Subgroups — #16810345

Order 3392.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#88322	C₂	1	1	yes	maximal, characteristic
2	C₄×#88322	C₂	1	1	yes	maximal, characteristic
3	C₄×C₈×C₅₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈×C₅₃	C₄	1	2	yes	—
5	C₄²×C₅₃	C₂²	1	1	yes	characteristic
6	C₂×#88322	C₄	1	2	yes	—
7	C₂×#88322	C₄	1	2	yes	—
8	C₂×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
9	C₂×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
10	C₂×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
11	C₈×C₅₃	—	2	2	no	—
12	#88322	—	2	2	no	—
13	#88322	C₈	1	4	yes	complemented
14	C₂²×C₅₃	C₄²	1	1	yes	characteristic
15	C₄×C₅₃	C₂×C₈	1	2	yes	—
16	C₄×C₅₃	M₁₆	1	2	yes	—
17	C₄×C₅₃	M₁₆	1	2	yes	—
18	C₂×C₅₃	C₄×C₈	1	1	yes	characteristic
19	C₂×C₅₃	#97	1	1	yes	characteristic
20	C₂×C₅₃	#97	1	1	yes	characteristic
21	#322	—	53	1	no	maximal, Sylow
22	C₅₃	#322	1	1	yes	characteristic, complemented, Sylow
23	C₄×C₈	—	53	1	no	—
24	C₄×C₈	—	53	1	no	—
25	C₄×C₈	D₅₃	1	1	yes	characteristic
26	C₂×C₈	—	53	2	no	—
27	C₂×C₈	—	53	2	no	—
28	C₂×C₈	Dic₅₃	1	2	yes	—
29	C₄²	C₂×D₅₃	1	1	yes	characteristic
30	C₂×C₄	C₄×D₅₃	1	1	yes	characteristic
31	C₂×C₄	C₄×D₅₃	1	1	yes	characteristic
32	C₂×C₄	C₂×Dic₅₃	1	1	yes	characteristic
33	C₈	—	2	2	no	—
34	C₈	—	53	4	no	—
35	C₈	—	106	2	no	—
36	C₂²	C₄×Dic₅₃	1	1	yes	characteristic
37	C₄	C₈×D₅₃	1	2	yes	—
38	C₄	#11719912	1	2	yes	—
39	C₄	#11719917	1	2	yes	—
40	C₂	C₈×Dic₅₃	1	1	yes	characteristic
41	C₂	#13133127	1	1	yes	characteristic
42	C₂	#13133128	1	1	yes	characteristic

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

N	H ≅ G/N	type
13. #88322	C₈	semidirect
22. C₅₃	#322	semidirect

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