Finite Group Databasebeta

← #21435630

Subgroups — #21435630

Order 7552.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14273748C211yesmaximal, characteristic, complemented
2#16838071C211yesmaximal, characteristic, complemented
3#16838046C211yesmaximal, characteristic, complemented
4#16837790C211yesmaximal, characteristic, complemented
5#16837648C211yesmaximal, characteristic, complemented
6#16837635C211yesmaximal, characteristic, complemented
7#16837622C211yesmaximal, characteristic, complemented
8#16837595C211yesmaximal, characteristic, complemented
9#16837564C211yesmaximal, characteristic, complemented
10#16837546C211yesmaximal, characteristic, complemented
11#16837544C211yesmaximal, characteristic, complemented
12#16837536C211yesmaximal, characteristic, complemented
13#16837503C211yesmaximal, characteristic, complemented
14#16837471C211yesmaximal, characteristic, complemented
15C2×AGL(1,ℤ/8)×C59C211yesmaximal, characteristic, complemented
16C2×#11745689C2211yescharacteristic, complemented
17C2×#11745687C2211yescharacteristic
18#14273748—24no—
19C2×#11745672C2211yescharacteristic, complemented
20C2×#11745660C2211yescharacteristic, complemented
21C2×#11745670C2211yescharacteristic, complemented
22C2×#11745669C2211yescharacteristic
23C2×#11745669C2211yescharacteristic
24C2×C8×D59C2211yescharacteristic, complemented
25#14273723—21no—
26#14273723C2211yescharacteristic, complemented
27#14273714C2211yescharacteristic
28#14273708—21no—
29#14273706C2211yescharacteristic
30#14273701—21no—
31#14273701C2211yescharacteristic
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#14273661C2211yescharacteristic, complemented
43Dic59⋊C8C2211yescharacteristic, complemented
44#14273652C2211yescharacteristic, complemented
45#14273651C2211yescharacteristic, complemented
46#14273649C2211yescharacteristic, complemented
47#14273648C2211yescharacteristic
48#14273648C2211yescharacteristic
49#14273648C2211yescharacteristic, complemented
50C22⋊(C59⋊C8)C2211yescharacteristic
51(C2×D59)⋊C8C2211yescharacteristic, complemented
52#14273637C2211yescharacteristic, 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⋊D59—21no—
78C2×C22⋊D59—21no—
79C2×C22⋊D59—21no—
80C2×C22⋊D59D411yescharacteristic
81C22×Dic59—21no—
82C22×Dic59—21no—
83#11745689—22no—
84#11745689—41no—
85#11745687—22no—
86#11745687—41no—
87C2×D236—21no—
88C2×D236C2311yescharacteristic
89C2×C4×D59—21no—
90C2×C4×D59C2311yescharacteristic
91C2×Dic118C2311yescharacteristic
92SD16×C59—22no—
93SD16×C59D414yescomplemented
94D8×C59—22no—
95D8×C59—22no—
96M16×C59—22no—
97C2×C8×C59C2311yescharacteristic
98C2×C8×C59C2311yescharacteristic
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—41no—
108#11745669—22no—
109#11745669—41no—
110(C2×D59)⋊C4—21no—
111(C2×D59)⋊C4D411yescharacteristic
112C4⋊Dic59—21no—
113C4⋊Dic59C2311yescharacteristic
114C4⋊Dic59C2311yescharacteristic
115Dic59⋊C4—21no—
116Dic59⋊C4D411yescharacteristic
117C4×Dic59—21no—
118C4×Dic59C2311yescharacteristic
119C2×C59⋊C8C2311yescharacteristic
120C2×C59⋊C8C2311yescharacteristic
121#11745660—22no—
122C8×D59—22no—
123C23×C59—21no—
124C23×C59—21no—
125C23×C59—21no—
126C23×C59—42no—
127C23×C59—42no—
128C23×C59—81no—
129C23×C59C2×D411yescharacteristic
130C22×D59—21no—
