Subgroups — D₃₂×D₉₇ #27144032

Order 12416.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₆×D₉₇	C₂	1	2	yes	maximal, complemented
2	D₃₁₀₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#20260570	C₂	1	2	yes	maximal, complemented
4	C₃₂×D₉₇	C₂	1	1	yes	maximal, characteristic, complemented
5	D₃₂×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented
6	D₈×D₉₇	—	2	2	no	—
7	D₁₅₅₂	C₂²	1	2	yes	complemented
8	#15690751	—	2	2	no	—
9	C₁₆×D₉₇	C₂²	1	1	yes	characteristic
10	#15690716	C₂²	1	1	yes	characteristic, complemented
11	D₁₆×C₉₇	C₂²	1	2	yes	complemented
12	C₃₂×C₉₇	C₂²	1	1	yes	characteristic, complemented
13	D₄×D₉₇	—	4	2	no	—
14	D₇₇₆	—	2	2	no	—
15	#13095496	—	4	2	no	—
16	C₈×D₉₇	D₄	1	1	yes	characteristic
17	#13095486	D₄	1	1	yes	characteristic
18	D₈×C₉₇	—	2	2	no	—
19	C₁₆×C₉₇	C₂³	1	1	yes	characteristic
20	C₂²×D₉₇	—	8	2	no	—
21	D₄×C₉₇	—	4	2	no	—
22	C₂²⋊D₉₇	—	8	2	no	—
23	D₃₈₈	—	4	2	no	—
24	C₄×D₉₇	D₈	1	1	yes	characteristic
25	C₈×C₉₇	C₂×D₄	1	1	yes	characteristic
26	#11715895	D₈	1	1	yes	characteristic
27	C₂²×C₉₇	—	8	2	no	—
28	C₂×D₉₇	—	8	2	no	—
29	C₂×D₉₇	—	16	4	no	—
30	C₂×D₉₇	D₁₆	1	1	yes	characteristic
31	C₄×C₉₇	C₂×D₈	1	1	yes	characteristic
32	Dic₉₇	D₁₆	1	1	yes	characteristic
33	C₂×C₉₇	—	16	2	no	—
34	C₂×C₉₇	C₂×D₁₆	1	1	yes	characteristic
35	D₉₇	—	16	2	no	—
36	D₉₇	D₃₂	1	2	yes	direct product factor
37	C₂×D₃₂	—	97	1	no	maximal, Sylow
38	C₉₇	C₂×D₃₂	1	1	yes	characteristic, complemented, Sylow
39	C₂×D₁₆	—	97	2	no	—
40	D₃₂	—	97	2	no	—
41	D₃₂	—	97	1	no	—
42	D₃₂	D₉₇	1	1	yes	characteristic, direct product factor
43	C₂×C₃₂	—	97	1	no	—
44	C₂×D₈	—	194	2	no	—
45	D₁₆	—	97	2	no	—
46	D₁₆	—	194	2	no	—
47	D₁₆	C₂×D₉₇	1	2	yes	complemented
48	C₂×C₁₆	—	97	1	no	—
49	C₃₂	—	97	1	no	—
50	C₃₂	C₂×D₉₇	1	1	yes	characteristic, complemented
51	C₂×D₄	—	388	2	no	—
52	D₈	—	2	2	no	—
53	D₈	—	388	2	no	—
54	D₈	—	194	2	no	—
55	C₂×C₈	—	97	1	no	—
56	C₁₆	—	97	1	no	—
57	C₁₆	C₂²×D₉₇	1	1	yes	characteristic
58	C₂³	—	776	2	no	—
59	D₄	—	4	2	no	—
60	D₄	—	776	2	no	—
61	D₄	—	388	2	no	—
62	C₂×C₄	—	97	1	no	—
63	C₈	—	97	1	no	—
64	C₈	D₄×D₉₇	1	1	yes	characteristic
65	C₂²	—	8	2	no	—
66	C₂²	—	776	2	no	—
67	C₂²	—	1552	4	no	—
68	C₂²	—	97	1	no	—
69	C₄	—	97	1	no	—
70	C₄	D₈×D₉₇	1	1	yes	characteristic
71	C₂	—	16	2	no	—
72	C₂	—	1552	2	no	—
73	C₂	—	97	2	no	—
74	C₂	D₁₆×D₉₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₁₆×D₉₇
commutator, cosocle	C₁₆×C₉₇	C₂³
Frattini	C₁₆	C₂²×D₉₇
Fitting	D₃₂×C₉₇	C₂
socle	C₂×C₉₇	C₂×D₁₆
hypercenter	D₃₂	D₉₇
hypocenter	C₉₇	C₂×D₃₂
LCS	G ▷ C₁₆×C₉₇ ▷ C₈×C₉₇ ▷ C₄×C₉₇ ▷ C₂×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ D₃₂

Complements

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

N	H ≅ G/N	type
1. D₁₆×D₉₇	C₂	semidirect
2. D₃₁₀₄	C₂	semidirect
3. #20260570	C₂	semidirect
4. C₃₂×D₉₇	C₂	semidirect
5. D₃₂×C₉₇	C₂	semidirect
7. D₁₅₅₂	C₂²	semidirect
10. #15690716	C₂²	semidirect
11. D₁₆×C₉₇	C₂²	semidirect
12. C₃₂×C₉₇	C₂²	semidirect
36. D₉₇	D₃₂	direct (N × H)
38. C₉₇	C₂×D₃₂	semidirect
42. D₃₂	D₉₇	direct (N × H)
47. D₁₆	C₂×D₉₇	semidirect
50. C₃₂	C₂×D₉₇	semidirect

Maximal subgroups

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

subgroup	index
D₁₆×D₉₇	2
D₃₁₀₄	2
#20260570	2
C₃₂×D₉₇	2
D₃₂×C₉₇	2
C₂×D₃₂	97

Subgroups — D32×D97 #27144032

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃₂×D₉₇ #27144032