Subgroups — #16837771

Order 3776.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14273727	C₂	1	1	yes	maximal, characteristic
2	#14273719	C₂	1	1	yes	maximal, characteristic
3	#14273652	C₂	1	4	yes	maximal
4	#97×C₅₉	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₁₁₈	C₂²	1	2	yes	—
6	C₂×C₈×C₅₉	C₂²	1	2	yes	—
7	C₄²×C₅₉	C₂²	1	1	yes	characteristic
8	C₄⋊Dic₅₉	—	2	2	no	—
9	C₄⋊Dic₅₉	C₂²	1	2	yes	—
10	Dic₅₉⋊C₄	—	2	2	no	—
11	C₂×C₄×C₅₉	D₄	1	2	yes	—
12	C₂×C₄×C₅₉	C₂³	1	1	yes	characteristic
13	C₂×Dic₅₉	—	2	2	no	—
14	C₂×Dic₅₉	—	2	2	no	—
15	Dic₁₁₈	—	2	4	no	—
16	C₈×C₅₉	—	2	2	no	—
17	C₂²×C₅₉	C₂×D₄	1	1	yes	characteristic
18	C₄×C₅₉	—	2	2	no	—
19	C₄×C₅₉	#41	1	2	yes	—
20	Dic₅₉	—	4	2	no	—
21	Dic₅₉	—	4	2	no	—
22	C₂×C₅₉	#124	1	1	yes	characteristic
23	C₂×C₅₉	#137	1	2	yes	—
24	#491	—	59	1	no	maximal, Sylow
25	C₅₉	#491	1	1	yes	characteristic, complemented, Sylow
26	C₄⋊Q₈	—	59	1	no	—
27	#125	—	59	1	no	—
28	#103	—	59	4	no	—
29	#97	D₅₉	1	1	yes	characteristic
30	C₂×Q₈	—	59	2	no	—
31	C₂×C₈	C₂×D₅₉	1	2	yes	—
32	C₄⋊C₄	—	59	2	no	—
33	C₄⋊C₄	—	118	2	no	—
34	C₄⋊C₄	—	118	2	no	—
35	C₄²	C₂×D₅₉	1	1	yes	characteristic
36	Q₈	—	118	4	no	—
37	C₂×C₄	—	118	2	no	—
38	C₂×C₄	—	118	2	no	—
39	C₂×C₄	D₂₃₆	1	2	yes	—
40	C₂×C₄	C₂²×D₅₉	1	1	yes	characteristic
41	C₈	—	2	2	no	—
42	C₂²	C₂×D₂₃₆	1	1	yes	characteristic
43	C₄	—	2	2	no	—
44	C₄	—	236	2	no	—
45	C₄	—	236	2	no	—
46	C₄	#11745685	1	2	yes	—
47	C₂	#14273715	1	1	yes	characteristic
48	C₂	#14273760	1	2	yes	—

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

N	H ≅ G/N	type
25. C₅₉	#491	semidirect

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