Subgroups — #13113024

Order 1664.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11718565	C₂	1	1	yes	maximal, characteristic
2	C₁₃×M₆₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#11718097	C₂	1	1	yes	maximal, characteristic, complemented
4	#88158	—	2	1	no	—
5	C₂×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
6	#88058	—	2	1	no	—
7	Dic₁₀₄	C₄	1	1	yes	characteristic, complemented
8	#88040	—	2	1	no	—
9	D₂₀₈	C₄	1	1	yes	characteristic, complemented
10	C₁₃×C₃₂	—	2	1	no	—
11	#6127	—	4	1	no	—
12	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
13	C₄⋊Dic₁₃	—	4	1	no	—
14	Dic₅₂	—	2	1	no	—
15	D₁₀₄	—	2	1	no	—
16	#6095	—	4	1	no	—
17	C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
18	C₁₃×C₁₆	D₄	1	1	yes	characteristic
19	#1418	—	13	1	no	maximal, Sylow
20	C₂×C₄×C₁₃	D₈	1	1	yes	characteristic
21	C₂²⋊D₁₃	—	8	1	no	—
22	C₂×Dic₁₃	—	8	1	no	—
23	D₅₂	—	4	1	no	—
24	C₄×D₁₃	—	8	1	no	—
25	Dic₂₆	—	4	1	no	—
26	C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
27	C₈×C₁₃	SD₁₆	1	1	yes	characteristic
28	#508	—	13	1	no	—
29	M₆₄	D₁₃	1	1	yes	characteristic, complemented
30	#367	—	13	1	no	—
31	C₂²×C₁₃	D₁₆	1	1	yes	characteristic
32	C₂×D₁₃	—	8	1	no	—
33	C₄×C₁₃	#102	1	1	yes	characteristic
34	C₄×C₁₃	SD₃₂	1	1	yes	characteristic
35	Dic₁₃	—	8	1	no	—
36	Dic₁₃	—	16	1	no	—
37	#135	—	26	1	no	—
38	Q₃₂	—	13	1	no	—
39	SD₃₂	—	26	1	no	—
40	D₁₆	—	13	1	no	—
41	C₂×C₁₆	C₂×D₁₃	1	1	yes	characteristic
42	#107	—	26	1	no	—
43	C₃₂	—	2	1	no	—
44	C₂×C₁₃	—	2	1	no	—
45	C₂×C₁₃	#357	1	1	yes	characteristic
46	D₁₃	—	16	1	no	—
47	#41	—	52	1	no	—
48	Q₁₆	—	26	1	no	—
49	SD₁₆	—	52	1	no	—
50	D₈	—	26	1	no	—
51	C₂×C₈	D₅₂	1	1	yes	characteristic
52	C₄⋊C₄	—	52	1	no	—
53	C₁₆	C₄×D₁₃	1	1	yes	characteristic
54	C₁₆	C₂²⋊D₁₃	1	1	yes	characteristic
55	C₁₃	#1418	1	1	yes	characteristic, complemented, Sylow
56	Q₈	—	52	1	no	—
57	D₄	—	52	1	no	—
58	D₄	—	104	1	no	—
59	C₂×C₄	—	104	1	no	—
60	C₂×C₄	—	104	1	no	—
61	C₂×C₄	D₁₀₄	1	1	yes	characteristic
62	C₈	#6095	1	1	yes	characteristic
63	C₈	#6103	1	1	yes	characteristic
64	C₂²	—	104	1	no	—
65	C₂²	D₂₀₈	1	1	yes	characteristic
66	C₄	—	104	1	no	—
67	C₄	—	208	1	no	—
68	C₄	#88040	1	1	yes	characteristic
69	C₄	#88061	1	1	yes	characteristic
70	C₂	—	2	1	no	—
71	C₂	—	208	1	no	—
72	C₂	#11718101	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11718101
commutator	C₁₃×C₁₆	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₁₃
Fitting	C₁₃×M₆₄	C₂
socle	C₂×C₁₃	#357
prime radical	#11718565	C₂
cosocle	C₂×C₁₃×C₁₆	C₂²
hypercenter	M₆₄	D₁₃
hypocenter	C₁₃	#1418
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
2. C₁₃×M₆₄	C₂	semidirect
3. #11718097	C₂	semidirect
7. Dic₁₀₄	C₄	semidirect
9. D₂₀₈	C₄	semidirect
29. M₆₄	D₁₃	semidirect
55. C₁₃	#1418	semidirect

Maximal subgroups

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

subgroup	index
#11718565	2
C₁₃×M₆₄	2
#11718097	2
#1418	13