Subgroups — C₂²×C₄×C₂²⋊D₅₉ #21437265

Order 7552.

2528 conjugacy classes of subgroups.

The subgroup lattice has 216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₂²⋊D₅₉	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₄×D₅₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₂²⋊D₅₉	C₂	1	24	yes	maximal, direct product factor
4	C₂²×Dic₅₉⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₂²⋊Dic₅₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×(C₂×D₅₉)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₄×Dic₅₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂⁴×C₄×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂⁴×D₅₉	C₂²	1	1	yes	characteristic
10	C₂²×C₂²⋊D₅₉	C₄	1	16	yes	direct product factor
11	C₂²×C₂²⋊D₅₉	C₂²	1	12	yes	—
12	C₂³×Dic₅₉	C₂²	1	1	yes	characteristic
13	C₂³×Dic₅₉	C₂²	1	1	yes	characteristic
14	C₂³×Dic₅₉	C₂²	1	1	yes	characteristic
15	C₂²×C₄×D₅₉	—	2	8	no	—
16	C₂²×C₄×D₅₉	C₂²	1	12	yes	complemented
17	C₄×C₂²⋊D₅₉	C₂²	1	64	yes	direct product factor
18	C₂×Dic₅₉⋊C₄	C₂²	1	12	yes	complemented
19	C₂×C₂²⋊Dic₅₉	C₂²	1	12	yes	complemented
20	C₂×(C₂×D₅₉)⋊C₄	C₂²	1	12	yes	complemented
21	C₂×C₄×Dic₅₉	C₂²	1	12	yes	complemented
22	C₂⁵×C₅₉	C₂²	1	1	yes	characteristic
23	C₂³×C₄×C₅₉	—	2	8	no	—
24	C₂³×C₄×C₅₉	C₂²	1	1	yes	characteristic
25	C₂³×C₄×C₅₉	C₂²	1	1	yes	characteristic
26	C₂³×C₄×C₅₉	C₂²	1	12	yes	complemented
27	C₂⁴×C₅₉	—	2	4	no	—
28	C₂⁴×C₅₉	—	2	4	no	—
29	C₂⁴×C₅₉	C₂×C₄	1	8	yes	complemented
30	C₂⁴×C₅₉	C₂³	1	6	yes	—
31	C₂⁴×C₅₉	C₂³	1	1	yes	characteristic
32	C₂³×D₅₉	—	2	4	no	—
33	C₂³×D₅₉	—	2	4	no	—
34	C₂³×D₅₉	C₂×C₄	1	8	yes	complemented
35	C₂³×D₅₉	C₂³	1	6	yes	—
36	C₂²×C₄×C₅₉	—	2	4	no	—
37	C₂²×C₄×C₅₉	—	2	48	no	—
38	C₂²×C₄×C₅₉	D₄	1	8	yes	complemented
39	C₂²×C₄×C₅₉	C₂³	1	6	yes	—
40	C₂²×C₄×C₅₉	C₂³	1	6	yes	—
41	C₂²×C₄×C₅₉	C₂³	1	16	yes	complemented
42	C₂×C₂²⋊D₅₉	C₂×C₄	1	96	yes	direct product factor
43	C₂×C₂²⋊D₅₉	C₂³	1	16	yes	—
44	C₂²×Dic₅₉	—	2	4	no	—
45	C₂²×Dic₅₉	—	2	4	no	—
46	C₂²×Dic₅₉	C₂×C₄	1	8	yes	complemented
47	C₂²×Dic₅₉	C₂³	1	6	yes	—
48	C₂²×Dic₅₉	C₂³	1	6	yes	—
49	C₂²×Dic₅₉	C₂³	1	6	yes	—
50	C₂×C₄×D₅₉	—	2	48	no	—
51	C₂×C₄×D₅₉	C₂³	1	16	yes	complemented
52	C₂²⋊Dic₅₉	C₂³	1	16	yes	complemented
53	(C₂×D₅₉)⋊C₄	C₂³	1	16	yes	complemented
54	Dic₅₉⋊C₄	C₂³	1	16	yes	complemented
55	C₄×Dic₅₉	C₂³	1	16	yes	complemented
56	C₂³×C₅₉	—	2	32	no	—
57	C₂³×C₅₉	—	2	12	no	—
