Subgroups — D₉₁₁₂ #72213946

Order 18224.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄₅₅₆	C₂	1	2	yes	maximal, complemented
2	C₈×C₁₇×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₁₁₃₉	—	2	2	no	—
4	C₄×C₁₇×C₆₇	C₂²	1	1	yes	characteristic
5	C₂×C₁₇×C₆₇	D₄	1	1	yes	characteristic
6	D₁₁₃₉	—	4	2	no	—
7	C₁₇×C₆₇	D₈	1	1	yes	characteristic, complemented, Hall
8	D₅₃₆	—	17	1	no	maximal, Hall
9	D₂₆₈	—	17	2	no	—
10	C₈×C₆₇	D₁₇	1	1	yes	characteristic, complemented
11	D₁₃₆	—	67	1	no	maximal, Hall
12	C₂×D₆₇	—	34	2	no	—
13	C₄×C₆₇	C₂×D₁₇	1	1	yes	characteristic
14	D₆₈	—	67	2	no	—
15	C₈×C₁₇	D₆₇	1	1	yes	characteristic, complemented
16	C₂×C₆₇	D₆₈	1	1	yes	characteristic
17	D₆₇	—	68	2	no	—
18	C₂×D₁₇	—	134	2	no	—
19	C₄×C₁₇	C₂×D₆₇	1	1	yes	characteristic
20	C₆₇	D₁₃₆	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₁₇	D₂₆₈	1	1	yes	characteristic
22	D₁₇	—	268	2	no	—
23	C₁₇	D₅₃₆	1	1	yes	characteristic, complemented, Sylow
24	D₈	—	1139	1	no	Sylow
25	D₄	—	1139	2	no	—
26	C₈	D₁₁₃₉	1	1	yes	characteristic, complemented
27	C₂²	—	2278	2	no	—
28	C₄	C₂×D₁₁₃₉	1	1	yes	characteristic
29	C₂	—	4556	2	no	—
30	C₂	D₄₅₅₆	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.