Finite Group Databasebeta

← #21435577

Subgroups — #21435577

Order 7552.

568 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14273752C211yesmaximal, characteristic, complemented
2C22×#11745669C211yesmaximal, characteristic, complemented
3D4×D236C211yesmaximal, characteristic, complemented
4#16837792C211yesmaximal, characteristic, complemented
5#16837653C211yesmaximal, characteristic, complemented
6#16837633C211yesmaximal, characteristic, complemented
7#16837614C211yesmaximal, characteristic, complemented
8#16837597C211yesmaximal, characteristic, complemented
9#16837552C211yesmaximal, characteristic, complemented
10#16837547C211yesmaximal, characteristic, complemented
11#16837536C211yesmaximal, characteristic, complemented
12#16837535C211yesmaximal, characteristic, complemented
13#16837512C211yesmaximal, characteristic, complemented
14#16837474C211yesmaximal, characteristic, complemented
15C59×#546C211yesmaximal, characteristic, complemented
16C22×D236C2211yescharacteristic
17C22×D236C2211yescharacteristic, complemented
18C2×D4×D59—21no—
19#14273752—24no—
20C2×#11745671C2211yescharacteristic, complemented
21C2×#11745671C2211yescharacteristic, complemented
22C2×#11745671C2211yescharacteristic, complemented
23C2×#11745669—24no—
24C2×#11745669C2211yescharacteristic
25C2×#11745669C2211yescharacteristic
26C2×#11745669C2211yescharacteristic, complemented
27C2×#11745669C2211yescharacteristic, complemented
28C2×#11745669C2211yescharacteristic, complemented
29C2×#11745669C2211yescharacteristic, complemented
30C2×#11745664C2211yescharacteristic, complemented
31C22×C59⋊C8C2211yescharacteristic, complemented
32#14273724C2211yescharacteristic, complemented
33#14273702—21no—
34#14273701C2211yescharacteristic
35#14273701C2211yescharacteristic, complemented
36#14273697—21no—
37#14273697—21no—
38C4×D236C2211yescharacteristic, complemented
39#14273658C2211yescharacteristic, complemented
40C4⋊(C59⋊C8)C2211yescharacteristic, complemented
41#14273651C2211yescharacteristic, complemented
42#14273648C2211yescharacteristic, complemented
43#14273648C2211yescharacteristic, complemented
44#14273647C2211yescharacteristic, complemented
45#14273647C2211yescharacteristic, complemented
46#14273647C2211yescharacteristic, complemented
47C22⋊(C59⋊C8)C2211yescharacteristic, complemented
48C22⋊(C59⋊C8)C2211yescharacteristic, complemented
49#14273638C2211yescharacteristic, complemented
50C2×#41×C59C2211yescharacteristic, complemented
51C22×D4×C59C2211yescharacteristic, complemented
52#124×C59C2211yescharacteristic, complemented
53#123×C59—21no—
54C22⋊Q8×C59C2211yescharacteristic, complemented
55#121×C59—21no—
56#121×C59C2211yescharacteristic, complemented
57#120×C59—21no—
58C4×D4×C59C2211yescharacteristic
59C4×D4×C59C2211yescharacteristic, complemented
60C2×C22⋊C4×C59—21no—
61C24×C59—21no—
62C23×D59—21no—
63C23×D59—21no—
64#41×C59—22no—
65#41×C59—41no—
66C2×Q8×C59C2311yescharacteristic
67C2×D4×C59—22no—
68C2×D4×C59—21no—
69C2×D4×C59—21no—
70C2×D4×C59—21no—
71C2×D4×C59—41no—
72C2×D4×C59D411yescharacteristic
