Subgroups — C₃×C₄×D₈ #5311

Order 192.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₈	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×D₄	C₂	1	2	yes	maximal, complemented
3	C₃×#107	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#102	C₂	1	2	yes	maximal, complemented
5	C₃×C₄×C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄×D₈	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂×C₃×D₄	C₂²	1	2	yes	—
8	C₂²×C₃×C₄	—	2	2	no	—
9	C₃×D₈	C₄	1	4	yes	direct product factor
10	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
12	C₃×C₄⋊C₄	C₂²	1	2	yes	—
13	C₃×C₂²⋊C₄	—	2	2	no	—
14	C₃×C₄²	C₂²	1	1	yes	characteristic
15	C₂×D₈	C₂×C₃	1	1	yes	characteristic
16	C₄×D₄	C₂×C₃	1	2	yes	complemented
17	#107	C₂×C₃	1	1	yes	characteristic, complemented
18	#102	C₂×C₃	1	2	yes	complemented
19	C₄×C₈	C₂×C₃	1	1	yes	characteristic, complemented
20	C₂³×C₃	—	2	2	no	—
21	C₃×D₄	—	2	2	no	—
22	C₃×D₄	C₂×C₄	1	4	yes	complemented
23	C₂×C₃×C₄	—	2	2	no	—
24	C₂×C₃×C₄	—	4	4	no	—
25	C₂×C₃×C₄	D₄	1	1	yes	characteristic
26	C₂×C₃×C₄	D₄	1	1	yes	characteristic
27	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
28	C₃×C₈	—	2	1	no	—
29	C₃×C₈	C₂×C₄	1	2	yes	complemented
30	C₂×D₄	C₂²×C₃	1	2	yes	—
31	C₂²×C₄	—	2	2	no	—
32	D₈	C₃×C₄	1	4	yes	direct product factor
33	C₂×C₈	C₂²×C₃	1	1	yes	characteristic
34	C₂×C₈	C₂²×C₃	1	1	yes	characteristic
35	C₄⋊C₄	C₂²×C₃	1	2	yes	—
36	C₂²⋊C₄	—	2	2	no	—
37	C₄²	C₂²×C₃	1	1	yes	characteristic
38	C₂²×C₃	—	2	4	no	—
39	C₂²×C₃	—	4	2	no	—
40	C₂²×C₃	—	4	2	no	—
41	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
42	C₃×C₄	—	2	1	no	—
43	C₃×C₄	—	4	2	no	—
44	C₃×C₄	D₈	1	2	yes	direct product factor
45	C₃×C₄	C₂²×C₄	1	1	yes	characteristic
46	C₃×C₄	#41	1	1	yes	characteristic
47	C₂³	—	2	2	no	—
48	D₄	—	2	2	no	—
49	D₄	C₂×C₃×C₄	1	4	yes	complemented
50	C₂×C₄	—	2	2	no	—
51	C₂×C₄	—	4	4	no	—
52	C₂×C₄	C₃×D₄	1	1	yes	characteristic
53	C₂×C₄	C₃×D₄	1	1	yes	characteristic
54	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
55	C₈	—	2	1	no	—
56	C₈	C₂×C₃×C₄	1	2	yes	complemented
57	C₂×C₃	—	4	4	no	—
58	C₂×C₃	C₄×D₄	1	1	yes	characteristic
59	C₂×C₃	C₂×D₈	1	1	yes	characteristic
60	C₂×C₃	#135	1	1	yes	characteristic
61	C₂²	—	2	4	no	—
62	C₂²	—	4	2	no	—
63	C₂²	—	4	2	no	—
64	C₂²	C₂×C₃×D₄	1	1	yes	characteristic
65	C₄	—	2	1	no	—
66	C₄	—	4	2	no	—
67	C₄	C₃×D₈	1	2	yes	direct product factor
68	C₄	C₂²×C₃×C₄	1	1	yes	characteristic
69	C₄	C₃×#41	1	1	yes	characteristic
70	C₃	C₄×D₈	1	1	yes	characteristic, direct product factor, Sylow
71	C₂	—	4	4	no	—
72	C₂	C₃×C₄×D₄	1	1	yes	characteristic
73	C₂	C₂×C₃×D₈	1	1	yes	characteristic
74	C₂	C₃×#135	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	D₄
commutator	C₄	C₂²×C₃×C₄
Frattini, cosocle	C₂×C₄	C₂³×C₃
socle	C₂²×C₃	C₂×D₄
prime radical	C₂×C₃×D₈	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×C₄² ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×D₄	C₂	semidirect
3. C₃×#107	C₂	semidirect
4. C₃×#102	C₂	semidirect
5. C₃×C₄×C₈	C₂	semidirect
6. C₄×D₈	C₃	direct (N × H)
9. C₃×D₈	C₄	direct (N × H)
16. C₄×D₄	C₂×C₃	semidirect
17. #107	C₂×C₃	semidirect
18. #102	C₂×C₃	semidirect
19. C₄×C₈	C₂×C₃	semidirect
22. C₃×D₄	C₂×C₄	semidirect
29. C₃×C₈	C₂×C₄	semidirect
32. D₈	C₃×C₄	direct (N × H)
44. C₃×C₄	D₈	direct (N × H)
49. D₄	C₂×C₃×C₄	semidirect
56. C₈	C₂×C₃×C₄	semidirect
67. C₄	C₃×D₈	direct (N × H)
70. C₃	C₄×D₈	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×D₈	2
C₃×C₄×D₄	2
C₃×#107	2
C₃×#102	2
C₃×C₄×C₈	2
C₄×D₈	3

Subgroups — C3×C4×D8 #5311

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×D₈ #5311