Finite Group Databasebeta

← #28495834

Subgroups — #28495834

Order 15104.

938 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837418C211yesmaximal, characteristic
2C22×#14273655C211yesmaximal, characteristic
3C2×#16837375C211yesmaximal, characteristic
4#21426503C211yesmaximal, characteristic, complemented
5C2×#16837173C211yesmaximal, characteristic, complemented
6C2×#16837158C211yesmaximal, characteristic, complemented
7C2×C59×#339C211yesmaximal, characteristic, complemented
8C22×#11745685C2211yescharacteristic
9C22×#11745664C2211yescharacteristic
10C2×#14273686C2211yescharacteristic
11C2×#14273686C2211yescharacteristic
12#16837418—22no—
13#16837418—22no—
14C2×#14273655—21no—
15C2×#14273655—21no—
16C2×#14273655—22no—
17C2×#14273655C414yescomplemented
18C2×#14273653—22no—
19#16837375—22no—
20#16837375—22no—
21C2×#14273641—22no—
22#16837272—21no—
23#16837268—21no—
24#16837262—22no—
25C4×C4⋊Dic59—22no—
26#16837173—22no—
27#16837158—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×#11745685D412yes—
44C22×Dic118Q811yescharacteristic
45C22×D236Q811yescharacteristic
46C22×C22⋊D59—21no—
47C22×C4×D59—21no—
48C2×#11745664—21no—
49C2×#11745664—21no—
50C2×#11745664—21no—
51C2×#11745664—21no—
52C2×#11745664—21no—
53C2×#11745664C2×C412yes—
54C22×C59⋊C8—21no—
55#14273686—21no—
56#14273686—21no—
57#14273686—21no—
58#14273686—21no—
59#14273686—21no—
60#14273686—21no—
61#14273686—21no—
62#14273686—21no—
63C2×C4⋊Dic59—24no—
64C2×C4⋊Dic59—21no—
65C2×C4⋊Dic59—21no—
66C2×C22⋊Dic59—21no—
67C2×C22⋊Dic59D412yes—
68C2×C4×Dic59—21no—
69C2×C4×Dic59D412yes—
70#14273655—24no—
71#14273655—24no—
72#14273653—28no—
73#14273641—28no—
74C59⋊#95—24no—
75C23×C4×C59—21no—
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×C59D412yes—
83C22×C8×C59—21no—
84#117×C59—21no—
85#117×C59—21no—
86#117×C59—21no—
87#117×C59D412yes—
88C2×C4⋊C4×C59—21no—
89C2×C22⋊C4×C59—21no—
90C2×C42×C59—21no—
91C2×C42×C59—21no—
92C2×C42×C59—21no—
93C2×C42×C59—21no—
94C2×C42×C59C2×C412yes—
95C2×C42×C59D411yescharacteristic
96C2×C42×C59D411yescharacteristic
97C2×C42×C59D412yes—
98C24×C59C2×D411yescharacteristic
99C23×D59—21no—
100C22×C4×C59—21no—
101C22×C4×C59—22no—
102C22×C4×C59—21no—
103C22×C4×C59—22no—
104C22×C4×C59—44no—
105C22×C4×C59—41no—
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—
129#11745685—22no—
130#11745685—22no—
131#11745685—22no—
132#11745685—22no—
133#11745685—22no—
134#11745685—22no—
135#11745685—22no—
136#11745685—22no—
137#11745685—41no—
138#11745685—41no—
139#11745685—41no—
140#11745685—41no—
141#11745685—41no—
142#11745685—41no—
143#11745685—41no—
144#11745685—41no—
145C2×D236—21no—
146C2×D236—21no—
147C2×D236—21no—
148C2×D236—21no—
149C2×D236—21no—
150C2×D236C4⋊C412yescomplemented
151C2×C4×D59—22no—
152C2×C4×D59—22no—
153C2×C4×D59—41no—
154C2×C4×D59—41no—
