Subgroups — D₉×D₉₆₁ #46829249

Order 34596.

45 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₈₆₄₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×D₉₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	D₉×C₉₆₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×D₉₆₁	—	3	1	no	maximal
5	C₉×C₉₆₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₂₈₈₃	—	3	1	no	—
7	C₃×D₉₆₁	D₃	1	1	yes	characteristic
8	D₃×C₉₆₁	—	3	1	no	—
9	C₂×D₉₆₁	—	9	1	no	Hall
10	C₃×C₉₆₁	C₂×D₃	1	1	yes	characteristic
11	C₂×C₉₆₁	—	9	1	no	—
12	D₉₆₁	—	9	1	no	—
13	D₉₆₁	D₉	1	1	yes	characteristic, direct product factor
14	D₉×D₃₁	—	31	1	no	maximal
15	C₉₆₁	C₂×D₉	1	1	yes	characteristic, complemented, Sylow
16	D₂₇₉	—	31	1	no	—
17	C₉×D₃₁	—	31	1	no	—
18	D₉×C₃₁	D₃₁	1	1	yes	characteristic
19	D₃×D₃₁	—	93	1	no	—
20	C₉×C₃₁	C₂×D₃₁	1	1	yes	characteristic
21	D₉₃	—	93	1	no	—
22	C₃×D₃₁	—	31	1	no	—
23	D₃×C₃₁	—	3	1	no	—
24	C₂×D₃₁	—	279	1	no	—
25	C₃×C₃₁	D₃×D₃₁	1	1	yes	characteristic
26	C₂×C₃₁	—	9	1	no	—
27	D₃₁	—	279	1	no	—
28	D₃₁	—	31	1	no	—
29	C₂×D₉	—	961	1	no	Hall
30	C₃₁	D₉×D₃₁	1	1	yes	characteristic
31	C₂×C₉	—	961	1	no	—
32	D₉	—	961	1	no	—
33	D₉	D₉₆₁	1	1	yes	characteristic, direct product factor
34	C₂×D₃	—	2883	1	no	—
35	C₉	C₂×D₉₆₁	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₃	—	961	1	no	—
37	D₃	—	3	1	no	—
38	D₃	—	2883	1	no	—
39	C₂²	—	8649	1	no	Sylow
40	C₃	D₃×D₉₆₁	1	1	yes	characteristic
41	C₂	—	9	1	no	—
42	C₂	—	961	1	no	—
43	C₂	—	8649	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₉₆₁	C₂²
Frattini, socle	C₃×C₃₁	D₃×D₃₁
LCS	G ▷ C₉×C₉₆₁
UCS	C₁

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.