Subgroups — #34095241

Order 20032.

54 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	—	2	2	no	—
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	—	4	2	no	—
8	C₂×#11929411	D₄	1	1	yes	characteristic
9	C₂×#11929411	Q₈	1	1	yes	characteristic
10	#14578816	—	2	1	no	—
11	C₄×D₃₁₃	C₂×C₄	1	1	yes	characteristic
12	#14578809	C₈	1	1	yes	characteristic, complemented
13	C₈×C₃₁₃	C₈	1	1	yes	characteristic, complemented
14	C₂×D₃₁₃	C₄⋊C₄	1	1	yes	characteristic
15	#11929411	—	2	1	no	—
16	#11929411	SD₁₆	1	2	yes	—
17	C₄×C₃₁₃	C₂×C₈	1	1	yes	characteristic
18	Dic₃₁₃	M₁₆	1	1	yes	characteristic
19	C₂×C₃₁₃	C₄⋊C₈	1	1	yes	characteristic
20	D₃₁₃	#106	1	1	yes	characteristic
21	D₃₁₃	#108	1	1	yes	characteristic
22	C₃₁₃	#334	1	1	yes	characteristic, complemented, Sylow
23	#334	—	313	1	no	maximal, Sylow
24	C₄⋊C₈	—	313	2	no	—
25	C₄×C₈	—	313	1	no	—
26	C₂×C₈	—	313	1	no	—
27	C₂×C₈	—	313	1	no	—
28	C₂×C₈	—	626	2	no	—
29	C₄²	—	313	1	no	—
30	C₂×C₄	—	313	1	no	—
31	C₂×C₄	—	313	1	no	—
32	C₂×C₄	—	313	1	no	—
33	C₈	—	313	1	no	—
34	C₈	—	626	1	no	—
35	C₈	—	1252	2	no	—
36	C₈	#14578818	1	1	yes	characteristic, complemented
37	C₂²	—	313	1	no	—
38	C₄	—	313	2	no	—
39	C₄	—	313	1	no	—
40	C₄	—	626	1	no	—
41	C₄	C₂×#14578818	1	1	yes	characteristic
42	C₂	—	313	1	no	—
43	C₂	—	313	1	no	—
44	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.