Finite Group Databasebeta

← #21427418

Subgroups — #21427418

Order 7552.

1116 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×D59C211yesmaximal, characteristic
2C2×#14273712C211yesmaximal, characteristic, complemented
3C2×#14273709C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×D59C211yesmaximal, characteristic, complemented
5#16837318C211yesmaximal, characteristic, complemented
6#16837317C211yesmaximal, characteristic, complemented
7#16837316C211yesmaximal, characteristic, complemented
8#16837280C211yesmaximal, characteristic, complemented
9#16837278C211yesmaximal, characteristic, complemented
10#16837276C211yesmaximal, characteristic, complemented
11#16837273C211yesmaximal, characteristic, complemented
12#16837257C211yesmaximal, characteristic, complemented
13#16837257C211yesmaximal, characteristic, complemented
14#16837257C211yesmaximal, characteristic, complemented
15C59×#394C211yesmaximal, characteristic, complemented
16C24×D59C2211yescharacteristic
17C24×D59C2211yescharacteristic
18C22×D236C2211yescharacteristic
19C22×C22⋊D59C2211yescharacteristic
20C22×C22⋊D59C2211yescharacteristic
21C2×D4×D59—24no—
22C2×D4×D59—24no—
23C2×D4×D59—24no—
24C22×C4×D59C2211yescharacteristic
25C22×C4×D59C2211yescharacteristic, complemented
26C22×C4×D59C2211yescharacteristic, complemented
27#14273712—24no—
28#14273709—24no—
29C2×C4⋊Dic59C2211yescharacteristic, complemented
30C2×Dic59⋊C4C2211yescharacteristic, complemented
31C2×Dic59⋊C4C2211yescharacteristic, complemented
32C2×C22⋊Dic59C2211yescharacteristic, complemented
33C2×C22⋊Dic59C2211yescharacteristic, complemented
34C2×C22⋊Dic59C2211yescharacteristic, complemented
35C2×C22⋊Dic59C2211yescharacteristic, complemented
36C2×(C2×D59)⋊C4C2211yescharacteristic
37C2×(C2×D59)⋊C4C2211yescharacteristic
38C2×(C2×D59)⋊C4C2211yescharacteristic
39C2×(C2×D59)⋊C4C2211yescharacteristic
40C2×(C2×D59)⋊C4C2211yescharacteristic, complemented
41C2×(C2×D59)⋊C4C2211yescharacteristic, complemented
42C2×(C2×D59)⋊C4C2211yescharacteristic, complemented
43C2×(C2×D59)⋊C4C2211yescharacteristic, complemented
44C2×(C2×D59)⋊C4C2211yescharacteristic, complemented
45C2×(C2×D59)⋊C4C2211yescharacteristic, complemented
46C22⋊C4×D59—24no—
47C59⋊#95C2211yescharacteristic, complemented
48C59⋊#95C2211yescharacteristic, complemented
49C59⋊#95C2211yescharacteristic, complemented
50C22×D4×C59C2211yescharacteristic
51C2×C4⋊C4×C59C2211yescharacteristic, complemented
52C2×C22⋊C4×C59C2211yescharacteristic, complemented
53C2×C22⋊C4×C59C2211yescharacteristic, complemented
54C2×C22⋊C4×C59C2211yescharacteristic, complemented
55C2×C22⋊C4×C59C2211yescharacteristic, complemented
56#95×C59C2211yescharacteristic, complemented
57C24×C59C2311yescharacteristic
58C24×C59C2311yescharacteristic
59C23×D59—22no—
60C23×D59—22no—
61C23×D59—22no—
62C23×D59—22no—
63C23×D59—22no—
64C23×D59—22no—
65C23×D59—22no—
66C23×D59—22no—
67C23×D59—22no—
68C23×D59—41no—
69C23×D59—41no—
70C23×D59—41no—
71C23×D59—41no—
72C23×D59D414yes—
73C23×D59C2311yescharacteristic
74C23×D59C2311yescharacteristic
75C23×D59C2311yescharacteristic
76C2×D4×C59—22no—
77C2×D4×C59—22no—
78C2×D4×C59—22no—
79C22×C4×C59C2311yescharacteristic
80C22×C4×C59C2311yescharacteristic
