Subgroups — C₂×C₇×C₄⋊C₄ #6519

Order 224.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₇	C₂	1	2	yes	maximal
2	C₂²×C₄×C₇	C₂	1	1	yes	maximal, characteristic
3	C₇×C₄⋊C₄	C₂	1	4	yes	maximal, direct product factor
4	C₂³×C₇	C₂²	1	1	yes	characteristic
5	C₂×C₄×C₇	—	2	4	no	—
6	C₂×C₄×C₇	C₄	1	4	yes	complemented
7	C₂×C₄×C₇	C₂²	1	4	yes	—
8	C₂×C₄×C₇	C₂²	1	2	yes	—
9	C₂×C₄⋊C₄	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₂²×C₇	C₂×C₄	1	2	yes	—
11	C₂²×C₇	D₄	1	2	yes	—
12	C₂²×C₇	Q₈	1	2	yes	—
13	C₂²×C₇	C₂³	1	1	yes	characteristic
14	C₄×C₇	—	2	4	no	—
15	C₄×C₇	C₂×C₄	1	4	yes	complemented
16	C₂²×C₄	C₂×C₇	1	2	yes	—
17	C₂²×C₄	C₂×C₇	1	1	yes	characteristic
18	C₄⋊C₄	C₂×C₇	1	4	yes	direct product factor
19	C₂×C₇	C₄⋊C₄	1	4	yes	direct product factor
20	C₂×C₇	C₂²×C₄	1	1	yes	characteristic
21	C₂×C₇	C₂×D₄	1	1	yes	characteristic
22	C₂×C₇	C₂×Q₈	1	1	yes	characteristic
23	C₂³	C₂²×C₇	1	1	yes	characteristic
24	C₂×C₄	—	2	4	no	—
25	C₂×C₄	C₄×C₇	1	4	yes	complemented
26	C₂×C₄	C₂²×C₇	1	4	yes	—
27	C₂×C₄	C₂²×C₇	1	2	yes	—
28	C₇	C₂×C₄⋊C₄	1	1	yes	characteristic, direct product factor, Sylow
29	C₂²	C₂×C₄×C₇	1	2	yes	—
30	C₂²	C₇×D₄	1	2	yes	—
31	C₂²	C₇×Q₈	1	2	yes	—
32	C₂²	C₂³×C₇	1	1	yes	characteristic
33	C₄	—	2	4	no	—
34	C₄	C₂×C₄×C₇	1	4	yes	complemented
35	C₂	C₇×C₄⋊C₄	1	4	yes	direct product factor
36	C₂	C₂²×C₄×C₇	1	1	yes	characteristic
37	C₂	C₂×C₇×D₄	1	1	yes	characteristic
38	C₂	C₂×C₇×Q₈	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₇	C₂²
commutator	C₂	C₂²×C₄×C₇
Frattini, cosocle	C₂²	C₂³×C₇
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₇×C₄⋊C₄	C₂	direct (N × H)
6. C₂×C₄×C₇	C₄	semidirect
9. C₂×C₄⋊C₄	C₇	direct (N × H)
15. C₄×C₇	C₂×C₄	semidirect
18. C₄⋊C₄	C₂×C₇	direct (N × H)
19. C₂×C₇	C₄⋊C₄	direct (N × H)
25. C₂×C₄	C₄×C₇	semidirect
28. C₇	C₂×C₄⋊C₄	direct (N × H)
34. C₄	C₂×C₄×C₇	semidirect
35. C₂	C₇×C₄⋊C₄	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄×C₇	2
C₇×C₄⋊C₄	2
C₂×C₄⋊C₄	7

Subgroups — C2×C7×C4⋊C4 #6519

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×C₄⋊C₄ #6519