Finite Group Databasebeta

← #28618744

Subgroups — #28618744

Order 15104.

752 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14273707C211yesmaximal, characteristic
2#21426492C211yesmaximal, characteristic
3#21425669C211yesmaximal, characteristic, complemented
4#21425645C211yesmaximal, characteristic, complemented
5#21425581C211yesmaximal, characteristic, complemented
6#21425530C211yesmaximal, characteristic
7#21425523C211yesmaximal, characteristic
8#21425518C211yesmaximal, characteristic, complemented
9#21425302C211yesmaximal, characteristic
10#21425294C211yesmaximal, characteristic
11C4×#14273660C211yesmaximal, characteristic, complemented
12C4×#14273650C211yesmaximal, characteristic, complemented
13C4×#14273652C211yesmaximal, characteristic, complemented
14C4×(C2×D59)⋊C8C211yesmaximal, characteristic
15C4×#106×C59C211yesmaximal, characteristic, complemented
16C2×#14273707C2211yescharacteristic
17C2×C4×Dic118C2211yescharacteristic
18C2×C42×D59C2211yescharacteristic
19C2×#14273660C2211yescharacteristic
20C2×#14273660C2211yescharacteristic
21C2×#14273652C2211yescharacteristic
22C2×#14273652C2211yescharacteristic
23C2×#14273650C2211yescharacteristic
24C2×#14273650C2211yescharacteristic
25C2×(C2×D59)⋊C8C2211yescharacteristic
26C2×(C2×D59)⋊C8C2211yescharacteristic
27C2×C4×C59⋊C8C2211yescharacteristic
28#16837307C2211yescharacteristic
29#16837301C2211yescharacteristic
30#16837287—21no—
31#16837276—21no—
32#16837269—21no—
33#16837267C2211yescharacteristic
34#16837267C2211yescharacteristic
35#16837264—21no—
36#16837259C2211yescharacteristic
37#16837259C2211yescharacteristic
38#16837259C2211yescharacteristic
39C4×C4⋊Dic59—21no—
40C4×C4⋊Dic59C2211yescharacteristic
41C4×(C2×D59)⋊C4—21no—
42C4×(C2×D59)⋊C4—21no—
43#16837248—21no—
44#16837165C2211yescharacteristic
45#16837165C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837164C2211yescharacteristic
48#16837164C2211yescharacteristic
49#16837164C2211yescharacteristic
50#16837156C2211yescharacteristic
51#16837156C2211yescharacteristic
52C2×#106×C59C2211yescharacteristic
53C2×#106×C59C2211yescharacteristic
54C2×C4×C8×C59C2211yescharacteristic
55C4×C4⋊C4×C59C2211yescharacteristic
56C4×C4⋊C4×C59C2211yescharacteristic
57C59×#340C2211yescharacteristic
58C59×#340C2211yescharacteristic
59C22×Dic118C2311yescharacteristic
60C22×C4×D59D411yescharacteristic
61C22×C4×D59D411yescharacteristic
62C22×C4×D59C2311yescharacteristic
63C22×C59⋊C8C2311yescharacteristic
64C22×C59⋊C8C2311yescharacteristic
65#14273707—22no—
66#14273707—22no—
67C4×Dic118—22no—
68C4×Dic118—22no—
69C2×C4⋊Dic59—21no—
70C2×C4⋊Dic59—21no—
71C2×C4⋊Dic59C2311yescharacteristic
72C2×C4⋊Dic59C2311yescharacteristic
73C2×C4⋊Dic59C2311yescharacteristic
74C2×Dic59⋊C4—21no—
