Subgroups — #38735025

Order 24896.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27159453	C₂	1	2	yes	maximal
2	C₁₆×D₃₈₉	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#13095555	—	2	2	no	—
4	C₈×D₃₈₉	C₂²	1	1	yes	characteristic
5	#20261941	C₄	1	1	yes	characteristic, complemented
6	C₁₆×C₃₈₉	C₄	1	1	yes	characteristic, complemented
7	C₂×#13095555	—	4	2	no	—
8	C₄×D₃₈₉	D₄	1	1	yes	characteristic
9	#15691005	Q₈	1	1	yes	characteristic
10	C₈×C₃₈₉	C₂×C₄	1	1	yes	characteristic
11	C₂×D₃₈₉	D₈	1	1	yes	characteristic
12	#13095555	—	8	2	no	—
13	C₄×C₃₈₉	C₄⋊C₄	1	1	yes	characteristic
14	Dic₃₈₉	Q₁₆	1	1	yes	characteristic
15	C₂×C₃₈₉	#107	1	1	yes	characteristic
16	D₃₈₉	D₁₆	1	1	yes	characteristic
17	D₃₈₉	Q₃₂	1	1	yes	characteristic
18	C₃₈₉	#366	1	1	yes	characteristic, complemented, Sylow
19	#366	—	389	1	no	maximal, Sylow
20	C₂×C₁₆	—	389	1	no	—
21	#107	—	389	2	no	—
22	C₂×C₈	—	389	1	no	—
23	C₄⋊C₄	—	778	2	no	—
24	C₁₆	—	389	1	no	—
25	C₁₆	#13095555	1	1	yes	characteristic, complemented
26	C₂×C₄	—	1556	2	no	—
27	C₂×C₄	—	389	1	no	—
28	C₈	—	389	1	no	—
29	C₈	C₂×#13095555	1	1	yes	characteristic
30	C₂²	—	389	1	no	—
31	C₄	—	3112	2	no	—
32	C₄	—	389	1	no	—
33	C₄	C₄⋊#13095555	1	1	yes	characteristic
34	C₂	—	389	1	no	—
35	C₂	—	389	1	no	—
36	C₂	#27159453	1	1	yes	characteristic

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

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