Finite Group Databasebeta

← #28630058

Subgroups — #28630058

Order 15104.

746 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×#16837694C211yesmaximal, characteristic, complemented
2C2×#16837463C211yesmaximal, characteristic
3#21426778C211yesmaximal, characteristic
4#21425527C211yesmaximal, characteristic
5#21425522C211yesmaximal, characteristic
6#21425299C211yesmaximal, characteristic
7#21425292C211yesmaximal, characteristic
8#21425049C211yesmaximal, characteristic, complemented
9#21424862C211yesmaximal, characteristic, complemented
10#21424836C211yesmaximal, characteristic, complemented
11#21424826C211yesmaximal, characteristic, complemented
12#21424785C211yesmaximal, characteristic, complemented
13#21424771C211yesmaximal, characteristic, complemented
14#21424108C211yesmaximal, characteristic, complemented
15C59×#2628C211yesmaximal, characteristic
16C2×#14273706C2211yescharacteristic
17C2×C4×Dic118C2211yescharacteristic
18#16837694—24no—
19#16837463—24no—
20C2×#14273660C2211yescharacteristic
21C2×#14273660C2211yescharacteristic
22C2×#14273660C2211yescharacteristic
23C2×#14273658C2211yescharacteristic
24C2×C4⋊(C59⋊C8)C2211yescharacteristic
25C2×C4⋊(C59⋊C8)C2211yescharacteristic
26C2×#14273650C2211yescharacteristic
27C2×#14273650C2211yescharacteristic
28C2×#14273650C2211yescharacteristic
29C2×#14273650C2211yescharacteristic
30C2×C22⋊(C59⋊C8)C2211yescharacteristic
31C2×C22⋊(C59⋊C8)C2211yescharacteristic
32C2×#14273638C2211yescharacteristic
33C2×C4×C59⋊C8C2211yescharacteristic
34#16837308C2211yescharacteristic
35#16837300C2211yescharacteristic
36#16837297—21no—
37#16837296—21no—
38#16837290—21no—
39#16837283—21no—
40#16837262C2211yescharacteristic
41C4×C4⋊Dic59C2211yescharacteristic
42#16837164C2211yescharacteristic
43#16837164C2211yescharacteristic
44#16837164C2211yescharacteristic
45#16837164C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837164C2211yescharacteristic
48#16837164C2211yescharacteristic
49#16837164C2211yescharacteristic
50C2×C4⋊Q8×C59C2211yescharacteristic
51C2×#117×C59C2211yescharacteristic
52C59×#400—21no—
53C59×#399—21no—
54C59×#395—21no—
55C59×#393—21no—
56C59×#389C2211yescharacteristic
57C59×#389C2211yescharacteristic
58C59×#382C2211yescharacteristic
59C59×#380C2211yescharacteristic
60C59×#380C2211yescharacteristic
61C22×Dic118C2311yescharacteristic
62C22×C59⋊C8C2311yescharacteristic
63C22×C59⋊C8C2311yescharacteristic
64C22×C59⋊C8C2311yescharacteristic
65C22×C59⋊C8C2311yescharacteristic
66#14273706—22no—
67#14273706—22no—
68C4×Dic118—22no—
69C4×Dic118—22no—
70C2×C4⋊Dic59C2311yescharacteristic
71C2×C4⋊Dic59C2311yescharacteristic
72C2×C4⋊Dic59C2311yescharacteristic
73C2×Dic59⋊C4—21no—
74C2×Dic59⋊C4—21no—
75C2×Dic59⋊C4—21no—