73C2×D4×C59C2311yescharacteristic
74C2×D4×C59C2311yescharacteristic
75C22×C4×C59—21no—
76C22×C4×C59—21no—
77C22×C4×C59C2311yescharacteristic
78C22×C4×C59C2311yescharacteristic
79C2×C22⋊D59—21no—
80C2×C22⋊D59—21no—
81D4×D59—44no—
82C2×D236—22no—
83C2×D236—22no—
84C2×D236—21no—
85C2×D236—21no—
86C2×D236—21no—
87C2×D236—21no—
88C2×D236—41no—
89C2×D236—41no—
90C2×D236C2311yescharacteristic
91C2×D236C2311yescharacteristic
92C2×D236C2311yescharacteristic
93C2×C4×D59—21no—
94C4⋊C4×C59—21no—
95C4⋊C4×C59D411yescharacteristic
96C4⋊C4×C59C2311yescharacteristic
97C22⋊C4×C59—21no—
98C22⋊C4×C59—21no—
99C22⋊C4×C59—21no—
100C22⋊C4×C59—21no—
101C22⋊C4×C59—21no—
102C22⋊C4×C59D411yescharacteristic
103C22⋊C4×C59D411yescharacteristic
104C42×C59C2311yescharacteristic
105#11745671—22no—
106#11745671—22no—
107#11745671—41no—
108#11745669—22no—
109#11745669—22no—
110#11745669—22no—
111#11745669—22no—
112#11745669—41no—
113#11745669D414yescomplemented
114(C2×D59)⋊C4—21no—
115(C2×D59)⋊C4—21no—
116(C2×D59)⋊C4—21no—
117C4⋊Dic59C2311yescharacteristic
118#11745664—22no—
119C2×C59⋊C8—22no—
120C2×C59⋊C8C2311yescharacteristic
121C2×C59⋊C8C2311yescharacteristic
122C2×C59⋊C8C2311yescharacteristic
123C2×C59⋊C8C2311yescharacteristic
124C23×C59—21no—
125C23×C59—21no—
126C23×C59—42no—
127C23×C59—42no—
128C23×C59—81no—
129C23×C59C2×D411yescharacteristic
130C23×C59C2×D411yescharacteristic
131C22×D59—21no—
132C22×D59—21no—
133C22×D59—21no—
134C22×D59—42no—
135C22×D59—42no—
136C22×D59—42no—
137C22×D59—42no—
138C22×D59—81no—
139C22×D59—81no—
140Q8×C59—21no—
141Q8×C59—21no—
142D4×C59—22no—
143D4×C59—21no—
144D4×C59—21no—
145D4×C59—21no—
146D4×C59—42no—
147D4×C59—42no—
148D4×C59—81no—
149D4×C59C2×D412yescomplemented
150C2×C4×C59—21no—
151C2×C4×C59—21no—
152C2×C4×C59—21no—
153C2×C4×C59—21no—
154C2×C4×C59—21no—
155C2×C4×C59—21no—
156C2×C4×C59—42no—
157C2×C4×C59—81no—
158C2×C4×C59C2×D411yescharacteristic
159C2×C4×C59C2×D411yescharacteristic
160C2×C4×C59C2×D411yescharacteristic
161C2×C4×C59C2×D411yescharacteristic
162C2×C4×C59C2411yescharacteristic
163C22⋊D59—42no—
164C22⋊D59—42no—
165C2×Dic59—21no—
166D236—21no—
167D236—21no—
168D236—21no—
169D236—21no—
170D236—21no—
171D236—42no—
172D236—42no—
173D236—42no—
174D236—81no—
175D236C2×D412yes—
176C4×D59—42no—
177C59⋊C8—21no—
178C59⋊C8—21no—
179C59⋊C8—21no—
180C59⋊C8C2×D412yescomplemented
181C22×C59—21no—
182C22×C59—21no—
183C22×C59—21no—
184C22×C59—22no—
185C22×C59—21no—
186C22×C59—21no—
187C22×C59—41no—
188C22×C59—41no—
189C22×C59—41no—
190C22×C59—41no—
191C22×C59—41no—
192C22×C59—84no—
193C22×C59AGL(1,ℤ/8)12yescomplemented
194C22×C59C22×D411yescharacteristic
195C2×D59—22no—
196C2×D59—41no—
197C2×D59—41no—
198C2×D59—41no—
199C2×D59—41no—
200C2×D59—41no—
201C2×D59—41no—
202C2×D59—41no—
203C2×D59—41no—
204C2×D59—84no—
205C2×D59—84no—
206C4×C59—21no—
207C4×C59—21no—
208C4×C59—21no—
209C4×C59—21no—
210C4×C59—41no—
211C4×C59—41no—
212C4×C59C22×D411yescharacteristic
213C4×C59H(5,𝔽2)11yescharacteristic
214Dic59—41no—
215#3264—591nomaximal, Sylow
216C2×C59—22no—
217C2×C59—41no—
