Subgroups — C₃×C₄×C₈×C₉₇ #72188106

Order 9312.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₈×C₉₇	C₂	1	2	yes	maximal
2	C₃×C₄²×C₉₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₄×C₉₇	C₄	1	2	yes	—
4	C₂×C₃×C₄×C₉₇	C₂²	1	1	yes	characteristic
5	C₃×C₈×C₉₇	C₄	1	4	yes	direct product factor
6	C₄×C₈×C₉₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₈×C₉₇	C₂×C₃	1	2	yes	—
8	C₄²×C₉₇	C₂×C₃	1	1	yes	characteristic
9	C₂²×C₃×C₉₇	C₂×C₄	1	1	yes	characteristic
10	C₃×C₄×C₉₇	C₈	1	4	yes	direct product factor
11	C₃×C₄×C₉₇	C₂×C₄	1	2	yes	—
12	C₂×C₄×C₉₇	C₃×C₄	1	2	yes	—
13	C₂×C₄×C₉₇	C₂²×C₃	1	1	yes	characteristic
14	C₈×C₉₇	C₃×C₄	1	4	yes	direct product factor
15	C₂×C₃×C₉₇	C₄²	1	1	yes	characteristic
16	C₂×C₃×C₉₇	C₂×C₈	1	2	yes	—
17	C₂²×C₉₇	C₂×C₃×C₄	1	1	yes	characteristic
18	C₄×C₉₇	C₃×C₈	1	4	yes	direct product factor
19	C₄×C₉₇	C₂×C₃×C₄	1	2	yes	—
20	C₃×C₉₇	C₄×C₈	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₉₇	C₃×C₄²	1	1	yes	characteristic
22	C₂×C₉₇	C₂×C₃×C₈	1	2	yes	—
23	C₉₇	C₃×C₄×C₈	1	1	yes	characteristic, direct product factor, Sylow
24	C₃×C₄×C₈	C₉₇	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₂×C₃×C₈	C₂×C₉₇	1	2	yes	—
26	C₃×C₄²	C₂×C₉₇	1	1	yes	characteristic
27	C₄×C₈	C₃×C₉₇	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₃×C₄	C₄×C₉₇	1	2	yes	—
29	C₂×C₃×C₄	C₂²×C₉₇	1	1	yes	characteristic
30	C₃×C₈	C₄×C₉₇	1	4	yes	direct product factor
31	C₂×C₈	C₂×C₃×C₉₇	1	2	yes	—
32	C₄²	C₂×C₃×C₉₇	1	1	yes	characteristic
33	C₂²×C₃	C₂×C₄×C₉₇	1	1	yes	characteristic
34	C₃×C₄	C₈×C₉₇	1	4	yes	direct product factor
35	C₃×C₄	C₂×C₄×C₉₇	1	2	yes	—
36	C₂×C₄	C₃×C₄×C₉₇	1	2	yes	—
37	C₂×C₄	C₂²×C₃×C₉₇	1	1	yes	characteristic
38	C₈	C₃×C₄×C₉₇	1	4	yes	direct product factor
39	C₂×C₃	C₄²×C₉₇	1	1	yes	characteristic
40	C₂×C₃	C₂×C₈×C₉₇	1	2	yes	—
41	C₂²	C₂×C₃×C₄×C₉₇	1	1	yes	characteristic
42	C₄	C₃×C₈×C₉₇	1	4	yes	direct product factor
43	C₄	C₂×C₃×C₄×C₉₇	1	2	yes	—
44	C₃	C₄×C₈×C₉₇	1	1	yes	characteristic, direct product factor, Sylow
45	C₂	C₃×C₄²×C₉₇	1	1	yes	characteristic
46	C₂	C₂×C₃×C₈×C₉₇	1	2	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₄	C₂²×C₃×C₉₇
socle, prime radical	C₂²×C₃×C₉₇	C₂×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₃×C₈×C₉₇	C₄	direct (N × H)
6. C₄×C₈×C₉₇	C₃	direct (N × H)
10. C₃×C₄×C₉₇	C₈	direct (N × H)
14. C₈×C₉₇	C₃×C₄	direct (N × H)
18. C₄×C₉₇	C₃×C₈	direct (N × H)
20. C₃×C₉₇	C₄×C₈	direct (N × H)
23. C₉₇	C₃×C₄×C₈	direct (N × H)
24. C₃×C₄×C₈	C₉₇	direct (N × H)
27. C₄×C₈	C₃×C₉₇	direct (N × H)
30. C₃×C₈	C₄×C₉₇	direct (N × H)
34. C₃×C₄	C₈×C₉₇	direct (N × H)
38. C₈	C₃×C₄×C₉₇	direct (N × H)
42. C₄	C₃×C₈×C₉₇	direct (N × H)
44. C₃	C₄×C₈×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
C₂×C₃×C₈×C₉₇	2
C₃×C₄²×C₉₇	2
C₄×C₈×C₉₇	3
C₃×C₄×C₈	97

Subgroups — C3×C4×C8×C97 #72188106

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×C₈×C₉₇ #72188106