Subgroups — C₈×C₄²⋊C₃ #68020

Order 384.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₄²⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₄²×C₈	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
3	C₈×A₄	—	4	1	no	maximal
4	C₂×C₄²⋊C₃	C₄	1	1	yes	characteristic
5	C₂×C₄×C₈	—	3	1	no	—
6	C₂×C₄×C₈	—	3	1	no	—
7	C₄³	C₂×C₃	1	1	yes	characteristic
8	C₄×A₄	—	4	1	no	—
9	C₄²⋊C₃	C₈	1	1	yes	characteristic, direct product factor
10	C₂²×C₈	—	3	1	no	—
11	C₂²×C₈	A₄	1	1	yes	characteristic
12	C₂×C₄²	—	3	1	no	—
13	C₂×C₄²	—	3	1	no	—
14	C₂×C₄²	C₃×C₄	1	1	yes	characteristic
15	C₄×C₈	—	3	4	no	—
16	C₄×C₈	—	3	2	no	—
17	C₄×C₈	—	3	2	no	—
18	C₂×A₄	—	4	1	no	—
19	C₃×C₈	—	16	1	no	—
20	C₂²×C₄	—	3	1	no	—
21	C₂²×C₄	—	3	1	no	—
22	C₂²×C₄	C₂×A₄	1	1	yes	characteristic
23	C₂×C₈	—	3	2	no	—
24	C₂×C₈	—	3	4	no	—
25	C₂×C₈	—	3	1	no	—
26	C₂×C₈	—	3	1	no	—
27	C₄²	—	3	1	no	—
28	C₄²	—	3	2	no	—
29	C₄²	—	3	2	no	—
30	C₄²	—	3	4	no	—
31	C₄²	C₃×C₈	1	1	yes	characteristic, complemented
32	A₄	—	4	1	no	—
33	C₃×C₄	—	16	1	no	—
34	C₂³	C₄×A₄	1	1	yes	characteristic
35	C₂×C₄	—	3	4	no	—
36	C₂×C₄	—	3	2	no	—
37	C₂×C₄	—	3	2	no	—
38	C₂×C₄	—	3	2	no	—
39	C₂×C₄	—	3	1	no	—
40	C₂×C₄	—	3	1	no	—
41	C₂×C₄	—	3	1	no	—
42	C₂×C₄	—	3	1	no	—
43	C₈	—	3	4	no	—
44	C₈	—	3	1	no	—
45	C₈	C₄²⋊C₃	1	1	yes	characteristic, direct product factor
46	C₂×C₃	—	16	1	no	—
47	C₂²	—	3	1	no	—
48	C₂²	—	3	1	no	—
49	C₂²	C₈×A₄	1	1	yes	characteristic
50	C₄	—	3	4	no	—
51	C₄	—	3	2	no	—
52	C₄	—	3	2	no	—
53	C₄	—	3	1	no	—
54	C₄	C₂×C₄²⋊C₃	1	1	yes	characteristic
55	C₃	—	16	1	no	Sylow
56	C₂	—	3	1	no	—
57	C₂	—	3	1	no	—
58	C₂	C₄×C₄²⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₈	C₄²⋊C₃
commutator, hypocenter	C₄²	C₃×C₈
Frattini	C₂²×C₄	C₂×A₄
Fitting	C₄²×C₈	C₃
socle	C₂³	C₄×A₄
prime radical	C₂×C₄²⋊C₃	C₄
cosocle	C₄³	C₂×C₃
LCS	G ▷ C₄²
UCS	C₁ ◁ C₈

Complements

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

N	H ≅ G/N	type
2. C₄²×C₈	C₃	semidirect
9. C₄²⋊C₃	C₈	direct (N × H)
31. C₄²	C₃×C₈	semidirect
45. C₈	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×C₈	3
C₈×A₄	4

Subgroups — C8×C42⋊C3 #68020

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×C₄²⋊C₃ #68020