Subgroups — C₄×C₇×Q₁₆ #90085

Order 448.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×Q₁₆	C₂	1	1	yes	maximal, characteristic
2	C₄×C₇×Q₈	C₂	1	2	yes	maximal
3	C₇×#107	C₂	1	1	yes	maximal, characteristic
4	C₇×#103	C₂	1	2	yes	maximal
5	C₄×C₇×C₈	C₂	1	1	yes	maximal, characteristic
6	C₂×C₇×Q₈	C₂²	1	2	yes	—
7	C₇×Q₁₆	C₄	1	4	yes	direct product factor
8	C₂×C₇×C₈	C₂²	1	1	yes	characteristic
9	C₂×C₇×C₈	C₂²	1	1	yes	characteristic
10	C₇×C₄⋊C₄	—	2	2	no	—
11	C₇×C₄⋊C₄	C₂²	1	2	yes	—
12	C₄²×C₇	—	2	2	no	—
13	C₄²×C₇	C₂²	1	1	yes	characteristic
14	C₄×Q₁₆	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₇×Q₈	—	2	2	no	—
16	C₇×Q₈	C₂×C₄	1	4	yes	—
17	C₂×C₄×C₇	—	2	2	no	—
18	C₂×C₄×C₇	—	2	2	no	—
19	C₂×C₄×C₇	D₄	1	1	yes	characteristic
20	C₂×C₄×C₇	D₄	1	1	yes	characteristic
21	C₂×C₄×C₇	C₂³	1	1	yes	characteristic
22	C₇×C₈	—	2	1	no	—
23	C₇×C₈	C₂×C₄	1	2	yes	—
24	C₂×Q₁₆	C₂×C₇	1	1	yes	characteristic
25	C₄×Q₈	C₂×C₇	1	2	yes	—
26	#107	C₂×C₇	1	1	yes	characteristic
27	#103	C₂×C₇	1	2	yes	—
28	C₄×C₈	C₂×C₇	1	1	yes	characteristic
29	C₂²×C₇	C₂×D₄	1	1	yes	characteristic
30	C₄×C₇	—	2	4	no	—
31	C₄×C₇	—	2	1	no	—
32	C₄×C₇	—	4	2	no	—
33	C₄×C₇	Q₁₆	1	2	yes	direct product factor
34	C₄×C₇	C₂²×C₄	1	1	yes	characteristic
35	C₄×C₇	#41	1	1	yes	characteristic
36	C₂×Q₈	C₂²×C₇	1	2	yes	—
37	Q₁₆	C₄×C₇	1	4	yes	direct product factor
38	C₂×C₈	C₂²×C₇	1	1	yes	characteristic
39	C₂×C₈	C₂²×C₇	1	1	yes	characteristic
40	C₄⋊C₄	—	2	2	no	—
41	C₄⋊C₄	C₂²×C₇	1	2	yes	—
42	C₄²	—	2	2	no	—
43	C₄²	C₂²×C₇	1	1	yes	characteristic
44	C₂×C₇	C₄×D₄	1	1	yes	characteristic
45	C₂×C₇	C₂×Q₁₆	1	1	yes	characteristic
46	C₂×C₇	#135	1	1	yes	characteristic
47	Q₈	—	2	2	no	—
48	Q₈	C₂×C₄×C₇	1	4	yes	—
49	C₂×C₄	—	2	2	no	—
50	C₂×C₄	—	2	2	no	—
51	C₂×C₄	C₇×D₄	1	1	yes	characteristic
52	C₂×C₄	C₇×D₄	1	1	yes	characteristic
53	C₂×C₄	C₂³×C₇	1	1	yes	characteristic
54	C₈	—	2	1	no	—
55	C₈	C₂×C₄×C₇	1	2	yes	—
56	C₇	C₄×Q₁₆	1	1	yes	characteristic, direct product factor, Sylow
57	C₂²	C₂×C₇×D₄	1	1	yes	characteristic
58	C₄	—	2	4	no	—
59	C₄	—	2	1	no	—
60	C₄	—	4	2	no	—
61	C₄	C₇×Q₁₆	1	2	yes	direct product factor
62	C₄	C₂²×C₄×C₇	1	1	yes	characteristic
63	C₄	C₇×#41	1	1	yes	characteristic
64	C₂	C₄×C₇×D₄	1	1	yes	characteristic
65	C₂	C₂×C₇×Q₁₆	1	1	yes	characteristic
66	C₂	C₇×#135	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	D₄
commutator	C₄	C₂²×C₄×C₇
Frattini, cosocle	C₂×C₄	C₂³×C₇
socle, prime radical	C₂²×C₇	C₂×D₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
7. C₇×Q₁₆	C₄	direct (N × H)
14. C₄×Q₁₆	C₇	direct (N × H)
33. C₄×C₇	Q₁₆	direct (N × H)
37. Q₁₆	C₄×C₇	direct (N × H)
56. C₇	C₄×Q₁₆	direct (N × H)
61. C₄	C₇×Q₁₆	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₇×Q₁₆	2
C₄×C₇×Q₈	2
C₇×#107	2
C₇×#103	2
C₄×C₇×C₈	2
C₄×Q₁₆	7

Subgroups — C4×C7×Q16 #90085

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₇×Q₁₆ #90085