Finite Group Databasebeta

← #28596535

Subgroups — #28596535

Order 15104.

730 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21433878C211yesmaximal, characteristic
2#21432521C211yesmaximal, characteristic
3#21425041C211yesmaximal, characteristic, complemented
4#21424869C211yesmaximal, characteristic, complemented
5#21424692C211yesmaximal, characteristic, complemented
6#21424692C211yesmaximal, characteristic, complemented
7#21424370C211yesmaximal, characteristic
8#21424370C211yesmaximal, characteristic
9#21424113C211yesmaximal, characteristic
10#21423981C211yesmaximal, characteristic, complemented
11#21423976C211yesmaximal, characteristic, complemented
12#21423968C211yesmaximal, characteristic, complemented
13#21423942C211yesmaximal, characteristic
14#21423935C211yesmaximal, characteristic
15C59×#2961C211yesmaximal, characteristic, complemented
16C2×#14273733C2211yescharacteristic
17C2×#14273733C2211yescharacteristic
18C4×#11745685C2211yescharacteristic
19#16837706C411yescharacteristic, complemented
20#16837706C411yescharacteristic, complemented
21#16837699C411yescharacteristic, complemented
22#16837699C411yescharacteristic, complemented
23#16837694C411yescharacteristic, complemented
24#16837689C411yescharacteristic, complemented
25#16837684C411yescharacteristic, complemented
26#16837679C411yescharacteristic, complemented
27C2×#14273662C2211yescharacteristic
28C2×#14273662C2211yescharacteristic
29#16837438C2211yescharacteristic
30#16837438C2211yescharacteristic
31C2×C4⋊(C59⋊C8)C2211yescharacteristic
32C2×#14273653C2211yescharacteristic
33C2×#14273653C2211yescharacteristic
34#16837396C2211yescharacteristic
35#16837396C2211yescharacteristic
36#16837359—21no—
37#16837359—21no—
38#16837357C2211yescharacteristic
39#16837357C2211yescharacteristic
40C4×#11745664C2211yescharacteristic
41#16837354—21no—
42C2×#14273637C2211yescharacteristic
43#97×D59—21no—
44C2×C8×Dic59C2211yescharacteristic
45C4×C4⋊Dic59C2211yescharacteristic
46#16837166C2211yescharacteristic
47#16837166C2211yescharacteristic
48#16837163C2211yescharacteristic
49#16837163C2211yescharacteristic
50#16837161C2211yescharacteristic
51#16837161C2211yescharacteristic
52#16837161C2211yescharacteristic
53#16837161C2211yescharacteristic
54#16837156C2211yescharacteristic
55#16837156C2211yescharacteristic
56C59×#533C2211yescharacteristic
57C59×#446—21no—
58C59×#446—21no—
59C59×#446—21no—
60C59×#446—21no—
61C59×#424C2211yescharacteristic
62C59×#424C2211yescharacteristic
63C59×#423C2211yescharacteristic
64C59×#405C2211yescharacteristic
65C59×#405C2211yescharacteristic
66C2×#97×C59C2211yescharacteristic
67C2×#11745685C2311yescharacteristic
68#14273733—22no—
