Finite Group Databasebeta

← #21427632

Subgroups — #21427632

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×#14273701C211yesmaximal, characteristic, complemented
2C2×#14273700C211yesmaximal, characteristic, complemented
3C2×#14273696C211yesmaximal, characteristic, complemented
4C2×#14273696C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊D59C211yesmaximal, characteristic, complemented
6#16837325C211yesmaximal, characteristic, complemented
7#16837317C211yesmaximal, characteristic, complemented
8#16837317C211yesmaximal, characteristic, complemented
9#16837311C211yesmaximal, characteristic, complemented
10#16837302C211yesmaximal, characteristic, complemented
11#16837295C211yesmaximal, characteristic, complemented
12#16837281C211yesmaximal, characteristic, complemented
13#16837278C211yesmaximal, characteristic, complemented
14#16837275C211yesmaximal, characteristic, complemented
15C22×C22⋊C4×C59C211yesmaximal, characteristic, complemented
16C22×D236C2211yescharacteristic, complemented
17C22×C22⋊D59C2211yescharacteristic
18C22×C22⋊D59C2211yescharacteristic
19C22×C22⋊D59C2211yescharacteristic
20C22×C22⋊D59C2211yescharacteristic
21C22×C22⋊D59C2211yescharacteristic
22C22×C22⋊D59C2211yescharacteristic
23C22×C4×D59C2211yescharacteristic, complemented
24#14273701—24no—
25#14273700—24no—
26#14273696—24no—
27#14273696—24no—
28C4×C22⋊D59—24no—
29C2×C4⋊Dic59C2211yescharacteristic, complemented
30C2×Dic59⋊C4C2211yescharacteristic, complemented
31C2×Dic59⋊C4C2211yescharacteristic, complemented
32C2×Dic59⋊C4C2211yescharacteristic, complemented
33C2×C22⋊Dic59C2211yescharacteristic
34C2×C22⋊Dic59C2211yescharacteristic
35C2×C22⋊Dic59C2211yescharacteristic
36C2×C22⋊Dic59C2211yescharacteristic
37C2×C22⋊Dic59C2211yescharacteristic
38C2×C22⋊Dic59C2211yescharacteristic
39C2×(C2×D59)⋊C4C2211yescharacteristic, complemented
40C2×(C2×D59)⋊C4C2211yescharacteristic, complemented
41C2×(C2×D59)⋊C4C2211yescharacteristic, complemented
42C2×(C2×D59)⋊C4C2211yescharacteristic, complemented
43C2×(C2×D59)⋊C4C2211yescharacteristic, complemented
44C2×C4×Dic59C2211yescharacteristic, complemented
45C59⋊#95C2211yescharacteristic, complemented
46C59⋊#95C2211yescharacteristic, complemented
47C59⋊#95C2211yescharacteristic, complemented
48C59⋊#95C2211yescharacteristic, complemented
49C25×C59C2211yescharacteristic
50C23×C4×C59C2211yescharacteristic
51C23×C4×C59C2211yescharacteristic
52C2×C22⋊C4×C59—24no—
53C2×C22⋊C4×C59C2211yescharacteristic
54C2×C22⋊C4×C59C2211yescharacteristic
55C2×C22⋊C4×C59C2211yescharacteristic
56C2×C22⋊C4×C59C2211yescharacteristic
57C24×C59—22no—
58C24×C59—22no—
59C24×C59—22no—
60C24×C59—22no—
61C24×C59—22no—
62C24×C59—41no—
63C24×C59—41no—
64C24×C59C2311yescharacteristic
65C24×C59C2311yescharacteristic
66C24×C59C2311yescharacteristic
67C23×D59C2311yescharacteristic
68C23×D59C2311yescharacteristic
69C22×C4×C59—22no—
70C22×C4×C59—22no—
71C22×C4×C59—22no—
72C22×C4×C59—22no—
73C22×C4×C59—41no—
74C22×C4×C59—41no—
75C22×C4×C59C2311yescharacteristic
76C22×C4×C59C2311yescharacteristic
77C22×C4×C59C2311yescharacteristic
78C22×C4×C59C2311yescharacteristic
79C2×C22⋊D59—22no—
80C2×C22⋊D59—22no—
81C2×C22⋊D59—22no—
82C2×C22⋊D59—22no—
83C2×C22⋊D59—22no—
84C2×C22⋊D59—22no—
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—41no—
93C2×C22⋊D59—41no—
94C2×C22⋊D59—41no—
95C2×C22⋊D59—41no—
96C2×C22⋊D59D414yescomplemented
97C22×Dic59C2311yescharacteristic
98C22×Dic59C2311yescharacteristic
99C22×Dic59C2311yescharacteristic
100C22×Dic59C2311yescharacteristic
101C22×Dic59C2311yescharacteristic
102C22×Dic59C2311yescharacteristic
103C2×D236—22no—
104C2×D236—22no—
105C2×D236—41no—
106C2×C4×D59—22no—
