Subgroups — #14272090

Order 1856.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11745210	C₂	1	2	yes	maximal
2	C₁₆×D₂₉	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#1181	—	2	2	no	—
4	C₈×D₂₉	C₂²	1	1	yes	characteristic
5	C₁₆×C₂₉	C₄	1	1	yes	characteristic, complemented
6	#90768	C₄	1	1	yes	characteristic, complemented
7	C₂×#1181	—	4	2	no	—
8	C₄×D₂₉	D₄	1	1	yes	characteristic
9	C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
10	#6597	Q₈	1	1	yes	characteristic
11	C₂×D₂₉	D₈	1	1	yes	characteristic
12	#1181	—	8	2	no	—
13	C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
14	Dic₂₉	Q₁₆	1	1	yes	characteristic
15	#367	—	29	1	no	maximal, Sylow
16	C₂×C₂₉	#107	1	1	yes	characteristic
17	D₂₉	SD₃₂	1	2	yes	—
18	C₂×C₁₆	—	29	1	no	—
19	#107	—	29	2	no	—
20	C₂₉	#367	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₈	—	29	1	no	—
22	C₄⋊C₄	—	58	2	no	—
23	C₁₆	—	29	1	no	—
24	C₁₆	#1181	1	1	yes	characteristic, complemented
25	C₂×C₄	—	29	1	no	—
26	C₂×C₄	—	116	2	no	—
27	C₈	—	29	1	no	—
28	C₈	C₂×#1181	1	1	yes	characteristic
29	C₂²	—	29	1	no	—
30	C₄	—	29	1	no	—
31	C₄	—	232	2	no	—
32	C₄	C₄⋊#1181	1	1	yes	characteristic
33	C₂	—	29	2	no	—
34	C₂	#11745210	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.