Finite Group Databasebeta

← #28495813

Subgroups — #28495813

Order 15104.

1078 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273655C211yesmaximal, characteristic
2C2×#16837404C211yesmaximal, characteristic
3#21426684C211yesmaximal, characteristic
4C2×#16837272C211yesmaximal, characteristic, complemented
5C2×#16837170C211yesmaximal, characteristic, complemented
6#21423817C211yesmaximal, characteristic, complemented
7C2×C59×#339C211yesmaximal, characteristic, complemented
8C22×#11745685C2211yescharacteristic
9C22×#11745664C2211yescharacteristic
10C22×C4⋊Dic59—22no—
11C22×C4⋊Dic59C2211yescharacteristic
12C22×C4⋊Dic59C2211yescharacteristic
13C2×#14273655—22no—
14C2×#14273655—22no—
15C2×#14273655C414yescomplemented
16#16837404—22no—
17#16837404—22no—
18C2×#14273652—21no—
19C2×#14273649—21no—
20#16837308—21no—
21#16837304—21no—
22#16837279—22no—
23#16837272—22no—
24#16837272—22no—
25#16837259—22no—
26#16837170—22no—
27#16837164—22no—
28C22×M16×C59C2211yescharacteristic
29C2×#117×C59C2211yescharacteristic
30C22×C42×C59C2211yescharacteristic
31C59×#339—22no—
32C2×#11745685—21no—
33C2×#11745685—21no—
34C2×#11745685—21no—
35C2×#11745685—21no—
36C2×#11745685—21no—
37C2×#11745685—21no—
38C2×#11745685—21no—
39C2×#11745685—21no—
40C2×#11745685—21no—
41C2×#11745685—21no—
42C2×#11745685C2×C412yes—
43C2×#11745685Q812yes—
44C22×Dic118D411yescharacteristic
45C22×D236D411yescharacteristic
46C22×C22⋊D59—21no—
47C23×Dic59—21no—
48C23×Dic59D412yes—
49C22×C4×D59—21no—
50C2×#11745664—21no—
51C2×#11745664—21no—
52C2×#11745664—21no—
53C2×#11745664—21no—
54C2×#11745664—21no—
55C2×#11745664C2×C412yes—
56C22×C59⋊C8—21no—
57C2×C4⋊Dic59—21no—
58C2×C4⋊Dic59—21no—
59C2×C4⋊Dic59—21no—
60C2×C4⋊Dic59—21no—
61C2×C4⋊Dic59—28no—
62C2×C4⋊Dic59—21no—
63C2×C4⋊Dic59—21no—
64C2×C4⋊Dic59—21no—
65C2×C4⋊Dic59—21no—
66C2×C4⋊Dic59—21no—
67C2×C4⋊Dic59—21no—
68C2×C4⋊Dic59—21no—
69C2×C4⋊Dic59—48no—
70C2×C4⋊Dic59D412yes—
71C2×(C2×D59)⋊C4—24no—
72#14273655—28no—
73#14273652—24no—
74#14273649—24no—
75C59⋊#95—24no—
76C23×C4×C59—21no—
77C23×C4×C59C2311yescharacteristic
78C2×M16×C59—21no—
79C2×M16×C59—21no—
80C2×M16×C59—21no—
81C2×M16×C59—21no—
82C2×M16×C59—21no—
83C2×M16×C59D412yes—
84C22×C8×C59—21no—
85#117×C59—21no—
86#117×C59—21no—
87#117×C59—21no—
88#117×C59—21no—
89C2×C4⋊C4×C59D412yes—
90C2×C22⋊C4×C59—21no—
91C2×C42×C59—21no—
92C2×C42×C59—21no—
93C2×C42×C59—21no—
94C2×C42×C59—21no—
95C2×C42×C59C2×C412yes—
96C2×C42×C59D412yes—
97C2×C42×C59D412yes—
98C24×C59C2×D411yescharacteristic
99C23×D59—21no—
100C22×C4×C59—24no—
101C22×C4×C59—24no—
102C22×C4×C59—22no—
