Subgroups — C₂²×C₇×C₄⋊C₄ #90534

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	2	yes	maximal
2	C₂³×C₄×C₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₇×C₄⋊C₄	C₂	1	12	yes	maximal, direct product factor
4	C₂⁴×C₇	C₂²	1	1	yes	characteristic
5	C₂²×C₄×C₇	—	2	8	no	—
6	C₂²×C₄×C₇	C₄	1	8	yes	complemented
7	C₂²×C₄×C₇	C₂²	1	12	yes	—
8	C₂²×C₄×C₇	C₂²	1	6	yes	—
9	C₇×C₄⋊C₄	C₂²	1	16	yes	direct product factor
10	C₂²×C₄⋊C₄	C₇	1	1	yes	maximal, characteristic, direct product factor, 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	—	2	24	no	—
16	C₂×C₄×C₇	C₂×C₄	1	24	yes	complemented
17	C₂×C₄×C₇	C₂³	1	8	yes	—
18	C₂×C₄×C₇	C₂³	1	4	yes	—
19	C₂³×C₄	C₂×C₇	1	2	yes	—
20	C₂³×C₄	C₂×C₇	1	1	yes	characteristic
21	C₂×C₄⋊C₄	C₂×C₇	1	12	yes	direct product factor
22	C₂²×C₇	C₄⋊C₄	1	16	yes	direct product factor
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	—	2	8	no	—
28	C₄×C₇	C₂²×C₄	1	8	yes	complemented
29	C₂⁴	C₂²×C₇	1	1	yes	characteristic
30	C₂²×C₄	—	2	8	no	—
31	C₂²×C₄	C₄×C₇	1	8	yes	complemented
32	C₂²×C₄	C₂²×C₇	1	12	yes	—
33	C₂²×C₄	C₂²×C₇	1	6	yes	—
34	C₄⋊C₄	C₂²×C₇	1	16	yes	direct product factor
35	C₂×C₇	C₂×C₄⋊C₄	1	12	yes	direct product factor
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	C₂×C₄×C₇	1	4	yes	—
40	C₂³	C₇×D₄	1	4	yes	—
41	C₂³	C₇×Q₈	1	4	yes	—
42	C₂³	C₂³×C₇	1	3	yes	—
43	C₂×C₄	—	2	24	no	—
44	C₂×C₄	C₂×C₄×C₇	1	24	yes	complemented
45	C₂×C₄	C₂³×C₇	1	8	yes	—
46	C₂×C₄	C₂³×C₇	1	4	yes	—
47	C₇	C₂²×C₄⋊C₄	1	1	yes	characteristic, direct product factor, Sylow
48	C₂²	C₇×C₄⋊C₄	1	16	yes	direct product factor
49	C₂²	C₂²×C₄×C₇	1	6	yes	—
50	C₂²	C₂×C₇×D₄	1	6	yes	—
51	C₂²	C₂×C₇×Q₈	1	6	yes	—
52	C₂²	C₂⁴×C₇	1	1	yes	characteristic
53	C₄	—	2	8	no	—
54	C₄	C₂²×C₄×C₇	1	8	yes	complemented
55	C₂	C₂×C₇×C₄⋊C₄	1	12	yes	direct product factor
56	C₂	C₂³×C₄×C₇	1	1	yes	characteristic
57	C₂	C₂²×C₇×D₄	1	1	yes	characteristic
58	C₂	C₂²×C₇×Q₈	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₂×C₇×C₄⋊C₄	C₂	direct (N × H)
6. C₂²×C₄×C₇	C₄	semidirect
9. C₇×C₄⋊C₄	C₂²	direct (N × H)
10. C₂²×C₄⋊C₄	C₇	direct (N × H)
16. C₂×C₄×C₇	C₂×C₄	semidirect
21. C₂×C₄⋊C₄	C₂×C₇	direct (N × H)
22. C₂²×C₇	C₄⋊C₄	direct (N × H)
28. C₄×C₇	C₂²×C₄	semidirect
31. C₂²×C₄	C₄×C₇	semidirect
34. C₄⋊C₄	C₂²×C₇	direct (N × H)
35. C₂×C₇	C₂×C₄⋊C₄	direct (N × H)
44. C₂×C₄	C₂×C₄×C₇	semidirect
47. C₇	C₂²×C₄⋊C₄	direct (N × H)
48. C₂²	C₇×C₄⋊C₄	direct (N × H)
54. C₄	C₂²×C₄×C₇	semidirect
55. C₂	C₂×C₇×C₄⋊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
C₂³×C₄×C₇	2
C₂×C₇×C₄⋊C₄	2
C₂²×C₄⋊C₄	7

Subgroups — C22×C7×C4⋊C4 #90534

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₇×C₄⋊C₄ #90534