Subgroups — D₄⋊(C₃⋊C₈) #4534

Order 192.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×D₄	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄⋊C₈	—	3	1	no	maximal, Sylow
5	C₂×C₃×D₄	C₄	1	1	yes	characteristic
6	C₂²×C₃×C₄	—	2	1	no	—
7	C₃×C₄⋊C₄	C₄	1	1	yes	characteristic
8	C₃×C₂²⋊C₄	—	2	1	no	—
9	C₃×C₄²	C₂²	1	1	yes	characteristic
10	C₂×C₃⋊C₈	—	2	1	no	—
11	C₂×C₃⋊C₈	—	2	1	no	—
12	C₄×D₄	D₃	1	1	yes	characteristic
13	C₄⋊C₈	—	3	1	no	—
14	C₄×C₈	—	3	1	no	—
15	C₂³×C₃	—	2	1	no	—
16	C₃×D₄	—	2	1	no	—
17	C₃×D₄	C₈	1	2	yes	complemented
18	C₂×C₃×C₄	—	2	1	no	—
19	C₂×C₃×C₄	—	4	1	no	—
20	C₂×C₃×C₄	—	4	1	no	—
21	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
22	C₂×C₃×C₄	D₄	1	1	yes	characteristic
23	C₂×C₃×C₄	D₄	1	1	yes	characteristic
24	C₃⋊C₈	—	2	2	no	—
25	C₃⋊C₈	—	4	1	no	—
26	C₂×D₄	Dic₃	1	1	yes	characteristic
27	C₂²×C₄	—	2	1	no	—
28	C₂×C₈	—	6	1	no	—
29	C₂×C₈	—	6	1	no	—
30	C₄⋊C₄	Dic₃	1	1	yes	characteristic
31	C₂²⋊C₄	—	2	1	no	—
32	C₄²	C₂×D₃	1	1	yes	characteristic
33	C₂²×C₃	—	2	2	no	—
34	C₂²×C₃	—	4	1	no	—
35	C₂²×C₃	—	4	1	no	—
36	C₂²×C₃	C₂²⋊C₄	1	1	yes	characteristic
37	C₃×C₄	—	2	1	no	—
38	C₃×C₄	—	4	1	no	—
39	C₃×C₄	C₂×C₈	1	1	yes	characteristic
40	C₃×C₄	M₁₆	1	1	yes	characteristic
41	C₃×C₄	D₈	1	1	yes	characteristic
42	C₃×C₄	SD₁₆	1	1	yes	characteristic
43	C₂³	—	2	1	no	—
44	D₄	—	2	1	no	—
45	D₄	C₃⋊C₈	1	2	yes	complemented
46	C₂×C₄	—	2	1	no	—
47	C₂×C₄	—	4	1	no	—
48	C₂×C₄	—	4	1	no	—
49	C₂×C₄	C₂×Dic₃	1	1	yes	characteristic
50	C₂×C₄	#67	1	1	yes	characteristic
51	C₂×C₄	#67	1	1	yes	characteristic
52	C₈	—	6	2	no	—
53	C₈	—	12	1	no	—
54	C₂×C₃	—	4	2	no	—
55	C₂×C₃	C₂²⋊C₈	1	1	yes	characteristic
56	C₂×C₃	#102	1	1	yes	characteristic
57	C₂×C₃	#104	1	1	yes	characteristic
58	C₂²	—	2	2	no	—
59	C₂²	—	4	1	no	—
60	C₂²	—	4	1	no	—
61	C₂²	#217	1	1	yes	characteristic
62	C₄	—	2	1	no	—
63	C₄	—	4	1	no	—
64	C₄	C₂×C₃⋊C₈	1	1	yes	characteristic
65	C₄	#208	1	1	yes	characteristic
66	C₄	#213	1	1	yes	characteristic
67	C₄	#214	1	1	yes	characteristic
68	C₃	D₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
69	C₂	—	4	2	no	—
70	C₂	#830	1	1	yes	characteristic
71	C₂	#832	1	1	yes	characteristic
72	C₂	#837	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#67
commutator	C₃×C₄	C₂×C₈
Frattini	C₄²	C₂×D₃
Fitting	C₃×C₄×D₄	C₂
socle	C₂²×C₃	C₂²⋊C₄
prime radical	C₂×C₃×D₄	C₄
cosocle	C₃×C₄²	C₂²
hypercenter	C₄×D₄	D₃
hypocenter	C₃	D₄⋊C₈
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×D₄

Complements

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

N	H ≅ G/N	type
2. C₄⋊(C₃⋊C₈)	C₂	semidirect
3. C₄×C₃⋊C₈	C₂	semidirect
17. C₃×D₄	C₈	semidirect
45. D₄	C₃⋊C₈	semidirect
68. C₃	D₄⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄×D₄	2
C₄⋊(C₃⋊C₈)	2
C₄×C₃⋊C₈	2
D₄⋊C₈	3

Subgroups — D4⋊(C3⋊C8) #4534

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄⋊(C₃⋊C₈) #4534