Subgroups — C₂²×C₄⋊Dic₇ #90476

Order 448.

418 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄×C₇	C₂	1	1	yes	maximal, characteristic
2	C₂³×Dic₇	C₂	1	2	yes	maximal
3	C₂×C₄⋊Dic₇	C₂	1	12	yes	maximal, direct product factor
4	C₂⁴×C₇	C₂²	1	1	yes	characteristic
5	C₂²×C₄×C₇	C₄	1	8	yes	complemented
6	C₂²×C₄×C₇	C₂²	1	6	yes	—
7	C₂²×Dic₇	—	2	8	no	—
8	C₂²×Dic₇	C₂²	1	12	yes	—
9	C₄⋊Dic₇	C₂²	1	16	yes	direct product factor
10	C₂²×C₄⋊C₄	—	7	1	no	maximal, Sylow
11	C₂³×C₇	C₂×C₄	1	4	yes	—
12	C₂³×C₇	D₄	1	4	yes	—
13	C₂³×C₇	Q₈	1	4	yes	—
14	C₂³×C₇	C₂³	1	3	yes	—
15	C₂×C₄×C₇	C₂×C₄	1	24	yes	complemented
16	C₂×C₄×C₇	C₂³	1	4	yes	—
17	C₂×Dic₇	—	2	24	no	—
18	C₂×Dic₇	C₂³	1	8	yes	—
19	C₂³×C₄	—	7	2	no	—
20	C₂³×C₄	D₇	1	1	yes	characteristic
21	C₂×C₄⋊C₄	—	7	12	no	—
22	C₂²×C₇	C₄⋊C₄	1	16	yes	complemented
23	C₂²×C₇	C₂²×C₄	1	6	yes	—
24	C₂²×C₇	C₂×D₄	1	6	yes	—
25	C₂²×C₇	C₂×Q₈	1	6	yes	—
26	C₂²×C₇	C₂⁴	1	1	yes	characteristic
27	C₄×C₇	C₂²×C₄	1	8	yes	complemented
28	Dic₇	—	2	8	no	—
29	C₂⁴	C₂×D₇	1	1	yes	characteristic
30	C₂²×C₄	—	7	12	no	—
31	C₂²×C₄	—	14	8	no	—
32	C₂²×C₄	Dic₇	1	8	yes	complemented
33	C₂²×C₄	C₂×D₇	1	6	yes	—
34	C₄⋊C₄	—	7	16	no	—
35	C₂×C₇	C₂×C₄⋊C₄	1	12	yes	complemented
36	C₂×C₇	C₂³×C₄	1	1	yes	characteristic
37	C₂×C₇	C₂²×D₄	1	1	yes	characteristic
38	C₂×C₇	C₂²×Q₈	1	1	yes	characteristic
39	C₂³	Dic₁₄	1	4	yes	—
40	C₂³	D₂₈	1	4	yes	—
41	C₂³	C₂×Dic₇	1	4	yes	—
42	C₂³	C₂²×D₇	1	3	yes	—
43	C₂×C₄	—	7	8	no	—
44	C₂×C₄	—	14	24	no	—
45	C₂×C₄	C₂×Dic₇	1	24	yes	complemented
46	C₂×C₄	C₂²×D₇	1	4	yes	—
47	C₇	C₂²×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
48	C₂²	C₄⋊Dic₇	1	16	yes	direct product factor
49	C₂²	C₂×Dic₁₄	1	6	yes	—
50	C₂²	C₂×D₂₈	1	6	yes	—
51	C₂²	C₂²×Dic₇	1	6	yes	—
52	C₂²	C₂³×D₇	1	1	yes	characteristic
53	C₄	—	14	8	no	—
54	C₄	C₂²×Dic₇	1	8	yes	complemented
55	C₂	C₂×C₄⋊Dic₇	1	12	yes	direct product factor
56	C₂	C₂²×Dic₁₄	1	1	yes	characteristic
57	C₂	C₂²×D₂₈	1	1	yes	characteristic
58	C₂	C₂³×Dic₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×D₇
commutator	C₂×C₇	C₂³×C₄
Frattini	C₂²	C₂³×D₇
Fitting	C₂³×C₄×C₇	C₂
socle, prime radical	C₂⁴×C₇	C₂²
cosocle	C₂²×C₇	C₂⁴
hypercenter	C₂³×C₄	D₇
hypocenter	C₇	C₂²×C₄⋊C₄
LCS	G ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
3. C₂×C₄⋊Dic₇	C₂	direct (N × H)
5. C₂²×C₄×C₇	C₄	semidirect
9. C₄⋊Dic₇	C₂²	direct (N × H)
15. C₂×C₄×C₇	C₂×C₄	semidirect
22. C₂²×C₇	C₄⋊C₄	semidirect
27. C₄×C₇	C₂²×C₄	semidirect
32. C₂²×C₄	Dic₇	semidirect
35. C₂×C₇	C₂×C₄⋊C₄	semidirect
45. C₂×C₄	C₂×Dic₇	semidirect
47. C₇	C₂²×C₄⋊C₄	semidirect
48. C₂²	C₄⋊Dic₇	direct (N × H)
54. C₄	C₂²×Dic₇	semidirect
55. C₂	C₂×C₄⋊Dic₇	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
C₂³×Dic₇	2
C₂×C₄⋊Dic₇	2
C₂²×C₄⋊C₄	7

Subgroups — C22×C4⋊Dic7 #90476

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₄⋊Dic₇ #90476