Finite Group Databasebeta

← #447×D59 #21433269

Subgroups — #447×D59 #21433269

Order 7552.

1048 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 1048 conjugacy classes of subgroups — too many to draw. Only its 155 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×D4×D59C211yesmaximal, characteristic, complemented
2C2×D8×D59C212yesmaximal, complemented
3#121×D59C211yesmaximal, characteristic, complemented
4#16837538C211yesmaximal, characteristic, complemented
5#16837537C212yesmaximal, complemented
6#16837536C211yesmaximal, characteristic, complemented
7#16837535C211yesmaximal, characteristic, complemented
8#16837534C212yesmaximal, complemented
9#102×D59C212yesmaximal, complemented
10C22⋊C8×D59C211yesmaximal, characteristic, complemented
11C59×#447C211yesmaximal, characteristic, complemented
12C24×D59—21no—
13C22×D236C2211yescharacteristic, complemented
14C22×C22⋊D59—21no—
15C2×D4×D59—28no—
16C2×D4×D59—21no—
17C2×D4×D59—21no—
18C2×D4×D59—21no—
19C2×D4×D59C2212yes—
20C2×D4×D59C2212yescomplemented
21C2×D4×D59C2211yescharacteristic, complemented
22C22×C4×D59C2211yescharacteristic
23C2×D472C2212yescomplemented
24C2×#11745669C2212yescomplemented
25C2×#11745669C2212yescomplemented
26D8×D59—28no—
27C2×C8×D59C2212yescomplemented
28#14273702C2211yescharacteristic, complemented
29#14273701C2211yescharacteristic, complemented
30#14273700—21no—
31#14273699—21no—
32#14273698C2211yescharacteristic, complemented
33C4⋊C4×D59C2211yescharacteristic, complemented
34C22⋊C4×D59—21no—
35#14273649C2212yescomplemented
36#14273648C2212yescomplemented
37#14273647C2212yescomplemented
38C22⋊(C59⋊C8)C2211yescharacteristic, complemented
39(C2×D59)⋊C8C2212yescomplemented
40C22×D4×C59C2211yescharacteristic, complemented
41C2×D8×C59C2212yescomplemented
42#121×C59C2211yescharacteristic, complemented
43#102×C59C2212yescomplemented
44C22⋊C8×C59C2211yescharacteristic, complemented
45C24×C59—21no—
46C23×D59—28no—
47C23×D59—21no—
48C23×D59—22no—
49C23×D59—22no—
50C23×D59—21no—
51C23×D59—44no—
52C23×D59—44no—
53C23×D59D411yescharacteristic
54C2×D4×C59—24no—
55C2×D4×C59—21no—
56C2×D4×C59—21no—
57C2×D4×C59C2312yes—
58C2×D4×C59C2311yescharacteristic, complemented
59C22×C4×C59C2311yescharacteristic
60C2×C22⋊D59—28no—
61C2×C22⋊D59—21no—
62C2×C22⋊D59—21no—
63C2×C22⋊D59—22no—
64C2×C22⋊D59—22no—
65C2×C22⋊D59—21no—
66C22×Dic59D411yescharacteristic
67D4×D59—28no—
68D4×D59—28no—
69D4×D59—24no—
70D4×D59—24no—
71D4×D59—24no—
72D4×D59—24no—
73D4×D59—44no—
74D4×D59D418yescomplemented
75C2×D236—21no—
76C2×D236—24no—
77C2×D236—21no—
78C2×D236C2312yes—
79C2×D236C2311yescharacteristic, complemented
80C2×C4×D59—24no—
81C2×C4×D59—21no—
82C2×C4×D59D411yescharacteristic
83C2×C4×D59D411yescharacteristic
84C2×C4×D59C2311yescharacteristic
85C2×C4×D59C2311yescharacteristic
86D8×C59—24no—
87C2×C8×C59C2312yescomplemented
88C4⋊C4×C59C2311yescharacteristic, complemented
89C22⋊C4×C59—21no—
90C22⋊Dic59—21no—
91#11745669—24no—
92#11745669—24no—
93(C2×D59)⋊C4—21no—
94(C2×D59)⋊C4—21no—
95C4⋊Dic59C2311yescharacteristic, complemented
96Dic59⋊C4—21no—
97C2×C59⋊C8C2312yescomplemented
98D472—24no—
99C8×D59—24no—
100C23×C59—24no—
101C23×C59—22no—
102C23×C59—21no—
103C23×C59—42no—
104C23×C59—42no—
105C23×C59C2×D411yescharacteristic
106C22×D59—22no—
107C22×D59—22no—
108C22×D59—24no—
109C22×D59—28no—
110C22×D59—22no—
111C22×D59—28no—
112C22×D59—21no—
113C22×D59—44no—
114C22×D59—432no—
115C22×D59—42no—
116C22×D59—42no—
117C22×D59—44no—
118C22×D59—44no—
119C22×D59—44no—
