Finite Group Databasebeta

← #28495867

Subgroups — #28495867

Order 15104.

866 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837430C211yesmaximal, characteristic, complemented
2C2×#16837418C211yesmaximal, characteristic
3C2×#16837396C211yesmaximal, characteristic
4C2×#16837384C211yesmaximal, characteristic
5C2×#16837166C211yesmaximal, characteristic, complemented
6C2×#16837158C211yesmaximal, characteristic, complemented
7C2×C59×#344C211yesmaximal, characteristic, complemented
8C22×#11745685C2211yescharacteristic
9C22×#11745664C2211yescharacteristic
10C23×C59⋊C8C2211yescharacteristic
11C2×#14273686C2211yescharacteristic
12#16837430—22no—
13#16837430—22no—
14C2×Dic59⋊C8—22no—
15#16837418—22no—
16#16837418C414yescomplemented
17C2×#14273653—22no—
18#16837396—22no—
19#16837396—22no—
20C2×#14273650—21no—
21C2×#14273647—21no—
22#16837384—22no—
23#16837384—22no—
24C2×#14273645—21no—
25C2×#14273643—21no—
26#16837166—22no—
27#16837158—22no—
28C22×M16×C59C2211yescharacteristic
29C22×M16×C59C2211yescharacteristic
30C2×#117×C59C2211yescharacteristic
31C59×#344—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—
47C22×C4×D59—21no—
48C2×#11745664—21no—
49C2×#11745664—21no—
50C2×#11745664—21no—
51C2×#11745664—21no—
52C2×#11745664—21no—
53C2×#11745664D412yes—
54C22×C59⋊C8—21no—
55C22×C59⋊C8—21no—
56C22×C59⋊C8—21no—
57C22×C59⋊C8—21no—
58C22×C59⋊C8—21no—
59C22×C59⋊C8—21no—
60C22×C59⋊C8—21no—
61C22×C59⋊C8D412yes—
62#14273686—21no—
63#14273686—21no—
64#14273686C2×C412yes—
65#14273686D412yes—
66C2×C4⋊Dic59—21no—
67C2×C22⋊Dic59—21no—
68C2×C4×Dic59D412yes—
69Dic59⋊C8—28no—
70#14273653—28no—
71#14273650—24no—
72#14273647—24no—
73#14273645—24no—
74#14273643—24no—
75C23×C4×C59C2311yescharacteristic
76C2×M16×C59—21no—
77C2×M16×C59—21no—
78C2×M16×C59—21no—
79C2×M16×C59—21no—
80C2×M16×C59—21no—
81C2×M16×C59—21no—
82C2×M16×C59—21no—
83C2×M16×C59—21no—
84C2×M16×C59—21no—
85C2×M16×C59—21no—
86C2×M16×C59C2×C412yes—
87C2×M16×C59D412yes—
88C22×C8×C59—21no—
89C22×C8×C59—21no—
90#117×C59—21no—
91#117×C59—21no—
92#117×C59—21no—
93#117×C59D412yes—
94C2×C4⋊C4×C59—21no—
95C2×C22⋊C4×C59—21no—
96C2×C42×C59—21no—
97C24×C59#4111yescharacteristic
98C23×D59—21no—
99C22×C4×C59—41no—
100C22×C4×C59C22×C411yescharacteristic
101C22×C4×C59C2×D411yescharacteristic
102C22×C4×C59C2×D411yescharacteristic
103C22×C4×C59C2×D411yescharacteristic
104C22×C4×C59C2×D411yescharacteristic
105C22×C4×C59C2×D411yescharacteristic
106C22×C4×C59C2×D411yescharacteristic
107C22×C4×C59C2×D411yescharacteristic
108C22×C4×C59C2×Q811yescharacteristic
109C22×C4×C59#4111yescharacteristic
110C22×C4×C59#4111yescharacteristic
111C22×C4×C59#4111yescharacteristic
112C22×C4×C59#4111yescharacteristic
113C22×C4×C59#4111yescharacteristic
114C2×C22⋊D59—22no—
115C2×C22⋊D59—22no—
116C2×C22⋊D59—41no—
117C2×C22⋊D59—41no—
