Finite Group Databasebeta

← #21435637

Subgroups — #21435637

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×#14273752C211yesmaximal, characteristic, complemented
2C2×#14273747C211yesmaximal, characteristic, complemented
3#16838048C211yesmaximal, characteristic, complemented
4#16837789C211yesmaximal, characteristic, complemented
5#16837646C211yesmaximal, characteristic, complemented
6#16837636C211yesmaximal, characteristic, complemented
7#16837624C211yesmaximal, characteristic, complemented
8#16837594C211yesmaximal, characteristic, complemented
9#16837564C211yesmaximal, characteristic, complemented
10#16837547C211yesmaximal, characteristic, complemented
11#16837545C211yesmaximal, characteristic, complemented
12#16837535C211yesmaximal, characteristic, complemented
13#16837500C211yesmaximal, characteristic, complemented
14#16837474C211yesmaximal, characteristic, complemented
15C59×#550C211yesmaximal, characteristic, complemented
16C2×#11745685C2211yescharacteristic
17C22×D236C2211yescharacteristic
18#14273752—24no—
19#14273747—24no—
20C2×#11745672C2211yescharacteristic, complemented
21C2×#11745670C2211yescharacteristic, complemented
22C2×#11745670C2211yescharacteristic, complemented
23C2×#11745671C2211yescharacteristic
24C2×#11745671C2211yescharacteristic
25C2×#11745669C2211yescharacteristic
26C2×#11745669C2211yescharacteristic
27C2×#11745669C2211yescharacteristic
28C2×#11745669C2211yescharacteristic
29C2×#11745664C2211yescharacteristic
30C22×C59⋊C8C2211yescharacteristic, complemented
31#14273715C2211yescharacteristic
32#14273712—21no—
33#14273706C2211yescharacteristic
34#14273701C2211yescharacteristic
35#14273700—21no—
36#14273695—21no—
37C4×D236C2211yescharacteristic
38C22⋊C4×D59—21no—
39#14273660C2211yescharacteristic, complemented
40C4⋊(C59⋊C8)C2211yescharacteristic, complemented
41#14273651C2211yescharacteristic, complemented
42#14273650C2211yescharacteristic, complemented
43#14273648C2211yescharacteristic, complemented
44#14273648C2211yescharacteristic, complemented
45#14273647C2211yescharacteristic
46#14273647C2211yescharacteristic
47C22⋊(C59⋊C8)C2211yescharacteristic
48C22⋊(C59⋊C8)C2211yescharacteristic, complemented
49#14273638C2211yescharacteristic, complemented
50C2×#41×C59C2211yescharacteristic
51C2×#41×C59C2211yescharacteristic, complemented
52#127×C59—21no—
53#127×C59C2211yescharacteristic, complemented
54#121×C59—21no—
55#121×C59—21no—
56#121×C59C2211yescharacteristic
57#121×C59C2211yescharacteristic, complemented
58C4×Q8×C59C2211yescharacteristic, complemented
59C4×D4×C59—21no—
60C4×D4×C59C2211yescharacteristic
61C23×D59—21no—
62#41×C59—22no—
63#41×C59—22no—
64#41×C59—41no—
65#41×C59—41no—
66C2×Q8×C59C2311yescharacteristic
67C2×D4×C59—21no—
68C2×D4×C59—21no—
69C2×D4×C59—21no—
70C2×D4×C59—21no—
71C2×D4×C59—21no—
72C2×D4×C59—21no—
73C2×D4×C59D411yescharacteristic
74C2×D4×C59C2311yescharacteristic
75C2×D4×C59C2311yescharacteristic
76C22×C4×C59—21no—
77C22×C4×C59—21no—
78C22×C4×C59C2311yescharacteristic
79C22×C4×C59C2311yescharacteristic
80C2×C22⋊D59—21no—
81C2×C22⋊D59—21no—
82#11745685—22no—
83#11745685—41no—
84C2×D236—22no—
85C2×D236—21no—
86C2×D236—41no—
87C2×D236C2311yescharacteristic
88C2×D236C2311yescharacteristic
89C2×C4×D59—21no—
90C2×C4×D59—21no—
91C2×Dic118C2311yescharacteristic
92C4⋊C4×C59—21no—
93C4⋊C4×C59D411yescharacteristic
94C4⋊C4×C59C2311yescharacteristic
95C22⋊C4×C59—21no—
96C22⋊C4×C59—21no—
97C22⋊C4×C59D411yescharacteristic
98C22⋊C4×C59D411yescharacteristic
99C42×C59—21no—
100C42×C59C2311yescharacteristic
101C22⋊Dic59—21no—
102#11745672—22no—
103#11745671—22no—
104#11745671D414yescomplemented
105#11745670—22no—
106#11745670—41no—
107#11745669—22no—
108#11745669—22no—
109#11745669—22no—
110#11745669—41no—
111(C2×D59)⋊C4—21no—
112(C2×D59)⋊C4—21no—
113(C2×D59)⋊C4—21no—
114(C2×D59)⋊C4—21no—
115C4⋊Dic59C2311yescharacteristic
116Dic59⋊C4—21no—
117#11745664—22no—
118C2×C59⋊C8—22no—
119C2×C59⋊C8C2311yescharacteristic
120C2×C59⋊C8C2311yescharacteristic
121C2×C59⋊C8C2311yescharacteristic
122C2×C59⋊C8C2311yescharacteristic
123C23×C59—21no—
124C23×C59—21no—
125C23×C59C2×D411yescharacteristic
126C23×C59C2×D411yescharacteristic
127C22×D59—21no—
128C22×D59—21no—
129C22×D59—42no—
130C22×D59—42no—
131C22×D59—81no—
132Q8×C59—21no—
133Q8×C59C2×D412yes—
134D4×C59—21no—
135D4×C59—21no—
136D4×C59—21no—
137D4×C59—21no—
138D4×C59—41no—
139D4×C59—42no—
140D4×C59—42no—
141D4×C59—42no—
142D4×C59—81no—
143D4×C59—81no—
144D4×C59—81no—
145C2×C4×C59—21no—
146C2×C4×C59—21no—
147C2×C4×C59—21no—
148C2×C4×C59—21no—
149C2×C4×C59—21no—
150C2×C4×C59—21no—
151C2×C4×C59—42no—
152C2×C4×C59—42no—
153C2×C4×C59C2×D411yescharacteristic
154C2×C4×C59C2×D411yescharacteristic
155C2×C4×C59C2×D411yescharacteristic