103C22×C4×C59—22no—
104C22×C4×C59—22no—
105C22×C4×C59—22no—
106C22×C4×C59C22×C411yescharacteristic
107C22×C4×C59C2×D411yescharacteristic
108C22×C4×C59C2×D411yescharacteristic
109C22×C4×C59C2×D411yescharacteristic
110C22×C4×C59C2×D411yescharacteristic
111C22×C4×C59C2×D411yescharacteristic
112C22×C4×C59C2×D411yescharacteristic
113C22×C4×C59C2×Q811yescharacteristic
114C22×C4×C59#4111yescharacteristic
115C22×C4×C59#4111yescharacteristic
116C22×C4×C59#4111yescharacteristic
117C22×C4×C59#4111yescharacteristic
118C22×C4×C59#4111yescharacteristic
119C22×C4×C59#4111yescharacteristic
120C2×C22⋊D59—22no—
121C2×C22⋊D59—22no—
122C2×C22⋊D59—41no—
123C2×C22⋊D59—41no—
124C2×C22⋊D59—41no—
125C2×C22⋊D59—41no—
126C22×Dic59—21no—
127C22×Dic59—22no—
128C22×Dic59—22no—
129C22×Dic59—22no—
130C22×Dic59—22no—
131C22×Dic59—44no—
132C22×Dic59—44no—
133C22×Dic59—41no—
134C22×Dic59—41no—
135#11745685—22no—
136#11745685—22no—
137#11745685—22no—
138#11745685—22no—
139#11745685—22no—
140#11745685—22no—
141#11745685—22no—
142#11745685—22no—
143#11745685—41no—
144#11745685—41no—
145#11745685—41no—
146#11745685—41no—
147#11745685—41no—
148#11745685—41no—
149#11745685—41no—
150#11745685—41no—
151C2×D236—21no—
152C2×D236—21no—
153C2×D236—21no—
154C2×D236—21no—
155C2×D236—21no—
156C2×D236C4⋊C412yescomplemented
157C2×C4×D59—22no—
158C2×C4×D59—22no—
159C2×C4×D59—41no—
160C2×C4×D59—41no—
161C2×C4×D59—41no—
162C2×C4×D59—41no—
163C2×Dic118—21no—
164C2×Dic118—21no—
165C2×Dic118—21no—
166C2×Dic118—21no—
167C2×Dic118—21no—
168C2×Dic118C4⋊C412yescomplemented
169M16×C59—22no—
170M16×C59—22no—
171M16×C59—41no—
172M16×C59—41no—
173C2×C8×C59—22no—
174C2×C8×C59—41no—
175C2×C8×C59—41no—
176C4⋊C4×C59—22no—
177C4⋊C4×C59—22no—
178C22⋊C4×C59—41no—
179C22⋊C4×C59—41no—
180C42×C59—22no—
181C42×C59—22no—
182C42×C59—22no—
183C42×C59—41no—
184C42×C59—41no—
185C42×C59C22⋊C414yescomplemented
186(C2×D59)⋊C4—84no—
187C4⋊Dic59—22no—
188C4⋊Dic59—22no—
189C4⋊Dic59—416no—
190C4⋊Dic59—41no—
191C4⋊Dic59—41no—
192C4⋊Dic59—41no—
193C4⋊Dic59—41no—
194C4⋊Dic59—41no—
195C4⋊Dic59—41no—
196#11745664—22no—
197#11745664—22no—
198#11745664—41no—
199#11745664—41no—
200C2×C59⋊C8—22no—
201C2×C59⋊C8—41no—
202C2×C59⋊C8—41no—
203C23×C59—22no—
204C23×C59—22no—
205C23×C59C4×D411yescharacteristic
206C23×C59#12011yescharacteristic
207C23×C59#12011yescharacteristic
208C23×C59#12111yescharacteristic
209C23×C59#12111yescharacteristic
210C23×C59C22⋊Q811yescharacteristic
211C23×C59#12411yescharacteristic
212C22×D59—22no—
213C22×D59—41no—
214C22×D59—41no—
215C22×D59—42no—
216C22×D59—42no—
217C2×C4×C59—24no—
218C2×C4×C59—28no—