218C2×C59—42no—
219C2×C59—81no—
220C2×C59D4211yescharacteristic
221C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
222C2×C59#57611yescharacteristic
223D59—42no—
224D59—81no—
225D59—81no—
226C2×AGL(1,ℤ/8)—591no—
227C22×D8—591no—
228#546D5911yescharacteristic, complemented
229D42—591no—
230#496—591no—
231#469—591no—
232#465—591no—
233#463—591no—
234#459—591no—
235#450—591no—
236#449—591no—
237#447—591no—
238#447—591no—
239#442—591no—
240#435—591no—
241C59#326411yescharacteristic, complemented, Sylow
242C2×#41C2×D5911yescharacteristic, complemented
243C22×D4—591no—
244C22×D4—591no—
245C22×D4—1181no—
246C22×D4C2×D5911yescharacteristic, complemented
247AGL(1,ℤ/8)—1184no—
248C2×SD16—591no—
249C2×SD16—591no—
250C2×SD16—591no—
251C2×D8—591no—
252C2×D8—591no—
253C2×D8—591no—
254C2×D8—591no—
255C2×D8—591no—
256C2×D8—591no—
257C2×D8—1184no—
258C2×M16—591no—
259C22×C8—591no—
260#127—591no—
261#124C2×D5911yescharacteristic, complemented
262#123—21no—
263C22⋊Q8C2×D5911yescharacteristic, complemented
264#121—21no—
265#121—591no—
266#121—591no—
267#121—1181no—
268#121C2×D5911yescharacteristic, complemented
269#120—21no—
270#120—1181no—
271#120—1181no—
272C4×D4—591no—
273C4×D4C2×D5911yescharacteristic
274C4×D4C2×D5911yescharacteristic, complemented
275C2×C22⋊C4—21no—
276#106—591no—
277C4⋊C8—591no—
278#103—591no—
279#102—591no—
280#102—591no—
281#102—591no—
282#102—591no—
283#102—591no—
284C22⋊C8—591no—
285C22⋊C8—591no—
286#97—591no—
287C24—21no—
288C24—1181no—
289C24—1181no—
290#41—22no—
291#41—41no—
292C2×Q8C22×D5911yescharacteristic
293C2×D4—22no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—41no—
298C2×D4—591no—
299C2×D4—591no—
300C2×D4—591no—
301C2×D4—1182no—
302C2×D4—1182no—
303C2×D4—1181no—
304C2×D4—1181no—
305C2×D4—1181no—
306C2×D4—1181no—
307C2×D4—1181no—
308C2×D4—1181no—
309C2×D4—2361no—
310C2×D4—2361no—
311C2×D4—2364no—
312C2×D4C22⋊D5911yescharacteristic
313C2×D4C22×D5911yescharacteristic
314C2×D4C22×D5911yescharacteristic
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—1181no—
318C22×C4C22×D5911yescharacteristic
319C22×C4C22×D5911yescharacteristic
320SD16—1182no—
321SD16—1182no—
322SD16—2361no—
323D8—594no—
324D8—1182no—
325D8—1182no—
326D8—1182no—
327D8—1182no—
328D8—2361no—
329M16—1182no—
330C2×C8—591no—
331C2×C8—591no—
332C2×C8—591no—
333C2×C8—591no—
334C2×C8—1182no—
335C4⋊C4—21no—
336C4⋊C4—591no—
337C4⋊C4C22⋊D5911yescharacteristic
338C4⋊C4C22×D5911yescharacteristic
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—21no—
342C22⋊C4—21no—
343C22⋊C4—21no—
344C22⋊C4—1181no—
345C22⋊C4—1181no—
346C22⋊C4—1181no—
347C22⋊C4C22⋊D5911yescharacteristic
348C22⋊C4C22⋊D5911yescharacteristic
349C42C22×D5911yescharacteristic
350C23—21no—
351C23—21no—
352C23—42no—
353C23—42no—
354C23—81no—
355C23—1181no—
356C23—1181no—
357C23—1181no—
358C23—4721no—
359C23—4721no—
360C23—2362no—
361C23—2362no—
362C23—2362no—
363C23—2362no—
364C23C2×C22⋊D5911yescharacteristic
365C23C2×C22⋊D5911yescharacteristic
366Q8—21no—
367Q8—21no—
368D4—22no—
369D4—21no—
370D4—21no—
371D4—21no—
372D4—42no—