76C2×C22⋊Dic59—21no—
77C2×C22⋊Dic59—21no—
78C2×C4×Dic59—21no—
79C2×C4×Dic59—21no—
80#14273660—22no—
81#14273660—22no—
82#14273660—22no—
83#14273658—22no—
84C4⋊(C59⋊C8)—22no—
85C4⋊(C59⋊C8)D414yes—
86#14273650—22no—
87#14273650—22no—
88#14273650—22no—
89#14273650—22no—
90C22⋊(C59⋊C8)—22no—
91C22⋊(C59⋊C8)—22no—
92#14273638—22no—
93C4×C59⋊C8—22no—
94C59⋊#95—21no—
95C59⋊#95—21no—
96C59⋊#95—21no—
97C59⋊#95—21no—
98C59⋊#95—21no—
99C22×Q8×C59—21no—
100C23×C4×C59C2311yescharacteristic
101C4⋊Q8×C59—22no—
102C4⋊Q8×C59—22no—
103#117×C59—22no—
104#117×C59—22no—
105C2×C4⋊C4×C59—21no—
106C2×C4⋊C4×C59—21no—
107C2×C4⋊C4×C59—21no—
108C2×C4⋊C4×C59D411yescharacteristic
109C2×C4⋊C4×C59D411yescharacteristic
110C2×C4⋊C4×C59C2311yescharacteristic
111C2×C4⋊C4×C59C2311yescharacteristic
112C2×C4⋊C4×C59C2311yescharacteristic
113C2×C4⋊C4×C59C2311yescharacteristic
114C2×C22⋊C4×C59—21no—
115C2×C22⋊C4×C59—21no—
116C2×C22⋊C4×C59D411yescharacteristic
117C2×C22⋊C4×C59D411yescharacteristic
118C2×C42×C59C2311yescharacteristic
119C2×C42×C59C2311yescharacteristic
120#95×C59—21no—
121#95×C59—21no—
122#95×C59—21no—
123#95×C59—21no—
124#95×C59—21no—
125#95×C59—21no—
126C24×C59C2×D411yescharacteristic
127C2×Q8×C59—42no—
128C2×Q8×C59—81no—
129C2×Q8×C59—81no—
130C22×C4×C59—21no—
131C22×C4×C59—21no—
132C22×C4×C59—21no—
133C22×C4×C59—21no—
134C22×C4×C59—21no—
135C22×C4×C59—21no—
136C22×C4×C59—21no—
137C22×C4×C59—21no—
138C22×C4×C59—21no—
139C22×C4×C59—21no—
140C22×C4×C59C2×D411yescharacteristic
141C22×C4×C59C2×D411yescharacteristic
142C22×C4×C59C2×D411yescharacteristic
143C22×C4×C59C2×D411yescharacteristic
144C22×C4×C59C2×D411yescharacteristic
145C22×C4×C59C2411yescharacteristic
146C22×Dic59—21no—
147C22×Dic59—21no—
148C22×Dic59—21no—
149C22×Dic59—21no—
150C2×Dic118—21no—
151C2×Dic118—21no—
152C2×Dic118—21no—
153C2×Dic118—21no—
154C2×Dic118—21no—
155C2×Dic118#4112yes—
156C4⋊C4×C59—22no—
157C4⋊C4×C59—22no—
158C4⋊C4×C59—21no—
159C4⋊C4×C59—21no—
160C4⋊C4×C59—21no—
161C4⋊C4×C59—21no—
162C4⋊C4×C59—21no—
163C4⋊C4×C59—21no—
164C4⋊C4×C59—21no—
165C4⋊C4×C59—21no—
166C4⋊C4×C59—42no—
167C4⋊C4×C59—81no—
168C4⋊C4×C59—81no—
169C22⋊C4×C59—22no—
170C22⋊C4×C59—22no—
171C22⋊C4×C59—81no—
172C22⋊C4×C59—81no—
173C42×C59—21no—
174C42×C59—21no—
175C42×C59C2×D412yes—
176C42×C59#4112yes—
177C22⋊Dic59—24no—
178C22⋊Dic59—81no—
179C4⋊Dic59—21no—
180C4⋊Dic59—21no—
181C4⋊Dic59—21no—
182C4⋊Dic59—21no—
183C4⋊Dic59—21no—
184C4⋊Dic59#4112yes—
185Dic59⋊C4—24no—
186Dic59⋊C4—42no—
187Dic59⋊C4—81no—
188C4×Dic59—42no—
189C4×Dic59—81no—
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⋊C8—21no—
199C2×C59⋊C8—21no—
200C2×C59⋊C8C2×D412yes—
201C2×C59⋊C8C2×D412yes—
202C23×C59—21no—
203C23×C59—21no—
204C23×C59—21no—
