Subgroups — C₃×C₉×#101 #11720605

Order 864.

190 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Q₈×C₉	C₂	1	1	yes	maximal, characteristic
2	C₃×C₉×M₁₆	C₂	1	2	yes	maximal
3	C₃²×#101	C₃	1	1	yes	maximal, characteristic
4	C₉×#101	C₃	1	3	yes	maximal, direct product factor
5	C₃×Q₈×C₉	—	2	2	no	—
6	C₂×C₃×C₄×C₉	C₄	1	2	yes	—
7	C₂×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
8	C₃×C₈×C₉	—	2	2	no	—
9	C₂×C₃²×Q₈	C₂×C₃	1	1	yes	characteristic
10	C₃²×M₁₆	C₂×C₃	1	2	yes	—
11	C₂×Q₈×C₉	C₂×C₃	1	3	yes	—
12	C₉×M₁₆	C₂×C₃	1	6	yes	—
13	C₂²×C₃×C₉	C₂×C₄	1	1	yes	characteristic
14	C₃×C₄×C₉	—	2	2	no	—
15	C₃×C₄×C₉	D₄	1	2	yes	—
16	C₃×#101	C₉	1	3	yes	direct product factor
17	C₃×#101	C₃²	1	1	yes	characteristic
18	C₃²×Q₈	—	2	2	no	—
19	C₂×C₃²×C₄	C₃×C₄	1	2	yes	—
20	C₂×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
21	C₃²×C₈	—	2	2	no	—
22	Q₈×C₉	—	2	6	no	—
23	C₂×C₄×C₉	C₃×C₄	1	6	yes	—
24	C₂×C₄×C₉	C₂²×C₃	1	3	yes	—
25	C₈×C₉	—	2	6	no	—
26	C₂×C₃×C₉	—	2	1	no	—
27	C₂×C₃×C₉	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×C₃×Q₈	C₂×C₉	1	3	yes	—
29	C₂×C₃×Q₈	C₂×C₃²	1	1	yes	characteristic
30	C₃×M₁₆	C₂×C₉	1	6	yes	—
31	C₃×M₁₆	C₂×C₃²	1	2	yes	—
32	C₂²×C₃²	C₂×C₃×C₄	1	1	yes	characteristic
33	C₃²×C₄	—	2	2	no	—
34	C₃²×C₄	C₃×D₄	1	2	yes	—
35	C₂²×C₉	C₂×C₃×C₄	1	3	yes	—
36	C₄×C₉	—	2	6	no	—
37	C₄×C₉	C₃×D₄	1	6	yes	—
38	#101	C₃×C₉	1	1	yes	characteristic, direct product factor, Sylow
39	C₃×C₉	#101	1	1	yes	characteristic, direct product factor, Sylow
40	C₃×Q₈	—	2	6	no	—
41	C₃×Q₈	—	2	2	no	—
42	C₂×C₃×C₄	C₄×C₉	1	6	yes	—
43	C₂×C₃×C₄	C₂²×C₉	1	3	yes	—
44	C₂×C₃×C₄	C₃²×C₄	1	2	yes	—
45	C₂×C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
46	C₃×C₈	—	2	6	no	—
47	C₃×C₈	—	2	2	no	—
48	C₂×C₃²	—	2	1	no	—
49	C₂×C₃²	C₃×C₂²⋊C₄	1	1	yes	characteristic
50	C₂×C₉	—	2	3	no	—
51	C₂×C₉	C₃×C₂²⋊C₄	1	3	yes	—
52	C₂×Q₈	C₂×C₃×C₉	1	1	yes	characteristic
53	M₁₆	C₂×C₃×C₉	1	2	yes	—
54	C₂²×C₃	C₂×C₄×C₉	1	3	yes	—
55	C₂²×C₃	C₂×C₃²×C₄	1	1	yes	characteristic
56	C₃×C₄	—	2	6	no	—
57	C₃×C₄	—	2	2	no	—
58	C₃×C₄	D₄×C₉	1	6	yes	—
59	C₃×C₄	C₃²×D₄	1	2	yes	—
60	C₃²	C₃×#101	1	1	yes	characteristic
61	C₉	C₃×#101	1	3	yes	direct product factor
62	Q₈	—	2	2	no	—
63	C₂×C₄	C₃×C₄×C₉	1	2	yes	—
64	C₂×C₄	C₂²×C₃×C₉	1	1	yes	characteristic
65	C₈	—	2	2	no	—
66	C₂×C₃	—	2	3	no	—
67	C₂×C₃	—	2	1	no	—
68	C₂×C₃	C₉×C₂²⋊C₄	1	3	yes	—
69	C₂×C₃	C₃²×C₂²⋊C₄	1	1	yes	characteristic
70	C₂²	C₂×C₃×C₄×C₉	1	1	yes	characteristic
71	C₄	—	2	2	no	—
72	C₄	C₃×D₄×C₉	1	2	yes	—
73	C₃	C₉×#101	1	3	yes	direct product factor
74	C₃	C₃²×#101	1	1	yes	characteristic
75	C₂	—	2	1	no	—
76	C₂	C₃×C₉×C₂²⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₉	C₂²⋊C₄
commutator	C₂²	C₂×C₃×C₄×C₉
Frattini, cosocle	C₂×C₃×C₄	C₂²×C₃²
socle	C₂×C₃²	C₃×C₂²⋊C₄
prime radical	C₂²×C₃²	C₂×C₃×C₄
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₉ ◁ C₂×C₃×C₄×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₉×#101	C₃	direct (N × H)
16. C₃×#101	C₉	direct (N × H)
38. #101	C₃×C₉	direct (N × H)
39. C₃×C₉	#101	direct (N × H)
61. C₉	C₃×#101	direct (N × H)
73. C₃	C₉×#101	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×Q₈×C₉	2
C₃×C₉×M₁₆	2
C₃²×#101	3
C₉×#101	3

Subgroups — C3×C9×#101 #11720605

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₉×#101 #11720605