Finite Group Databasebeta

← #21427629

Subgroups — #21427629

Order 7552.

922 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14273698C211yesmaximal, characteristic, complemented
2C2×#14273695C211yesmaximal, characteristic, complemented
3C2×#14273695C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊D59C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×D59C211yesmaximal, characteristic, complemented
6#16837324C211yesmaximal, characteristic, complemented
7#16837316C211yesmaximal, characteristic, complemented
8#16837316C211yesmaximal, characteristic, complemented
9#16837310C211yesmaximal, characteristic, complemented
10#16837302C211yesmaximal, characteristic, complemented
11#16837295C211yesmaximal, characteristic, complemented
12#16837281C211yesmaximal, characteristic, complemented
13#16837278C211yesmaximal, characteristic, complemented
14#16837273C211yesmaximal, characteristic, complemented
15C2×#121×C59C211yesmaximal, characteristic, complemented
16C24×D59C2211yescharacteristic
17C22×C22⋊D59C2211yescharacteristic
18C22×C22⋊D59C2211yescharacteristic
19C22×C22⋊D59C2211yescharacteristic
20C22×C22⋊D59C2211yescharacteristic
21C22×C4×D59C2211yescharacteristic
22C22×C4×D59C2211yescharacteristic
23#14273698—24no—
24#14273695—24no—
25#14273695—24no—
26C4×C22⋊D59—24no—
27C2×C4⋊Dic59C2211yescharacteristic, complemented
28C2×Dic59⋊C4C2211yescharacteristic, complemented
29C2×Dic59⋊C4C2211yescharacteristic, complemented
30C2×C22⋊Dic59C2211yescharacteristic
31C2×C22⋊Dic59C2211yescharacteristic
32C2×C22⋊Dic59C2211yescharacteristic
33C2×C22⋊Dic59C2211yescharacteristic, complemented
34C2×C22⋊Dic59C2211yescharacteristic, complemented
35C2×C22⋊Dic59C2211yescharacteristic, complemented
36C2×C22⋊Dic59C2211yescharacteristic, complemented
37C2×(C2×D59)⋊C4C2211yescharacteristic
38C2×(C2×D59)⋊C4C2211yescharacteristic
39C2×(C2×D59)⋊C4C2211yescharacteristic
40C2×(C2×D59)⋊C4C2211yescharacteristic
41C2×(C2×D59)⋊C4C2211yescharacteristic
42C2×(C2×D59)⋊C4C2211yescharacteristic
43C22⋊C4×D59—24no—
44C2×C4×Dic59C2211yescharacteristic, complemented
45C59⋊#95C2211yescharacteristic, complemented
46C59⋊#95C2211yescharacteristic, complemented
47C59⋊#95C2211yescharacteristic, complemented
48C59⋊#95C2211yescharacteristic, complemented
49C22×D4×C59C2211yescharacteristic
50C22×D4×C59C2211yescharacteristic
51C22×D4×C59C2211yescharacteristic, complemented
52C23×C4×C59C2211yescharacteristic, complemented
53#121×C59—24no—
54C2×C4⋊C4×C59C2211yescharacteristic, complemented
55C2×C22⋊C4×C59C2211yescharacteristic
56C2×C22⋊C4×C59C2211yescharacteristic, complemented
57C24×C59C2311yescharacteristic
58C24×C59C2311yescharacteristic
