Finite Group Databasebeta

← #28510721

Subgroups — #28510721

Order 15104.

1342 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837267C211yesmaximal, characteristic
2C2×C4⋊C4×Dic59C211yesmaximal, characteristic
3C2×C4×C4⋊Dic59C211yesmaximal, characteristic
4#21422363C212yesmaximal
5#21422356C212yesmaximal
6#21422330C212yesmaximal
7#21422326C211yesmaximal, characteristic
8#21422325C211yesmaximal, characteristic
9#21422325C211yesmaximal, characteristic
10#21422320C212yesmaximal
11C59×C4⋊#95C211yesmaximal, characteristic
12C22×C4⋊Dic59C2211yescharacteristic
13C22×C4⋊Dic59C2211yescharacteristic
14C22×C4⋊Dic59C2211yescharacteristic
15C22×C4⋊Dic59C2211yescharacteristic
16C22×C4×Dic59C2212yes—
17C22×C4×Dic59C2211yescharacteristic
18C22×C4×Dic59C2211yescharacteristic
19#16837267—24no—
20C4⋊C4×Dic59—24no—
21C4×C4⋊Dic59C418yescomplemented
22C2×C59⋊#95C2212yes—
23C2×C59⋊#95C2212yes—
24C2×C59⋊#95C2212yes—
25C2×C59⋊#95C2212yes—
26C2×C59⋊#95C2212yes—
27C2×C59⋊#95C2212yes—
28C2×C59⋊#95C2212yes—
29C2×C59⋊#95C2212yes—
30C2×C59⋊#95C2212yes—
31C2×C59⋊#95C2211yescharacteristic
32C2×C59⋊#95C2211yescharacteristic
33C22×C4⋊C4×C59C2211yescharacteristic
34C22×C4⋊C4×C59C2211yescharacteristic
35C22×C42×C59C2211yescharacteristic
36C2×#95×C59C2212yes—
37C2×#95×C59C2212yes—
38C23×Dic59C2312yes—
39C23×Dic59C2311yescharacteristic
40C23×Dic59C2311yescharacteristic
41C23×Dic59C2311yescharacteristic
42C23×Dic59C2312yes—
43C23×Dic59C2311yescharacteristic
44C2×C4⋊Dic59—22no—
45C2×C4⋊Dic59—22no—
46C2×C4⋊Dic59—22no—
47C2×C4⋊Dic59—22no—
48C2×C4⋊Dic59—22no—
49C2×C4⋊Dic59—22no—
50C2×C4⋊Dic59—22no—
51C2×C4⋊Dic59—22no—
52C2×C4⋊Dic59—22no—
53C2×C4⋊Dic59C2×C414yes—
54C2×C4⋊Dic59C2×C414yes—
55C2×C4⋊Dic59Q814yes—
56C2×C4×Dic59—22no—
57C2×C4×Dic59—22no—
58C2×C4×Dic59—22no—
59C2×C4×Dic59—22no—
60C2×C4×Dic59—24no—
61C2×C4×Dic59—24no—
62C2×C4×Dic59—42no—
63C2×C4×Dic59C2×C414yes—
64C2×C4×Dic59C2×C414yes—
65C59⋊#95—24no—
66C59⋊#95—24no—
67C59⋊#95—24no—
68C59⋊#95—24no—
69C59⋊#95—24no—
70C59⋊#95—42no—
71C59⋊#95—42no—
72C59⋊#95—42no—
73C59⋊#95—42no—
74C59⋊#95C2×C414yes—
75C59⋊#95C2×C414yes—
76C23×C4×C59C2312yes—
77C23×C4×C59C2311yescharacteristic
78C23×C4×C59C2312yes—
79C23×C4×C59C2311yescharacteristic
80C23×C4×C59C2311yescharacteristic
81C2×C4⋊C4×C59—22no—
82C2×C4⋊C4×C59—22no—
83C2×C4⋊C4×C59—22no—
84C2×C4⋊C4×C59—22no—
85C2×C4⋊C4×C59—22no—
86C2×C4⋊C4×C59D414yes—
87C2×C42×C59—22no—
88C2×C42×C59—22no—
89C2×C42×C59C2×C414yes—
90#95×C59—24no—
91#95×C59—42no—
92C24×C59C2411yescharacteristic
93C22×C4×C59—21no—
94C22×C4×C59—21no—
95C22×C4×C59—21no—