373D4—42no—
374D4—81no—
375D4—592no—
376D4—1181no—
377D4—1181no—
378D4—1181no—
379D4—1181no—
380D4—1181no—
381D4—4721no—
382D4—2362no—
383D4—2362no—
384D4—2362no—
385D4—2362no—
386D4—2362no—
387D4D4×D5912yescomplemented
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—42no—
395C2×C4—81no—
396C2×C4—1181no—
397C2×C4—2362no—
398C2×C4C2×C22⋊D5911yescharacteristic
399C2×C4C2×C22⋊D5911yescharacteristic
400C2×C4C2×C22⋊D5911yescharacteristic
401C2×C4C2×C22⋊D5911yescharacteristic
402C2×C4C23×D5911yescharacteristic
403C8—592no—
404C8—1181no—
405C8—1181no—
406C8—1181no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—22no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—84no—
419C22—1182no—
420C22—4724no—
421C22—4724no—
422C22—2361no—
423C22—2361no—
424C22—2361no—
425C22—2361no—
426C22—2361no—
427C22—2361no—
428C22—2361no—
429C22—2361no—
430C22#1427375212yescomplemented
431C22C22×C22⋊D5911yescharacteristic
432C4—21no—
433C4—21no—
434C4—21no—
435C4—21no—
436C4—41no—
437C4—41no—
438C4—2361no—
439C4C2×D4×D5911yescharacteristic
440C4#1427377211yescharacteristic
441C2—22no—
442C2—41no—
443C2—42no—
444C2—81no—
445C2—4721no—
446C2—4721no—
447C2—2362no—
448C2D4×C22⋊D5911yescharacteristic
449C2C2×#1427375211yescharacteristic
450C2#1683820511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#546C2
socleC22×C59C22×D4
hypercenter#546D59
hypocenterC59#3264
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. C2×#14273752C2semidirect
2. C22×#11745669C2semidirect
3. D4×D236C2semidirect
4. #16837792C2semidirect
5. #16837653C2semidirect
6. #16837633C2semidirect
7. #16837614C2semidirect
8. #16837597C2semidirect
9. #16837552C2semidirect
10. #16837547C2semidirect
11. #16837536C2semidirect
12. #16837535C2semidirect
13. #16837512C2semidirect
14. #16837474C2semidirect
15. C59×#546C2semidirect
17. C22×D236C22semidirect
20. C2×#11745671C22semidirect
21. C2×#11745671C22semidirect
22. C2×#11745671C22semidirect
26. C2×#11745669C22semidirect
27. C2×#11745669C22semidirect
28. C2×#11745669C22semidirect
29. C2×#11745669C22semidirect
30. C2×#11745664C22semidirect
31. C22×C59⋊C8C22semidirect
32. #14273724C22semidirect
35. #14273701C22semidirect
38. C4×D236C22semidirect
39. #14273658C22semidirect
40. C4⋊(C59⋊C8)C22semidirect
41. #14273651C22semidirect
42. #14273648C22semidirect
43. #14273648C22semidirect
44. #14273647C22semidirect
45. #14273647C22semidirect
46. #14273647C22semidirect
47. C22⋊(C59⋊C8)C22semidirect
48. C22⋊(C59⋊C8)C22semidirect
49. #14273638C22semidirect
50. C2×#41×C59C22semidirect
51. C22×D4×C59C22semidirect
52. #124×C59C22semidirect
54. C22⋊Q8×C59C22semidirect
56. #121×C59C22semidirect
59. C4×D4×C59C22semidirect
113. #11745669D4semidirect
149. D4×C59C2×D4semidirect
180. C59⋊C8C2×D4semidirect
193. C22×C59AGL(1,ℤ/8)semidirect
228. #546D59semidirect
241. C59#3264semidirect
242. C2×#41C2×D59semidirect
246. C22×D4C2×D59semidirect
261. #124C2×D59semidirect
263. C22⋊Q8C2×D59semidirect
268. #121C2×D59semidirect
274. C4×D4C2×D59semidirect
387. D4D4×D59semidirect
430. C22#14273752semidirect