59C24×C59C2311yescharacteristic
60C23×D59—22no—
61C23×D59—22no—
62C23×D59—22no—
63C23×D59—22no—
64C23×D59—22no—
65C23×D59—41no—
66C23×D59—41no—
67C23×D59C2311yescharacteristic
68C23×D59C2311yescharacteristic
69C2×D4×C59—22no—
70C2×D4×C59—22no—
71C2×D4×C59—22no—
72C2×D4×C59—22no—
73C2×D4×C59—22no—
74C2×D4×C59—22no—
75C2×D4×C59—41no—
76C2×D4×C59—41no—
77C2×D4×C59—41no—
78C22×C4×C59—22no—
79C22×C4×C59—22no—
80C22×C4×C59—41no—
81C22×C4×C59C2311yescharacteristic
82C22×C4×C59C2311yescharacteristic
83C22×C4×C59C2311yescharacteristic
84C22×C4×C59C2311yescharacteristic
85C2×C22⋊D59—22no—
86C2×C22⋊D59—22no—
87C2×C22⋊D59—22no—
88C2×C22⋊D59—22no—
89C2×C22⋊D59—22no—
90C2×C22⋊D59—22no—
91C2×C22⋊D59—22no—
92C2×C22⋊D59—22no—
93C2×C22⋊D59—22no—
94C2×C22⋊D59—41no—
95C2×C22⋊D59—41no—
96C2×C22⋊D59D414yescomplemented
97C22×Dic59C2311yescharacteristic
98C22×Dic59C2311yescharacteristic
99C22×Dic59C2311yescharacteristic
100C22×Dic59C2311yescharacteristic
101C22×Dic59C2311yescharacteristic
102C22×Dic59C2311yescharacteristic
103C2×C4×D59—22no—
104C2×C4×D59—22no—
105C2×C4×D59—22no—
106C2×C4×D59—22no—
107C2×C4×D59—41no—
108C2×C4×D59—41no—
109C4⋊C4×C59—22no—
110C22⋊C4×C59—22no—
111C22⋊C4×C59D414yescomplemented
112C22⋊Dic59—22no—
113C22⋊Dic59—22no—
114C22⋊Dic59—22no—
115C22⋊Dic59—22no—
116C22⋊Dic59—22no—
117C22⋊Dic59—22no—
118C22⋊Dic59—41no—
119(C2×D59)⋊C4—22no—
120(C2×D59)⋊C4—22no—
121(C2×D59)⋊C4—22no—
122(C2×D59)⋊C4—22no—
123(C2×D59)⋊C4—22no—
124(C2×D59)⋊C4D414yescomplemented
125C4⋊Dic59—22no—
126Dic59⋊C4—22no—
127Dic59⋊C4—41no—
128C4×Dic59—22no—
129C23×C59—21no—
130C23×C59—21no—
131C23×C59—21no—
132C23×C59—21no—
133C23×C59—21no—
134C23×C59—21no—
135C23×C59—21no—
136C23×C59—21no—
137C23×C59—21no—
138C23×C59—21no—
139C23×C59—21no—
140C23×C59—21no—
141C23×C59—21no—
142C23×C59—21no—
143C23×C59—21no—
144C23×C59—21no—
145C23×C59—21no—
146C23×C59—21no—
147C23×C59—21no—
148C23×C59C2×D412yes—
149C23×C59C2×D412yes—
150C23×C59C2411yescharacteristic
151C22×D59—21no—
152C22×D59—21no—
153C22×D59—21no—
154C22×D59—21no—
155C22×D59—28no—
156C22×D59—21no—
157C22×D59—21no—
158C22×D59—21no—
159C22×D59—21no—
160C22×D59—21no—
161C22×D59—21no—
162C22×D59—44no—
163C22×D59—44no—
164C22×D59—44no—
165C22×D59—44no—
166C22×D59—44no—
167C22×D59—44no—
168C22×D59C2×D412yes—
169C22×D59C2×D412yes—
170C22×D59#4112yes—
171C22×D59#4112yes—
172D4×C59—44no—
173D4×C59—44no—
174D4×C59—44no—
175C2×C4×C59—21no—
176C2×C4×C59—21no—
177C2×C4×C59—21no—
178C2×C4×C59—21no—
179C2×C4×C59—21no—
180C2×C4×C59—21no—
181C2×C4×C59—21no—
182C2×C4×C59—21no—
183C2×C4×C59—21no—
184C2×C4×C59—44no—
185C2×C4×C59C2×D412yes—
186C2×C4×C59C2×D412yes—
187C2×C4×C59C2×D412yes—
188C22⋊D59—28no—
189C22⋊D59—44no—
