Subgroups — #23749451

Order 9536.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#18011845	C₂	1	2	yes	maximal
2	C₂×C₁₆×C₁₄₉	C₂	1	1	yes	maximal, characteristic
3	C₄⋊Dic₁₄₉	—	2	2	no	—
4	C₂×C₈×C₁₄₉	C₂²	1	1	yes	characteristic
5	C₁₆×C₁₄₉	C₄	1	2	yes	complemented
6	C₂×Dic₁₄₉	—	4	2	no	—
7	C₂×C₄×C₁₄₉	D₄	1	1	yes	characteristic
8	C₈×C₁₄₉	C₂×C₄	1	1	yes	characteristic
9	C₈×C₁₄₉	Q₈	1	1	yes	characteristic
10	C₂²×C₁₄₉	D₈	1	1	yes	characteristic
11	C₄×C₁₄₉	C₄⋊C₄	1	1	yes	characteristic
12	C₄×C₁₄₉	Q₁₆	1	1	yes	characteristic
13	Dic₁₄₉	—	8	2	no	—
14	C₂×C₁₄₉	#107	1	1	yes	characteristic
15	C₂×C₁₄₉	D₁₆	1	1	yes	characteristic
16	C₂×C₁₄₉	Q₃₂	1	1	yes	characteristic
17	C₁₄₉	#366	1	1	yes	characteristic, complemented, Sylow
18	#366	—	149	1	no	maximal, Sylow
19	C₂×C₁₆	D₁₄₉	1	1	yes	characteristic
20	#107	—	149	2	no	—
21	C₂×C₈	C₂×D₁₄₉	1	1	yes	characteristic
22	C₄⋊C₄	—	298	2	no	—
23	C₁₆	Dic₁₄₉	1	2	yes	complemented
24	C₂×C₄	—	596	2	no	—
25	C₂×C₄	D₅₉₆	1	1	yes	characteristic
26	C₈	C₂×Dic₁₄₉	1	1	yes	characteristic
27	C₈	Dic₂₉₈	1	1	yes	characteristic
28	C₂²	D₁₁₉₂	1	1	yes	characteristic
29	C₄	—	1192	2	no	—
30	C₄	C₄⋊Dic₁₄₉	1	1	yes	characteristic
31	C₄	Dic₅₉₆	1	1	yes	characteristic
32	C₂	#18011845	1	1	yes	characteristic
33	C₂	D₂₃₈₄	1	1	yes	characteristic
34	C₂	Dic₁₁₉₂	1	1	yes	characteristic

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