Subgroups — #14270912

Order 1856.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#6597	C₂	1	2	yes	maximal
3	C₂×Q₈×C₂₉	C₄	1	2	yes	—
4	C₄⋊C₄×C₂₉	—	2	2	no	—
5	C₄²×C₂₉	C₂²	1	1	yes	characteristic
6	C₂×#6597	—	2	2	no	—
7	Q₈×C₂₉	—	4	2	no	—
8	C₂×C₄×C₂₉	—	2	2	no	—
9	C₂×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
10	C₂×C₄×C₂₉	D₄	1	2	yes	—
11	#6597	—	4	2	no	—
12	C₂²×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
13	C₄×C₂₉	—	2	1	no	—
14	C₄×C₂₉	—	4	2	no	—
15	C₄×C₂₉	SD₁₆	1	2	yes	—
16	C₄×C₂₉	Q₁₆	1	2	yes	—
17	#333	—	29	1	no	maximal, Sylow
18	C₂×C₂₉	#100	1	1	yes	characteristic
19	C₂×C₂₉	#103	1	2	yes	—
20	C₄⋊Q₈	D₂₉	1	1	yes	characteristic
21	C₄⋊C₈	—	29	2	no	—
22	C₂₉	#333	1	1	yes	characteristic, complemented, Sylow
23	C₂×Q₈	Dic₂₉	1	2	yes	—
24	C₂×C₈	—	58	2	no	—
25	C₄⋊C₄	—	2	2	no	—
26	C₄²	C₂×D₂₉	1	1	yes	characteristic
27	Q₈	—	4	2	no	—
28	C₂×C₄	—	2	2	no	—
29	C₂×C₄	C₂×Dic₂₉	1	1	yes	characteristic
30	C₂×C₄	C₂²⋊D₂₉	1	2	yes	—
31	C₈	—	116	2	no	—
32	C₂²	C₂²⋊Dic₂₉	1	1	yes	characteristic
33	C₄	—	2	1	no	—
34	C₄	—	4	2	no	—
35	C₄	#90784	1	2	yes	—
36	C₄	#90785	1	2	yes	—
37	C₂	#11745181	1	1	yes	characteristic
38	C₂	#11745183	1	2	yes	—

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

N	H ≅ G/N	type
22. C₂₉	#333	semidirect

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