131C22×D59C2×D411yescharacteristic
132Q8×C59—21no—
133Q8×C59C2×D412yes—
134D4×C59—21no—
135D4×C59—21no—
136D4×C59—21no—
137D4×C59—21no—
138D4×C59—21no—
139D4×C59—42no—
140D4×C59—42no—
141D4×C59C2×D412yes—
142C2×C4×C59—21no—
143C2×C4×C59—21no—
144C2×C4×C59—21no—
145C2×C4×C59—42no—
146C2×C4×C59C2×D411yescharacteristic
147C2×C4×C59C2411yescharacteristic
148C22⋊D59—41no—
149C22⋊D59—42no—
150C22⋊D59—42no—
151C22⋊D59—81no—
152C22⋊D59—81no—
153C22⋊D59—81no—
154C22⋊D59—81no—
155C2×Dic59—21no—
156C2×Dic59—21no—
157C2×Dic59—21no—
158C2×Dic59—42no—
159C2×Dic59—81no—
160C2×Dic59C2×D411yescharacteristic
161C2×Dic59C2×D411yescharacteristic
162C2×Dic59C2×D411yescharacteristic
163D236—21no—
164D236—21no—
165D236—42no—
166C4×D59—21no—
167C4×D59—21no—
168C4×D59—42no—
169Dic118—21no—
170Dic118—21no—
171C8×C59—21no—
172C8×C59C2×D412yes—
173C59⋊C8—21no—
174C59⋊C8—21no—
175C22×C59—22no—
176C22×C59—21no—
177C22×C59—21no—
178C22×C59—21no—
179C22×C59—41no—
180C22×C59—41no—
181C22×C59—41no—
182C22×C59—41no—
183C22×C59—41no—
184C22×C59—41no—
185C22×C59—41no—
186C22×C59—41no—
187C22×C59—84no—
188C22×C59C22×D411yescharacteristic
189C2×D59—21no—
190C2×D59—21no—
191C2×D59—21no—
192C2×D59—41no—
193C2×D59—41no—
194C2×D59—41no—
195C4×C59—22no—
196C4×C59—21no—
197C4×C59C22×D411yescharacteristic
198C4×C59H(5,𝔽2)11yescharacteristic
199Dic59—21no—
200Dic59—21no—
201Dic59—21no—
202Dic59—41no—
203Dic59—41no—
204Dic59—41no—
205#3268—591nomaximal, Sylow
206C2×C59—41no—
207C2×C59—42no—
208C2×C59—81no—
209C2×C59—81no—
210C2×C59D4211yescharacteristic
211C2×C59#57511yescharacteristic
212C2×C59#57611yescharacteristic
213D59—41no—
214D59—81no—
215C2×AGL(1,ℤ/8)D5911yescharacteristic, complemented
216C2×#135—591no—
217#550—591no—
218#546—591no—
219#496—591no—
220#468—591no—
221#466—591no—
222#464—591no—
223#459—591no—
224#452—591no—
225#449—591no—
226#449—591no—
227#447—591no—
228#440—591no—
229#435—591no—
230C59#326811yescharacteristic, complemented, Sylow
231C2×#41—591no—
232C2×#41—591no—
233C2×#41C2×D5911yescharacteristic
234C22×D4C2×D5911yescharacteristic
235AGL(1,ℤ/8)—24no—
236#135—1184no—
237C2×Q16—591no—
238C2×SD16—591no—
239C2×SD16—591no—
240C2×SD16C2×D5911yescharacteristic
241C2×SD16C2×D5911yescharacteristic
242C2×D8—591no—
243C2×D8—591no—
244C2×D8C2×D5911yescharacteristic
245C2×D8C2×D5911yescharacteristic
246C2×M16C2×D5911yescharacteristic
247C22×C8—591no—
248#127—591no—
249#127—1181no—
250#124—591no—
251#123—1181no—
252C22⋊Q8—591no—
253#121—591no—
254#121—591no—
255#121—591no—
256#121—1181no—
257#121—1181no—
258#121—1181no—
259#120—1181no—
260C4×Q8—591no—
261C4×D4—591no—
262C4×D4—591no—
263C4×D4—1181no—
264C2×C22⋊C4—1181no—
265#107—591no—
266C4⋊C8—591no—
267#103—591no—
268#103—591no—
269#102—591no—
270#102—591no—
271#102—591no—
272#102—591no—
273C22⋊C8—591no—
274C22⋊C8—591no—
275#97—591no—
276C24—21no—
277#41—22no—
278#41—41no—
279#41—1182no—
280#41—1182no—
281#41—2361no—
282#41—2361no—
283C2×Q8—591no—
284C2×Q8C22×D5911yescharacteristic
285C2×D4—22no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—41no—
289C2×D4—591no—
290C2×D4—591no—
291C2×D4—1181no—
292C2×D4—1181no—
293C2×D4—1181no—
294C2×D4—1181no—
295C2×D4—1181no—
296C2×D4—1181no—
297C2×D4—1181no—
298C2×D4C22×D5911yescharacteristic