58	C₂³×C₅₉	—	2	12	no	—
59	C₂³×C₅₉	C₂²×C₄	1	4	yes	—
60	C₂³×C₅₉	C₂²×C₄	1	24	yes	complemented
61	C₂³×C₅₉	C₂×D₄	1	4	yes	—
62	C₂³×C₅₉	#41	1	4	yes	—
63	C₂³×C₅₉	C₂⁴	1	4	yes	—
64	C₂³×C₅₉	C₂⁴	1	3	yes	—
65	C₂²×D₅₉	—	2	32	no	—
66	C₂²×D₅₉	—	2	12	no	—
67	C₂²×D₅₉	—	2	12	no	—
68	C₂²×D₅₉	C₂²×C₄	1	24	yes	complemented
69	C₂²×D₅₉	C₂⁴	1	4	yes	—
70	C₂×C₄×C₅₉	—	2	12	no	—
71	C₂×C₄×C₅₉	—	2	32	no	—
72	C₂×C₄×C₅₉	C₂×D₄	1	24	yes	complemented
73	C₂×C₄×C₅₉	C₂⁴	1	4	yes	—
74	C₂×C₄×C₅₉	C₂⁴	1	4	yes	—
75	C₂²⋊D₅₉	C₂²×C₄	1	64	yes	direct product factor
76	C₂×Dic₅₉	—	2	12	no	—
77	C₂×Dic₅₉	—	2	12	no	—
78	C₂×Dic₅₉	C₂²×C₄	1	24	yes	complemented
79	C₂×Dic₅₉	C₂⁴	1	4	yes	—
80	C₂×Dic₅₉	C₂⁴	1	4	yes	—
81	C₂×Dic₅₉	C₂⁴	1	4	yes	—
82	C₄×D₅₉	—	2	32	no	—
83	C₂²×C₅₉	—	2	48	no	—
84	C₂²×C₅₉	—	2	4	no	—
85	C₂²×C₅₉	—	2	4	no	—
86	C₂²×C₅₉	C₄×D₄	1	16	yes	complemented
87	C₂²×C₅₉	C₂³×C₄	1	6	yes	—
88	C₂²×C₅₉	C₂³×C₄	1	8	yes	complemented
89	C₂²×C₅₉	C₂²×D₄	1	6	yes	—
90	C₂²×C₅₉	C₂×#41	1	6	yes	—
91	C₂²×C₅₉	C₂⁵	1	1	yes	characteristic
92	C₂×D₅₉	—	2	48	no	—
93	C₂×D₅₉	—	2	4	no	—
94	C₂×D₅₉	—	2	4	no	—
95	C₂×D₅₉	C₂³×C₄	1	8	yes	complemented
96	C₄×C₅₉	—	2	4	no	—
97	C₄×C₅₉	C₂²×D₄	1	8	yes	complemented
98	Dic₅₉	—	2	4	no	—
99	Dic₅₉	—	2	4	no	—
100	Dic₅₉	C₂³×C₄	1	8	yes	complemented
101	C₂²×C₄×D₄	—	59	1	no	maximal, Sylow
102	C₂×C₅₉	—	2	8	no	—
103	C₂×C₅₉	C₂×C₄×D₄	1	12	yes	complemented
104	C₂×C₅₉	C₂⁴×C₄	1	1	yes	characteristic
105	C₂×C₅₉	C₂³×D₄	1	1	yes	characteristic
106	C₂×C₅₉	C₂²×#41	1	1	yes	characteristic
107	D₅₉	—	2	8	no	—
108	C₂³×D₄	—	59	1	no	—
109	C₂⁴×C₄	—	59	1	no	—
110	C₂⁴×C₄	D₅₉	1	1	yes	characteristic, complemented
111	C₂×C₄×D₄	—	59	24	no	—
112	C₂²×C₄⋊C₄	—	59	1	no	—
113	C₂²×C₂²⋊C₄	—	59	1	no	—
114	C₂²×C₂²⋊C₄	—	59	1	no	—
115	C₂²×C₄²	—	59	1	no	—
116	C₅₉	C₂²×C₄×D₄	1	1	yes	characteristic, complemented, Sylow
117	C₂⁵	—	59	1	no	—
118	C₂⁵	C₂×D₅₉	1	1	yes	characteristic
119	C₂²×D₄	—	59	16	no	—
120	C₂²×D₄	—	59	12	no	—
121	C₂³×C₄	—	2	8	no	—
122	C₂³×C₄	—	59	1	no	—
123	C₂³×C₄	—	59	1	no	—
124	C₂³×C₄	—	59	1	no	—
125	C₂³×C₄	—	59	12	no	—
126	C₂³×C₄	—	118	8	no	—
127	C₂³×C₄	C₂×D₅₉	1	1	yes	characteristic
128	C₂³×C₄	C₂×D₅₉	1	1	yes	characteristic
129	C₂³×C₄	C₂×D₅₉	1	12	yes	complemented
130	C₄×D₄	—	59	64	no	—
131	C₂×C₄⋊C₄	—	59	12	no	—
132	C₂×C₂²⋊C₄	—	59	12	no	—
133	C₂×C₂²⋊C₄	—	59	12	no	—
134	C₂×C₄²	—	59	12	no	—
135	C₂⁴	—	2	4	no	—
136	C₂⁴	—	2	4	no	—
137	C₂⁴	—	59	8	no	—
