Finite Group Databasebeta

← C22×C59×#353 #28445461

Subgroups — C22×C59×#353 #28445461

Order 15104.

2062 conjugacy classes of subgroups; only the 382 normal subgroups are shown.

normal subgroups only

This group has 2062 conjugacy classes of subgroups — too many to draw. Only its 382 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#127×C59C211yesmaximal, characteristic
2C22×#99×C59C212yesmaximal, complemented
3C2×C59×#353C2112yesmaximal, direct product factor
4C23×D4×C59—22no—
5C23×D4×C59C411yescharacteristic, complemented
6C23×D4×C59C2211yescharacteristic
7C2×#127×C59—26no—
8C2×#127×C59C416yescomplemented
9C2×#127×C59C2216yes—
10C22×C22⋊C4×C59—22no—
11C22×C42×C59C411yescharacteristic, complemented
12C2×#99×C59—26no—
13C2×#99×C59C22112yescomplemented
14C59×#353C22116yesdirect product factor
15C25×C59—21no—
16C25×C59D412yes—
17C22×D4×C59—212no—
18C22×D4×C59—212no—
19C22×D4×C59—23no—
20C22×D4×C59—43no—
21C22×D4×C59—41no—
22C22×D4×C59—43no—
23C22×D4×C59—41no—
24C22×D4×C59—416no—
25C22×D4×C59C2×C413yes—
26C22×D4×C59C2×C416yescomplemented
27C22×D4×C59D416yes—
28C22×D4×C59C2313yes—
29C23×C4×C59—21no—
30C23×C4×C59—42no—
31C23×C4×C59C2×C411yescharacteristic
32#127×C59—212no—
33#127×C59—212no—
34#127×C59C2×C4112yescomplemented
35#127×C59C2314yes—
36C2×C22⋊C4×C59—212no—
37C2×C22⋊C4×C59—46no—
38C2×C42×C59—23no—
39C2×C42×C59C2×C416yescomplemented
40#99×C59—212no—
41#99×C59C2318yescomplemented
42C24×C59—22no—
43C24×C59—26no—
44C24×C59—26no—
45C24×C59—48no—
46C24×C59—48no—
47C24×C59—43no—
48C24×C59—41no—
49C24×C59C22⋊C416yes—
50C24×C59C22⋊C411yescharacteristic
51C24×C59C2×D416yes—
52C2×D4×C59—224no—
53C2×D4×C59—28no—
54C2×D4×C59—26no—
55C2×D4×C59—43no—
56C2×D4×C59—43no—
57C2×D4×C59—46no—
58C2×D4×C59—46no—
59C2×D4×C59—43no—
60C2×D4×C59—43no—
61C2×D4×C59—448no—
62C2×D4×C59—448no—
63C2×D4×C59—46no—
64C2×D4×C59—46no—
65C2×D4×C59—46no—
66C2×D4×C59—46no—
67C2×D4×C59C22⋊C416yes—
68C2×D4×C59C22×C413yes—
69C2×D4×C59C22×C414yescomplemented
70C2×D4×C59C2×D416yes—
71C2×D4×C59C2411yescharacteristic
72C22×C4×C59—28no—
73C22×C4×C59—23no—
74C22×C4×C59—21no—
75C22×C4×C59—26no—
76C22×C4×C59—412no—
77C22×C4×C59—88no—
78C22×C4×C59C22⋊C413yes—
79C22×C4×C59C22×C413yes—
80C22⋊C4×C59—28no—
81C22⋊C4×C59—412no—
82C42×C59—26no—
83C42×C59C22×C414yescomplemented
84C23×C59—24no—
85C23×C59—26no—
86C23×C59—26no—
87C23×C59—26no—
88C23×C59—26no—
89C23×C59—24no—
90C23×C59—412no—
91C23×C59—412no—
92C23×C59—424no—
93C23×C59—48no—
94C23×C59—46no—
95C23×C59—46no—
96C23×C59—812no—
97C23×C59—812no—
98C23×C59—84no—
99C23×C59#9913yes—
100C23×C59#9911yescharacteristic
101C23×C59C2×C22⋊C413yes—
102C23×C59C2×C22⋊C416yes—
103C23×C59C22×D412yes—
