Subgroups — D₃₂×D₁₀₇ #28338757

Order 13696.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₆×D₁₀₇	C₂	1	2	yes	maximal, complemented
2	D₃₄₂₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#20292462	C₂	1	2	yes	maximal, complemented
4	C₃₂×D₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
5	D₃₂×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
6	D₈×D₁₀₇	—	2	2	no	—
7	D₁₇₁₂	C₂²	1	2	yes	complemented
8	#16812050	—	2	2	no	—
9	C₁₆×D₁₀₇	C₂²	1	1	yes	characteristic
10	C₁₀₇⋊C₃₂	C₂²	1	1	yes	characteristic, complemented
11	D₁₆×C₁₀₇	C₂²	1	2	yes	complemented
12	C₃₂×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
13	D₄×D₁₀₇	—	4	2	no	—
14	D₈₅₆	—	2	2	no	—
15	#13133803	—	4	2	no	—
16	C₈×D₁₀₇	D₄	1	1	yes	characteristic
17	C₁₀₇⋊C₁₆	D₄	1	1	yes	characteristic
18	D₈×C₁₀₇	—	2	2	no	—
19	C₁₆×C₁₀₇	C₂³	1	1	yes	characteristic
20	C₂²×D₁₀₇	—	8	2	no	—
21	D₄×C₁₀₇	—	4	2	no	—
22	C₂²⋊D₁₀₇	—	8	2	no	—
23	D₄₂₈	—	4	2	no	—
24	C₄×D₁₀₇	D₈	1	1	yes	characteristic
25	C₈×C₁₀₇	C₂×D₄	1	1	yes	characteristic
26	C₁₀₇⋊C₈	D₈	1	1	yes	characteristic
27	C₂²×C₁₀₇	—	8	2	no	—
28	C₂×D₁₀₇	—	8	2	no	—
29	C₂×D₁₀₇	—	16	4	no	—
30	C₂×D₁₀₇	D₁₆	1	1	yes	characteristic
31	C₄×C₁₀₇	C₂×D₈	1	1	yes	characteristic
32	Dic₁₀₇	D₁₆	1	1	yes	characteristic
33	C₂×C₁₀₇	—	16	2	no	—
34	C₂×C₁₀₇	C₂×D₁₆	1	1	yes	characteristic
35	D₁₀₇	—	16	2	no	—
36	D₁₀₇	D₃₂	1	2	yes	direct product factor
37	C₂×D₃₂	—	107	1	no	maximal, Sylow
38	C₁₀₇	C₂×D₃₂	1	1	yes	characteristic, complemented, Sylow
39	C₂×D₁₆	—	107	2	no	—
40	D₃₂	—	107	2	no	—
41	D₃₂	—	107	1	no	—
42	D₃₂	D₁₀₇	1	1	yes	characteristic, direct product factor
43	C₂×C₃₂	—	107	1	no	—
44	C₂×D₈	—	214	2	no	—
45	D₁₆	—	107	2	no	—
46	D₁₆	—	214	2	no	—
47	D₁₆	C₂×D₁₀₇	1	2	yes	complemented
48	C₂×C₁₆	—	107	1	no	—
49	C₃₂	—	107	1	no	—
50	C₃₂	C₂×D₁₀₇	1	1	yes	characteristic, complemented
51	C₂×D₄	—	428	2	no	—
52	D₈	—	2	2	no	—
53	D₈	—	428	2	no	—
54	D₈	—	214	2	no	—
55	C₂×C₈	—	107	1	no	—
56	C₁₆	—	107	1	no	—
57	C₁₆	C₂²×D₁₀₇	1	1	yes	characteristic
58	C₂³	—	856	2	no	—
59	D₄	—	4	2	no	—
60	D₄	—	856	2	no	—
61	D₄	—	428	2	no	—
62	C₂×C₄	—	107	1	no	—
63	C₈	—	107	1	no	—
64	C₈	D₄×D₁₀₇	1	1	yes	characteristic
65	C₂²	—	8	2	no	—
66	C₂²	—	856	2	no	—
67	C₂²	—	107	1	no	—
68	C₂²	—	1712	4	no	—
69	C₄	—	107	1	no	—
70	C₄	D₈×D₁₀₇	1	1	yes	characteristic
71	C₂	—	16	2	no	—
72	C₂	—	107	2	no	—
73	C₂	—	1712	2	no	—
74	C₂	D₁₆×D₁₀₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₁₆×D₁₀₇
commutator, cosocle	C₁₆×C₁₀₇	C₂³
Frattini	C₁₆	C₂²×D₁₀₇
Fitting	D₃₂×C₁₀₇	C₂
socle	C₂×C₁₀₇	C₂×D₁₆
hypercenter	D₃₂	D₁₀₇
hypocenter	C₁₀₇	C₂×D₃₂
LCS	G ▷ C₁₆×C₁₀₇ ▷ C₈×C₁₀₇ ▷ C₄×C₁₀₇ ▷ C₂×C₁₀₇ ▷ C₁₀₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ D₃₂

Complements

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

N	H ≅ G/N	type
1. D₁₆×D₁₀₇	C₂	semidirect
2. D₃₄₂₄	C₂	semidirect
3. #20292462	C₂	semidirect
4. C₃₂×D₁₀₇	C₂	semidirect
5. D₃₂×C₁₀₇	C₂	semidirect
7. D₁₇₁₂	C₂²	semidirect
10. C₁₀₇⋊C₃₂	C₂²	semidirect
11. D₁₆×C₁₀₇	C₂²	semidirect
12. C₃₂×C₁₀₇	C₂²	semidirect
36. D₁₀₇	D₃₂	direct (N × H)
38. C₁₀₇	C₂×D₃₂	semidirect
42. D₃₂	D₁₀₇	direct (N × H)
47. D₁₆	C₂×D₁₀₇	semidirect
50. C₃₂	C₂×D₁₀₇	semidirect

Maximal subgroups

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

subgroup	index
D₁₆×D₁₀₇	2
D₃₄₂₄	2
#20292462	2
C₃₂×D₁₀₇	2
D₃₂×C₁₀₇	2
C₂×D₃₂	107

Subgroups — D32×D107 #28338757

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃₂×D₁₀₇ #28338757