Finite Group Databasebeta

← #21435727

Subgroups — #21435727

Order 7552.

498 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14273756C211yesmaximal, characteristic, complemented
2#16838059C211yesmaximal, characteristic, complemented
3#16838046C211yesmaximal, characteristic, complemented
4#16837785C211yesmaximal, characteristic, complemented
5#16837660C211yesmaximal, characteristic, complemented
6#16837652C211yesmaximal, characteristic, complemented
7#16837622C211yesmaximal, characteristic, complemented
8#16837615C211yesmaximal, characteristic, complemented
9#16837564C211yesmaximal, characteristic, complemented
10#16837553C211yesmaximal, characteristic, complemented
11#16837544C211yesmaximal, characteristic, complemented
12#16837539C211yesmaximal, characteristic, complemented
13SD16×Dic59C211yesmaximal, characteristic, complemented
14#16837478C211yesmaximal, characteristic, complemented
15C2×AGL(1,ℤ/8)×C59C211yesmaximal, characteristic, complemented
16C2×#11745687C2211yescharacteristic
17C2×Q8×D59C2211yescharacteristic, complemented
18#14273756—24no—
19C2×Dic236C2211yescharacteristic, complemented
20C2×#11745672C2211yescharacteristic, complemented
21C2×#11745670C2211yescharacteristic
22C2×#11745670C2211yescharacteristic
23C2×#11745670C2211yescharacteristic, complemented
24C2×#11745659C2211yescharacteristic, complemented
25#14273714—21no—
26#14273714C2211yescharacteristic
27#14273714C2211yescharacteristic, complemented
28#14273708—21no—
29#14273706—21no—
30#14273706C2211yescharacteristic
31#14273706C2211yescharacteristic
32#14273699—21no—
33#14273698—21no—
34#14273698C2211yescharacteristic
35#14273698C2211yescharacteristic, complemented
36#14273696—21no—
37Q8×Dic59C2211yescharacteristic, complemented
38D4×Dic59C2211yescharacteristic
39C4×C22⋊D59—21no—
40C4×C22⋊D59C2211yescharacteristic
41C2×C22⋊Dic59—21no—
42#14273659C2211yescharacteristic, complemented
43Dic59⋊C8C2211yescharacteristic, complemented
44#14273652C2211yescharacteristic, complemented
45#14273652C2211yescharacteristic, complemented
46#14273651C2211yescharacteristic, complemented
47#14273648C2211yescharacteristic
48#14273648C2211yescharacteristic
49#14273648C2211yescharacteristic, complemented
50C22⋊(C59⋊C8)C2211yescharacteristic
51(C2×D59)⋊C8C2211yescharacteristic, complemented
52C8×Dic59C2211yescharacteristic, complemented
53C2×#41×C59C2211yescharacteristic
54C22×D4×C59C2211yescharacteristic
55AGL(1,ℤ/8)×C59—24no—
56C2×SD16×C59C2211yescharacteristic
57C2×SD16×C59C2211yescharacteristic
58C2×D8×C59C2211yescharacteristic
59C2×D8×C59C2211yescharacteristic
60C2×M16×C59C2211yescharacteristic
61C24×C59—21no—
62#41×C59—22no—
63#41×C59—41no—
64C2×Q8×C59C2311yescharacteristic
65C2×D4×C59—22no—
66C2×D4×C59—21no—
67C2×D4×C59—21no—
68C2×D4×C59—41no—
69C2×D4×C59C2311yescharacteristic
70C2×D4×C59C2311yescharacteristic
71C2×D4×C59C2311yescharacteristic
72C22×C4×C59—21no—
73C22×C4×C59C2311yescharacteristic
74C2×C22⋊D59—21no—
75C2×C22⋊D59—21no—
76C2×C22⋊D59—21no—
77C2×C22⋊D59D411yescharacteristic
78C22×Dic59—21no—
79C22×Dic59—21no—
80Q8×D59—22no—
81Q8×D59—41no—
82#11745687—22no—
83#11745687—41no—
84C2×C4×D59—21no—
85C2×C4×D59C2311yescharacteristic
86C2×Dic118—21no—
87C2×Dic118C2311yescharacteristic
88C2×Dic118C2311yescharacteristic
89SD16×C59—22no—
90SD16×C59D414yescomplemented
91D8×C59—22no—
92D8×C59—22no—
93M16×C59—22no—
94C2×C8×C59C2311yescharacteristic
95C2×C8×C59C2311yescharacteristic
96C22⋊Dic59—21no—
97C22⋊Dic59—21no—
98C22⋊Dic59—21no—
99C22⋊Dic59—21no—
100C22⋊Dic59—21no—
101C22⋊Dic59—21no—