69#14273733—22no—
70#14273733—22no—
71#14273733Q814yescomplemented
72C2×#11745664C2311yescharacteristic
73C2×#11745664C2311yescharacteristic
74C2×#11745659—21no—
75C2×#11745659—21no—
76C22×C59⋊C8C2311yescharacteristic
77C22×C59⋊C8C2311yescharacteristic
78C2×C8×D59—21no—
79C2×C8×D59—21no—
80C4×Dic118C2×C411yescharacteristic
81C4×Dic118C2×C411yescharacteristic
82C4×D236C2×C411yescharacteristic
83C4×D236C2×C411yescharacteristic
84C4×C22⋊D59—21no—
85C4×C22⋊D59—21no—
86#14273686C2311yescharacteristic
87#14273684—21no—
88C2×C4⋊Dic59—21no—
89C2×C4×Dic59C2311yescharacteristic
90C2×C4×Dic59C2311yescharacteristic
91C42×D59—21no—
92#14273662—22no—
93#14273662—22no—
94#14273660C2×C411yescharacteristic
95#14273660C2×C411yescharacteristic
96#14273660C2×C411yescharacteristic
97#14273660C2×C411yescharacteristic
98#14273658C2×C411yescharacteristic
99#14273658C2×C411yescharacteristic
100#14273658C2×C411yescharacteristic
101#14273658C2×C411yescharacteristic
102C4⋊(C59⋊C8)C2×C411yescharacteristic
103C4⋊(C59⋊C8)C2×C411yescharacteristic
104C4⋊(C59⋊C8)C2×C411yescharacteristic
105C4⋊(C59⋊C8)C2×C411yescharacteristic
106#14273653—22no—
107#14273653—22no—
108#14273650C2×C411yescharacteristic
109#14273650C2×C411yescharacteristic
110#14273650C2×C411yescharacteristic
111#14273650C2×C411yescharacteristic
112#14273647C2×C411yescharacteristic
113#14273647C2×C411yescharacteristic
114#14273647C2×C411yescharacteristic
115#14273647C2×C411yescharacteristic
116#14273638—21no—
117#14273637—21no—
118#14273637—21no—
119#14273637—22no—
120C4×C59⋊C8—21no—
121C8×Dic59—21no—
122C8×Dic59—21no—
123C8×Dic59—22no—
124C59⋊#95—21no—
125C2×M16×C59C2311yescharacteristic
126C2×M16×C59C2311yescharacteristic
127C22×C8×C59C2311yescharacteristic
128C22×C8×C59C2311yescharacteristic
129C4⋊Q8×C59C2×C411yescharacteristic
130C4⋊Q8×C59C2×C411yescharacteristic
131#125×C59C2×C411yescharacteristic
132#125×C59C2×C411yescharacteristic
133C22⋊Q8×C59—21no—
134C22⋊Q8×C59—21no—
135C4×Q8×C59—21no—
136C4×Q8×C59—21no—
137#117×C59C2311yescharacteristic
138#117×C59C2311yescharacteristic
139C2×C42×C59C2311yescharacteristic
140C4⋊C8×C59—21no—
141C4⋊C8×C59—21no—
142C4⋊C8×C59—21no—
143C4⋊C8×C59—21no—
144C4⋊C8×C59—21no—
145C4⋊C8×C59—21no—
146#97×C59—21no—
147#97×C59—21no—
148#97×C59D411yescharacteristic
149#97×C59D411yescharacteristic
150#97×C59D411yescharacteristic
151#97×C59D411yescharacteristic
152C4×C8×C59—21no—
153C4×C8×C59—21no—
154C2×Q8×C59—21no—
155C2×Q8×C59—21no—
156C22×C4×C59#4111yescharacteristic
157C22×C4×C59#4111yescharacteristic
158C22×C4×C59C2411yescharacteristic
159C2×C22⋊D59—21no—
160C22×Dic59—21no—
161C22×Dic59—21no—
162#11745685—21no—
163#11745685—21no—
164#11745685C2×Q812yes—
