Finite Group Databasebeta

← #21427638

Subgroups — #21427638

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×#14273699C211yesmaximal, characteristic, complemented
2C2×#14273695C211yesmaximal, characteristic, complemented
3C2×#14273695C211yesmaximal, characteristic, complemented
4C2×D4×Dic59C211yesmaximal, characteristic, complemented
5C22×(C2×D59)⋊C4C211yesmaximal, characteristic, complemented
6#16837324C211yesmaximal, characteristic, complemented
7#16837318C211yesmaximal, characteristic, complemented
8#16837317C211yesmaximal, characteristic, complemented
9#16837310C211yesmaximal, characteristic, complemented
10#16837302C211yesmaximal, characteristic, complemented
11#16837292C211yesmaximal, characteristic, complemented
12#16837282C211yesmaximal, characteristic, complemented
13#16837279C211yesmaximal, characteristic, complemented
14#16837275C211yesmaximal, characteristic, complemented
15C2×#121×C59C211yesmaximal, characteristic, complemented
16C24×D59C2211yescharacteristic
17C22×C22⋊D59C2211yescharacteristic
18C22×C22⋊D59C2211yescharacteristic
19C22×C22⋊D59C2211yescharacteristic
20C22×C22⋊D59C2211yescharacteristic
21C23×Dic59C2211yescharacteristic
22C23×Dic59C2211yescharacteristic, complemented
23#14273699—24no—
24#14273695—24no—
25#14273695—24no—
26D4×Dic59—24no—
27C2×C4⋊Dic59C2211yescharacteristic, complemented
28C2×Dic59⋊C4C2211yescharacteristic, complemented
29C2×Dic59⋊C4C2211yescharacteristic, complemented
30C2×C22⋊Dic59C2211yescharacteristic
31C2×C22⋊Dic59C2211yescharacteristic
32C2×C22⋊Dic59C2211yescharacteristic, complemented
33C2×C22⋊Dic59C2211yescharacteristic, complemented
34C2×C22⋊Dic59C2211yescharacteristic, complemented
35C2×(C2×D59)⋊C4—24no—
36C2×(C2×D59)⋊C4C2211yescharacteristic
37C2×(C2×D59)⋊C4C2211yescharacteristic
38C2×(C2×D59)⋊C4C2211yescharacteristic
39C2×(C2×D59)⋊C4C2211yescharacteristic
40C2×(C2×D59)⋊C4C2211yescharacteristic
41C2×(C2×D59)⋊C4C2211yescharacteristic
42C2×(C2×D59)⋊C4C2211yescharacteristic
43C2×(C2×D59)⋊C4C2211yescharacteristic
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
53#121×C59—24no—
54C2×C4⋊C4×C59C2211yescharacteristic, complemented
55C2×C22⋊C4×C59C2211yescharacteristic, complemented
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—22no—
76C2×D4×C59—41no—
77C2×D4×C59D414yescomplemented
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—41no—
94C2×C22⋊D59—41no—
95C2×C22⋊D59—41no—
96C2×C22⋊D59—41no—
97C22×Dic59—22no—
98C22×Dic59—22no—
99C22×Dic59—22no—
100C22×Dic59—22no—
101C22×Dic59—41no—
102C22×Dic59—41no—
103C22×Dic59C2311yescharacteristic
104C22×Dic59C2311yescharacteristic
105C22×Dic59C2311yescharacteristic
106C22×Dic59C2311yescharacteristic
107C22×Dic59C2311yescharacteristic
108C22×Dic59C2311yescharacteristic
109C4⋊C4×C59—22no—
110C22⋊C4×C59—22no—
111C22⋊C4×C59—22no—
112C22⋊Dic59—22no—
113C22⋊Dic59—22no—
114C22⋊Dic59—22no—
115C22⋊Dic59—41no—
116C22⋊Dic59D414yescomplemented
117(C2×D59)⋊C4—22no—
118(C2×D59)⋊C4—22no—
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×C59C2×D412yes—
147C23×C59C2×D412yes—
148C23×C59C2×D412yes—
149C23×C59#4112yes—
150C23×C59C2411yescharacteristic
151C22×D59—28no—
152C22×D59—21no—
153C22×D59—21no—
154C22×D59—21no—
155C22×D59—21no—
156C22×D59—21no—
157C22×D59—21no—
158C22×D59—21no—
159C22×D59—21no—
160C22×D59—21no—
161C22×D59—21no—
162C22×D59—21no—
163C22×D59—21no—
164C22×D59—44no—
165C22×D59—44no—
166C22×D59—44no—
167C22×D59—44no—
168C22×D59—44no—
169C22×D59—44no—
170C22×D59C2×D412yes—
171C22×D59#4112yes—
172D4×C59—28no—
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—21no—
185C2×C4×C59—44no—
186C2×C4×C59C2×D412yes—
187C2×C4×C59C2×D412yes—
188C22⋊D59—44no—
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—44no—
208C2×Dic59—44no—
209C2×Dic59C2×D412yes—
210C2×Dic59C2×D412yes—
211C2×Dic59C2×D412yes—
212C22×C59—22no—
213C22×C59—22no—
214C22×C59—22no—
215C22×C59—22no—
216C22×C59—22no—
217C22×C59—22no—
218C22×C59—22no—
219C22×C59—22no—
220C22×C59—22no—
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#12114yescomplemented
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—416no—
247C2×D59—41no—
248C2×D59—41no—
249C2×D59—41no—
250C2×D59—41no—
251C2×D59—41no—
252C2×D59—41no—
