Subgroups — D₁₁₁₄₄ #72215813

Order 22288.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅₅₇₂	C₂	1	2	yes	maximal, complemented
2	C₇×C₈×C₁₉₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₁₃₉₃	—	2	2	no	—
4	C₄×C₇×C₁₉₉	C₂²	1	1	yes	characteristic
5	D₁₅₉₂	—	7	1	no	maximal, Hall
6	C₂×C₇×C₁₉₉	D₄	1	1	yes	characteristic
7	D₁₃₉₃	—	4	2	no	—
8	D₇₉₆	—	7	2	no	—
9	C₈×C₁₉₉	D₇	1	1	yes	characteristic, complemented
10	C₇×C₁₉₉	D₈	1	1	yes	characteristic, complemented, Hall
11	C₂×D₁₉₉	—	14	2	no	—
12	C₄×C₁₉₉	C₂×D₇	1	1	yes	characteristic
13	C₂×C₁₉₉	D₂₈	1	1	yes	characteristic
14	D₁₉₉	—	28	2	no	—
15	C₁₉₉	D₅₆	1	1	yes	characteristic, complemented, Sylow
16	D₅₆	—	199	1	no	maximal, Hall
17	D₂₈	—	199	2	no	—
18	C₇×C₈	D₁₉₉	1	1	yes	characteristic, complemented
19	C₂×D₇	—	398	2	no	—
20	C₄×C₇	C₂×D₁₉₉	1	1	yes	characteristic
21	D₈	—	1393	1	no	Sylow
22	C₂×C₇	D₇₉₆	1	1	yes	characteristic
23	D₇	—	796	2	no	—
24	D₄	—	1393	2	no	—
25	C₈	D₁₃₉₃	1	1	yes	characteristic, complemented
26	C₇	D₁₅₉₂	1	1	yes	characteristic, complemented, Sylow
27	C₂²	—	2786	2	no	—
28	C₄	C₂×D₁₃₉₃	1	1	yes	characteristic
29	C₂	—	5572	2	no	—
30	C₂	D₅₅₇₂	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.