Subgroups — #16837639

Order 3776.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄₇₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₈×D₅₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#14273702	C₂	1	2	yes	maximal, complemented
4	#14273647	C₂	1	2	yes	maximal, complemented
5	#107×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₂₃₆	—	2	2	no	—
7	C₂×D₂₃₆	C₂²	1	2	yes	—
8	C₂×C₄×D₅₉	C₂²	1	1	yes	characteristic
9	C₂×C₈×C₅₉	C₂²	1	1	yes	characteristic
10	C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
11	(C₂×D₅₉)⋊C₄	—	2	2	no	—
12	C₂×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
13	D₄₇₂	—	2	2	no	—
14	C₈×D₅₉	—	2	2	no	—
15	C₂²×D₅₉	—	2	2	no	—
16	C₂²×D₅₉	D₄	1	1	yes	characteristic
17	C₂×C₄×C₅₉	—	2	2	no	—
18	C₂×C₄×C₅₉	C₂³	1	1	yes	characteristic
19	C₂×Dic₅₉	D₄	1	1	yes	characteristic
20	D₂₃₆	—	2	2	no	—
21	D₂₃₆	—	2	2	no	—
22	D₂₃₆	—	4	4	no	—
23	C₄×D₅₉	—	2	1	no	—
24	C₄×D₅₉	—	2	1	no	—
25	C₈×C₅₉	D₄	1	2	yes	complemented
26	C₅₉⋊C₈	—	2	1	no	—
27	C₂²×C₅₉	C₂×D₄	1	1	yes	characteristic
28	C₂×D₅₉	—	2	1	no	—
29	C₂×D₅₉	—	2	1	no	—
30	C₂×D₅₉	—	4	2	no	—
31	C₂×D₅₉	—	4	2	no	—
32	C₂×D₅₉	—	4	2	no	—
33	C₂×D₅₉	D₈	1	2	yes	complemented
34	C₄×C₅₉	—	4	2	no	—
35	C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
36	C₄×C₅₉	#41	1	1	yes	characteristic
37	Dic₅₉	—	2	1	no	—
38	C₂×C₅₉	#121	1	1	yes	characteristic
39	C₂×C₅₉	C₂×D₈	1	1	yes	characteristic
40	C₂×C₅₉	#135	1	1	yes	characteristic
41	D₅₉	—	2	2	no	—
42	D₅₉	—	8	2	no	—
43	#466	—	59	1	no	maximal, Sylow
44	C₅₉	#466	1	1	yes	characteristic, complemented, Sylow
45	C₂×D₈	—	59	1	no	—
46	C₂²×C₈	—	59	1	no	—
47	#121	—	59	2	no	—
48	#107	D₅₉	1	1	yes	characteristic, complemented
49	#102	—	59	2	no	—
50	C₂×D₄	—	59	2	no	—
51	C₂×D₄	—	118	2	no	—
52	C₂²×C₄	—	59	1	no	—
53	D₈	—	118	2	no	—
54	C₂×C₈	—	59	1	no	—
55	C₂×C₈	—	118	2	no	—
56	C₂×C₈	C₂×D₅₉	1	1	yes	characteristic
57	C₄⋊C₄	C₂×D₅₉	1	2	yes	—
58	C₂²⋊C₄	—	118	2	no	—
59	C₂³	—	59	1	no	—
60	C₂³	—	118	2	no	—
61	D₄	—	118	2	no	—
62	D₄	—	118	2	no	—
63	D₄	—	236	4	no	—
64	C₂×C₄	—	2	2	no	—
65	C₂×C₄	—	59	1	no	—
66	C₂×C₄	—	118	1	no	—
67	C₂×C₄	—	118	1	no	—
68	C₂×C₄	C₂²×D₅₉	1	1	yes	characteristic
69	C₈	—	118	1	no	—
70	C₈	D₂₃₆	1	2	yes	complemented
71	C₂²	—	59	2	no	—
72	C₂²	—	118	1	no	—
73	C₂²	—	118	1	no	—
74	C₂²	—	236	2	no	—
75	C₂²	—	236	2	no	—
76	C₂²	—	236	2	no	—
77	C₂²	D₄×D₅₉	1	1	yes	characteristic
78	C₄	—	4	2	no	—
79	C₄	—	118	1	no	—
80	C₄	C₂×D₂₃₆	1	1	yes	characteristic
81	C₄	#11745689	1	1	yes	characteristic
82	C₂	—	118	2	no	—
83	C₂	—	472	2	no	—
84	C₂	#14273702	1	1	yes	characteristic
85	C₂	D₈×D₅₉	1	1	yes	characteristic
86	C₂	#14273750	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₅₉
commutator, cosocle	C₂×C₄×C₅₉	C₂³
Frattini	C₂×C₄	C₂²×D₅₉
Fitting	#107×C₅₉	C₂
socle	C₂²×C₅₉	C₂×D₄
hypercenter	#107	D₅₉
hypocenter	C₅₉	#466
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

Complements

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

N	H ≅ G/N	type
1. C₂×D₄₇₂	C₂	semidirect
2. C₂×C₈×D₅₉	C₂	semidirect
3. #14273702	C₂	semidirect
4. #14273647	C₂	semidirect
5. #107×C₅₉	C₂	semidirect
25. C₈×C₅₉	D₄	semidirect
33. C₂×D₅₉	D₈	semidirect
44. C₅₉	#466	semidirect
48. #107	D₅₉	semidirect
70. C₈	D₂₃₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄₇₂	2
C₂×C₈×D₅₉	2
#14273702	2
#14273647	2
#107×C₅₉	2
#466	59