Subgroups — #26042196

Order 11584.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19153891	C₂	1	1	yes	maximal, characteristic, complemented
2	#19153884	C₂	1	1	yes	maximal, characteristic, complemented
3	#19153839	C₂	1	1	yes	maximal, characteristic
4	C₄⋊#10624382	—	2	1	no	—
5	#15668452	—	2	1	no	—
6	#15668450	—	2	1	no	—
7	#15668436	—	2	1	no	—
8	D₁₄₄₈	C₄	1	1	yes	characteristic, complemented
9	C₈×D₁₈₁	C₂²	1	1	yes	characteristic
10	Q₁₆×C₁₈₁	C₄	1	1	yes	characteristic, complemented
11	C₂×#10624382	—	4	1	no	—
12	D₇₂₄	—	2	1	no	—
13	D₇₂₄	—	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	—	4	1	no	—
20	C₂×D₁₈₁	D₈	1	1	yes	characteristic
21	#10624382	—	8	1	no	—
22	C₄×C₁₈₁	—	4	1	no	—
23	C₄×C₁₈₁	C₂²⋊C₄	1	1	yes	characteristic
24	Dic₁₈₁	SD₁₆	1	1	yes	characteristic
25	C₂×C₁₈₁	#102	1	1	yes	characteristic
26	D₁₈₁	—	2	1	no	—
27	D₁₈₁	—	8	1	no	—
28	C₁₈₁	#360	1	1	yes	characteristic, complemented, Sylow
29	#360	—	181	1	no	maximal, Sylow
30	#135	—	181	1	no	—
31	M₃₂	—	181	1	no	—
32	#106	—	181	1	no	—
33	#41	—	362	1	no	—
34	Q₁₆	#10624382	1	1	yes	characteristic, complemented
35	SD₁₆	—	362	1	no	—
36	D₈	—	181	1	no	—
37	C₂×C₈	—	181	1	no	—
38	C₄⋊C₄	—	362	1	no	—
39	C₁₆	—	362	1	no	—
40	Q₈	—	2	1	no	—
41	D₄	—	362	1	no	—
42	D₄	—	724	1	no	—
43	C₂×C₄	—	181	1	no	—
44	C₂×C₄	—	724	1	no	—
45	C₂×C₄	—	724	1	no	—
46	C₈	—	181	1	no	—
47	C₈	C₂×#10624382	1	1	yes	characteristic
48	C₂²	—	181	1	no	—
49	C₂²	—	724	1	no	—
50	C₄	—	4	1	no	—
51	C₄	—	1448	1	no	—
52	C₄	—	181	1	no	—
53	C₄	C₂²⋊#10624382	1	1	yes	characteristic
54	C₂	—	362	1	no	—
55	C₂	—	1448	1	no	—
56	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	#19153839	C₂
cosocle	C₈×D₁₈₁	C₂²
hypercenter	Q₁₆	#10624382
hypocenter	C₁₈₁	#360
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
1. #19153891	C₂	semidirect
2. #19153884	C₂	semidirect
8. D₁₄₄₈	C₄	semidirect
10. Q₁₆×C₁₈₁	C₄	semidirect
28. C₁₈₁	#360	semidirect
34. Q₁₆	#10624382	semidirect

Maximal subgroups

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

subgroup	index
#19153891	2
#19153884	2
#19153839	2
#360	181