Finite Group Databasebeta

← #28596693

Subgroups — #28596693

Order 15104.

818 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837759C211yesmaximal, characteristic
2#21426807C211yesmaximal, characteristic
3#21425066C211yesmaximal, characteristic, complemented
4#21424910C211yesmaximal, characteristic
5#21424792C211yesmaximal, characteristic
6#21424785C211yesmaximal, characteristic, complemented
7#21424778C211yesmaximal, characteristic
8#21424771C211yesmaximal, characteristic, complemented
9#21424223C211yesmaximal, characteristic, complemented
10#21423929C211yesmaximal, characteristic, complemented
11#21423924C211yesmaximal, characteristic
12C4×#14273650C211yesmaximal, characteristic, complemented
13C4×#14273647C211yesmaximal, characteristic
14#21423783C211yesmaximal, characteristic, complemented
15C59×#2330C211yesmaximal, characteristic, complemented
16C2×#14273715C2211yescharacteristic
17C2×C4×Dic118C2211yescharacteristic
18C2×C4×D236C2211yescharacteristic
19#16837759C418yescomplemented
20C2×#14273650C2211yescharacteristic
21C2×#14273650C2211yescharacteristic
22C2×#14273650C2211yescharacteristic
23C2×#14273650C2211yescharacteristic
24C2×#14273647C2211yescharacteristic
25C2×#14273647C2211yescharacteristic
26C2×#14273647C2211yescharacteristic
27C2×#14273647C2211yescharacteristic
28C2×#14273638C2211yescharacteristic
29C2×#14273638C2211yescharacteristic
30C2×#14273638C2211yescharacteristic
31C2×C4×C59⋊C8C2211yescharacteristic
32C2×C4×C59⋊C8C2211yescharacteristic
33C2×C4×C59⋊C8C2211yescharacteristic
34#16837308C2211yescharacteristic
35#16837304C2211yescharacteristic
36#16837294—21no—
37#16837294—21no—
38#16837276—21no—
39#16837276—21no—
40#16837272C2211yescharacteristic
41#16837164C2211yescharacteristic
42#16837164C2211yescharacteristic
43#16837164C2211yescharacteristic
44#16837164C2211yescharacteristic
45#16837164C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837164C2211yescharacteristic
48#16837164C2211yescharacteristic
49C2×#125×C59C2211yescharacteristic
50C59×#389—21no—
51C59×#389—21no—
52C59×#389C2211yescharacteristic
53C59×#389C2211yescharacteristic
54C59×#387—21no—
55C59×#387—21no—
56C59×#384C2211yescharacteristic
57C4×C4⋊C4×C59C2211yescharacteristic
58C4×C4⋊C4×C59C2211yescharacteristic
59C59×#376C2211yescharacteristic
60C22×Dic118C2311yescharacteristic
61C22×D236C2311yescharacteristic
62C22×C4×D59—21no—
63C22×C59⋊C8C2311yescharacteristic
64C22×C59⋊C8C2311yescharacteristic
65C22×C59⋊C8C2311yescharacteristic
66C22×C59⋊C8C2311yescharacteristic
67#14273715—22no—
68#14273715C2×C414yes—
69C4×Dic118—22no—
70C4×Dic118—22no—
71C4×D236—22no—
72C4×D236—22no—
73C2×C4⋊Dic59—21no—
74C2×C4⋊Dic59—21no—
75C2×C4⋊Dic59C2311yescharacteristic
76C2×C4⋊Dic59C2311yescharacteristic
77C2×Dic59⋊C4—21no—
78C2×(C2×D59)⋊C4—21no—
79C2×(C2×D59)⋊C4—21no—
80C2×(C2×D59)⋊C4—21no—
81C2×(C2×D59)⋊C4—21no—
82C2×(C2×D59)⋊C4—21no—
83C2×C4×Dic59—21no—