96C22×C4×C59—21no—
97C22×C4×C59—22no—
98C22×C4×C59—21no—
99C22×C4×C59—21no—
100C22×C4×C59—22no—
101C22×C4×C59—22no—
102C22×C4×C59—22no—
103C22×C4×C59—21no—
104C22×C4×C59—22no—
105C22×C4×C59—21no—
106C22×C4×C59—21no—
107C22×C4×C59—21no—
108C22×C4×C59—22no—
109C22×C4×C59—22no—
110C22×C4×C59—22no—
111C22×C4×C59—22no—
112C22×C4×C59—22no—
113C22×C4×C59—22no—
114C22×C4×C59—22no—
115C22×C4×C59—22no—
116C22×C4×C59C22×C412yes—
117C22×C4×C59C22×C412yes—
118C22×C4×C59C22×C412yes—
119C22×C4×C59C2×D414yes—
120C22×C4×C59C2×D412yes—
121C22×C4×C59C2×Q812yes—
122C22×C4×C59#4112yes—
123C22×C4×C59#4112yes—
124C22×C4×C59#4112yes—
125C22×C4×C59#4112yes—
126C22×C4×C59#4112yes—
127C22×C4×C59#4112yes—
128C22×Dic59—21no—
129C22×Dic59—21no—
130C22×Dic59—21no—
131C22×Dic59—21no—
132C22×Dic59—21no—
133C22×Dic59—21no—
134C22×Dic59—21no—
135C22×Dic59—22no—
136C22×Dic59—22no—
137C22×Dic59—21no—
138C22×Dic59—21no—
139C22×Dic59—21no—
140C22×Dic59—22no—
141C22×Dic59—21no—
142C22×Dic59—21no—
143C22×Dic59—21no—
144C22×Dic59—21no—
145C22×Dic59—21no—
146C22×Dic59—21no—
147C22×Dic59—22no—
148C22×Dic59—21no—
149C22×Dic59—21no—
150C22×Dic59—21no—
151C22×Dic59—22no—
152C22×Dic59—22no—
153C22×Dic59—21no—
154C22×Dic59—21no—
155C22×Dic59—21no—
156C22×Dic59—22no—
157C22×Dic59—22no—
158C22×Dic59—22no—
159C22×Dic59—22no—
160C22×Dic59—22no—
161C22×Dic59—22no—
162C22×Dic59—22no—
163C22×Dic59C22×C412yes—
164C22×Dic59C22×C412yes—
165C22×Dic59C22×C412yes—
166C22×Dic59C22×C412yes—
167C22×Dic59C2×Q814yes—
168C22×Dic59#4112yes—
169C22×Dic59#4112yes—
170C4⋊C4×C59—28no—
171C4⋊C4×C59—44no—
172C42×C59—28no—
173C4⋊Dic59—28no—
174C4⋊Dic59—28no—
175C4⋊Dic59—28no—
176C4⋊Dic59—44no—
177C4×Dic59—28no—
178C4×Dic59—28no—
179C4×Dic59—48no—
180C23×C59C23×C411yescharacteristic
181C23×C59C22×D411yescharacteristic
182C23×C59C22×Q811yescharacteristic
183C23×C59C2×#4111yescharacteristic
184C23×C59C2×#4111yescharacteristic
185C23×C59C2×#4111yescharacteristic
186C23×C59C2×#4111yescharacteristic
187C23×C59C2×#4111yescharacteristic
188C23×C59C2×#4111yescharacteristic
189C23×C59C2×#4111yescharacteristic
190C23×C59C2×#4111yescharacteristic
191C23×C59H(5,𝔽2)11yescharacteristic
192C23×C59H(5,𝔽2)11yescharacteristic
193C23×C592−1+411yescharacteristic
194C23×C592−1+411yescharacteristic
195C2×C4×C59—22no—
196C2×C4×C59—22no—
197C2×C4×C59—22no—
198C2×C4×C59—22no—
199C2×C4×C59—22no—
200C2×C4×C59—22no—
201C2×C4×C59—22no—
202C2×C4×C59—22no—
203C2×C4×C59—22no—
204C2×C4×C59—24no—
205C2×C4×C59—24no—
206C2×C4×C59—24no—
207C2×C4×C59—42no—
208C2×C4×C59—41no—
209C2×C4×C59—41no—
