Subgroups — C₂³×C₄²⋊C₃ #85568

Order 384.

580 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄²⋊C₃	C₂	1	7	yes	maximal, direct product factor
2	C₂³×C₄²	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
3	C₂³×A₄	—	4	1	no	maximal
4	C₂×C₄²⋊C₃	C₂²	1	7	yes	direct product factor
5	C₂⁴×C₄	—	3	1	no	—
6	C₂²×C₄²	—	3	7	no	—
7	C₂²×C₄²	C₂×C₃	1	7	yes	complemented
8	C₂²×A₄	—	4	7	no	—
9	C₄²⋊C₃	C₂³	1	1	yes	characteristic, direct product factor
10	C₂⁵	A₄	1	1	yes	characteristic
11	C₂³×C₄	—	3	14	no	—
12	C₂³×C₄	—	3	2	no	—
13	C₂³×C₄	—	3	7	no	—
14	C₂³×C₄	—	3	7	no	—
15	C₂×C₄²	—	3	21	no	—
16	C₂×C₄²	—	3	14	no	—
17	C₂×C₄²	C₂²×C₃	1	7	yes	complemented
18	C₂³×C₃	—	16	1	no	—
19	C₂×A₄	—	4	7	no	—
20	C₂⁴	—	3	7	no	—
21	C₂⁴	—	3	1	no	—
22	C₂⁴	C₂×A₄	1	7	yes	—
23	C₂²×C₄	—	3	42	no	—
24	C₂²×C₄	—	3	42	no	—
25	C₂²×C₄	—	3	14	no	—
26	C₂²×C₄	—	3	14	no	—
27	C₂²×C₄	—	3	7	no	—
28	C₂²×C₄	—	3	21	no	—
29	C₄²	—	3	7	no	—
30	C₄²	—	3	14	no	—
31	C₄²	C₂³×C₃	1	1	yes	characteristic, complemented
32	C₂²×C₃	—	16	7	no	—
33	A₄	—	4	1	no	—
34	C₂³	—	3	21	no	—
35	C₂³	—	3	14	no	—
36	C₂³	—	3	7	no	—
37	C₂³	—	3	7	no	—
38	C₂³	C₄²⋊C₃	1	1	yes	characteristic, direct product factor
39	C₂³	C₂²×A₄	1	7	yes	—
40	C₂×C₄	—	3	14	no	—
41	C₂×C₄	—	3	42	no	—
42	C₂×C₄	—	3	14	no	—
43	C₂×C₄	—	3	42	no	—
44	C₂×C₄	—	3	1	no	—
45	C₂×C₄	—	3	7	no	—
46	C₂×C₃	—	16	7	no	—
47	C₂²	—	3	7	no	—
48	C₂²	—	3	14	no	—
49	C₂²	—	3	7	no	—
50	C₂²	—	3	21	no	—
51	C₂²	C₂×C₄²⋊C₃	1	7	yes	direct product factor
52	C₂²	C₂³×A₄	1	1	yes	characteristic
53	C₄	—	3	2	no	—
54	C₄	—	3	14	no	—
55	C₃	—	16	1	no	Sylow
56	C₂	—	3	1	no	—
57	C₂	—	3	7	no	—
58	C₂	C₂²×C₄²⋊C₃	1	7	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂³	C₄²⋊C₃
commutator, cosocle, hypocenter	C₄²	C₂³×C₃
Frattini	C₂²	C₂³×A₄
Fitting	C₂³×C₄²	C₃
socle	C₂⁵	A₄
LCS	G ▷ C₄²
UCS	C₁ ◁ C₂³

Complements

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

N	H ≅ G/N	type
1. C₂²×C₄²⋊C₃	C₂	direct (N × H)
2. C₂³×C₄²	C₃	semidirect
4. C₂×C₄²⋊C₃	C₂²	direct (N × H)
7. C₂²×C₄²	C₂×C₃	semidirect
9. C₄²⋊C₃	C₂³	direct (N × H)
17. C₂×C₄²	C₂²×C₃	semidirect
31. C₄²	C₂³×C₃	semidirect
38. C₂³	C₄²⋊C₃	direct (N × H)
51. C₂²	C₂×C₄²⋊C₃	direct (N × H)
58. C₂	C₂²×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
C₂²×C₄²⋊C₃	2
C₂³×C₄²	3
C₂³×A₄	4

Subgroups — C23×C42⋊C3 #85568

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₄²⋊C₃ #85568