Subgroups — C₉×#107 #63409

Order 288.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×C₉	C₂	1	1	yes	maximal, characteristic
2	C₉×C₄⋊C₄	C₂	1	2	yes	maximal
3	C₃×#107	C₃	1	1	yes	maximal, characteristic
4	C₂×C₄×C₉	—	2	2	no	—
5	C₂×C₄×C₉	C₂²	1	1	yes	characteristic
6	C₈×C₉	C₄	1	2	yes	complemented
7	C₂×C₃×C₈	C₂×C₃	1	1	yes	characteristic
8	C₃×C₄⋊C₄	C₂×C₃	1	2	yes	—
9	C₂²×C₉	D₄	1	1	yes	characteristic
10	C₄×C₉	—	4	2	no	—
11	C₄×C₉	C₂×C₄	1	1	yes	characteristic
12	C₄×C₉	Q₈	1	1	yes	characteristic
13	#107	C₉	1	1	yes	characteristic, direct product factor, Sylow
14	C₂×C₃×C₄	—	2	2	no	—
15	C₂×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
16	C₃×C₈	C₃×C₄	1	2	yes	—
17	C₂×C₉	C₄⋊C₄	1	1	yes	characteristic
18	C₂×C₉	D₈	1	1	yes	characteristic
19	C₂×C₉	Q₁₆	1	1	yes	characteristic
20	C₂×C₈	C₂×C₉	1	1	yes	characteristic
21	C₄⋊C₄	C₂×C₉	1	2	yes	—
22	C₂²×C₃	C₃×D₄	1	1	yes	characteristic
23	C₃×C₄	—	4	2	no	—
24	C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
25	C₃×C₄	C₃×Q₈	1	1	yes	characteristic
26	C₉	#107	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₄	—	2	2	no	—
28	C₂×C₄	C₂²×C₉	1	1	yes	characteristic
29	C₈	C₄×C₉	1	2	yes	complemented
30	C₂×C₃	C₃×C₄⋊C₄	1	1	yes	characteristic
31	C₂×C₃	C₃×D₈	1	1	yes	characteristic
32	C₂×C₃	C₃×Q₁₆	1	1	yes	characteristic
33	C₂²	D₄×C₉	1	1	yes	characteristic
34	C₄	—	4	2	no	—
35	C₄	C₂×C₄×C₉	1	1	yes	characteristic
36	C₄	Q₈×C₉	1	1	yes	characteristic
37	C₃	C₃×#107	1	1	yes	characteristic
38	C₂	C₉×C₄⋊C₄	1	1	yes	characteristic
39	C₂	C₉×D₈	1	1	yes	characteristic
40	C₂	C₉×Q₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	D₄
commutator	C₄	C₂×C₄×C₉
Frattini, cosocle	C₂×C₃×C₄	C₂²×C₃
socle, prime radical	C₂²×C₃	C₃×D₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₂×C₄×C₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
6. C₈×C₉	C₄	semidirect
13. #107	C₉	direct (N × H)
26. C₉	#107	direct (N × H)
29. C₈	C₄×C₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₈×C₉	2
C₉×C₄⋊C₄	2
C₃×#107	3

Subgroups — C9×#107 #63409

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#107 #63409