Subgroups — Dic₂₅₅₆ #72212792

Order 10224.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₁₂₇₈	C₂	1	2	yes	maximal
2	Dic₈₅₂	—	3	1	no	maximal
3	C₈×C₉×C₇₁	C₂	1	1	yes	maximal, characteristic
4	Dic₆₃₉	—	2	2	no	—
5	C₄×C₉×C₇₁	C₂²	1	1	yes	characteristic
6	Dic₄₂₆	—	3	2	no	—
7	C₃×C₈×C₇₁	D₃	1	1	yes	characteristic
8	C₂×C₉×C₇₁	D₄	1	1	yes	characteristic
9	Dic₂₈₄	—	9	1	no	Hall
10	C₃×C₄×C₇₁	C₂×D₃	1	1	yes	characteristic
11	Dic₂₁₃	—	6	2	no	—
12	C₉×C₇₁	Q₁₆	1	1	yes	characteristic, complemented, Hall
13	Dic₁₄₂	—	9	2	no	—
14	C₈×C₇₁	D₉	1	1	yes	characteristic
15	C₂×C₃×C₇₁	D₁₂	1	1	yes	characteristic
16	C₄×C₇₁	C₂×D₉	1	1	yes	characteristic
17	Dic₇₁	—	18	2	no	—
18	C₃×C₇₁	Dic₁₂	1	1	yes	characteristic
19	Dic₃₆	—	71	1	no	maximal, Hall
20	C₂×C₇₁	D₃₆	1	1	yes	characteristic
21	Dic₁₈	—	71	2	no	—
22	C₈×C₉	D₇₁	1	1	yes	characteristic
23	C₇₁	Dic₃₆	1	1	yes	characteristic, complemented, Sylow
24	Dic₁₂	—	213	1	no	—
25	C₄×C₉	C₂×D₇₁	1	1	yes	characteristic
26	Dic₉	—	142	2	no	—
27	Dic₆	—	213	2	no	—
28	C₃×C₈	D₂₁₃	1	1	yes	characteristic
29	C₂×C₉	D₂₈₄	1	1	yes	characteristic
30	Q₁₆	—	639	1	no	Sylow
31	C₃×C₄	C₂×D₂₁₃	1	1	yes	characteristic
32	Dic₃	—	426	2	no	—
33	C₉	Dic₂₈₄	1	1	yes	characteristic, complemented, Sylow
34	Q₈	—	639	2	no	—
35	C₈	D₆₃₉	1	1	yes	characteristic
36	C₂×C₃	D₈₅₂	1	1	yes	characteristic
37	C₄	—	1278	2	no	—
38	C₄	C₂×D₆₃₉	1	1	yes	characteristic
39	C₃	Dic₈₅₂	1	1	yes	characteristic
40	C₂	D₂₅₅₆	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.