Subgroups — D₁₀₈₉₆ #72215647

Order 21792.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅₄₄₈	C₂	1	2	yes	maximal, complemented
2	D₂₇₂₄	—	2	2	no	—
3	C₃×C₁₆×C₂₂₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₈×C₂₂₇	C₂²	1	1	yes	characteristic
5	D₃₆₃₂	—	3	1	no	maximal, Hall
6	D₁₈₁₆	—	3	2	no	—
7	C₁₆×C₂₂₇	D₃	1	1	yes	characteristic, complemented
8	C₂×D₆₈₁	—	4	2	no	—
9	C₃×C₄×C₂₂₇	D₄	1	1	yes	characteristic
10	D₉₀₈	—	6	2	no	—
11	C₈×C₂₂₇	C₂×D₃	1	1	yes	characteristic
12	C₂×C₃×C₂₂₇	D₈	1	1	yes	characteristic
13	D₆₈₁	—	8	2	no	—
14	C₂×D₂₂₇	—	12	2	no	—
15	C₄×C₂₂₇	D₁₂	1	1	yes	characteristic
16	C₃×C₂₂₇	D₁₆	1	1	yes	characteristic, complemented, Hall
17	C₂×C₂₂₇	D₂₄	1	1	yes	characteristic
18	D₂₂₇	—	24	2	no	—
19	C₂₂₇	D₄₈	1	1	yes	characteristic, complemented, Sylow
20	D₄₈	—	227	1	no	maximal, Hall
21	D₂₄	—	227	2	no	—
22	C₃×C₁₆	D₂₂₇	1	1	yes	characteristic, complemented
23	D₁₆	—	681	1	no	Sylow
24	D₁₂	—	454	2	no	—
25	C₃×C₈	C₂×D₂₂₇	1	1	yes	characteristic
26	D₈	—	681	2	no	—
27	C₁₆	D₆₈₁	1	1	yes	characteristic, complemented
28	C₂×D₃	—	908	2	no	—
29	C₃×C₄	D₉₀₈	1	1	yes	characteristic
30	D₄	—	1362	2	no	—
31	C₈	C₂×D₆₈₁	1	1	yes	characteristic
32	C₂×C₃	D₁₈₁₆	1	1	yes	characteristic
33	D₃	—	1816	2	no	—
34	C₂²	—	2724	2	no	—
35	C₄	D₂₇₂₄	1	1	yes	characteristic
36	C₃	D₃₆₃₂	1	1	yes	characteristic, complemented, Sylow
37	C₂	—	5448	2	no	—
38	C₂	D₅₄₄₈	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.