Subgroups — C₂×D₃₁₈₄ #27164439

Order 12736.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₅₉₂	C₂	1	2	yes	maximal, complemented
2	D₃₁₈₄	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₁₆×C₁₉₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₇₉₆	—	2	2	no	—
5	D₁₅₉₂	—	2	2	no	—
6	D₁₅₉₂	C₂²	1	4	yes	complemented
7	C₂×C₈×C₁₉₉	C₂²	1	1	yes	characteristic
8	C₁₆×C₁₉₉	C₂²	1	2	yes	complemented
9	C₂²×D₁₉₉	—	4	2	no	—
10	D₇₉₆	—	2	4	no	—
11	D₇₉₆	—	4	2	no	—
12	C₂×C₄×C₁₉₉	D₄	1	1	yes	characteristic
13	C₈×C₁₉₉	D₄	1	1	yes	characteristic
14	C₈×C₁₉₉	C₂³	1	1	yes	characteristic
15	C₂²×C₁₉₉	D₈	1	1	yes	characteristic
16	C₂×D₁₉₉	—	4	4	no	—
17	C₂×D₁₉₉	—	8	4	no	—
18	C₄×C₁₉₉	D₈	1	1	yes	characteristic
19	C₄×C₁₉₉	C₂×D₄	1	1	yes	characteristic
20	C₂×C₁₉₉	D₁₆	1	2	yes	complemented
21	C₂×C₁₉₉	C₂×D₈	1	1	yes	characteristic
22	D₁₉₉	—	8	4	no	—
23	C₁₉₉	C₂×D₁₆	1	1	yes	characteristic, complemented, Sylow
24	C₂×D₁₆	—	199	1	no	maximal, Sylow
25	C₂×D₈	—	199	2	no	—
26	D₁₆	—	199	4	no	—
27	C₂×C₁₆	D₁₉₉	1	1	yes	characteristic, complemented
28	C₂×D₄	—	398	2	no	—
29	D₈	—	398	2	no	—
30	D₈	—	199	4	no	—
31	C₂×C₈	C₂×D₁₉₉	1	1	yes	characteristic
32	C₁₆	C₂×D₁₉₉	1	2	yes	complemented
33	C₂³	—	796	2	no	—
34	D₄	—	796	2	no	—
35	D₄	—	398	4	no	—
36	C₂×C₄	D₇₉₆	1	1	yes	characteristic
37	C₈	D₇₉₆	1	1	yes	characteristic
38	C₈	C₂²×D₁₉₉	1	1	yes	characteristic
39	C₂²	—	796	4	no	—
40	C₂²	—	1592	4	no	—
41	C₂²	D₁₅₉₂	1	1	yes	characteristic
42	C₄	D₁₅₉₂	1	1	yes	characteristic
43	C₄	C₂×D₇₉₆	1	1	yes	characteristic
44	C₂	—	1592	4	no	—
45	C₂	D₃₁₈₄	1	2	yes	direct product factor
46	C₂	C₂×D₁₅₉₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₁₅₉₂
commutator, cosocle	C₈×C₁₉₉	C₂³
Frattini	C₈	C₂²×D₁₉₉
Fitting	C₂×C₁₆×C₁₉₉	C₂
socle	C₂²×C₁₉₉	D₈
hypercenter	C₂×C₁₆	D₁₉₉
hypocenter	C₁₉₉	C₂×D₁₆
LCS	G ▷ C₈×C₁₉₉ ▷ C₄×C₁₉₉ ▷ C₂×C₁₉₉ ▷ C₁₉₉
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×D₁₅₉₂	C₂	semidirect
2. D₃₁₈₄	C₂	direct (N × H)
3. C₂×C₁₆×C₁₉₉	C₂	semidirect
6. D₁₅₉₂	C₂²	semidirect
8. C₁₆×C₁₉₉	C₂²	semidirect
20. C₂×C₁₉₉	D₁₆	semidirect
23. C₁₉₉	C₂×D₁₆	semidirect
27. C₂×C₁₆	D₁₉₉	semidirect
32. C₁₆	C₂×D₁₉₉	semidirect
45. C₂	D₃₁₈₄	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×D₁₅₉₂	2
D₃₁₈₄	2
C₂×C₁₆×C₁₉₉	2
C₂×D₁₆	199

Subgroups — C2×D3184 #27164439

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃₁₈₄ #27164439