Subgroups — #27186293

Order 12928.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20266103	C₂	1	2	yes	maximal
2	C₃₂×D₁₀₁	C₂	1	1	yes	maximal, characteristic
3	#15692324	—	2	2	no	—
4	C₁₆×D₁₀₁	C₂²	1	1	yes	characteristic
5	#15692161	C₄	1	1	yes	characteristic, complemented
6	C₃₂×C₁₀₁	C₄	1	1	yes	characteristic, complemented
7	C₄⋊#87938	—	4	2	no	—
8	C₈×D₁₀₁	D₄	1	1	yes	characteristic
9	#13108049	Q₈	1	1	yes	characteristic
10	C₁₆×C₁₀₁	C₂×C₄	1	1	yes	characteristic
11	C₂×#87938	—	8	2	no	—
12	C₄×D₁₀₁	D₈	1	1	yes	characteristic
13	C₈×C₁₀₁	C₄⋊C₄	1	1	yes	characteristic
14	#11717579	Q₁₆	1	1	yes	characteristic
15	C₂×D₁₀₁	D₁₆	1	1	yes	characteristic
16	#87938	—	16	2	no	—
17	C₄×C₁₀₁	#107	1	1	yes	characteristic
18	Dic₁₀₁	Q₃₂	1	1	yes	characteristic
19	C₂×C₁₀₁	#366	1	1	yes	characteristic
20	D₁₀₁	D₃₂	1	1	yes	characteristic
21	D₁₀₁	Q₆₄	1	1	yes	characteristic
22	#1423	—	101	1	no	maximal, Sylow
23	C₁₀₁	#1423	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₃₂	—	101	1	no	—
25	#366	—	101	2	no	—
26	C₂×C₁₆	—	101	1	no	—
27	#107	—	202	2	no	—
28	C₃₂	—	101	1	no	—
29	C₃₂	#87938	1	1	yes	characteristic, complemented
30	C₂×C₈	—	101	1	no	—
31	C₄⋊C₄	—	404	2	no	—
32	C₁₆	—	101	1	no	—
33	C₁₆	C₂×#87938	1	1	yes	characteristic
34	C₂×C₄	—	808	2	no	—
35	C₂×C₄	—	101	1	no	—
36	C₈	—	101	1	no	—
37	C₈	C₄⋊#87938	1	1	yes	characteristic
38	C₂²	—	101	1	no	—
39	C₄	—	1616	2	no	—
40	C₄	—	101	1	no	—
41	C₄	#15692324	1	1	yes	characteristic
42	C₂	—	101	1	no	—
43	C₂	—	101	1	no	—
44	C₂	#20266103	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.