Subgroups — #16834654

Order 3712.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14272089	C₂	1	2	yes	maximal
2	C₃₂×D₂₉	C₂	1	1	yes	maximal, characteristic
3	#11745210	—	2	2	no	—
4	C₁₆×D₂₉	C₂²	1	1	yes	characteristic
5	C₂₉×C₃₂	C₄	1	1	yes	characteristic, complemented
6	#11745142	C₄	1	1	yes	characteristic, complemented
7	C₄⋊#1181	—	4	2	no	—
8	C₈×D₂₉	D₄	1	1	yes	characteristic
9	C₁₆×C₂₉	C₂×C₄	1	1	yes	characteristic
10	#90768	Q₈	1	1	yes	characteristic
11	C₂×#1181	—	8	2	no	—
12	C₄×D₂₉	D₈	1	1	yes	characteristic
13	C₈×C₂₉	C₄⋊C₄	1	1	yes	characteristic
14	#6597	Q₁₆	1	1	yes	characteristic
15	#1424	—	29	1	no	maximal, Sylow
16	C₂×D₂₉	D₁₆	1	1	yes	characteristic
17	#1181	—	16	2	no	—
18	C₄×C₂₉	#107	1	1	yes	characteristic
19	Dic₂₉	Q₃₂	1	1	yes	characteristic
20	C₂×C₃₂	—	29	1	no	—
21	#366	—	29	2	no	—
22	C₂×C₂₉	#366	1	1	yes	characteristic
23	D₂₉	SD₆₄	1	2	yes	—
24	C₂×C₁₆	—	29	1	no	—
25	#107	—	58	2	no	—
26	C₃₂	—	29	1	no	—
27	C₃₂	#1181	1	1	yes	characteristic, complemented
28	C₂₉	#1424	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₈	—	29	1	no	—
30	C₄⋊C₄	—	116	2	no	—
31	C₁₆	—	29	1	no	—
32	C₁₆	C₂×#1181	1	1	yes	characteristic
33	C₂×C₄	—	29	1	no	—
34	C₂×C₄	—	232	2	no	—
35	C₈	—	29	1	no	—
36	C₈	C₄⋊#1181	1	1	yes	characteristic
37	C₂²	—	29	1	no	—
38	C₄	—	29	1	no	—
39	C₄	—	464	2	no	—
40	C₄	#11745210	1	1	yes	characteristic
41	C₂	—	29	2	no	—
42	C₂	#14272089	1	1	yes	characteristic

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.