102C22⋊Dic59—21no—
103C22⋊Dic59—21no—
104C22⋊Dic59—21no—
105C22⋊Dic59D411yescharacteristic
106#11745672—22no—
107#11745670—22no—
108#11745670—41no—
109#11745670—41no—
110(C2×D59)⋊C4D411yescharacteristic
111C4⋊Dic59—21no—
112C4⋊Dic59C2311yescharacteristic
113C4⋊Dic59C2311yescharacteristic
114Dic59⋊C4—21no—
115Dic59⋊C4—21no—
116Dic59⋊C4D411yescharacteristic
117C4×Dic59—21no—
118C4×Dic59C2311yescharacteristic
119C2×C59⋊C8C2311yescharacteristic
120C2×C59⋊C8C2311yescharacteristic
121Dic236—22no—
122#11745659—22no—
123C23×C59—21no—
124C23×C59—21no—
125C23×C59—21no—
126C23×C59—42no—
127C23×C59—42no—
128C23×C59—81no—
129C23×C59C2×D411yescharacteristic
130C22×D59C2×D411yescharacteristic
131Q8×C59—21no—
132Q8×C59C2×D412yes—
133D4×C59—21no—
134D4×C59—21no—
135D4×C59—21no—
136D4×C59—21no—
137D4×C59—21no—
138D4×C59—42no—
139D4×C59—42no—
140D4×C59C2×D412yes—
141C2×C4×C59—21no—
142C2×C4×C59—21no—
143C2×C4×C59—21no—
144C2×C4×C59—42no—
145C2×C4×C59C2×D411yescharacteristic
146C2×C4×C59C2411yescharacteristic
147C22⋊D59—41no—
148C22⋊D59—42no—
149C22⋊D59—42no—
150C22⋊D59—81no—
151C2×Dic59—21no—
152C2×Dic59—21no—
153C2×Dic59—21no—
154C2×Dic59—21no—
155C2×Dic59—42no—
156C2×Dic59—81no—
157C2×Dic59C2×D411yescharacteristic
158C2×Dic59C2×D411yescharacteristic
159C2×Dic59C2×D411yescharacteristic
160C4×D59—21no—
161C4×D59—21no—
162C4×D59—42no—
163Dic118—21no—
164Dic118—21no—
165Dic118—21no—
166Dic118—21no—
167Dic118—42no—
168C8×C59—21no—
169C8×C59C2×D412yes—
170C59⋊C8—21no—
171C59⋊C8—21no—
172C22×C59—22no—
173C22×C59—21no—
174C22×C59—21no—
175C22×C59—21no—
176C22×C59—41no—
177C22×C59—41no—
178C22×C59—41no—
179C22×C59—41no—
180C22×C59—41no—
181C22×C59—41no—
182C22×C59—41no—
183C22×C59—41no—
184C22×C59—84no—
185C22×C59C22×D411yescharacteristic
186C2×D59—21no—
187C2×D59—21no—
188C2×D59—21no—
189C4×C59—22no—
190C4×C59—21no—
191C4×C59C22×D411yescharacteristic
192C4×C59H(5,𝔽2)11yescharacteristic
193Dic59—21no—
194Dic59—21no—
195Dic59—21no—
196Dic59—41no—
197Dic59—41no—
198Dic59—41no—
199Dic59—41no—
200#3275—591nomaximal, Sylow
201C2×C59—41no—
202C2×C59—42no—
203C2×C59—81no—
204C2×C59—81no—
205C2×C59D4211yescharacteristic
206C2×C59#57511yescharacteristic
207C2×C59#57711yescharacteristic
208D59—41no—
209C2×#137—591no—
210C2×AGL(1,ℤ/8)D5911yescharacteristic, complemented
211#548—591no—
212#546—591no—
213#495—591no—
214#470—591no—
215#469—591no—
216#464—591no—
217#463—591no—
218#452—591no—
219#450—591no—
220#449—591no—
221#448—591no—
222C4×SD16—591no—
223#436—591no—
224C59#327511yescharacteristic, complemented, Sylow
225C2×#41—591no—
226C2×#41C2×D5911yescharacteristic
227C22×Q8—591no—
228C22×D4C2×D5911yescharacteristic
229#137—1184no—
230AGL(1,ℤ/8)—24no—
231C2×Q16—591no—
232C2×Q16—591no—
233C2×SD16—591no—
234C2×SD16—591no—
235C2×SD16—591no—
236C2×SD16C2×D5911yescharacteristic
237C2×SD16C2×D5911yescharacteristic
238C2×D8C2×D5911yescharacteristic
239C2×D8C2×D5911yescharacteristic
240C2×M16—591no—
241C2×M16C2×D5911yescharacteristic
242#124—591no—
243#124—591no—
244#124—1181no—
245#123—1181no—
246C22⋊Q8—591no—
247C22⋊Q8—591no—
248C22⋊Q8—1181no—
249#121—591no—
250#121—591no—
251#121—1181no—
252#121—1181no—
253#120—1181no—
254C4×Q8—591no—
255C4×D4—591no—
256C4×D4—591no—
257C4×D4—1181no—
258C2×C22⋊C4—1181no—
259#106—591no—
260C4⋊C8—591no—
261#103—591no—
262#103—591no—
263#103—591no—
264#102—591no—
265#102—591no—
266#102—591no—
267C22⋊C8—591no—
268C22⋊C8—591no—
269C4×C8—591no—
270C24—21no—
271#41—22no—
272#41—41no—
273#41—1182no—
274#41—2361no—
275C2×Q8—591no—
276C2×Q8—591no—
277C2×Q8—1181no—