118C2×C22⋊D59—41no—
119C2×C22⋊D59—41no—
120C22×Dic59—22no—
121C22×Dic59—21no—
122#11745685—22no—
123#11745685—22no—
124#11745685—22no—
125#11745685—22no—
126#11745685—22no—
127#11745685—22no—
128#11745685—22no—
129#11745685—22no—
130#11745685—41no—
131#11745685—41no—
132#11745685—41no—
133#11745685—41no—
134#11745685—41no—
135#11745685—41no—
136#11745685—41no—
137#11745685—41no—
138C2×D236—21no—
139C2×D236—21no—
140C2×D236—21no—
141C2×D236—21no—
142C2×D236—21no—
143C2×D236C4⋊C412yes—
144C2×C4×D59—22no—
145C2×C4×D59—22no—
146C2×C4×D59—41no—
147C2×C4×D59—41no—
148C2×C4×D59—41no—
149C2×C4×D59—41no—
150C2×Dic118—21no—
151C2×Dic118—21no—
152C2×Dic118—21no—
153C2×Dic118—21no—
154C2×Dic118—21no—
155C2×Dic118C4⋊C412yes—
156M16×C59—22no—
157M16×C59—22no—
158M16×C59—22no—
159M16×C59—22no—
160M16×C59—41no—
161M16×C59—41no—
162M16×C59—41no—
163M16×C59—41no—
164C2×C8×C59—22no—
165C2×C8×C59—22no—
166C2×C8×C59—41no—
167C2×C8×C59—41no—
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—41no—
176C22⋊Dic59—22no—
177C22⋊Dic59—22no—
178C4⋊Dic59—22no—
179C4⋊Dic59—22no—
180C4×Dic59—22no—
181C4×Dic59C22⋊C414yes—
182#11745664—22no—
183#11745664—22no—
184#11745664—41no—
185#11745664—41no—
186C2×C59⋊C8—22no—
187C2×C59⋊C8—22no—
188C2×C59⋊C8—22no—
189C2×C59⋊C8—22no—
190C2×C59⋊C8—41no—
191C2×C59⋊C8—41no—
192C2×C59⋊C8—41no—
193C2×C59⋊C8—41no—
194C2×C59⋊C8—41no—
195C2×C59⋊C8—41no—
196C23×C59—42no—
197C23×C59C4×D411yescharacteristic
198C23×C59#12111yescharacteristic
199C23×C59C22⋊Q811yescharacteristic
200C23×C59#12311yescharacteristic
201C23×C59#12311yescharacteristic
202C23×C59#12311yescharacteristic
203C23×C59#12611yescharacteristic
204C22×D59—22no—
205C22×D59—41no—
206C22×D59—41no—
207C22×D59—82no—
208C2×C4×C59—42no—
209C2×C4×C59—82no—
210C2×C4×C59C2×C22⋊C411yescharacteristic
211C2×C4×C59C2×C4⋊C411yescharacteristic
212C2×C4×C59#11711yescharacteristic
213C2×C4×C59C4×D411yescharacteristic
214C2×C4×C59C4×D411yescharacteristic
215C2×C4×C59C4×D411yescharacteristic
216C2×C4×C59#12011yescharacteristic
217C2×C4×C59#12011yescharacteristic
218C2×C4×C59#12011yescharacteristic
219C2×C4×C59#12111yescharacteristic
220C2×C4×C59#12111yescharacteristic
221C2×C4×C59#12111yescharacteristic
222C2×C4×C59#12111yescharacteristic
223C2×C4×C59#12111yescharacteristic
224C2×C4×C59#12111yescharacteristic
225C2×C4×C59#12111yescharacteristic
226C2×C4×C59C22⋊Q811yescharacteristic
227C2×C4×C59C22⋊Q811yescharacteristic
228C2×C4×C59C22⋊Q811yescharacteristic
229C2×C4×C59C22⋊Q811yescharacteristic
230C2×C4×C59C22⋊Q811yescharacteristic
231C2×C4×C59#12311yescharacteristic
232C2×C4×C59#12311yescharacteristic
233C2×C4×C59#12411yescharacteristic
234C2×C4×C59#12411yescharacteristic
235C2×C4×C59#12411yescharacteristic
236C2×C4×C59#12611yescharacteristic
237C2×C4×C59#12711yescharacteristic
