Subgroups — C₂×C₄×Dic₆ #5467

Order 192.

298 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₄²	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₃⋊C₄	C₂	1	2	yes	maximal
5	C₂×C₄×Dic₃	C₂	1	2	yes	maximal
6	C₄×Dic₆	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₄×Q₈	—	3	1	no	maximal, Sylow
8	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
9	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
11	C₂²×Dic₃	C₂²	1	2	yes	—
12	C₂²×Dic₃	C₂²	1	2	yes	—
13	C₂×Dic₆	C₄	1	8	yes	direct product factor
14	C₂×Dic₆	C₂²	1	4	yes	—
15	C₃×C₄²	C₂²	1	4	yes	—
16	C₄⋊Dic₃	C₂²	1	4	yes	—
17	Dic₃⋊C₄	C₂²	1	8	yes	—
18	C₄×Dic₃	C₂²	1	8	yes	—
19	C₂²×Q₈	—	3	1	no	—
20	C₄×Q₈	—	3	8	no	—
21	C₂×C₄⋊C₄	—	3	2	no	—
22	C₂×C₄⋊C₄	—	3	1	no	—
23	C₂×C₄²	—	3	2	no	—
24	C₂×C₄²	D₃	1	1	yes	characteristic
25	C₂³×C₃	C₂³	1	1	yes	characteristic
26	C₂×C₃×C₄	—	2	2	no	—
27	C₂×C₃×C₄	C₂×C₄	1	4	yes	—
28	C₂×C₃×C₄	Q₈	1	4	yes	complemented
29	C₂×C₃×C₄	C₂³	1	2	yes	—
30	C₂×C₃×C₄	C₂³	1	2	yes	—
31	C₂×C₃×C₄	C₂³	1	2	yes	—
32	C₂×Dic₃	—	2	4	no	—
33	C₂×Dic₃	C₂×C₄	1	8	yes	—
34	C₂×Dic₃	C₂³	1	4	yes	—
35	C₂×Dic₃	C₂³	1	4	yes	—
36	Dic₆	C₂×C₄	1	16	yes	direct product factor
37	C₂×Q₈	—	3	8	no	—
38	C₂×Q₈	—	3	4	no	—
39	C₂²×C₄	—	3	2	no	—
40	C₂²×C₄	—	3	2	no	—
41	C₂²×C₄	C₂×D₃	1	1	yes	characteristic
42	C₂²×C₄	C₂×D₃	1	1	yes	characteristic
43	C₂²×C₄	C₂×D₃	1	1	yes	characteristic
44	C₄⋊C₄	—	3	8	no	—
45	C₄⋊C₄	—	3	4	no	—
46	C₄²	—	3	8	no	—
47	C₄²	C₂×D₃	1	4	yes	—
48	C₂²×C₃	C₂²×C₄	1	2	yes	—
49	C₂²×C₃	C₂×Q₈	1	2	yes	—
50	C₂²×C₃	#41	1	2	yes	—
51	C₂²×C₃	C₂⁴	1	1	yes	characteristic
52	C₃×C₄	—	2	2	no	—
53	C₃×C₄	C₂²×C₄	1	4	yes	—
54	C₃×C₄	C₂×Q₈	1	4	yes	complemented
55	Dic₃	—	2	4	no	—
56	Dic₃	C₂²×C₄	1	8	yes	—
57	C₂³	C₂²×D₃	1	1	yes	characteristic
58	Q₈	—	3	16	no	—
59	C₂×C₄	—	2	2	no	—
60	C₂×C₄	—	3	8	no	—
61	C₂×C₄	—	3	4	no	—
62	C₂×C₄	—	3	4	no	—
63	C₂×C₄	—	6	4	no	—
64	C₂×C₄	Dic₆	1	4	yes	direct product factor
65	C₂×C₄	C₄×D₃	1	4	yes	—
66	C₂×C₄	C₂²×D₃	1	2	yes	—
67	C₂×C₄	C₂²×D₃	1	2	yes	—
68	C₂×C₄	C₂²×D₃	1	2	yes	—
69	C₂×C₃	C₄×Q₈	1	4	yes	complemented
70	C₂×C₃	C₂³×C₄	1	1	yes	characteristic
71	C₂×C₃	C₂²×Q₈	1	1	yes	characteristic
72	C₂×C₃	C₂×#41	1	1	yes	characteristic
73	C₂²	C₂×Dic₆	1	2	yes	—
74	C₂²	C₂×C₄×D₃	1	2	yes	—
75	C₂²	#235	1	2	yes	—
76	C₂²	C₂³×D₃	1	1	yes	characteristic
77	C₄	—	2	2	no	—
78	C₄	—	3	8	no	—
79	C₄	—	6	4	no	—
80	C₄	C₂×Dic₆	1	4	yes	direct product factor
81	C₄	C₂×C₄×D₃	1	4	yes	—
82	C₃	C₂×C₄×Q₈	1	1	yes	characteristic, complemented, Sylow
83	C₂	C₄×Dic₆	1	4	yes	direct product factor
84	C₂	C₂²×Dic₆	1	1	yes	characteristic
85	C₂	C₂²×C₄×D₃	1	1	yes	characteristic
86	C₂	C₂×#235	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₃
commutator	C₂×C₃	C₂³×C₄
Frattini	C₂²	C₂³×D₃
Fitting	C₂×C₃×C₄²	C₂
socle, prime radical	C₂³×C₃	C₂³
cosocle	C₂²×C₃	C₂⁴
hypercenter	C₂×C₄²	D₃
hypocenter	C₃	C₂×C₄×Q₈
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
6. C₄×Dic₆	C₂	direct (N × H)
13. C₂×Dic₆	C₄	direct (N × H)
28. C₂×C₃×C₄	Q₈	semidirect
36. Dic₆	C₂×C₄	direct (N × H)
54. C₃×C₄	C₂×Q₈	semidirect
64. C₂×C₄	Dic₆	direct (N × H)
69. C₂×C₃	C₄×Q₈	semidirect
80. C₄	C₂×Dic₆	direct (N × H)
82. C₃	C₂×C₄×Q₈	semidirect
83. C₂	C₄×Dic₆	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×Dic₆	2
C₂×C₃×C₄²	2
C₂×C₄⋊Dic₃	2
C₂×Dic₃⋊C₄	2
C₂×C₄×Dic₃	2
C₄×Dic₆	2
C₂×C₄×Q₈	3

Subgroups — C2×C4×Dic6 #5467

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×Dic₆ #5467