Subgroups — #14270992

Order 1856.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#108	C₂	1	1	yes	maximal, characteristic
2	#11745167	C₂	1	1	yes	maximal, characteristic
3	C₂×#90768	C₂	1	1	yes	maximal, characteristic
4	M₁₆×C₂₉	—	2	1	no	—
5	C₂×C₈×C₂₉	C₂²	1	1	yes	characteristic
6	#90777	—	2	1	no	—
7	#90768	C₄	1	2	yes	—
8	C₂×C₄×C₂₉	D₄	1	1	yes	characteristic
9	C₈×C₂₉	—	4	1	no	—
10	C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
11	C₈×C₂₉	Q₈	1	1	yes	characteristic
12	#6597	—	4	1	no	—
13	C₂²×C₂₉	Q₁₆	1	1	yes	characteristic
14	C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₂₉	D₈	1	1	yes	characteristic
16	#368	—	29	1	no	maximal, Sylow
17	C₂×C₂₉	—	2	1	no	—
18	C₂×C₂₉	#107	1	1	yes	characteristic
19	C₂×C₁₆	—	29	1	no	—
20	#108	—	29	1	no	—
21	#108	D₂₉	1	1	yes	characteristic
22	C₂₉	#368	1	1	yes	characteristic, complemented, Sylow
23	M₁₆	—	2	1	no	—
24	M₁₆	—	58	1	no	—
25	C₂×C₈	C₂×D₂₉	1	1	yes	characteristic
26	C₁₆	—	29	2	no	—
27	C₂×C₄	C₂²⋊D₂₉	1	1	yes	characteristic
28	C₈	—	4	1	no	—
29	C₈	—	116	1	no	—
30	C₈	Dic₅₈	1	1	yes	characteristic
31	C₈	C₄×D₂₉	1	1	yes	characteristic
32	C₂²	#90785	1	1	yes	characteristic
33	C₄	#90779	1	1	yes	characteristic
34	C₄	#90782	1	1	yes	characteristic
35	C₂	—	2	1	no	—
36	C₂	#11745155	1	1	yes	characteristic

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

N	H ≅ G/N	type
22. C₂₉	#368	semidirect

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