Subgroups — #37548879

Order 23168.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19153866	C₂	1	2	yes	maximal
2	C₁₆×Dic₁₈₁	C₂	1	1	yes	maximal, characteristic
3	#19153866	—	2	2	no	—
4	C₂×#15668424	C₂²	1	1	yes	characteristic
5	C₈×Dic₁₈₁	C₄	1	1	yes	characteristic
6	C₂×C₁₆×C₁₈₁	C₄	1	1	yes	characteristic
7	C₂×#13089678	C₈	1	1	yes	characteristic
8	C₄×Dic₁₈₁	C₈	1	1	yes	characteristic
9	#15668424	D₄	1	1	yes	characteristic
10	#15668424	Q₈	1	1	yes	characteristic
11	C₂×C₈×C₁₈₁	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₁₈₁	—	2	1	no	—
13	C₂×Dic₁₈₁	C₁₆	1	1	yes	characteristic
14	C₂×Dic₁₈₁	C₁₆	1	1	yes	characteristic
15	#13089678	—	2	1	no	—
16	C₂×C₄×C₁₈₁	C₂×C₈	1	1	yes	characteristic
17	C₈×C₁₈₁	C₄⋊C₄	1	1	yes	characteristic
18	C₈×C₁₈₁	M₁₆	1	1	yes	characteristic
19	C₂²×C₁₈₁	C₂×C₁₆	1	1	yes	characteristic
20	C₄×C₁₈₁	C₄⋊C₈	1	1	yes	characteristic
21	C₄×C₁₈₁	M₃₂	1	1	yes	characteristic
22	Dic₁₈₁	—	2	1	no	—
23	Dic₁₈₁	C₃₂	1	2	yes	complemented
24	C₂×C₁₈₁	C₄⋊C₁₆	1	1	yes	characteristic
25	C₂×C₁₈₁	C₂×C₃₂	1	1	yes	characteristic
26	C₂×C₁₈₁	M₆₄	1	1	yes	characteristic
27	C₁₈₁	C₄⋊C₃₂	1	1	yes	characteristic, complemented, Sylow
28	C₄⋊C₃₂	—	181	1	no	maximal, Sylow
29	C₂×C₃₂	—	181	2	no	—
30	C₄×C₁₆	—	181	1	no	—
31	C₂×C₁₆	—	181	1	no	—
32	C₂×C₁₆	#10624382	1	1	yes	characteristic
33	C₄×C₈	—	181	1	no	—
34	C₃₂	—	362	2	no	—
35	C₂×C₈	—	181	1	no	—
36	C₂×C₈	C₂×#10624382	1	1	yes	characteristic
37	C₄²	—	181	1	no	—
38	C₁₆	—	2	1	no	—
39	C₁₆	—	181	1	no	—
40	C₁₆	—	181	1	no	—
41	C₂×C₄	—	181	1	no	—
42	C₂×C₄	—	181	1	no	—
43	C₂×C₄	D₁₈₁⋊C₈	1	1	yes	characteristic
44	C₈	—	362	1	no	—
45	C₈	C₄⋊#10624382	1	1	yes	characteristic
46	C₈	#15668458	1	1	yes	characteristic
47	C₂²	D₁₈₁⋊C₁₆	1	1	yes	characteristic
48	C₄	—	362	1	no	—
49	C₄	—	181	2	no	—
50	C₄	#19153883	1	1	yes	characteristic
51	C₄	#19153891	1	1	yes	characteristic
52	C₂	#26042200	1	1	yes	characteristic
53	C₂	D₁₈₁⋊C₃₂	1	1	yes	characteristic
54	C₂	#26042212	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×#10624382
commutator	C₂×C₁₈₁	C₂×C₃₂
Fitting	C₂×C₁₆×C₁₈₁	C₄
socle, prime radical	C₂²×C₁₈₁	C₂×C₁₆
cosocle	C₂×#15668424	C₂²
hypercenter	C₂×C₁₆	#10624382
hypocenter	C₁₈₁	C₄⋊C₃₂
LCS	G ▷ C₂×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
23. Dic₁₈₁	C₃₂	semidirect
27. C₁₈₁	C₄⋊C₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19153866	2
C₁₆×Dic₁₈₁	2
C₄⋊C₃₂	181