Subgroups — Q₃₂×Dic₁₈₁ #37535580

Order 23168.

150 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₁₆×Dic₁₈₁	C₂	1	2	yes	maximal
2	#26041105	C₂	1	1	yes	maximal, characteristic
3	#26041083	C₂	1	2	yes	maximal
4	C₁₆×Dic₁₈₁	C₂	1	1	yes	maximal, characteristic
5	C₂×Q₃₂×C₁₈₁	C₂	1	1	yes	maximal, characteristic
6	Q₈×Dic₁₈₁	—	2	2	no	—
7	C₂×#15668424	C₂²	1	1	yes	characteristic
8	#19153750	C₂²	1	2	yes	—
9	#19153740	—	2	2	no	—
10	C₈×Dic₁₈₁	C₂²	1	1	yes	characteristic
11	C₂×Q₁₆×C₁₈₁	C₂²	1	2	yes	—
12	Q₃₂×C₁₈₁	C₄	1	4	yes	complemented
13	C₂×C₁₆×C₁₈₁	C₂²	1	1	yes	characteristic
14	C₂×#13089678	D₄	1	1	yes	characteristic
15	C₄⋊Dic₁₈₁	—	2	2	no	—
16	C₄⋊Dic₁₈₁	—	4	2	no	—
17	C₄×Dic₁₈₁	—	4	2	no	—
18	C₄×Dic₁₈₁	D₄	1	1	yes	characteristic
19	#15668424	—	2	1	no	—
20	C₂×Q₈×C₁₈₁	—	2	2	no	—
21	Q₁₆×C₁₈₁	—	2	2	no	—
22	Q₁₆×C₁₈₁	C₂×C₄	1	4	yes	—
23	C₂×C₈×C₁₈₁	C₂³	1	1	yes	characteristic
24	C₁₆×C₁₈₁	C₂×C₄	1	2	yes	—
25	C₂×Dic₁₈₁	—	4	2	no	—
26	C₂×Dic₁₈₁	D₈	1	1	yes	characteristic
27	C₂×Dic₁₈₁	D₈	1	1	yes	characteristic
28	#13089678	—	2	1	no	—
29	Q₈×C₁₈₁	—	2	4	no	—
30	Q₈×C₁₈₁	—	4	2	no	—
31	C₂×C₄×C₁₈₁	—	4	2	no	—
32	C₂×C₄×C₁₈₁	C₂×D₄	1	1	yes	characteristic
33	C₈×C₁₈₁	C₂²×C₄	1	1	yes	characteristic
34	C₈×C₁₈₁	#41	1	1	yes	characteristic
35	C₂²×C₁₈₁	C₂×D₈	1	1	yes	characteristic
36	C₄×C₁₈₁	—	4	4	no	—
37	C₄×C₁₈₁	C₄×D₄	1	1	yes	characteristic
38	C₄×C₁₈₁	#135	1	1	yes	characteristic
39	Dic₁₈₁	—	2	1	no	—
40	Dic₁₈₁	—	8	2	no	—
41	Dic₁₈₁	Q₃₂	1	2	yes	direct product factor
42	C₂×C₁₈₁	C₄×D₈	1	1	yes	characteristic
43	C₂×C₁₈₁	C₂×Q₃₂	1	1	yes	characteristic
44	C₂×C₁₈₁	#508	1	1	yes	characteristic
45	C₁₈₁	C₄×Q₃₂	1	1	yes	characteristic, complemented, Sylow
46	C₄×Q₃₂	—	181	1	no	maximal, Sylow
47	C₂×Q₃₂	D₁₈₁	1	1	yes	characteristic
48	C₄×Q₁₆	—	181	2	no	—
49	#366	—	181	1	no	—
50	#358	—	181	2	no	—
51	C₄×C₁₆	—	181	1	no	—
52	C₂×Q₁₆	C₂×D₁₈₁	1	2	yes	—
53	C₄×Q₈	—	362	2	no	—
54	Q₃₂	Dic₁₈₁	1	4	yes	direct product factor
55	C₂×C₁₆	—	181	1	no	—
56	C₂×C₁₆	C₂×D₁₈₁	1	1	yes	characteristic
57	#107	—	181	2	no	—
58	#103	—	362	2	no	—
59	C₄×C₈	—	181	1	no	—
60	C₂×Q₈	—	2	2	no	—
61	Q₁₆	—	2	2	no	—
62	Q₁₆	C₂×Dic₁₈₁	1	4	yes	—
63	C₂×C₈	—	181	1	no	—
64	C₂×C₈	C₂²×D₁₈₁	1	1	yes	characteristic
65	C₄⋊C₄	—	362	2	no	—
66	C₄⋊C₄	—	724	2	no	—
67	C₄²	—	181	1	no	—
68	C₄²	—	724	2	no	—
69	C₁₆	—	362	1	no	—
70	C₁₆	C₂×Dic₁₈₁	1	2	yes	—
71	Q₈	—	2	4	no	—
72	Q₈	—	4	2	no	—
73	C₂×C₄	—	4	2	no	—
74	C₂×C₄	—	181	1	no	—
75	C₂×C₄	—	181	1	no	—
76	C₂×C₄	—	724	2	no	—
77	C₂×C₄	D₄×D₁₈₁	1	1	yes	characteristic
78	C₈	—	362	1	no	—
79	C₈	C₂²×Dic₁₈₁	1	1	yes	characteristic
80	C₈	#15668448	1	1	yes	characteristic
81	C₂²	D₈×D₁₈₁	1	1	yes	characteristic
82	C₄	—	4	4	no	—
83	C₄	—	362	1	no	—
84	C₄	—	1448	2	no	—
85	C₄	—	181	2	no	—
86	C₄	D₄×Dic₁₈₁	1	1	yes	characteristic
87	C₄	#19153835	1	1	yes	characteristic
88	C₂	D₈×Dic₁₈₁	1	1	yes	characteristic
89	C₂	Q₃₂×D₁₈₁	1	1	yes	characteristic
90	C₂	#26041712	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₈×D₁₈₁
commutator	C₈×C₁₈₁	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₁₈₁
Fitting	C₂×Q₃₂×C₁₈₁	C₂
socle, prime radical	C₂²×C₁₈₁	C₂×D₈
cosocle	C₂×C₈×C₁₈₁	C₂³
hypercenter	C₂×Q₃₂	D₁₈₁
hypocenter	C₁₈₁	C₄×Q₃₂
LCS	G ▷ C₈×C₁₈₁ ▷ C₄×C₁₈₁ ▷ C₂×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₃₂

Complements

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

N	H ≅ G/N	type
12. Q₃₂×C₁₈₁	C₄	semidirect
41. Dic₁₈₁	Q₃₂	direct (N × H)
45. C₁₈₁	C₄×Q₃₂	semidirect
54. Q₃₂	Dic₁₈₁	direct (N × H)

Maximal subgroups

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

subgroup	index
Q₁₆×Dic₁₈₁	2
#26041105	2
#26041083	2
C₁₆×Dic₁₈₁	2
C₂×Q₃₂×C₁₈₁	2
C₄×Q₃₂	181

Subgroups — Q32×Dic181 #37535580

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₃₂×Dic₁₈₁ #37535580