Subgroups — C₂²×C₄²×C₇ #90532

Order 448.

498 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄×C₇	C₂	1	3	yes	maximal
2	C₂×C₄²×C₇	C₂	1	12	yes	maximal, direct product factor
3	C₂⁴×C₇	C₂²	1	1	yes	characteristic
4	C₂²×C₄×C₇	C₄	1	24	yes	direct product factor
5	C₂²×C₄×C₇	C₂²	1	18	yes	—
6	C₄²×C₇	C₂²	1	16	yes	direct product factor
7	C₂²×C₄²	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
8	C₂³×C₇	C₂×C₄	1	12	yes	—
9	C₂³×C₇	C₂³	1	3	yes	—
10	C₂×C₄×C₇	C₂×C₄	1	72	yes	direct product factor
11	C₂×C₄×C₇	C₂³	1	12	yes	—
12	C₂³×C₄	C₂×C₇	1	3	yes	—
13	C₂×C₄²	C₂×C₇	1	12	yes	direct product factor
14	C₂²×C₇	C₄²	1	16	yes	direct product factor
15	C₂²×C₇	C₂²×C₄	1	18	yes	—
16	C₂²×C₇	C₂⁴	1	1	yes	characteristic
17	C₄×C₇	C₂²×C₄	1	24	yes	direct product factor
18	C₂⁴	C₂²×C₇	1	1	yes	characteristic
19	C₂²×C₄	C₄×C₇	1	24	yes	direct product factor
20	C₂²×C₄	C₂²×C₇	1	18	yes	—
21	C₄²	C₂²×C₇	1	16	yes	direct product factor
22	C₂×C₇	C₂×C₄²	1	12	yes	direct product factor
23	C₂×C₇	C₂³×C₄	1	3	yes	—
24	C₂³	C₂×C₄×C₇	1	12	yes	—
25	C₂³	C₂³×C₇	1	3	yes	—
26	C₂×C₄	C₂×C₄×C₇	1	72	yes	direct product factor
27	C₂×C₄	C₂³×C₇	1	12	yes	—
28	C₇	C₂²×C₄²	1	1	yes	characteristic, direct product factor, Sylow
29	C₂²	C₄²×C₇	1	16	yes	direct product factor
30	C₂²	C₂²×C₄×C₇	1	18	yes	—
31	C₂²	C₂⁴×C₇	1	1	yes	characteristic
32	C₄	C₂²×C₄×C₇	1	24	yes	direct product factor
33	C₂	C₂×C₄²×C₇	1	12	yes	direct product factor
34	C₂	C₂³×C₄×C₇	1	3	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²	C₂⁴×C₇
socle, prime radical	C₂⁴×C₇	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×C₇	C₂	direct (N × H)
4. C₂²×C₄×C₇	C₄	direct (N × H)
6. C₄²×C₇	C₂²	direct (N × H)
7. C₂²×C₄²	C₇	direct (N × H)
10. C₂×C₄×C₇	C₂×C₄	direct (N × H)
13. C₂×C₄²	C₂×C₇	direct (N × H)
14. C₂²×C₇	C₄²	direct (N × H)
17. C₄×C₇	C₂²×C₄	direct (N × H)
19. C₂²×C₄	C₄×C₇	direct (N × H)
21. C₄²	C₂²×C₇	direct (N × H)
22. C₂×C₇	C₂×C₄²	direct (N × H)
26. C₂×C₄	C₂×C₄×C₇	direct (N × H)
28. C₇	C₂²×C₄²	direct (N × H)
29. C₂²	C₄²×C₇	direct (N × H)
32. C₄	C₂²×C₄×C₇	direct (N × H)
33. C₂	C₂×C₄²×C₇	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×C₇	2
C₂×C₄²×C₇	2
C₂²×C₄²	7

Subgroups — C22×C42×C7 #90532

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₄²×C₇ #90532