Subgroups — C₂²×C₅₉⋊C₁₆ #16837814

Order 3776.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉⋊C₁₆	C₂	1	6	yes	maximal, direct product factor
2	C₂²×C₈×C₅₉	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄×C₅₉	C₄	1	1	yes	characteristic
4	C₂×C₈×C₅₉	C₄	1	3	yes	—
5	C₂×C₈×C₅₉	C₂²	1	3	yes	—
6	C₅₉⋊C₁₆	C₂²	1	4	yes	direct product factor
7	C₂³×C₅₉	C₈	1	1	yes	characteristic
8	C₂×C₄×C₅₉	C₈	1	3	yes	—
9	C₂×C₄×C₅₉	C₂×C₄	1	3	yes	—
10	C₈×C₅₉	C₂×C₄	1	3	yes	—
11	C₈×C₅₉	C₂³	1	1	yes	characteristic
12	C₂²×C₅₉	C₁₆	1	4	yes	complemented
13	C₂²×C₅₉	C₂×C₈	1	3	yes	—
14	C₄×C₅₉	C₂×C₈	1	3	yes	—
15	C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
16	C₂×C₅₉	C₂×C₁₆	1	6	yes	complemented
17	C₂×C₅₉	C₂²×C₈	1	1	yes	characteristic
18	C₂²×C₁₆	—	59	1	no	maximal, Sylow
19	C₅₉	C₂²×C₁₆	1	1	yes	characteristic, complemented, Sylow
20	C₂²×C₈	D₅₉	1	1	yes	characteristic
21	C₂×C₁₆	—	59	6	no	—
22	C₂²×C₄	Dic₅₉	1	1	yes	characteristic
23	C₂×C₈	Dic₅₉	1	3	yes	—
24	C₂×C₈	C₂×D₅₉	1	3	yes	—
25	C₁₆	—	59	4	no	—
26	C₂³	C₅₉⋊C₈	1	1	yes	characteristic
27	C₂×C₄	C₅₉⋊C₈	1	3	yes	—
28	C₂×C₄	C₂×Dic₅₉	1	3	yes	—
29	C₈	C₂×Dic₅₉	1	3	yes	—
30	C₈	C₂²×D₅₉	1	1	yes	characteristic
31	C₂²	C₅₉⋊C₁₆	1	4	yes	direct product factor
32	C₂²	C₂×C₅₉⋊C₈	1	3	yes	—
33	C₄	C₂×C₅₉⋊C₈	1	3	yes	—
34	C₄	C₂²×Dic₅₉	1	1	yes	characteristic
35	C₂	C₂×C₅₉⋊C₁₆	1	6	yes	direct product factor
36	C₂	C₂²×C₅₉⋊C₈	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.