Subgroups — C₄×D₂₄ #4692

Order 192.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₄	C₂	1	1	yes	maximal, characteristic
2	C₄×D₁₂	C₂	1	2	yes	maximal, complemented
3	C₃×C₄×C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#821	C₂	1	2	yes	maximal, complemented
5	#818	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄×D₈	—	3	1	no	maximal, Sylow
7	C₂×D₁₂	C₂²	1	2	yes	—
8	C₂×C₄×D₃	—	2	2	no	—
9	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
11	C₃×C₄²	C₂²	1	1	yes	characteristic
12	(C₂×D₃)⋊C₄	—	2	2	no	—
13	C₄⋊Dic₃	C₂²	1	2	yes	—
14	D₂₄	C₄	1	4	yes	direct product factor
15	C₂×D₈	—	3	1	no	—
16	C₄×D₄	—	3	2	no	—
17	#107	—	3	1	no	—
18	#102	—	3	2	no	—
19	C₄×C₈	D₃	1	1	yes	characteristic, complemented
20	C₂²×D₃	—	2	2	no	—
21	C₂×C₃×C₄	D₄	1	1	yes	characteristic
22	C₂×C₃×C₄	D₄	1	1	yes	characteristic
23	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
24	C₂×Dic₃	—	2	2	no	—
25	D₁₂	—	2	2	no	—
26	D₁₂	C₂×C₄	1	4	yes	complemented
27	C₄×D₃	—	4	4	no	—
28	C₃×C₈	—	2	1	no	—
29	C₃×C₈	C₂×C₄	1	2	yes	complemented
30	C₂×D₄	—	3	2	no	—
31	C₂²×C₄	—	6	2	no	—
32	D₈	—	3	4	no	—
33	C₂×C₈	C₂×D₃	1	1	yes	characteristic
34	C₂×C₈	C₂×D₃	1	1	yes	characteristic
35	C₄⋊C₄	—	3	2	no	—
36	C₂²⋊C₄	—	6	2	no	—
37	C₄²	C₂×D₃	1	1	yes	characteristic
38	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
39	C₂×D₃	—	2	4	no	—
40	C₂×D₃	—	4	2	no	—
41	C₂×D₃	—	4	2	no	—
42	C₃×C₄	—	2	1	no	—
43	C₃×C₄	D₈	1	2	yes	complemented
44	C₃×C₄	C₂²×C₄	1	1	yes	characteristic
45	C₃×C₄	#41	1	1	yes	characteristic
46	Dic₃	—	4	2	no	—
47	C₂³	—	6	2	no	—
48	D₄	—	3	4	no	—
49	D₄	—	6	2	no	—
50	C₂×C₄	—	6	2	no	—
51	C₂×C₄	—	12	4	no	—
52	C₂×C₄	D₁₂	1	1	yes	characteristic
53	C₂×C₄	D₁₂	1	1	yes	characteristic
54	C₂×C₄	C₂²×D₃	1	1	yes	characteristic
55	C₈	—	2	1	no	—
56	C₈	C₄×D₃	1	2	yes	complemented
57	C₂×C₃	C₄×D₄	1	1	yes	characteristic
58	C₂×C₃	C₂×D₈	1	1	yes	characteristic
59	C₂×C₃	#135	1	1	yes	characteristic
60	D₃	—	4	4	no	—
61	C₂²	—	6	4	no	—
62	C₂²	—	12	2	no	—
63	C₂²	—	12	2	no	—
64	C₂²	C₂×D₁₂	1	1	yes	characteristic
65	C₄	—	2	1	no	—
66	C₄	—	12	2	no	—
67	C₄	D₂₄	1	2	yes	direct product factor
68	C₄	C₂×C₄×D₃	1	1	yes	characteristic
69	C₄	#235	1	1	yes	characteristic
70	C₃	C₄×D₈	1	1	yes	characteristic, complemented, Sylow
71	C₂	—	12	4	no	—
72	C₂	C₄×D₁₂	1	1	yes	characteristic
73	C₂	C₂×D₂₄	1	1	yes	characteristic
74	C₂	#904	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₁₂
commutator	C₃×C₄	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₃
Fitting	C₃×C₄×C₈	C₂
socle	C₂²×C₃	C₂×D₄
prime radical	C₂×D₂₄	C₂
cosocle	C₂×C₃×C₄	C₂³
hypercenter	C₄×C₈	D₃
hypocenter	C₃	C₄×D₈
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
2. C₄×D₁₂	C₂	semidirect
3. C₃×C₄×C₈	C₂	semidirect
4. #821	C₂	semidirect
5. #818	C₂	semidirect
14. D₂₄	C₄	direct (N × H)
19. C₄×C₈	D₃	semidirect
26. D₁₂	C₂×C₄	semidirect
29. C₃×C₈	C₂×C₄	semidirect
43. C₃×C₄	D₈	semidirect
56. C₈	C₄×D₃	semidirect
67. C₄	D₂₄	direct (N × H)
70. C₃	C₄×D₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₂₄	2
C₄×D₁₂	2
C₃×C₄×C₈	2
#821	2
#818	2
C₄×D₈	3

Subgroups — C4×D24 #4692

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×D₂₄ #4692