Subgroups — #14272023

Order 1856.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11745306	C₂	1	1	yes	maximal, characteristic
2	#11745220	C₂	1	2	yes	maximal
3	C₂×Q₈×C₂₉	C₄	1	1	yes	characteristic
4	C₂×Dic₅₈	C₄	1	1	yes	characteristic
5	C₂×#6599	—	2	2	no	—
6	#90779	—	2	2	no	—
7	C₄×Dic₂₉	C₂²	1	1	yes	characteristic
8	Q₈×C₂₉	—	4	1	no	—
9	C₂×C₄×C₂₉	—	2	1	no	—
10	C₂×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
11	C₂×Dic₂₉	—	2	1	no	—
12	C₂×Dic₂₉	D₄	1	2	yes	—
13	Dic₅₈	—	4	1	no	—
14	#6599	—	4	2	no	—
15	C₂²×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
16	C₄×C₂₉	—	2	1	no	—
17	C₄×C₂₉	—	4	1	no	—
18	Dic₂₉	—	4	1	no	—
19	Dic₂₉	SD₁₆	1	2	yes	—
20	Dic₂₉	Q₁₆	1	2	yes	—
21	#333	—	29	1	no	maximal, Sylow
22	C₂×C₂₉	#100	1	1	yes	characteristic
23	C₂×C₂₉	#103	1	2	yes	—
24	C₄⋊Q₈	—	29	1	no	—
25	C₄⋊C₈	—	29	2	no	—
26	C₂₉	#333	1	1	yes	characteristic, complemented, Sylow
27	C₂×Q₈	—	29	1	no	—
28	C₂×Q₈	#1181	1	1	yes	characteristic
29	C₂×C₈	—	58	2	no	—
30	C₄⋊C₄	—	58	2	no	—
31	C₄²	—	29	1	no	—
32	Q₈	—	4	1	no	—
33	Q₈	—	116	1	no	—
34	C₂×C₄	—	2	1	no	—
35	C₂×C₄	—	29	2	no	—
36	C₂×C₄	—	58	1	no	—
37	C₂×C₄	C₂×#1181	1	1	yes	characteristic
38	C₈	—	116	2	no	—
39	C₂²	C₂²⋊#1181	1	1	yes	characteristic
40	C₄	—	2	1	no	—
41	C₄	—	4	1	no	—
42	C₄	—	29	2	no	—
43	C₄	—	29	2	no	—
44	C₄	—	116	1	no	—
45	C₂	#11745225	1	2	yes	—
46	C₂	#11745229	1	1	yes	characteristic

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

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

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