205C23×C59—21no—
206C23×C59—21no—
207C23×C59—21no—
208C23×C59—21no—
209C23×C59C22×D411yescharacteristic
210Q8×C59—84no—
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—21no—
219C2×C4×C59—21no—
220C2×C4×C59—21no—
221C2×C4×C59—21no—
222C2×C4×C59—21no—
223C2×C4×C59—21no—
224C2×C4×C59—41no—
225C2×C4×C59—41no—
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×C59—41no—
237C2×C4×C59—41no—
238C2×C4×C59—41no—
239C2×C4×C59—41no—
240C2×C4×C59#12112yes—
241C2×C4×C59#12112yes—
242C2×C4×C59C22×D411yescharacteristic
243C2×C4×C59C2×#4111yescharacteristic
244C2×C4×C59C2×#4111yescharacteristic
245C2×C4×C59C2×#4111yescharacteristic
246C2×C4×C592−1+411yescharacteristic
247C2×C4×C592−1+411yescharacteristic
248C2×Dic59—22no—
249C2×Dic59—22no—
250C2×Dic59—41no—
251C2×Dic59—41no—
252C2×Dic59—41no—
253C2×Dic59—41no—
254C2×Dic59—41no—
255C2×Dic59—41no—
256C2×Dic59—41no—
257C2×Dic59—41no—
258C2×Dic59—41no—
259C2×Dic59—41no—
260Dic118—22no—
261Dic118—22no—
262Dic118—41no—
263Dic118—41no—
264C59⋊C8—22no—
265C59⋊C8—22no—
266C59⋊C8—41no—
267C59⋊C8—41no—
268#24714—591nomaximal, Sylow
269C22×C59—41no—
270C22×C59—41no—
271C22×C59—41no—
272C22×C59—41no—
273C22×C59—41no—
274C22×C59—41no—
275C22×C59—41no—
276C22×C59C2×#12111yescharacteristic
277C22×C59#52511yescharacteristic
278C22×C59#53611yescharacteristic
279C22×C59#57611yescharacteristic
280C22×C59#57711yescharacteristic
281C22×C59#57811yescharacteristic
282C22×C59#57811yescharacteristic
283C4×C59—22no—
284C4×C59—22no—
285C4×C59—41no—
286C4×C59—41no—
287C4×C59—41no—
288C4×C59—81no—
289C4×C59—81no—
290C4×C59—81no—
291C4×C59—81no—
292C4×C59#54711yescharacteristic
293C4×C59#54811yescharacteristic
294C4×C59#55211yescharacteristic
295C4×C59#55611yescharacteristic
296Dic59—42no—
297Dic59—42no—
298Dic59—81no—
299Dic59—81no—
300C2×#477—591no—
301C2×#433—591no—
302#2628D5911yescharacteristic
303#2323—591no—
304#2076—591no—
305#2075—591no—
306#2036—591no—
307#2035—591no—
308#1988—591no—
309#1949—591no—
310#1944—591no—
311#1942—591no—
312#1935—591no—
313#1933—591no—
314#1805—591no—
315C2×C59—81no—
316C2×C59#241511yescharacteristic
317C2×C59#305911yescharacteristic
318C2×C59#306211yescharacteristic
319C2×C59#312111yescharacteristic
320C2×C59#312411yescharacteristic
321C2×C59#324211yescharacteristic
322C2×C59#324311yescharacteristic
323C2×C4⋊Q8C2×D5911yescharacteristic
324C2×C22⋊Q8—591no—
325C2×C4×Q8—591no—
326C2×#117C2×D5911yescharacteristic
327#477—1184no—
328#433—1184no—
329C2×#107—591no—
330C2×#107—591no—
331C2×#107—591no—
332C2×#106—591no—
333C2×C4⋊C8—591no—
334C2×C4⋊C8—591no—
335C2×#103—591no—
336C2×#103—591no—
337C2×#103—591no—
338C2×#103—591no—
339C2×C22⋊C8—591no—
340C2×C22⋊C8—591no—
341C2×#97—591no—
342C2×C4×C8—591no—
343#400—21no—
