Subgroups — C₈×#14578818 #34095235

Order 20032.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#14578818	C₂	1	2	yes	maximal
2	C₈×#11929411	C₂	1	1	yes	maximal, characteristic
3	C₂×#14578818	C₄	1	4	yes	—
4	#19097569	C₄	1	1	yes	characteristic
5	C₄×#11929411	C₂²	1	1	yes	characteristic
6	C₈×D₃₁₃	C₄	1	1	yes	characteristic
7	#14578818	C₈	1	8	yes	direct product factor
8	C₂×#11929411	C₂×C₄	1	2	yes	—
9	#14578816	C₈	1	2	yes	complemented
10	C₄×D₃₁₃	C₂×C₄	1	1	yes	characteristic
11	#14578809	C₈	1	1	yes	characteristic, complemented
12	C₈×C₃₁₃	C₈	1	1	yes	characteristic, complemented
13	C₂×D₃₁₃	C₄²	1	1	yes	characteristic
14	#11929411	C₂×C₈	1	4	yes	—
15	C₄×C₃₁₃	C₂×C₈	1	1	yes	characteristic
16	Dic₃₁₃	C₂×C₈	1	1	yes	characteristic
17	C₂×C₃₁₃	C₄×C₈	1	1	yes	characteristic
18	D₃₁₃	C₄×C₈	1	2	yes	—
19	C₃₁₃	C₈²	1	1	yes	characteristic, complemented, Sylow
20	C₈²	—	313	1	no	maximal, Sylow
21	C₄×C₈	—	313	1	no	—
22	C₄×C₈	—	313	2	no	—
23	C₂×C₈	—	313	1	no	—
24	C₂×C₈	—	313	4	no	—
25	C₂×C₈	—	313	1	no	—
26	C₄²	—	313	1	no	—
27	C₂×C₄	—	313	2	no	—
28	C₂×C₄	—	313	1	no	—
29	C₈	—	313	2	no	—
30	C₈	—	313	8	no	—
31	C₈	—	313	1	no	—
32	C₈	#14578818	1	1	yes	characteristic, direct product factor
33	C₂²	—	313	1	no	—
34	C₄	—	313	4	no	—
35	C₄	—	313	1	no	—
36	C₄	C₂×#14578818	1	1	yes	characteristic
37	C₂	—	313	2	no	—
38	C₂	C₄×#14578818	1	1	yes	characteristic

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

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