210C2×C4×C59—41no—
211C2×C4×C59—42no—
212C2×C4×C59—41no—
213C2×C4×C59—42no—
214C2×C4×C59—42no—
215C2×C4×C59—42no—
216C2×C4×C59—42no—
217C2×C4×C59—42no—
218C2×C4×C59—42no—
219C2×C4×C59—42no—
220C2×C4×C59—42no—
221C2×C4×C59—42no—
222C2×C4×C59#11714yes—
223C2×C4×C59#11714yes—
224C2×C4×C59C4×D414yes—
225C2×C4×C59C4×Q814yes—
226C2×C4×C59C22⋊Q814yes—
227C2×C4×C59#12314yes—
228C2×C4×C59#12514yes—
229C2×C4×C59#12614yes—
230C2×Dic59—22no—
231C2×Dic59—22no—
232C2×Dic59—22no—
233C2×Dic59—22no—
234C2×Dic59—22no—
235C2×Dic59—22no—
236C2×Dic59—22no—
237C2×Dic59—22no—
238C2×Dic59—22no—
239C2×Dic59—22no—
240C2×Dic59—22no—
241C2×Dic59—22no—
242C2×Dic59—22no—
243C2×Dic59—22no—
244C2×Dic59—22no—
245C2×Dic59—24no—
246C2×Dic59—24no—
247C2×Dic59—24no—
248C2×Dic59—42no—
249C2×Dic59—42no—
250C2×Dic59—42no—
251C2×Dic59—41no—
252C2×Dic59—41no—
253C2×Dic59—41no—
254C2×Dic59—41no—
255C2×Dic59—41no—
256C2×Dic59—41no—
257C2×Dic59—42no—
258C2×Dic59—41no—
259C2×Dic59—41no—
260C2×Dic59—41no—
261C2×Dic59—41no—
262C2×Dic59—41no—
263C2×Dic59—41no—
264C2×Dic59—42no—
265C2×Dic59—42no—
266C2×Dic59—42no—
267C2×Dic59—42no—
268C2×Dic59—42no—
269C2×Dic59—42no—
270C2×Dic59—42no—
271C2×Dic59#11714yes—
272#13885—591nomaximal, Sylow
273C22×C59C2×#11711yescharacteristic
274C22×C59C2×#11711yescharacteristic
275C22×C59C2×#11711yescharacteristic
276C22×C59C2×C4×D411yescharacteristic
277C22×C59C2×C4×Q811yescharacteristic
278C22×C59#52011yescharacteristic
279C22×C59#52011yescharacteristic
280C22×C59C2×C22⋊Q811yescharacteristic
281C22×C59C2×#12311yescharacteristic
282C22×C59C2×#12511yescharacteristic
283C22×C59C2×#12611yescharacteristic
284C22×C59#52911yescharacteristic
285C22×C59#52911yescharacteristic
286C22×C59#52911yescharacteristic
287C22×C59#52911yescharacteristic
288C22×C59#54011yescharacteristic
289C22×C59#54111yescharacteristic
290C22×C59#54211yescharacteristic
291C22×C59#54211yescharacteristic
292C22×C59#54611yescharacteristic
293C22×C59#54711yescharacteristic
294C22×C59#54811yescharacteristic
295C22×C59#55011yescharacteristic
296C22×C59#55211yescharacteristic
297C22×C59#55311yescharacteristic
298C22×C59#55411yescharacteristic
299C22×C59#55411yescharacteristic
300C22×C59#55511yescharacteristic
301C22×C59#55611yescharacteristic
302C22×C59#55611yescharacteristic
303C22×C59#55611yescharacteristic
304C22×C59#55711yescharacteristic
305C22×C59#55711yescharacteristic
306C22×C59#55911yescharacteristic
307C22×C59#55911yescharacteristic
308C4×C59—24no—
309C4×C59—42no—
310C4×C59—44no—
311C4×C59—82no—
312C4×C59#38718yes—
313Dic59—24no—
