Subgroups — #39910336

Order 26176.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#15692552	C₂	1	2	yes	maximal
2	C₈×#13109888	C₂	1	1	yes	maximal, characteristic
3	C₂×#15692552	—	2	2	no	—
4	#20266996	C₄	1	1	yes	characteristic
5	C₄×#13109888	C₂²	1	1	yes	characteristic
6	C₈×D₄₀₉	C₄	1	1	yes	characteristic
7	#15692552	—	4	2	no	—
8	C₂×#13109888	D₄	1	1	yes	characteristic
9	C₂×#13109888	Q₈	1	1	yes	characteristic
10	#15692550	—	2	1	no	—
11	C₄×D₄₀₉	C₂×C₄	1	1	yes	characteristic
12	#15692543	C₈	1	1	yes	characteristic, complemented
13	C₈×C₄₀₉	C₈	1	1	yes	characteristic, complemented
14	C₂×D₄₀₉	C₄⋊C₄	1	1	yes	characteristic
15	#13109888	—	2	1	no	—
16	#13109888	SD₁₆	1	2	yes	—
17	C₄×C₄₀₉	C₂×C₈	1	1	yes	characteristic
18	Dic₄₀₉	M₁₆	1	1	yes	characteristic
19	C₂×C₄₀₉	C₄⋊C₈	1	1	yes	characteristic
20	D₄₀₉	#106	1	1	yes	characteristic
21	D₄₀₉	#108	1	1	yes	characteristic
22	C₄₀₉	#334	1	1	yes	characteristic, complemented, Sylow
23	#334	—	409	1	no	maximal, Sylow
24	C₄⋊C₈	—	409	2	no	—
25	C₄×C₈	—	409	1	no	—
26	C₂×C₈	—	818	2	no	—
27	C₂×C₈	—	409	1	no	—
28	C₂×C₈	—	409	1	no	—
29	C₄²	—	409	1	no	—
30	C₂×C₄	—	409	1	no	—
31	C₂×C₄	—	409	1	no	—
32	C₂×C₄	—	409	1	no	—
33	C₈	—	818	1	no	—
34	C₈	—	1636	2	no	—
35	C₈	—	409	1	no	—
36	C₈	#15692552	1	1	yes	characteristic, complemented
37	C₂²	—	409	1	no	—
38	C₄	—	818	1	no	—
39	C₄	—	409	2	no	—
40	C₄	—	409	1	no	—
41	C₄	C₂×#15692552	1	1	yes	characteristic
42	C₂	—	409	1	no	—
43	C₂	—	409	1	no	—
44	C₂	C₄⋊#15692552	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.