238C22⋊D59—42no—
239C22⋊D59—42no—
240C22⋊D59—42no—
241C22⋊D59—42no—
242C2×Dic59—22no—
243C2×Dic59—24no—
244C2×Dic59—44no—
245C2×Dic59—41no—
246C2×Dic59—41no—
247D236—22no—
248D236—22no—
249D236—41no—
250D236—41no—
251C4×D59—42no—
252C4×D59—42no—
253C4×D59—42no—
254C4×D59—42no—
255Dic118—22no—
256Dic118—22no—
257Dic118—41no—
258Dic118—41no—
259C8×C59—42no—
260C8×C59—42no—
261C59⋊C8—42no—
262C59⋊C8—42no—
263#11086—591nomaximal, Sylow
264C22×C59—22no—
265C22×C59—22no—
266C22×C59—22no—
267C22×C59—41no—
268C22×C59—41no—
269C22×C59—41no—
270C22×C59—41no—
271C22×C59#38511yescharacteristic
272C22×C59#38611yescharacteristic
273C22×C59#38811yescharacteristic
274C22×C59#39411yescharacteristic
275C22×C59#39611yescharacteristic
276C22×C59#39711yescharacteristic
277C22×C59#39911yescharacteristic
278C2×D59—42no—
279C2×D59—82no—
280C2×D59—82no—
281C2×D59—82no—
282C4×C59—82no—
283C4×C59#38011yescharacteristic
284C4×C59#38511yescharacteristic
285C4×C59#38811yescharacteristic
286C4×C59#39011yescharacteristic
287C4×C59#39211yescharacteristic
288C4×C59#39311yescharacteristic
289C4×C59#39411yescharacteristic
290C4×C59#39611yescharacteristic
291Dic59—44no—
292Dic59—42no—
293C2×#424—591no—
294C2×#421—591no—
295C2×#416—591no—
296C2×#413—591no—
297C2×#344D5911yescharacteristic, complemented
298C2×#341—591no—
299C2×H(3,ℤ/4)—591no—
300C2×C59—21no—
301C2×C59—21no—
302C2×C59—21no—
303C2×C59—21no—
304C2×C59—21no—
305C2×C59—21no—
306C2×C59#143911yescharacteristic
307C2×C59#208012yes—
308D59—82no—
309C22×#41—591no—
310C22×M16—591no—
311C22×M16C2×D5911yescharacteristic
312C22×M16C2×D5911yescharacteristic
313C23×C8—591no—
314C2×#117—591no—
315C2×#117C2×D5911yescharacteristic
316#424—1182no—
317#424—1182no—
318C2×C4⋊C8—1182no—
319#421—594no—
320#421—1182no—
321C2×#104—1182no—
322#416—1182no—
323#416—1182no—
324C2×#103—1181no—
325C2×#102—1181no—
326#413—1182no—
327#413—1182no—
328C2×#101—1181no—
329C2×#100—1181no—
330#344—22no—
331#341—1182no—
332H(3,ℤ/4)—1182no—
333C59#1108611yescharacteristic, complemented, Sylow
334C2×#41—592no—
335C2×#41—592no—
336C2×#41—1181no—
337C2×#41—1181no—
338C2×#41—1181no—
339C2×#41—1181no—
340C2×#41—1181no—
341C2×#41—1181no—
342C2×#41—1181no—
343C2×#41—1181no—
344C2×#41—1181no—
345C2×#41—1181no—
346C22×Q8—591no—
347C22×D4—591no—
348C22×D4—1181no—
349C23×C4—1181no—
350C23×C4C22×D5911yescharacteristic
351C2×M16—21no—
352C2×M16—21no—
353C2×M16—21no—
354C2×M16—21no—
355C2×M16—21no—
356C2×M16—21no—
357C2×M16—21no—
358C2×M16—21no—
359C2×M16—21no—
360C2×M16—21no—
361C2×M16—592no—
362C2×M16—1181no—
363C2×M16—1181no—
364C2×M16—1181no—
365C2×M16—1181no—
366C2×M16—1181no—
367C2×M16C4×D5912yes—
368C2×M16D23612yes—
369C22×C8—21no—
370C22×C8—21no—
371C22×C8—592no—
372C22×C8—1181no—
373C22×C8—1181no—
374C22×C8—1181no—
375C22×C8—1181no—
376C22×C8—1181no—
