Finite Group Databasebeta

← #21435572

Subgroups — #21435572

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×#14273753C211yesmaximal, characteristic, complemented
2C22×#11745669C211yesmaximal, characteristic, complemented
3#16838048C211yesmaximal, characteristic, complemented
4#16837789C211yesmaximal, characteristic, complemented
5#16837653C211yesmaximal, characteristic, complemented
6#16837629C211yesmaximal, characteristic, complemented
7#16837617C211yesmaximal, characteristic, complemented
8#16837594C211yesmaximal, characteristic, complemented
9#16837553C211yesmaximal, characteristic, complemented
10#16837545C211yesmaximal, characteristic, complemented
11#16837536C211yesmaximal, characteristic, complemented
12#16837535C211yesmaximal, characteristic, complemented
13#16837512C211yesmaximal, characteristic, complemented
14#16837474C211yesmaximal, characteristic, complemented
15D42×C59C211yesmaximal, characteristic, complemented
16C2×#11745685C2211yescharacteristic, complemented
17C22×D236C2211yescharacteristic, complemented
18#14273753—24no—
19C2×#11745670C2211yescharacteristic, complemented
20C2×#11745670C2211yescharacteristic, complemented
21C2×#11745670C2211yescharacteristic, complemented
22C2×#11745669—24no—
23C2×#11745669C2211yescharacteristic
24C2×#11745669C2211yescharacteristic
25C2×#11745669C2211yescharacteristic, complemented
26C2×#11745669C2211yescharacteristic, complemented
27C2×#11745669C2211yescharacteristic, complemented
28C2×#11745669C2211yescharacteristic, complemented
29C2×#11745664C2211yescharacteristic, complemented
30C22×C59⋊C8C2211yescharacteristic, complemented
31#14273715C2211yescharacteristic, complemented
32#14273712—21no—
33#14273706C2211yescharacteristic, complemented
34#14273701C2211yescharacteristic, complemented
35#14273700—21no—
36#14273695—21no—
37C4×D236C2211yescharacteristic, complemented
38C22⋊C4×D59—21no—
39#14273658C2211yescharacteristic, complemented
40C4⋊(C59⋊C8)C2211yescharacteristic, complemented
41#14273650C2211yescharacteristic, complemented
42#14273648C2211yescharacteristic, complemented
43#14273648C2211yescharacteristic, complemented
44#14273648C2211yescharacteristic, complemented
45#14273647C2211yescharacteristic, complemented
46#14273647C2211yescharacteristic, complemented
47C22⋊(C59⋊C8)C2211yescharacteristic, complemented
48C22⋊(C59⋊C8)C2211yescharacteristic, complemented
49#14273638C2211yescharacteristic, complemented
50C22×D4×C59—21no—
51C22×D4×C59C2211yescharacteristic
52C22×D4×C59C2211yescharacteristic, complemented
53#127×C59C2211yescharacteristic, complemented
54#121×C59—21no—
55#121×C59C2211yescharacteristic
56#121×C59C2211yescharacteristic, complemented
57#120×C59—21no—
58#120×C59—21no—
59C4×D4×C59C2211yescharacteristic
60C4×D4×C59C2211yescharacteristic, complemented
61C24×C59—21no—
62C24×C59—21no—
63C23×D59—21no—
64C2×D4×C59—22no—
65C2×D4×C59—22no—
66C2×D4×C59—21no—
67C2×D4×C59—21no—
68C2×D4×C59—21no—
69C2×D4×C59—21no—
70C2×D4×C59—21no—
71C2×D4×C59—21no—
72C2×D4×C59—41no—
73C2×D4×C59—41no—
74C2×D4×C59—44no—
75C2×D4×C59D411yescharacteristic
76C2×D4×C59C2311yescharacteristic
77C2×D4×C59C2311yescharacteristic
78C2×D4×C59C2311yescharacteristic
79C22×C4×C59—21no—
80C22×C4×C59C2311yescharacteristic
81C22×C4×C59C2311yescharacteristic
82C2×C22⋊D59—21no—
83C2×C22⋊D59—21no—
84#11745685—22no—
85#11745685—41no—
86C2×D236—22no—
87C2×D236—21no—
88C2×D236—41no—
89C2×D236C2311yescharacteristic
90C2×D236C2311yescharacteristic
91C2×C4×D59—21no—
92C2×C4×D59—21no—
