Subgroups — C₂×Q₈×A₄ #5940

Order 192.

205 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×A₄	C₂	1	4	yes	maximal, direct product factor
2	C₂×C₄×A₄	C₂	1	3	yes	maximal
3	C₂³×Q₈	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
4	C₂²×A₄	C₂²	1	1	yes	characteristic
5	C₂×C₃×Q₈	—	4	1	no	maximal
6	C₄×A₄	C₂²	1	6	yes	—
7	C₂²×Q₈	—	3	3	no	—
8	C₂²×Q₈	—	3	4	no	—
9	C₂²×Q₈	—	3	1	no	—
10	C₂²×Q₈	C₂×C₃	1	4	yes	complemented
11	C₂³×C₄	C₂×C₃	1	3	yes	—
12	C₂×A₄	Q₈	1	2	yes	direct product factor
13	C₂×A₄	C₂³	1	1	yes	characteristic
14	C₃×Q₈	—	4	4	no	—
15	C₂×C₃×C₄	—	4	3	no	—
16	C₂⁴	C₂²×C₃	1	1	yes	characteristic
17	C₂×Q₈	—	3	12	no	—
18	C₂×Q₈	—	3	12	no	—
19	C₂×Q₈	—	3	2	no	—
20	C₂×Q₈	—	3	4	no	—
21	C₂×Q₈	—	3	4	no	—
22	C₂×Q₈	—	3	3	no	—
23	C₂×Q₈	A₄	1	1	yes	characteristic, direct product factor
24	C₂²×C₄	—	3	3	no	—
25	C₂²×C₄	—	3	3	no	—
26	C₂²×C₄	—	3	6	no	—
27	C₂²×C₄	C₂²×C₃	1	6	yes	—
28	C₂²×C₃	—	4	1	no	—
29	A₄	C₂×Q₈	1	1	yes	characteristic, direct product factor
30	C₃×C₄	—	4	6	no	—
31	C₂³	—	3	1	no	—
32	C₂³	—	3	2	no	—
33	C₂³	—	3	1	no	—
34	C₂³	C₃×Q₈	1	2	yes	complemented
35	C₂³	C₂³×C₃	1	1	yes	characteristic
36	Q₈	—	3	8	no	—
37	Q₈	—	3	12	no	—
38	Q₈	C₂×A₄	1	4	yes	direct product factor
39	C₂×C₄	—	3	6	no	—
40	C₂×C₄	—	3	3	no	—
41	C₂×C₄	—	3	6	no	—
42	C₂×C₄	—	3	6	no	—
43	C₂×C₄	—	3	6	no	—
44	C₂×C₄	C₂×A₄	1	3	yes	—
45	C₂×C₃	—	4	2	no	—
46	C₂×C₃	—	4	1	no	—
47	C₂²	—	3	2	no	—
48	C₂²	—	3	1	no	—
49	C₂²	—	3	2	no	—
50	C₂²	—	3	2	no	—
51	C₂²	—	3	2	no	—
52	C₂²	—	3	1	no	—
53	C₂²	—	3	1	no	—
54	C₂²	C₂×C₃×Q₈	1	1	yes	characteristic, complemented
55	C₂²	C₂²×A₄	1	1	yes	characteristic
56	C₄	—	3	6	no	—
57	C₄	C₂²×A₄	1	6	yes	—
58	C₃	—	4	1	no	Sylow
59	C₂	—	3	2	no	—
60	C₂	—	3	1	no	—
61	C₂	—	3	1	no	—
62	C₂	Q₈×A₄	1	2	yes	direct product factor
63	C₂	C₂³×A₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×A₄
commutator, cosocle	C₂³	C₂³×C₃
Frattini	C₂	C₂³×A₄
Fitting	C₂³×Q₈	C₃
socle	C₂⁴	C₂²×C₃
prime radical	C₂²×A₄	C₂²
hypercenter	C₂×Q₈	A₄
hypocenter	C₂²	C₂×C₃×Q₈
LCS	G ▷ C₂³ ▷ C₂²
UCS	C₁ ◁ C₂² ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
1. Q₈×A₄	C₂	direct (N × H)
3. C₂³×Q₈	C₃	semidirect
10. C₂²×Q₈	C₂×C₃	semidirect
12. C₂×A₄	Q₈	direct (N × H)
23. C₂×Q₈	A₄	direct (N × H)
29. A₄	C₂×Q₈	direct (N × H)
34. C₂³	C₃×Q₈	semidirect
38. Q₈	C₂×A₄	direct (N × H)
54. C₂²	C₂×C₃×Q₈	semidirect
62. C₂	Q₈×A₄	direct (N × H)

Maximal subgroups

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

subgroup	index
Q₈×A₄	2
C₂×C₄×A₄	2
C₂³×Q₈	3
C₂×C₃×Q₈	4

Subgroups — C2×Q8×A4 #5940

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Q₈×A₄ #5940