Subgroups — #14271565

Order 1856.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11745232	C₂	1	2	yes	maximal
2	C₄×C₈×C₂₉	C₂	1	1	yes	maximal, characteristic
3	#11745166	C₂	1	2	yes	maximal
4	#11745165	C₂	1	2	yes	maximal
5	C₂×C₈×C₂₉	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₂₉	C₂²	1	1	yes	characteristic
7	C₄²×C₂₉	C₂²	1	1	yes	characteristic
8	C₄⋊Dic₂₉	C₂²	1	4	yes	—
9	#90779	—	2	4	no	—
10	C₂×C₄×C₂₉	D₄	1	2	yes	—
11	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
12	C₂×Dic₂₉	—	2	4	no	—
13	C₈×C₂₉	Q₈	1	2	yes	—
14	C₈×C₂₉	Q₈	1	2	yes	—
15	C₂²×C₂₉	C₂×D₄	1	1	yes	characteristic
16	C₄×C₂₉	—	2	2	no	—
17	C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
18	C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
19	Dic₂₉	—	4	4	no	—
20	#499	—	29	1	no	maximal, Sylow
21	C₂×C₂₉	C₄⋊Q₈	1	1	yes	characteristic
22	C₂×C₂₉	#135	1	2	yes	—
23	#125	—	29	2	no	—
24	#107	—	29	2	no	—
25	#106	—	29	2	no	—
26	C₄×C₈	D₂₉	1	1	yes	characteristic
27	C₂₉	#499	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₈	C₂×D₂₉	1	1	yes	characteristic
29	C₂×C₈	C₂×D₂₉	1	1	yes	characteristic
30	C₄⋊C₄	—	29	4	no	—
31	C₄⋊C₄	—	58	4	no	—
32	C₄²	C₂×D₂₉	1	1	yes	characteristic
33	C₂×C₄	—	58	4	no	—
34	C₂×C₄	D₁₁₆	1	2	yes	—
35	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
36	C₈	Dic₅₈	1	2	yes	—
37	C₈	Dic₅₈	1	2	yes	—
38	C₂²	C₂×D₁₁₆	1	1	yes	characteristic
39	C₄	—	2	2	no	—
40	C₄	—	116	4	no	—
41	C₄	C₂×Dic₅₈	1	1	yes	characteristic
42	C₄	C₂×Dic₅₈	1	1	yes	characteristic
43	C₂	#11745231	1	1	yes	characteristic
44	C₂	#11745266	1	2	yes	—

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

N	H ≅ G/N	type
27. C₂₉	#499	semidirect

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