Subgroups — #26042193

Order 11584.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₈₁⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	#19153887	C₂	1	1	yes	maximal, characteristic, complemented
3	#19153835	C₂	1	1	yes	maximal, characteristic
4	#15668459	—	2	1	no	—
5	#15668452	—	2	1	no	—
6	#15668448	—	2	1	no	—
7	Dic₇₂₄	C₄	1	1	yes	characteristic
8	#15668437	—	2	1	no	—
9	C₈×D₁₈₁	C₂²	1	1	yes	characteristic
10	D₈×C₁₈₁	C₄	1	1	yes	characteristic
11	#13089685	—	4	1	no	—
12	Dic₃₆₂	—	2	1	no	—
13	C₂²⋊D₁₈₁	—	4	1	no	—
14	C₂×Dic₁₈₁	—	4	1	no	—
15	C₄×D₁₈₁	D₄	1	1	yes	characteristic
16	#13089678	D₄	1	1	yes	characteristic
17	D₄×C₁₈₁	—	2	1	no	—
18	C₈×C₁₈₁	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₁₈₁	—	4	1	no	—
20	C₂×D₁₈₁	SD₁₆	1	1	yes	characteristic
21	C₄×C₁₈₁	C₂²⋊C₄	1	1	yes	characteristic
22	Dic₁₈₁	—	4	1	no	—
23	Dic₁₈₁	D₈	1	1	yes	characteristic
24	C₂×C₁₈₁	—	8	1	no	—
25	C₂×C₁₈₁	#102	1	1	yes	characteristic
26	D₁₈₁	—	2	1	no	—
27	C₁₈₁	#359	1	1	yes	characteristic, complemented, Sylow
28	#359	—	181	1	no	maximal, Sylow
29	#135	—	181	1	no	—
30	C₂×C₁₆	—	181	1	no	—
31	#108	—	181	1	no	—
32	#41	—	362	1	no	—
33	Q₁₆	—	181	1	no	—
34	SD₁₆	—	362	1	no	—
35	D₈	#10624382	1	1	yes	characteristic
36	M₁₆	—	362	1	no	—
37	C₂×C₈	—	181	1	no	—
38	C₁₆	—	362	1	no	—
39	Q₈	—	362	1	no	—
40	D₄	—	2	1	no	—
41	D₄	—	724	1	no	—
42	C₂×C₄	—	181	1	no	—
43	C₂×C₄	—	724	1	no	—
44	C₈	—	181	1	no	—
45	C₈	—	724	1	no	—
46	C₈	C₂×#10624382	1	1	yes	characteristic
47	C₂²	—	4	1	no	—
48	C₂²	—	181	1	no	—
49	C₄	—	181	1	no	—
50	C₄	—	724	1	no	—
51	C₄	C₂²⋊#10624382	1	1	yes	characteristic
52	C₂	—	8	1	no	—
53	C₂	—	362	1	no	—
54	C₂	#19153878	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#19153878
commutator	C₈×C₁₈₁	C₂×C₄
Frattini	C₈	C₂×#10624382
Fitting	D₈×C₁₈₁	C₄
socle	C₂×C₁₈₁	#102
prime radical	#19153835	C₂
cosocle	C₈×D₁₈₁	C₂²
hypercenter	D₈	#10624382
hypocenter	C₁₈₁	#359
LCS	G ▷ C₈×C₁₈₁ ▷ C₄×C₁₈₁ ▷ C₂×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ D₈

Complements

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

N	H ≅ G/N	type
1. D₁₈₁⋊C₁₆	C₂	semidirect
2. #19153887	C₂	semidirect
27. C₁₈₁	#359	semidirect

Maximal subgroups

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

subgroup	index
D₁₈₁⋊C₁₆	2
#19153887	2
#19153835	2
#359	181