Subgroups — C₂×C₃×C₄⋊C₈ #5296

Order 192.

138 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₈	C₂	1	2	yes	maximal
2	C₂×C₃×C₄²	C₂	1	1	yes	maximal, characteristic
3	C₃×C₄⋊C₈	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄⋊C₈	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂²×C₃×C₄	C₄	1	1	yes	characteristic
6	C₂²×C₃×C₄	C₄	1	1	yes	characteristic
7	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
8	C₂×C₃×C₈	—	2	4	no	—
9	C₂×C₃×C₈	C₂²	1	4	yes	—
10	C₃×C₄²	C₄	1	2	yes	—
11	C₃×C₄²	C₂²	1	2	yes	—
12	C₂²×C₈	C₂×C₃	1	2	yes	—
13	C₂×C₄²	C₂×C₃	1	1	yes	characteristic
14	C₄⋊C₈	C₂×C₃	1	4	yes	direct product factor
15	C₂³×C₃	C₂×C₄	1	1	yes	characteristic
16	C₂×C₃×C₄	—	2	2	no	—
17	C₂×C₃×C₄	C₈	1	4	yes	complemented
18	C₂×C₃×C₄	C₂×C₄	1	2	yes	—
19	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
20	C₂×C₃×C₄	C₂×C₄	1	2	yes	—
21	C₂×C₃×C₄	D₄	1	2	yes	—
22	C₂×C₃×C₄	Q₈	1	2	yes	—
23	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
24	C₃×C₈	—	2	4	no	—
25	C₂²×C₄	C₃×C₄	1	1	yes	characteristic
26	C₂²×C₄	C₃×C₄	1	1	yes	characteristic
27	C₂²×C₄	C₂²×C₃	1	1	yes	characteristic
28	C₂×C₈	—	2	4	no	—
29	C₂×C₈	C₂²×C₃	1	4	yes	—
30	C₄²	C₃×C₄	1	2	yes	—
31	C₄²	C₂²×C₃	1	2	yes	—
32	C₂²×C₃	C₄⋊C₄	1	2	yes	—
33	C₂²×C₃	C₂×C₈	1	2	yes	—
34	C₂²×C₃	M₁₆	1	2	yes	—
35	C₂²×C₃	C₂²×C₄	1	1	yes	characteristic
36	C₃×C₄	—	2	2	no	—
37	C₃×C₄	C₄⋊C₄	1	2	yes	—
38	C₃×C₄	C₂×C₈	1	4	yes	complemented
39	C₃×C₄	C₂×D₄	1	1	yes	characteristic
40	C₃×C₄	C₂×Q₈	1	1	yes	characteristic
41	C₂³	C₂×C₃×C₄	1	1	yes	characteristic
42	C₂×C₄	—	2	2	no	—
43	C₂×C₄	C₃×C₈	1	4	yes	complemented
44	C₂×C₄	C₂×C₃×C₄	1	2	yes	—
45	C₂×C₄	C₂×C₃×C₄	1	1	yes	characteristic
46	C₂×C₄	C₂×C₃×C₄	1	2	yes	—
47	C₂×C₄	C₃×D₄	1	2	yes	—
48	C₂×C₄	C₃×Q₈	1	2	yes	—
49	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
50	C₈	—	2	4	no	—
51	C₂×C₃	C₄⋊C₈	1	4	yes	direct product factor
52	C₂×C₃	C₂×C₄⋊C₄	1	1	yes	characteristic
53	C₂×C₃	C₂²×C₈	1	1	yes	characteristic
54	C₂×C₃	C₂×M₁₆	1	1	yes	characteristic
55	C₂²	C₃×C₄⋊C₄	1	2	yes	—
56	C₂²	C₂×C₃×C₈	1	2	yes	—
57	C₂²	C₃×M₁₆	1	2	yes	—
58	C₂²	C₂²×C₃×C₄	1	1	yes	characteristic
59	C₄	—	2	2	no	—
60	C₄	C₃×C₄⋊C₄	1	2	yes	—
61	C₄	C₂×C₃×C₈	1	4	yes	complemented
62	C₄	C₂×C₃×D₄	1	1	yes	characteristic
63	C₄	C₂×C₃×Q₈	1	1	yes	characteristic
64	C₃	C₂×C₄⋊C₈	1	1	yes	characteristic, direct product factor, Sylow
65	C₂	C₃×C₄⋊C₈	1	4	yes	direct product factor
66	C₂	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
67	C₂	C₂²×C₃×C₈	1	1	yes	characteristic
68	C₂	C₂×C₃×M₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃×C₄	C₂²
commutator	C₂	C₂²×C₃×C₈
Frattini, cosocle	C₂×C₄	C₂³×C₃
socle, prime radical	C₂³×C₃	C₂×C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃×C₄⋊C₈	C₂	direct (N × H)
4. C₂×C₄⋊C₈	C₃	direct (N × H)
14. C₄⋊C₈	C₂×C₃	direct (N × H)
17. C₂×C₃×C₄	C₈	semidirect
38. C₃×C₄	C₂×C₈	semidirect
43. C₂×C₄	C₃×C₈	semidirect
51. C₂×C₃	C₄⋊C₈	direct (N × H)
61. C₄	C₂×C₃×C₈	semidirect
64. C₃	C₂×C₄⋊C₈	direct (N × H)
65. C₂	C₃×C₄⋊C₈	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×C₈	2
C₂×C₃×C₄²	2
C₃×C₄⋊C₈	2
C₂×C₄⋊C₈	3

Subgroups — C2×C3×C4⋊C8 #5296

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₄⋊C₈ #5296