219C2×C4×C59—24no—
220C2×C4×C59—28no—
221C2×C4×C59—24no—
222C2×C4×C59—42no—
223C2×C4×C59—42no—
224C2×C4×C59—42no—
225C2×C4×C59C2×C22⋊C411yescharacteristic
226C2×C4×C59C2×C4⋊C411yescharacteristic
227C2×C4×C59#11711yescharacteristic
228C2×C4×C59C4×D411yescharacteristic
229C2×C4×C59C4×D411yescharacteristic
230C2×C4×C59C4×D411yescharacteristic
231C2×C4×C59#12011yescharacteristic
232C2×C4×C59#12111yescharacteristic
233C2×C4×C59#12111yescharacteristic
234C2×C4×C59#12111yescharacteristic
235C2×C4×C59#12111yescharacteristic
236C2×C4×C59#12111yescharacteristic
237C2×C4×C59#12111yescharacteristic
238C2×C4×C59C22⋊Q811yescharacteristic
239C2×C4×C59C22⋊Q811yescharacteristic
240C2×C4×C59C22⋊Q811yescharacteristic
241C2×C4×C59C22⋊Q811yescharacteristic
242C2×C4×C59C22⋊Q811yescharacteristic
243C2×C4×C59#12311yescharacteristic
244C2×C4×C59#12311yescharacteristic
245C2×C4×C59#12311yescharacteristic
246C2×C4×C59#12311yescharacteristic
247C2×C4×C59#12311yescharacteristic
248C2×C4×C59#12411yescharacteristic
249C2×C4×C59#12411yescharacteristic
250C2×C4×C59#12611yescharacteristic
251C2×C4×C59#12611yescharacteristic
252C2×C4×C59#12711yescharacteristic
253C22⋊D59—42no—
254C22⋊D59—42no—
255C22⋊D59—42no—
256C22⋊D59—42no—
257C2×Dic59—22no—
258C2×Dic59—41no—
259C2×Dic59—41no—
260C2×Dic59—44no—
261C2×Dic59—44no—
262C2×Dic59—42no—
263C2×Dic59—42no—
264C2×Dic59—44no—
265C2×Dic59—82no—
266C2×Dic59—82no—
267C2×Dic59—82no—
268D236—22no—
269D236—22no—
270D236—41no—
271D236—41no—
272C4×D59—42no—
273C4×D59—42no—
274C4×D59—42no—
275C4×D59—42no—
276Dic118—22no—
277Dic118—22no—
278Dic118—41no—
279Dic118—41no—
280C8×C59—42no—
281C59⋊C8—42no—
282#11078—591nomaximal, Sylow
283C22×C59—22no—
284C22×C59—22no—
285C22×C59—21no—
286C22×C59—21no—
287C22×C59—21no—
288C22×C59—21no—
289C22×C59—22no—
290C22×C59—22no—
291C22×C59#38511yescharacteristic
292C22×C59#38611yescharacteristic
293C22×C59#38811yescharacteristic
294C22×C59#39211yescharacteristic
295C22×C59#39311yescharacteristic
296C22×C59#39411yescharacteristic
297C22×C59#39611yescharacteristic
298C22×C59#45312yes—
299C22×C59#45612yes—
300C2×D59—44no—
301C2×D59—42no—
302C2×D59—81no—
303C2×D59—81no—
304C2×D59—82no—
305C4×C59—28no—
306C4×C59—82no—
307C4×C59#38011yescharacteristic
308C4×C59#38511yescharacteristic
309C4×C59#38811yescharacteristic
310C4×C59#39011yescharacteristic
311C4×C59#39411yescharacteristic
312C4×C59#39611yescharacteristic
313C4×C59#39711yescharacteristic
314C4×C59#39911yescharacteristic
315Dic59—42no—
316Dic59—82no—
317Dic59—82no—
318C22×#104—591no—
319C2×#417—591no—
320#2311—591no—
321C2×#384—591no—
