Subgroups — Dic₃×C₂²⋊A₄ #10596632

Order 576.

538 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₂²⋊A₄	C₂	1	1	yes	maximal, characteristic
2	C₂⁴×Dic₃	C₃	1	1	yes	maximal, characteristic, complemented
3	C₄×C₂²⋊A₄	—	3	1	no	maximal
4	C₃×C₂²⋊A₄	C₄	1	1	yes	characteristic, complemented
5	Dic₃×A₄	—	4	5	no	maximal
6	C₂⁵×C₃	C₂×C₃	1	1	yes	characteristic
7	C₂×C₂²⋊A₄	—	2	1	no	—
8	C₂×C₂²⋊A₄	D₃	1	1	yes	characteristic
9	C₂³×Dic₃	—	3	5	no	—
10	C₂³×Dic₃	—	3	5	no	—
11	C₂×C₃×A₄	—	4	5	no	—
12	C₂⁴×C₄	—	3	1	no	Sylow
13	C₂⁴×C₃	—	3	5	no	—
14	C₂⁴×C₃	—	3	5	no	—
15	C₂⁴×C₃	C₃×C₄	1	1	yes	characteristic, complemented
16	C₂²⋊A₄	—	2	1	no	—
17	C₂²⋊A₄	Dic₃	1	1	yes	characteristic, direct product factor
18	C₂²×Dic₃	—	3	30	no	—
19	C₂²×Dic₃	—	3	10	no	—
20	C₂²×Dic₃	—	3	5	no	—
21	C₂²×Dic₃	A₄	1	5	yes	complemented
22	C₄×A₄	—	12	5	no	—
23	C₃×A₄	—	4	5	no	—
24	C₃×Dic₃	—	16	1	no	—
25	C₂⁵	C₃×D₃	1	1	yes	characteristic
26	C₂³×C₄	—	9	5	no	—
27	C₂³×C₄	—	9	5	no	—
28	C₂³×C₃	—	3	10	no	—
29	C₂³×C₃	—	3	30	no	—
30	C₂³×C₃	—	3	5	no	—
31	C₂³×C₃	—	3	5	no	—
32	C₂³×C₃	C₂×A₄	1	5	yes	—
33	C₂×A₄	—	4	5	no	—
34	C₂×A₄	—	8	5	no	—
35	C₂×Dic₃	—	3	30	no	—
36	C₂×Dic₃	—	3	5	no	—
37	C₂×Dic₃	—	3	5	no	—
38	C₂×C₃²	—	16	1	no	—
39	C₂⁴	—	3	5	no	—
40	C₂⁴	—	3	5	no	—
41	C₂⁴	C₃×Dic₃	1	1	yes	characteristic, complemented
42	C₂²×C₄	—	3	5	no	—
43	C₂²×C₄	—	9	10	no	—
44	C₂²×C₄	—	9	30	no	—
45	C₂²×C₄	—	9	5	no	—
46	C₂²×C₃	—	3	5	no	—
47	C₂²×C₃	—	3	30	no	—
48	C₂²×C₃	—	3	10	no	—
49	C₂²×C₃	—	3	5	no	—
50	C₂²×C₃	C₄×A₄	1	5	yes	complemented
51	A₄	—	4	5	no	—
52	A₄	—	8	5	no	—
53	C₃×C₄	—	48	1	no	—
54	Dic₃	—	3	5	no	—
55	Dic₃	C₂²⋊A₄	1	1	yes	characteristic, direct product factor
56	C₃²	—	16	1	no	Sylow
57	C₂³	—	3	10	no	—
58	C₂³	—	3	30	no	—
59	C₂³	—	3	5	no	—
60	C₂³	—	3	5	no	—
61	C₂³	D₃×A₄	1	5	yes	—
62	C₂×C₄	—	9	5	no	—
63	C₂×C₄	—	9	30	no	—
64	C₂×C₄	—	9	5	no	—
65	C₂×C₃	—	3	5	no	—
66	C₂×C₃	—	3	5	no	—
67	C₂×C₃	—	16	1	no	—
68	C₂×C₃	—	32	1	no	—
69	C₂×C₃	C₂×C₂²⋊A₄	1	1	yes	characteristic
70	C₂²	—	3	5	no	—
71	C₂²	—	3	10	no	—
72	C₂²	—	3	30	no	—
73	C₂²	—	3	5	no	—
74	C₂²	Dic₃×A₄	1	5	yes	complemented
75	C₄	—	3	1	no	—
76	C₄	—	9	5	no	—
77	C₃	—	16	1	no	—
78	C₃	—	32	1	no	—
79	C₃	C₄×C₂²⋊A₄	1	1	yes	characteristic, complemented
80	C₂	—	3	5	no	—
81	C₂	—	3	5	no	—
82	C₂	D₃×C₂²⋊A₄	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃×C₂²⋊A₄
commutator, hypocenter	C₂⁴×C₃	C₃×C₄
Fitting, socle, cosocle	C₂⁵×C₃	C₂×C₃
prime radical	C₂×C₃×C₂²⋊A₄	C₂
LCS	G ▷ C₂⁴×C₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
2. C₂⁴×Dic₃	C₃	semidirect
4. C₃×C₂²⋊A₄	C₄	semidirect
15. C₂⁴×C₃	C₃×C₄	semidirect
17. C₂²⋊A₄	Dic₃	direct (N × H)
21. C₂²×Dic₃	A₄	semidirect
41. C₂⁴	C₃×Dic₃	semidirect
50. C₂²×C₃	C₄×A₄	semidirect
55. Dic₃	C₂²⋊A₄	direct (N × H)
74. C₂²	Dic₃×A₄	semidirect
79. C₃	C₄×C₂²⋊A₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₂²⋊A₄	2
C₂⁴×Dic₃	3
C₄×C₂²⋊A₄	3
Dic₃×A₄	4

Subgroups — Dic3×C22⋊A4 #10596632

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₃×C₂²⋊A₄ #10596632