Finite Group Databasebeta

← #28495945

Subgroups — #28495945

Order 15104.

882 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837438C211yesmaximal, characteristic, complemented
2C2×#16837375C211yesmaximal, characteristic
3C2×#16837375C211yesmaximal, characteristic
4C2×#16837370C211yesmaximal, characteristic
5#21423812C211yesmaximal, characteristic, complemented
6C2×#16837159C211yesmaximal, characteristic, complemented
7C2×C59×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
8C22×#11745685C2211yescharacteristic
9C23×C59⋊C8C2211yescharacteristic
10C2×#14273686C2211yescharacteristic
11C2×#14273686C2211yescharacteristic
12#16837438—22no—
13#16837438—22no—
14C2×#14273660—21no—
15C2×#14273658—21no—
16#16837375—22no—
17#16837375—22no—
18#16837375—22no—
19#16837375—22no—
20C2×#14273641—22no—
21C2×#14273641—22no—
22#16837370—22no—
23#16837370—21no—
24#16837370—21no—
25C2×(C2×D59)⋊C8C414yescomplemented
26#16837164—22no—
27#16837159—22no—
28C22×M16×C59C2211yescharacteristic
29C2×#117×C59C2211yescharacteristic
30C2×#117×C59C2211yescharacteristic
31C59×H(3,ℤ/4)—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×#11745685—21no—
43C2×#11745685—21no—
44C22×Dic118Q811yescharacteristic
45C22×D236Q811yescharacteristic
46C22×C22⋊D59D412yes—
47C22×C4×D59C2×C412yes—
48C22×C59⋊C8—21no—
49C22×C59⋊C8—21no—
50C22×C59⋊C8—21no—
51C22×C59⋊C8—21no—
52C22×C59⋊C8C2×C412yes—
53C22×C59⋊C8D412yes—
54C22×C59⋊C8D411yescharacteristic
55C22×C59⋊C8D411yescharacteristic
56#14273686—21no—
57#14273686—21no—
58#14273686—21no—
59#14273686—21no—
60#14273686—21no—
61#14273686—21no—
62#14273686D412yes—
63#14273686D412yes—
64C2×C4⋊Dic59—21no—
65C2×C4⋊Dic59—21no—
66C2×C22⋊Dic59—21no—
67C2×C22⋊Dic59—21no—
68C2×C4×Dic59—21no—
69C2×C4×Dic59—21no—
70#14273660—24no—
71#14273658—24no—
72#14273641—28no—
73#14273641—28no—
74(C2×D59)⋊C8—24no—
75(C2×D59)⋊C8—24no—
76C23×C4×C59C2311yescharacteristic
77C2×M16×C59—21no—
78C2×M16×C59—21no—
79C2×M16×C59—21no—
80C2×M16×C59—21no—
81C2×M16×C59—21no—
82C2×M16×C59—21no—
83C22×C8×C59C2×C412yes—
84#117×C59—21no—
85#117×C59—21no—
86#117×C59—21no—
87#117×C59—21no—
88#117×C59—21no—
89#117×C59—21no—
90#117×C59D412yes—
91#117×C59D412yes—
92C2×C4⋊C4×C59—21no—
93C2×C4⋊C4×C59—21no—
94C2×C22⋊C4×C59—21no—
95C2×C22⋊C4×C59—21no—
96C2×C42×C59—21no—
97C2×C42×C59—21no—
98C24×C59C2×D411yescharacteristic
99C23×D59C4⋊C412yes—
100C22×C4×C59—41no—
101C22×C4×C59—41no—
102C22×C4×C59C22×C411yescharacteristic
103C22×C4×C59C2×D411yescharacteristic
104C22×C4×C59C2×D411yescharacteristic
105C22×C4×C59C2×D411yescharacteristic
106C22×C4×C59C2×D411yescharacteristic
107C22×C4×C59C2×D411yescharacteristic
108C22×C4×C59C2×D411yescharacteristic
109C22×C4×C59C2×Q811yescharacteristic
110C22×C4×C59#4111yescharacteristic
111C22×C4×C59#4111yescharacteristic
112C22×C4×C59#4111yescharacteristic
113C22×C4×C59#4111yescharacteristic
114C22×C4×C59#4111yescharacteristic
115C22×C4×C59#4111yescharacteristic
