Subgroups — #37548827

Order 23168.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₈₁⋊C₃₂	C₂	1	1	yes	maximal, characteristic
2	C₁₆×#10624382	C₂	1	1	yes	maximal, characteristic
3	C₃₂×D₁₈₁	C₂	1	1	yes	maximal, characteristic
4	D₁₈₁⋊C₁₆	C₄	1	1	yes	characteristic
5	C₈×#10624382	C₄	1	1	yes	characteristic
6	#19153866	C₄	1	2	yes	complemented
7	C₁₆×D₁₈₁	C₂²	1	1	yes	characteristic
8	#19153722	C₄	1	1	yes	characteristic, complemented
9	C₃₂×C₁₈₁	C₄	1	1	yes	characteristic, complemented
10	D₁₈₁⋊C₈	C₈	1	1	yes	characteristic
11	C₄×#10624382	C₈	1	1	yes	characteristic
12	#15668452	C₈	1	2	yes	—
13	C₈×D₁₈₁	C₂×C₄	1	1	yes	characteristic
14	#15668424	C₂×C₄	1	1	yes	characteristic
15	C₁₆×C₁₈₁	C₂×C₄	1	1	yes	characteristic
16	C₂×#10624382	C₁₆	1	2	yes	—
17	#13089685	C₁₆	1	2	yes	—
18	C₄×D₁₈₁	C₂×C₈	1	1	yes	characteristic
19	#13089678	C₂×C₈	1	1	yes	characteristic
20	C₈×C₁₈₁	C₄²	1	1	yes	characteristic
21	C₂×D₁₈₁	C₂×C₁₆	1	1	yes	characteristic
22	#10624382	—	2	2	no	—
23	C₄×C₁₈₁	C₄×C₈	1	1	yes	characteristic
24	Dic₁₈₁	C₂×C₁₆	1	1	yes	characteristic
25	C₂×C₁₈₁	C₄×C₁₆	1	1	yes	characteristic
26	D₁₈₁	M₆₄	1	2	yes	—
27	C₁₈₁	#1397	1	1	yes	characteristic, complemented, Sylow
28	#1397	—	181	1	no	maximal, Sylow
29	C₂×C₃₂	—	181	1	no	—
30	C₂×C₃₂	—	181	1	no	—
31	C₄×C₁₆	—	181	1	no	—
32	C₂×C₁₆	—	181	1	no	—
33	C₂×C₁₆	—	181	1	no	—
34	C₄×C₈	—	181	1	no	—
35	C₃₂	—	181	2	no	—
36	C₃₂	—	181	1	no	—
37	C₃₂	#10624382	1	1	yes	characteristic, complemented
38	C₂×C₈	—	181	1	no	—
39	C₂×C₈	—	181	1	no	—
40	C₄²	—	181	1	no	—
41	C₁₆	—	181	2	no	—
42	C₁₆	—	181	1	no	—
43	C₁₆	C₂×#10624382	1	1	yes	characteristic
44	C₂×C₄	—	181	2	no	—
45	C₂×C₄	—	181	1	no	—
46	C₈	—	181	2	no	—
47	C₈	—	181	1	no	—
48	C₈	C₄×#10624382	1	1	yes	characteristic
49	C₂²	—	181	1	no	—
50	C₄	—	362	2	no	—
51	C₄	—	181	1	no	—
52	C₄	C₈×#10624382	1	1	yes	characteristic
53	C₂	—	181	2	no	—
54	C₂	C₁₆×#10624382	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₁₆	C₂×#10624382
commutator, socle	C₂×C₁₈₁	C₄×C₁₆
Fitting	C₃₂×C₁₈₁	C₄
prime radical	C₂×D₁₈₁	C₂×C₁₆
cosocle	C₁₆×D₁₈₁	C₂²
hypercenter	C₃₂	#10624382
hypocenter	C₁₈₁	#1397
LCS	G ▷ C₂×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₁₆ ◁ C₃₂

Complements

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

N	H ≅ G/N	type
6. #19153866	C₄	semidirect
8. #19153722	C₄	semidirect
9. C₃₂×C₁₈₁	C₄	semidirect
27. C₁₈₁	#1397	semidirect
37. C₃₂	#10624382	semidirect

Maximal subgroups

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

subgroup	index
D₁₈₁⋊C₃₂	2
C₁₆×#10624382	2
C₃₂×D₁₈₁	2
#1397	181