81C22×C4×C59C2311yescharacteristic
82C22×C4×C59C2311yescharacteristic
83C22×C4×C59C2311yescharacteristic
84C2×C22⋊D59—22no—
85C2×C22⋊D59—22no—
86C2×C22⋊D59—22no—
87C2×C22⋊D59—22no—
88C2×C22⋊D59—22no—
89C2×C22⋊D59D414yes—
90C22×Dic59C2311yescharacteristic
91C22×Dic59C2311yescharacteristic
92C22×Dic59C2311yescharacteristic
93C22×Dic59C2311yescharacteristic
94C22×Dic59C2311yescharacteristic
95D4×D59—232no—
96C2×D236—22no—
97C2×D236—22no—
98C2×D236D414yes—
99C2×C4×D59—22no—
100C2×C4×D59—22no—
101C2×C4×D59—22no—
102C2×C4×D59—22no—
103C2×C4×D59—22no—
104C2×C4×D59—22no—
105C2×C4×D59—22no—
106C2×C4×D59—41no—
107C2×C4×D59—41no—
108C4⋊C4×C59—22no—
109C22⋊C4×C59—22no—
110C22⋊C4×C59—22no—
111C22⋊C4×C59—41no—
112C22⋊C4×C59—41no—
113C22⋊Dic59—22no—
114C22⋊Dic59—22no—
115C22⋊Dic59—41no—
116C22⋊Dic59—41no—
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)⋊C4—22no—
125(C2×D59)⋊C4—41no—
126(C2×D59)⋊C4—41no—
127C4⋊Dic59—22no—
128Dic59⋊C4—22no—
129Dic59⋊C4—22no—
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×C59C2×D412yes—
143C23×C59C2×D412yes—
144C23×C59C2411yescharacteristic
145C22×D59—21no—
146C22×D59—21no—
147C22×D59—21no—
148C22×D59—21no—
149C22×D59—21no—
150C22×D59—21no—
151C22×D59—21no—
152C22×D59—21no—
153C22×D59—28no—
154C22×D59—21no—
155C22×D59—21no—
156C22×D59—21no—
157C22×D59—21no—
158C22×D59—21no—
159C22×D59—21no—
160C22×D59—28no—
161C22×D59—28no—
162C22×D59—44no—
163C22×D59—44no—
164C22×D59—44no—
165C22×D59—44no—
166C22×D59—44no—
167C22×D59—44no—
168C22×D59—44no—
169C22×D59—44no—
170C22×D59—44no—
171C22×D59—44no—
172C22×D59—44no—
173C22×D59C2×D412yes—
174C22×D59C2×D412yes—
175C22×D59C2×D412yes—
176C22×D59C2×D412yes—
177C22×D59C2×D412yes—
178C22×D59#4112yes—
179C22×D59#4112yes—
180D4×C59—28no—
181C2×C4×C59—21no—
182C2×C4×C59—21no—
183C2×C4×C59—21no—
184C2×C4×C59—21no—
185C2×C4×C59—21no—
186C2×C4×C59—21no—
187C2×C4×C59—21no—
188C2×C4×C59—21no—
189C2×C4×C59—21no—
190C2×C4×C59—21no—
191C2×C4×C59—21no—
192C2×C4×C59—21no—
193C2×C4×C59—21no—
194C2×C4×C59—21no—
195C2×C4×C59C2×D412yes—
196C22⋊D59—28no—
197C22⋊D59—28no—
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×Dic59—21no—
209C2×Dic59—21no—
210C2×Dic59—21no—
211C2×Dic59—21no—
212C2×Dic59C2×D412yes—
213D236—28no—
214C4×D59—28no—
215C4×D59—44no—
216C4×D59—44no—
217C22×C59—22no—
218C22×C59—22no—
219C22×C59—22no—
220C22×C59—22no—
221C22×C59—22no—
222C22×C59—22no—
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×C59C22×D411yescharacteristic
232C22×C59C22×D411yescharacteristic
233C22×C59C22×D411yescharacteristic
234C22×C59C2×#4111yescharacteristic
235C22×C59C2×#4111yescharacteristic
236C22×C59H(5,𝔽2)11yescharacteristic
237C22×C59H(5,𝔽2)11yescharacteristic
238C2×D59—22no—
239C2×D59—22no—
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—22no—
250C2×D59—22no—
251C2×D59—22no—
252C2×D59—22no—
253C2×D59—416no—
254C2×D59—416no—
255C2×D59—41no—
256C2×D59—41no—
257C2×D59—41no—
258C2×D59—41no—
259C2×D59#12014yes—
260C2×D59#12314yescomplemented
261C4×C59—22no—
262C4×C59—41no—
263C4×C59—41no—
264C4×C59—41no—
265C4×C59—41no—
266Dic59—22no—
267Dic59—41no—
268Dic59—41no—
269Dic59—41no—
270Dic59—41no—
271#2405—591nomaximal, Sylow
272C2×C59—42no—
273C2×C59—42no—
274C2×C59C2×#12011yescharacteristic
