Subgroups — C₂×Dic₃₀₄ #14565940

Order 2432.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₅₂	C₂	1	2	yes	maximal
2	Dic₃₀₄	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₁₉×C₃₂	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₇₆	—	2	2	no	—
5	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
6	Dic₁₅₂	—	2	2	no	—
7	Dic₁₅₂	C₂²	1	4	yes	—
8	C₁₉×C₃₂	C₂²	1	2	yes	—
9	C₂×Dic₃₈	—	4	2	no	—
10	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
11	Dic₇₆	—	2	4	no	—
12	Dic₇₆	—	4	2	no	—
13	C₁₆×C₁₉	D₄	1	1	yes	characteristic
14	C₁₆×C₁₉	C₂³	1	1	yes	characteristic
15	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
16	C₂×Dic₁₉	—	8	2	no	—
17	Dic₃₈	—	4	4	no	—
18	Dic₃₈	—	8	2	no	—
19	C₈×C₁₉	D₈	1	1	yes	characteristic
20	C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
21	C₂×Q₆₄	—	19	1	no	maximal, Sylow
22	C₂²×C₁₉	D₁₆	1	1	yes	characteristic
23	C₄×C₁₉	D₁₆	1	1	yes	characteristic
24	C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
25	Dic₁₉	—	8	4	no	—
26	C₂×Q₃₂	—	19	2	no	—
27	Q₆₄	—	19	4	no	—
28	C₂×C₃₂	D₁₉	1	1	yes	characteristic
29	C₂×C₁₉	Q₆₄	1	2	yes	complemented
30	C₂×C₁₉	C₂×D₁₆	1	1	yes	characteristic
31	C₂×Q₁₆	—	38	2	no	—
32	Q₃₂	—	19	4	no	—
33	Q₃₂	—	38	2	no	—
34	C₂×C₁₆	C₂×D₁₉	1	1	yes	characteristic
35	C₃₂	C₂×D₁₉	1	2	yes	—
36	C₁₉	C₂×Q₆₄	1	1	yes	characteristic, complemented, Sylow
37	C₂×Q₈	—	76	2	no	—
38	Q₁₆	—	38	4	no	—
39	Q₁₆	—	76	2	no	—
40	C₂×C₈	D₇₆	1	1	yes	characteristic
41	C₁₆	D₇₆	1	1	yes	characteristic
42	C₁₆	C₂²×D₁₉	1	1	yes	characteristic
43	Q₈	—	76	4	no	—
44	Q₈	—	152	2	no	—
45	C₂×C₄	—	152	2	no	—
46	C₂×C₄	D₁₅₂	1	1	yes	characteristic
47	C₈	D₁₅₂	1	1	yes	characteristic
48	C₈	C₂×D₇₆	1	1	yes	characteristic
49	C₂²	D₃₀₄	1	1	yes	characteristic
50	C₄	—	152	4	no	—
51	C₄	D₃₀₄	1	1	yes	characteristic
52	C₄	C₂×D₁₅₂	1	1	yes	characteristic
53	C₂	Dic₃₀₄	1	2	yes	direct product factor
54	C₂	C₂×D₃₀₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₃₀₄
commutator, cosocle	C₁₆×C₁₉	C₂³
Frattini	C₁₆	C₂²×D₁₉
Fitting	C₂×C₁₉×C₃₂	C₂
socle, prime radical	C₂²×C₁₉	D₁₆
hypercenter	C₂×C₃₂	D₁₉
hypocenter	C₁₉	C₂×Q₆₄
LCS	G ▷ C₁₆×C₁₉ ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
2. Dic₃₀₄	C₂	direct (N × H)
29. C₂×C₁₉	Q₆₄	semidirect
36. C₁₉	C₂×Q₆₄	semidirect
53. C₂	Dic₃₀₄	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×Dic₁₅₂	2
Dic₃₀₄	2
C₂×C₁₉×C₃₂	2
C₂×Q₆₄	19

Subgroups — C2×Dic304 #14565940

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Dic₃₀₄ #14565940