D₁₃
commutator, socle	C₂²×C₁₃	C₂×C₄²
Fitting	C₈²×C₁₃	C₂
prime radical	C₂²×D₁₃	C₄²
cosocle	C₄²×C₁₃	C₂³
hypercenter	C₈²	D₁₃
hypocenter	C₁₃	#1455
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
2. C₈²×C₁₃	C₂	semidirect
3. #11718047	C₂	semidirect
20. C₈×C₁₃	M₁₆	semidirect
24. C₈²	D₁₃	semidirect
42. C₁₃	#1455	semidirect
48. C₈	#6094	semidirect

Maximal subgroups

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

subgroup	index
C₄×#6094	2
C₈²×C₁₃	2
#11718047	2
#1455	13