275C2×C59C2×#12311yescharacteristic
276C2×C59#53411yescharacteristic
277C2×C59#54611yescharacteristic
278C2×C59#54611yescharacteristic
279C2×C59#54611yescharacteristic
280C2×C59#54611yescharacteristic
281D59—24no—
282D59—24no—
283D59—42no—
284C23×D4—591no—
285C2×#123—591no—
286C2×#123—591no—
287C22×C22⋊C4—591no—
288#394—591no—
289#394—591no—
290#394—591no—
291#394D5911yescharacteristic, complemented
292#386—591no—
293#386—591no—
294#385—591no—
295#385—591no—
296#379—591no—
297#379—591no—
298#379—591no—
299C59#240511yescharacteristic, complemented, Sylow
300C25—591no—
301C25—591no—
302C22×D4—591no—
303C22×D4—591no—
304C22×D4—591no—
305C22×D4—1184no—
306C22×D4—1184no—
307C22×D4—1184no—
308C22×D4C2×D5911yescharacteristic
309C23×C4—591no—
310C23×C4—591no—
311C23×C4—591no—
312#123—1184no—
313#123—1184no—
314C2×C4⋊C4—591no—
315C2×C4⋊C4—591no—
316C2×C4⋊C4—591no—
317C2×C4⋊C4C2×D5911yescharacteristic, complemented
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—591no—
328C2×C22⋊C4—591no—
329C2×C22⋊C4—591no—
330C2×C22⋊C4—591no—
331C2×C22⋊C4—591no—
332C2×C22⋊C4—1184no—
333C2×C22⋊C4C2×D5911yescharacteristic, complemented
334C2×C22⋊C4C2×D5911yescharacteristic, complemented
335C2×C22⋊C4C2×D5911yescharacteristic, complemented
336C2×C22⋊C4C2×D5911yescharacteristic, complemented
337#95—591no—
338#95—591no—
339#95—591no—
340#95C2×D5911yescharacteristic, complemented
341C24—591no—
342C24—591no—
343C24—591no—
344C24—594no—
345C24—1182no—
346C24—1182no—
347C24—1182no—
348C24—1182no—
349C24—1182no—
350C24—1182no—
351C24—1182no—
352C24—1182no—
353C24—1182no—
354C24—2361no—
355C24—2361no—
356C24—2361no—
357C24—2361no—
358C24C22×D5911yescharacteristic
359C24C22×D5911yescharacteristic
360C2×D4—22no—
361C2×D4—22no—
362C2×D4—22no—
363C2×D4—594no—
364C2×D4—594no—
365C2×D4—1182no—
366C2×D4—1182no—
367C2×D4—1182no—
368C2×D4—11832no—
369C2×D4—1182no—
370C2×D4—1182no—
371C2×D4—1182no—
372C2×D4—1182no—
373C22×C4—591no—
374C22×C4—591no—
375C22×C4—591no—
376C22×C4—591no—
377C22×C4—591no—
378C22×C4—1182no—
379C22×C4—1182no—
380C22×C4—1182no—
381C22×C4—1182no—
382C22×C4—1182no—
383C22×C4—1182no—
384C22×C4—1182no—
385C22×C4—2361no—
386C22×C4—2361no—
387C22×C4C22×D5911yescharacteristic
388C22×C4C22×D5911yescharacteristic
389C22×C4C22×D5911yescharacteristic
390C22×C4C22×D5911yescharacteristic
391C22×C4C22×D5911yescharacteristic
392C4⋊C4—22no—
393C4⋊C4—1182no—
394C4⋊C4—1182no—
395C4⋊C4—1182no—
396C22⋊C4—22no—
397C22⋊C4—22no—
398C22⋊C4—41no—
399C22⋊C4—41no—
400C22⋊C4—1182no—
401C22⋊C4—1182no—
402C22⋊C4—1182no—
403C22⋊C4—1182no—
404C22⋊C4—1182no—
405C22⋊C4—1182no—
406C22⋊C4—1182no—
407C22⋊C4—1182no—
408C22⋊C4—1182no—
409C22⋊C4—1182no—
410C22⋊C4—2361no—
411C22⋊C4—2361no—
412C22⋊C4—2361no—
413C22⋊C4—2361no—
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—592no—
431C23—592no—
432C23—592no—
433C23—1188no—
434C23—1188no—
435C23—1188no—
436C23—1181no—
437C23—1181no—
438C23—1181no—
439C23—1181no—
440C23—1181no—
441C23—1181no—
442C23—1181no—
443C23—1181no—
444C23—1181no—
445C23—1181no—
446C23—1181no—
447C23—1181no—
448C23—1181no—
449C23—1181no—
450C23—2364no—
451C23—2364no—
452C23—2364no—
453C23—2364no—
454C23—2364no—
455C23—2364no—
456C23—2364no—
457C23—2364no—
