Subgroups — C₁₄₉⋊#401 #23749568

Order 9536.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#18011818	C₂	1	3	yes	maximal
2	#18011818	C₂	1	3	yes	maximal
3	#95×C₁₄₉	C₂	1	1	yes	maximal, characteristic
4	C₂²×Dic₁₄₉	C₂²	1	3	yes	—
5	C₂²×Dic₁₄₉	C₂²	1	1	yes	characteristic
6	C₂²×C₄×C₁₄₉	C₂²	1	3	yes	—
7	C₂×Dic₁₄₉	—	2	3	no	—
8	C₂×Dic₁₄₉	—	2	3	no	—
9	C₂×Dic₁₄₉	—	2	3	no	—
10	C₂×Dic₁₄₉	—	2	3	no	—
11	C₂³×C₁₄₉	C₂³	1	1	yes	characteristic
12	C₂×C₄×C₁₄₉	—	2	6	no	—
13	C₂×C₄×C₁₄₉	—	2	3	no	—
14	C₂²×C₁₄₉	#41	1	3	yes	—
15	C₂²×C₁₄₉	#41	1	3	yes	—
16	C₂²×C₁₄₉	#41	1	1	yes	characteristic
17	C₄×C₁₄₉	—	4	3	no	—
18	Dic₁₄₉	—	4	1	no	—
19	Dic₁₄₉	—	4	3	no	—
20	C₂×C₁₄₉	#126	1	3	yes	—
21	C₂×C₁₄₉	#126	1	1	yes	characteristic
22	C₂×C₁₄₉	#126	1	3	yes	—
23	C₁₄₉	#401	1	1	yes	characteristic, complemented, Sylow
24	#401	—	149	1	no	maximal, Sylow
25	#95	—	149	3	no	—
26	#95	—	149	3	no	—
27	#95	D₁₄₉	1	1	yes	characteristic
28	C₂²×C₄	—	149	3	no	—
29	C₂²×C₄	—	149	1	no	—
30	C₂²×C₄	C₂×D₁₄₉	1	3	yes	—
31	C₂³	C₂²×D₁₄₉	1	1	yes	characteristic
32	C₂×C₄	—	2	6	no	—
33	C₂×C₄	—	2	3	no	—
34	C₂×C₄	—	298	3	no	—
35	C₂×C₄	—	298	3	no	—
36	C₂×C₄	—	298	3	no	—
37	C₂×C₄	—	298	3	no	—
38	C₂²	#14558735	1	3	yes	—
39	C₂²	#14558736	1	3	yes	—
40	C₂²	#14558737	1	1	yes	characteristic
41	C₄	—	4	3	no	—
42	C₄	—	596	1	no	—
43	C₄	—	596	3	no	—
44	C₂	#18011904	1	3	yes	—
45	C₂	#18011905	1	1	yes	characteristic
46	C₂	#18011906	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₁₄₉
commutator, socle, prime radical, cosocle	C₂³×C₁₄₉	C₂³
Fitting	#95×C₁₄₉	C₂
hypercenter	#95	D₁₄₉
hypocenter	C₁₄₉	#401
LCS	G ▷ C₂³×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂³ ◁ #95

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

N	H ≅ G/N	type
23. C₁₄₉	#401	semidirect