Subgroups — #23750489

Order 9536.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#11924753	C₂	1	2	yes	maximal
2	C₈×Dic₁₄₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#11924753	—	2	2	no	—
4	C₂×#11924746	C₄	1	1	yes	characteristic
5	C₄×Dic₁₄₉	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₁₄₉	C₄	1	1	yes	characteristic
7	#11924753	—	4	2	no	—
8	C₂×Dic₁₄₉	D₄	1	1	yes	characteristic
9	C₂×Dic₁₄₉	Q₈	1	1	yes	characteristic
10	#11924746	C₈	1	2	yes	complemented
11	C₂×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
12	C₈×C₁₄₉	—	2	1	no	—
13	C₂²×C₁₄₉	C₄⋊C₄	1	1	yes	characteristic
14	C₄×C₁₄₉	C₂×C₈	1	1	yes	characteristic
15	C₄×C₁₄₉	M₁₆	1	1	yes	characteristic
16	Dic₁₄₉	—	2	1	no	—
17	Dic₁₄₉	D₈	1	1	yes	characteristic
18	Dic₁₄₉	Q₁₆	1	1	yes	characteristic
19	C₂×C₁₄₉	C₄⋊C₈	1	1	yes	characteristic
20	C₂×C₁₄₉	#107	1	1	yes	characteristic
21	C₂×C₁₄₉	#108	1	1	yes	characteristic
22	C₁₄₉	#335	1	1	yes	characteristic, complemented, Sylow
23	#335	—	149	1	no	maximal, Sylow
24	C₄⋊C₈	—	149	2	no	—
25	C₄×C₈	—	149	1	no	—
26	C₂×C₈	—	298	2	no	—
27	C₂×C₈	—	149	1	no	—
28	C₂×C₈	#10597010	1	1	yes	characteristic
29	C₄²	—	149	1	no	—
30	C₂×C₄	—	149	1	no	—
31	C₂×C₄	—	149	1	no	—
32	C₂×C₄	C₂×#10597010	1	1	yes	characteristic
33	C₈	—	2	1	no	—
34	C₈	—	596	2	no	—
35	C₈	—	149	2	no	—
36	C₂²	C₄⋊#10597010	1	1	yes	characteristic
37	C₄	—	298	1	no	—
38	C₄	—	149	1	no	—
39	C₄	—	149	1	no	—
40	C₄	D₁₄₉⋊C₈	1	1	yes	characteristic
41	C₄	#14558745	1	1	yes	characteristic
42	C₂	#18011978	1	1	yes	characteristic
43	C₂	#18011980	1	1	yes	characteristic
44	C₂	#18011981	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₄⋊#10597010
commutator	C₄×C₁₄₉	C₂×C₈
Frattini	C₂×C₄	C₂×#10597010
Fitting	C₂×C₈×C₁₄₉	C₄
socle, prime radical	C₂²×C₁₄₉	C₄⋊C₄
cosocle	C₄×Dic₁₄₉	C₂²
hypercenter	C₂×C₈	#10597010
hypocenter	C₁₄₉	#335
LCS	G ▷ C₄×C₁₄₉ ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
10. #11924746	C₈	semidirect
22. C₁₄₉	#335	semidirect