Subgroups — #27189804

Order 13088.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20266998	C₂	1	1	yes	maximal, characteristic, complemented
2	#20266997	C₂	1	2	yes	maximal, complemented
3	#20266996	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#15692550	C₂	1	2	yes	maximal, complemented
5	#20266987	C₂	1	1	yes	maximal, characteristic
6	#15692550	C₂²	1	1	yes	characteristic
7	#15692550	C₂²	1	2	yes	—
8	#15692550	C₂²	1	1	yes	characteristic
9	Dic₈₁₈	C₄	1	1	yes	characteristic
10	C₂²⋊D₄₀₉	C₄	1	2	yes	—
11	C₂×Dic₄₀₉	C₂²	1	2	yes	—
12	C₄×D₄₀₉	C₂²	1	1	yes	characteristic
13	D₄×C₄₀₉	C₄	1	1	yes	characteristic
14	C₂²×C₄₀₉	C₂×C₄	1	2	yes	—
15	C₂×D₄₀₉	C₂×C₄	1	1	yes	characteristic
16	C₄×C₄₀₉	C₂×C₄	1	1	yes	characteristic
17	Dic₄₀₉	C₂×C₄	1	2	yes	—
18	Dic₄₀₉	C₂³	1	1	yes	characteristic
19	C₂×C₄₀₉	—	2	2	no	—
20	C₂×C₄₀₉	C₂²×C₄	1	1	yes	characteristic
21	D₄₀₉	—	2	1	no	—
22	C₄₀₉	#131	1	1	yes	characteristic, complemented, Sylow
23	#131	—	409	1	no	maximal, Sylow
24	#41	—	409	1	no	—
25	M₁₆	—	409	2	no	—
26	M₁₆	—	409	1	no	—
27	C₂×C₈	—	409	2	no	—
28	C₂×C₈	—	409	1	no	—
29	Q₈	—	409	1	no	—
30	D₄	—	409	2	no	—
31	D₄	#13109888	1	1	yes	characteristic
32	C₂×C₄	—	409	2	no	—
33	C₂×C₄	—	409	1	no	—
34	C₈	—	409	1	no	—
35	C₈	—	409	2	no	—
36	C₈	—	409	1	no	—
37	C₂²	—	409	1	no	—
38	C₂²	C₂×#13109888	1	2	yes	—
39	C₄	—	409	1	no	—
40	C₄	—	409	2	no	—
41	C₄	C₂×#13109888	1	1	yes	characteristic
42	C₂	—	2	2	no	—
43	C₂	—	818	1	no	—
44	C₂	C₂²×#13109888	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.