116C2×C22⋊D59—22no—
117C2×C22⋊D59—22no—
118C2×C22⋊D59—22no—
119C2×C22⋊D59—22no—
120C2×C22⋊D59—22no—
121C2×C22⋊D59—22no—
122C22×Dic59—41no—
123C22×Dic59—41no—
124C22×Dic59C4⋊C412yes—
125#11745685—41no—
126#11745685—41no—
127#11745685—41no—
128#11745685—41no—
129#11745685—41no—
130#11745685—41no—
131#11745685—41no—
132#11745685—41no—
133#11745685—41no—
134#11745685—41no—
135#11745685—41no—
136#11745685—41no—
137#11745685—41no—
138#11745685—41no—
139#11745685—41no—
140#11745685—41no—
141C2×D236—21no—
142C2×D236—21no—
143C2×D236—21no—
144C2×D236—21no—
145C2×D236—21no—
146C2×D236—21no—
147C2×C4×D59—22no—
148C2×C4×D59—22no—
149C2×C4×D59—22no—
150C2×C4×D59—22no—
151C2×C4×D59—22no—
152C2×C4×D59—22no—
153C2×Dic118—21no—
154C2×Dic118—21no—
155C2×Dic118—21no—
156C2×Dic118—21no—
157C2×Dic118—21no—
158C2×Dic118—21no—
159M16×C59—41no—
160M16×C59—41no—
161M16×C59—41no—
162M16×C59—41no—
163C2×C8×C59—22no—
164C2×C8×C59—22no—
165C2×C8×C59—22no—
166C4⋊C4×C59—22no—
167C4⋊C4×C59—22no—
168C4⋊C4×C59—41no—
169C4⋊C4×C59—41no—
170C22⋊C4×C59—22no—
171C22⋊C4×C59—22no—
172C22⋊C4×C59—41no—
173C22⋊C4×C59—41no—
174C42×C59—22no—
175C42×C59—22no—
176C42×C59—41no—
177C42×C59—41no—
178C22⋊Dic59—22no—
179C22⋊Dic59—22no—
180C22⋊Dic59—41no—
181C22⋊Dic59—41no—
182C4⋊Dic59—22no—
183C4⋊Dic59—22no—
184C4⋊Dic59—41no—
185C4⋊Dic59—41no—
186C4×Dic59—22no—
187C4×Dic59—22no—
188C4×Dic59—41no—
189C4×Dic59—41no—
190C2×C59⋊C8—22no—
191C2×C59⋊C8—22no—
192C2×C59⋊C8—21no—
193C2×C59⋊C8—21no—
194C2×C59⋊C8—22no—
195C2×C59⋊C8—22no—
196C2×C59⋊C8—21no—
197C2×C59⋊C8—21no—
198C2×C59⋊C8C22⋊C412yes—
199C2×C59⋊C8C22⋊C412yes—
200C23×C59—42no—
201C23×C59C2×C4⋊C411yescharacteristic
202C23×C59#12011yescharacteristic
203C23×C59#12011yescharacteristic
204C23×C59#12111yescharacteristic
205C23×C59#12111yescharacteristic
206C23×C59#12311yescharacteristic
207C23×C59#12311yescharacteristic
208C22×D59—22no—
209C22×D59—22no—
210C22×D59—22no—
211C22×D59—44no—
212C2×C4×C59—42no—
213C2×C4×C59—42no—
214C2×C4×C59—82no—
215C2×C4×C59—82no—
216C2×C4×C59C2×C22⋊C411yescharacteristic
217C2×C4×C59#11711yescharacteristic
218C2×C4×C59C4×D411yescharacteristic
219C2×C4×C59C4×D411yescharacteristic
220C2×C4×C59C4×D411yescharacteristic
221C2×C4×C59C4×D411yescharacteristic
222C2×C4×C59#12011yescharacteristic
223C2×C4×C59#12111yescharacteristic
224C2×C4×C59#12111yescharacteristic
225C2×C4×C59#12111yescharacteristic
226C2×C4×C59#12111yescharacteristic
227C2×C4×C59#12111yescharacteristic
228C2×C4×C59#12111yescharacteristic
229C2×C4×C59C22⋊Q811yescharacteristic
230C2×C4×C59C22⋊Q811yescharacteristic
231C2×C4×C59C22⋊Q811yescharacteristic
232C2×C4×C59C22⋊Q811yescharacteristic
233C2×C4×C59C22⋊Q811yescharacteristic
234C2×C4×C59C22⋊Q811yescharacteristic
235C2×C4×C59#12311yescharacteristic
236C2×C4×C59#12311yescharacteristic
237C2×C4×C59#12311yescharacteristic
238C2×C4×C59#12411yescharacteristic
239C2×C4×C59#12411yescharacteristic
240C2×C4×C59#12411yescharacteristic
