Subgroups — C₃×C₄×C₁₆×C₉₇ #72196413

Order 18624.

116 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×C₈×C₉₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₁₆×C₉₇	C₂	1	2	yes	maximal
3	C₂×C₃×C₈×C₉₇	C₄	1	1	yes	characteristic
4	C₂×C₃×C₈×C₉₇	C₂²	1	1	yes	characteristic
5	C₃×C₄²×C₉₇	C₄	1	1	yes	characteristic
6	C₃×C₁₆×C₉₇	C₄	1	4	yes	direct product factor
7	C₂×C₃×C₄×C₉₇	C₈	1	2	yes	—
8	C₂×C₃×C₄×C₉₇	C₂×C₄	1	1	yes	characteristic
9	C₃×C₈×C₉₇	C₈	1	2	yes	—
10	C₃×C₈×C₉₇	C₂×C₄	1	2	yes	—
11	C₄×C₁₆×C₉₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂×C₁₆×C₉₇	C₂×C₃	1	2	yes	—
13	C₄×C₈×C₉₇	C₂×C₃	1	1	yes	characteristic
14	C₂×C₈×C₉₇	C₃×C₄	1	1	yes	characteristic
15	C₂×C₈×C₉₇	C₂²×C₃	1	1	yes	characteristic
16	C₄²×C₉₇	C₃×C₄	1	1	yes	characteristic
17	C₁₆×C₉₇	C₃×C₄	1	4	yes	direct product factor
18	C₂²×C₃×C₉₇	C₂×C₈	1	1	yes	characteristic
19	C₃×C₄×C₉₇	C₁₆	1	4	yes	direct product factor
20	C₃×C₄×C₉₇	C₄²	1	1	yes	characteristic
21	C₃×C₄×C₉₇	C₂×C₈	1	1	yes	characteristic
22	C₂×C₄×C₉₇	C₃×C₈	1	2	yes	—
23	C₂×C₄×C₉₇	C₂×C₃×C₄	1	1	yes	characteristic
24	C₈×C₉₇	C₃×C₈	1	2	yes	—
25	C₈×C₉₇	C₂×C₃×C₄	1	2	yes	—
26	C₂×C₃×C₉₇	C₄×C₈	1	1	yes	characteristic
27	C₂×C₃×C₉₇	C₂×C₁₆	1	2	yes	—
28	C₂²×C₉₇	C₂×C₃×C₈	1	1	yes	characteristic
29	C₄×C₉₇	C₃×C₁₆	1	4	yes	direct product factor
30	C₄×C₉₇	C₃×C₄²	1	1	yes	characteristic
31	C₄×C₉₇	C₂×C₃×C₈	1	1	yes	characteristic
32	C₃×C₉₇	C₄×C₁₆	1	1	yes	characteristic, direct product factor, Hall
33	C₂×C₉₇	C₃×C₄×C₈	1	1	yes	characteristic
34	C₂×C₉₇	C₂×C₃×C₁₆	1	2	yes	—
35	C₃×C₄×C₁₆	C₉₇	1	1	yes	maximal, characteristic, direct product factor, Hall
36	C₉₇	C₃×C₄×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
37	C₂×C₃×C₁₆	C₂×C₉₇	1	2	yes	—
38	C₃×C₄×C₈	C₂×C₉₇	1	1	yes	characteristic
39	C₄×C₁₆	C₃×C₉₇	1	1	yes	characteristic, direct product factor, Sylow
40	C₂×C₃×C₈	C₄×C₉₇	1	1	yes	characteristic
41	C₂×C₃×C₈	C₂²×C₉₇	1	1	yes	characteristic
42	C₃×C₄²	C₄×C₉₇	1	1	yes	characteristic
43	C₃×C₁₆	C₄×C₉₇	1	4	yes	direct product factor
44	C₂×C₁₆	C₂×C₃×C₉₇	1	2	yes	—
45	C₄×C₈	C₂×C₃×C₉₇	1	1	yes	characteristic
46	C₂×C₃×C₄	C₈×C₉₇	1	2	yes	—
47	C₂×C₃×C₄	C₂×C₄×C₉₇	1	1	yes	characteristic
48	C₃×C₈	C₈×C₉₇	1	2	yes	—
49	C₃×C₈	C₂×C₄×C₉₇	1	2	yes	—
50	C₂×C₈	C₃×C₄×C₉₇	1	1	yes	characteristic
51	C₂×C₈	C₂²×C₃×C₉₇	1	1	yes	characteristic
52	C₄²	C₃×C₄×C₉₇	1	1	yes	characteristic
53	C₁₆	C₃×C₄×C₉₇	1	4	yes	direct product factor
54	C₂²×C₃	C₂×C₈×C₉₇	1	1	yes	characteristic
55	C₃×C₄	C₁₆×C₉₇	1	4	yes	direct product factor
56	C₃×C₄	C₄²×C₉₇	1	1	yes	characteristic
57	C₃×C₄	C₂×C₈×C₉₇	1	1	yes	characteristic
58	C₂×C₄	C₃×C₈×C₉₇	1	2	yes	—
59	C₂×C₄	C₂×C₃×C₄×C₉₇	1	1	yes	characteristic
60	C₈	C₃×C₈×C₉₇	1	2	yes	—
61	C₈	C₂×C₃×C₄×C₉₇	1	2	yes	—
62	C₂×C₃	C₄×C₈×C₉₇	1	1	yes	characteristic
63	C₂×C₃	C₂×C₁₆×C₉₇	1	2	yes	—
64	C₂²	C₂×C₃×C₈×C₉₇	1	1	yes	characteristic
65	C₄	C₃×C₁₆×C₉₇	1	4	yes	direct product factor
66	C₄	C₃×C₄²×C₉₇	1	1	yes	characteristic
67	C₄	C₂×C₃×C₈×C₉₇	1	1	yes	characteristic
68	C₃	C₄×C₁₆×C₉₇	1	1	yes	characteristic, direct product factor, Sylow
69	C₂	C₂×C₃×C₁₆×C₉₇	1	2	yes	—
70	C₂	C₃×C₄×C₈×C₉₇	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₈	C₂²×C₃×C₉₇
socle, prime radical	C₂²×C₃×C₉₇	C₂×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₃×C₁₆×C₉₇	C₄	direct (N × H)
11. C₄×C₁₆×C₉₇	C₃	direct (N × H)
17. C₁₆×C₉₇	C₃×C₄	direct (N × H)
19. C₃×C₄×C₉₇	C₁₆	direct (N × H)
29. C₄×C₉₇	C₃×C₁₆	direct (N × H)
32. C₃×C₉₇	C₄×C₁₆	direct (N × H)
35. C₃×C₄×C₁₆	C₉₇	direct (N × H)
36. C₉₇	C₃×C₄×C₁₆	direct (N × H)
39. C₄×C₁₆	C₃×C₉₇	direct (N × H)
43. C₃×C₁₆	C₄×C₉₇	direct (N × H)
53. C₁₆	C₃×C₄×C₉₇	direct (N × H)
55. C₃×C₄	C₁₆×C₉₇	direct (N × H)
65. C₄	C₃×C₁₆×C₉₇	direct (N × H)
68. C₃	C₄×C₁₆×C₉₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₄×C₈×C₉₇	2
C₂×C₃×C₁₆×C₉₇	2
C₄×C₁₆×C₉₇	3
C₃×C₄×C₁₆	97

Subgroups — C3×C4×C16×C97 #72196413

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×C₁₆×C₉₇ #72196413