Subgroups — C₂×C₃×C₄⋊Q₈ #5861

Order 192.

290 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×Q₈	C₂	1	2	yes	maximal
2	C₃×C₄⋊Q₈	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₃×C₄⋊C₄	C₂	1	4	yes	maximal
4	C₂×C₃×C₄²	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊Q₈	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₂×C₃×Q₈	—	2	8	no	—
7	C₂×C₃×Q₈	C₂²	1	8	yes	—
8	C₂²×C₃×C₄	C₂²	1	4	yes	—
9	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₄	C₂²	1	2	yes	—
11	C₃×C₄⋊C₄	C₂²	1	16	yes	—
12	C₃×C₄²	C₂²	1	4	yes	—
13	C₂²×Q₈	C₂×C₃	1	2	yes	—
14	C₄⋊Q₈	C₂×C₃	1	8	yes	direct product factor
15	C₂×C₄⋊C₄	C₂×C₃	1	4	yes	—
16	C₂×C₄²	C₂×C₃	1	1	yes	characteristic
17	C₂³×C₃	C₂³	1	1	yes	characteristic
18	C₃×Q₈	—	2	16	no	—
19	C₂×C₃×C₄	—	2	8	no	—
20	C₂×C₃×C₄	D₄	1	4	yes	—
21	C₂×C₃×C₄	Q₈	1	8	yes	complemented
22	C₂×C₃×C₄	C₂³	1	8	yes	—
23	C₂×C₃×C₄	C₂³	1	2	yes	—
24	C₂×C₃×C₄	C₂³	1	4	yes	—
25	C₂×Q₈	—	2	8	no	—
26	C₂×Q₈	C₂²×C₃	1	8	yes	—
27	C₂²×C₄	C₂²×C₃	1	4	yes	—
28	C₂²×C₄	C₂²×C₃	1	1	yes	characteristic
29	C₂²×C₄	C₂²×C₃	1	2	yes	—
30	C₄⋊C₄	C₂²×C₃	1	16	yes	—
31	C₄²	C₂²×C₃	1	4	yes	—
32	C₂²×C₃	C₂×D₄	1	2	yes	—
33	C₂²×C₃	C₂×Q₈	1	4	yes	—
34	C₂²×C₃	C₂⁴	1	1	yes	characteristic
35	C₃×C₄	—	2	8	no	—
36	C₃×C₄	C₂×D₄	1	4	yes	—
37	C₃×C₄	C₂×Q₈	1	8	yes	complemented
38	C₂³	C₂³×C₃	1	1	yes	characteristic
39	Q₈	—	2	16	no	—
40	C₂×C₄	—	2	8	no	—
41	C₂×C₄	C₃×D₄	1	4	yes	—
42	C₂×C₄	C₃×Q₈	1	8	yes	complemented
43	C₂×C₄	C₂³×C₃	1	8	yes	—
44	C₂×C₄	C₂³×C₃	1	2	yes	—
45	C₂×C₄	C₂³×C₃	1	4	yes	—
46	C₂×C₃	C₄⋊Q₈	1	4	yes	direct product factor
47	C₂×C₃	C₂²×D₄	1	1	yes	characteristic
48	C₂×C₃	C₂²×Q₈	1	2	yes	—
49	C₂²	C₂×C₃×D₄	1	2	yes	—
50	C₂²	C₂×C₃×Q₈	1	4	yes	—
51	C₂²	C₂⁴×C₃	1	1	yes	characteristic
52	C₄	—	2	8	no	—
53	C₄	C₂×C₃×D₄	1	4	yes	—
54	C₄	C₂×C₃×Q₈	1	8	yes	complemented
55	C₃	C₂×C₄⋊Q₈	1	1	yes	characteristic, direct product factor, Sylow
56	C₂	C₃×C₄⋊Q₈	1	4	yes	direct product factor
57	C₂	C₂²×C₃×D₄	1	1	yes	characteristic
58	C₂	C₂²×C₃×Q₈	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₃	C₂³
commutator, Frattini, cosocle	C₂²	C₂⁴×C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₄⋊Q₈	C₂	direct (N × H)
5. C₂×C₄⋊Q₈	C₃	direct (N × H)
14. C₄⋊Q₈	C₂×C₃	direct (N × H)
21. C₂×C₃×C₄	Q₈	semidirect
37. C₃×C₄	C₂×Q₈	semidirect
42. C₂×C₄	C₃×Q₈	semidirect
46. C₂×C₃	C₄⋊Q₈	direct (N × H)
54. C₄	C₂×C₃×Q₈	semidirect
55. C₃	C₂×C₄⋊Q₈	direct (N × H)
56. C₂	C₃×C₄⋊Q₈	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×C₃×Q₈	2
C₃×C₄⋊Q₈	2
C₂×C₃×C₄⋊C₄	2
C₂×C₃×C₄²	2
C₂×C₄⋊Q₈	3

Subgroups — C2×C3×C4⋊Q8 #5861

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₄⋊Q₈ #5861