104D4×C59—46no—
105D4×C59—43no—
106D4×C59—46no—
107D4×C59—41no—
108D4×C59—44no—
109D4×C59—448no—
110D4×C59—416no—
111D4×C59—412no—
112C2×C4×C59—224no—
113C2×C4×C59—24no—
114C2×C4×C59—23no—
115C2×C4×C59—23no—
116C2×C4×C59—23no—
117C2×C4×C59—23no—
118C2×C4×C59—48no—
119C2×C4×C59—824no—
120C2×C4×C59C2×C22⋊C413yes—
121C2×C4×C59C23×C411yescharacteristic
122C22×#353C5911yesmaximal, characteristic, direct product factor, Sylow
123C22×C59—26no—
124C22×C59—26no—
125C22×C59—22no—
126C22×C59—26no—
127C22×C59—46no—
128C22×C59—42no—
129C22×C59—48no—
130C22×C59—412no—
131C22×C59—412no—
132C22×C59—44no—
133C22×C59—86no—
134C22×C59—86no—
135C22×C59—812no—
136C22×C59—812no—
137C22×C59#35314yesdirect product factor
138C22×C59C2×#9913yes—
139C22×C59C2×#9913yes—
140C22×C59C22×C22⋊C411yescharacteristic
141C4×C59—28no—
142C4×C59—23no—
143C4×C59—21no—
144C4×C59—88no—
145C22×#127C2×C5911yescharacteristic
146C22×#99C2×C5912yescomplemented
147C2×#353C2×C59112yesdirect product factor
148C2×C59—21no—
149C2×C59—23no—
150C2×C59—42no—
151C2×C59—46no—
152C2×C59—84no—
153C2×C59C2×#35316yesdirect product factor
154C2×C59C22×#9911yescharacteristic
155C23×D4—22no—
156C23×D4C4×C5911yescharacteristic, complemented
157C23×D4C22×C5911yescharacteristic
158C2×#127—26no—
159C2×#127C4×C5916yescomplemented
160C2×#127C22×C5916yes—
161C22×C22⋊C4—22no—
162C22×C42C4×C5911yescharacteristic, complemented
163C2×#99—26no—
164C2×#99C22×C59112yescomplemented
165#353C22×C59116yesdirect product factor
166C59C22×#35311yescharacteristic, direct product factor, Sylow
167C25—21no—
168C25D4×C5912yes—
169C22×D4—212no—
170C22×D4—212no—
171C22×D4—23no—
172C22×D4—41no—
173C22×D4—43no—
174C22×D4—43no—
175C22×D4—41no—
176C22×D4—416no—
177C22×D4C2×C4×C5913yes—
178C22×D4C2×C4×C5916yescomplemented
179C22×D4D4×C5916yes—
180C22×D4C23×C5913yes—
181C23×C4—21no—
182C23×C4—42no—
183C23×C4C2×C4×C5911yescharacteristic
184#127—212no—
185#127—212no—
186#127C2×C4×C59112yescomplemented
187#127C23×C5914yes—
188C2×C22⋊C4—212no—
189C2×C22⋊C4—46no—
190C2×C42—23no—
191C2×C42C2×C4×C5916yescomplemented
192#99—212no—
193#99C23×C5918yescomplemented
194C24—22no—
195C24—26no—
196C24—26no—
197C24—48no—
198C24—48no—
199C24—43no—
200C24—41no—
201C24C22⋊C4×C5911yescharacteristic
202C24C22⋊C4×C5916yes—
203C24C2×D4×C5916yes—
204C2×D4—224no—
205C2×D4—28no—
206C2×D4—26no—
207C2×D4—43no—
208C2×D4—43no—
209C2×D4—46no—
210C2×D4—46no—
211C2×D4—43no—
212C2×D4—43no—
213C2×D4—46no—
214C2×D4—46no—
215C2×D4—448no—
216C2×D4—448no—
217C2×D4—46no—
218C2×D4—46no—
219C2×D4C22⋊C4×C5916yes—
220C2×D4C22×C4×C5913yes—
221C2×D4C22×C4×C5914yescomplemented
222C2×D4C2×D4×C5916yes—
223C2×D4C24×C5911yescharacteristic