322C2×#343—591no—
323#1736—591no—
324C2×#339D5911yescharacteristic, complemented
325C2×C59—21no—
326C2×C59—21no—
327C2×C59—21no—
328C2×C59—21no—
329C2×C59#143911yescharacteristic
330C2×C59#185912yes—
331C2×C59#200211yescharacteristic
332C2×C59#200511yescharacteristic
333C2×C59#203912yes—
334D59—82no—
335C22×#41—591no—
336C22×M16—591no—
337C22×M16C2×D5911yescharacteristic
338C2×#117C2×D5911yescharacteristic
339C22×C4⋊C4—591no—
340C22×C4⋊C4—591no—
341C22×C4⋊C4—1182no—
342C22×C42C2×D5911yescharacteristic
343C2×#104—594no—
344C2×#104—1182no—
345C2×#104—1182no—
346#417—1182no—
347#417—1182no—
348C2×#103—1181no—
349C2×#102—1181no—
350#391—1181no—
351#390—1181no—
352#386—1182no—
353#384—1182no—
354#384—1182no—
355#380—1182no—
356#343—1182no—
357#340—1182no—
358#339—22no—
359C59#1107811yescharacteristic, complemented, Sylow
360C2×#41—592no—
361C2×#41—592no—
362C2×#41—1181no—
363C2×#41—1181no—
364C2×#41—1181no—
365C2×#41—1181no—
366C2×#41—1181no—
367C2×#41—1181no—
368C2×#41—1181no—
369C2×#41—1181no—
370C2×#41—1181no—
371C2×#41—1181no—
372C22×Q8—591no—
373C22×D4—591no—
374C22×D4—1181no—
375C23×C4—21no—
376C23×C4—592no—
377C23×C4—1181no—
378C23×C4—1181no—
379C23×C4C22×D5911yescharacteristic
380C2×M16—21no—
381C2×M16—21no—
382C2×M16—21no—
383C2×M16—21no—
384C2×M16—21no—
385C2×M16—592no—
386C2×M16—1181no—
387C2×M16—1181no—
388C2×M16—1181no—
389C2×M16—1181no—
390C2×M16—1181no—
391C2×M16D23612yes—
392C22×C8—21no—
393C22×C8—1181no—
394#117—21no—
395#117—21no—
396#117—21no—
397#117—21no—
398C2×C4⋊C4—592no—
399C2×C4⋊C4—1181no—
400C2×C4⋊C4—1181no—
401C2×C4⋊C4—1181no—
402C2×C4⋊C4—1181no—
403C2×C4⋊C4—1188no—
404C2×C4⋊C4—1181no—
405C2×C4⋊C4—1181no—
406C2×C4⋊C4—1181no—
407C2×C4⋊C4—1181no—
408C2×C4⋊C4—1181no—
409C2×C4⋊C4—1181no—
410C2×C4⋊C4—1181no—
411C2×C4⋊C4—2368no—
412C2×C4⋊C4D23612yes—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—1184no—
415C2×C42—21no—
416C2×C42—21no—
417C2×C42—21no—
418C2×C42—21no—
419C2×C42C4×D5912yes—
420C2×C42D23612yes—
421C2×C42C22⋊D5912yes—
422#104—1188no—
423#103—1184no—
424#102—1184no—
425#95—1184no—
426C24—1181no—
427C24D4×D5911yescharacteristic
428#41—1182no—
429#41—1182no—
430#41—1182no—
431#41—1182no—
432#41—1182no—
433#41—1182no—
434#41—1182no—
435#41—1182no—
436#41—2361no—
437#41—2361no—
438#41—2361no—
439#41—2361no—
440#41—2361no—
441#41—2361no—
442#41—2361no—
443#41—2361no—
444C2×Q8—592no—
445C2×Q8—1181no—
446C2×Q8—1181no—
447C2×Q8—1181no—
448C2×Q8—1181no—
449C2×Q8—1181no—
450C2×D4—592no—
451C2×D4—1182no—
452C2×D4—1182no—
453C2×D4—1181no—
454C2×D4—1181no—
455C2×D4—1181no—
456C2×D4—1181no—
