Subgroups — #34093987

Order 20032.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅₀₀₈	C₂	1	1	yes	maximal, characteristic, complemented
2	#23756403	C₂	1	1	yes	maximal, characteristic, complemented
3	D₁₆×C₃₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₂₅₀₄	—	2	1	no	—
5	D₈×C₃₁₃	—	2	1	no	—
6	C₁₆×C₃₁₃	C₂²	1	1	yes	characteristic
7	D₁₂₅₂	—	4	1	no	—
8	D₄×C₃₁₃	—	4	1	no	—
9	C₈×C₃₁₃	D₄	1	1	yes	characteristic
10	C₂²×C₃₁₃	—	8	1	no	—
11	C₂×D₃₁₃	—	8	1	no	—
12	C₄×C₃₁₃	D₈	1	1	yes	characteristic
13	C₂×C₃₁₃	—	16	1	no	—
14	C₂×C₃₁₃	D₁₆	1	1	yes	characteristic
15	D₃₁₃	—	16	1	no	—
16	C₃₁₃	D₃₂	1	1	yes	characteristic, complemented, Sylow
17	D₃₂	—	313	1	no	maximal, Sylow
18	D₁₆	—	313	1	no	—
19	D₁₆	D₃₁₃	1	1	yes	characteristic, complemented
20	C₃₂	—	313	1	no	—
21	D₈	—	2	1	no	—
22	D₈	—	626	1	no	—
23	C₁₆	C₂×D₃₁₃	1	1	yes	characteristic
24	D₄	—	4	1	no	—
25	D₄	—	1252	1	no	—
26	C₈	C₂²⋊D₃₁₃	1	1	yes	characteristic
27	C₂²	—	8	1	no	—
28	C₂²	—	2504	1	no	—
29	C₄	#19097546	1	1	yes	characteristic
30	C₂	—	16	1	no	—
31	C₂	—	5008	1	no	—
32	C₂	#23756438	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.