Subgroups — C₂×C₇×C₄⋊Q₈ #90552

Order 448.

290 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×Q₈	C₂	1	2	yes	maximal
2	C₇×C₄⋊Q₈	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₇×C₄⋊C₄	C₂	1	4	yes	maximal
4	C₂×C₄²×C₇	C₂	1	1	yes	maximal, characteristic
5	C₂×C₇×Q₈	—	2	8	no	—
6	C₂×C₇×Q₈	C₂²	1	8	yes	—
7	C₂²×C₄×C₇	C₂²	1	4	yes	—
8	C₂²×C₄×C₇	C₂²	1	1	yes	characteristic
9	C₂²×C₄×C₇	C₂²	1	2	yes	—
10	C₇×C₄⋊C₄	C₂²	1	16	yes	—
11	C₄²×C₇	C₂²	1	4	yes	—
12	C₂×C₄⋊Q₈	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₂³×C₇	C₂³	1	1	yes	characteristic
14	C₇×Q₈	—	2	16	no	—
15	C₂×C₄×C₇	—	2	8	no	—
16	C₂×C₄×C₇	D₄	1	4	yes	—
17	C₂×C₄×C₇	Q₈	1	8	yes	complemented
18	C₂×C₄×C₇	C₂³	1	8	yes	—
19	C₂×C₄×C₇	C₂³	1	2	yes	—
20	C₂×C₄×C₇	C₂³	1	4	yes	—
21	C₂²×Q₈	C₂×C₇	1	2	yes	—
22	C₄⋊Q₈	C₂×C₇	1	8	yes	direct product factor
23	C₂×C₄⋊C₄	C₂×C₇	1	4	yes	—
24	C₂×C₄²	C₂×C₇	1	1	yes	characteristic
25	C₂²×C₇	C₂×D₄	1	2	yes	—
26	C₂²×C₇	C₂×Q₈	1	4	yes	—
27	C₂²×C₇	C₂⁴	1	1	yes	characteristic
28	C₄×C₇	—	2	8	no	—
29	C₄×C₇	C₂×D₄	1	4	yes	—
30	C₄×C₇	C₂×Q₈	1	8	yes	complemented
31	C₂×Q₈	—	2	8	no	—
32	C₂×Q₈	C₂²×C₇	1	8	yes	—
33	C₂²×C₄	C₂²×C₇	1	4	yes	—
34	C₂²×C₄	C₂²×C₇	1	1	yes	characteristic
35	C₂²×C₄	C₂²×C₇	1	2	yes	—
36	C₄⋊C₄	C₂²×C₇	1	16	yes	—
37	C₄²	C₂²×C₇	1	4	yes	—
38	C₂×C₇	C₄⋊Q₈	1	4	yes	direct product factor
39	C₂×C₇	C₂²×D₄	1	1	yes	characteristic
40	C₂×C₇	C₂²×Q₈	1	2	yes	—
41	C₂³	C₂³×C₇	1	1	yes	characteristic
42	Q₈	—	2	16	no	—
43	C₂×C₄	—	2	8	no	—
44	C₂×C₄	C₇×D₄	1	4	yes	—
45	C₂×C₄	C₇×Q₈	1	8	yes	complemented
46	C₂×C₄	C₂³×C₇	1	8	yes	—
47	C₂×C₄	C₂³×C₇	1	2	yes	—
48	C₂×C₄	C₂³×C₇	1	4	yes	—
49	C₇	C₂×C₄⋊Q₈	1	1	yes	characteristic, direct product factor, Sylow
50	C₂²	C₂×C₇×D₄	1	2	yes	—
51	C₂²	C₂×C₇×Q₈	1	4	yes	—
52	C₂²	C₂⁴×C₇	1	1	yes	characteristic
53	C₄	—	2	8	no	—
54	C₄	C₂×C₇×D₄	1	4	yes	—
55	C₄	C₂×C₇×Q₈	1	8	yes	complemented
56	C₂	C₇×C₄⋊Q₈	1	4	yes	direct product factor
57	C₂	C₂²×C₇×D₄	1	1	yes	characteristic
58	C₂	C₂²×C₇×Q₈	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₇×C₄⋊Q₈	C₂	direct (N × H)
12. C₂×C₄⋊Q₈	C₇	direct (N × H)
17. C₂×C₄×C₇	Q₈	semidirect
22. C₄⋊Q₈	C₂×C₇	direct (N × H)
30. C₄×C₇	C₂×Q₈	semidirect
38. C₂×C₇	C₄⋊Q₈	direct (N × H)
45. C₂×C₄	C₇×Q₈	semidirect
49. C₇	C₂×C₄⋊Q₈	direct (N × H)
55. C₄	C₂×C₇×Q₈	semidirect
56. C₂	C₇×C₄⋊Q₈	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×C₇×Q₈	2
C₇×C₄⋊Q₈	2
C₂×C₇×C₄⋊C₄	2
C₂×C₄²×C₇	2
C₂×C₄⋊Q₈	7

Subgroups — C2×C7×C4⋊Q8 #90552

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×C₄⋊Q₈ #90552