138	C₂⁴	—	59	6	no	—
139	C₂⁴	—	118	4	no	—
140	C₂⁴	—	118	4	no	—
141	C₂⁴	C₄×D₅₉	1	8	yes	complemented
142	C₂⁴	C₂²×D₅₉	1	6	yes	—
143	C₂⁴	C₂²×D₅₉	1	1	yes	characteristic
144	C₂×D₄	—	59	96	no	—
145	C₂×D₄	—	59	16	no	—
146	C₂²×C₄	—	2	4	no	—
147	C₂²×C₄	—	2	48	no	—
148	C₂²×C₄	—	59	8	no	—
149	C₂²×C₄	—	59	6	no	—
150	C₂²×C₄	—	59	6	no	—
151	C₂²×C₄	—	59	6	no	—
152	C₂²×C₄	—	59	16	no	—
153	C₂²×C₄	—	118	4	no	—
154	C₂²×C₄	—	118	4	no	—
155	C₂²×C₄	—	118	48	no	—
156	C₂²×C₄	C₂²⋊D₅₉	1	8	yes	direct product factor
157	C₂²×C₄	C₂²×D₅₉	1	6	yes	—
158	C₂²×C₄	C₂²×D₅₉	1	6	yes	—
159	C₂²×C₄	C₂²×D₅₉	1	16	yes	complemented
160	C₄⋊C₄	—	59	16	no	—
161	C₂²⋊C₄	—	59	16	no	—
162	C₂²⋊C₄	—	59	16	no	—
163	C₄²	—	59	16	no	—
164	C₂³	—	2	32	no	—
165	C₂³	—	2	12	no	—
166	C₂³	—	2	12	no	—
167	C₂³	—	59	24	no	—
168	C₂³	—	59	4	no	—
169	C₂³	—	118	32	no	—
170	C₂³	—	118	12	no	—
171	C₂³	—	118	12	no	—
172	C₂³	C₂×C₄×D₅₉	1	4	yes	—
173	C₂³	C₂×C₄×D₅₉	1	24	yes	complemented
174	C₂³	#11745685	1	4	yes	—
175	C₂³	C₂×C₂²⋊D₅₉	1	4	yes	—
176	C₂³	C₂³×D₅₉	1	4	yes	—
177	C₂³	C₂³×D₅₉	1	3	yes	—
178	D₄	—	59	64	no	—
179	C₂×C₄	—	2	12	no	—
180	C₂×C₄	—	2	32	no	—
181	C₂×C₄	—	59	24	no	—
182	C₂×C₄	—	59	4	no	—
183	C₂×C₄	—	59	4	no	—
184	C₂×C₄	—	59	4	no	—
185	C₂×C₄	—	118	12	no	—
186	C₂×C₄	—	118	12	no	—
187	C₂×C₄	—	118	32	no	—
188	C₂×C₄	C₂×C₂²⋊D₅₉	1	24	yes	direct product factor
189	C₂×C₄	C₂³×D₅₉	1	4	yes	—
190	C₂×C₄	C₂³×D₅₉	1	4	yes	—
191	C₂²	—	2	4	no	—
192	C₂²	—	2	4	no	—
193	C₂²	—	2	48	no	—
194	C₂²	—	59	8	no	—
195	C₂²	—	118	4	no	—
196	C₂²	—	118	4	no	—
197	C₂²	—	118	48	no	—
198	C₂²	C₄×C₂²⋊D₅₉	1	16	yes	direct product factor
199	C₂²	C₂²×C₄×D₅₉	1	6	yes	—
200	C₂²	C₂²×C₄×D₅₉	1	8	yes	complemented
201	C₂²	C₂²×C₂²⋊D₅₉	1	6	yes	—
202	C₂²	C₂×#11745685	1	6	yes	—
203	C₂²	C₂⁴×D₅₉	1	1	yes	characteristic
204	C₄	—	2	4	no	—
205	C₄	—	59	8	no	—
206	C₄	—	118	4	no	—
207	C₄	—	118	4	no	—
208	C₄	C₂²×C₂²⋊D₅₉	1	8	yes	direct product factor
209	C₂	—	2	8	no	—
210	C₂	—	118	8	no	—
211	C₂	C₂×C₄×C₂²⋊D₅₉	1	12	yes	direct product factor
212	C₂	C₂³×C₄×D₅₉	1	1	yes	characteristic
213	C₂	C₂³×C₂²⋊D₅₉	1	1	yes	characteristic
214	C₂	C₂²×#11745685	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄	C₂×D₅₉
commutator	C₂×C₅₉	C₂⁴×C₄
Frattini	C₂²	C₂⁴×D₅₉
Fitting	C₂⁴×C₄×C₅₉	C₂
socle	C₂⁴×C₅₉	C₂³
hypercenter	C₂⁴×C₄	D₅₉
hypocenter	C₅₉	C₂²×C₄×D₄
LCS	G ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂³×C₄ ◁ C₂⁴×C₄

