Subgroups — Dic₄₄₂₄ #72215899

Order 17696.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₂₂₁₂	C₂	1	2	yes	maximal
2	Dic₁₁₀₆	—	2	2	no	—
3	C₇×C₁₆×C₇₉	C₂	1	1	yes	maximal, characteristic
4	C₇×C₈×C₇₉	C₂²	1	1	yes	characteristic
5	Dic₆₃₂	—	7	1	no	maximal, Hall
6	Dic₅₅₃	—	4	2	no	—
7	C₄×C₇×C₇₉	D₄	1	1	yes	characteristic
8	Dic₃₁₆	—	7	2	no	—
9	C₁₆×C₇₉	D₇	1	1	yes	characteristic
10	C₂×C₇×C₇₉	D₈	1	1	yes	characteristic
11	Dic₁₅₈	—	14	2	no	—
12	C₈×C₇₉	C₂×D₇	1	1	yes	characteristic
13	C₇×C₇₉	Q₃₂	1	1	yes	characteristic, complemented, Hall
14	C₄×C₇₉	D₂₈	1	1	yes	characteristic
15	Dic₇₉	—	28	2	no	—
16	Dic₅₆	—	79	1	no	maximal, Hall
17	C₂×C₇₉	D₅₆	1	1	yes	characteristic
18	Dic₂₈	—	79	2	no	—
19	C₇×C₁₆	D₇₉	1	1	yes	characteristic
20	C₇₉	Dic₅₆	1	1	yes	characteristic, complemented, Sylow
21	Dic₁₄	—	158	2	no	—
22	C₇×C₈	C₂×D₇₉	1	1	yes	characteristic
23	Q₃₂	—	553	1	no	Sylow
24	C₄×C₇	D₃₁₆	1	1	yes	characteristic
25	Dic₇	—	316	2	no	—
26	Q₁₆	—	553	2	no	—
27	C₁₆	D₅₅₃	1	1	yes	characteristic
28	C₂×C₇	D₆₃₂	1	1	yes	characteristic
29	Q₈	—	1106	2	no	—
30	C₈	C₂×D₅₅₃	1	1	yes	characteristic
31	C₇	Dic₆₃₂	1	1	yes	characteristic, complemented, Sylow
32	C₄	—	2212	2	no	—
33	C₄	D₂₂₁₂	1	1	yes	characteristic
34	C₂	D₄₄₂₄	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.