Subgroups — D₃₀₉₈₄ #72298331

Order 61968.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₅₄₉₂	C₂	1	2	yes	maximal, complemented
2	C₃×C₈×C₁₂₉₁	C₂	1	1	yes	maximal, characteristic, complemented
3	D₁₀₃₂₈	—	3	1	no	maximal, Hall
4	C₂×D₃₈₇₃	—	2	2	no	—
5	C₃×C₄×C₁₂₉₁	C₂²	1	1	yes	characteristic
6	D₅₁₆₄	—	3	2	no	—
7	C₈×C₁₂₉₁	D₃	1	1	yes	characteristic, complemented
8	C₂×C₃×C₁₂₉₁	D₄	1	1	yes	characteristic
9	D₃₈₇₃	—	4	2	no	—
10	C₂×D₁₂₉₁	—	6	2	no	—
11	C₄×C₁₂₉₁	C₂×D₃	1	1	yes	characteristic
12	C₃×C₁₂₉₁	D₈	1	1	yes	characteristic, complemented, Hall
13	C₂×C₁₂₉₁	D₁₂	1	1	yes	characteristic
14	D₁₂₉₁	—	12	2	no	—
15	C₁₂₉₁	D₂₄	1	1	yes	characteristic, complemented, Sylow
16	D₂₄	—	1291	1	no	maximal, Hall
17	D₁₂	—	1291	2	no	—
18	C₃×C₈	D₁₂₉₁	1	1	yes	characteristic, complemented
19	D₈	—	3873	1	no	Sylow
20	C₂×D₃	—	2582	2	no	—
21	C₃×C₄	C₂×D₁₂₉₁	1	1	yes	characteristic
22	D₄	—	3873	2	no	—
23	C₈	D₃₈₇₃	1	1	yes	characteristic, complemented
24	C₂×C₃	D₅₁₆₄	1	1	yes	characteristic
25	D₃	—	5164	2	no	—
26	C₂²	—	7746	2	no	—
27	C₄	C₂×D₃₈₇₃	1	1	yes	characteristic
28	C₃	D₁₀₃₂₈	1	1	yes	characteristic, complemented, Sylow
29	C₂	—	15492	2	no	—
30	C₂	D₁₅₄₉₂	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.