190C22⋊D59—44no—
191C22⋊D59—44no—
192C2×Dic59—21no—
193C2×Dic59—21no—
194C2×Dic59—21no—
195C2×Dic59—21no—
196C2×Dic59—21no—
197C2×Dic59—21no—
198C2×Dic59—21no—
199C2×Dic59—21no—
200C2×Dic59—21no—
201C2×Dic59—21no—
202C2×Dic59—21no—
203C2×Dic59—21no—
204C2×Dic59—21no—
205C2×Dic59—21no—
206C2×Dic59—21no—
207C2×Dic59—21no—
208C2×Dic59C2×D412yes—
209C2×Dic59C2×D412yes—
210C4×D59—44no—
211C4×D59—44no—
212C22×C59—22no—
213C22×C59—22no—
214C22×C59—22no—
215C22×C59—22no—
216C22×C59—22no—
217C22×C59—22no—
218C22×C59—41no—
219C22×C59—41no—
220C22×C59—41no—
221C22×C59—41no—
222C22×C59—41no—
223C22×C59—41no—
224C22×C59—41no—
225C22×C59—41no—
226C22×C59—41no—
227C22×C59—41no—
228C22×C59—41no—
229C22×C59—41no—
230C22×C59—41no—
231C22×C59—41no—
232C22×C59—41no—
233C22×C59C22×D411yescharacteristic
234C22×C59C22×D411yescharacteristic
235C22×C59C22×D411yescharacteristic
236C22×C59C2×#4111yescharacteristic
237C22×C59C2×#4111yescharacteristic
238C22×C59H(5,𝔽2)11yescharacteristic
239C22×C59H(5,𝔽2)11yescharacteristic
240C2×D59—22no—
241C2×D59—22no—
242C2×D59—22no—
243C2×D59—22no—
244C2×D59—22no—
245C2×D59—22no—
246C2×D59—22no—
247C2×D59—22no—
248C2×D59—22no—
249C2×D59—416no—
250C2×D59—41no—
251C2×D59—41no—
252C2×D59—41no—
253C2×D59—41no—
254C2×D59#12114yescomplemented
255C4×C59—22no—
256C4×C59—22no—
257C4×C59—22no—
258C4×C59—41no—
259Dic59—22no—
260Dic59—22no—
261Dic59—41no—
262Dic59—41no—
263Dic59—41no—
264Dic59—41no—
265#2424—591nomaximal, Sylow
266C2×C59—42no—
267C2×C59—42no—
268C2×C59—81no—
269C2×C59C2×#12111yescharacteristic
270C2×C59#52511yescharacteristic
271C2×C59#53811yescharacteristic
272C2×C59D4211yescharacteristic
273C2×C59D4211yescharacteristic
274C2×C59#54611yescharacteristic
275C2×C59#54611yescharacteristic
276D59—24no—
277D59—42no—
278C2×#121—591no—
279C2×#121D5911yescharacteristic, complemented
280C2×#120—591no—
281C2×#120—591no—
282C2×C4×D4—591no—
283C22×C22⋊C4—591no—
284#396—591no—
285#394—591no—
286#394—591no—
287#392—591no—
288#390—591no—
289#388—591no—
290#386—591no—
291#386—591no—
292#385—591no—
293C59#242411yescharacteristic, complemented, Sylow
294C25—591no—
295C22×D4—591no—
296C22×D4—591no—
297C22×D4—591no—
298C22×D4—591no—
299C22×D4C2×D5911yescharacteristic
300C22×D4C2×D5911yescharacteristic
301C22×D4C2×D5911yescharacteristic, complemented
302C23×C4—591no—
303C23×C4—591no—
304C23×C4C2×D5911yescharacteristic, complemented
305#121—24no—
306#121—1184no—
307#120—1184no—
308#120—1184no—
309C4×D4—1184no—
310C2×C4⋊C4—591no—
311C2×C4⋊C4—591no—
312C2×C4⋊C4—591no—
313C2×C4⋊C4C2×D5911yescharacteristic, complemented
314C2×C22⋊C4—591no—
315C2×C22⋊C4—591no—
316C2×C22⋊C4—591no—
317C2×C22⋊C4—591no—
318C2×C22⋊C4—591no—
