Subgroups — #37548756

Order 23168.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26042201	C₂	1	2	yes	maximal
2	C₁₆×Dic₁₈₁	C₂	1	1	yes	maximal, characteristic
3	#19153890	—	2	2	no	—
4	C₂×#15668424	C₄	1	1	yes	characteristic
5	C₈×Dic₁₈₁	C₂²	1	1	yes	characteristic
6	C₂×C₁₆×C₁₈₁	C₄	1	1	yes	characteristic
7	#15668452	—	4	2	no	—
8	C₂×#13089678	D₄	1	1	yes	characteristic
9	C₄×Dic₁₈₁	Q₈	1	1	yes	characteristic
10	#15668424	—	2	1	no	—
11	C₂×C₈×C₁₈₁	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₁₈₁	C₈	1	2	yes	—
13	C₂×Dic₁₈₁	—	2	1	no	—
14	#13089678	D₈	1	1	yes	characteristic
15	#13089678	Q₁₆	1	1	yes	characteristic
16	C₂×C₄×C₁₈₁	C₄⋊C₄	1	1	yes	characteristic
17	C₈×C₁₈₁	C₂×C₈	1	1	yes	characteristic
18	C₈×C₁₈₁	M₁₆	1	1	yes	characteristic
19	C₂²×C₁₈₁	#108	1	1	yes	characteristic
20	C₄×C₁₈₁	C₄⋊C₈	1	1	yes	characteristic
21	C₄×C₁₈₁	#107	1	1	yes	characteristic
22	Dic₁₈₁	—	2	2	no	—
23	C₂×C₁₈₁	—	2	1	no	—
24	C₂×C₁₈₁	#335	1	1	yes	characteristic
25	C₁₈₁	#1373	1	1	yes	characteristic, complemented, Sylow
26	#1373	—	181	1	no	maximal, Sylow
27	#364	—	181	2	no	—
28	C₄×C₁₆	—	181	1	no	—
29	M₃₂	—	362	2	no	—
30	C₂×C₁₆	—	181	1	no	—
31	C₂×C₁₆	#10624382	1	1	yes	characteristic
32	C₄×C₈	—	181	1	no	—
33	C₂×C₈	—	181	1	no	—
34	C₂×C₈	C₂×#10624382	1	1	yes	characteristic
35	C₄²	—	181	1	no	—
36	C₁₆	—	362	1	no	—
37	C₁₆	—	724	2	no	—
38	C₁₆	#13089685	1	2	yes	—
39	C₂×C₄	—	362	1	no	—
40	C₂×C₄	C₄⋊#10624382	1	1	yes	characteristic
41	C₈	—	181	1	no	—
42	C₈	—	181	1	no	—
43	C₈	C₂×#13089685	1	1	yes	characteristic
44	C₈	#15668459	1	1	yes	characteristic
45	C₂²	#19153887	1	1	yes	characteristic
46	C₄	—	362	2	no	—
47	C₄	C₄⋊#13089685	1	1	yes	characteristic
48	C₄	#19153885	1	1	yes	characteristic
49	C₂	—	2	1	no	—
50	C₂	#26042142	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#19153885
commutator	C₈×C₁₈₁	C₂×C₈
Frattini	C₂×C₈	C₂×#10624382
Fitting	C₂×C₁₆×C₁₈₁	C₄
socle	C₂×C₁₈₁	#335
prime radical	C₂²×C₁₈₁	#108
cosocle	C₈×Dic₁₈₁	C₂²
hypercenter	C₂×C₁₆	#10624382
hypocenter	C₁₈₁	#1373
LCS	G ▷ C₈×C₁₈₁ ▷ C₄×C₁₈₁ ▷ C₂×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
25. C₁₈₁	#1373	semidirect

Maximal subgroups

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

subgroup	index
#26042201	2
C₁₆×Dic₁₈₁	2
#1373	181