155C2×C4×D59—41no—
156C2×C4×D59—41no—
157C2×Dic118—21no—
158C2×Dic118—21no—
159C2×Dic118—21no—
160C2×Dic118—21no—
161C2×Dic118—21no—
162C2×Dic118C4⋊C412yescomplemented
163M16×C59—22no—
164M16×C59—22no—
165M16×C59—41no—
166M16×C59—41no—
167C2×C8×C59—22no—
168C2×C8×C59—41no—
169C2×C8×C59—41no—
170C4⋊C4×C59—22no—
171C4⋊C4×C59—41no—
172C22⋊C4×C59—22no—
173C22⋊C4×C59—41no—
174C42×C59—22no—
175C42×C59—22no—
176C42×C59—21no—
177C42×C59—21no—
178C42×C59—22no—
179C42×C59—41no—
180C42×C59C22⋊C412yes—
181C42×C59C22⋊C412yes—
182C22⋊Dic59—22no—
183C22⋊Dic59—22no—
184C22⋊Dic59—41no—
185C22⋊Dic59—41no—
186C4⋊Dic59—48no—
187C4⋊Dic59—41no—
188C4⋊Dic59—41no—
189C4⋊Dic59—41no—
190C4⋊Dic59—41no—
191C4×Dic59—22no—
192C4×Dic59—22no—
193C4×Dic59—41no—
194C4×Dic59—41no—
195#11745664—22no—
196#11745664—22no—
197#11745664—41no—
198#11745664—41no—
199C2×C59⋊C8—22no—
200C2×C59⋊C8—41no—
201C2×C59⋊C8—41no—
202C23×C59—42no—
203C23×C59C4×D411yescharacteristic
204C23×C59#12011yescharacteristic
205C23×C59#12011yescharacteristic
206C23×C59#12111yescharacteristic
207C23×C59#12111yescharacteristic
208C23×C59C22⋊Q811yescharacteristic
209C23×C59#12411yescharacteristic
210C22×D59—22no—
211C22×D59—41no—
212C22×D59—41no—
213C22×D59—82no—
214C2×C4×C59—24no—
215C2×C4×C59—22no—
216C2×C4×C59—22no—
217C2×C4×C59—44no—
218C2×C4×C59—44no—
219C2×C4×C59—42no—
220C2×C4×C59—42no—
221C2×C4×C59—82no—
222C2×C4×C59C2×C22⋊C411yescharacteristic
223C2×C4×C59C2×C4⋊C411yescharacteristic
224C2×C4×C59#11711yescharacteristic
225C2×C4×C59C4×D411yescharacteristic
226C2×C4×C59C4×D411yescharacteristic
227C2×C4×C59C4×D411yescharacteristic
228C2×C4×C59#12011yescharacteristic
229C2×C4×C59#12111yescharacteristic
230C2×C4×C59#12111yescharacteristic
231C2×C4×C59#12111yescharacteristic
232C2×C4×C59#12111yescharacteristic
233C2×C4×C59#12111yescharacteristic
234C2×C4×C59#12111yescharacteristic
235C2×C4×C59C22⋊Q811yescharacteristic
236C2×C4×C59C22⋊Q811yescharacteristic
237C2×C4×C59C22⋊Q811yescharacteristic
238C2×C4×C59C22⋊Q811yescharacteristic
239C2×C4×C59C22⋊Q811yescharacteristic
240C2×C4×C59#12311yescharacteristic
241C2×C4×C59#12311yescharacteristic
242C2×C4×C59#12311yescharacteristic
243C2×C4×C59#12311yescharacteristic
244C2×C4×C59#12311yescharacteristic
245C2×C4×C59#12411yescharacteristic
246C2×C4×C59#12411yescharacteristic
247C2×C4×C59#12611yescharacteristic
248C2×C4×C59#12611yescharacteristic
249C2×C4×C59#12711yescharacteristic
250C22⋊D59—42no—
251C22⋊D59—42no—
252C22⋊D59—42no—
253C22⋊D59—42no—
254C2×Dic59—22no—
255C2×Dic59—41no—
256C2×Dic59—41no—
257C2×Dic59—44no—
258C2×Dic59—44no—
259C2×Dic59—42no—
260C2×Dic59—42no—
261D236—22no—
262D236—22no—
263D236—41no—
264D236—41no—
265C4×D59—42no—
266C4×D59—42no—
267C4×D59—42no—
268C4×D59—42no—
269Dic118—22no—
270Dic118—22no—
271Dic118—41no—
272Dic118—41no—