165#11745685#4112yes—
166C2×D236C22×C411yescharacteristic
167C2×C4×D59—21no—
168C2×C4×D59—21no—
169C2×C4×D59—21no—
170C2×Dic118C22×C411yescharacteristic
171M16×C59—21no—
172M16×C59—21no—
173M16×C59—21no—
174M16×C59—21no—
175C2×C8×C59—21no—
176C2×C8×C59—21no—
177C2×C8×C59—21no—
178C2×C8×C59—21no—
179C2×C8×C59C2×D411yescharacteristic
180C2×C8×C59C2×D411yescharacteristic
181C2×C8×C59C2×D411yescharacteristic
182C2×C8×C59C2×D411yescharacteristic
183C2×C8×C59C2×Q812yes—
184C2×C8×C59#4112yes—
185C4⋊C4×C59—21no—
186C4⋊C4×C59—21no—
187C4⋊C4×C59—21no—
188C4⋊C4×C59—21no—
189C4⋊C4×C59—21no—
190C4⋊C4×C59—21no—
191C4⋊C4×C59C22×C411yescharacteristic
192C4⋊C4×C59C22×C411yescharacteristic
193C4⋊C4×C59C22×C411yescharacteristic
194C4⋊C4×C59C22×C411yescharacteristic
195C22⋊C4×C59—21no—
196C22⋊C4×C59—21no—
197C42×C59—21no—
198C42×C59—21no—
199C42×C59C22×C411yescharacteristic
200C42×C59C22×C411yescharacteristic
201C42×C59C2×D411yescharacteristic
202C42×C59C2×D411yescharacteristic
203C22⋊Dic59—21no—
204(C2×D59)⋊C4—21no—
205(C2×D59)⋊C4—21no—
206C4⋊Dic59—42no—
207C4⋊Dic59C22×C411yescharacteristic
208C4⋊Dic59C22×C411yescharacteristic
209Dic59⋊C4—21no—
210Dic59⋊C4—21no—
211C4×Dic59—21no—
212C4×Dic59—21no—
213C4×Dic59—21no—
214C4×Dic59—21no—
215C4×Dic59—21no—
216C4×Dic59—21no—
217C4×Dic59—21no—
218#11745664—21no—
219#11745664—21no—
220#11745664C2×Q812yes—
221#11745664#4112yes—
222C2×C59⋊C8—21no—
223C2×C59⋊C8—21no—
224C2×C59⋊C8—21no—
225C2×C59⋊C8—21no—
226C2×C59⋊C8—21no—
227C2×C59⋊C8—21no—
228C2×C59⋊C8C22×C411yescharacteristic
229C2×C59⋊C8C22×C411yescharacteristic
230C2×C59⋊C8C22×C411yescharacteristic
231C2×C59⋊C8C22×C411yescharacteristic
232#11745659—24no—
233#11745659—24no—
234C8×D59—24no—
235C8×D59—24no—
236C23×C59C2×#4111yescharacteristic
237C22×D59—21no—
238Q8×C59—81no—
239Q8×C59—81no—
240C2×C4×C59—21no—
241C2×C4×C59—21no—
242C2×C4×C59—21no—
243C2×C4×C59—21no—
244C2×C4×C59—41no—
245C2×C4×C59—41no—
246C2×C4×C59C4×D411yescharacteristic
247C2×C4×C59C4×D411yescharacteristic
248C2×C4×C59C4×D411yescharacteristic
249C2×C4×C59C4×D411yescharacteristic
250C2×C4×C59C23×C411yescharacteristic
251C2×C4×C59C22×D411yescharacteristic
252C2×C4×C59C22×Q811yescharacteristic
253C2×C4×C59C2×#4111yescharacteristic
254C2×C4×C59C2×#4111yescharacteristic
255C2×C4×C59C2×#4111yescharacteristic
256C22⋊D59—22no—
257C22⋊D59—22no—
258C2×Dic59—21no—
259C2×Dic59—22no—
260C2×Dic59—21no—
261C2×Dic59—21no—
262C2×Dic59—41no—
263C2×Dic59—41no—
264C2×Dic59—41no—
265C2×Dic59—41no—
266C2×Dic59—41no—
267D236—21no—
268D236C4×Q812yes—
269C4×D59—22no—
270C4×D59—22no—
271C4×D59—81no—
272C4×D59—81no—
273Dic118—21no—
274Dic118C4×Q812yes—
275C8×C59—21no—
276C8×C59—21no—
277C8×C59—41no—