Complements

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

N	H ≅ G/N	type
2. C₂³×C₄×D₅₉	C₂	semidirect
3. C₂×C₄×C₂²⋊D₅₉	C₂	direct (N × H)
4. C₂²×Dic₅₉⋊C₄	C₂	semidirect
5. C₂²×C₂²⋊Dic₅₉	C₂	semidirect
6. C₂²×(C₂×D₅₉)⋊C₄	C₂	semidirect
7. C₂²×C₄×Dic₅₉	C₂	semidirect
8. C₂⁴×C₄×C₅₉	C₂	semidirect
10. C₂²×C₂²⋊D₅₉	C₄	direct (N × H)
16. C₂²×C₄×D₅₉	C₂²	semidirect
17. C₄×C₂²⋊D₅₉	C₂²	direct (N × H)
18. C₂×Dic₅₉⋊C₄	C₂²	semidirect
19. C₂×C₂²⋊Dic₅₉	C₂²	semidirect
20. C₂×(C₂×D₅₉)⋊C₄	C₂²	semidirect
21. C₂×C₄×Dic₅₉	C₂²	semidirect
26. C₂³×C₄×C₅₉	C₂²	semidirect
29. C₂⁴×C₅₉	C₂×C₄	semidirect
34. C₂³×D₅₉	C₂×C₄	semidirect
38. C₂²×C₄×C₅₉	D₄	semidirect
41. C₂²×C₄×C₅₉	C₂³	semidirect
42. C₂×C₂²⋊D₅₉	C₂×C₄	direct (N × H)
46. C₂²×Dic₅₉	C₂×C₄	semidirect
51. C₂×C₄×D₅₉	C₂³	semidirect
52. C₂²⋊Dic₅₉	C₂³	semidirect
53. (C₂×D₅₉)⋊C₄	C₂³	semidirect
54. Dic₅₉⋊C₄	C₂³	semidirect
55. C₄×Dic₅₉	C₂³	semidirect
60. C₂³×C₅₉	C₂²×C₄	semidirect
68. C₂²×D₅₉	C₂²×C₄	semidirect
72. C₂×C₄×C₅₉	C₂×D₄	semidirect
75. C₂²⋊D₅₉	C₂²×C₄	direct (N × H)
78. C₂×Dic₅₉	C₂²×C₄	semidirect
86. C₂²×C₅₉	C₄×D₄	semidirect
88. C₂²×C₅₉	C₂³×C₄	semidirect
95. C₂×D₅₉	C₂³×C₄	semidirect
97. C₄×C₅₉	C₂²×D₄	semidirect
100. Dic₅₉	C₂³×C₄	semidirect
103. C₂×C₅₉	C₂×C₄×D₄	semidirect
110. C₂⁴×C₄	D₅₉	semidirect
116. C₅₉	C₂²×C₄×D₄	semidirect
129. C₂³×C₄	C₂×D₅₉	semidirect
141. C₂⁴	C₄×D₅₉	semidirect
156. C₂²×C₄	C₂²⋊D₅₉	direct (N × H)
159. C₂²×C₄	C₂²×D₅₉	semidirect
173. C₂³	C₂×C₄×D₅₉	semidirect
188. C₂×C₄	C₂×C₂²⋊D₅₉	direct (N × H)
198. C₂²	C₄×C₂²⋊D₅₉	direct (N × H)
200. C₂²	C₂²×C₄×D₅₉	semidirect
208. C₄	C₂²×C₂²⋊D₅₉	direct (N × H)
211. C₂	C₂×C₄×C₂²⋊D₅₉	direct (N × H)

Subgroups — C22×C4×C22⋊D59 #21437265

Conjugacy classes of subgroups

Complements

Subgroups — C₂²×C₄×C₂²⋊D₅₉ #21437265