Subgroups — C₈×#15691012 #38734939

Order 24896.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#15691012	C₂	1	2	yes	maximal
2	C₈×Dic₃₈₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#15691012	C₄	1	4	yes	—
4	C₂×#15691005	C₄	1	1	yes	characteristic
5	C₄×Dic₃₈₉	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₃₈₉	C₄	1	1	yes	characteristic
7	#15691012	C₈	1	8	yes	direct product factor
8	C₂×Dic₃₈₉	C₂×C₄	1	2	yes	—
9	#15691005	C₈	1	2	yes	complemented
10	C₂×C₄×C₃₈₉	C₂×C₄	1	1	yes	characteristic
11	C₈×C₃₈₉	C₈	1	2	yes	complemented
12	C₂²×C₃₈₉	C₄²	1	1	yes	characteristic
13	C₄×C₃₈₉	C₂×C₈	1	1	yes	characteristic
14	C₄×C₃₈₉	C₂×C₈	1	1	yes	characteristic
15	Dic₃₈₉	C₂×C₈	1	4	yes	—
16	C₂×C₃₈₉	C₄×C₈	1	2	yes	—
17	C₂×C₃₈₉	C₄×C₈	1	1	yes	characteristic
18	C₃₈₉	C₈²	1	1	yes	characteristic, complemented, Sylow
19	C₈²	—	389	1	no	maximal, Sylow
20	C₄×C₈	—	389	2	no	—
21	C₄×C₈	—	389	1	no	—
22	C₂×C₈	—	389	4	no	—
23	C₂×C₈	—	389	1	no	—
24	C₂×C₈	#13095555	1	1	yes	characteristic
25	C₄²	—	389	1	no	—
26	C₂×C₄	—	389	2	no	—
27	C₂×C₄	C₂×#13095555	1	1	yes	characteristic
28	C₈	—	389	8	no	—
29	C₈	—	389	2	no	—
30	C₈	#15691012	1	2	yes	direct product factor
31	C₂²	C₄×#13095555	1	1	yes	characteristic
32	C₄	—	389	4	no	—
33	C₄	C₂×#15691012	1	1	yes	characteristic
34	C₄	D₃₈₉⋊C₈	1	1	yes	characteristic
35	C₂	C₈×#13095555	1	2	yes	—
36	C₂	C₄×#15691012	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.