Subgroups — #16834656

Order 3712.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14272091	C₂	1	2	yes	maximal
2	C₃₂×D₂₉	C₂	1	1	yes	maximal, characteristic
3	#11745212	—	2	2	no	—
4	C₁₆×D₂₉	C₂²	1	1	yes	characteristic
5	C₂₉×C₃₂	C₄	1	1	yes	characteristic
6	#11745142	C₄	1	1	yes	characteristic
7	#90796	—	4	2	no	—
8	C₈×D₂₉	D₄	1	1	yes	characteristic
9	C₁₆×C₂₉	C₂×C₄	1	1	yes	characteristic
10	#90768	Q₈	1	1	yes	characteristic
11	C₄×D₂₉	D₈	1	1	yes	characteristic
12	#6599	—	8	2	no	—
13	C₈×C₂₉	C₄⋊C₄	1	1	yes	characteristic
14	#6597	Q₁₆	1	1	yes	characteristic
15	#1425	—	29	1	no	maximal, Sylow
16	C₂×D₂₉	Q₃₂	1	1	yes	characteristic
17	C₄×C₂₉	#107	1	1	yes	characteristic
18	Dic₂₉	D₁₆	1	1	yes	characteristic
19	C₂×C₃₂	—	29	1	no	—
20	#368	—	29	2	no	—
21	C₂×C₂₉	#366	1	1	yes	characteristic
22	D₂₉	—	2	1	no	—
23	C₂×C₁₆	—	29	1	no	—
24	#108	—	58	2	no	—
25	C₃₂	—	29	1	no	—
26	C₃₂	#1181	1	1	yes	characteristic
27	C₂₉	#1425	1	1	yes	characteristic, complemented, Sylow
28	M₁₆	—	116	2	no	—
29	C₂×C₈	—	29	1	no	—
30	C₁₆	—	29	1	no	—
31	C₁₆	C₂×#1181	1	1	yes	characteristic
32	C₂×C₄	—	29	1	no	—
33	C₈	—	29	1	no	—
34	C₈	—	232	2	no	—
35	C₈	C₄⋊#1181	1	1	yes	characteristic
36	C₂²	—	29	1	no	—
37	C₄	—	29	1	no	—
38	C₄	#11745210	1	1	yes	characteristic
39	C₂	—	58	1	no	—
40	C₂	#14272089	1	1	yes	characteristic

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

N	H ≅ G/N	type
27. C₂₉	#1425	semidirect

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