241C2×C4×C59#12611yescharacteristic
242C2×C4×C59#12611yescharacteristic
243C2×C4×C59#12711yescharacteristic
244C22⋊D59—42no—
245C22⋊D59—42no—
246C22⋊D59—42no—
247C22⋊D59—42no—
248C2×Dic59—22no—
249C2×Dic59—22no—
250C2×Dic59—22no—
251C2×Dic59—42no—
252C2×Dic59—42no—
253C2×Dic59—82no—
254C2×Dic59—82no—
255D236—41no—
256D236—41no—
257D236—41no—
258D236—41no—
259C4×D59—42no—
260C4×D59—42no—
261C4×D59—42no—
262C4×D59—42no—
263Dic118—41no—
264Dic118—41no—
265Dic118—41no—
266Dic118—41no—
267C8×C59—42no—
268C59⋊C8—22no—
269C59⋊C8—22no—
270#11098—591nomaximal, Sylow
271C22×C59—22no—
272C22×C59—22no—
273C22×C59—22no—
274C22×C59—41no—
275C22×C59—41no—
276C22×C59—41no—
277C22×C59—41no—
278C22×C59#38011yescharacteristic
279C22×C59#38511yescharacteristic
280C22×C59#38511yescharacteristic
281C22×C59#39211yescharacteristic
282C22×C59#39411yescharacteristic
283C22×C59#39411yescharacteristic
284C22×C59#39711yescharacteristic
285C2×D59—44no—
286C2×D59—42no—
287C2×D59—82no—
288C2×D59—82no—
289C4×C59—82no—
290C4×C59—82no—
291C4×C59#38611yescharacteristic
292C4×C59#38811yescharacteristic
293C4×C59#38811yescharacteristic
294C4×C59#39011yescharacteristic
295C4×C59#39311yescharacteristic
296C4×C59#39611yescharacteristic
297C4×C59#39611yescharacteristic
298C4×C59#39911yescharacteristic
299Dic59—42no—
300Dic59—82no—
301Dic59—82no—
302C2×#427—591no—
303C2×#410—591no—
304C2×#410—591no—
305C2×#408—591no—
306#1735—591no—
307C2×H(3,ℤ/4)—591no—
308C2×H(3,ℤ/4)D5911yescharacteristic, complemented
309C2×C59—21no—
310C2×C59—21no—
311C2×C59—21no—
312C2×C59—21no—
313C2×C59—21no—
314C2×C59—21no—
315C2×C59#143911yescharacteristic
316C2×C59#181212yes—
317D59—82no—
318C22×#41—591no—
319C22×M16C2×D5911yescharacteristic
320C23×C8—591no—
321C2×#117—591no—
322C2×#117—591no—
323C2×#117C2×D5911yescharacteristic
324C2×#117C2×D5911yescharacteristic
325#427—1182no—
326#427—1182no—
327C2×#107—1181no—
328C2×#106—1181no—
329#410—1182no—
330#410—1182no—
331#410—1182no—
332#410—1182no—
333C2×#99—1182no—
334C2×#99—1182no—
335#408—1182no—
336#408—1181no—
337#408—1181no—
338C2×C22⋊C8—594no—
339#340—1182no—
340H(3,ℤ/4)—22no—
341H(3,ℤ/4)—1182no—
342C59#1109811yescharacteristic, complemented, Sylow
343C2×#41—1181no—
344C2×#41—1181no—
345C2×#41—1181no—
346C2×#41—1181no—
347C2×#41—1181no—
348C2×#41—1181no—
349C2×#41—1181no—
350C2×#41—1181no—
351C2×#41—1181no—
352C2×#41—1181no—
353C2×#41—1181no—
354C2×#41—1181no—
355C22×Q8—591no—
356C22×D4—592no—
357C22×D4—591no—
358C23×C4—592no—
359C23×C4C22×D5911yescharacteristic
360C2×M16—21no—
361C2×M16—21no—
362C2×M16—21no—
363C2×M16—21no—
364C2×M16—21no—
365C2×M16—21no—
366C22×C8—592no—
367C22×C8—592no—
368C22×C8—591no—
369C22×C8—591no—
370C22×C8—1181no—
371C22×C8—1181no—
372C22×C8—1181no—
373C22×C8—1181no—
374C22×C8C4×D5912yes—
375#117—21no—
376#117—21no—
377#117—21no—
378#117—21no—
379#117—21no—
380#117—21no—
381#117—592no—
382#117—592no—
383#117—1181no—
384#117—1181no—
385#117—1181no—
