Subgroups — D₇×C₄⋊C₄ #6454

Order 224.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₇	C₂	1	2	yes	maximal
2	C₂×C₄×D₇	C₂	1	1	yes	maximal, characteristic
3	C₇×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄⋊Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
5	Dic₇⋊C₄	C₂	1	2	yes	maximal, complemented
6	C₂²×D₇	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₇	C₂²	1	2	yes	—
8	C₂×C₄×C₇	C₂²	1	1	yes	characteristic
9	C₂×Dic₇	C₂²	1	2	yes	—
10	C₂×Dic₇	C₂²	1	1	yes	characteristic
11	C₄×D₇	—	2	4	no	—
12	C₄×D₇	C₄	1	4	yes	complemented
13	C₂×C₄⋊C₄	—	7	1	no	maximal, Sylow
14	C₂²×C₇	C₂³	1	1	yes	characteristic
15	C₂×D₇	C₂×C₄	1	2	yes	—
16	C₂×D₇	D₄	1	2	yes	—
17	C₂×D₇	Q₈	1	2	yes	—
18	C₄×C₇	—	2	2	no	—
19	C₄×C₇	C₂×C₄	1	2	yes	complemented
20	Dic₇	—	2	2	no	—
21	Dic₇	C₂×C₄	1	2	yes	complemented
22	C₂²×C₄	—	7	1	no	—
23	C₂²×C₄	—	7	2	no	—
24	C₄⋊C₄	—	7	2	no	—
25	C₄⋊C₄	—	7	1	no	—
26	C₄⋊C₄	D₇	1	1	yes	characteristic, direct product factor
27	C₂×C₇	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₇	C₂×D₄	1	1	yes	characteristic
29	C₂×C₇	C₂×Q₈	1	1	yes	characteristic
30	D₇	C₄⋊C₄	1	4	yes	direct product factor
31	C₂³	—	7	1	no	—
32	C₂×C₄	—	7	1	no	—
33	C₂×C₄	—	7	4	no	—
34	C₂×C₄	—	7	2	no	—
35	C₂×C₄	—	14	4	no	—
36	C₂×C₄	C₂×D₇	1	2	yes	—
37	C₂×C₄	C₂×D₇	1	1	yes	characteristic
38	C₇	C₂×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
39	C₂²	—	7	2	no	—
40	C₂²	—	7	2	no	—
41	C₂²	—	7	2	no	—
42	C₂²	C₂²×D₇	1	1	yes	characteristic
43	C₄	—	2	2	no	—
44	C₄	—	7	2	no	—
45	C₄	—	14	2	no	—
46	C₄	C₄×D₇	1	2	yes	complemented
47	C₂	—	7	4	no	—
48	C₂	C₂×C₄×D₇	1	1	yes	characteristic
49	C₂	D₄×D₇	1	1	yes	characteristic
50	C₂	Q₈×D₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₇
commutator	C₂×C₇	C₂²×C₄
Fitting	C₇×C₄⋊C₄	C₂
socle, cosocle	C₂²×C₇	C₂³
prime radical	C₂²×D₇	C₂²
hypercenter	C₄⋊C₄	D₇
hypocenter	C₇	C₂×C₄⋊C₄
LCS	G ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
3. C₇×C₄⋊C₄	C₂	semidirect
4. C₄⋊Dic₇	C₂	semidirect
5. Dic₇⋊C₄	C₂	semidirect
12. C₄×D₇	C₄	semidirect
19. C₄×C₇	C₂×C₄	semidirect
21. Dic₇	C₂×C₄	semidirect
26. C₄⋊C₄	D₇	direct (N × H)
30. D₇	C₄⋊C₄	direct (N × H)
38. C₇	C₂×C₄⋊C₄	semidirect
46. C₄	C₄×D₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×D₇	2
C₇×C₄⋊C₄	2
C₄⋊Dic₇	2
Dic₇⋊C₄	2
C₂×C₄⋊C₄	7

Subgroups — D7×C4⋊C4 #6454

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇×C₄⋊C₄ #6454