Subgroups — #117×Dic₅₉ #21426439

Order 7552.

752 conjugacy classes of subgroups.

The subgroup lattice has 174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14273686	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×Dic₅₉	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₄×Dic₅₉	C₂	1	4	yes	maximal, complemented
4	C₂²⋊C₄×Dic₅₉	C₂	1	4	yes	maximal
5	#16837248	C₂	1	2	yes	maximal, complemented
6	C₄²×Dic₅₉	C₂	1	2	yes	maximal, complemented
7	C₂×#117×C₅₉	C₂	1	1	yes	maximal, characteristic
8	C₂³×Dic₅₉	C₂²	1	2	yes	—
9	#14273686	C₄	1	8	yes	complemented
10	C₂×C₄⋊Dic₅₉	C₂²	1	2	yes	—
11	C₂×C₂²⋊Dic₅₉	C₂²	1	2	yes	—
12	C₂×C₄×Dic₅₉	C₄	1	8	yes	complemented
13	C₂×C₄×Dic₅₉	C₂²	1	8	yes	—
14	C₂×C₄×Dic₅₉	C₂²	1	1	yes	characteristic
15	C₂×C₄×Dic₅₉	C₂²	1	1	yes	characteristic
16	C₂×C₄×Dic₅₉	C₂²	1	2	yes	—
17	C₂×C₄×Dic₅₉	C₂²	1	2	yes	—
18	C₅₉⋊#95	C₂²	1	8	yes	—
19	C₂³×C₄×C₅₉	C₂²	1	1	yes	characteristic
20	#117×C₅₉	C₄	1	8	yes	complemented
21	C₂×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
22	C₂×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
23	C₂×C₄²×C₅₉	C₂²	1	2	yes	—
24	C₂⁴×C₅₉	C₂³	1	1	yes	characteristic
25	C₂²×C₄×C₅₉	C₂×C₄	1	4	yes	—
26	C₂²×C₄×C₅₉	C₂×C₄	1	4	yes	—
27	C₂²×C₄×C₅₉	C₂×C₄	1	4	yes	—
28	C₂²×C₄×C₅₉	C₂³	1	4	yes	—
29	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
30	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
31	C₂²×Dic₅₉	—	2	8	no	—
32	C₂²×Dic₅₉	C₂×C₄	1	8	yes	—
33	C₂²×Dic₅₉	C₂³	1	2	yes	—
34	C₂²×Dic₅₉	C₂³	1	4	yes	—
35	C₂²×Dic₅₉	C₂³	1	2	yes	—
36	C₄⋊C₄×C₅₉	C₂×C₄	1	8	yes	complemented
37	C₂²⋊C₄×C₅₉	C₂×C₄	1	8	yes	—
38	C₄²×C₅₉	C₂×C₄	1	8	yes	complemented
39	C₂²⋊Dic₅₉	C₂×C₄	1	8	yes	—
40	C₄⋊Dic₅₉	C₂×C₄	1	8	yes	complemented
41	C₄×Dic₅₉	—	2	16	no	—
42	C₄×Dic₅₉	C₂×C₄	1	4	yes	—
43	C₄×Dic₅₉	C₂×C₄	1	8	yes	—
44	C₄×Dic₅₉	C₂×C₄	1	4	yes	—
45	C₄×Dic₅₉	C₂×C₄	1	8	yes	complemented
46	C₂³×C₅₉	—	2	4	no	—
47	C₂³×C₅₉	C₂²×C₄	1	2	yes	—
48	C₂³×C₅₉	C₂²×C₄	1	2	yes	—
49	C₂³×C₅₉	C₂²×C₄	1	2	yes	—
50	C₂³×C₅₉	C₂⁴	1	1	yes	characteristic
51	C₂×C₄×C₅₉	—	2	8	no	—
52	C₂×C₄×C₅₉	C₄²	1	16	yes	complemented
53	C₂×C₄×C₅₉	C₂²×C₄	1	2	yes	—
54	C₂×C₄×C₅₉	C₂²×C₄	1	2	yes	—
55	C₂×C₄×C₅₉	C₂²×C₄	1	2	yes	—