84#14273650—22no—
85#14273650—22no—
86#14273650C2×C414yescomplemented
87#14273650C2×C414yescomplemented
88#14273647—22no—
89#14273647—22no—
90#14273647C2×C414yes—
91#14273647C2×C414yes—
92#14273638—22no—
93#14273638—22no—
94#14273638—22no—
95C4×C59⋊C8—22no—
96C4×C59⋊C8—22no—
97C4×C59⋊C8C2×C414yescomplemented
98C59⋊#95—21no—
99C59⋊#95—21no—
100#125×C59—22no—
101#125×C59C2×C414yescomplemented
102C2×C4⋊C4×C59—21no—
103C2×C4⋊C4×C59—21no—
104C2×C4⋊C4×C59—21no—
105C2×C4⋊C4×C59—21no—
106C2×C4⋊C4×C59—21no—
107C2×C4⋊C4×C59—21no—
108C2×C4⋊C4×C59C2311yescharacteristic
109C2×C4⋊C4×C59C2311yescharacteristic
110C2×C4⋊C4×C59C2311yescharacteristic
111C2×C4⋊C4×C59C2311yescharacteristic
112C2×C42×C59—21no—
113C2×C42×C59—21no—
114C2×C42×C59C2311yescharacteristic
115C2×C42×C59C2311yescharacteristic
116C2×C42×C59C2311yescharacteristic
117#95×C59—21no—
118#95×C59—21no—
119#95×C59—21no—
120#95×C59—21no—
121#95×C59D411yescharacteristic
122#95×C59D411yescharacteristic
123#95×C59D411yescharacteristic
124#95×C59D411yescharacteristic
125C23×D59—21no—
126C22×C4×C59—21no—
127C22×C4×C59—21no—
128C22×C4×C59—21no—
129C22×C4×C59—21no—
130C22×C4×C59C2×D411yescharacteristic
131C22×C4×C59C2×D411yescharacteristic
132C22×C4×C59C2×D411yescharacteristic
133C22×C4×C59C2×D411yescharacteristic
134C22×C4×C59C2×D411yescharacteristic
135C22×C4×C59C2×D411yescharacteristic
136C22×C4×C59C2411yescharacteristic
137C22×Dic59—21no—
138C22×Dic59—21no—
139C22×Dic59—21no—
140C2×D236—21no—
141C2×D236—21no—
142C2×D236—21no—
143C2×D236—21no—
144C2×D236—21no—
145C2×D236C22×C412yes—
146C2×C4×D59—42no—
147C2×C4×D59—81no—
148C2×C4×D59—81no—
149C2×Dic118—21no—
150C2×Dic118—21no—
151C2×Dic118—21no—
152C2×Dic118—21no—
153C2×Dic118—21no—
154C2×Dic118C22×C412yes—
155C4⋊C4×C59—24no—
156C4⋊C4×C59—24no—
157C4⋊C4×C59—21no—
158C4⋊C4×C59—21no—
159C4⋊C4×C59—21no—
160C4⋊C4×C59—21no—
161C4⋊C4×C59—21no—
162C4⋊C4×C59—21no—
163C4⋊C4×C59—81no—
164C4⋊C4×C59—81no—
165C4⋊C4×C59—81no—
166C4⋊C4×C59—81no—
167C4⋊C4×C59C22×C412yes—
168C4⋊C4×C59C22×C412yes—
169C42×C59—21no—
170C42×C59—21no—
171C42×C59—81no—
172C42×C59—81no—
173C42×C59C22×C412yes—
174C42×C59#4112yes—
175C42×C59#4112yes—
176C42×C59#4112yes—
177(C2×D59)⋊C4—24no—
178(C2×D59)⋊C4—24no—
179(C2×D59)⋊C4—42no—
180(C2×D59)⋊C4—81no—
181(C2×D59)⋊C4—81no—
182C4⋊Dic59—21no—
183C4⋊Dic59—21no—
184C4⋊Dic59—21no—
185C4⋊Dic59—21no—
186C4⋊Dic59—81no—
187C4⋊Dic59—81no—
188Dic59⋊C4—42no—
189C4×Dic59—42no—
190C2×C59⋊C8—21no—
191C2×C59⋊C8—21no—
192C2×C59⋊C8—21no—
193C2×C59⋊C8—21no—
194C2×C59⋊C8—21no—
195C2×C59⋊C8—21no—
196C2×C59⋊C8—21no—
197C2×C59⋊C8—21no—
198C2×C59⋊C8C22×C412yes—
199C2×C59⋊C8C22×C412yes—
200C2×C59⋊C8#4112yes—
201C2×C59⋊C8#4112yes—
202C23×C59C22×D411yescharacteristic
203C22×D59—22no—
204C22×D59—41no—
205C22×D59—41no—
206C22×D59—41no—
207C22×D59—41no—
208C22×D59—41no—
209C22×D59—41no—
210C2×C4×C59—21no—
211C2×C4×C59—21no—
212C2×C4×C59—21no—
213C2×C4×C59—21no—
