Subgroups — #16810440

Order 3392.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₂₁₂	C₂	1	1	yes	maximal, characteristic
2	#13133153	C₂	1	1	yes	maximal, characteristic
3	M₃₂×C₅₃	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₁₀₆	—	2	1	no	—
5	C₂×C₈×C₅₃	C₂²	1	1	yes	characteristic
6	#11719917	—	2	1	no	—
7	Dic₂₁₂	—	2	1	no	—
8	Dic₂₁₂	C₄	1	2	yes	—
9	C₁₆×C₅₃	—	2	1	no	—
10	C₂×C₄×C₅₃	D₄	1	1	yes	characteristic
11	C₂×Dic₅₃	—	4	1	no	—
12	Dic₁₀₆	—	2	2	no	—
13	Dic₁₀₆	—	4	1	no	—
14	C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
15	C₈×C₅₃	D₄	1	1	yes	characteristic
16	#88322	—	4	1	no	—
17	C₂²×C₅₃	SD₁₆	1	1	yes	characteristic
18	C₄×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
19	C₄×C₅₃	D₈	1	1	yes	characteristic
20	Dic₅₃	—	4	2	no	—
21	C₂×C₅₃	—	2	1	no	—
22	C₂×C₅₃	#102	1	1	yes	characteristic
23	#362	—	53	1	no	maximal, Sylow
24	C₅₃	#362	1	1	yes	characteristic, complemented, Sylow
25	C₂×Q₁₆	—	53	1	no	—
26	M₃₂	D₅₃	1	1	yes	characteristic
27	#108	—	53	1	no	—
28	C₂×Q₈	—	106	1	no	—
29	Q₁₆	—	53	2	no	—
30	Q₁₆	—	106	1	no	—
31	M₁₆	—	106	1	no	—
32	C₂×C₈	C₂×D₅₃	1	1	yes	characteristic
33	C₁₆	—	2	1	no	—
34	Q₈	—	106	2	no	—
35	Q₈	—	212	1	no	—
36	C₂×C₄	—	212	1	no	—
37	C₂×C₄	D₂₁₂	1	1	yes	characteristic
38	C₈	—	212	1	no	—
39	C₈	C₄×D₅₃	1	1	yes	characteristic
40	C₈	C₂²⋊D₅₃	1	1	yes	characteristic
41	C₂²	#11719913	1	1	yes	characteristic
42	C₄	—	212	2	no	—
43	C₄	D₄₂₄	1	1	yes	characteristic
44	C₄	#11719921	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	C₂	#13133139	1	1	yes	characteristic

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

N	H ≅ G/N	type
24. C₅₃	#362	semidirect

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