278C8×C59—41no—
279C8×C59C22⋊Q812yes—
280C8×C59C22⋊Q812yes—
281C59⋊C8—21no—
282C59⋊C8—21no—
283C59⋊C8—21no—
284C59⋊C8—21no—
285C59⋊C8—22no—
286C59⋊C8—22no—
287#21629—591nomaximal, Sylow
288C22×C59—21no—
289C22×C59—21no—
290C22×C59C2×C4×D411yescharacteristic
291C22×C59#52911yescharacteristic
292C22×C59#53311yescharacteristic
293C2×D59—22no—
294C2×D59—41no—
295C2×D59—41no—
296C4×C59—21no—
297C4×C59—21no—
298C4×C59—21no—
299C4×C59—21no—
300C4×C59—41no—
301C4×C59—41no—
302C4×C59—41no—
303C4×C59—41no—
304C4×C59C2×C4×Q811yescharacteristic
305C4×C59C4×#4111yescharacteristic
306C4×C59C2×C22⋊Q811yescharacteristic
307C4×C59#52511yescharacteristic
308Dic59—22no—
309Dic59—42no—
310Dic59—41no—
311Dic59—41no—
312Dic59—81no—
313#3076—591no—
314#2961D5911yescharacteristic, complemented
315#2875—591no—
316#1986—591no—
317#1950—591no—
318#1922—591no—
319#1922—591no—
320#1866—591no—
321#1866—591no—
322#1806—591no—
323#1773—591no—
324#1772—591no—
325#1771—591no—
326#1765—591no—
327#1764—591no—
328C2×C59—21no—
329C2×C59—21no—
330C2×C59C4×C22⋊Q811yescharacteristic
331C2×C59#295611yescharacteristic
332C2×C59#295711yescharacteristic
333D59—42no—
334C2×#131—591no—
335C2×#131—591no—
336#533C2×D5911yescharacteristic
337C4×#41—591no—
338#479—591no—
339#479—591no—
340#478—591no—
341#478—591no—
342#477—591no—
343#476—591no—
344#475—591no—
345#474—591no—
346#446—21no—
347#446—21no—
348#446—21no—
349#446—21no—
350C2×#108—591no—
351C2×#108—591no—
352#427—591no—
353#427—591no—
354#424C2×D5911yescharacteristic
355#424C2×D5911yescharacteristic
356#423C2×D5911yescharacteristic
357C2×C4⋊C8—591no—
358C2×#104—591no—
359C2×#104—591no—
360#416—591no—
361#416—591no—
362#405—591no—
363#405—591no—
364#405—1181no—
365#405—1181no—
366#405C2×D5911yescharacteristic
367#405C2×D5911yescharacteristic
368C4×M16—591no—
369C4×M16—1181no—
370C2×#97—591no—
371C2×#97—1181no—
372C2×#97C2×D5911yescharacteristic
373C2×C4×C8—591no—
374C4×C4⋊C4—591no—
375#341—591no—
376#341—591no—
377#339—591no—
378#339—591no—
379#339—591no—
380#339—591no—
381#339—591no—
382#339—591no—
383#336—591no—
384#336—591no—
385C59#2162911yescharacteristic, complemented, Sylow
386C2×#41—591no—
387#131—594no—
388#131—1182no—
389#131—1182no—
390#131—1182no—
391C2×M16—591no—
392C2×M16—591no—
393C2×M16—1181no—
394C2×M16—1181no—
395C2×M16C22×D5911yescharacteristic
396C2×M16C22×D5911yescharacteristic
397C22×C8—591no—
398C22×C8—591no—
399C22×C8—1181no—
400C22×C8—1181no—
401C22×C8C22×D5911yescharacteristic
402C22×C8C22×D5911yescharacteristic
403C4⋊Q8C4×D5911yescharacteristic
404C4⋊Q8C4×D5911yescharacteristic
405#125C4×D5911yescharacteristic
406#125C4×D5911yescharacteristic
407C22⋊Q8—21no—
408C22⋊Q8—21no—
