Subgroups — #23749347

Order 9536.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#11924746	C₂	1	1	yes	maximal, characteristic
2	C₄×#11924746	C₂	1	1	yes	maximal, characteristic
3	C₄×C₈×C₁₄₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#11924746	C₄	1	2	yes	—
5	C₂×#11924746	C₄	1	2	yes	—
6	C₂×C₈×C₁₄₉	C₄	1	2	yes	—
7	C₄²×C₁₄₉	C₂²	1	1	yes	characteristic
8	#11924746	—	2	2	no	—
9	#11924746	C₈	1	4	yes	complemented
10	C₂×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
11	C₂×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
13	C₈×C₁₄₉	—	2	2	no	—
14	C₂²×C₁₄₉	C₄²	1	1	yes	characteristic
15	C₄×C₁₄₉	C₂×C₈	1	2	yes	—
16	C₄×C₁₄₉	M₁₆	1	2	yes	—
17	C₄×C₁₄₉	M₁₆	1	2	yes	—
18	C₂×C₁₄₉	C₄×C₈	1	1	yes	characteristic
19	C₂×C₁₄₉	#97	1	1	yes	characteristic
20	C₂×C₁₄₉	#97	1	1	yes	characteristic
21	C₁₄₉	#322	1	1	yes	characteristic, complemented, Sylow
22	#322	—	149	1	no	maximal, Sylow
23	C₄×C₈	—	149	1	no	—
24	C₄×C₈	—	149	1	no	—
25	C₄×C₈	D₁₄₉	1	1	yes	characteristic
26	C₂×C₈	—	149	2	no	—
27	C₂×C₈	—	149	2	no	—
28	C₂×C₈	Dic₁₄₉	1	2	yes	—
29	C₄²	C₂×D₁₄₉	1	1	yes	characteristic
30	C₂×C₄	C₄×D₁₄₉	1	1	yes	characteristic
31	C₂×C₄	C₄×D₁₄₉	1	1	yes	characteristic
32	C₂×C₄	C₂×Dic₁₄₉	1	1	yes	characteristic
33	C₈	—	2	2	no	—
34	C₈	—	298	2	no	—
35	C₈	—	149	4	no	—
36	C₂²	C₄×Dic₁₄₉	1	1	yes	characteristic
37	C₄	C₈×D₁₄₉	1	2	yes	—
38	C₄	#14558719	1	2	yes	—
39	C₄	#14558720	1	2	yes	—
40	C₂	C₈×Dic₁₄₉	1	1	yes	characteristic
41	C₂	#18011821	1	1	yes	characteristic
42	C₂	#18011822	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂×D₁₄₉
commutator	C₂×C₁₄₉	C₄×C₈
Fitting	C₄×C₈×C₁₄₉	C₂
socle, prime radical	C₂²×C₁₄₉	C₄²
cosocle	C₄²×C₁₄₉	C₂²
hypercenter	C₄×C₈	D₁₄₉
hypocenter	C₁₄₉	#322
LCS	G ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
9. #11924746	C₈	semidirect
21. C₁₄₉	#322	semidirect