214C2×C4×C59—21no—
215C2×C4×C59—21no—
216C2×C4×C59—21no—
217C2×C4×C59—21no—
218C2×C4×C59—22no—
219C2×C4×C59—22no—
220C2×C4×C59—21no—
221C2×C4×C59—21no—
222C2×C4×C59—21no—
223C2×C4×C59—21no—
224C2×C4×C59—21no—
225C2×C4×C59—21no—
226C2×C4×C59—41no—
227C2×C4×C59—41no—
228C2×C4×C59—41no—
229C2×C4×C59—41no—
230C2×C4×C59—41no—
231C2×C4×C59—41no—
232C2×C4×C59—41no—
233C2×C4×C59—41no—
234C2×C4×C59—41no—
235C2×C4×C59—41no—
236C2×C4×C59C4×D412yes—
237C2×C4×C59C4×D412yes—
238C2×C4×C59#12412yes—
239C2×C4×C59#12412yes—
240C2×C4×C59C23×C411yescharacteristic
241C2×C4×C59C2×#4111yescharacteristic
242C2×C4×C59C2×#4111yescharacteristic
243C2×C4×C59C2×#4111yescharacteristic
244C2×C4×C59C2×#4111yescharacteristic
245C2×C4×C59C2×#4111yescharacteristic
246C2×Dic59—22no—
247C2×Dic59—41no—
248C2×Dic59—41no—
249C2×Dic59—41no—
250C2×Dic59—41no—
251C2×Dic59—41no—
252C2×Dic59—41no—
253C2×Dic59—41no—
254C2×Dic59—41no—
255D236—22no—
256D236—22no—
257D236—41no—
258D236—41no—
259C4×D59—84no—
260Dic118—22no—
261Dic118—22no—
262Dic118—41no—
263Dic118—41no—
264C59⋊C8—22no—
265C59⋊C8—22no—
266C59⋊C8—22no—
267C59⋊C8—22no—
268#21643—591nomaximal, Sylow
269C22×C59C2×C4×D411yescharacteristic
270C22×C59C2×#12411yescharacteristic
271C22×C59#53211yescharacteristic
272C22×C59#57611yescharacteristic
273C22×C59#57711yescharacteristic
274C22×C59#57711yescharacteristic
275C22×C59#57811yescharacteristic
276C2×D59—42no—
277C2×D59—42no—
278C2×D59—42no—
279C2×D59—81no—
280C2×D59—81no—
281C2×D59—81no—
282C2×D59—81no—
283C4×C59—22no—
284C4×C59—22no—
285C4×C59—22no—
286C4×C59—22no—
287C4×C59—41no—
288C4×C59—41no—
289C4×C59—42no—
290C4×C59—42no—
291C4×C59—81no—
292C4×C59—81no—
293C4×C59C4×#4111yescharacteristic
294C4×C59C4×#4111yescharacteristic
295C4×C59#52911yescharacteristic
296C4×C59#52911yescharacteristic
297Dic59—42no—
298Dic59—81no—
299Dic59—81no—
300C2×#488—591no—
301#2330D5911yescharacteristic, complemented
302#2326—591no—
303#1992—591no—
304#1959—591no—
305#1936—591no—
306#1935—591no—
307#1934—591no—
308#1933—591no—
309#1834—591no—
310#1763—591no—
311#1762—591no—
312C4×#103—591no—
313C4×#102—591no—
314#1726—591no—
315C2×C59C4×#12411yescharacteristic
316C2×C59#295111yescharacteristic
317C2×C59#295211yescharacteristic
318C2×C59#313611yescharacteristic
319C2×C59#313711yescharacteristic
320C2×C59#317811yescharacteristic
321C2×C59#317911yescharacteristic
322D59—82no—
323C2×#125C2×D5911yescharacteristic
324C2×#124—591no—
325C2×C4×Q8—591no—
326C2×C4×D4—591no—
327#488—598no—
328C2×#103—591no—
329C2×#103—591no—
330C2×#103—591no—
331C2×#103—591no—
332C2×#102—591no—
333C2×#102—591no—
334C2×#102—591no—
335C2×#102—591no—
336C2×#97—591no—
337C2×#97—591no—
338C2×#97—591no—
339C2×C4×C8—591no—
340C2×C4×C8—591no—
341C2×C4×C8—591no—
342#391—591no—
343#390—591no—
344#389—21no—
345#389—21no—
346#389C2×D5911yescharacteristic
347#389C2×D5911yescharacteristic
348#388—1181no—
349#388—1181no—
350#387—21no—