120C22×D59—42no—
121C22×D59—42no—
122C22×D59—42no—
123C22×D59D814yescomplemented
124C22×D59C2×D411yescharacteristic
125C22×D59C2×D411yescharacteristic
126D4×C59—24no—
127D4×C59—22no—
128D4×C59—22no—
129D4×C59—42no—
130D4×C59C2×D414yescomplemented
131C2×C4×C59—22no—
132C2×C4×C59—21no—
133C2×C4×C59C2×D411yescharacteristic
134C2×C4×C59C2411yescharacteristic
135C22⋊D59—28no—
136C22⋊D59—28no—
137C22⋊D59—42no—
138C22⋊D59—42no—
139C22⋊D59—42no—
140C2×Dic59—22no—
141C2×Dic59—21no—
142C2×Dic59C2×D411yescharacteristic
143C2×Dic59C2×D411yescharacteristic
144D236—24no—
145D236—22no—
146D236—22no—
147D236—42no—
148D236C2×D414yescomplemented
149C4×D59—22no—
150C4×D59—22no—
151C4×D59—22no—
152C4×D59—42no—
153C4×D59C2×D414yes—
154C8×C59—22no—
155C59⋊C8—22no—
156C22×C59—21no—
157C22×C59—21no—
158C22×C59—24no—
159C22×C59—48no—
160C22×C59—42no—
161C22×C59—42no—
162C22×C59—41no—
163C22×C59—41no—
164C22×C59—41no—
165C22×C59C2×D812yescomplemented
166C22×C59C22×D411yescharacteristic
167C2×D59—21no—
168C2×D59—21no—
169C2×D59—28no—
170C2×D59—24no—
171C2×D59—416no—
172C2×D59—48no—
173C2×D59—42no—
174C2×D59—42no—
175C2×D59—416no—
176C2×D59—41no—
177C2×D59—41no—
178C2×D59—41no—
179C2×D59—84no—
180C2×D59#12012yes—
181C2×D59C2×D812yes—
182C2×D59C2×D812yescomplemented
183C2×D59AGL(1,ℤ/8)12yes—
184C4×C59—21no—
185C4×C59—41no—
186C4×C59C22×D412yes—
187Dic59—21no—
188Dic59—41no—
189Dic59#12012yes—
190C2×#447—591nomaximal, Sylow
191C2×C59—22no—
192C2×C59—44no—
193C2×C59—81no—
194C2×C59C2×#12011yescharacteristic
195C2×C59C22×D811yescharacteristic
196C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
197D59—22no—
198D59—44no—
199D59—81no—
200D59#44714yesdirect product factor
201C23×D4—591no—
202C22×D8—592no—
203C2×#121—591no—
204#447—591no—
205#447—592no—
206#447—591no—
207#447—592no—
208#447—591no—
209#447D5911yescharacteristic, direct product factor
210C2×#102—592no—
211C2×C22⋊C8—591no—
212C59C2×#44711yescharacteristic, complemented, Sylow
213C25—1181no—
214C22×D4—592no—
215C22×D4—592no—
216C22×D4—591no—
217C22×D4—591no—
218C22×D4—1181no—
219C22×D4—1181no—
220C22×D4—1181no—
221C22×D4—1188no—
222C22×D4—1181no—
223C22×D4C2×D5911yescharacteristic, complemented
224C23×C4—591no—
225C2×D8—592no—
226C2×D8—592no—
227C2×D8—592no—
228C2×D8—1188no—
229C2×D8C2×D5912yescomplemented
230C22×C8—592no—
231#121—591no—
232#121—591no—
233#121—591no—
234#121—1181no—
235#121—1181no—
236#121C2×D5911yescharacteristic, complemented
237C2×C4⋊C4—591no—
238C2×C22⋊C4—1181no—
239#102—592no—
240#102—592no—
241#102—592no—
242#102C2×D5912yescomplemented
243C22⋊C8—591no—
244C22⋊C8—592no—
245C22⋊C8C2×D5911yescharacteristic, complemented
246C24—21no—
247C24—591no—
248C24—1182no—
249C24—1182no—
250C24—1181no—
251C24—1188no—
252C24—1181no—
253C24—2364no—
254C24—2364no—
255C2×D4—24no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—598no—
259C2×D4—592no—
260C2×D4—591no—
261C2×D4—1184no—
262C2×D4—1181no—
263C2×D4—1184no—
264C2×D4—1184no—
265C2×D4—1182no—
266C2×D4—1182no—
267C2×D4—1181no—
268C2×D4—1184no—
269C2×D4—1188no—
270C2×D4—1188no—
271C2×D4—1188no—
272C2×D4—1184no—
273C2×D4—1181no—
274C2×D4—1181no—
275C2×D4—1181no—
276C2×D4—2364no—
277C2×D4C22×D5912yes—
278C2×D4C22×D5911yescharacteristic, complemented
279C22×C4—591no—
280C22×C4—591no—
281C22×C4—591no—
282C22×C4—591no—
283C22×C4—591no—
284C22×C4—1184no—
285C22×C4—1181no—
286C22×C4C22×D5911yescharacteristic
287D8—24no—
288D8—1184no—
289D8—1184no—
290D8—1184no—
291C2×C8—592no—
292C2×C8—1184no—