409C4×Q8—21no—
410C4×Q8—21no—
411C4×Q8—591no—
412C4×Q8—591no—
413C4×D4—591no—
414C4×D4—591no—
415C4×D4—1181no—
416C4×D4—1181no—
417#117—591no—
418#117—1181no—
419#117C22×D5911yescharacteristic
420#117C22×D5911yescharacteristic
421C2×C4⋊C4—1181no—
422C2×C42—591no—
423C2×C42—591no—
424C2×C42—1181no—
425C2×C42C22×D5911yescharacteristic
426#108—1182no—
427#108—1182no—
428#107—591no—
429#107—591no—
430#107—591no—
431#107—591no—
432#106—591no—
433#106—591no—
434#106—591no—
435#106—591no—
436C4⋊C8—21no—
437C4⋊C8—21no—
438C4⋊C8—21no—
439C4⋊C8—21no—
440C4⋊C8—21no—
441C4⋊C8—21no—
442C4⋊C8—591no—
443C4⋊C8—591no—
444C4⋊C8—591no—
445C4⋊C8—591no—
446#104—1182no—
447#104—1182no—
448#103—591no—
449#103—591no—
450#103—591no—
451#103—591no—
452#102—591no—
453#102—591no—
454#102—591no—
455#102—591no—
456#97—21no—
457#97—21no—
458#97—1182no—
459#97—1181no—
460#97—1181no—
461#97—1181no—
462#97C22⋊D5911yescharacteristic
463#97C22⋊D5911yescharacteristic
464#97C22⋊D5911yescharacteristic
465#97C22⋊D5911yescharacteristic
466C4×C8—21no—
467C4×C8—21no—
468C4×C8—1182no—
469C4×C8—1181no—
470C4×C8—1181no—
471C4×C8—1181no—
472#95—1181no—
473#41—592no—
474#41—592no—
475#41—1181no—
476#41—1181no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—591no—
480C2×D4—591no—
481C2×D4—1181no—
482C22×C4—1181no—
483C22×C4—1181no—
484C22×C4—1181no—
485C22×C4—1181no—
486C22×C4—1181no—
487C22×C4#1174568511yescharacteristic
488C22×C4#1174568511yescharacteristic
489C22×C4C23×D5911yescharacteristic
490M16—21no—
491M16—21no—
492M16—21no—
493M16—21no—
494M16—592no—
495M16—592no—
496M16—1184no—
497M16—1181no—
498M16—1181no—
499M16—1184no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—591no—
505C2×C8—591no—
506C2×C8—591no—
507C2×C8—591no—
508C2×C8—1184no—
509C2×C8—1181no—
510C2×C8—1181no—
511C2×C8—1181no—
512C2×C8—1181no—
513C2×C8—1181no—
514C2×C8—1181no—
515C2×C8—1184no—
516C2×C8Q8×D5912yes—
517C2×C8#1174568912yes—
518C2×C8C2×C22⋊D5911yescharacteristic
519C2×C8C2×C22⋊D5911yescharacteristic
520C2×C8C2×C22⋊D5911yescharacteristic
521C2×C8C2×C22⋊D5911yescharacteristic
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—591no—
529C4⋊C4—591no—
530C4⋊C4—1181no—
531C4⋊C4—1181no—
532C4⋊C4—2362no—
533C4⋊C4C2×C4×D5911yescharacteristic
534C4⋊C4C2×C4×D5911yescharacteristic
535C4⋊C4C2×C4×D5911yescharacteristic
536C4⋊C4C2×C4×D5911yescharacteristic
537C22⋊C4—21no—
538C22⋊C4—21no—
539C22⋊C4—1181no—
540C22⋊C4—1181no—
541C22⋊C4—1181no—
542C42—21no—
543C42—21no—
544C42—1181no—
545C42—1181no—
546C42—1181no—
547C42—1181no—
548C42—1181no—
549C42—1181no—
550C42—1181no—
551C42C2×C4×D5911yescharacteristic
552C42C2×C4×D5911yescharacteristic
553C42C2×C22⋊D5911yescharacteristic
