Subgroups — #26042198

Order 11584.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19153891	C₂	1	1	yes	maximal, characteristic
2	#19153886	C₂	1	1	yes	maximal, characteristic
3	Q₁₆×D₁₈₁	C₂	1	1	yes	maximal, characteristic
4	#15668459	—	2	1	no	—
5	#15668452	—	2	1	no	—
6	Q₈×D₁₈₁	—	2	1	no	—
7	Dic₇₂₄	C₄	1	1	yes	characteristic
8	#15668439	—	2	1	no	—
9	C₈×D₁₈₁	C₂²	1	1	yes	characteristic
10	Q₁₆×C₁₈₁	C₄	1	1	yes	characteristic
11	#13089685	—	4	1	no	—
12	Dic₃₆₂	—	2	1	no	—
13	Dic₃₆₂	—	4	1	no	—
14	C₄×D₁₈₁	—	4	1	no	—
15	C₄×D₁₈₁	D₄	1	1	yes	characteristic
16	#13089678	D₄	1	1	yes	characteristic
17	Q₈×C₁₈₁	—	2	1	no	—
18	C₈×C₁₈₁	C₂×C₄	1	1	yes	characteristic
19	C₂×D₁₈₁	SD₁₆	1	1	yes	characteristic
20	C₄×C₁₈₁	—	4	1	no	—
21	C₄×C₁₈₁	C₂²⋊C₄	1	1	yes	characteristic
22	Dic₁₈₁	—	4	1	no	—
23	Dic₁₈₁	D₈	1	1	yes	characteristic
24	C₂×C₁₈₁	#102	1	1	yes	characteristic
25	D₁₈₁	—	2	1	no	—
26	C₁₈₁	#362	1	1	yes	characteristic, complemented, Sylow
27	#362	—	181	1	no	maximal, Sylow
28	C₂×Q₁₆	—	181	1	no	—
29	M₃₂	—	181	1	no	—
30	#108	—	181	1	no	—
31	C₂×Q₈	—	362	1	no	—
32	Q₁₆	—	362	1	no	—
33	Q₁₆	—	181	1	no	—
34	Q₁₆	#10624382	1	1	yes	characteristic
35	M₁₆	—	362	1	no	—
36	C₂×C₈	—	181	1	no	—
37	C₁₆	—	362	1	no	—
38	Q₈	—	2	1	no	—
39	Q₈	—	362	1	no	—
40	Q₈	—	724	1	no	—
41	C₂×C₄	—	181	1	no	—
42	C₂×C₄	—	724	1	no	—
43	C₈	—	181	1	no	—
44	C₈	—	724	1	no	—
45	C₈	C₂×#10624382	1	1	yes	characteristic
46	C₂²	—	181	1	no	—
47	C₄	—	4	1	no	—
48	C₄	—	181	1	no	—
49	C₄	—	724	1	no	—
50	C₄	C₂²⋊#10624382	1	1	yes	characteristic
51	C₂	—	362	1	no	—
52	C₂	#19153878	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#19153878
commutator	C₈×C₁₈₁	C₂×C₄
Frattini	C₈	C₂×#10624382
Fitting	Q₁₆×C₁₈₁	C₄
socle	C₂×C₁₈₁	#102
prime radical	C₂×D₁₈₁	SD₁₆
cosocle	C₈×D₁₈₁	C₂²
hypercenter	Q₁₆	#10624382
hypocenter	C₁₈₁	#362
LCS	G ▷ C₈×C₁₈₁ ▷ C₄×C₁₈₁ ▷ C₂×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
26. C₁₈₁	#362	semidirect

Maximal subgroups

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

subgroup	index
#19153891	2
#19153886	2
Q₁₆×D₁₈₁	2
#362	181