Subgroups — C₂²×C₄²×C₃₉₇ #38762165

Order 25408.

498 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄×C₃₉₇	C₂	1	3	yes	maximal
2	C₂×C₄²×C₃₉₇	C₂	1	12	yes	maximal, direct product factor
3	C₂⁴×C₃₉₇	C₂²	1	1	yes	characteristic
4	C₂²×C₄×C₃₉₇	C₄	1	24	yes	direct product factor
5	C₂²×C₄×C₃₉₇	C₂²	1	18	yes	—
6	C₄²×C₃₉₇	C₂²	1	16	yes	direct product factor
7	C₂³×C₃₉₇	C₂×C₄	1	12	yes	—
8	C₂³×C₃₉₇	C₂³	1	3	yes	—
9	C₂×C₄×C₃₉₇	C₂×C₄	1	72	yes	direct product factor
10	C₂×C₄×C₃₉₇	C₂³	1	12	yes	—
11	C₂²×C₃₉₇	C₄²	1	16	yes	direct product factor
12	C₂²×C₃₉₇	C₂²×C₄	1	18	yes	—
13	C₂²×C₃₉₇	C₂⁴	1	1	yes	characteristic
14	C₄×C₃₉₇	C₂²×C₄	1	24	yes	direct product factor
15	C₂×C₃₉₇	C₂×C₄²	1	12	yes	direct product factor
16	C₂×C₃₉₇	C₂³×C₄	1	3	yes	—
17	C₃₉₇	C₂²×C₄²	1	1	yes	characteristic, direct product factor, Sylow
18	C₂²×C₄²	C₃₉₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂³×C₄	C₂×C₃₉₇	1	3	yes	—
20	C₂×C₄²	C₂×C₃₉₇	1	12	yes	direct product factor
21	C₂⁴	C₂²×C₃₉₇	1	1	yes	characteristic
22	C₂²×C₄	C₄×C₃₉₇	1	24	yes	direct product factor
23	C₂²×C₄	C₂²×C₃₉₇	1	18	yes	—
24	C₄²	C₂²×C₃₉₇	1	16	yes	direct product factor
25	C₂³	C₂×C₄×C₃₉₇	1	12	yes	—
26	C₂³	C₂³×C₃₉₇	1	3	yes	—
27	C₂×C₄	C₂×C₄×C₃₉₇	1	72	yes	direct product factor
28	C₂×C₄	C₂³×C₃₉₇	1	12	yes	—
29	C₂²	C₄²×C₃₉₇	1	16	yes	direct product factor
30	C₂²	C₂²×C₄×C₃₉₇	1	18	yes	—
31	C₂²	C₂⁴×C₃₉₇	1	1	yes	characteristic
32	C₄	C₂²×C₄×C₃₉₇	1	24	yes	direct product factor
33	C₂	C₂×C₄²×C₃₉₇	1	12	yes	direct product factor
34	C₂	C₂³×C₄×C₃₉₇	1	3	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²	C₂⁴×C₃₉₇
socle, prime radical	C₂⁴×C₃₉₇	C₂²
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄²×C₃₉₇	C₂	direct (N × H)
4. C₂²×C₄×C₃₉₇	C₄	direct (N × H)
6. C₄²×C₃₉₇	C₂²	direct (N × H)
9. C₂×C₄×C₃₉₇	C₂×C₄	direct (N × H)
11. C₂²×C₃₉₇	C₄²	direct (N × H)
14. C₄×C₃₉₇	C₂²×C₄	direct (N × H)
15. C₂×C₃₉₇	C₂×C₄²	direct (N × H)
17. C₃₉₇	C₂²×C₄²	direct (N × H)
18. C₂²×C₄²	C₃₉₇	direct (N × H)
20. C₂×C₄²	C₂×C₃₉₇	direct (N × H)
22. C₂²×C₄	C₄×C₃₉₇	direct (N × H)
24. C₄²	C₂²×C₃₉₇	direct (N × H)
27. C₂×C₄	C₂×C₄×C₃₉₇	direct (N × H)
29. C₂²	C₄²×C₃₉₇	direct (N × H)
32. C₄	C₂²×C₄×C₃₉₇	direct (N × H)
33. C₂	C₂×C₄²×C₃₉₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₄×C₃₉₇	2
C₂×C₄²×C₃₉₇	2
C₂²×C₄²	397

Subgroups — C22×C42×C397 #38762165

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₄²×C₃₉₇ #38762165