377C22×C8—1181no—
378C22×C8—1181no—
379#117—21no—
380#117—21no—
381#117—21no—
382#117—592no—
383#117—592no—
384#117—1181no—
385#117—1181no—
386#117C22⋊D5912yes—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—1181no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—1181no—
391C2×C42—21no—
392C2×C42—592no—
393C4⋊C8—1188no—
394#104—1188no—
395#103—1184no—
396#102—1184no—
397#101—1184no—
398#100—1184no—
399C24—1181no—
400C24#1174568511yescharacteristic
401#41—1182no—
402#41—1182no—
403#41—1182no—
404#41—1182no—
405#41—1182no—
406#41—1182no—
407#41—1182no—
408#41—1182no—
409#41—2361no—
410#41—2361no—
411#41—2361no—
412#41—2361no—
413#41—2361no—
414#41—2361no—
415#41—2361no—
416#41—2361no—
417C2×Q8—592no—
418C2×Q8—1181no—
419C2×Q8—1181no—
420C2×Q8—1181no—
421C2×Q8—1181no—
422C2×Q8—1181no—
423C2×D4—592no—
424C2×D4—1182no—
425C2×D4—1182no—
426C2×D4—1181no—
427C2×D4—1181no—
428C2×D4—1181no—
429C2×D4—1181no—
430C2×D4—1181no—
431C2×D4—2361no—
432C2×D4—2361no—
433C2×D4—2361no—
434C2×D4—2361no—
435C22×C4—41no—
436C22×C4—1181no—
437C22×C4—1182no—
438C22×C4—1182no—
439C22×C4—1182no—
440C22×C4—2361no—
441C22×C4—2361no—
442C22×C4—2361no—
443C22×C4—2361no—
444C22×C4C2×C4×D5911yescharacteristic
445C22×C4C2×D23611yescharacteristic
446C22×C4#1174568511yescharacteristic
447C22×C4#1174568511yescharacteristic
448C22×C4#1174568511yescharacteristic
449C22×C4D4×D5911yescharacteristic
450C22×C4D4×D5911yescharacteristic
451C22×C4D4×D5911yescharacteristic
452C22×C4D4×D5911yescharacteristic
453C22×C4D4×D5911yescharacteristic
454C22×C4#1174568711yescharacteristic
455C22×C4Q8×D5911yescharacteristic
456C22×C4#1174568911yescharacteristic
457C22×C4C2×C22⋊D5911yescharacteristic
458M16—22no—
459M16—22no—
460M16—22no—
461M16—22no—
462M16—41no—
463M16—41no—
464M16—41no—
465M16—41no—
466M16—1182no—
467M16—1182no—
468M16—2361no—
469M16—2361no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—41no—
473C2×C8—41no—
474C2×C8—41no—
475C2×C8—41no—
476C2×C8—1182no—
477C2×C8—1182no—
478C2×C8—1182no—
479C2×C8—1182no—
480C2×C8—2361no—
481C2×C8—2361no—
482C2×C8—2361no—
483C2×C8—2361no—
484C2×C8—2361no—
485C2×C8—2361no—
486C4⋊C4—22no—
487C4⋊C4—41no—
488C4⋊C4—1182no—
489C4⋊C4—1182no—
490C22⋊C4—22no—
491C22⋊C4—41no—
492C22⋊C4—1182no—
493C22⋊C4—1182no—
494C42—22no—
495C42—41no—
496C42—594no—
497C42—1182no—
498C23—42no—
499C23—1182no—
500C23—4722no—
501C23—2361no—
502C23—2361no—
503C23C4×D23611yescharacteristic
504C23#1427370011yescharacteristic
505C23#1427370511yescharacteristic
506C23#1427370911yescharacteristic
507C23#1427371011yescharacteristic
508C23#1427371211yescharacteristic
509C23#1427372111yescharacteristic
510Q8—1182no—
511Q8—1182no—
512Q8—2361no—
513Q8—2361no—
514D4—1182no—
515D4—1182no—
516D4—2362no—
517D4—2362no—
518D4—2362no—
519D4—2362no—
520D4—2361no—