554C42C2×C22⋊D5911yescharacteristic
555C23—1181no—
556C23C2×#1174568511yescharacteristic
557Q8—81no—
558Q8—81no—
559Q8—592no—
560Q8—1181no—
561D4—592no—
562D4—1182no—
563D4—1182no—
564D4—1181no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—1181no—
572C2×C4—1182no—
573C2×C4—1182no—
574C2×C4—1182no—
575C2×C4—1181no—
576C2×C4—1181no—
577C2×C4—4721no—
578C2×C4—4721no—
579C2×C4—2361no—
580C2×C4—2361no—
581C2×C4—2361no—
582C2×C4—2361no—
583C2×C4—2361no—
584C2×C4C4×C22⋊D5911yescharacteristic
585C2×C4C4×C22⋊D5911yescharacteristic
586C2×C4C4×C22⋊D5911yescharacteristic
587C2×C4C4×C22⋊D5911yescharacteristic
588C2×C4C22×C4×D5911yescharacteristic
589C2×C4C22×C22⋊D5911yescharacteristic
590C2×C4C2×Q8×D5911yescharacteristic
591C2×C4#41×D5911yescharacteristic
592C2×C4#41×D5911yescharacteristic
593C2×C4C2×#1174568911yescharacteristic
594C8—21no—
595C8—21no—
596C8—41no—
597C8—41no—
598C8—1182no—
599C8—1182no—
600C8—1181no—
601C8—1181no—
602C8—1181no—
603C8—1181no—
604C8#1427370312yes—
605C8#1427370312yes—
606C22—21no—
607C22—21no—
608C22—1182no—
609C22—2361no—
610C22—2361no—
611C22C2×C4×C22⋊D5911yescharacteristic
612C22#1683793911yescharacteristic
613C22#1683795611yescharacteristic
614C4—21no—
615C4—21no—
616C4—21no—
617C4—21no—
618C4—41no—
619C4—41no—
620C4—41no—
621C4—41no—
622C4—1182no—
623C4—4721no—
624C4—2362no—
625C4—2361no—
626C4—2361no—
627C4C4×Q8×D5911yescharacteristic
628C4C4×#1174568911yescharacteristic
629C4C2×#1427370311yescharacteristic
630C4#1683790911yescharacteristic
631C2—21no—
632C2—21no—
633C2—2362no—
634C2C4×#1427370311yescharacteristic
635C2#2143300311yescharacteristic
636C2#2143301111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#2961C2
socleC22×C59C2×C4×D4
prime radicalC2×#11745685C23
cosocleC22×C4×C59C24
hypercenter#2961D59
hypocenterC59#21629
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×#97 ◁ #2961

Complements

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

NH ≅ G/Ntype
3. #21425041C2semidirect
4. #21424869C2semidirect
5. #21424692C2semidirect
6. #21424692C2semidirect
10. #21423981C2semidirect
11. #21423976C2semidirect
12. #21423968C2semidirect
15. C59×#2961C2semidirect
19. #16837706C4semidirect
20. #16837706C4semidirect
21. #16837699C4semidirect
22. #16837699C4semidirect
23. #16837694C4semidirect
24. #16837689C4semidirect
25. #16837684C4semidirect
26. #16837679C4semidirect
71. #14273733Q8semidirect
314. #2961D59semidirect
385. C59#21629semidirect

Maximal subgroups

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

subgroupindex
#214338782
#214325212
#214250412
#214248692
#214246922
#214243702
#214241132
#214239812
#214239762
#214239682
#214239422
#214239352
C59×#29612
#2162959