351#387—21no—
352#385—1181no—
353#385—1181no—
354#384—591no—
355#384C2×D5911yescharacteristic
356C4×C4⋊C4C2×D5911yescharacteristic
357C4×C4⋊C4C2×D5911yescharacteristic
358#376C2×D5911yescharacteristic
359#340—591no—
360#340—591no—
361#340—591no—
362#340—591no—
363#340—591no—
364#340—591no—
365#340—591no—
366#340—591no—
367C59#2164311yescharacteristic, complemented, Sylow
368C22×Q8—591no—
369C22×D4—591no—
370C23×C4—1181no—
371C22×C8—591no—
372C22×C8—591no—
373C22×C8—591no—
374C22×C8—591no—
375#125—22no—
376#125C4×D5914yescomplemented
377#124—594no—
378#124—1182no—
379C4×Q8—1182no—
380C4×Q8—1182no—
381C4×D4—1182no—
382C4×D4—1182no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—591no—
390C2×C4⋊C4—591no—
391C2×C4⋊C4—1181no—
392C2×C4⋊C4—1181no—
393C2×C4⋊C4—1181no—
394C2×C4⋊C4C22×D5911yescharacteristic
395C2×C4⋊C4C22×D5911yescharacteristic
396C2×C4⋊C4C22×D5911yescharacteristic
397C2×C4⋊C4C22×D5911yescharacteristic
398C2×C22⋊C4—1181no—
399C2×C22⋊C4—1181no—
400C2×C22⋊C4—1181no—
401C2×C22⋊C4—1181no—
402C2×C22⋊C4—1181no—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42—1181no—
406C2×C42C22×D5911yescharacteristic
407C2×C42C22×D5911yescharacteristic
408C2×C42C22×D5911yescharacteristic
409#103—594no—
410#103—594no—
411#103—1182no—
412#103—1182no—
413#102—594no—
414#102—594no—
415#102—1182no—
416#102—1182no—
417#97—1182no—
418#97—1182no—
419#97—1182no—
420C4×C8—594no—
421C4×C8—1182no—
422C4×C8—1182no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—1181no—
428#95—1181no—
429#95C22⋊D5911yescharacteristic
430#95C22⋊D5911yescharacteristic
431#95C22⋊D5911yescharacteristic
432#95C22⋊D5911yescharacteristic
433C24—1181no—
434C2×Q8—592no—
435C2×Q8—1181no—
436C2×Q8—1181no—
437C2×Q8—1181no—
438C2×Q8—1181no—
439C2×Q8—1181no—
440C2×D4—592no—
441C2×D4—1181no—
442C2×D4—1181no—
443C2×D4—1181no—
444C2×D4—1181no—
445C2×D4—1181no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—1181no—
451C22×C4—1181no—
452C22×C4—1181no—
453C22×C4—4721no—
454C22×C4—4721no—
455C22×C4—2362no—
456C22×C4C2×C22⋊D5911yescharacteristic
457C22×C4C2×C22⋊D5911yescharacteristic
458C22×C4C2×C22⋊D5911yescharacteristic
459C22×C4C2×C22⋊D5911yescharacteristic
460C22×C4C2×C22⋊D5911yescharacteristic
461C22×C4C2×C22⋊D5911yescharacteristic
462C22×C4C23×D5911yescharacteristic
463C2×C8—592no—
464C2×C8—592no—
465C2×C8—592no—
466C2×C8—592no—
467C2×C8—1181no—
468C2×C8—1181no—
469C2×C8—1181no—
470C2×C8—1181no—
471C2×C8—1181no—
472C2×C8—1181no—
473C2×C8—1181no—
474C2×C8—1181no—
475C4⋊C4—24no—
476C4⋊C4—24no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—81no—
484C4⋊C4—81no—
485C4⋊C4—81no—
486C4⋊C4—81no—
487C4⋊C4—1181no—
488C4⋊C4—1181no—
489C4⋊C4—1181no—
490C4⋊C4—1181no—
491C4⋊C4—4721no—
492C4⋊C4—4721no—
493C4⋊C4—2362no—
494C4⋊C4C2×C4×D5912yes—
495C4⋊C4C2×C4×D5912yes—
496C22⋊C4—1184no—
497C22⋊C4—1184no—
498C22⋊C4—4721no—
499C22⋊C4—4721no—
500C22⋊C4—2362no—
501C42—21no—
502C42—21no—
