Subgroups — D₁₆×D₉₇ #20261154

Order 6208.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₈×D₉₇	C₂	1	2	yes	maximal, complemented
2	D₁₅₅₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#15690751	C₂	1	2	yes	maximal, complemented
4	C₁₆×D₉₇	C₂	1	1	yes	maximal, characteristic, complemented
5	D₁₆×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented
6	D₄×D₉₇	—	2	2	no	—
7	D₇₇₆	C₂²	1	2	yes	complemented
8	#13095496	—	2	2	no	—
9	C₈×D₉₇	C₂²	1	1	yes	characteristic
10	#13095486	C₂²	1	1	yes	characteristic, complemented
11	D₈×C₉₇	C₂²	1	2	yes	complemented
12	C₁₆×C₉₇	C₂²	1	1	yes	characteristic, complemented
13	C₂²×D₉₇	—	4	2	no	—
14	D₄×C₉₇	—	2	2	no	—
15	C₂²⋊D₉₇	—	4	2	no	—
16	D₃₈₈	—	2	2	no	—
17	C₄×D₉₇	D₄	1	1	yes	characteristic
18	C₈×C₉₇	C₂³	1	1	yes	characteristic
19	#11715895	D₄	1	1	yes	characteristic
20	C₂²×C₉₇	—	4	2	no	—
21	C₂×D₉₇	—	4	2	no	—
22	C₂×D₉₇	—	8	4	no	—
23	C₂×D₉₇	D₈	1	1	yes	characteristic
24	C₄×C₉₇	C₂×D₄	1	1	yes	characteristic
25	Dic₉₇	D₈	1	1	yes	characteristic
26	C₂×C₉₇	—	8	2	no	—
27	C₂×C₉₇	C₂×D₈	1	1	yes	characteristic
28	D₉₇	—	8	2	no	—
29	D₉₇	D₁₆	1	2	yes	direct product factor
30	C₉₇	C₂×D₁₆	1	1	yes	characteristic, complemented, Sylow
31	C₂×D₁₆	—	97	1	no	maximal, Sylow
32	C₂×D₈	—	97	2	no	—
33	D₁₆	—	97	2	no	—
34	D₁₆	—	97	1	no	—
35	D₁₆	D₉₇	1	1	yes	characteristic, direct product factor
36	C₂×C₁₆	—	97	1	no	—
37	C₂×D₄	—	194	2	no	—
38	D₈	—	97	2	no	—
39	D₈	—	194	2	no	—
40	D₈	C₂×D₉₇	1	2	yes	complemented
41	C₂×C₈	—	97	1	no	—
42	C₁₆	—	97	1	no	—
43	C₁₆	C₂×D₉₇	1	1	yes	characteristic, complemented
44	C₂³	—	388	2	no	—
45	D₄	—	2	2	no	—
46	D₄	—	388	2	no	—
47	D₄	—	194	2	no	—
48	C₂×C₄	—	97	1	no	—
49	C₈	—	97	1	no	—
50	C₈	C₂²×D₉₇	1	1	yes	characteristic
51	C₂²	—	4	2	no	—
52	C₂²	—	776	4	no	—
53	C₂²	—	97	1	no	—
54	C₂²	—	388	2	no	—
55	C₄	—	97	1	no	—
56	C₄	D₄×D₉₇	1	1	yes	characteristic
57	C₂	—	8	2	no	—
58	C₂	—	776	2	no	—
59	C₂	—	97	2	no	—
60	C₂	D₈×D₉₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×D₉₇
commutator	C₈×C₉₇	C₂³
Frattini	C₈	C₂²×D₉₇
Fitting	D₁₆×C₉₇	C₂
socle	C₂×C₉₇	C₂×D₈
hypercenter	D₁₆	D₉₇
hypocenter	C₉₇	C₂×D₁₆
LCS	G ▷ C₈×C₉₇ ▷ C₄×C₉₇ ▷ C₂×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ D₁₆

Complements

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

N	H ≅ G/N	type
1. D₈×D₉₇	C₂	semidirect
2. D₁₅₅₂	C₂	semidirect
3. #15690751	C₂	semidirect
4. C₁₆×D₉₇	C₂	semidirect
5. D₁₆×C₉₇	C₂	semidirect
7. D₇₇₆	C₂²	semidirect
10. #13095486	C₂²	semidirect
11. D₈×C₉₇	C₂²	semidirect
12. C₁₆×C₉₇	C₂²	semidirect
29. D₉₇	D₁₆	direct (N × H)
30. C₉₇	C₂×D₁₆	semidirect
35. D₁₆	D₉₇	direct (N × H)
40. D₈	C₂×D₉₇	semidirect
43. C₁₆	C₂×D₉₇	semidirect

Subgroups — D16×D97 #20261154

Conjugacy classes of subgroups

Complements

Subgroups — D₁₆×D₉₇ #20261154