386#117—1181no—
387#117—1181no—
388#117—1181no—
389#117D23612yes—
390#117C22⋊D5912yes—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—1181no—
394C2×C4⋊C4—1181no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—1181no—
398C2×C22⋊C4—1181no—
399C2×C42—21no—
400C2×C42—21no—
401C2×C42—1181no—
402C2×C42—1181no—
403#107—1184no—
404#106—1184no—
405#99—1188no—
406#99—1188no—
407C22⋊C8—1184no—
408C22⋊C8—1184no—
409C24—592no—
410C24D4×D5911yescharacteristic
411#41—2361no—
412#41—2361no—
413#41—2361no—
414#41—2361no—
415#41—2361no—
416#41—2361no—
417#41—2361no—
418#41—2361no—
419#41—2361no—
420#41—2361no—
421#41—2361no—
422#41—2361no—
423#41—2361no—
424#41—2361no—
425#41—2361no—
426#41—2361no—
427C2×Q8—1181no—
428C2×Q8—1181no—
429C2×Q8—1181no—
430C2×Q8—1181no—
431C2×Q8—1181no—
432C2×Q8—1181no—
433C2×D4—1182no—
434C2×D4—1182no—
435C2×D4—1182no—
436C2×D4—1182no—
437C2×D4—1182no—
438C2×D4—1182no—
439C2×D4—1181no—
440C2×D4—1181no—
441C2×D4—1181no—
442C2×D4—1181no—
443C2×D4—1181no—
444C2×D4—1181no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—592no—
448C22×C4—1182no—
449C22×C4—1182no—
450C22×C4—1182no—
451C22×C4—1182no—
452C22×C4—1182no—
453C22×C4—1182no—
454C22×C4—2361no—
455C22×C4—2361no—
456C22×C4C2×C4×D5911yescharacteristic
457C22×C4C2×D23611yescharacteristic
458C22×C4#1174568511yescharacteristic
459C22×C4#1174568511yescharacteristic
460C22×C4#1174568511yescharacteristic
461C22×C4#1174568511yescharacteristic
462C22×C4D4×D5911yescharacteristic
463C22×C4D4×D5911yescharacteristic
464C22×C4D4×D5911yescharacteristic
465C22×C4D4×D5911yescharacteristic
466C22×C4#1174568711yescharacteristic
467C22×C4Q8×D5911yescharacteristic
468C22×C4#1174568911yescharacteristic
469C22×C4C2×C22⋊D5911yescharacteristic
470M16—41no—
471M16—41no—
472M16—41no—
473M16—41no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—592no—
478C2×C8—592no—
479C2×C8—1182no—
480C2×C8—1182no—
481C2×C8—1181no—
482C2×C8—1181no—
483C2×C8—1182no—
484C2×C8—1182no—
485C2×C8—1181no—
486C2×C8—1181no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—41no—
490C4⋊C4—41no—
491C4⋊C4—1182no—
492C4⋊C4—1182no—
493C4⋊C4—2361no—
494C4⋊C4—2361no—
495C22⋊C4—22no—
496C22⋊C4—22no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C22⋊C4—1182no—
500C22⋊C4—1182no—
501C22⋊C4—2361no—
502C22⋊C4—2361no—
503C42—22no—
504C42—22no—
505C42—41no—
506C42—41no—
507C42—1182no—
508C42—1182no—
509C42—2361no—
510C42—2361no—
511C23—42no—
512C23—1182no—
513C23—1182no—
514C23—1182no—
515C23—2364no—
516C23C4⋊C4×D5911yescharacteristic
517C23#1427369511yescharacteristic
518C23#1427369711yescharacteristic
519C23#1427370011yescharacteristic
520C23#1427370011yescharacteristic
521C23#1427370911yescharacteristic
522C23#1427371211yescharacteristic
523Q8—2361no—
524Q8—2361no—
525Q8—2361no—
526Q8—2361no—
527D4—2362no—
528D4—2362no—
529D4—2362no—
530D4—2362no—
531D4—2361no—
532D4—2361no—
533D4—2361no—