344#399—21no—
345#395—21no—
346#393—21no—
347#391—591no—
348#389—591no—
349#389—1181no—
350#389C2×D5911yescharacteristic
351#389C2×D5911yescharacteristic
352#388—1181no—
353#388—1181no—
354#387—1181no—
355#382C2×D5911yescharacteristic
356#380—591no—
357#380C2×D5911yescharacteristic
358#380C2×D5911yescharacteristic
359C4×C4⋊C4—591no—
360#340—591no—
361#340—591no—
362#340—591no—
363#340—591no—
364#340—591no—
365#340—591no—
366#340—591no—
367#340—591no—
368C59#2471411yescharacteristic, complemented, Sylow
369C22×Q8—21no—
370C22×Q8—591no—
371C23×C4C22×D5911yescharacteristic
372C22×C8—591no—
373C22×C8—591no—
374C22×C8—591no—
375C22×C8—591no—
376C4⋊Q8—22no—
377C4⋊Q8—22no—
378C22⋊Q8—1182no—
379C22⋊Q8—1182no—
380C4×Q8—1182no—
381C4×Q8—1182no—
382#117—22no—
383#117—22no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—591no—
388C2×C4⋊C4—591no—
389C2×C4⋊C4—591no—
390C2×C4⋊C4—1181no—
391C2×C4⋊C4—1181no—
392C2×C4⋊C4—1181no—
393C2×C4⋊C4C22⋊D5911yescharacteristic
394C2×C4⋊C4C22⋊D5911yescharacteristic
395C2×C4⋊C4C22×D5911yescharacteristic
396C2×C4⋊C4C22×D5911yescharacteristic
397C2×C4⋊C4C22×D5911yescharacteristic
398C2×C4⋊C4C22×D5911yescharacteristic
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—1181no—
402C2×C22⋊C4—1181no—
403C2×C22⋊C4C22⋊D5911yescharacteristic
404C2×C22⋊C4C22⋊D5911yescharacteristic
405C2×C42—1181no—
406C2×C42—1181no—
407C2×C42C22×D5911yescharacteristic
408C2×C42C22×D5911yescharacteristic
409#107—1182no—
410#107—1182no—
411#107—1182no—
412#106—1182no—
413C4⋊C8—594no—
414C4⋊C8—1182no—
415#103—1182no—
416#103—1182no—
417#103—1182no—
418#103—1182no—
419C22⋊C8—1182no—
420C22⋊C8—1182no—
421#97—1182no—
422C4×C8—1182no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—1181no—
430#95—1181no—
431#95—1181no—
432#95—1181no—
433#95—1181no—
434C24C2×C22⋊D5911yescharacteristic
435C2×Q8—42no—
436C2×Q8—81no—
437C2×Q8—81no—
438C2×Q8—592no—
439C2×Q8—1181no—
440C2×Q8—1181no—
441C2×Q8—1181no—
442C2×Q8—1181no—
443C2×Q8—1181no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—1181no—
455C22×C4—1181no—
456C22×C4—1181no—
457C22×C4—1181no—
458C22×C4C2×C22⋊D5911yescharacteristic
459C22×C4C2×C22⋊D5911yescharacteristic
460C22×C4C2×C22⋊D5911yescharacteristic
461C22×C4C2×C22⋊D5911yescharacteristic
462C22×C4C2×C22⋊D5911yescharacteristic
463C22×C4C23×D5911yescharacteristic
464C2×C8—592no—
465C2×C8—592no—
466C2×C8—1181no—
467C2×C8—1181no—
468C2×C8—1181no—
469C2×C8—1181no—
470C2×C8—1181no—
471C2×C8—1181no—
472C2×C8—1181no—
473C2×C8—1181no—
474C2×C8—1181no—
475C2×C8—1181no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—42no—
487C4⋊C4—81no—
488C4⋊C4—81no—
489C4⋊C4—592no—
490C4⋊C4—1184no—
491C4⋊C4—1181no—
492C4⋊C4—1181no—
493C4⋊C4—1181no—
494C4⋊C4—1181no—