319C2×C22⋊C4—591no—
320C2×C22⋊C4—591no—
321C2×C22⋊C4—591no—
322C2×C22⋊C4—591no—
323C2×C22⋊C4—591no—
324C2×C22⋊C4—591no—
325C2×C22⋊C4—591no—
326C2×C22⋊C4—591no—
327C2×C22⋊C4—1184no—
328C2×C22⋊C4C2×D5911yescharacteristic
329C2×C22⋊C4C2×D5911yescharacteristic, complemented
330C2×C42—591no—
331#95—591no—
332#95—591no—
333#95—591no—
334#95—591no—
335C24—591no—
336C24—591no—
337C24—1182no—
338C24—1182no—
339C24—1182no—
340C24—1182no—
341C24—1182no—
342C24—2361no—
343C24—2361no—
344C24C22×D5911yescharacteristic
345C24C22×D5911yescharacteristic
346C24C22×D5911yescharacteristic
347C2×D4—22no—
348C2×D4—22no—
349C2×D4—22no—
350C2×D4—22no—
351C2×D4—22no—
352C2×D4—22no—
353C2×D4—41no—
354C2×D4—41no—
355C2×D4—41no—
356C2×D4—594no—
357C2×D4—1182no—
358C2×D4—1182no—
359C2×D4—1182no—
360C2×D4—1182no—
361C2×D4—1182no—
362C2×D4—1182no—
363C2×D4—1182no—
364C2×D4—1182no—
365C2×D4—1182no—
366C2×D4—2361no—
367C2×D4—2361no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—41no—
371C22×C4—591no—
372C22×C4—591no—
373C22×C4—591no—
374C22×C4—591no—
375C22×C4—591no—
376C22×C4—591no—
377C22×C4—1182no—
378C22×C4—1182no—
379C22×C4—1182no—
380C22×C4—1182no—
381C22×C4—2361no—
382C22×C4—2361no—
383C22×C4C22×D5911yescharacteristic
384C22×C4C22×D5911yescharacteristic
385C22×C4C22×D5911yescharacteristic
386C22×C4C22×D5911yescharacteristic
387C4⋊C4—22no—
388C4⋊C4—1182no—
389C4⋊C4—1182no—
390C4⋊C4—2361no—
391C22⋊C4—22no—
392C22⋊C4—594no—
393C22⋊C4—1182no—
394C22⋊C4—1182no—
395C22⋊C4—1182no—
396C22⋊C4—1182no—
397C22⋊C4—1182no—
398C22⋊C4—1182no—
399C22⋊C4—1182no—
400C22⋊C4—1182no—
401C22⋊C4—1182no—
402C22⋊C4—1182no—
403C22⋊C4—1182no—
404C22⋊C4—2361no—
405C22⋊C4C22⋊D5914yescomplemented
406C42—1182no—
407C23—21no—
408C23—21no—
409C23—21no—
410C23—21no—
411C23—21no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—21no—
419C23—21no—
420C23—21no—
421C23—21no—
422C23—21no—
423C23—21no—
424C23—21no—
425C23—21no—
426C23—592no—
427C23—592no—
428C23—592no—
429C23—592no—
430C23—1188no—
431C23—1181no—
432C23—1181no—
433C23—1181no—
434C23—1181no—
435C23—1181no—
436C23—1181no—
437C23—1181no—
438C23—1181no—
439C23—1181no—
440C23—1181no—
441C23—2364no—
442C23—2364no—
443C23—2364no—
444C23—2364no—
445C23—2364no—
446C23—2364no—
447C23D4×D5912yes—
448C23C2×C22⋊D5912yes—
449C23C23×D5911yescharacteristic
450D4—44no—
451D4—44no—
452D4—44no—
453D4—1188no—
454D4—2364no—
455D4—2364no—
456D4—2364no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—44no—
467C2×C4—592no—
468C2×C4—592no—
469C2×C4—1181no—
470C2×C4—1181no—
471C2×C4—1181no—
472C2×C4—1181no—
473C2×C4—1181no—
474C2×C4—1181no—
475C2×C4—1181no—
476C2×C4—1181no—
477C2×C4—1181no—
478C2×C4—1181no—
479C2×C4—1181no—