224C22×C4—28no—
225C22×C4—23no—
226C22×C4—21no—
227C22×C4—26no—
228C22×C4—412no—
229C22×C4—88no—
230C22×C4C22⋊C4×C5913yes—
231C22×C4C22×C4×C5913yes—
232C22⋊C4—28no—
233C22⋊C4—412no—
234C42—26no—
235C42C22×C4×C5914yescomplemented
236C23—24no—
237C23—26no—
238C23—26no—
239C23—26no—
240C23—26no—
241C23—24no—
242C23—412no—
243C23—412no—
244C23—424no—
245C23—48no—
246C23—46no—
247C23—46no—
248C23—812no—
249C23—812no—
250C23—84no—
251C23#99×C5913yes—
252C23#99×C5911yescharacteristic
253C23C2×C22⋊C4×C5913yes—
254C23C2×C22⋊C4×C5916yes—
255C23C22×D4×C5912yes—
256D4—46no—
257D4—43no—
258D4—46no—
259D4—41no—
260D4—44no—
261D4—448no—
262D4—416no—
263D4—412no—
264C2×C4—224no—
265C2×C4—23no—
266C2×C4—23no—
267C2×C4—23no—
268C2×C4—23no—
269C2×C4—24no—
270C2×C4—48no—
271C2×C4—824no—
272C2×C4C2×C22⋊C4×C5913yes—
273C2×C4C23×C4×C5911yescharacteristic
274C22—26no—
275C22—26no—
276C22—22no—
277C22—26no—
278C22—46no—
279C22—42no—
280C22—48no—
281C22—412no—
282C22—412no—
283C22—44no—
284C22—86no—
285C22—86no—
286C22—812no—
287C22—812no—
288C22C59×#35314yesdirect product factor
289C22C2×#99×C5913yes—
290C22C2×#99×C5913yes—
291C22C22×C22⋊C4×C5911yescharacteristic
292C4—28no—
293C4—23no—
294C4—21no—
295C4—88no—
296C2—21no—
297C2—23no—
298C2—42no—
299C2—46no—
300C2—84no—
301C2C2×C59×#35316yesdirect product factor
302C2C22×#99×C5911yescharacteristic
subgroupG/H
center, socleC23×C59#99
commutatorC2×C4C23×C4×C59
Frattini, cosocleC2×D4C24×C59
prime radicalC22×#127×C59C2
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C23×C59 ◁ C24×C59 ◁ C23×D4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×#99×C59C2semidirect
3. C2×C59×#353C2direct (N × H)
5. C23×D4×C59C4semidirect
8. C2×#127×C59C4semidirect
11. C22×C42×C59C4semidirect
13. C2×#99×C59C22semidirect
14. C59×#353C22direct (N × H)
26. C22×D4×C59C2×C4semidirect
34. #127×C59C2×C4semidirect
39. C2×C42×C59C2×C4semidirect
41. #99×C59C23semidirect
69. C2×D4×C59C22×C4semidirect
83. C42×C59C22×C4semidirect
122. C22×#353C59direct (N × H)
137. C22×C59#353direct (N × H)
146. C22×#99C2×C59semidirect
147. C2×#353C2×C59direct (N × H)
153. C2×C59C2×#353direct (N × H)
156. C23×D4C4×C59semidirect
159. C2×#127C4×C59semidirect
162. C22×C42C4×C59semidirect
164. C2×#99C22×C59semidirect
165. #353C22×C59direct (N × H)
166. C59C22×#353direct (N × H)
178. C22×D4C2×C4×C59semidirect
186. #127C2×C4×C59semidirect
191. C2×C42C2×C4×C59semidirect
193. #99C23×C59semidirect
221. C2×D4C22×C4×C59semidirect
235. C42C22×C4×C59semidirect
288. C22C59×#353direct (N × H)
301. C2C2×C59×#353direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#127×C592
C22×#99×C592
C2×C59×#3532
C22×#35359