Subgroups — #16837677

Order 3776.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14273757	C₂	1	2	yes	maximal
2	C₂×Dic₂₃₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#14273663	C₂	1	1	yes	maximal, characteristic, complemented
4	#14273645	C₂	1	2	yes	maximal, complemented
5	#131×C₅₉	C₂	1	1	yes	maximal, characteristic
6	#41×C₅₉	C₂²	1	1	yes	characteristic
7	C₂×Dic₁₁₈	C₂²	1	2	yes	—
8	M₁₆×C₅₉	—	2	1	no	—
9	M₁₆×C₅₉	C₂²	1	1	yes	characteristic
10	C₂×C₈×C₅₉	—	2	1	no	—
11	C₂×C₈×C₅₉	C₂²	1	1	yes	characteristic
12	#11745672	—	2	2	no	—
13	#11745670	—	2	2	no	—
14	#11745664	C₂²	1	2	yes	—
15	Dic₂₃₆	—	2	1	no	—
16	Dic₂₃₆	—	2	1	no	—
17	Q₈×C₅₉	D₄	1	1	yes	characteristic
18	D₄×C₅₉	—	2	1	no	—
19	D₄×C₅₉	D₄	1	1	yes	characteristic
20	C₂×C₄×C₅₉	—	2	1	no	—
21	C₂×C₄×C₅₉	C₂³	1	1	yes	characteristic
22	C₂×Dic₅₉	—	2	2	no	—
23	Dic₁₁₈	—	2	2	no	—
24	Dic₁₁₈	—	2	2	no	—
25	C₈×C₅₉	—	2	1	no	—
26	C₈×C₅₉	D₄	1	1	yes	characteristic
27	C₈×C₅₉	D₄	1	1	yes	characteristic
28	C₅₉⋊C₈	—	2	2	no	—
29	C₂²×C₅₉	—	2	1	no	—
30	C₂²×C₅₉	#41	1	1	yes	characteristic
31	C₄×C₅₉	—	2	1	no	—
32	C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
33	C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
34	Dic₅₉	—	4	2	no	—
35	C₂×C₅₉	—	2	1	no	—
36	C₂×C₅₉	—	4	1	no	—
37	C₂×C₅₉	#121	1	1	yes	characteristic
38	#473	—	59	1	no	maximal, Sylow
39	C₅₉	#473	1	1	yes	characteristic, complemented, Sylow
40	#137	—	59	2	no	—
41	C₂×Q₁₆	—	59	1	no	—
42	#131	D₅₉	1	1	yes	characteristic
43	#108	—	59	1	no	—
44	#101	—	59	2	no	—
45	#41	C₂×D₅₉	1	1	yes	characteristic
46	C₂×Q₈	—	59	2	no	—
47	Q₁₆	—	118	2	no	—
48	Q₁₆	—	118	1	no	—
49	Q₁₆	—	118	1	no	—
50	SD₁₆	—	118	2	no	—
51	M₁₆	—	2	1	no	—
52	M₁₆	—	59	2	no	—
53	M₁₆	C₂×D₅₉	1	1	yes	characteristic
54	C₂×C₈	—	2	1	no	—
55	C₂×C₈	C₂×D₅₉	1	1	yes	characteristic
56	Q₈	—	118	2	no	—
57	Q₈	—	118	2	no	—
58	Q₈	D₂₃₆	1	1	yes	characteristic
59	D₄	—	2	1	no	—
60	D₄	D₂₃₆	1	1	yes	characteristic
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	—	118	2	no	—
63	C₂×C₄	C₂²×D₅₉	1	1	yes	characteristic
64	C₈	—	2	1	no	—
65	C₈	—	118	2	no	—
66	C₈	C₂²⋊D₅₉	1	1	yes	characteristic
67	C₈	C₂²⋊D₅₉	1	1	yes	characteristic
68	C₂²	—	2	1	no	—
69	C₂²	#11745685	1	1	yes	characteristic
70	C₄	—	2	1	no	—
71	C₄	—	236	2	no	—
72	C₄	C₂×D₂₃₆	1	1	yes	characteristic
73	C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
74	C₂	—	2	1	no	—
75	C₂	—	4	1	no	—
76	C₂	#14273701	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14273701
commutator, cosocle	C₂×C₄×C₅₉	C₂³
Frattini	C₂×C₄	C₂²×D₅₉
Fitting	#131×C₅₉	C₂
socle	C₂×C₅₉	#121
prime radical	#41×C₅₉	C₂²
hypercenter	#131	D₅₉
hypocenter	C₅₉	#473
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #131

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₂₃₆	C₂	semidirect
3. #14273663	C₂	semidirect
4. #14273645	C₂	semidirect
39. C₅₉	#473	semidirect

Maximal subgroups

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

subgroup	index
#14273757	2
C₂×Dic₂₃₆	2
#14273663	2
#14273645	2
#131×C₅₉	2
#473	59