314Dic59—42no—
315Dic59—42no—
316Dic59—42no—
317Dic59—44no—
318Dic59—82no—
319C2×#382—591no—
320C2×C4×C4⋊C4—591no—
321C2×C4×C4⋊C4—591no—
322#1445—592no—
323#1443—592no—
324#1436—592no—
325C4⋊#95—591no—
326C4⋊#95—591no—
327C4⋊#95—591no—
328C4⋊#95D5911yescharacteristic
329#1434—592no—
330C2×C59#228311yescharacteristic
331C2×C59C2×#38711yescharacteristic
332C2×C59#231411yescharacteristic
333C2×C59#235211yescharacteristic
334C2×C59#235411yescharacteristic
335C2×C59#235511yescharacteristic
336C2×C59#235511yescharacteristic
337C2×C59#244711yescharacteristic
338C2×C59#244811yescharacteristic
339C2×C59#245311yescharacteristic
340C2×C59#245411yescharacteristic
341C2×C59#250811yescharacteristic
342C2×C59#250911yescharacteristic
343C2×C59#251311yescharacteristic
344C2×C59#251411yescharacteristic
345C22×C4⋊C4—591no—
346C22×C4⋊C4—591no—
347C22×C4⋊C4—591no—
348C22×C4⋊C4—591no—
349C22×C4⋊C4C2×D5911yescharacteristic
350C22×C4⋊C4C2×D5911yescharacteristic
351C22×C42—591no—
352C22×C42—591no—
353C22×C42—592no—
354C22×C42C2×D5911yescharacteristic
355#382—1184no—
356C4×C4⋊C4—598no—
357C4×C4⋊C4—1184no—
358C2×#95—591no—
359C2×#95—591no—
360C2×#95—592no—
361C2×#95—592no—
362C2×#95—592no—
363C2×#95—592no—
364C2×#95—592no—
365C2×#95—592no—
366C2×#95—592no—
367C2×#95—592no—
368C2×#95—592no—
369C2×#95C2×D5912yes—
370C2×#95C2×D5912yes—
371C59#1388511yescharacteristic, complemented, Sylow
372C23×C4—591no—
373C23×C4—591no—
374C23×C4—591no—
375C23×C4—591no—
376C23×C4—592no—
377C23×C4—592no—
378C23×C4C22×D5912yes—
379C23×C4C22×D5911yescharacteristic
380C23×C4C22×D5912yes—
381C23×C4C22×D5911yescharacteristic
382C23×C4C22×D5911yescharacteristic
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—594no—
389C2×C4⋊C4—594no—
390C2×C4⋊C4—594no—
391C2×C4⋊C4—1182no—
392C2×C4⋊C4—1182no—
393C2×C4⋊C4—1182no—
394C2×C4⋊C4—1182no—
395C2×C4⋊C4—1182no—
396C2×C4⋊C4—1182no—
397C2×C4⋊C4—1182no—
398C2×C4⋊C4—1182no—
399C2×C4⋊C4—1182no—
400C2×C4⋊C4D23614yes—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—594no—
404C2×C42—594no—
405C2×C42—1182no—
406C2×C42—1182no—
407C2×C42—1182no—
408C2×C42—1182no—
409C2×C42—1184no—
410C2×C42—1184no—
411C2×C42—2362no—
412C2×C42C4×D5914yes—
413#95—24no—
414#95—42no—
415#95—594no—
416#95—594no—
417#95—1184no—
418#95—1184no—
419#95—1184no—
420#95—1184no—
421#95—1184no—
422#95—2362no—
423#95—2362no—
424#95—2362no—
425#95—2362no—
426C24C23×D5911yescharacteristic
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—592no—
451C22×C4—592no—
452C22×C4—592no—
453C22×C4—592no—
454C22×C4—592no—
455C22×C4—592no—
