Subgroups — C₈×#11719908 #20272630

Order 6784.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#11719908	C₂	1	2	yes	maximal
2	C₈²×C₅₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#11719908	C₄	1	4	yes	—
4	C₄×C₈×C₅₃	C₄	1	2	yes	—
5	C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₅₃	C₈	1	4	yes	—
7	C₂×C₈×C₅₃	C₂×C₄	1	2	yes	—
8	C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
9	#11719908	C₈	1	8	yes	direct product factor
10	C₂×C₄×C₅₃	C₄²	1	1	yes	characteristic
11	C₂×C₄×C₅₃	C₂×C₈	1	2	yes	—
12	C₈×C₅₃	C₁₆	1	8	yes	complemented
13	C₈×C₅₃	C₂×C₈	1	4	yes	—
14	C₂²×C₅₃	C₄×C₈	1	1	yes	characteristic
15	C₄×C₅₃	C₄×C₈	1	2	yes	—
16	C₄×C₅₃	C₂×C₁₆	1	4	yes	—
17	C₈×C₁₆	—	53	1	no	maximal, Sylow
18	C₂×C₅₃	C₈²	1	1	yes	characteristic
19	C₂×C₅₃	C₄×C₁₆	1	2	yes	—
20	C₄×C₁₆	—	53	2	no	—
21	C₈²	D₅₃	1	1	yes	characteristic
22	C₅₃	C₈×C₁₆	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₁₆	—	53	4	no	—
24	C₄×C₈	Dic₅₃	1	2	yes	—
25	C₄×C₈	C₂×D₅₃	1	1	yes	characteristic
26	C₂×C₈	#88322	1	4	yes	—
27	C₂×C₈	C₄×D₅₃	1	2	yes	—
28	C₄²	C₂×Dic₅₃	1	1	yes	characteristic
29	C₁₆	—	53	8	no	—
30	C₂×C₄	C₂×#88322	1	2	yes	—
31	C₂×C₄	C₄×Dic₅₃	1	1	yes	characteristic
32	C₈	#11719908	1	8	yes	direct product factor
33	C₈	C₈×D₅₃	1	4	yes	—
34	C₂²	C₄×#88322	1	1	yes	characteristic
35	C₄	C₈×Dic₅₃	1	2	yes	—
36	C₄	C₂×#11719908	1	4	yes	—
37	C₂	C₈×#88322	1	1	yes	characteristic
38	C₂	C₄×#11719908	1	2	yes	—

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