458C23—2364no—
459C23—2364no—
460C23—2364no—
461C23D4×D5912yes—
462C23D4×D5912yes—
463C23C23×D5911yescharacteristic
464D4—28no—
465D4—1188no—
466D4—1188no—
467D4—1188no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—592no—
483C2×C4—1188no—
484C2×C4—1181no—
485C2×C4—1181no—
486C2×C4—1181no—
487C2×C4—1181no—
488C2×C4—1181no—
489C2×C4—1181no—
490C2×C4—1181no—
491C2×C4—1181no—
492C2×C4—1181no—
493C2×C4—1181no—
494C2×C4—1181no—
495C2×C4—1181no—
496C2×C4—1181no—
497C2×C4—1181no—
498C2×C4—2364no—
499C2×C4—2364no—
500C2×C4D4×D5912yes—
501C22—22no—
502C22—22no—
503C22—22no—
504C22—22no—
505C22—22no—
506C22—22no—
507C22—41no—
508C22—41no—
509C22—41no—
510C22—41no—
511C22—41no—
512C22—41no—
513C22—41no—
514C22—41no—
515C22—594no—
516C22—594no—
517C22—1182no—
518C22—1182no—
519C22—1182no—
520C22—1182no—
521C22—1182no—
522C22—1182no—
523C22—1182no—
524C22—1182no—
525C22—1182no—
526C22—1182no—
527C22—1182no—
528C22—1182no—
529C22—1182no—
530C22—1182no—
531C22—1182no—
532C22—23616no—
533C22—23616no—
534C22—2361no—
535C22—2361no—
536C22—2361no—
537C22—2361no—
538C22C2×D4×D5911yescharacteristic
539C22C2×D4×D5911yescharacteristic
540C22C2×D4×D5911yescharacteristic
541C22#41×D5911yescharacteristic
542C22#41×D5911yescharacteristic
543C22#1427377211yescharacteristic
544C22#1427377311yescharacteristic
545C4—22no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—1182no—
551C4—2361no—
552C4—2361no—
553C4—2361no—
554C4—2361no—
555C2—42no—
556C2—42no—
557C2—1184no—
558C2—1184no—
559C2—2362no—
560C2#120×D5911yescharacteristic
561C2#123×D5911yescharacteristic
562C2#1683796011yescharacteristic
563C2#1683804111yescharacteristic
564C2#1683804411yescharacteristic
565C2#1683804511yescharacteristic
566C2#1683804911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#394C2
hypercenter#394D59
hypocenterC59#2405
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×#14273712C2semidirect
3. C2×#14273709C2semidirect
4. C2×C22⋊C4×D59C2semidirect
5. #16837318C2semidirect
6. #16837317C2semidirect
7. #16837316C2semidirect
8. #16837280C2semidirect
9. #16837278C2semidirect
10. #16837276C2semidirect
11. #16837273C2semidirect
12. #16837257C2semidirect
13. #16837257C2semidirect
14. #16837257C2semidirect
15. C59×#394C2semidirect
25. C22×C4×D59C22semidirect
26. C22×C4×D59C22semidirect
29. C2×C4⋊Dic59C22semidirect
30. C2×Dic59⋊C4C22semidirect
31. C2×Dic59⋊C4C22semidirect
32. C2×C22⋊Dic59C22semidirect
33. C2×C22⋊Dic59C22semidirect
34. C2×C22⋊Dic59C22semidirect
35. C2×C22⋊Dic59C22semidirect
40. C2×(C2×D59)⋊C4C22semidirect
41. C2×(C2×D59)⋊C4C22semidirect
42. C2×(C2×D59)⋊C4C22semidirect
43. C2×(C2×D59)⋊C4C22semidirect
44. C2×(C2×D59)⋊C4C22semidirect
45. C2×(C2×D59)⋊C4C22semidirect
47. C59⋊#95C22semidirect
48. C59⋊#95C22semidirect
49. C59⋊#95C22semidirect
51. C2×C4⋊C4×C59C22semidirect
52. C2×C22⋊C4×C59C22semidirect
53. C2×C22⋊C4×C59C22semidirect
54. C2×C22⋊C4×C59C22semidirect
55. C2×C22⋊C4×C59C22semidirect
56. #95×C59C22semidirect
260. C2×D59#123semidirect
291. #394D59semidirect
299. C59#2405semidirect
317. C2×C4⋊C4C2×D59semidirect
333. C2×C22⋊C4C2×D59semidirect
334. C2×C22⋊C4C2×D59semidirect
335. C2×C22⋊C4C2×D59semidirect
336. C2×C22⋊C4C2×D59semidirect
340. #95C2×D59semidirect