56	C₂×C₄×C₅₉	C₂²×C₄	1	2	yes	—
57	C₂×C₄×C₅₉	C₂²×C₄	1	8	yes	—
58	C₂×C₄×C₅₉	C₂²×C₄	1	2	yes	—
59	C₂×C₄×C₅₉	C₂²×C₄	1	2	yes	—
60	C₂×Dic₅₉	—	2	8	no	—
61	C₂×Dic₅₉	—	2	4	no	—
62	C₂×Dic₅₉	—	2	16	no	—
63	C₂×Dic₅₉	C₂²×C₄	1	4	yes	—
64	C₂×Dic₅₉	C₂²×C₄	1	8	yes	—
65	C₂×Dic₅₉	C₂²×C₄	1	4	yes	—
66	C₂×Dic₅₉	#41	1	8	yes	—
67	C₂²×C₅₉	—	2	4	no	—
68	C₂²×C₅₉	—	2	4	no	—
69	C₂²×C₅₉	—	2	4	no	—
70	C₂²×C₅₉	C₂×C₄²	1	4	yes	—
71	C₂²×C₅₉	C₂³×C₄	1	1	yes	characteristic
72	C₂²×C₅₉	C₂³×C₄	1	1	yes	characteristic
73	C₂²×C₅₉	C₂³×C₄	1	1	yes	characteristic
74	C₂²×C₅₉	C₂×#41	1	4	yes	—
75	C₄×C₅₉	—	2	8	no	—
76	C₄×C₅₉	C₂×C₄²	1	4	yes	—
77	C₄×C₅₉	C₂×C₄²	1	4	yes	—
78	Dic₅₉	—	2	4	no	—
79	Dic₅₉	—	2	8	no	—
80	Dic₅₉	#117	1	8	yes	direct product factor
81	C₄×#117	—	59	1	no	maximal, Sylow
82	C₂×C₅₉	—	2	4	no	—
83	C₂×C₅₉	C₂²×C₄²	1	1	yes	characteristic
84	C₂×C₅₉	C₂×#117	1	2	yes	—
85	C₂×C₅₉	C₄×#41	1	2	yes	—
86	C₂×C₅₉	C₄×#41	1	2	yes	—
87	C₂×#117	—	59	1	no	—
88	C₂×#117	D₅₉	1	1	yes	characteristic
89	C₂²×C₄²	—	59	1	no	—
90	C₄×C₄⋊C₄	—	59	4	no	—
91	C₄×C₂²⋊C₄	—	59	4	no	—
92	#376	—	59	2	no	—
93	C₄³	—	59	2	no	—
94	C₅₉	C₄×#117	1	1	yes	characteristic, complemented, Sylow
95	C₂³×C₄	—	59	2	no	—
96	C₂³×C₄	C₂×D₅₉	1	1	yes	characteristic
97	#117	—	59	8	no	—
98	#117	Dic₅₉	1	8	yes	direct product factor
99	C₂×C₄⋊C₄	—	59	2	no	—
100	C₂×C₄⋊C₄	C₂×D₅₉	1	2	yes	—
101	C₂×C₂²⋊C₄	—	59	2	no	—
102	C₂×C₂²⋊C₄	C₂×D₅₉	1	2	yes	—
103	C₂×C₄²	—	59	8	no	—
104	C₂×C₄²	—	59	2	no	—
105	C₂×C₄²	—	59	2	no	—
106	C₂×C₄²	—	59	1	no	—
107	C₂×C₄²	—	59	1	no	—
108	C₂×C₄²	—	59	8	no	—
109	C₂×C₄²	C₂×D₅₉	1	2	yes	—
110	#95	—	59	8	no	—
111	C₂⁴	C₂²×D₅₉	1	1	yes	characteristic
112	C₂²×C₄	—	59	2	no	—
113	C₂²×C₄	—	59	8	no	—
114	C₂²×C₄	—	59	2	no	—
115	C₂²×C₄	—	59	4	no	—
116	C₂²×C₄	—	118	8	no	—
117	C₂²×C₄	C₄×D₅₉	1	4	yes	—
118	C₂²×C₄	C₄×D₅₉	1	4	yes	—
119	C₂²×C₄	C₂×Dic₅₉	1	4	yes	—
120	C₂²×C₄	C₂²×D₅₉	1	4	yes	—
121	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
122	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
123	C₄⋊C₄	—	59	8	no	—
124	C₄⋊C₄	C₂×Dic₅₉	1	8	yes	complemented
125	C₂²⋊C₄	—	59	8	no	—
126	C₂²⋊C₄	C₂×Dic₅₉	1	8	yes	—
127	C₄²	—	59	4	no	—
128	C₄²	—	59	8	no	—
129	C₄²	—	59	4	no	—
