Subgroups — Q₈×C₄²⋊C₃ #73163

Order 384.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₄²⋊C₃	C₂	1	3	yes	maximal
2	C₄²×Q₈	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
3	Q₈×A₄	—	4	1	no	maximal
4	C₂×C₄²⋊C₃	C₂²	1	1	yes	characteristic
5	C₂×C₄×Q₈	—	3	1	no	—
6	C₄×C₄⋊C₄	—	3	3	no	—
7	C₄³	C₂×C₃	1	3	yes	—
8	C₄×A₄	—	4	3	no	—
9	C₄²⋊C₃	Q₈	1	1	yes	characteristic, direct product factor
10	C₂²×Q₈	A₄	1	1	yes	characteristic
11	C₄×Q₈	—	3	6	no	—
12	C₄×Q₈	—	3	2	no	—
13	C₂×C₄⋊C₄	—	3	3	no	—
14	C₂×C₄²	—	3	3	no	—
15	C₂×C₄²	—	3	3	no	—
16	C₂×C₄²	C₂²×C₃	1	1	yes	characteristic
17	#95	—	3	2	no	—
18	C₂×A₄	—	4	1	no	—
19	C₃×Q₈	—	16	1	no	—
20	C₂×Q₈	—	3	3	no	—
21	C₂×Q₈	—	3	1	no	—
22	C₂²×C₄	—	3	1	no	—
23	C₂²×C₄	—	3	3	no	—
24	C₂²×C₄	C₂×A₄	1	3	yes	—
25	C₄⋊C₄	—	3	6	no	—
26	C₄⋊C₄	—	3	6	no	—
27	C₄²	—	3	1	no	—
28	C₄²	—	3	6	no	—
29	C₄²	—	3	6	no	—
30	C₄²	—	6	6	no	—
31	C₄²	C₃×Q₈	1	1	yes	characteristic, complemented
32	A₄	—	4	1	no	—
33	C₃×C₄	—	16	3	no	—
34	C₂³	C₂²×A₄	1	1	yes	characteristic
35	Q₈	—	3	2	no	—
36	Q₈	—	3	3	no	—
37	Q₈	C₄²⋊C₃	1	1	yes	characteristic, direct product factor
38	C₂×C₄	—	3	2	no	—
39	C₂×C₄	—	3	2	no	—
40	C₂×C₄	—	3	1	no	—
41	C₂×C₄	—	3	1	no	—
42	C₂×C₄	—	3	3	no	—
43	C₂×C₄	—	3	3	no	—
44	C₂×C₄	—	3	6	no	—
45	C₂×C₄	—	6	6	no	—
46	C₂×C₃	—	16	1	no	—
47	C₂²	—	3	1	no	—
48	C₂²	—	3	1	no	—
49	C₂²	Q₈×A₄	1	1	yes	characteristic
50	C₄	—	3	2	no	—
51	C₄	—	3	2	no	—
52	C₄	—	3	3	no	—
53	C₄	—	6	6	no	—
54	C₄	C₂×C₄²⋊C₃	1	3	yes	—
55	C₃	—	16	1	no	Sylow
56	C₂	—	3	1	no	—
57	C₂	—	3	1	no	—
58	C₂	C₂²×C₄²⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²×C₄²⋊C₃
commutator, cosocle	C₂×C₄²	C₂²×C₃
Frattini, socle	C₂³	C₂²×A₄
Fitting	C₄²×Q₈	C₃
prime radical	C₂×C₄²⋊C₃	C₂²
hypercenter	Q₈	C₄²⋊C₃
hypocenter	C₄²	C₃×Q₈
LCS	G ▷ C₂×C₄² ▷ C₄²
UCS	C₁ ◁ C₂ ◁ Q₈

Complements

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

N	H ≅ G/N	type
2. C₄²×Q₈	C₃	semidirect
9. C₄²⋊C₃	Q₈	direct (N × H)
31. C₄²	C₃×Q₈	semidirect
37. Q₈	C₄²⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₄²⋊C₃	2
C₄²×Q₈	3
Q₈×A₄	4

Subgroups — Q8×C42⋊C3 #73163

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×C₄²⋊C₃ #73163