Subgroups — Q₁₆×#3866 #14558571

Order 2368.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×#3866	C₂	1	2	yes	maximal
2	#11924605	C₂	1	1	yes	maximal, characteristic
3	#11924599	C₂	1	2	yes	maximal
4	C₈×#3866	C₂	1	1	yes	maximal, characteristic
5	Q₁₆×D₃₇	C₂	1	1	yes	maximal, characteristic
6	Q₈×D₃₇	C₂²	1	2	yes	—
7	C₄⋊#3866	—	2	2	no	—
8	C₄⋊#3866	C₂²	1	2	yes	—
9	C₄×#3866	—	2	2	no	—
10	C₄×#3866	C₂²	1	1	yes	characteristic
11	D₃₇⋊C₈	C₂²	1	1	yes	characteristic
12	Q₁₆×C₃₇	C₄	1	1	yes	characteristic, complemented
13	#10596942	C₄	1	2	yes	complemented
14	Dic₁₄₈	C₄	1	1	yes	characteristic, complemented
15	C₈×D₃₇	C₂²	1	1	yes	characteristic
16	C₂×#3866	—	2	2	no	—
17	C₂×#3866	D₄	1	1	yes	characteristic
18	C₂×#3866	D₄	1	1	yes	characteristic
19	Q₈×C₃₇	C₂×C₄	1	2	yes	—
20	C₄×D₃₇	—	2	2	no	—
21	C₄×D₃₇	C₂³	1	1	yes	characteristic
22	Dic₇₄	—	2	2	no	—
23	Dic₇₄	C₂×C₄	1	2	yes	—
24	#64438	—	2	1	no	—
25	C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
26	#64436	C₂×C₄	1	1	yes	characteristic
27	C₂×D₃₇	C₂×D₄	1	1	yes	characteristic
28	#3866	—	2	1	no	—
29	#3866	—	4	2	no	—
30	#3866	Q₁₆	1	2	yes	direct product factor
31	C₄×C₃₇	—	2	2	no	—
32	C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
33	Dic₃₇	—	2	2	no	—
34	Dic₃₇	#41	1	1	yes	characteristic
35	C₂×C₃₇	C₄×D₄	1	1	yes	characteristic
36	D₃₇	C₂×Q₁₆	1	1	yes	characteristic
37	D₃₇	#135	1	1	yes	characteristic
38	C₄×Q₁₆	—	37	1	no	maximal, Sylow
39	C₃₇	C₄×Q₁₆	1	1	yes	characteristic, complemented, Sylow
40	C₂×Q₁₆	—	37	1	no	—
41	C₄×Q₈	—	37	2	no	—
42	#107	—	37	1	no	—
43	#103	—	37	2	no	—
44	C₄×C₈	—	37	1	no	—
45	C₂×Q₈	—	37	2	no	—
46	Q₁₆	—	37	2	no	—
47	Q₁₆	—	37	1	no	—
48	Q₁₆	#3866	1	1	yes	characteristic, direct product factor
49	C₂×C₈	—	37	1	no	—
50	C₂×C₈	—	37	1	no	—
51	C₄⋊C₄	—	37	2	no	—
52	C₄⋊C₄	—	74	2	no	—
53	C₄²	—	37	1	no	—
54	C₄²	—	74	2	no	—
55	Q₈	—	37	2	no	—
56	Q₈	—	74	2	no	—
57	Q₈	C₂×#3866	1	2	yes	—
58	C₂×C₄	—	37	1	no	—
59	C₂×C₄	—	37	1	no	—
60	C₂×C₄	—	37	1	no	—
61	C₂×C₄	—	74	2	no	—
62	C₂×C₄	—	74	2	no	—
63	C₈	—	37	1	no	—
64	C₈	—	74	1	no	—
65	C₈	C₂×#3866	1	1	yes	characteristic
66	C₂²	—	37	1	no	—
67	C₄	—	2	2	no	—
68	C₄	—	37	2	no	—
69	C₄	—	37	1	no	—
70	C₄	—	74	1	no	—
71	C₄	—	74	2	no	—
72	C₄	—	148	2	no	—
73	C₄	C₂²×#3866	1	1	yes	characteristic
74	C₂	—	37	1	no	—
75	C₂	—	37	1	no	—
76	C₂	D₄×#3866	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×#3866
commutator	C₄×C₃₇	C₂²×C₄
Frattini	C₄	C₂²×#3866
Fitting	Q₁₆×C₃₇	C₄
socle	C₂×C₃₇	C₄×D₄
prime radical	C₂×D₃₇	C₂×D₄
cosocle	C₄×D₃₇	C₂³
hypercenter	Q₁₆	#3866
hypocenter	C₃₇	C₄×Q₁₆
LCS	G ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
12. Q₁₆×C₃₇	C₄	semidirect
13. #10596942	C₄	semidirect
14. Dic₁₄₈	C₄	semidirect
30. #3866	Q₁₆	direct (N × H)
39. C₃₇	C₄×Q₁₆	semidirect
48. Q₁₆	#3866	direct (N × H)

Maximal subgroups

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

subgroup	index
Q₈×#3866	2
#11924605	2
#11924599	2
C₈×#3866	2
Q₁₆×D₃₇	2
C₄×Q₁₆	37

Subgroups — Q16×#3866 #14558571

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₁₆×#3866 #14558571