107C2×C4×D59—22no—
108C2×C4×D59—41no—
109C22⋊C4×C59—22no—
110C22⋊C4×C59—22no—
111C22⋊C4×C59—22no—
112C22⋊C4×C59D414yescomplemented
113C22⋊Dic59—22no—
114C22⋊Dic59—22no—
115C22⋊Dic59—22no—
116C22⋊Dic59—22no—
117C22⋊Dic59—22no—
118C22⋊Dic59D414yescomplemented
119(C2×D59)⋊C4—22no—
120(C2×D59)⋊C4—22no—
121(C2×D59)⋊C4—22no—
122(C2×D59)⋊C4—22no—
123(C2×D59)⋊C4—41no—
124C4⋊Dic59—22no—
125Dic59⋊C4—22no—
126Dic59⋊C4—22no—
127Dic59⋊C4—41no—
128C4×Dic59—22no—
129C23×C59—21no—
130C23×C59—21no—
131C23×C59—21no—
132C23×C59—21no—
133C23×C59—28no—
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—44no—
147C23×C59—44no—
148C23×C59—44no—
149C23×C59—44no—
150C23×C59—44no—
151C23×C59—44no—
152C23×C59C2×D412yes—
153C23×C59C2×D412yes—
154C23×C59C2×D412yes—
155C23×C59#4112yes—
156C23×C59#4112yes—
157C23×C59C2411yescharacteristic
158C22×D59—21no—
159C22×D59—21no—
160C22×D59—21no—
161C22×D59—21no—
162C22×D59—21no—
163C22×D59—21no—
164C22×D59—21no—
165C22×D59—21no—
166C22×D59—21no—
167C22×D59—21no—
168C22×D59—21no—
169C22×D59—21no—
170C22×D59—21no—
171C22×D59C2×D412yes—
172C2×C4×C59—21no—
173C2×C4×C59—21no—
174C2×C4×C59—21no—
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—44no—
183C2×C4×C59—44no—
184C2×C4×C59C2×D412yes—
185C2×C4×C59C2×D412yes—
186C22⋊D59—28no—
187C22⋊D59—44no—
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×Dic59C2×D412yes—
208C2×Dic59C2×D412yes—
209C2×Dic59C2×D412yes—
210D236—44no—
211C4×D59—44no—
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—22no—
222C22×C59—22no—
223C22×C59—22no—
224C22×C59—416no—
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×C59#12114yescomplemented
234C22×C59C22×D411yescharacteristic
235C22×C59C22×D411yescharacteristic
236C22×C59C22×D411yescharacteristic
237C22×C59C2×#4111yescharacteristic
238C22×C59C2×#4111yescharacteristic
239C22×C59H(5,𝔽2)11yescharacteristic
240C22×C59H(5,𝔽2)11yescharacteristic
241C2×D59—22no—
242C2×D59—22no—
243C2×D59—22no—
244C2×D59—41no—
245C2×D59—41no—
246C2×D59—41no—
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—42no—
269C2×C59C2×#12111yescharacteristic
270C2×C59#52511yescharacteristic
271C2×C59#53811yescharacteristic
272C2×C59D4211yescharacteristic
273C2×C59D4211yescharacteristic
274C2×C59#54611yescharacteristic
275C2×C59#54611yescharacteristic
276D59—42no—
277D59—81no—
278C2×#121—591no—
279C2×#121—591no—
280C2×#120—591no—
281C2×#120—591no—
282C2×C4×D4—591no—
283C22×C22⋊C4D5911yescharacteristic, complemented
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
294C25C2×D5911yescharacteristic
295C22×D4—591no—
296C22×D4—591no—
297C22×D4—591no—
298C22×D4—591no—
299C22×D4—591no—
300C22×D4—591no—
301C22×D4—591no—
302C23×C4—591no—
303C23×C4C2×D5911yescharacteristic
304C23×C4C2×D5911yescharacteristic
305#121—1184no—
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⋊C4—591no—
314C2×C22⋊C4—24no—
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⋊C4C2×D5911yescharacteristic
327C2×C22⋊C4C2×D5911yescharacteristic
328C2×C22⋊C4C2×D5911yescharacteristic
329C2×C22⋊C4C2×D5911yescharacteristic
330C2×C42—591no—
331#95—591no—
332#95—591no—
333#95—591no—
334#95—591no—
335C24—22no—
336C24—22no—
337C24—22no—
338C24—22no—
339C24—22no—
340C24—41no—
341C24—41no—
342C24—591no—
343C24—591no—
344C24C22×D5911yescharacteristic
345C24C22×D5911yescharacteristic
346C24C22×D5911yescharacteristic
347C2×D4—594no—
348C2×D4—1182no—
349C2×D4—1182no—
350C2×D4—1182no—
351C2×D4—1182no—
352C2×D4—1182no—
353C2×D4—1182no—
354C2×D4—1182no—
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×D4—2361no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—41no—
373C22×C4—41no—
374C22×C4—591no—
375C22×C4—591no—
376C22×C4—591no—
