Subgroups — D₇×D₁₆ #89682

Order 448.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₇×D₈	C₂	1	2	yes	maximal, complemented
2	C₇×D₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#6400	C₂	1	2	yes	maximal, complemented
4	D₁₁₂	C₂	1	1	yes	maximal, characteristic, complemented
5	D₇×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	D₄×D₇	—	2	2	no	—
7	C₇×D₈	C₂²	1	2	yes	complemented
8	#1141	—	2	2	no	—
9	D₅₆	C₂²	1	2	yes	complemented
10	C₈×D₇	C₂²	1	1	yes	characteristic
11	C₇×C₁₆	C₂²	1	1	yes	characteristic, complemented
12	C₇⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
13	C₂×D₁₆	—	7	1	no	maximal, Sylow
14	C₂²×D₇	—	4	2	no	—
15	C₇×D₄	—	2	2	no	—
16	C₂²⋊D₇	—	4	2	no	—
17	D₂₈	—	2	2	no	—
18	C₄×D₇	D₄	1	1	yes	characteristic
19	C₇×C₈	C₂³	1	1	yes	characteristic
20	C₇⋊C₈	D₄	1	1	yes	characteristic
21	C₂×D₈	—	7	2	no	—
22	D₁₆	—	7	2	no	—
23	D₁₆	—	7	1	no	—
24	D₁₆	D₇	1	1	yes	characteristic, direct product factor
25	C₂×C₁₆	—	7	1	no	—
26	C₂²×C₇	—	4	2	no	—
27	C₂×D₇	—	4	2	no	—
28	C₂×D₇	—	8	4	no	—
29	C₂×D₇	D₈	1	1	yes	characteristic
30	C₄×C₇	C₂×D₄	1	1	yes	characteristic
31	Dic₇	D₈	1	1	yes	characteristic
32	C₂×D₄	—	14	2	no	—
33	D₈	—	7	2	no	—
34	D₈	—	14	2	no	—
35	D₈	C₂×D₇	1	2	yes	complemented
36	C₂×C₈	—	7	1	no	—
37	C₁₆	—	7	1	no	—
38	C₁₆	C₂×D₇	1	1	yes	characteristic, complemented
39	C₂×C₇	—	8	2	no	—
40	C₂×C₇	C₂×D₈	1	1	yes	characteristic
41	D₇	—	8	2	no	—
42	D₇	D₁₆	1	2	yes	direct product factor
43	C₂³	—	28	2	no	—
44	D₄	—	2	2	no	—
45	D₄	—	14	2	no	—
46	D₄	—	28	2	no	—
47	C₂×C₄	—	7	1	no	—
48	C₈	—	7	1	no	—
49	C₈	C₂²×D₇	1	1	yes	characteristic
50	C₇	C₂×D₁₆	1	1	yes	characteristic, complemented, Sylow
51	C₂²	—	4	2	no	—
52	C₂²	—	7	1	no	—
53	C₂²	—	28	2	no	—
54	C₂²	—	56	4	no	—
55	C₄	—	7	1	no	—
56	C₄	D₄×D₇	1	1	yes	characteristic
57	C₂	—	7	2	no	—
58	C₂	—	8	2	no	—
59	C₂	—	56	2	no	—
60	C₂	D₇×D₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₇×D₈
commutator, cosocle	C₇×C₈	C₂³
Frattini	C₈	C₂²×D₇
Fitting	C₇×D₁₆	C₂
socle	C₂×C₇	C₂×D₈
hypercenter	D₁₆	D₇
hypocenter	C₇	C₂×D₁₆
LCS	G ▷ C₇×C₈ ▷ C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ D₁₆

Complements

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

N	H ≅ G/N	type
1. D₇×D₈	C₂	semidirect
2. C₇×D₁₆	C₂	semidirect
3. #6400	C₂	semidirect
4. D₁₁₂	C₂	semidirect
5. D₇×C₁₆	C₂	semidirect
7. C₇×D₈	C₂²	semidirect
9. D₅₆	C₂²	semidirect
11. C₇×C₁₆	C₂²	semidirect
12. C₇⋊C₁₆	C₂²	semidirect
24. D₁₆	D₇	direct (N × H)
35. D₈	C₂×D₇	semidirect
38. C₁₆	C₂×D₇	semidirect
42. D₇	D₁₆	direct (N × H)
50. C₇	C₂×D₁₆	semidirect

Maximal subgroups

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

subgroup	index
D₇×D₈	2
C₇×D₁₆	2
#6400	2
D₁₁₂	2
D₇×C₁₆	2
C₂×D₁₆	7

Subgroups — D7×D16 #89682

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇×D₁₆ #89682