Subgroups — #26042323

Order 11584.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19153904	C₂	1	2	yes	maximal, complemented
2	#19153887	C₂	1	1	yes	maximal, characteristic, complemented
3	#19153881	C₂	1	2	yes	maximal, complemented
4	C₈×#10624382	C₂	1	1	yes	maximal, characteristic, complemented
5	#19153839	C₂	1	1	yes	maximal, characteristic
6	#15668459	—	2	2	no	—
7	#15668459	C₂²	1	2	yes	—
8	D₁₈₁⋊C₈	—	2	2	no	—
9	D₁₈₁⋊C₈	C₂²	1	1	yes	characteristic
10	C₄×#10624382	C₂²	1	1	yes	characteristic
11	#15668450	C₂²	1	2	yes	—
12	#15668436	C₄	1	2	yes	complemented
13	D₁₄₄₈	C₄	1	1	yes	characteristic, complemented
14	C₈×D₁₈₁	C₂²	1	1	yes	characteristic
15	Q₁₆×C₁₈₁	C₄	1	1	yes	characteristic, complemented
16	C₂×#10624382	—	2	1	no	—
17	#13089685	—	2	2	no	—
18	#13089685	D₄	1	1	yes	characteristic
19	#13089685	D₄	1	1	yes	characteristic
20	D₇₂₄	—	2	2	no	—
21	D₇₂₄	C₂×C₄	1	2	yes	—
22	C₄×D₁₈₁	—	2	2	no	—
23	C₄×D₁₈₁	C₂³	1	1	yes	characteristic
24	#13089678	C₂×C₄	1	1	yes	characteristic
25	Q₈×C₁₈₁	C₂×C₄	1	2	yes	—
26	C₈×C₁₈₁	C₂×C₄	1	1	yes	characteristic
27	C₂×D₁₈₁	—	2	2	no	—
28	C₂×D₁₈₁	#41	1	1	yes	characteristic
29	#10624382	—	2	2	no	—
30	C₄×C₁₈₁	—	2	2	no	—
31	C₄×C₁₈₁	C₂²×C₄	1	1	yes	characteristic
32	Dic₁₈₁	C₂×D₄	1	1	yes	characteristic
33	C₂×C₁₈₁	C₄×D₄	1	1	yes	characteristic
34	D₁₈₁	—	2	1	no	—
35	D₁₈₁	—	4	2	no	—
36	C₁₈₁	#443	1	1	yes	characteristic, complemented, Sylow
37	#443	—	181	1	no	maximal, Sylow
38	#135	—	181	1	no	—
39	#131	—	181	2	no	—
40	#108	—	181	1	no	—
41	#104	—	181	2	no	—
42	C₄×C₈	—	181	1	no	—
43	#41	—	181	2	no	—
44	Q₁₆	#10624382	1	1	yes	characteristic, complemented
45	SD₁₆	—	181	2	no	—
46	D₈	—	181	1	no	—
47	M₁₆	—	362	2	no	—
48	M₁₆	—	181	2	no	—
49	C₂×C₈	—	362	2	no	—
50	C₂×C₈	—	181	1	no	—
51	C₂×C₈	—	181	1	no	—
52	C₄²	—	181	1	no	—
53	Q₈	C₂×#10624382	1	2	yes	—
54	D₄	—	362	2	no	—
55	D₄	—	181	2	no	—
56	C₂×C₄	—	362	2	no	—
57	C₂×C₄	—	362	1	no	—
58	C₂×C₄	—	181	1	no	—
59	C₈	—	362	2	no	—
60	C₈	—	181	1	no	—
61	C₈	—	181	1	no	—
62	C₈	—	181	1	no	—
63	C₈	C₂×#10624382	1	1	yes	characteristic
64	C₂²	—	362	2	no	—
65	C₂²	—	181	1	no	—
66	C₄	—	2	2	no	—
67	C₄	—	362	2	no	—
68	C₄	—	181	1	no	—
69	C₄	C₂²×#10624382	1	1	yes	characteristic
70	C₂	—	362	1	no	—
71	C₂	—	724	2	no	—
72	C₂	D₄×#10624382	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×#10624382
commutator	C₄×C₁₈₁	C₂²×C₄
Frattini	C₄	C₂²×#10624382
Fitting	Q₁₆×C₁₈₁	C₄
socle	C₂×C₁₈₁	C₄×D₄
prime radical	#19153839	C₂
cosocle	C₄×D₁₈₁	C₂³
hypercenter	Q₁₆	#10624382
hypocenter	C₁₈₁	#443
LCS	G ▷ C₄×C₁₈₁ ▷ C₂×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
1. #19153904	C₂	semidirect
2. #19153887	C₂	semidirect
3. #19153881	C₂	semidirect
4. C₈×#10624382	C₂	semidirect
12. #15668436	C₄	semidirect
13. D₁₄₄₈	C₄	semidirect
15. Q₁₆×C₁₈₁	C₄	semidirect
36. C₁₈₁	#443	semidirect
44. Q₁₆	#10624382	semidirect

Maximal subgroups

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

subgroup	index
#19153904	2
#19153887	2
#19153881	2
C₈×#10624382	2
#19153839	2
#443	181