273C8×C59—42no—
274C59⋊C8—42no—
275#11081—591nomaximal, Sylow
276C22×C59—22no—
277C22×C59—22no—
278C22×C59—22no—
279C22×C59—41no—
280C22×C59—41no—
281C22×C59—41no—
282C22×C59—41no—
283C22×C59#38511yescharacteristic
284C22×C59#38611yescharacteristic
285C22×C59#38811yescharacteristic
286C22×C59#39211yescharacteristic
287C22×C59#39311yescharacteristic
288C22×C59#39411yescharacteristic
289C22×C59#39611yescharacteristic
290C2×D59—42no—
291C2×D59—82no—
292C2×D59—82no—
293C2×D59—82no—
294C4×C59—24no—
295C4×C59—42no—
296C4×C59—82no—
297C4×C59#38011yescharacteristic
298C4×C59#38511yescharacteristic
299C4×C59#38811yescharacteristic
300C4×C59#39011yescharacteristic
301C4×C59#39411yescharacteristic
302C4×C59#39611yescharacteristic
303C4×C59#39711yescharacteristic
304C4×C59#39911yescharacteristic
305Dic59—42no—
306Dic59—82no—
307Dic59—82no—
308C2×#421—591no—
309C22×#104—591no—
310C2×#410—591no—
311#2285—591no—
312C2×#344—591no—
313C2×#339D5911yescharacteristic, complemented
314C2×H(3,ℤ/4)—591no—
315C2×C59—21no—
316C2×C59—21no—
317C2×C59—21no—
318C2×C59—21no—
319C2×C59—21no—
320C2×C59—21no—
321C2×C59#143911yescharacteristic
322C2×C59#203112yes—
323D59—82no—
324C22×#41—591no—
325C22×M16—591no—
326C22×M16C2×D5911yescharacteristic
327C2×#117—591no—
328C2×#117—591no—
329C2×#117C2×D5911yescharacteristic
330C22×C42C2×D5911yescharacteristic
331#421—1182no—
332#421—1182no—
333C2×#104—594no—
334C2×#104—1182no—
335C2×#104—1181no—
336C2×#104—1181no—
337C2×#104—1182no—
338#410—1182no—
339#410—1182no—
340C2×#99—1182no—
341#384—1181no—
342#382—1181no—
343#380—1182no—
344C4×C4⋊C4—1182no—
345#344—1182no—
346#339—22no—
347H(3,ℤ/4)—1182no—
348C59#1108111yescharacteristic, complemented, Sylow
349C2×#41—592no—
350C2×#41—592no—
351C2×#41—1181no—
352C2×#41—1181no—
353C2×#41—1181no—
354C2×#41—1181no—
355C2×#41—1181no—
356C2×#41—1181no—
357C2×#41—1181no—
358C2×#41—1181no—
359C2×#41—1181no—
360C2×#41—1181no—
361C22×Q8—591no—
362C22×D4—591no—
363C22×D4—1181no—
364C23×C4—21no—
365C23×C4—1181no—
366C23×C4C22×D5911yescharacteristic
367C2×M16—21no—
368C2×M16—21no—
369C2×M16—21no—
370C2×M16—21no—
371C2×M16—21no—
372C2×M16—592no—
373C2×M16—1181no—
374C2×M16—1181no—
375C2×M16—1181no—
376C2×M16—1181no—
377C2×M16—1181no—
378C2×M16D23612yes—
379C22×C8—21no—
380C22×C8—1181no—
381#117—21no—
382#117—21no—
383#117—21no—
384#117—1181no—
385#117—1181no—
386#117—1181no—
387#117—1181no—
388#117—1181no—
389#117—1181no—
390#117—1181no—
391#117—1181no—
392#117D23612yes—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—1184no—
395C2×C4⋊C4—1181no—
396C2×C4⋊C4—1181no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—592no—
399C2×C22⋊C4—1181no—
400C2×C42—21no—
401C2×C42—21no—
402C2×C42—21no—
403C2×C42—21no—
404C2×C42—592no—
405C2×C42—1181no—
406C2×C42C4×D5912yes—
407C2×C42D23611yescharacteristic