293C2×C8C22×D5912yescomplemented
294C4⋊C4—591no—
295C4⋊C4—1181no—
296C4⋊C4C22×D5911yescharacteristic, complemented
297C22⋊C4—21no—
298C22⋊C4—1181no—
299C22⋊C4—1181no—
300C22⋊C4—1181no—
301C23—24no—
302C23—22no—
303C23—21no—
304C23—42no—
305C23—42no—
306C23—591no—
307C23—594no—
308C23—591no—
309C23—1182no—
310C23—1182no—
311C23—1188no—
312C23—1184no—
313C23—1188no—
314C23—1182no—
315C23—1181no—
316C23—2362no—
317C23—2362no—
318C23—2362no—
319C23—2362no—
320C23—2364no—
321C23—2364no—
322C23—2364no—
323C23—23632no—
324C23—2364no—
325C23—2362no—
326C23D4×D5911yescharacteristic
327D4—24no—
328D4—22no—
329D4—22no—
330D4—42no—
331D4—594no—
332D4—1184no—
333D4—1188no—
334D4—1188no—
335D4—1182no—
336D4—1182no—
337D4—2362no—
338D4—2362no—
339D4—2362no—
340D4—2362no—
341D4D4×D5914yescomplemented
342C2×C4—22no—
343C2×C4—21no—
344C2×C4—591no—
345C2×C4—594no—
346C2×C4—591no—
347C2×C4—1182no—
348C2×C4—1182no—
349C2×C4—1182no—
350C2×C4—1182no—
351C2×C4—1181no—
352C2×C4—2362no—
353C2×C4D4×D5911yescharacteristic
354C2×C4C23×D5911yescharacteristic
355C8—22no—
356C8—1182no—
357C22—21no—
358C22—21no—
359C22—24no—
360C22—48no—
361C22—42no—
362C22—42no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—592no—
367C22—592no—
368C22—592no—
369C22—592no—
370C22—1188no—
371C22—1181no—
372C22—1181no—
373C22—1184no—
374C22—4724no—
375C22—2368no—
376C22—23616no—
377C22—23616no—
378C22—2361no—
379C22—2361no—
380C22—2361no—
381C22—2362no—
382C22—2362no—
383C22D8×D5912yescomplemented
384C22C2×D4×D5911yescharacteristic
385C4—21no—
386C4—41no—
387C4—592no—
388C4—1181no—
389C4—2361no—
390C4C2×D4×D5912yes—
391C2—22no—
392C2—44no—
393C2—81no—
394C2—594no—
395C2—1182no—
396C2—4721no—
397C2—2364no—
398C2#120×D5911yescharacteristic
399C2C2×D8×D5911yescharacteristic
400C2AGL(1,ℤ/8)×D5911yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#447C2
socleC22×C59C22×D4
hypercenter#447D59
hypocenterC59C2×#447
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. C22×D4×D59C2semidirect
2. C2×D8×D59C2semidirect
3. #121×D59C2semidirect
4. #16837538C2semidirect
5. #16837537C2semidirect
6. #16837536C2semidirect
7. #16837535C2semidirect
8. #16837534C2semidirect
9. #102×D59C2semidirect
10. C22⋊C8×D59C2semidirect
11. C59×#447C2semidirect
13. C22×D236C22semidirect
20. C2×D4×D59C22semidirect
21. C2×D4×D59C22semidirect
23. C2×D472C22semidirect
24. C2×#11745669C22semidirect
25. C2×#11745669C22semidirect
27. C2×C8×D59C22semidirect
28. #14273702C22semidirect
29. #14273701C22semidirect
32. #14273698C22semidirect
33. C4⋊C4×D59C22semidirect
35. #14273649C22semidirect
36. #14273648C22semidirect
37. #14273647C22semidirect
38. C22⋊(C59⋊C8)C22semidirect
39. (C2×D59)⋊C8C22semidirect
40. C22×D4×C59C22semidirect
41. C2×D8×C59C22semidirect
42. #121×C59C22semidirect
43. #102×C59C22semidirect
44. C22⋊C8×C59C22semidirect
58. C2×D4×C59C23semidirect
74. D4×D59D4semidirect
79. C2×D236C23semidirect
87. C2×C8×C59C23semidirect
88. C4⋊C4×C59C23semidirect
95. C4⋊Dic59C23semidirect
97. C2×C59⋊C8C23semidirect
123. C22×D59D8semidirect
130. D4×C59C2×D4semidirect
148. D236C2×D4semidirect
165. C22×C59C2×D8semidirect
182. C2×D59C2×D8semidirect
200. D59#447direct (N × H)
209. #447D59direct (N × H)
212. C59C2×#447semidirect
223. C22×D4C2×D59semidirect
229. C2×D8C2×D59semidirect
236. #121C2×D59semidirect
242. #102C2×D59semidirect
245. C22⋊C8C2×D59semidirect
278. C2×D4C22×D59semidirect
293. C2×C8C22×D59semidirect
296. C4⋊C4C22×D59semidirect
341. D4D4×D59semidirect
383. C22D8×D59semidirect