Subgroups — C₄×C₄⋊Dic₃ #4934

Order 192.

194 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄²	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊Dic₃	C₂	1	2	yes	maximal
3	C₂×C₄×Dic₃	C₂	1	2	yes	maximal
4	C₃⋊#95	C₂	1	2	yes	maximal
5	C₄×C₄⋊C₄	—	3	1	no	maximal, Sylow
6	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
7	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
8	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
9	C₂²×Dic₃	C₂²	1	4	yes	—
10	C₃×C₄²	C₄	1	4	yes	complemented
11	C₄⋊Dic₃	C₄	1	8	yes	direct product factor
12	C₄×Dic₃	—	2	4	no	—
13	C₂×C₄⋊C₄	—	3	2	no	—
14	C₂×C₄²	—	3	2	no	—
15	C₂×C₄²	D₃	1	1	yes	characteristic
16	#95	—	3	2	no	—
17	C₂³×C₃	C₂³	1	1	yes	characteristic
18	C₂×C₃×C₄	—	2	2	no	—
19	C₂×C₃×C₄	C₂×C₄	1	4	yes	—
20	C₂×C₃×C₄	C₂×C₄	1	2	yes	—
21	C₂×C₃×C₄	C₂×C₄	1	2	yes	—
22	C₂×C₃×C₄	C₂×C₄	1	2	yes	—
23	C₂×C₃×C₄	D₄	1	2	yes	—
24	C₂×C₃×C₄	Q₈	1	2	yes	—
25	C₂×Dic₃	—	2	4	no	—
26	C₂×Dic₃	—	2	4	no	—
27	C₂×Dic₃	C₂×C₄	1	8	yes	—
28	C₂²×C₄	—	3	4	no	—
29	C₂²×C₄	C₂×D₃	1	1	yes	characteristic
30	C₂²×C₄	C₂×D₃	1	1	yes	characteristic
31	C₂²×C₄	C₂×D₃	1	1	yes	characteristic
32	C₄⋊C₄	—	3	8	no	—
33	C₄²	—	6	4	no	—
34	C₄²	Dic₃	1	4	yes	complemented
35	C₂²×C₃	C₂²×C₄	1	2	yes	—
36	C₂²×C₃	C₂²×C₄	1	1	yes	characteristic
37	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
38	C₂²×C₃	C₂×Q₈	1	1	yes	characteristic
39	C₂²×C₃	#41	1	2	yes	—
40	C₃×C₄	—	2	2	no	—
41	C₃×C₄	C₄²	1	4	yes	complemented
42	C₃×C₄	C₄⋊C₄	1	4	yes	complemented
43	Dic₃	—	2	8	no	—
44	C₂³	C₂²×D₃	1	1	yes	characteristic
45	C₂×C₄	—	2	2	no	—
46	C₂×C₄	—	3	8	no	—
47	C₂×C₄	—	6	4	no	—
48	C₂×C₄	—	6	4	no	—
49	C₂×C₄	Dic₆	1	2	yes	—
50	C₂×C₄	C₄×D₃	1	4	yes	—
51	C₂×C₄	D₁₂	1	2	yes	—
52	C₂×C₄	C₂×Dic₃	1	2	yes	—
53	C₂×C₄	C₂×Dic₃	1	2	yes	—
54	C₂×C₄	C₂×Dic₃	1	2	yes	—
55	C₂×C₃	C₂×C₄²	1	1	yes	characteristic
56	C₂×C₃	C₂×C₄⋊C₄	1	1	yes	characteristic
57	C₂×C₃	#117	1	1	yes	characteristic
58	C₂×C₃	C₄×D₄	1	2	yes	—
59	C₂×C₃	C₄×Q₈	1	2	yes	—
60	C₂²	C₂×Dic₆	1	1	yes	characteristic
61	C₂²	C₂×C₄×D₃	1	2	yes	—
62	C₂²	C₂×D₁₂	1	1	yes	characteristic
63	C₂²	#235	1	2	yes	—
64	C₂²	C₂²×Dic₃	1	1	yes	characteristic
65	C₄	—	2	2	no	—
66	C₄	—	6	8	no	—
67	C₄	C₄×Dic₃	1	4	yes	complemented
68	C₄	C₄⋊Dic₃	1	4	yes	direct product factor
69	C₃	C₄×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
70	C₂	C₄×Dic₆	1	2	yes	—
71	C₂	C₄×D₁₂	1	2	yes	—
72	C₂	C₂×C₄×Dic₃	1	1	yes	characteristic
73	C₂	C₂×C₄⋊Dic₃	1	1	yes	characteristic
74	C₂	#926	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₃
commutator	C₂×C₃	C₂×C₄²
Frattini	C₂³	C₂²×D₃
Fitting	C₂×C₃×C₄²	C₂
socle, prime radical, cosocle	C₂³×C₃	C₂³
hypercenter	C₂×C₄²	D₃
hypocenter	C₃	C₄×C₄⋊C₄
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
10. C₃×C₄²	C₄	semidirect
11. C₄⋊Dic₃	C₄	direct (N × H)
34. C₄²	Dic₃	semidirect
41. C₃×C₄	C₄²	semidirect
42. C₃×C₄	C₄⋊C₄	semidirect
67. C₄	C₄×Dic₃	semidirect
68. C₄	C₄⋊Dic₃	direct (N × H)
69. C₃	C₄×C₄⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄²	2
C₂×C₄⋊Dic₃	2
C₂×C₄×Dic₃	2
C₃⋊#95	2
C₄×C₄⋊C₄	3

Subgroups — C4×C4⋊Dic3 #4934

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₄⋊Dic₃ #4934