408C2×C42D23611yescharacteristic
409C2×C42C22⋊D5912yes—
410#104—1188no—
411#104—1184no—
412#104—1184no—
413#99—1188no—
414#95—1184no—
415C24—1181no—
416C24D4×D5911yescharacteristic
417#41—1182no—
418#41—1182no—
419#41—1182no—
420#41—1182no—
421#41—1182no—
422#41—1182no—
423#41—1182no—
424#41—1182no—
425#41—2361no—
426#41—2361no—
427#41—2361no—
428#41—2361no—
429#41—2361no—
430#41—2361no—
431#41—2361no—
432#41—2361no—
433C2×Q8—592no—
434C2×Q8—1181no—
435C2×Q8—1181no—
436C2×Q8—1181no—
437C2×Q8—1181no—
438C2×Q8—1181no—
439C2×D4—592no—
440C2×D4—1182no—
441C2×D4—1182no—
442C2×D4—1181no—
443C2×D4—1181no—
444C2×D4—1181no—
445C2×D4—1181no—
446C2×D4—1181no—
447C2×D4—2361no—
448C2×D4—2361no—
449C2×D4—2361no—
450C2×D4—2361no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—44no—
456C22×C4—41no—
457C22×C4—1181no—
458C22×C4—1182no—
459C22×C4—1182no—
460C22×C4—1182no—
461C22×C4—1182no—
462C22×C4—2361no—
463C22×C4—2361no—
464C22×C4—2361no—
465C22×C4—2361no—
466C22×C4C2×C4×D5911yescharacteristic
467C22×C4C2×D23611yescharacteristic
468C22×C4C2×D23611yescharacteristic
469C22×C4C2×D23611yescharacteristic
470C22×C4#1174568511yescharacteristic
471C22×C4#1174568511yescharacteristic
472C22×C4D4×D5911yescharacteristic
473C22×C4D4×D5911yescharacteristic
474C22×C4#1174568711yescharacteristic
475C22×C4#1174568711yescharacteristic
476C22×C4#1174568711yescharacteristic
477C22×C4Q8×D5911yescharacteristic
478C22×C4#1174568911yescharacteristic
479C22×C4C2×C22⋊D5911yescharacteristic
480M16—22no—
481M16—22no—
482M16—41no—
483M16—41no—
484M16—1182no—
485M16—1182no—
486M16—2361no—
487M16—2361no—
488C2×C8—22no—
489C2×C8—41no—
490C2×C8—41no—
491C2×C8—1182no—
492C2×C8—2361no—
493C2×C8—2361no—
494C4⋊C4—22no—
495C4⋊C4—41no—
496C4⋊C4—2368no—
497C4⋊C4—2361no—
498C4⋊C4—2361no—
499C4⋊C4—2361no—
500C4⋊C4—2361no—
501C22⋊C4—22no—
502C22⋊C4—41no—
503C22⋊C4—1182no—
504C22⋊C4—1182no—
505C22⋊C4—2361no—
506C22⋊C4—2361no—
507C42—22no—
508C42—22no—
509C42—21no—
510C42—21no—
511C42—22no—
512C42—41no—
513C42—1182no—
514C42—1182no—
515C42—2361no—
516C42—2361no—
517C42(C2×D59)⋊C412yes—
518C42(C2×D59)⋊C412yes—
519C23—42no—
520C23—1182no—
521C23—4722no—
522C23—2361no—
523C23—2361no—
524C23(C22⋊D59)⋊C411yescharacteristic
525C23#1427369711yescharacteristic
526C23#1427369711yescharacteristic
527C23#1427369911yescharacteristic
528C23#1427370211yescharacteristic
529C23#1427370511yescharacteristic
530C23#1427371311yescharacteristic
531Q8—1182no—
532Q8—1182no—
533Q8—2361no—
534Q8—2361no—
535D4—1182no—
536D4—1182no—
537D4—2362no—
538D4—2362no—
539D4—2362no—
540D4—2362no—
541D4—2361no—
542D4—2361no—
543C2×C4—24no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—44no—
547C2×C4—44no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—82no—
551C2×C4—1182no—
552C2×C4—2364no—
553C2×C4—2364no—