495C4⋊C4—1181no—
496C4⋊C4—4721no—
497C4⋊C4—2362no—
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—81no—
501C22⋊C4—81no—
502C22⋊C4—1184no—
503C22⋊C4—4721no—
504C42—21no—
505C42—21no—
506C42—4721no—
507C42—2362no—
508C42D4×D5912yes—
509C42#1174568712yes—
510C23—21no—
511C23—21no—
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23C22×C22⋊D5911yescharacteristic
518Q8—84no—
519Q8—1182no—
520Q8—1182no—
521Q8—2361no—
522Q8—2361no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
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—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
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—1182no—
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×C4—2361no—
563C2×C4—2361no—
564C2×C4#1427369912yes—
565C2×C4#1427369912yes—
566C2×C4C2×D4×D5911yescharacteristic
567C2×C4#41×D5911yescharacteristic
568C2×C4#41×D5911yescharacteristic
569C2×C4C2×#1174568711yescharacteristic
570C2×C4#1427377511yescharacteristic
571C2×C4#1427377511yescharacteristic
572C8—1182no—
573C8—1182no—
574C8—2361no—
575C8—2361no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22C2×#1427369911yescharacteristic
584C22#1683790911yescharacteristic
585C22#1683797611yescharacteristic
586C22#1683820511yescharacteristic
587C22#1683821311yescharacteristic
588C22#1683821711yescharacteristic
589C22#1683821711yescharacteristic
590C4—22no—
591C4—22no—
592C4—41no—
593C4—41no—
594C4—41no—
595C4—81no—
596C4—81no—
597C4—81no—
598C4—81no—
599C4—4721no—
600C4—4721no—
601C4—2362no—
602C4—2362no—
603C4#1683805411yescharacteristic
604C4#1683806211yescharacteristic
605C4#1683808611yescharacteristic
606C4#1683812311yescharacteristic
607C2—81no—
608C2#2142752611yescharacteristic
609C2#2143374811yescharacteristic
610C2#2143377211yescharacteristic
611C2#2143431911yescharacteristic
612C2#2143435211yescharacteristic
613C2#2143536411yescharacteristic
614C2#2143537911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC59×#2628C2
socleC23×C59C22×D4
prime radicalC24×C59C2×D4
hypercenter#2628D59
hypocenterC59#24714
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2628

Complements

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

NH ≅ G/Ntype
1. C2×#16837694C2semidirect
8. #21425049C2semidirect
9. #21424862C2semidirect
10. #21424836C2semidirect
11. #21424826C2semidirect
12. #21424785C2semidirect
13. #21424771C2semidirect
14. #21424108C2semidirect
368. C59#24714semidirect

Maximal subgroups

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

subgroupindex
C2×#168376942
C2×#168374632
#214267782
#214255272
#214255222
#214252992
#214252922
#214250492
#214248622
#214248362
#214248262
#214247852
#214247712
#214241082
C59×#26282
#2471459