Subgroups — C₃×C₈×D₄ #5308

Order 192.

134 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, complemented
2	C₃×C₄×D₄	C₂	1	1	yes	maximal, characteristic
3	C₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₂²⋊C₈	C₂	1	2	yes	maximal, complemented
5	C₃×C₄×C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈×D₄	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂×C₃×D₄	C₄	1	1	yes	characteristic
8	C₂²×C₃×C₄	C₂²	1	2	yes	—
9	C₂×C₃×C₈	—	2	4	no	—
10	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₈	C₂²	1	2	yes	—
12	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
13	C₃×C₄⋊C₄	C₄	1	1	yes	characteristic
14	C₃×C₂²⋊C₄	C₄	1	2	yes	—
15	C₃×C₄²	C₂²	1	1	yes	characteristic
16	C₂²×C₈	C₂×C₃	1	2	yes	complemented
17	C₄×D₄	C₂×C₃	1	1	yes	characteristic
18	C₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
19	C₂²⋊C₈	C₂×C₃	1	2	yes	complemented
20	C₄×C₈	C₂×C₃	1	1	yes	characteristic, complemented
21	C₂³×C₃	C₂×C₄	1	2	yes	—
22	C₃×D₄	C₈	1	4	yes	direct product factor
23	C₂×C₃×C₄	—	2	2	no	—
24	C₂×C₃×C₄	—	2	2	no	—
25	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
26	C₂×C₃×C₄	C₂×C₄	1	2	yes	—
27	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
28	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
29	C₃×C₈	—	2	2	no	—
30	C₃×C₈	—	2	1	no	—
31	C₃×C₈	D₄	1	2	yes	direct product factor
32	C₂×D₄	C₃×C₄	1	1	yes	characteristic
33	C₂²×C₄	C₂²×C₃	1	2	yes	—
34	C₂×C₈	—	2	4	no	—
35	C₂×C₈	C₂²×C₃	1	1	yes	characteristic
36	C₂×C₈	C₂²×C₃	1	2	yes	—
37	C₂×C₈	C₂²×C₃	1	1	yes	characteristic
38	C₄⋊C₄	C₃×C₄	1	1	yes	characteristic
39	C₂²⋊C₄	C₃×C₄	1	2	yes	—
40	C₄²	C₂²×C₃	1	1	yes	characteristic
41	C₂²×C₃	—	2	2	no	—
42	C₂²×C₃	—	2	2	no	—
43	C₂²×C₃	C₂×C₈	1	4	yes	complemented
44	C₂²×C₃	C₂²×C₄	1	1	yes	characteristic
45	C₃×C₄	—	2	2	no	—
46	C₃×C₄	—	2	1	no	—
47	C₃×C₄	C₂×C₈	1	2	yes	complemented
48	C₃×C₄	C₂×D₄	1	1	yes	characteristic
49	C₃×C₄	#41	1	1	yes	characteristic
50	C₂³	C₂×C₃×C₄	1	2	yes	—
51	D₄	C₃×C₈	1	4	yes	direct product factor
52	C₂×C₄	—	2	2	no	—
53	C₂×C₄	—	2	2	no	—
54	C₂×C₄	C₂×C₃×C₄	1	1	yes	characteristic
55	C₂×C₄	C₂×C₃×C₄	1	2	yes	—
56	C₂×C₄	C₂×C₃×C₄	1	1	yes	characteristic
57	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
58	C₈	—	2	2	no	—
59	C₈	—	2	1	no	—
60	C₈	C₃×D₄	1	2	yes	direct product factor
61	C₂×C₃	—	2	4	no	—
62	C₂×C₃	C₄×D₄	1	1	yes	characteristic
63	C₂×C₃	C₂²×C₈	1	1	yes	characteristic
64	C₂×C₃	#131	1	1	yes	characteristic
65	C₂²	—	2	2	no	—
66	C₂²	—	2	2	no	—
67	C₂²	C₂×C₃×C₈	1	4	yes	complemented
68	C₂²	C₂²×C₃×C₄	1	1	yes	characteristic
69	C₄	—	2	2	no	—
70	C₄	—	2	1	no	—
71	C₄	C₂×C₃×C₈	1	2	yes	complemented
72	C₄	C₂×C₃×D₄	1	1	yes	characteristic
73	C₄	C₃×#41	1	1	yes	characteristic
74	C₃	C₈×D₄	1	1	yes	characteristic, direct product factor, Sylow
75	C₂	—	2	4	no	—
76	C₂	C₃×C₄×D₄	1	1	yes	characteristic
77	C₂	C₂²×C₃×C₈	1	1	yes	characteristic
78	C₂	C₃×#131	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₈	C₂²
commutator	C₂	C₂²×C₃×C₈
Frattini, cosocle	C₂×C₄	C₂³×C₃
socle	C₂²×C₃	C₂²×C₄
prime radical	C₂×C₃×D₄	C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₈	C₂	semidirect
3. C₃×C₄⋊C₈	C₂	semidirect
4. C₃×C₂²⋊C₈	C₂	semidirect
5. C₃×C₄×C₈	C₂	semidirect
6. C₈×D₄	C₃	direct (N × H)
16. C₂²×C₈	C₂×C₃	semidirect
18. C₄⋊C₈	C₂×C₃	semidirect
19. C₂²⋊C₈	C₂×C₃	semidirect
20. C₄×C₈	C₂×C₃	semidirect
22. C₃×D₄	C₈	direct (N × H)
31. C₃×C₈	D₄	direct (N × H)
43. C₂²×C₃	C₂×C₈	semidirect
47. C₃×C₄	C₂×C₈	semidirect
51. D₄	C₃×C₈	direct (N × H)
60. C₈	C₃×D₄	direct (N × H)
67. C₂²	C₂×C₃×C₈	semidirect
71. C₄	C₂×C₃×C₈	semidirect
74. C₃	C₈×D₄	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
C₃×C₄×D₄	2
C₃×C₄⋊C₈	2
C₃×C₂²⋊C₈	2
C₃×C₄×C₈	2
C₈×D₄	3

Subgroups — C3×C8×D4 #5308

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₈×D₄ #5308