Subgroups — C₂×D₃₅₆₈ #28384001

Order 14272.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₇₈₄	C₂	1	2	yes	maximal, complemented
2	D₃₅₆₈	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₁₆×C₂₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₈₉₂	—	2	2	no	—
5	D₁₇₈₄	—	2	2	no	—
6	D₁₇₈₄	C₂²	1	4	yes	complemented
7	C₂×C₈×C₂₂₃	C₂²	1	1	yes	characteristic
8	C₁₆×C₂₂₃	C₂²	1	2	yes	complemented
9	C₂²×D₂₂₃	—	4	2	no	—
10	D₈₉₂	—	2	4	no	—
11	D₈₉₂	—	4	2	no	—
12	C₂×C₄×C₂₂₃	D₄	1	1	yes	characteristic
13	C₈×C₂₂₃	D₄	1	1	yes	characteristic
14	C₈×C₂₂₃	C₂³	1	1	yes	characteristic
15	C₂²×C₂₂₃	D₈	1	1	yes	characteristic
16	C₂×D₂₂₃	—	4	4	no	—
17	C₂×D₂₂₃	—	8	4	no	—
18	C₄×C₂₂₃	D₈	1	1	yes	characteristic
19	C₄×C₂₂₃	C₂×D₄	1	1	yes	characteristic
20	C₂×C₂₂₃	D₁₆	1	2	yes	complemented
21	C₂×C₂₂₃	C₂×D₈	1	1	yes	characteristic
22	D₂₂₃	—	8	4	no	—
23	C₂₂₃	C₂×D₁₆	1	1	yes	characteristic, complemented, Sylow
24	C₂×D₁₆	—	223	1	no	maximal, Sylow
25	C₂×D₈	—	223	2	no	—
26	D₁₆	—	223	4	no	—
27	C₂×C₁₆	D₂₂₃	1	1	yes	characteristic, complemented
28	C₂×D₄	—	446	2	no	—
29	D₈	—	446	2	no	—
30	D₈	—	223	4	no	—
31	C₂×C₈	C₂×D₂₂₃	1	1	yes	characteristic
32	C₁₆	C₂×D₂₂₃	1	2	yes	complemented
33	C₂³	—	892	2	no	—
34	D₄	—	892	2	no	—
35	D₄	—	446	4	no	—
36	C₂×C₄	D₈₉₂	1	1	yes	characteristic
37	C₈	D₈₉₂	1	1	yes	characteristic
38	C₈	C₂²×D₂₂₃	1	1	yes	characteristic
39	C₂²	—	892	4	no	—
40	C₂²	—	1784	4	no	—
41	C₂²	D₁₇₈₄	1	1	yes	characteristic
42	C₄	D₁₇₈₄	1	1	yes	characteristic
43	C₄	C₂×D₈₉₂	1	1	yes	characteristic
44	C₂	—	1784	4	no	—
45	C₂	D₃₅₆₈	1	2	yes	direct product factor
46	C₂	C₂×D₁₇₈₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₁₇₈₄
commutator, cosocle	C₈×C₂₂₃	C₂³
Frattini	C₈	C₂²×D₂₂₃
Fitting	C₂×C₁₆×C₂₂₃	C₂
socle	C₂²×C₂₂₃	D₈
hypercenter	C₂×C₁₆	D₂₂₃
hypocenter	C₂₂₃	C₂×D₁₆
LCS	G ▷ C₈×C₂₂₃ ▷ C₄×C₂₂₃ ▷ C₂×C₂₂₃ ▷ C₂₂₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×D₁₇₈₄	C₂	semidirect
2. D₃₅₆₈	C₂	direct (N × H)
3. C₂×C₁₆×C₂₂₃	C₂	semidirect
6. D₁₇₈₄	C₂²	semidirect
8. C₁₆×C₂₂₃	C₂²	semidirect
20. C₂×C₂₂₃	D₁₆	semidirect
23. C₂₂₃	C₂×D₁₆	semidirect
27. C₂×C₁₆	D₂₂₃	semidirect
32. C₁₆	C₂×D₂₂₃	semidirect
45. C₂	D₃₅₆₈	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×D₁₇₈₄	2
D₃₅₆₈	2
C₂×C₁₆×C₂₂₃	2
C₂×D₁₆	223

Subgroups — C2×D3568 #28384001

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃₅₆₈ #28384001