Subgroups — D₇×Q₃₂ #89689

Order 448.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₇×Q₁₆	C₂	1	2	yes	maximal
2	C₇×Q₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#6403	C₂	1	2	yes	maximal, complemented
4	Dic₅₆	C₂	1	1	yes	maximal, characteristic, complemented
5	D₇×C₁₆	C₂	1	1	yes	maximal, characteristic
6	Q₈×D₇	—	2	2	no	—
7	C₇×Q₁₆	C₂²	1	2	yes	—
8	#1144	—	2	2	no	—
9	Dic₂₈	C₂²	1	2	yes	—
10	C₈×D₇	C₂²	1	1	yes	characteristic
11	C₇×C₁₆	C₂²	1	1	yes	characteristic
12	C₇⋊C₁₆	C₂²	1	1	yes	characteristic
13	C₂×Q₃₂	—	7	1	no	maximal, Sylow
14	C₇×Q₈	—	2	2	no	—
15	C₄×D₇	—	4	2	no	—
16	C₄×D₇	D₄	1	1	yes	characteristic
17	Dic₁₄	—	2	2	no	—
18	Dic₁₄	—	4	2	no	—
19	C₇×C₈	C₂³	1	1	yes	characteristic
20	C₇⋊C₈	D₄	1	1	yes	characteristic
21	C₂×Q₁₆	—	7	2	no	—
22	Q₃₂	—	7	2	no	—
23	Q₃₂	—	7	1	no	—
24	Q₃₂	D₇	1	1	yes	characteristic, direct product factor
25	C₂×C₁₆	—	7	1	no	—
26	C₂×D₇	D₈	1	1	yes	characteristic
27	C₄×C₇	—	4	2	no	—
28	C₄×C₇	C₂×D₄	1	1	yes	characteristic
29	Dic₇	—	4	2	no	—
30	Dic₇	D₈	1	1	yes	characteristic
31	C₂×Q₈	—	14	2	no	—
32	Q₁₆	—	7	2	no	—
33	Q₁₆	—	14	2	no	—
34	Q₁₆	C₂×D₇	1	2	yes	—
35	C₂×C₈	—	7	1	no	—
36	C₁₆	—	7	1	no	—
37	C₁₆	C₂×D₇	1	1	yes	characteristic
38	C₂×C₇	C₂×D₈	1	1	yes	characteristic
39	D₇	Q₃₂	1	2	yes	direct product factor
40	Q₈	—	2	2	no	—
41	Q₈	—	14	2	no	—
42	Q₈	—	28	2	no	—
43	C₂×C₄	—	7	1	no	—
44	C₂×C₄	—	28	2	no	—
45	C₈	—	7	1	no	—
46	C₈	C₂²×D₇	1	1	yes	characteristic
47	C₇	C₂×Q₃₂	1	1	yes	characteristic, complemented, Sylow
48	C₂²	—	7	1	no	—
49	C₄	—	4	2	no	—
50	C₄	—	7	1	no	—
51	C₄	—	28	2	no	—
52	C₄	D₄×D₇	1	1	yes	characteristic
53	C₂	—	7	2	no	—
54	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×Q₃₂	C₂
socle	C₂×C₇	C₂×D₈
prime radical	C₂×D₇	D₈
hypercenter	Q₃₂	D₇
hypocenter	C₇	C₂×Q₃₂
LCS	G ▷ C₇×C₈ ▷ C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₃₂

Complements

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

N	H ≅ G/N	type
2. C₇×Q₃₂	C₂	semidirect
3. #6403	C₂	semidirect
4. Dic₅₆	C₂	semidirect
24. Q₃₂	D₇	direct (N × H)
39. D₇	Q₃₂	direct (N × H)
47. C₇	C₂×Q₃₂	semidirect

Maximal subgroups

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

subgroup	index
D₇×Q₁₆	2
C₇×Q₃₂	2
#6403	2
Dic₅₆	2
D₇×C₁₆	2
C₂×Q₃₂	7

Subgroups — D7×Q32 #89689

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇×Q₃₂ #89689