377C22×C4—591no—
378C22×C4—591no—
379C22×C4—591no—
380C22×C4—1182no—
381C22×C4—1182no—
382C22×C4—2361no—
383C22×C4C22×D5911yescharacteristic
384C22×C4C22×D5911yescharacteristic
385C22×C4C22×D5911yescharacteristic
386C22×C4C22×D5911yescharacteristic
387C4⋊C4—1182no—
388C4⋊C4—1182no—
389C4⋊C4—1182no—
390C4⋊C4—2361no—
391C22⋊C4—22no—
392C22⋊C4—22no—
393C22⋊C4—22no—
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—2361no—
405C22⋊C4C22⋊D5914yescomplemented
406C42—1182no—
407C23—21no—
408C23—21no—
409C23—21no—
410C23—21no—
411C23—28no—
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—44no—
425C23—44no—
426C23—44no—
427C23—44no—
428C23—44no—
429C23—44no—
430C23—592no—
431C23—1181no—
432C23—1181no—
433C23—1181no—
434C23—1181no—
435C23—1181no—
436C23—1181no—
437C23—1181no—
438C23—1181no—
439C23—1181no—
440C23—1181no—
441C23—1181no—
442C23—1181no—
443C23—1181no—
444C23#1174568512yes—
445C23#1174568512yes—
446C23D4×D5912yes—
447C23D4×D5912yes—
448C23C2×C22⋊D5912yes—
449C23C23×D5911yescharacteristic
450D4—1188no—
451D4—2364no—
452D4—2364no—
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—44no—
469C2×C4—592no—
470C2×C4—592no—
471C2×C4—592no—
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—1181no—
487C2×C4—2364no—
488C2×C4C2×C22⋊D5912yes—
489C2×C4C2×C22⋊D5912yes—
490C22—22no—
491C22—22no—
492C22—22no—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—22no—
497C22—22no—
498C22—22no—
499C22—22no—
500C22—22no—
501C22—22no—
502C22—416no—
503C22—41no—
504C22—41no—
505C22—41no—
506C22—41no—
507C22—41no—
508C22—41no—
509C22—41no—
510C22—41no—
511C22—1182no—
512C22—1182no—
513C22—1182no—
514C22—2361no—
515C22—2361no—
516C22—2361no—
517C22—2361no—
518C22—2361no—
519C22—2361no—
520C22—2361no—
521C22—2361no—
522C22—2361no—
523C22—2361no—
524C22—2361no—
525C22#1427370014yescomplemented
526C22C2×D4×D5911yescharacteristic
527C22C2×D4×D5911yescharacteristic
528C22C22×C22⋊D5911yescharacteristic
529C22C2×#1174568511yescharacteristic
530C22C2×#1174568511yescharacteristic
531C22#1427377211yescharacteristic
532C22#1427377211yescharacteristic
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—42no—
546C2—4721no—
547C2—2362no—
548C2C2×#1427370011yescharacteristic
549C2#1683791311yescharacteristic
550C2#1683799011yescharacteristic
551C2D4×C22⋊D5911yescharacteristic
552C2D4×C22⋊D5911yescharacteristic
553C2#1683804211yescharacteristic
554C2#1683804211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC22×C22⋊C4×C59C2
hypercenterC22×C22⋊C4D59
hypocenterC59#2424
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#14273701C2semidirect
2. C2×#14273700C2semidirect
3. C2×#14273696C2semidirect
4. C2×#14273696C2semidirect
5. C2×C4×C22⋊D59C2semidirect
6. #16837325C2semidirect
7. #16837317C2semidirect
8. #16837317C2semidirect
9. #16837311C2semidirect
10. #16837302C2semidirect
11. #16837295C2semidirect
12. #16837281C2semidirect
13. #16837278C2semidirect
14. #16837275C2semidirect
15. C22×C22⋊C4×C59C2semidirect
16. C22×D236C22semidirect
23. C22×C4×D59C22semidirect
29. C2×C4⋊Dic59C22semidirect
30. C2×Dic59⋊C4C22semidirect
31. C2×Dic59⋊C4C22semidirect
32. C2×Dic59⋊C4C22semidirect
39. C2×(C2×D59)⋊C4C22semidirect
40. C2×(C2×D59)⋊C4C22semidirect
41. C2×(C2×D59)⋊C4C22semidirect
42. C2×(C2×D59)⋊C4C22semidirect
43. C2×(C2×D59)⋊C4C22semidirect
44. C2×C4×Dic59C22semidirect
45. C59⋊#95C22semidirect
46. C59⋊#95C22semidirect
47. C59⋊#95C22semidirect
48. C59⋊#95C22semidirect
96. C2×C22⋊D59D4semidirect
112. C22⋊C4×C59D4semidirect
118. C22⋊Dic59D4semidirect
233. C22×C59#121semidirect
283. C22×C22⋊C4D59semidirect
293. C59#2424semidirect
405. C22⋊C4C22⋊D59semidirect
525. C22#14273700semidirect