Subgroups — #14271561

Order 1856.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11745231	C₂	1	2	yes	maximal
2	C₄×C₈×C₂₉	C₂	1	1	yes	maximal, characteristic
3	#11745165	C₂	1	4	yes	maximal
4	C₂×Dic₅₈	—	2	2	no	—
5	C₂×C₈×C₂₉	C₂²	1	2	yes	—
6	C₄²×C₂₉	C₂²	1	1	yes	characteristic
7	C₄⋊Dic₂₉	—	2	2	no	—
8	C₄⋊Dic₂₉	C₂²	1	4	yes	—
9	C₂×C₄×C₂₉	D₄	1	2	yes	—
10	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
11	C₂×Dic₂₉	—	2	4	no	—
12	Dic₅₈	—	4	4	no	—
13	C₈×C₂₉	Q₈	1	4	yes	complemented
14	C₂²×C₂₉	C₂×D₄	1	1	yes	characteristic
15	C₄×C₂₉	SD₁₆	1	4	yes	—
16	C₄×C₂₉	C₂×Q₈	1	2	yes	—
17	Dic₂₉	—	4	4	no	—
18	#498	—	29	1	no	maximal, Sylow
19	C₂×C₂₉	C₄⋊Q₈	1	1	yes	characteristic
20	C₂×C₂₉	C₂×SD₁₆	1	2	yes	—
21	C₄⋊Q₈	—	29	2	no	—
22	#106	—	29	4	no	—
23	C₄×C₈	D₂₉	1	1	yes	characteristic
24	C₂₉	#498	1	1	yes	characteristic, complemented, Sylow
25	C₂×Q₈	—	58	2	no	—
26	C₂×C₈	C₂×D₂₉	1	2	yes	—
27	C₄⋊C₄	—	29	4	no	—
28	C₄⋊C₄	—	58	2	no	—
29	C₄²	C₂×D₂₉	1	1	yes	characteristic
30	Q₈	—	116	4	no	—
31	C₂×C₄	—	58	4	no	—
32	C₂×C₄	D₁₁₆	1	2	yes	—
33	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
34	C₈	Dic₅₈	1	4	yes	complemented
35	C₂²	C₂×D₁₁₆	1	1	yes	characteristic
36	C₄	—	116	4	no	—
37	C₄	#90773	1	4	yes	—
38	C₄	C₂×Dic₅₈	1	2	yes	—
39	C₂	#11745231	1	1	yes	characteristic
40	C₂	C₂×#90773	1	2	yes	—

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.