554C2×C4—2362no—
555C2×C4—2362no—
556C2×C4—2361no—
557C2×C4—2361no—
558C2×C4—2362no—
559C2×C4—2362no—
560C2×C4—2362no—
561C2×C4—2362no—
562C2×C4C2×(C2×D59)⋊C411yescharacteristic
563C2×C4C4⋊C4×D5911yescharacteristic
564C2×C4#1427368511yescharacteristic
565C2×C4(C22⋊D59)⋊C411yescharacteristic
566C2×C4C4×D23611yescharacteristic
567C2×C4C4×D23611yescharacteristic
568C2×C4#1427369711yescharacteristic
569C2×C4#1427369811yescharacteristic
570C2×C4#1427369911yescharacteristic
571C2×C4#1427370111yescharacteristic
572C2×C4#1427370111yescharacteristic
573C2×C4#1427370211yescharacteristic
574C2×C4#1427370211yescharacteristic
575C2×C4#1427370311yescharacteristic
576C2×C4#1427370511yescharacteristic
577C2×C4#1427370711yescharacteristic
578C2×C4#1427370711yescharacteristic
579C2×C4#1427370711yescharacteristic
580C2×C4#1427370911yescharacteristic
581C2×C4#1427370911yescharacteristic
582C2×C4#1427371111yescharacteristic
583C2×C4#1427371111yescharacteristic
584C2×C4#1427371111yescharacteristic
585C2×C4#1427371311yescharacteristic
586C2×C4#1427371511yescharacteristic
587C2×C4#1427372211yescharacteristic
588C2×C4#1427372211yescharacteristic
589C2×C4#1427372411yescharacteristic
590C8—42no—
591C8—2362no—
592C22—22no—
593C22—22no—
594C22—22no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—4722no—
600C22—4722no—
601C22—4722no—
602C22—2362no—
603C22#1683727611yescharacteristic
604C22#1683727911yescharacteristic
605C22#1683729411yescharacteristic
606C22#1683731211yescharacteristic
607C22#1683731511yescharacteristic
608C22#1683731811yescharacteristic
609C22#1683732411yescharacteristic
610C4—24no—
611C4—42no—
612C4—82no—
613C4—4722no—
614C4—4722no—
615C4—2362no—
616C4#1683725911yescharacteristic
617C4#1683727611yescharacteristic
618C4#1683729411yescharacteristic
619C4#1683730411yescharacteristic
620C4#1683731811yescharacteristic
621C4#1683732411yescharacteristic
622C4#1683732911yescharacteristic
623C4#1683733911yescharacteristic
624C2—21no—
625C2—21no—
626C2—21no—
627C2—21no—
628C2—21no—
629C2—21no—
630C2—4722no—
631C2#2142234211yescharacteristic
632C2#2142526912yes—
subgroupG/H
centerC2×C4#14273713
commutatorC22×C4×C59C22×C4
FrattiniC23×C4C22×D59
FittingC2×C59×#339C2
socleC22×C59#393
prime radicalC22×#11745685C22
cosocleC23×C4×C59C23
hypercenterC2×#339D59
hypocenterC59#11081
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
4. #21426503C2semidirect
5. C2×#16837173C2semidirect
6. C2×#16837158C2semidirect
7. C2×C59×#339C2semidirect
17. C2×#14273655C4semidirect
150. C2×D236C4⋊C4semidirect
162. C2×Dic118C4⋊C4semidirect
313. C2×#339D59semidirect
348. C59#11081semidirect

Maximal subgroups

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

subgroupindex
C2×#168374182
C22×#142736552
C2×#168373752
#214265032
C2×#168371732
C2×#168371582
C2×C59×#3392
#1108159