Subgroups — D₃×C₂²⋊(C₂²⋊C₉) #11724062

Order 864.

598 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂²⋊(C₂²⋊C₉)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁴×C₃×D₃	C₃	1	1	yes	maximal, characteristic
3	C₂×C₂²⋊(C₂²⋊C₉)	—	3	1	no	maximal
4	D₃×C₂²⋊C₉	—	4	5	no	maximal
5	C₂⁴×C₃²	C₂×C₃	1	1	yes	characteristic
6	C₂³×C₃×D₃	—	3	5	no	—
7	C₂³×C₃×D₃	—	3	5	no	—
8	C₂²⋊(C₂²⋊C₉)	—	2	1	no	—
9	C₂²⋊(C₂²⋊C₉)	D₃	1	1	yes	characteristic, direct product factor
10	C₃×C₂²⋊C₉	—	4	5	no	—
11	C₂⁵×C₃	—	3	1	no	—
12	C₂⁴×D₃	C₉	1	1	yes	characteristic, complemented
13	C₂³×C₃²	—	3	5	no	—
14	C₂²×C₃×D₃	—	3	30	no	—
15	C₂²×C₃×D₃	—	3	10	no	—
16	C₂²×C₃×D₃	—	3	5	no	—
17	C₂²×C₃×D₃	A₄	1	5	yes	—
18	C₂×C₂²⋊C₉	—	12	5	no	—
19	D₃×C₉	—	16	1	no	—
20	C₂⁴×C₃	—	2	1	no	—
21	C₂⁴×C₃	—	9	5	no	—
22	C₂⁴×C₃	—	9	5	no	—
23	C₂⁴×C₃	C₂×C₉	1	1	yes	characteristic, complemented
24	C₂⁴×C₃	C₃×D₃	1	1	yes	characteristic
25	C₂³×D₃	—	3	5	no	—
26	C₂³×D₃	—	3	5	no	—
27	C₂²×C₃²	—	3	10	no	—
28	C₂²×C₃²	C₂×A₄	1	5	yes	—
29	C₂×C₃×D₃	—	3	30	no	—
30	C₂×C₃×D₃	—	3	5	no	—
31	C₂×C₃×D₃	—	3	5	no	—
32	C₂²⋊C₉	—	4	5	no	—
33	C₂²⋊C₉	—	8	5	no	—
34	C₂⁵	—	3	1	no	Sylow
35	C₃×C₉	—	16	1	no	Sylow
36	C₂³×C₃	—	3	5	no	—
37	C₂³×C₃	—	3	5	no	—
38	C₂³×C₃	—	3	5	no	—
39	C₂³×C₃	—	6	5	no	—
40	C₂³×C₃	—	9	10	no	—
41	C₂³×C₃	—	9	30	no	—
42	C₂³×C₃	—	9	5	no	—
43	C₂²×D₃	—	3	30	no	—
44	C₂²×D₃	—	3	10	no	—
45	C₂²×D₃	—	3	5	no	—
46	C₂²×D₃	C₂²⋊C₉	1	5	yes	complemented
47	C₂×C₃²	—	3	5	no	—
48	C₃×D₃	—	3	5	no	—
49	C₃×D₃	C₂²⋊A₄	1	1	yes	characteristic
50	C₂×C₉	—	48	1	no	—
51	C₂⁴	—	9	5	no	—
52	C₂⁴	—	9	5	no	—
53	C₂⁴	D₃×C₉	1	1	yes	characteristic, complemented
54	C₂²×C₃	—	2	5	no	—
55	C₂²×C₃	—	3	10	no	—
56	C₂²×C₃	—	3	10	no	—
57	C₂²×C₃	—	6	10	no	—
58	C₂²×C₃	—	9	5	no	—
59	C₂²×C₃	—	9	5	no	—
60	C₂²×C₃	—	9	30	no	—
61	C₂²×C₃	C₂×C₂²⋊C₉	1	5	yes	complemented
62	C₂²×C₃	D₃×A₄	1	5	yes	—
63	C₂×D₃	—	3	30	no	—
64	C₂×D₃	—	3	5	no	—
65	C₂×D₃	—	3	5	no	—
66	C₃²	C₂×C₂²⋊A₄	1	1	yes	characteristic
67	C₉	—	16	1	no	—
68	C₉	—	32	1	no	—
69	C₂³	—	3	5	no	—
70	C₂³	—	3	5	no	—
71	C₂³	—	9	10	no	—
72	C₂³	—	9	30	no	—
73	C₂³	—	9	5	no	—
74	C₂×C₃	—	3	5	no	—
75	C₂×C₃	—	3	1	no	—
76	C₂×C₃	—	3	5	no	—
77	C₂×C₃	—	6	5	no	—
78	C₂×C₃	—	9	5	no	—
79	D₃	—	3	5	no	—
80	D₃	C₂²⋊(C₂²⋊C₉)	1	1	yes	characteristic, direct product factor
81	C₂²	—	3	10	no	—
82	C₂²	—	9	5	no	—
83	C₂²	—	9	5	no	—
84	C₂²	—	9	30	no	—
85	C₂²	D₃×C₂²⋊C₉	1	5	yes	complemented
86	C₃	—	2	1	no	—
87	C₃	C₂×C₂²⋊(C₂²⋊C₉)	1	1	yes	characteristic, complemented
88	C₃	D₃×C₂²⋊A₄	1	1	yes	characteristic
89	C₂	—	3	5	no	—
90	C₂	—	3	1	no	—
91	C₂	—	9	5	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₃	D₃×C₂²⋊A₄
commutator, hypocenter	C₂⁴×C₃	C₂×C₉
Fitting, socle, cosocle	C₂⁴×C₃²	C₂×C₃
prime radical	C₂⁴×C₃×D₃	C₃
LCS	G ▷ C₂⁴×C₃
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₂²⋊(C₂²⋊C₉)	C₂	semidirect
9. C₂²⋊(C₂²⋊C₉)	D₃	direct (N × H)
12. C₂⁴×D₃	C₉	semidirect
23. C₂⁴×C₃	C₂×C₉	semidirect
46. C₂²×D₃	C₂²⋊C₉	semidirect
53. C₂⁴	D₃×C₉	semidirect
61. C₂²×C₃	C₂×C₂²⋊C₉	semidirect
80. D₃	C₂²⋊(C₂²⋊C₉)	direct (N × H)
85. C₂²	D₃×C₂²⋊C₉	semidirect
87. C₃	C₂×C₂²⋊(C₂²⋊C₉)	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₂²⋊(C₂²⋊C₉)	2
C₂⁴×C₃×D₃	3
C₂×C₂²⋊(C₂²⋊C₉)	3
D₃×C₂²⋊C₉	4

Subgroups — D3×C22⋊(C22⋊C9) #11724062

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₂²⋊(C₂²⋊C₉) #11724062