Subgroups — Dic₁₃₈₉₂ #72290213

Order 55568.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₆₉₄₆	C₂	1	2	yes	maximal
2	C₈×C₂₃×C₁₅₁	C₂	1	1	yes	maximal, characteristic
3	Dic₃₄₇₃	—	2	2	no	—
4	C₄×C₂₃×C₁₅₁	C₂²	1	1	yes	characteristic
5	C₂×C₂₃×C₁₅₁	D₄	1	1	yes	characteristic
6	C₂₃×C₁₅₁	Q₁₆	1	1	yes	characteristic, complemented, Hall
7	Dic₆₀₄	—	23	1	no	maximal, Hall
8	Dic₃₀₂	—	23	2	no	—
9	C₈×C₁₅₁	D₂₃	1	1	yes	characteristic
10	C₄×C₁₅₁	C₂×D₂₃	1	1	yes	characteristic
11	Dic₁₅₁	—	46	2	no	—
12	Dic₉₂	—	151	1	no	maximal, Hall
13	C₂×C₁₅₁	D₉₂	1	1	yes	characteristic
14	Dic₄₆	—	151	2	no	—
15	C₈×C₂₃	D₁₅₁	1	1	yes	characteristic
16	C₁₅₁	Dic₉₂	1	1	yes	characteristic, complemented, Sylow
17	C₄×C₂₃	C₂×D₁₅₁	1	1	yes	characteristic
18	Dic₂₃	—	302	2	no	—
19	C₂×C₂₃	D₆₀₄	1	1	yes	characteristic
20	C₂₃	Dic₆₀₄	1	1	yes	characteristic, complemented, Sylow
21	Q₁₆	—	3473	1	no	Sylow
22	Q₈	—	3473	2	no	—
23	C₈	D₃₄₇₃	1	1	yes	characteristic
24	C₄	—	6946	2	no	—
25	C₄	C₂×D₃₄₇₃	1	1	yes	characteristic
26	C₂	D₁₃₈₉₂	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.