Subgroups — C₂×Dic₇⋊C₄ #6486

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	1	yes	maximal, characteristic
2	C₂²×Dic₇	C₂	1	1	yes	maximal, characteristic
3	C₂²×Dic₇	C₂	1	1	yes	maximal, characteristic
4	Dic₇⋊C₄	C₂	1	4	yes	maximal, direct product factor
5	C₂³×C₇	C₂²	1	1	yes	characteristic
6	C₂×C₄×C₇	—	2	2	no	—
7	C₂×C₄×C₇	C₂²	1	2	yes	—
8	C₂×Dic₇	—	2	2	no	—
9	C₂×Dic₇	C₄	1	4	yes	complemented
10	C₂×Dic₇	C₂²	1	2	yes	—
11	C₂×Dic₇	C₂²	1	2	yes	—
12	C₂×C₄⋊C₄	—	7	1	no	maximal, Sylow
13	C₂²×C₇	C₂×C₄	1	2	yes	—
14	C₂²×C₇	D₄	1	2	yes	—
15	C₂²×C₇	Q₈	1	2	yes	—
16	C₂²×C₇	C₂³	1	1	yes	characteristic
17	C₄×C₇	—	2	2	no	—
18	Dic₇	—	2	2	no	—
19	Dic₇	C₂×C₄	1	4	yes	complemented
20	C₂²×C₄	—	7	1	no	—
21	C₂²×C₄	—	7	1	no	—
22	C₂²×C₄	D₇	1	1	yes	characteristic
23	C₄⋊C₄	—	7	4	no	—
24	C₂×C₇	C₄⋊C₄	1	4	yes	complemented
25	C₂×C₇	C₂²×C₄	1	1	yes	characteristic
26	C₂×C₇	C₂×D₄	1	1	yes	characteristic
27	C₂×C₇	C₂×Q₈	1	1	yes	characteristic
28	C₂³	C₂×D₇	1	1	yes	characteristic
29	C₂×C₄	—	2	2	no	—
30	C₂×C₄	—	7	4	no	—
31	C₂×C₄	—	7	2	no	—
32	C₂×C₄	—	7	2	no	—
33	C₂×C₄	—	14	2	no	—
34	C₂×C₄	C₂×D₇	1	2	yes	—
35	C₇	C₂×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
36	C₂²	Dic₁₄	1	2	yes	—
37	C₂²	C₄×D₇	1	2	yes	—
38	C₂²	C₂²⋊D₇	1	2	yes	—
39	C₂²	C₂²×D₇	1	1	yes	characteristic
40	C₄	—	2	2	no	—
41	C₄	—	7	4	no	—
42	C₄	—	14	2	no	—
43	C₂	Dic₇⋊C₄	1	4	yes	direct product factor
44	C₂	C₂×Dic₁₄	1	1	yes	characteristic
45	C₂	C₂×C₄×D₇	1	1	yes	characteristic
46	C₂	C₂×C₂²⋊D₇	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. Dic₇⋊C₄	C₂	direct (N × H)
9. C₂×Dic₇	C₄	semidirect
19. Dic₇	C₂×C₄	semidirect
24. C₂×C₇	C₄⋊C₄	semidirect
35. C₇	C₂×C₄⋊C₄	semidirect
43. C₂	Dic₇⋊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
C₂²×Dic₇	2
Dic₇⋊C₄	2
C₂×C₄⋊C₄	7

Subgroups — C2×Dic7⋊C4 #6486

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Dic₇⋊C₄ #6486