130	C₄²	—	59	8	no	—
131	C₄²	—	118	16	no	—
132	C₄²	C₂×Dic₅₉	1	8	yes	complemented
133	C₂³	—	2	4	no	—
134	C₂³	C₂×C₄×D₅₉	1	2	yes	—
135	C₂³	C₂×C₄×D₅₉	1	2	yes	—
136	C₂³	C₂²×Dic₅₉	1	2	yes	—
137	C₂³	C₂³×D₅₉	1	1	yes	characteristic
138	C₂×C₄	—	2	8	no	—
139	C₂×C₄	—	59	4	no	—
140	C₂×C₄	—	59	8	no	—
141	C₂×C₄	—	59	4	no	—
142	C₂×C₄	—	59	8	no	—
143	C₂×C₄	—	118	16	no	—
144	C₂×C₄	—	118	8	no	—
145	C₂×C₄	—	118	4	no	—
146	C₂×C₄	C₄×Dic₅₉	1	16	yes	complemented
147	C₂×C₄	C₂×C₄×D₅₉	1	2	yes	—
148	C₂×C₄	C₂×C₄×D₅₉	1	2	yes	—
149	C₂×C₄	C₂×C₄×D₅₉	1	2	yes	—
150	C₂×C₄	C₂×C₄×D₅₉	1	2	yes	—
151	C₂×C₄	C₂²×Dic₅₉	1	8	yes	—
152	C₂×C₄	C₂²×Dic₅₉	1	2	yes	—
153	C₂×C₄	C₂²×Dic₅₉	1	2	yes	—
154	C₂²	—	2	4	no	—
155	C₂²	—	2	4	no	—
156	C₂²	—	2	4	no	—
157	C₂²	C₂×C₄×Dic₅₉	1	4	yes	—
158	C₂²	C₂²×C₄×D₅₉	1	1	yes	characteristic
159	C₂²	C₂²×C₄×D₅₉	1	1	yes	characteristic
160	C₂²	C₂³×Dic₅₉	1	1	yes	characteristic
161	C₂²	#41×D₅₉	1	4	yes	—
162	C₄	—	2	8	no	—
163	C₄	—	59	8	no	—
164	C₄	—	118	4	no	—
165	C₄	—	118	8	no	—
166	C₄	C₂×C₄×Dic₅₉	1	4	yes	—
167	C₄	C₂×C₄×Dic₅₉	1	4	yes	—
168	C₂	—	2	4	no	—
169	C₂	C₂²×C₄×Dic₅₉	1	1	yes	characteristic
170	C₂	#117×D₅₉	1	2	yes	—
171	C₂	#16837870	1	2	yes	—
172	C₂	#41×Dic₅₉	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂²×D₅₉
commutator	C₂×C₅₉	C₂²×C₄²
Frattini	C₂³	C₂³×D₅₉
Fitting	C₂×#117×C₅₉	C₂
socle	C₂³×C₅₉	C₂⁴
hypercenter	C₂×#117	D₅₉
hypocenter	C₅₉	C₄×#117
LCS	G ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#117

Complements

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

N	H ≅ G/N	type
3. C₄⋊C₄×Dic₅₉	C₂	semidirect
5. #16837248	C₂	semidirect
6. C₄²×Dic₅₉	C₂	semidirect
9. #14273686	C₄	semidirect
12. C₂×C₄×Dic₅₉	C₄	semidirect
20. #117×C₅₉	C₄	semidirect
36. C₄⋊C₄×C₅₉	C₂×C₄	semidirect
38. C₄²×C₅₉	C₂×C₄	semidirect
40. C₄⋊Dic₅₉	C₂×C₄	semidirect
45. C₄×Dic₅₉	C₂×C₄	semidirect
52. C₂×C₄×C₅₉	C₄²	semidirect
80. Dic₅₉	#117	direct (N × H)
94. C₅₉	C₄×#117	semidirect
98. #117	Dic₅₉	direct (N × H)
124. C₄⋊C₄	C₂×Dic₅₉	semidirect
132. C₄²	C₂×Dic₅₉	semidirect
146. C₂×C₄	C₄×Dic₅₉	semidirect

Subgroups — #117×Dic59 #21426439

Conjugacy classes of subgroups

Complements

Subgroups — #117×Dic₅₉ #21426439