503C42—81no—
504C42—81no—
505C42—2362no—
506C42C2×C4×D5912yes—
507C42#1174568512yes—
508C42#1174568912yes—
509C42#1174568912yes—
510C23—1182no—
511C23—2361no—
512C23—2361no—
513C23—2361no—
514C23—2361no—
515C23—2361no—
516C23—2361no—
517C23C22×C22⋊D5911yescharacteristic
518Q8—1182no—
519Q8—1182no—
520Q8—2361no—
521Q8—2361no—
522D4—1182no—
523D4—1182no—
524D4—2361no—
525D4—2361no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—1182no—
553C2×C4—4724no—
554C2×C4—2361no—
555C2×C4—2361no—
556C2×C4—2361no—
557C2×C4—2361no—
558C2×C4—2361no—
559C2×C4—2361no—
560C2×C4—2361no—
561C2×C4—2361no—
562C2×C4C4×C22⋊D5912yes—
563C2×C4C4×C22⋊D5912yes—
564C2×C4#1427371612yes—
565C2×C4#1427371612yes—
566C2×C4C22×C4×D5911yescharacteristic
567C2×C4#41×D5911yescharacteristic
568C2×C4#41×D5911yescharacteristic
569C2×C4C2×#1174568511yescharacteristic
570C2×C4C2×#1174568911yescharacteristic
571C2×C4C2×#1174568911yescharacteristic
572C8—1182no—
573C8—1182no—
574C8—1182no—
575C8—1182no—
576C22—4721no—
577C22—4721no—
578C22—4721no—
579C22—4721no—
580C22—2362no—
581C22—2362no—
582C22—2362no—
583C22C2×C4×C22⋊D5911yescharacteristic
584C22C2×#1427371611yescharacteristic
585C22#1683794811yescharacteristic
586C22#1683820511yescharacteristic
587C22#1683821011yescharacteristic
588C22#1683821311yescharacteristic
589C22#1683821711yescharacteristic
590C4—22no—
591C4—22no—
592C4—22no—
593C4—22no—
594C4—42no—
595C4—41no—
596C4—42no—
597C4—41no—
598C4—81no—
599C4—81no—
600C4—4721no—
601C4—4721no—
602C4—2362no—
603C4C4×#1174568911yescharacteristic
604C4C4×#1174568911yescharacteristic
605C4#1683793911yescharacteristic
606C4#1683793911yescharacteristic
607C2—4722no—
608C2C4×#1427371611yescharacteristic
609C2#2143296911yescharacteristic
610C2#2143297711yescharacteristic
611C2#2143445511yescharacteristic
612C2#2143446611yescharacteristic
613C2#2143476611yescharacteristic
614C2#2143478111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#2330C2
socleC23×C59C22×D4
prime radicalC22×D236C23
cosocleC22×C4×C59C24
hypercenter#2330D59
hypocenterC59#21643
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ #376 ◁ #2330

Complements

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

NH ≅ G/Ntype
3. #21425066C2semidirect
6. #21424785C2semidirect
8. #21424771C2semidirect
9. #21424223C2semidirect
10. #21423929C2semidirect
12. C4×#14273650C2semidirect
14. #21423783C2semidirect
15. C59×#2330C2semidirect
19. #16837759C4semidirect
86. #14273650C2×C4semidirect
87. #14273650C2×C4semidirect
97. C4×C59⋊C8C2×C4semidirect
101. #125×C59C2×C4semidirect
301. #2330D59semidirect
367. C59#21643semidirect
376. #125C4×D59semidirect

Maximal subgroups

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

subgroupindex
C2×#168377592
#214268072
#214250662
#214249102
#214247922
#214247852
#214247782
#214247712
#214242232
#214239292
#214239242
C4×#142736502
C4×#142736472
#214237832
C59×#23302
#2164359