534D4—2361no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—82no—
538C2×C4—82no—
539C2×C4—1182no—
540C2×C4—1182no—
541C2×C4—1182no—
542C2×C4—4722no—
543C2×C4—4722no—
544C2×C4—2362no—
545C2×C4—2362no—
546C2×C4—2362no—
547C2×C4—2362no—
548C2×C4—2362no—
549C2×C4—2362no—
550C2×C4C22⋊C4×D5911yescharacteristic
551C2×C4#1427368411yescharacteristic
552C2×C4(C22⋊D59)⋊C411yescharacteristic
553C2×C4C4×C22⋊D5911yescharacteristic
554C2×C4#1427368911yescharacteristic
555C2×C4C4×D23611yescharacteristic
556C2×C4#1427369711yescharacteristic
557C2×C4#1427369911yescharacteristic
558C2×C4#1427370011yescharacteristic
559C2×C4#1427370011yescharacteristic
560C2×C4#1427370011yescharacteristic
561C2×C4#1427370111yescharacteristic
562C2×C4#1427370211yescharacteristic
563C2×C4#1427370311yescharacteristic
564C2×C4#1427370511yescharacteristic
565C2×C4#1427370511yescharacteristic
566C2×C4#1427370511yescharacteristic
567C2×C4#1427370511yescharacteristic
568C2×C4#1427370711yescharacteristic
569C2×C4#1427371011yescharacteristic
570C2×C4#1427371211yescharacteristic
571C2×C4#1427371211yescharacteristic
572C2×C4#1427371311yescharacteristic
573C2×C4#1427371311yescharacteristic
574C2×C4#1427371511yescharacteristic
575C2×C4#1427372111yescharacteristic
576C2×C4#1427372211yescharacteristic
577C2×C4#1427372311yescharacteristic
578C8—42no—
579C8—1182no—
580C8—1182no—
581C22—22no—
582C22—22no—
583C22—22no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—4722no—
589C22—4722no—
590C22—2362no—
591C22—2364no—
592C22#1683726111yescharacteristic
593C22#1683727311yescharacteristic
594C22#1683727611yescharacteristic
595C22#1683731111yescharacteristic
596C22#1683731711yescharacteristic
597C22#1683732011yescharacteristic
598C22#1683733111yescharacteristic
599C4—82no—
600C4—82no—
601C4—4722no—
602C4—4722no—
603C4—2362no—
604C4#1683728011yescharacteristic
605C4#1683729111yescharacteristic
606C4#1683729311yescharacteristic
607C4#1683730211yescharacteristic
608C4#1683731511yescharacteristic
609C4#1683732411yescharacteristic
610C4#1683732611yescharacteristic
611C4#1683733711yescharacteristic
612C2—21no—
613C2—21no—
614C2—21no—
615C2—21no—
616C2—21no—
617C2—21no—
618C2—4722no—
619C2#2142234011yescharacteristic
620C2#2142414112yes—
subgroupG/H
centerC2×C4#14273684
commutatorC22×C4×C59C22×C4
FrattiniC23×C4C22×D59
FittingC2×C59×H(3,ℤ/4)C2
socleC22×C59#380
prime radicalC22×#11745685C22
cosocleC23×C4×C59C23
hypercenterC2×H(3,ℤ/4)D59
hypocenterC59#11098
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C22×M16 ◁ C2×H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
1. C2×#16837438C2semidirect
5. #21423812C2semidirect
6. C2×#16837159C2semidirect
7. C2×C59×H(3,ℤ/4)C2semidirect
25. C2×(C2×D59)⋊C8C4semidirect
308. C2×H(3,ℤ/4)D59semidirect
342. C59#11098semidirect

Maximal subgroups

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

subgroupindex
C2×#168374382
C2×#168373752
C2×#168373702
#214238122
C2×#168371592
C2×C59×H(3,ℤ/4)2
#1109859