Subgroups — #14272091

Order 1856.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

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

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