Subgroups — #28378194

Order 13952.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20295952	C₂	1	2	yes	maximal
2	C₃₂×D₁₀₉	C₂	1	1	yes	maximal, characteristic
3	#16812768	—	2	2	no	—
4	C₁₆×D₁₀₉	C₂²	1	1	yes	characteristic
5	#16812605	C₄	1	1	yes	characteristic, complemented
6	C₃₂×C₁₀₉	C₄	1	1	yes	characteristic, complemented
7	C₄⋊#89137	—	4	2	no	—
8	C₈×D₁₀₉	D₄	1	1	yes	characteristic
9	#13182004	Q₈	1	1	yes	characteristic
10	C₁₆×C₁₀₉	C₂×C₄	1	1	yes	characteristic
11	C₂×#89137	—	8	2	no	—
12	C₄×D₁₀₉	D₈	1	1	yes	characteristic
13	C₈×C₁₀₉	C₄⋊C₄	1	1	yes	characteristic
14	#11724784	Q₁₆	1	1	yes	characteristic
15	C₂×D₁₀₉	D₁₆	1	1	yes	characteristic
16	#89137	—	16	2	no	—
17	C₄×C₁₀₉	#107	1	1	yes	characteristic
18	Dic₁₀₉	Q₃₂	1	1	yes	characteristic
19	C₂×C₁₀₉	#366	1	1	yes	characteristic
20	D₁₀₉	SD₆₄	1	2	yes	—
21	#1424	—	109	1	no	maximal, Sylow
22	C₁₀₉	#1424	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₃₂	—	109	1	no	—
24	#366	—	109	2	no	—
25	C₂×C₁₆	—	109	1	no	—
26	#107	—	218	2	no	—
27	C₃₂	—	109	1	no	—
28	C₃₂	#89137	1	1	yes	characteristic, complemented
29	C₂×C₈	—	109	1	no	—
30	C₄⋊C₄	—	436	2	no	—
31	C₁₆	—	109	1	no	—
32	C₁₆	C₂×#89137	1	1	yes	characteristic
33	C₂×C₄	—	872	2	no	—
34	C₂×C₄	—	109	1	no	—
35	C₈	—	109	1	no	—
36	C₈	C₄⋊#89137	1	1	yes	characteristic
37	C₂²	—	109	1	no	—
38	C₄	—	109	1	no	—
39	C₄	—	1744	2	no	—
40	C₄	#16812768	1	1	yes	characteristic
41	C₂	—	109	2	no	—
42	C₂	#20295952	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.