457C2×D4—1181no—
458C2×D4—2361no—
459C2×D4—2361no—
460C2×D4—2361no—
461C2×D4—2361no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—1181no—
469C22×C4—1182no—
470C22×C4—1182no—
471C22×C4—1182no—
472C22×C4—1182no—
473C22×C4—1182no—
474C22×C4—1182no—
475C22×C4—2364no—
476C22×C4—2361no—
477C22×C4—2361no—
478C22×C4—2364no—
479C22×C4—2361no—
480C22×C4—2361no—
481C22×C4—2361no—
482C22×C4—2361no—
483C22×C4C2×C4×D5911yescharacteristic
484C22×C4C2×D23611yescharacteristic
485C22×C4C2×D23611yescharacteristic
486C22×C4C2×D23611yescharacteristic
487C22×C4#1174568511yescharacteristic
488C22×C4#1174568511yescharacteristic
489C22×C4D4×D5911yescharacteristic
490C22×C4D4×D5911yescharacteristic
491C22×C4#1174568711yescharacteristic
492C22×C4#1174568711yescharacteristic
493C22×C4#1174568711yescharacteristic
494C22×C4Q8×D5911yescharacteristic
495C22×C4#1174568911yescharacteristic
496C22×C4C2×C22⋊D5911yescharacteristic
497M16—22no—
498M16—22no—
499M16—41no—
500M16—41no—
501M16—1182no—
502M16—1182no—
503M16—2361no—
504M16—2361no—
505C2×C8—22no—
506C2×C8—41no—
507C2×C8—41no—
508C2×C8—1182no—
509C2×C8—2361no—
510C2×C8—2361no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—1182no—
514C4⋊C4—1182no—
515C4⋊C4—23616no—
516C4⋊C4—2361no—
517C4⋊C4—2361no—
518C4⋊C4—2361no—
519C4⋊C4—2361no—
520C4⋊C4—2361no—
521C4⋊C4—2361no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—4724no—
525C42—22no—
526C42—22no—
527C42—22no—
528C42—41no—
529C42—41no—
530C42(C2×D59)⋊C414yescomplemented
531C23—22no—
532C23—22no—
533C23—1182no—
534C23—2361no—
535C23—2362no—
536C23—2361no—
537C23—2362no—
538C23(C22⋊D59)⋊C411yescharacteristic
539C23#1427369711yescharacteristic
540C23#1427369711yescharacteristic
541C23#1427369911yescharacteristic
542C23#1427370211yescharacteristic
543C23#1427370511yescharacteristic
544C23#1427371311yescharacteristic
545Q8—1182no—
546Q8—1182no—
547Q8—2361no—
548Q8—2361no—
549D4—1182no—
550D4—1182no—
551D4—2362no—
552D4—2362no—
553D4—2362no—
554D4—2362no—
555D4—2361no—
556D4—2361no—
557C2×C4—24no—
558C2×C4—28no—
559C2×C4—28no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—1182no—
566C2×C4—4722no—
567C2×C4—4722no—
568C2×C4—4722no—
569C2×C4—2364no—
570C2×C4—2364no—
571C2×C4—2362no—
572C2×C4—2362no—
573C2×C4—2364no—
574C2×C4—2361no—
575C2×C4—2361no—
576C2×C4—2362no—
577C2×C4—2362no—
578C2×C4—2362no—
579C2×C4—2362no—
580C2×C4C2×(C2×D59)⋊C411yescharacteristic
581C2×C4C4⋊C4×D5911yescharacteristic
582C2×C4#1427368511yescharacteristic
583C2×C4(C22⋊D59)⋊C411yescharacteristic
584C2×C4C4×D23611yescharacteristic
585C2×C4C4×D23611yescharacteristic