93C2×Dic118C2311yescharacteristic
94C4⋊C4×C59D411yescharacteristic
95C4⋊C4×C59C2311yescharacteristic
96C22⋊C4×C59—21no—
97C22⋊C4×C59—21no—
98C22⋊C4×C59—21no—
99C22⋊C4×C59D411yescharacteristic
100C22⋊C4×C59D411yescharacteristic
101C42×C59C2311yescharacteristic
102C22⋊Dic59—21no—
103#11745670—22no—
104#11745670—22no—
105#11745670—41no—
106#11745669—22no—
107#11745669—22no—
108#11745669—22no—
109#11745669—22no—
110#11745669—41no—
111#11745669D414yescomplemented
112(C2×D59)⋊C4—21no—
113(C2×D59)⋊C4—21no—
114(C2×D59)⋊C4—21no—
115(C2×D59)⋊C4—21no—
116C4⋊Dic59C2311yescharacteristic
117Dic59⋊C4—21no—
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—21no—
127C23×C59—42no—
128C23×C59—42no—
129C23×C59—42no—
130C23×C59—42no—
131C23×C59—81no—
132C23×C59—81no—
133C23×C59C2×D411yescharacteristic
134C23×C59C2×D411yescharacteristic
135C22×D59—21no—
136C22×D59—21no—
137C22×D59—42no—
138C22×D59—42no—
139C22×D59—81no—
140D4×C59—22no—
141D4×C59—21no—
142D4×C59—21no—
143D4×C59—21no—
144D4×C59—21no—
145D4×C59—21no—
146D4×C59—42no—
147D4×C59—42no—
148D4×C59—42no—
149D4×C59—42no—
150D4×C59—42no—
151D4×C59—81no—
152D4×C59C2×D412yes—
153C2×C4×C59—21no—
154C2×C4×C59—21no—
155C2×C4×C59—21no—
156C2×C4×C59—21no—
157C2×C4×C59—21no—
158C2×C4×C59—42no—
159C2×C4×C59C2×D411yescharacteristic
160C2×C4×C59C2×D411yescharacteristic
161C2×C4×C59C2×D411yescharacteristic
162C2×C4×C59C2×D411yescharacteristic
163C2×C4×C59C2411yescharacteristic
164C22⋊D59—42no—
165C22⋊D59—81no—
166C2×Dic59—21no—
167C2×Dic59—21no—
168D236—21no—
169D236—21no—
170D236—21no—
171D236—42no—
172D236C2×D412yescomplemented
173C4×D59—42no—
174C4×D59—81no—
175Dic118—21no—
176Dic118—21no—
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—41no—
193C22×C59—41no—
194C22×C59—41no—
195C22×C59—84no—
196C22×C59—84no—
197C22×C59AGL(1,ℤ/8)12yescomplemented
198C22×C59C22×D411yescharacteristic
199C2×D59—22no—
200C2×D59—41no—
201C2×D59—41no—
202C2×D59—41no—
203C2×D59—41no—
204C2×D59—41no—
205C2×D59—84no—
206C4×C59—21no—
207C4×C59—21no—
208C4×C59—21no—
209C4×C59—21no—
210C4×C59—41no—
211C4×C59C22×D411yescharacteristic
212C4×C59H(5,𝔽2)11yescharacteristic
213Dic59—41no—
214Dic59—41no—
215#3264—591nomaximal, Sylow
216C2×C59—22no—
217C2×C59—41no—
218C2×C59—42no—
219C2×C59—81no—
220C2×C59—81no—
221C2×C59D4211yescharacteristic
222C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
223C2×C59#57611yescharacteristic
224D59—42no—
225D59—81no—
226C2×AGL(1,ℤ/8)—591no—
227C22×D8—591no—
228#546—591no—
229D42D5911yescharacteristic, complemented
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×#41—591no—
243C22×D4—21no—
244C22×D4—591no—
245C22×D4C2×D5911yescharacteristic
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#127C2×D5911yescharacteristic, complemented
261#124—591no—
262#123—1181no—
263C22⋊Q8—591no—
264#121—21no—
265#121—591no—
266#121—1181no—
267#121C2×D5911yescharacteristic
268#121C2×D5911yescharacteristic, complemented
269#120—21no—
270#120—21no—
271#120—1181no—
272C4×D4—591no—
273C4×D4C2×D5911yescharacteristic
274C4×D4C2×D5911yescharacteristic, complemented
275C2×C22⋊C4—1181no—
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—21no—
289C24—1181no—
290#41—1182no—
291#41—2361no—
292C2×Q8—591no—
293C2×D4—22no—
294C2×D4—22no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—44no—
304C2×D4—591no—
305C2×D4—591no—
306C2×D4—1182no—
307C2×D4—1181no—
308C2×D4—1181no—
309C2×D4—1181no—
310C2×D4—2361no—
311C2×D4C22⋊D5911yescharacteristic
312C2×D4C22×D5911yescharacteristic
