Subgroups — C₈×#15692550 #39910087

Order 26176.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#15692550	C₂	1	2	yes	maximal
2	C₈×Dic₄₀₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#15692550	C₄	1	4	yes	—
4	C₂×#15692543	C₄	1	1	yes	characteristic
5	C₄×Dic₄₀₉	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₄₀₉	C₄	1	1	yes	characteristic
7	#15692550	C₈	1	8	yes	direct product factor
8	C₂×Dic₄₀₉	C₂×C₄	1	2	yes	—
9	#15692543	C₈	1	2	yes	complemented
10	C₂×C₄×C₄₀₉	C₂×C₄	1	1	yes	characteristic
11	C₈×C₄₀₉	C₈	1	2	yes	complemented
12	C₂²×C₄₀₉	C₄²	1	1	yes	characteristic
13	C₄×C₄₀₉	C₂×C₈	1	1	yes	characteristic
14	C₄×C₄₀₉	C₂×C₈	1	1	yes	characteristic
15	Dic₄₀₉	C₂×C₈	1	4	yes	—
16	C₂×C₄₀₉	C₄×C₈	1	2	yes	—
17	C₂×C₄₀₉	C₄×C₈	1	1	yes	characteristic
18	C₄₀₉	C₈²	1	1	yes	characteristic, complemented, Sylow
19	C₈²	—	409	1	no	maximal, Sylow
20	C₄×C₈	—	409	2	no	—
21	C₄×C₈	—	409	1	no	—
22	C₂×C₈	—	409	4	no	—
23	C₂×C₈	—	409	1	no	—
24	C₂×C₈	#13109888	1	1	yes	characteristic
25	C₄²	—	409	1	no	—
26	C₂×C₄	—	409	2	no	—
27	C₂×C₄	C₂×#13109888	1	1	yes	characteristic
28	C₈	—	409	8	no	—
29	C₈	—	409	2	no	—
30	C₈	#15692550	1	2	yes	direct product factor
31	C₂²	C₄×#13109888	1	1	yes	characteristic
32	C₄	—	409	4	no	—
33	C₄	C₂×#15692550	1	1	yes	characteristic
34	C₄	#20266996	1	1	yes	characteristic
35	C₂	C₈×#13109888	1	2	yes	—
36	C₂	C₄×#15692550	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.