Subgroups — #26042148

Order 11584.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₈₁⋊M₁₆	C₂	1	2	yes	maximal
2	C₂×#15668432	C₂	1	1	yes	maximal, characteristic
3	#15668459	—	2	2	no	—
4	#15668458	—	2	2	no	—
5	D₁₈₁⋊C₈	C₄	1	4	yes	—
6	C₂×C₄×D₁₈₁	C₂²	1	1	yes	characteristic
7	#15668432	—	2	2	no	—
8	C₂×#13089678	C₄	1	1	yes	characteristic
9	C₂×C₈×C₁₈₁	C₄	1	1	yes	characteristic
10	#13089685	—	2	4	no	—
11	C₂²×D₁₈₁	Q₈	1	1	yes	characteristic
12	C₂×Dic₁₈₁	D₄	1	1	yes	characteristic
13	C₄×D₁₈₁	C₂×C₄	1	2	yes	—
14	C₄×D₁₈₁	D₄	1	2	yes	—
15	#13089678	—	2	1	no	—
16	C₂×C₄×C₁₈₁	C₂×C₄	1	1	yes	characteristic
17	C₈×C₁₈₁	—	2	1	no	—
18	C₂²×C₁₈₁	C₄⋊C₄	1	1	yes	characteristic
19	C₂×D₁₈₁	—	4	1	no	—
20	C₂×D₁₈₁	C₄⋊C₄	1	2	yes	—
21	C₄×C₁₈₁	C₄²	1	1	yes	characteristic
22	C₄×C₁₈₁	C₂²⋊C₄	1	1	yes	characteristic
23	Dic₁₈₁	C₂²⋊C₄	1	2	yes	—
24	C₂×C₁₈₁	—	2	1	no	—
25	C₂×C₁₈₁	#95	1	1	yes	characteristic
26	D₁₈₁	—	2	2	no	—
27	C₁₈₁	#338	1	1	yes	characteristic, complemented, Sylow
28	#338	—	181	1	no	maximal, Sylow
29	C₂×M₁₆	—	181	2	no	—
30	C₂×M₁₆	—	181	1	no	—
31	C₂²×C₄	—	181	1	no	—
32	M₁₆	—	362	2	no	—
33	M₁₆	—	362	2	no	—
34	M₁₆	—	362	2	no	—
35	C₂×C₈	—	181	4	no	—
36	C₂×C₈	—	181	1	no	—
37	C₂×C₈	#10624382	1	1	yes	characteristic
38	C₂³	—	181	1	no	—
39	C₂×C₄	—	181	1	no	—
40	C₂×C₄	—	181	2	no	—
41	C₂×C₄	—	181	2	no	—
42	C₂×C₄	C₂×#10624382	1	1	yes	characteristic
43	C₈	—	2	1	no	—
44	C₈	—	362	4	no	—
45	C₈	—	362	1	no	—
46	C₂²	—	181	2	no	—
47	C₂²	—	724	1	no	—
48	C₂²	C₄⋊#10624382	1	1	yes	characteristic
49	C₄	—	181	2	no	—
50	C₄	C₄×#10624382	1	1	yes	characteristic
51	C₄	C₂²⋊#10624382	1	1	yes	characteristic
52	C₂	—	2	1	no	—
53	C₂	—	362	2	no	—
54	C₂	(C₂×#10624382)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄×#10624382
commutator	C₄×C₁₈₁	C₄²
Frattini	C₂×C₄	C₂×#10624382
Fitting	C₂×C₈×C₁₈₁	C₄
socle	C₂×C₁₈₁	#95
prime radical	C₂²×D₁₈₁	Q₈
cosocle	C₂×C₄×D₁₈₁	C₂²
hypercenter	C₂×C₈	#10624382
hypocenter	C₁₈₁	#338
LCS	G ▷ C₄×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
27. C₁₈₁	#338	semidirect

Maximal subgroups

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

subgroup	index
D₁₈₁⋊M₁₆	2
C₂×#15668432	2
#338	181