521D4—2361no—
522C2×C4—42no—
523C2×C4—82no—
524C2×C4—1182no—
525C2×C4—1184no—
526C2×C4—2364no—
527C2×C4—2361no—
528C2×C4—2361no—
529C2×C4—2362no—
530C2×C4—2362no—
531C2×C4—2362no—
532C2×C4—2362no—
533C2×C4C22⋊C4×D5911yescharacteristic
534C2×C4C4⋊C4×D5911yescharacteristic
535C2×C4#1427368411yescharacteristic
536C2×C4(C22⋊D59)⋊C411yescharacteristic
537C2×C4C4×C22⋊D5911yescharacteristic
538C2×C4#1427368911yescharacteristic
539C2×C4#1427369511yescharacteristic
540C2×C4#1427369711yescharacteristic
541C2×C4#1427369711yescharacteristic
542C2×C4#1427369911yescharacteristic
543C2×C4#1427370011yescharacteristic
544C2×C4#1427370011yescharacteristic
545C2×C4#1427370011yescharacteristic
546C2×C4#1427370011yescharacteristic
547C2×C4#1427370111yescharacteristic
548C2×C4#1427370211yescharacteristic
549C2×C4#1427370311yescharacteristic
550C2×C4#1427370511yescharacteristic
551C2×C4#1427370511yescharacteristic
552C2×C4#1427370511yescharacteristic
553C2×C4#1427370711yescharacteristic
554C2×C4#1427371211yescharacteristic
555C2×C4#1427371211yescharacteristic
556C2×C4#1427371311yescharacteristic
557C2×C4#1427371311yescharacteristic
558C2×C4#1427371511yescharacteristic
559C2×C4#1427372211yescharacteristic
560C2×C4#1427372311yescharacteristic
561C8—42no—
562C8—42no—
563C8—2362no—
564C8—2362no—
565C22—22no—
566C22—22no—
567C22—22no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—4722no—
573C22—4722no—
574C22—4722no—
575C22—2362no—
576C22#1683727611yescharacteristic
577C22#1683728011yescharacteristic
578C22#1683729311yescharacteristic
579C22#1683731711yescharacteristic
580C22#1683732611yescharacteristic
581C22#1683733111yescharacteristic
582C22#1683733711yescharacteristic
583C4—82no—
584C4—2364no—
585C4—2362no—
586C4#1683726111yescharacteristic
587C4#1683727311yescharacteristic
588C4#1683729111yescharacteristic
589C4#1683730211yescharacteristic
590C4#1683731111yescharacteristic
591C4#1683731511yescharacteristic
592C4#1683732011yescharacteristic
593C4#1683732411yescharacteristic
594C2—21no—
595C2—21no—
596C2—21no—
597C2—21no—
598C2—21no—
599C2—21no—
600C2—4722no—
601C2#2142234011yescharacteristic
602C2#2142555112yes—
subgroupG/H
centerC2×C4#14273713
commutatorC22×C4×C59C22×C4
FrattiniC23×C4C22×D59
FittingC2×C59×#344C2
socleC22×C59#397
prime radicalC22×#11745685C22
cosocleC23×C4×C59C23
hypercenterC2×#344D59
hypocenterC59#11086
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
1. C2×#16837430C2semidirect
5. C2×#16837166C2semidirect
6. C2×#16837158C2semidirect
7. C2×C59×#344C2semidirect
16. #16837418C4semidirect
297. C2×#344D59semidirect
333. C59#11086semidirect

Maximal subgroups

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

subgroupindex
C2×#168374302
C2×#168374182
C2×#168373962
C2×#168373842
C2×#168371662
C2×#168371582
C2×C59×#3442
#1108659