Subgroups — #16811539

Order 3392.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13133292	C₂	1	1	yes	maximal, characteristic, complemented
2	#13133285	C₂	1	1	yes	maximal, characteristic, complemented
3	#13133236	C₂	1	1	yes	maximal, characteristic
4	#11719947	—	2	1	no	—
5	C₄⋊#6157	—	2	1	no	—
6	D₈×C₅₃	C₄	1	1	yes	characteristic, complemented
7	#11719923	—	2	1	no	—
8	Dic₂₁₂	C₄	1	1	yes	characteristic, complemented
9	C₈×D₅₃	C₂²	1	1	yes	characteristic
10	#11719910	—	2	1	no	—
11	C₂×#6157	—	4	1	no	—
12	D₄×C₅₃	—	2	1	no	—
13	C₂²⋊D₅₃	—	4	1	no	—
14	C₂×Dic₅₃	—	4	1	no	—
15	C₄×D₅₃	D₄	1	1	yes	characteristic
16	Dic₁₀₆	—	2	1	no	—
17	C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
18	#88322	D₄	1	1	yes	characteristic
19	C₂²×C₅₃	—	4	1	no	—
20	C₂×D₅₃	D₈	1	1	yes	characteristic
21	#6157	—	8	1	no	—
22	C₄×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
23	Dic₅₃	—	4	1	no	—
24	Dic₅₃	SD₁₆	1	1	yes	characteristic
25	C₂×C₅₃	—	8	1	no	—
26	C₂×C₅₃	#102	1	1	yes	characteristic
27	D₅₃	—	2	1	no	—
28	#360	—	53	1	no	maximal, Sylow
29	C₅₃	#360	1	1	yes	characteristic, complemented, Sylow
30	#135	—	53	1	no	—
31	M₃₂	—	53	1	no	—
32	#106	—	53	1	no	—
33	#41	—	106	1	no	—
34	Q₁₆	—	53	1	no	—
35	SD₁₆	—	106	1	no	—
36	D₈	#6157	1	1	yes	characteristic, complemented
37	C₂×C₈	—	53	1	no	—
38	C₄⋊C₄	—	106	1	no	—
39	C₁₆	—	106	1	no	—
40	Q₈	—	106	1	no	—
41	D₄	—	2	1	no	—
42	D₄	—	212	1	no	—
43	C₂×C₄	—	53	1	no	—
44	C₂×C₄	—	212	1	no	—
45	C₂×C₄	—	212	1	no	—
46	C₈	—	53	1	no	—
47	C₈	C₂×#6157	1	1	yes	characteristic
48	C₂²	—	4	1	no	—
49	C₂²	—	53	1	no	—
50	C₄	—	53	1	no	—
51	C₄	—	424	1	no	—
52	C₄	—	212	1	no	—
53	C₄	C₂²⋊#6157	1	1	yes	characteristic
54	C₂	—	8	1	no	—
55	C₂	—	106	1	no	—
56	C₂	#13133279	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#13133279
commutator	C₈×C₅₃	C₂×C₄
Frattini	C₈	C₂×#6157
Fitting	D₈×C₅₃	C₄
socle	C₂×C₅₃	#102
prime radical	#13133236	C₂
cosocle	C₈×D₅₃	C₂²
hypercenter	D₈	#6157
hypocenter	C₅₃	#360
LCS	G ▷ C₈×C₅₃ ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ D₈

Complements

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

N	H ≅ G/N	type
1. #13133292	C₂	semidirect
2. #13133285	C₂	semidirect
6. D₈×C₅₃	C₄	semidirect
8. Dic₂₁₂	C₄	semidirect
29. C₅₃	#360	semidirect
36. D₈	#6157	semidirect

Maximal subgroups

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

subgroup	index
#13133292	2
#13133285	2
#13133236	2
#360	53