586C2×C4#1427369711yescharacteristic
587C2×C4#1427369811yescharacteristic
588C2×C4#1427369911yescharacteristic
589C2×C4#1427370111yescharacteristic
590C2×C4#1427370111yescharacteristic
591C2×C4#1427370211yescharacteristic
592C2×C4#1427370211yescharacteristic
593C2×C4#1427370311yescharacteristic
594C2×C4#1427370511yescharacteristic
595C2×C4#1427370711yescharacteristic
596C2×C4#1427370711yescharacteristic
597C2×C4#1427370711yescharacteristic
598C2×C4#1427370911yescharacteristic
599C2×C4#1427370911yescharacteristic
600C2×C4#1427371111yescharacteristic
601C2×C4#1427371111yescharacteristic
602C2×C4#1427371111yescharacteristic
603C2×C4#1427371311yescharacteristic
604C2×C4#1427371511yescharacteristic
605C2×C4#1427372211yescharacteristic
606C2×C4#1427372211yescharacteristic
607C2×C4#1427372411yescharacteristic
608C8—42no—
609C8—2362no—
610C22—22no—
611C22—22no—
612C22—22no—
613C22—22no—
614C22—21no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—4722no—
619C22—4721no—
620C22—4721no—
621C22—2362no—
622C22—2364no—
623C22#1683727611yescharacteristic
624C22#1683727911yescharacteristic
625C22#1683729411yescharacteristic
626C22#1683731211yescharacteristic
627C22#1683731511yescharacteristic
628C22#1683731811yescharacteristic
629C22#1683732411yescharacteristic
630C22#1683757112yes—
631C22#1683758612yes—
632C4—28no—
633C4—82no—
634C4—4722no—
635C4—4722no—
636C4—2362no—
637C4#1683725911yescharacteristic
638C4#1683727611yescharacteristic
639C4#1683729411yescharacteristic
640C4#1683730411yescharacteristic
641C4#1683731811yescharacteristic
642C4#1683732411yescharacteristic
643C4#1683732911yescharacteristic
644C4#1683733911yescharacteristic
645C2—21no—
646C2—21no—
647C2—21no—
648C2—21no—
649C2—4722no—
650C2#2142234211yescharacteristic
651C2#2142432312yes—
652C2#2142511411yescharacteristic
653C2#2142513511yescharacteristic
654C2#2142531912yes—
subgroupG/H
centerC23#14273697
commutatorC22×C4×C59C22×C4
FrattiniC23×C4C22×D59
FittingC2×C59×#339C2
socleC23×C59#120
prime radicalC22×#11745685C22
cosocleC23×C4×C59C23
hypercenterC2×#339D59
hypocenterC59#11078
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
4. C2×#16837272C2semidirect
5. C2×#16837170C2semidirect
6. #21423817C2semidirect
7. C2×C59×#339C2semidirect
15. C2×#14273655C4semidirect
156. C2×D236C4⋊C4semidirect
168. C2×Dic118C4⋊C4semidirect
185. C42×C59C22⋊C4semidirect
324. C2×#339D59semidirect
359. C59#11078semidirect
530. C42(C2×D59)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#142736552
C2×#168374042
#214266842
C2×#168372722
C2×#168371702
#214238172
C2×C59×#3392
#1107859