156C2×C4×C59C2×D411yescharacteristic
157C2×C4×C59C2411yescharacteristic
158C22⋊D59—42no—
159C22⋊D59—81no—
160C2×Dic59—21no—
161C2×Dic59—21no—
162D236—21no—
163D236—21no—
164D236—21no—
165D236—42no—
166D236C2×D412yes—
167C4×D59—42no—
168C4×D59—81no—
169Dic118—21no—
170Dic118—21no—
171C59⋊C8—21no—
172C59⋊C8—21no—
173C59⋊C8—21no—
174C59⋊C8C2×D412yes—
175C22×C59—21no—
176C22×C59—21no—
177C22×C59—21no—
178C22×C59—21no—
179C22×C59—21no—
180C22×C59—21no—
181C22×C59—41no—
182C22×C59—41no—
183C22×C59—41no—
184C22×C59—41no—
185C22×C59—41no—
186C22×C59—41no—
187C22×C59C22×D411yescharacteristic
188C2×D59—22no—
189C2×D59—41no—
190C2×D59—41no—
191C2×D59—41no—
192C2×D59—41no—
193C2×D59—41no—
194C2×D59—84no—
195C4×C59—21no—
196C4×C59—21no—
197C4×C59—22no—
198C4×C59—21no—
199C4×C59—21no—
200C4×C59—41no—
201C4×C59C22×D411yescharacteristic
202C4×C59H(5,𝔽2)11yescharacteristic
203Dic59—41no—
204Dic59—41no—
205#3268—591nomaximal, Sylow
206C2×C59—41no—
207C2×C59—41no—
208C2×C59—81no—
209C2×C59—81no—
210C2×C59D4211yescharacteristic
211C2×C59#57511yescharacteristic
212C2×C59#57611yescharacteristic
213D59—42no—
214D59—81no—
215C2×AGL(1,ℤ/8)—591no—
216C2×#135—591no—
217#550D5911yescharacteristic, complemented
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×#41C2×D5911yescharacteristic
233C2×#41C2×D5911yescharacteristic, complemented
234C22×D4—591no—
235AGL(1,ℤ/8)—1184no—
236#135—1184no—
237C2×Q16—591no—
238C2×SD16—591no—
239C2×SD16—591no—
240C2×SD16—591no—
241C2×SD16—591no—
242C2×D8—591no—
243C2×D8—591no—
244C2×D8—591no—
245C2×D8—591no—
246C2×M16—591no—
247C22×C8—591no—
248#127—21no—
249#127C2×D5911yescharacteristic, complemented
250#124—591no—
251#123—1181no—
252C22⋊Q8—591no—
253#121—21no—
254#121—21no—
255#121—591no—
256#121—1181no—
257#121C2×D5911yescharacteristic
258#121C2×D5911yescharacteristic, complemented
259#120—1181no—
260C4×Q8C2×D5911yescharacteristic, complemented
261C4×D4—21no—
262C4×D4—591no—
263C4×D4C2×D5911yescharacteristic
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—1181no—
277#41—22no—
278#41—22no—
279#41—41no—
280#41—41no—
281#41—1182no—
282#41—2361no—
283C2×Q8—591no—
284C2×Q8C22×D5911yescharacteristic
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—591no—
292C2×D4—591no—
293C2×D4—1182no—
294C2×D4—1181no—
295C2×D4—1181no—
296C2×D4—1181no—
297C2×D4—2361no—
298C2×D4C22⋊D5911yescharacteristic
299C2×D4C22×D5911yescharacteristic
300C2×D4C22×D5911yescharacteristic
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—1181no—
304C22×C4—1181no—
305C22×C4C22×D5911yescharacteristic
306C22×C4C22×D5911yescharacteristic
307Q16—1182no—
308SD16—594no—
309SD16—1182no—
310SD16—1182no—
311SD16—2361no—
312D8—1182no—
313D8—1182no—
314D8—1182no—
315D8—2361no—
316M16—1182no—
317C2×C8—591no—
318C2×C8—591no—
319C2×C8—591no—
320C2×C8—591no—
321C2×C8—1182no—
322C4⋊C4—21no—
323C4⋊C4—591no—
324C4⋊C4—1181no—
325C4⋊C4C22⋊D5911yescharacteristic
326C4⋊C4C22×D5911yescharacteristic
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—1181no—
330C22⋊C4—1181no—
331C22⋊C4—1181no—
332C22⋊C4—1181no—
333C22⋊C4—1181no—
334C22⋊C4C22⋊D5911yescharacteristic
335C22⋊C4C22⋊D5911yescharacteristic
336C42—21no—
337C42C22×D5911yescharacteristic
338C23—21no—
339C23—21no—
340C23—1181no—
341C23—1181no—
342C23—4721no—
343C23—2362no—
344C23—2362no—
345C23C2×C22⋊D5911yescharacteristic
346C23C2×C22⋊D5911yescharacteristic
347Q8—21no—
348Q8—1181no—
349Q8—1181no—
350Q8D4×D5912yes—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—21no—
355D4—41no—
356D4—42no—
357D4—42no—
358D4—42no—
359D4—81no—
360D4—81no—
361D4—81no—
362D4—592no—
363D4—1181no—
364D4—1181no—
365D4—1181no—
366D4—4721no—
367D4—2362no—
368D4—2362no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—1181no—
378C2×C4—1181no—
379C2×C4—4721no—
380C2×C4—2362no—
381C2×C4C2×C22⋊D5911yescharacteristic
382C2×C4C2×C22⋊D5911yescharacteristic
383C2×C4C2×C22⋊D5911yescharacteristic
384C2×C4C2×C22⋊D5911yescharacteristic
385C2×C4C23×D5911yescharacteristic
386C8—592no—
387C8—1181no—
388C8—1181no—
389C8—1181no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—1182no—
403C22—4724no—
404C22—2361no—
405C22—2361no—
406C22—2361no—
407C22—2361no—
408C22—2361no—
409C22C22×C22⋊D5911yescharacteristic
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—22no—
415C4—41no—
416C4—2361no—
417C4—2361no—
418C4C2×D4×D5911yescharacteristic
419C4#1427377211yescharacteristic
420C2—41no—
421C2—41no—
422C2—81no—
423C2—81no—
424C2—4721no—
425C2—2362no—
426C2D4×C22⋊D5911yescharacteristic
427C2#1683820011yescharacteristic
428C2#1683820511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#550C2
socleC22×C59C22×D4
hypercenter#550D59
hypocenterC59#3268
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ #550

