Subgroups — #28378195

Order 13952.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20295954	C₂	1	2	yes	maximal
2	C₃₂×D₁₀₉	C₂	1	1	yes	maximal, characteristic
3	#16812770	—	2	2	no	—
4	C₁₆×D₁₀₉	C₂²	1	1	yes	characteristic
5	#16812605	C₄	1	1	yes	characteristic
6	C₃₂×C₁₀₉	C₄	1	1	yes	characteristic
7	#13182039	—	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	C₄×D₁₀₉	D₈	1	1	yes	characteristic
12	#11724786	—	8	2	no	—
13	C₈×C₁₀₉	C₄⋊C₄	1	1	yes	characteristic
14	#11724784	Q₁₆	1	1	yes	characteristic
15	C₂×D₁₀₉	Q₃₂	1	1	yes	characteristic
16	C₄×C₁₀₉	#107	1	1	yes	characteristic
17	Dic₁₀₉	D₁₆	1	1	yes	characteristic
18	C₂×C₁₀₉	#366	1	1	yes	characteristic
19	D₁₀₉	—	2	1	no	—
20	#1425	—	109	1	no	maximal, Sylow
21	C₁₀₉	#1425	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₃₂	—	109	1	no	—
23	#368	—	109	2	no	—
24	C₂×C₁₆	—	109	1	no	—
25	#108	—	218	2	no	—
26	C₃₂	—	109	1	no	—
27	C₃₂	#89137	1	1	yes	characteristic
28	M₁₆	—	436	2	no	—
29	C₂×C₈	—	109	1	no	—
30	C₁₆	—	109	1	no	—
31	C₁₆	C₂×#89137	1	1	yes	characteristic
32	C₂×C₄	—	109	1	no	—
33	C₈	—	872	2	no	—
34	C₈	—	109	1	no	—
35	C₈	C₄⋊#89137	1	1	yes	characteristic
36	C₂²	—	109	1	no	—
37	C₄	—	109	1	no	—
38	C₄	#16812768	1	1	yes	characteristic
39	C₂	—	218	1	no	—
40	C₂	#20295952	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
21. C₁₀₉	#1425	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.