278C2×Q8—1182no—
279C2×Q8—2361no—
280C2×Q8C22×D5911yescharacteristic
281C2×D4—22no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—41no—
285C2×D4—591no—
286C2×D4—1181no—
287C2×D4—1181no—
288C2×D4—1181no—
289C2×D4C22×D5911yescharacteristic
290C2×D4C22×D5911yescharacteristic
291C2×D4C22×D5911yescharacteristic
292C22×C4—21no—
293C22×C4—591no—
294C22×C4—1181no—
295C22×C4—1181no—
296C22×C4—1181no—
297C22×C4C22×D5911yescharacteristic
298Q16—1182no—
299Q16—1182no—
300SD16—22no—
301SD16—1182no—
302SD16—2361no—
303SD16—2361no—
304SD16C22⋊D5914yescomplemented
305D8—22no—
306D8—22no—
307M16—22no—
308M16—1182no—
309C2×C8—591no—
310C2×C8—591no—
311C2×C8C22×D5911yescharacteristic
312C2×C8C22×D5911yescharacteristic
313C4⋊C4—591no—
314C4⋊C4—591no—
315C4⋊C4—591no—
316C4⋊C4—1181no—
317C4⋊C4—1181no—
318C4⋊C4—1181no—
319C22⋊C4—591no—
320C22⋊C4—591no—
321C22⋊C4—1181no—
322C22⋊C4—1181no—
323C22⋊C4—1181no—
324C22⋊C4—1181no—
325C22⋊C4—1181no—
326C22⋊C4—1181no—
327C22⋊C4—1181no—
328C22⋊C4—1181no—
329C22⋊C4—1181no—
330C42—591no—
331C42—1181no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—42no—
336C23—42no—
337C23—81no—
338C23—591no—
339C23D4×D5911yescharacteristic
340Q8—21no—
341Q8—1181no—
342Q8—1181no—
343Q8—1181no—
344Q8—1181no—
345Q8—2362no—
346Q8C2×C22⋊D5912yes—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—21no—
351D4—21no—
352D4—42no—
353D4—42no—
354D4—4721no—
355D4—2361no—
356D4—2362no—
357D4—2362no—
358D4C2×C22⋊D5912yes—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—42no—
363C2×C4—591no—
364C2×C4—591no—
365C2×C4—591no—
366C2×C4—1181no—
367C2×C4—1181no—
368C2×C4—1181no—
369C2×C4—1181no—
370C2×C4—1181no—
371C2×C4—1181no—
372C2×C4—4721no—
373C2×C4—2362no—
374C2×C4—2362no—
375C2×C4D4×D5911yescharacteristic
376C2×C4C23×D5911yescharacteristic
377C8—21no—
378C8—1181no—
379C8—1181no—
380C8C2×C22⋊D5912yes—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—22no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—84no—
394C22—1181no—
395C22—1181no—
396C22—1181no—
397C22C2×D4×D5911yescharacteristic
398C4—21no—
399C4—22no—
400C4—1181no—
401C4—1181no—
402C4—1181no—
403C4—2361no—
404C4—2361no—
405C4—2361no—
406C4—2361no—
407C4C22×C22⋊D5911yescharacteristic
408C4#1427377211yescharacteristic
409C2—41no—
410C2—42no—
411C2—81no—
412C2—81no—
413C2—2361no—
414C2D4×C22⋊D5911yescharacteristic
415C2#1683819811yescharacteristic
416C2#1683821211yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC2×AGL(1,ℤ/8)×C59C2
socleC22×C59C22×D4
hypercenterC2×AGL(1,ℤ/8)D59
hypocenterC59#3275
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×#14273756C2semidirect
2. #16838059C2semidirect
3. #16838046C2semidirect
4. #16837785C2semidirect
5. #16837660C2semidirect
6. #16837652C2semidirect
7. #16837622C2semidirect
8. #16837615C2semidirect
9. #16837564C2semidirect
10. #16837553C2semidirect
11. #16837544C2semidirect
12. #16837539C2semidirect
13. SD16×Dic59C2semidirect
14. #16837478C2semidirect
15. C2×AGL(1,ℤ/8)×C59C2semidirect
17. C2×Q8×D59C22semidirect
19. C2×Dic236C22semidirect
20. C2×#11745672C22semidirect
23. C2×#11745670C22semidirect
24. C2×#11745659C22semidirect
27. #14273714C22semidirect
35. #14273698C22semidirect
37. Q8×Dic59C22semidirect
42. #14273659C22semidirect
43. Dic59⋊C8C22semidirect
44. #14273652C22semidirect
45. #14273652C22semidirect
46. #14273651C22semidirect
49. #14273648C22semidirect
51. (C2×D59)⋊C8C22semidirect
52. C8×Dic59C22semidirect
90. SD16×C59D4semidirect
210. C2×AGL(1,ℤ/8)D59semidirect
224. C59#3275semidirect
304. SD16C22⋊D59semidirect