456C22×C4—594no—
457C22×C4—1181no—
458C22×C4—1181no—
459C22×C4—1181no—
460C22×C4—1181no—
461C22×C4—1181no—
462C22×C4—1181no—
463C22×C4—1181no—
464C22×C4—1182no—
465C22×C4—1182no—
466C22×C4—1181no—
467C22×C4—1181no—
468C22×C4—1182no—
469C22×C4—1181no—
470C22×C4—1181no—
471C22×C4—1181no—
472C22×C4—1181no—
473C22×C4—1181no—
474C22×C4—1182no—
475C22×C4—1181no—
476C22×C4—1181no—
477C22×C4—1181no—
478C22×C4—1182no—
479C22×C4—1182no—
480C22×C4—1181no—
481C22×C4—1181no—
482C22×C4—1181no—
483C22×C4—1181no—
484C22×C4—1181no—
485C22×C4—1182no—
486C22×C4—1182no—
487C22×C4—1182no—
488C22×C4—1182no—
489C22×C4—1182no—
490C22×C4—1182no—
491C22×C4—1182no—
492C22×C4C2×C4×D5912yes—
493C22×C4C2×C4×D5912yes—
494C22×C4C2×C4×D5912yes—
495C22×C4C2×D23614yes—
496C22×C4C2×D23612yes—
497C22×C4#1174568512yes—
498C22×C4#1174568712yes—
499C22×C4#1174568712yes—
500C22×C4#1174568712yes—
501C22×C4#1174568712yes—
502C22×C4Q8×D5912yes—
503C22×C4#1174568912yes—
504C4⋊C4—28no—
505C4⋊C4—44no—
506C4⋊C4—1188no—
507C4⋊C4—1188no—
508C4⋊C4—1188no—
509C4⋊C4—2364no—
510C42—28no—
511C42—1188no—
512C42—1188no—
513C42—2368no—
514C23C22×C4×D5911yescharacteristic
515C23C22×D23611yescharacteristic
516C23C2×Q8×D5911yescharacteristic
517C23#41×D5911yescharacteristic
518C23#41×D5911yescharacteristic
519C23C2×#1174568711yescharacteristic
520C23C2×#1174568711yescharacteristic
521C23C2×#1174568711yescharacteristic
522C23C2×#1174568711yescharacteristic
523C23C2×#1174568511yescharacteristic
524C23C2×#1174568911yescharacteristic
525C23#1427377211yescharacteristic
526C23#1427377311yescharacteristic
527C23#1427377411yescharacteristic
528C23#1427377511yescharacteristic
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—42no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—42no—
546C2×C4—41no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—594no—
557C2×C4—1182no—
558C2×C4—1182no—
559C2×C4—1182no—
560C2×C4—1182no—
561C2×C4—1182no—
562C2×C4—1182no—
563C2×C4—1184no—
564C2×C4—1184no—
565C2×C4—1182no—
566C2×C4—1182no—
567C2×C4—1182no—
568C2×C4—1184no—
569C2×C4—1182no—
570C2×C4—1182no—
571C2×C4—1182no—
572C2×C4—1182no—
573C2×C4—1182no—
574C2×C4—1182no—
575C2×C4—2362no—
576C2×C4—2362no—
577C2×C4—2362no—
578C2×C4—2362no—
579C2×C4—2362no—
580C2×C4—2362no—
581C2×C4—2362no—
582C2×C4—2362no—
583C2×C4—2362no—
584C2×C4—2362no—
585C2×C4—2361no—
586C2×C4—2361no—
587C2×C4—2361no—
588C2×C4—2361no—
589C2×C4—2361no—
590C2×C4—2361no—
591C2×C4—2362no—
592C2×C4—2361no—
593C2×C4—2361no—
594C2×C4—2361no—
595C2×C4—2361no—
596C2×C4—2361no—
597C2×C4—2361no—