480C2×C4—1181no—
481C2×C4—1181no—
482C2×C4—1181no—
483C2×C4—1181no—
484C2×C4—1181no—
485C2×C4—2364no—
486C2×C4—2364no—
487C2×C4D4×D5912yes—
488C2×C4C2×C22⋊D5912yes—
489C2×C4C2×C22⋊D5912yes—
490C22—22no—
491C22—22no—
492C22—22no—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—41no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—41no—
503C22—41no—
504C22—41no—
505C22—41no—
506C22—41no—
507C22—41no—
508C22—41no—
509C22—41no—
510C22—41no—
511C22—594no—
512C22—1182no—
513C22—1182no—
514C22—1182no—
515C22—1182no—
516C22—1182no—
517C22—1182no—
518C22—1182no—
519C22—1182no—
520C22—1182no—
521C22—23616no—
522C22—2361no—
523C22—2361no—
524C22—2361no—
525C22—2361no—
526C22C2×D4×D5911yescharacteristic
527C22C2×D4×D5911yescharacteristic
528C22C22×C22⋊D5911yescharacteristic
529C22#41×D5911yescharacteristic
530C22#41×D5911yescharacteristic
531C22#1427377211yescharacteristic
532C22#1427377211yescharacteristic
533C4—22no—
534C4—22no—
535C4—22no—
536C4—41no—
537C4—1182no—
538C4—1182no—
539C4—2361no—
540C4—2361no—
541C4—2361no—
542C4—2361no—
543C2—42no—
544C2—42no—
545C2—81no—
546C2—1184no—
547C2—2362no—
548C2#121×D5911yescharacteristic
549C2#1683790911yescharacteristic
550C2#1683798411yescharacteristic
551C2D4×C22⋊D5911yescharacteristic
552C2D4×C22⋊D5911yescharacteristic
553C2#1683804111yescharacteristic
554C2#1683804911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC2×#121×C59C2
hypercenterC2×#121D59
hypocenterC59#2424
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#14273698C2semidirect
2. C2×#14273695C2semidirect
3. C2×#14273695C2semidirect
4. C2×C4×C22⋊D59C2semidirect
5. C2×C22⋊C4×D59C2semidirect
6. #16837324C2semidirect
7. #16837316C2semidirect
8. #16837316C2semidirect
9. #16837310C2semidirect
10. #16837302C2semidirect
11. #16837295C2semidirect
12. #16837281C2semidirect
13. #16837278C2semidirect
14. #16837273C2semidirect
15. C2×#121×C59C2semidirect
27. C2×C4⋊Dic59C22semidirect
28. C2×Dic59⋊C4C22semidirect
29. C2×Dic59⋊C4C22semidirect
33. C2×C22⋊Dic59C22semidirect
34. C2×C22⋊Dic59C22semidirect
35. C2×C22⋊Dic59C22semidirect
36. C2×C22⋊Dic59C22semidirect
44. C2×C4×Dic59C22semidirect
45. C59⋊#95C22semidirect
46. C59⋊#95C22semidirect
47. C59⋊#95C22semidirect
48. C59⋊#95C22semidirect
51. C22×D4×C59C22semidirect
52. C23×C4×C59C22semidirect
54. C2×C4⋊C4×C59C22semidirect
56. C2×C22⋊C4×C59C22semidirect
96. C2×C22⋊D59D4semidirect
111. C22⋊C4×C59D4semidirect
124. (C2×D59)⋊C4D4semidirect
254. C2×D59#121semidirect
279. C2×#121D59semidirect
293. C59#2424semidirect
301. C22×D4C2×D59semidirect
304. C23×C4C2×D59semidirect
313. C2×C4⋊C4C2×D59semidirect
329. C2×C22⋊C4C2×D59semidirect
405. C22⋊C4C22⋊D59semidirect