Subgroups — C₂²×C₄×Dic₇ #90473

Order 448.

498 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	C₄	1	16	yes	direct product factor
8	C₂²×Dic₇	C₂²	1	12	yes	—
9	C₄×Dic₇	C₂²	1	16	yes	direct product factor
10	C₂²×C₄²	—	7	1	no	maximal, Sylow
11	C₂³×C₇	C₂×C₄	1	8	yes	—
12	C₂³×C₇	C₂×C₄	1	4	yes	—
13	C₂³×C₇	C₂³	1	3	yes	—
14	C₂×C₄×C₇	C₂×C₄	1	24	yes	complemented
15	C₂×C₄×C₇	C₂³	1	4	yes	—
16	C₂×Dic₇	C₂×C₄	1	48	yes	direct product factor
17	C₂×Dic₇	C₂³	1	8	yes	—
18	C₂³×C₄	—	7	2	no	—
19	C₂³×C₄	D₇	1	1	yes	characteristic
20	C₂×C₄²	—	7	12	no	—
21	C₂²×C₇	C₄²	1	16	yes	complemented
22	C₂²×C₇	C₂²×C₄	1	12	yes	—
23	C₂²×C₇	C₂²×C₄	1	6	yes	—
24	C₂²×C₇	C₂⁴	1	1	yes	characteristic
25	C₄×C₇	C₂²×C₄	1	8	yes	complemented
26	Dic₇	C₂²×C₄	1	16	yes	direct product factor
27	C₂⁴	C₂×D₇	1	1	yes	characteristic
28	C₂²×C₄	—	7	16	no	—
29	C₂²×C₄	—	7	12	no	—
30	C₂²×C₄	Dic₇	1	8	yes	direct product factor
31	C₂²×C₄	C₂×D₇	1	6	yes	—
32	C₄²	—	7	16	no	—
33	C₂×C₇	C₂×C₄²	1	12	yes	complemented
34	C₂×C₇	C₂³×C₄	1	2	yes	—
35	C₂×C₇	C₂³×C₄	1	1	yes	characteristic
36	C₂³	C₄×D₇	1	8	yes	—
37	C₂³	C₂×Dic₇	1	4	yes	—
38	C₂³	C₂²×D₇	1	3	yes	—
39	C₂×C₄	—	7	48	no	—
40	C₂×C₄	—	7	8	no	—
41	C₂×C₄	C₂×Dic₇	1	24	yes	direct product factor
42	C₂×C₄	C₂²×D₇	1	4	yes	—
43	C₇	C₂²×C₄²	1	1	yes	characteristic, complemented, Sylow
44	C₂²	C₄×Dic₇	1	16	yes	direct product factor
45	C₂²	C₂×C₄×D₇	1	12	yes	—
46	C₂²	C₂²×Dic₇	1	6	yes	—
47	C₂²	C₂³×D₇	1	1	yes	characteristic
48	C₄	—	7	16	no	—
49	C₄	C₂²×Dic₇	1	8	yes	direct product factor
50	C₂	C₂×C₄×Dic₇	1	12	yes	direct product factor
51	C₂	C₂²×C₄×D₇	1	2	yes	—
52	C₂	C₂³×Dic₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂³×C₄	D₇
commutator, hypocenter	C₇	C₂²×C₄²
Frattini	C₂²	C₂³×D₇
Fitting	C₂³×C₄×C₇	C₂
socle, prime radical	C₂⁴×C₇	C₂²
cosocle	C₂²×C₇	C₂⁴
LCS	G ▷ C₇
UCS	C₁ ◁ 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
7. C₂²×Dic₇	C₄	direct (N × H)
9. C₄×Dic₇	C₂²	direct (N × H)
14. C₂×C₄×C₇	C₂×C₄	semidirect
16. C₂×Dic₇	C₂×C₄	direct (N × H)
21. C₂²×C₇	C₄²	semidirect
25. C₄×C₇	C₂²×C₄	semidirect
26. Dic₇	C₂²×C₄	direct (N × H)
30. C₂²×C₄	Dic₇	direct (N × H)
33. C₂×C₇	C₂×C₄²	semidirect
41. C₂×C₄	C₂×Dic₇	direct (N × H)
43. C₇	C₂²×C₄²	semidirect
44. C₂²	C₄×Dic₇	direct (N × H)
49. C₄	C₂²×Dic₇	direct (N × H)
50. 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×C₄²	7

Subgroups — C22×C4×Dic7 #90473

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₄×Dic₇ #90473