Subgroups — D₁₆₉₂₈ #72272913

Order 33856.

51 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₈₄₆₄	C₂	1	2	yes	maximal, complemented
2	D₄₂₃₂	—	2	2	no	—
3	D₂₁₁₆	—	4	2	no	—
4	C₃₂×C₅₂₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₆×C₅₂₉	C₂²	1	1	yes	characteristic
6	C₈×C₅₂₉	D₄	1	1	yes	characteristic
7	C₂×D₅₂₉	—	8	2	no	—
8	C₄×C₅₂₉	D₈	1	1	yes	characteristic
9	D₇₃₆	—	23	1	no	maximal
10	C₂×C₅₂₉	D₁₆	1	1	yes	characteristic
11	D₅₂₉	—	16	2	no	—
12	D₃₆₈	—	23	2	no	—
13	C₂₃×C₃₂	D₂₃	1	1	yes	characteristic
14	C₅₂₉	D₃₂	1	1	yes	characteristic, complemented, Sylow
15	D₁₈₄	—	46	2	no	—
16	C₁₆×C₂₃	C₂×D₂₃	1	1	yes	characteristic
17	D₉₂	—	92	2	no	—
18	C₈×C₂₃	D₉₂	1	1	yes	characteristic
19	C₂×D₂₃	—	184	2	no	—
20	C₄×C₂₃	D₁₈₄	1	1	yes	characteristic
21	D₃₂	—	529	1	no	Sylow
22	C₂×C₂₃	D₃₆₈	1	1	yes	characteristic
23	D₂₃	—	368	2	no	—
24	D₁₆	—	529	2	no	—
25	C₃₂	D₅₂₉	1	1	yes	characteristic, complemented
26	C₂₃	D₇₃₆	1	1	yes	characteristic
27	D₈	—	1058	2	no	—
28	C₁₆	C₂×D₅₂₉	1	1	yes	characteristic
29	D₄	—	2116	2	no	—
30	C₈	D₂₁₁₆	1	1	yes	characteristic
31	C₂²	—	4232	2	no	—
32	C₄	D₄₂₃₂	1	1	yes	characteristic
33	C₂	—	8464	2	no	—
34	C₂	D₈₄₆₄	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.