Complements

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

NH ≅ G/Ntype
1. C2×#14273752C2semidirect
2. C2×#14273747C2semidirect
3. #16838048C2semidirect
4. #16837789C2semidirect
5. #16837646C2semidirect
6. #16837636C2semidirect
7. #16837624C2semidirect
8. #16837594C2semidirect
9. #16837564C2semidirect
10. #16837547C2semidirect
11. #16837545C2semidirect
12. #16837535C2semidirect
13. #16837500C2semidirect
14. #16837474C2semidirect
15. C59×#550C2semidirect
20. C2×#11745672C22semidirect
21. C2×#11745670C22semidirect
22. C2×#11745670C22semidirect
30. C22×C59⋊C8C22semidirect
39. #14273660C22semidirect
40. C4⋊(C59⋊C8)C22semidirect
41. #14273651C22semidirect
42. #14273650C22semidirect
43. #14273648C22semidirect
44. #14273648C22semidirect
48. C22⋊(C59⋊C8)C22semidirect
49. #14273638C22semidirect
51. C2×#41×C59C22semidirect
53. #127×C59C22semidirect
57. #121×C59C22semidirect
58. C4×Q8×C59C22semidirect
104. #11745671D4semidirect
217. #550D59semidirect
230. C59#3268semidirect
233. C2×#41C2×D59semidirect
249. #127C2×D59semidirect
258. #121C2×D59semidirect
260. C4×Q8C2×D59semidirect