Subgroups — #34094993

Order 20032.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#14578816	C₂	1	2	yes	maximal
2	C₈×Dic₃₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#14578816	C₄	1	4	yes	—
4	C₂×#14578809	C₄	1	1	yes	characteristic
5	C₄×Dic₃₁₃	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₃₁₃	C₄	1	1	yes	characteristic
7	#14578816	—	2	4	no	—
8	C₂×Dic₃₁₃	C₂×C₄	1	2	yes	—
9	#14578809	C₈	1	2	yes	complemented
10	C₂×C₄×C₃₁₃	C₂×C₄	1	1	yes	characteristic
11	C₈×C₃₁₃	C₈	1	2	yes	complemented
12	C₂²×C₃₁₃	C₄²	1	1	yes	characteristic
13	C₄×C₃₁₃	C₂×C₈	1	1	yes	characteristic
14	C₄×C₃₁₃	C₂×C₈	1	1	yes	characteristic
15	Dic₃₁₃	M₁₆	1	4	yes	—
16	C₂×C₃₁₃	C₄×C₈	1	1	yes	characteristic
17	C₂×C₃₁₃	#97	1	2	yes	—
18	C₃₁₃	#322	1	1	yes	characteristic, complemented, Sylow
19	#322	—	313	1	no	maximal, Sylow
20	C₄×C₈	—	313	2	no	—
21	C₄×C₈	—	313	1	no	—
22	C₂×C₈	—	313	1	no	—
23	C₂×C₈	—	313	4	no	—
24	C₂×C₈	#11929411	1	1	yes	characteristic
25	C₄²	—	313	1	no	—
26	C₂×C₄	—	313	2	no	—
27	C₂×C₄	C₂×#11929411	1	1	yes	characteristic
28	C₈	—	313	2	no	—
29	C₈	—	626	4	no	—
30	C₈	#14578816	1	2	yes	complemented
31	C₂²	C₄×#11929411	1	1	yes	characteristic
32	C₄	—	313	4	no	—
33	C₄	C₂×#14578816	1	1	yes	characteristic
34	C₄	#19097569	1	1	yes	characteristic
35	C₂	C₄×#14578816	1	1	yes	characteristic
36	C₂	#23756551	1	2	yes	—

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.