Subgroups — #28383415

Order 14272.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₅₆₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₂₃⋊C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	D₁₆×C₂₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₇₈₄	—	2	1	no	—
5	D₈×C₂₂₃	—	2	1	no	—
6	C₁₆×C₂₂₃	C₂²	1	1	yes	characteristic
7	D₈₉₂	—	4	1	no	—
8	D₄×C₂₂₃	—	4	1	no	—
9	C₈×C₂₂₃	D₄	1	1	yes	characteristic
10	C₂²×C₂₂₃	—	8	1	no	—
11	C₂×D₂₂₃	—	8	1	no	—
12	C₄×C₂₂₃	D₈	1	1	yes	characteristic
13	C₂×C₂₂₃	—	16	1	no	—
14	C₂×C₂₂₃	D₁₆	1	1	yes	characteristic
15	D₂₂₃	—	16	1	no	—
16	C₂₂₃	D₃₂	1	1	yes	characteristic, complemented, Sylow
17	D₃₂	—	223	1	no	maximal, Sylow
18	D₁₆	—	223	1	no	—
19	D₁₆	D₂₂₃	1	1	yes	characteristic, complemented
20	C₃₂	—	223	1	no	—
21	D₈	—	2	1	no	—
22	D₈	—	446	1	no	—
23	C₁₆	C₂×D₂₂₃	1	1	yes	characteristic
24	D₄	—	4	1	no	—
25	D₄	—	892	1	no	—
26	C₈	C₂²⋊D₂₂₃	1	1	yes	characteristic
27	C₂²	—	8	1	no	—
28	C₂²	—	1784	1	no	—
29	C₄	#16813155	1	1	yes	characteristic
30	C₂	—	16	1	no	—
31	C₂	—	3568	1	no	—
32	C₂	#20297245	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.