Subgroups — C₂²×Dic₃⋊C₄ #5783

Order 192.

418 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₄	C₂	1	1	yes	maximal, characteristic
2	C₂³×Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₂³×Dic₃	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₃⋊C₄	C₂	1	12	yes	maximal, direct product factor
5	C₂²×C₄⋊C₄	—	3	1	no	maximal, Sylow
6	C₂⁴×C₃	C₂²	1	1	yes	characteristic
7	C₂²×C₃×C₄	—	2	4	no	—
8	C₂²×C₃×C₄	C₂²	1	6	yes	—
9	C₂²×Dic₃	—	2	4	no	—
10	C₂²×Dic₃	C₄	1	8	yes	complemented
11	C₂²×Dic₃	C₂²	1	6	yes	—
12	C₂²×Dic₃	C₂²	1	6	yes	—
13	Dic₃⋊C₄	C₂²	1	16	yes	direct product factor
14	C₂³×C₄	—	3	1	no	—
15	C₂³×C₄	—	3	1	no	—
16	C₂³×C₄	D₃	1	1	yes	characteristic
17	C₂×C₄⋊C₄	—	3	12	no	—
18	C₂³×C₃	C₂×C₄	1	4	yes	—
19	C₂³×C₃	D₄	1	4	yes	—
20	C₂³×C₃	Q₈	1	4	yes	—
21	C₂³×C₃	C₂³	1	3	yes	—
22	C₂×C₃×C₄	—	2	12	no	—
23	C₂×C₃×C₄	C₂³	1	4	yes	—
24	C₂×Dic₃	—	2	12	no	—
25	C₂×Dic₃	C₂×C₄	1	24	yes	complemented
26	C₂×Dic₃	C₂³	1	4	yes	—
27	C₂×Dic₃	C₂³	1	4	yes	—
28	C₂⁴	C₂×D₃	1	1	yes	characteristic
29	C₂²×C₄	—	2	4	no	—
30	C₂²×C₄	—	3	8	no	—
31	C₂²×C₄	—	3	6	no	—
32	C₂²×C₄	—	3	6	no	—
33	C₂²×C₄	—	6	4	no	—
34	C₂²×C₄	C₂×D₃	1	6	yes	—
35	C₄⋊C₄	—	3	16	no	—
36	C₂²×C₃	C₄⋊C₄	1	16	yes	complemented
37	C₂²×C₃	C₂²×C₄	1	6	yes	—
38	C₂²×C₃	C₂×D₄	1	6	yes	—
39	C₂²×C₃	C₂×Q₈	1	6	yes	—
40	C₂²×C₃	C₂⁴	1	1	yes	characteristic
41	C₃×C₄	—	2	4	no	—
42	Dic₃	—	2	4	no	—
43	Dic₃	C₂²×C₄	1	8	yes	complemented
44	C₂³	Dic₆	1	4	yes	—
45	C₂³	C₄×D₃	1	4	yes	—
46	C₂³	#67	1	4	yes	—
47	C₂³	C₂²×D₃	1	3	yes	—
48	C₂×C₄	—	2	12	no	—
49	C₂×C₄	—	3	24	no	—
50	C₂×C₄	—	3	4	no	—
51	C₂×C₄	—	3	4	no	—
52	C₂×C₄	—	6	12	no	—
53	C₂×C₄	C₂²×D₃	1	4	yes	—
54	C₂×C₃	C₂×C₄⋊C₄	1	12	yes	complemented
55	C₂×C₃	C₂³×C₄	1	1	yes	characteristic
56	C₂×C₃	C₂²×D₄	1	1	yes	characteristic
57	C₂×C₃	C₂²×Q₈	1	1	yes	characteristic
58	C₂²	Dic₃⋊C₄	1	16	yes	direct product factor
59	C₂²	C₂×Dic₆	1	6	yes	—
60	C₂²	C₂×C₄×D₃	1	6	yes	—
61	C₂²	C₂×#67	1	6	yes	—
62	C₂²	C₂³×D₃	1	1	yes	characteristic
63	C₄	—	2	4	no	—
64	C₄	—	3	8	no	—
65	C₄	—	6	4	no	—
66	C₃	C₂²×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
67	C₂	C₂×Dic₃⋊C₄	1	12	yes	direct product factor
68	C₂	C₂²×Dic₆	1	1	yes	characteristic
69	C₂	C₂²×C₄×D₃	1	1	yes	characteristic
70	C₂	C₂²×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×D₃
commutator	C₂×C₃	C₂³×C₄
Frattini	C₂²	C₂³×D₃
Fitting	C₂³×C₃×C₄	C₂
socle, prime radical	C₂⁴×C₃	C₂²
cosocle	C₂²×C₃	C₂⁴
hypercenter	C₂³×C₄	D₃
hypocenter	C₃	C₂²×C₄⋊C₄
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
4. C₂×Dic₃⋊C₄	C₂	direct (N × H)
10. C₂²×Dic₃	C₄	semidirect
13. Dic₃⋊C₄	C₂²	direct (N × H)
25. C₂×Dic₃	C₂×C₄	semidirect
36. C₂²×C₃	C₄⋊C₄	semidirect
43. Dic₃	C₂²×C₄	semidirect
54. C₂×C₃	C₂×C₄⋊C₄	semidirect
58. C₂²	Dic₃⋊C₄	direct (N × H)
66. C₃	C₂²×C₄⋊C₄	semidirect
67. C₂	C₂×Dic₃⋊C₄	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×C₄	2
C₂³×Dic₃	2
C₂×Dic₃⋊C₄	2
C₂²×C₄⋊C₄	3

Subgroups — C22×Dic3⋊C4 #5783

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×Dic₃⋊C₄ #5783