Subgroups — C₂²×C₂²⋊Dic₇ #90530

Order 448.

674 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₇	C₂	1	1	yes	maximal, characteristic
2	C₂³×Dic₇	C₂	1	2	yes	maximal, complemented
3	C₂×C₂²⋊Dic₇	C₂	1	12	yes	maximal, direct product factor
4	C₂⁴×C₇	—	2	8	no	—
5	C₂⁴×C₇	C₄	1	8	yes	complemented
6	C₂⁴×C₇	C₂²	1	6	yes	—
7	C₂⁴×C₇	C₂²	1	1	yes	characteristic
8	C₂²×Dic₇	—	2	8	no	—
9	C₂²×Dic₇	C₂²	1	12	yes	complemented
10	C₂²⋊Dic₇	C₂²	1	16	yes	direct product factor
11	C₂²×C₂²⋊C₄	—	7	1	no	maximal, Sylow
12	C₂³×C₇	—	2	32	no	—
13	C₂³×C₇	—	2	24	no	—
14	C₂³×C₇	C₂×C₄	1	4	yes	—
15	C₂³×C₇	C₂×C₄	1	24	yes	complemented
16	C₂³×C₇	D₄	1	8	yes	—
17	C₂³×C₇	C₂³	1	4	yes	—
18	C₂³×C₇	C₂³	1	3	yes	—
19	C₂×Dic₇	—	2	24	no	—
20	C₂×Dic₇	C₂³	1	8	yes	complemented
21	C₂⁵	D₇	1	1	yes	characteristic
22	C₂³×C₄	—	7	2	no	—
23	C₂×C₂²⋊C₄	—	7	12	no	—
24	C₂²×C₇	—	2	48	no	—
25	C₂²×C₇	—	2	8	no	—
26	C₂²×C₇	C₂²⋊C₄	1	16	yes	complemented
27	C₂²×C₇	C₂²×C₄	1	6	yes	—
28	C₂²×C₇	C₂²×C₄	1	8	yes	complemented
29	C₂²×C₇	C₂×D₄	1	12	yes	—
30	C₂²×C₇	C₂⁴	1	1	yes	characteristic
31	Dic₇	—	2	8	no	—
32	C₂⁴	—	2	8	no	—
33	C₂⁴	Dic₇	1	8	yes	complemented
34	C₂⁴	C₂×D₇	1	6	yes	—
35	C₂⁴	C₂×D₇	1	1	yes	characteristic
36	C₂²×C₄	—	7	12	no	—
37	C₂²×C₄	—	14	8	no	—
38	C₂²⋊C₄	—	7	16	no	—
39	C₂×C₇	—	2	8	no	—
40	C₂×C₇	C₂×C₂²⋊C₄	1	12	yes	complemented
41	C₂×C₇	C₂³×C₄	1	1	yes	characteristic
42	C₂×C₇	C₂²×D₄	1	2	yes	—
43	C₂³	—	2	32	no	—
44	C₂³	—	2	24	no	—
45	C₂³	C₂×Dic₇	1	4	yes	—
46	C₂³	C₂×Dic₇	1	24	yes	complemented
47	C₂³	C₂²⋊D₇	1	8	yes	—
48	C₂³	C₂²×D₇	1	4	yes	—
49	C₂³	C₂²×D₇	1	3	yes	—
50	C₂×C₄	—	7	8	no	—
51	C₂×C₄	—	14	24	no	—
52	C₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
53	C₂²	—	2	48	no	—
54	C₂²	—	2	8	no	—
55	C₂²	C₂²⋊Dic₇	1	16	yes	direct product factor
56	C₂²	C₂²×Dic₇	1	6	yes	—
57	C₂²	C₂²×Dic₇	1	8	yes	complemented
58	C₂²	C₂×C₂²⋊D₇	1	12	yes	—
59	C₂²	C₂³×D₇	1	1	yes	characteristic
60	C₄	—	14	8	no	—
61	C₂	—	2	8	no	—
62	C₂	C₂×C₂²⋊Dic₇	1	12	yes	direct product factor
63	C₂	C₂³×Dic₇	1	1	yes	characteristic
64	C₂	C₂²×C₂²⋊D₇	1	2	yes	—

	subgroup	G/H
center	C₂⁴	C₂×D₇
commutator	C₂×C₇	C₂³×C₄
Frattini	C₂²	C₂³×D₇
Fitting, prime radical	C₂⁵×C₇	C₂
socle	C₂⁴×C₇	C₂²
cosocle	C₂²×C₇	C₂⁴
hypercenter	C₂⁵	D₇
hypocenter	C₇	C₂²×C₂²⋊C₄
LCS	G ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂⁴ ◁ C₂⁵

Complements

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

N	H ≅ G/N	type
2. C₂³×Dic₇	C₂	semidirect
3. C₂×C₂²⋊Dic₇	C₂	direct (N × H)
5. C₂⁴×C₇	C₄	semidirect
9. C₂²×Dic₇	C₂²	semidirect
10. C₂²⋊Dic₇	C₂²	direct (N × H)
15. C₂³×C₇	C₂×C₄	semidirect
20. C₂×Dic₇	C₂³	semidirect
26. C₂²×C₇	C₂²⋊C₄	semidirect
28. C₂²×C₇	C₂²×C₄	semidirect
33. C₂⁴	Dic₇	semidirect
40. C₂×C₇	C₂×C₂²⋊C₄	semidirect
46. C₂³	C₂×Dic₇	semidirect
52. C₇	C₂²×C₂²⋊C₄	semidirect
55. C₂²	C₂²⋊Dic₇	direct (N × H)
57. C₂²	C₂²×Dic₇	semidirect
62. C₂	C₂×C₂²⋊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
C₂⁵×C₇	2
C₂³×Dic₇	2
C₂×C₂²⋊Dic₇	2
C₂²×C₂²⋊C₄	7

Subgroups — C22×C22⋊Dic7 #90530

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₂²⋊Dic₇ #90530