253C2×D59—41no—
254C2×D59—41no—
255C4×C59—22no—
256C4×C59—22no—
257C4×C59—41no—
258C4×C59—41no—
259Dic59—22no—
260Dic59—22no—
261Dic59—22no—
262Dic59—41no—
263Dic59—41no—
264Dic59—41no—
265#2424—591nomaximal, Sylow
266C2×C59—24no—
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—42no—
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
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, complemented
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—22no—
354C2×D4—41no—
355C2×D4—1182no—
356C2×D4—1182no—
357C2×D4—1182no—
358C2×D4—1182no—
359C2×D4—1182no—
360C2×D4—1182no—
361C2×D4—1182no—
362C2×D4—1182no—
363C2×D4—2361no—
364C2×D4—2361no—
365C2×D4—2361no—
366C2×D4—2361no—
367C2×D4C22⋊D5914yescomplemented
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—22no—
393C22⋊C4—594no—
394C22⋊C4—594no—
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—1182no—
405C22⋊C4—2361no—
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—592no—
425C23—592no—
426C23—1188no—
427C23—1181no—
428C23—1181no—
429C23—1181no—
430C23—1181no—
431C23—1181no—
432C23—1181no—
433C23—1181no—
434C23—1181no—
435C23—1181no—
436C23—1181no—
437C23—1181no—
438C23—1181no—
439C23—2364no—
440C23—2364no—
441C23—2364no—
442C23—2364no—
443C23—2364no—
444C23—2364no—
445C23D4×D5912yes—
446C23#1174568712yes—
447C23C2×C22⋊D5912yes—
448C23C2×C22⋊D5912yes—
449C23C23×D5911yescharacteristic
450D4—28no—
451D4—44no—
452D4—44no—
453D4—2364no—
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—21no—
467C2×C4—44no—
468C2×C4—592no—
469C2×C4—592no—
470C2×C4—592no—
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—1181no—
486C2×C4—2364no—
487C2×C4—2364no—
488C2×C4D4×D5912yes—
489C2×C4C2×C22⋊D5912yes—
490C22—22no—
491C22—22no—
492C22—22no—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—22no—
497C22—22no—
498C22—22no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—41no—
503C22—41no—
504C22—41no—
505C22—41no—
506C22—41no—
507C22—41no—
508C22—41no—
509C22—41no—
510C22—1182no—
511C22—1182no—
512C22—1182no—
513C22—1182no—
514C22—1182no—
515C22—1182no—
516C22—23616no—
517C22—2361no—
518C22—2361no—
519C22—2361no—
520C22—2361no—
521C22—2361no—
522C22—2361no—
523C22—2361no—
524C22—2361no—
525C22#1427369914yescomplemented
526C22C2×D4×D5911yescharacteristic
527C22C2×D4×D5911yescharacteristic
528C22C22×C22⋊D5911yescharacteristic
529C22#41×D5911yescharacteristic
530C22C2×#1174568711yescharacteristic
531C22#1427377211yescharacteristic
532C22#1427377311yescharacteristic
533C4—22no—
534C4—22no—
535C4—41no—
536C4—41no—
537C4—1182no—
538C4—1182no—
539C4—1182no—
540C4—2361no—
541C4—2361no—
542C4—2361no—
543C2—24no—
544C2—42no—
545C2—81no—
546C2—2362no—
547C2—2362no—
548C2C2×#1427369911yescharacteristic
549C2#1683791211yescharacteristic
550C2#1683798911yescharacteristic
551C2D4×C22⋊D5911yescharacteristic
552C2#1683803611yescharacteristic
553C2#1683804011yescharacteristic
554C2#1683804111yescharacteristic
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×#14273699C2semidirect
2. C2×#14273695C2semidirect
3. C2×#14273695C2semidirect
4. C2×D4×Dic59C2semidirect
5. C22×(C2×D59)⋊C4C2semidirect
6. #16837324C2semidirect
7. #16837318C2semidirect
8. #16837317C2semidirect
9. #16837310C2semidirect
10. #16837302C2semidirect
11. #16837292C2semidirect
12. #16837282C2semidirect
13. #16837279C2semidirect
14. #16837275C2semidirect
15. C2×#121×C59C2semidirect
22. C23×Dic59C22semidirect
27. C2×C4⋊Dic59C22semidirect
28. C2×Dic59⋊C4C22semidirect
29. C2×Dic59⋊C4C22semidirect
32. C2×C22⋊Dic59C22semidirect
33. C2×C22⋊Dic59C22semidirect
34. C2×C22⋊Dic59C22semidirect
44. C2×C4×Dic59C22semidirect
45. C59⋊#95C22semidirect
46. C59⋊#95C22semidirect
47. C59⋊#95C22semidirect
48. C59⋊#95C22semidirect
51. C22×D4×C59C22semidirect
54. C2×C4⋊C4×C59C22semidirect
55. C2×C22⋊C4×C59C22semidirect
56. C2×C22⋊C4×C59C22semidirect
77. C2×D4×C59D4semidirect
116. C22⋊Dic59D4semidirect
124. (C2×D59)⋊C4D4semidirect
232. C22×C59#121semidirect
279. C2×#121D59semidirect
293. C59#2424semidirect
301. C22×D4C2×D59semidirect
313. C2×C4⋊C4C2×D59semidirect
328. C2×C22⋊C4C2×D59semidirect
329. C2×C22⋊C4C2×D59semidirect
367. C2×D4C22⋊D59semidirect
525. C22#14273699semidirect