299C2×D4C22×D5911yescharacteristic
300C2×D4C22×D5911yescharacteristic
301C22×C4—21no—
302C22×C4—591no—
303C22×C4—1181no—
304C22×C4—1181no—
305C22×C4—1181no—
306C22×C4C22×D5911yescharacteristic
307Q16—1182no—
308SD16—22no—
309SD16—1182no—
310SD16—2361no—
311SD16C22⋊D5914yescomplemented
312D8—22no—
313D8—22no—
314D8—1182no—
315D8—2361no—
316M16—22no—
317C2×C8—591no—
318C2×C8—591no—
319C2×C8—1182no—
320C2×C8C22×D5911yescharacteristic
321C2×C8C22×D5911yescharacteristic
322C4⋊C4—591no—
323C4⋊C4—591no—
324C4⋊C4—591no—
325C4⋊C4—1181no—
326C4⋊C4—1181no—
327C22⋊C4—591no—
328C22⋊C4—591no—
329C22⋊C4—1181no—
330C22⋊C4—1181no—
331C22⋊C4—1181no—
332C22⋊C4—1181no—
333C22⋊C4—1181no—
334C22⋊C4—1181no—
335C22⋊C4—1181no—
336C42—591no—
337C42—1181no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—42no—
342C23—42no—
343C23—81no—
344C23—591no—
345C23—1181no—
346C23D4×D5911yescharacteristic
347Q8—21no—
348Q8—1181no—
349Q8—1181no—
350Q8C2×C22⋊D5912yes—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—21no—
355D4—21no—
356D4—42no—
357D4—42no—
358D4—1181no—
359D4—1181no—
360D4—4721no—
361D4—4721no—
362D4—4721no—
363D4—4721no—
364D4—2362no—
365D4—2361no—
366D4—2362no—
367D4—2362no—
368D4C2×C22⋊D5912yes—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—42no—
373C2×C4—591no—
374C2×C4—591no—
375C2×C4—591no—
376C2×C4—1181no—
377C2×C4—1181no—
378C2×C4—1181no—
379C2×C4—1181no—
380C2×C4—1181no—
381C2×C4—4721no—
382C2×C4—2362no—
383C2×C4—2362no—
384C2×C4D4×D5911yescharacteristic
385C2×C4C23×D5911yescharacteristic
386C8—21no—
387C8—1181no—
388C8—1181no—
389C8C2×C22⋊D5912yes—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—22no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—84no—
403C22—1181no—
404C22—1181no—
405C22—1181no—
406C22—2361no—
407C22—2361no—
408C22—2361no—
409C22C2×D4×D5911yescharacteristic
410C4—21no—
411C4—22no—
412C4—1181no—
413C4—1181no—
414C4—1181no—
415C4—2361no—
416C4—2361no—
417C4—2361no—
418C4C22×C22⋊D5911yescharacteristic
419C4#1427377211yescharacteristic
420C2—41no—
421C2—42no—
422C2—81no—
423C2—81no—
424C2—4721no—
425C2—2361no—
426C2D4×C22⋊D5911yescharacteristic
427C2#1683819811yescharacteristic
428C2#1683820611yescharacteristic
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#3268
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×#14273748C2semidirect
2. #16838071C2semidirect
3. #16838046C2semidirect
4. #16837790C2semidirect
5. #16837648C2semidirect
6. #16837635C2semidirect
7. #16837622C2semidirect
8. #16837595C2semidirect
9. #16837564C2semidirect
10. #16837546C2semidirect
11. #16837544C2semidirect
12. #16837536C2semidirect
13. #16837503C2semidirect
14. #16837471C2semidirect
15. C2×AGL(1,ℤ/8)×C59C2semidirect
16. C2×#11745689C22semidirect
19. C2×#11745672C22semidirect
20. C2×#11745660C22semidirect
21. C2×#11745670C22semidirect
24. C2×C8×D59C22semidirect
26. #14273723C22semidirect
35. #14273698C22semidirect
37. Q8×Dic59C22semidirect
42. #14273661C22semidirect
43. Dic59⋊C8C22semidirect
44. #14273652C22semidirect
45. #14273651C22semidirect
46. #14273649C22semidirect
49. #14273648C22semidirect
51. (C2×D59)⋊C8C22semidirect
52. #14273637C22semidirect
93. SD16×C59D4semidirect
215. C2×AGL(1,ℤ/8)D59semidirect
230. C59#3268semidirect
311. SD16C22⋊D59semidirect