598C2×C4#1427368314yes—
599C2×C4#1427368514yes—
600C2×C4C4×D23614yes—
601C2×C4#1427369214yes—
602C2×C4#1427370714yes—
603C2×C4#1427371114yes—
604C2×C4#1427371714yes—
605C2×C4#1427372014yes—
606C22#117×D5911yescharacteristic
607C22C2×#1427368311yescharacteristic
608C22C2×#1427368511yescharacteristic
609C22C2×C4×D23611yescharacteristic
610C22C2×#1427369211yescharacteristic
611C22#1683788211yescharacteristic
612C22#1683788311yescharacteristic
613C22C2×#1427370711yescharacteristic
614C22C2×#1427371111yescharacteristic
615C22C2×#1427371711yescharacteristic
616C22C2×#1427372011yescharacteristic
617C22#1683793311yescharacteristic
618C22#1683793311yescharacteristic
619C22#1683793811yescharacteristic
620C22#1683793811yescharacteristic
621C22#1683800511yescharacteristic
622C22#1683801211yescharacteristic
623C22#1683801911yescharacteristic
624C22#1683802511yescharacteristic
625C22#1683804711yescharacteristic
626C22#1683805611yescharacteristic
627C22#1683806411yescharacteristic
628C22#1683807411yescharacteristic
629C22#1683809311yescharacteristic
630C22#1683810211yescharacteristic
631C22#1683810811yescharacteristic
632C22#1683811311yescharacteristic
633C22#1683811711yescharacteristic
634C22#1683812111yescharacteristic
635C22#1683812511yescharacteristic
636C22#1683812611yescharacteristic
637C22#1683812711yescharacteristic
638C22#1683812911yescharacteristic
639C22#1683813411yescharacteristic
640C22#1683813811yescharacteristic
641C4—24no—
642C4—42no—
643C4—44no—
644C4—82no—
645C4—1184no—
646C4—4722no—
647C4—2362no—
648C4—2362no—
649C4—2362no—
650C4—2364no—
651C4#1683728718yes—
652C2#2142649111yescharacteristic
653C2C2×#1683728711yescharacteristic
654C2#2142670311yescharacteristic
655C2#2142702811yescharacteristic
656C2#2142704311yescharacteristic
657C2#2142704811yescharacteristic
658C2#2142705511yescharacteristic
659C2#2142788111yescharacteristic
660C2#2142789211yescharacteristic
661C2#2142795511yescharacteristic
662C2#2142796611yescharacteristic
663C2#2142863211yescharacteristic
664C2#2142864311yescharacteristic
665C2#2142869111yescharacteristic
666C2#2142870211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutatorC23×C59C23×C4
FittingC59×C4⋊#95C2
socle, prime radical, cosocleC24×C59C24
hypercenterC4⋊#95D59
hypocenterC59#13885
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
21. C4×C4⋊Dic59C4semidirect
371. C59#13885semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168372672
C2×C4⋊C4×Dic592
C2×C4×C4⋊Dic592
#214223632
#214223562
#214223302
#214223262
#214223252
#214223202
C59×C4⋊#952
#1388559