313C2×D4C22×D5911yescharacteristic
314C2×D4C22×D5911yescharacteristic
315C22×C4—21no—
316C22×C4—1181no—
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—591no—
336C4⋊C4—1181no—
337C4⋊C4C22⋊D5911yescharacteristic
338C4⋊C4C22×D5911yescharacteristic
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—21no—
342C22⋊C4—1181no—
343C22⋊C4—1181no—
344C22⋊C4—1181no—
345C22⋊C4—1181no—
346C22⋊C4—1181no—
347C22⋊C4C22⋊D5911yescharacteristic
348C22⋊C4C22⋊D5911yescharacteristic
349C42C22×D5911yescharacteristic
350C23—21no—
351C23—21no—
352C23—21no—
353C23—42no—
354C23—42no—
355C23—42no—
356C23—42no—
357C23—81no—
358C23—81no—
359C23—1181no—
360C23—1181no—
361C23—4721no—
362C23—2362no—
363C23—2362no—
364C23C2×C22⋊D5911yescharacteristic
365C23C2×C22⋊D5911yescharacteristic
366Q8—1181no—
367Q8—1181no—
368D4—22no—
369D4—21no—
370D4—21no—
371D4—21no—
372D4—21no—
373D4—21no—
374D4—42no—
375D4—42no—
376D4—42no—
377D4—42no—
378D4—42no—
379D4—81no—
380D4—592no—
381D4—1181no—
382D4—1181no—
383D4—1181no—
384D4—4721no—
385D4—2362no—
386D4—2362no—
387D4D4×D5912yes—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—42no—
394C2×C4—1181no—
395C2×C4—1181no—
396C2×C4—4721no—
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—41no—
419C22—41no—
420C22—41no—
421C22—84no—
422C22—84no—
423C22—1182no—
424C22—4724no—
425C22—2361no—
426C22—2361no—
427C22—2361no—
428C22—2361no—
429C22—2361no—
430C22#1427375312yescomplemented
431C22C22×C22⋊D5911yescharacteristic
432C4—21no—
433C4—21no—
434C4—21no—
435C4—21no—
436C4—41no—
437C4—2361no—
438C4—2361no—
439C4C2×D4×D5911yescharacteristic
440C4#1427377211yescharacteristic
441C2—22no—
442C2—41no—
443C2—42no—
444C2—81no—
445C2—81no—
446C2—4721no—
447C2—2362no—
448C2D4×C22⋊D5911yescharacteristic
449C2C2×#1427375311yescharacteristic
450C2#1683820511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingD42×C59C2
socleC22×C59C22×D4
hypercenterD42D59
hypocenterC59#3264
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. C2×#14273753C2semidirect
2. C22×#11745669C2semidirect
3. #16838048C2semidirect
4. #16837789C2semidirect
5. #16837653C2semidirect
6. #16837629C2semidirect
7. #16837617C2semidirect
8. #16837594C2semidirect
9. #16837553C2semidirect
10. #16837545C2semidirect
11. #16837536C2semidirect
12. #16837535C2semidirect
13. #16837512C2semidirect
14. #16837474C2semidirect
15. D42×C59C2semidirect
16. C2×#11745685C22semidirect
17. C22×D236C22semidirect
19. C2×#11745670C22semidirect
20. C2×#11745670C22semidirect
21. C2×#11745670C22semidirect
25. C2×#11745669C22semidirect
26. C2×#11745669C22semidirect
27. C2×#11745669C22semidirect
28. C2×#11745669C22semidirect
29. C2×#11745664C22semidirect
30. C22×C59⋊C8C22semidirect
31. #14273715C22semidirect
33. #14273706C22semidirect
34. #14273701C22semidirect
37. C4×D236C22semidirect
39. #14273658C22semidirect
40. C4⋊(C59⋊C8)C22semidirect
41. #14273650C22semidirect
42. #14273648C22semidirect
43. #14273648C22semidirect
44. #14273648C22semidirect
45. #14273647C22semidirect
46. #14273647C22semidirect
47. C22⋊(C59⋊C8)C22semidirect
48. C22⋊(C59⋊C8)C22semidirect
49. #14273638C22semidirect
52. C22×D4×C59C22semidirect
53. #127×C59C22semidirect
56. #121×C59C22semidirect
60. C4×D4×C59C22semidirect
111. #11745669D4semidirect
172. D236C2×D4semidirect
180. C59⋊C8C2×D4semidirect
197. C22×C59AGL(1,ℤ/8)semidirect
229. D42D59semidirect
241. C59#3264semidirect
246. C22×D4C2×D59semidirect
260. #127C2×D59semidirect
268. #121C2×D59semidirect
274. C4×D4C2×D59semidirect
430. C22#14273753semidirect