75C2×(C2×D59)⋊C4—21no—
76C2×(C2×D59)⋊C4—21no—
77C2×(C2×D59)⋊C4—21no—
78C2×(C2×D59)⋊C4—21no—
79C2×C4×Dic59—21no—
80C2×C4×Dic59—21no—
81C2×C4×Dic59D411yescharacteristic
82C2×C4×Dic59D411yescharacteristic
83C2×C4×Dic59C2311yescharacteristic
84C42×D59—22no—
85C42×D59—22no—
86#14273660—22no—
87#14273660—22no—
88#14273652—22no—
89#14273652—22no—
90#14273650—22no—
91#14273650—22no—
92(C2×D59)⋊C8—22no—
93(C2×D59)⋊C8—22no—
94C4×C59⋊C8—22no—
95C59⋊#95—21no—
96C59⋊#95—21no—
97C59⋊#95—21no—
98C59⋊#95—21no—
99C59⋊#95—21no—
100C59⋊#95—21no—
101C59⋊#95—21no—
102C59⋊#95—21no—
103C59⋊#95—21no—
104C59⋊#95—21no—
105C59⋊#95—21no—
106C22×C8×C59C2311yescharacteristic
107C22×C8×C59C2311yescharacteristic
108C2×C4⋊C4×C59C2311yescharacteristic
109C2×C4⋊C4×C59C2311yescharacteristic
110C2×C4⋊C4×C59C2311yescharacteristic
111C2×C4⋊C4×C59C2311yescharacteristic
112C2×C42×C59—21no—
113C2×C42×C59—21no—
114C2×C42×C59C2311yescharacteristic
115#106×C59—22no—
116#106×C59—22no—
117C4×C8×C59—22no—
118#95×C59—21no—
119#95×C59—21no—
120C23×D59C2×D411yescharacteristic
121C22×C4×C59—21no—
122C22×C4×C59—21no—
123C22×C4×C59—21no—
124C22×C4×C59—21no—
125C22×C4×C59C2×D411yescharacteristic
126C22×C4×C59C2×D411yescharacteristic
127C22×C4×C59C2411yescharacteristic
128C22×Dic59—21no—
129C22×Dic59—21no—
130C22×Dic59—21no—
131C22×Dic59—21no—
132C22×Dic59C2×D411yescharacteristic
133C22×Dic59C2×D411yescharacteristic
134C22×Dic59C2×D411yescharacteristic
135C2×C4×D59—22no—
136C2×C4×D59—22no—
137C2×C4×D59—22no—
138C2×C4×D59—22no—
139C2×C4×D59—22no—
140C2×C4×D59—21no—
141C2×C4×D59—21no—
142C2×C4×D59—21no—
143C2×C4×D59—21no—
144C2×C4×D59—21no—
145C2×C4×D59—21no—
146C2×C4×D59—41no—
147C2×Dic118—21no—
148C2×Dic118—21no—
149C2×Dic118—21no—
150C2×Dic118—21no—
151C2×Dic118—21no—
152C2×Dic118#4112yes—
153C2×C8×C59—21no—
154C2×C8×C59—21no—
155C2×C8×C59—21no—
156C2×C8×C59—21no—
157C2×C8×C59—21no—
158C2×C8×C59#4112yes—
159C4⋊C4×C59—21no—
160C4⋊C4×C59—21no—
161C4⋊C4×C59—21no—
162C4⋊C4×C59—21no—
163C4⋊C4×C59—21no—
164C4⋊C4×C59—21no—
165C4⋊C4×C59—21no—
166C4⋊C4×C59#4112yes—
167C42×C59—42no—
168C42×C59—42no—
169C42×C59#4112yes—
170C42×C59#4112yes—
171(C2×D59)⋊C4—24no—
172(C2×D59)⋊C4—42no—
173(C2×D59)⋊C4—42no—
174(C2×D59)⋊C4—42no—
175C4⋊Dic59—24no—
176C4⋊Dic59—21no—
177C4⋊Dic59—21no—
178C4⋊Dic59—21no—
179C4⋊Dic59—21no—
180C4⋊Dic59—21no—
181C4⋊Dic59—21no—
182C4⋊Dic59—42no—
183Dic59⋊C4—42no—
184C4×Dic59—22no—
185C4×Dic59—22no—
186C4×Dic59—21no—
187C4×Dic59—21no—
188C4×Dic59—42no—
189C4×Dic59—42no—
190C2×C59⋊C8—21no—
191C2×C59⋊C8—21no—
192C2×C59⋊C8—21no—
193C2×C59⋊C8—21no—
194C2×C59⋊C8—21no—
195C2×C59⋊C8#4112yes—
196C23×C59C22×D411yescharacteristic
197C22×D59—21no—
198C22×D59—21no—
199C22×D59—21no—
200C22×D59—21no—
201C22×D59—21no—
202C22×D59—21no—
203C22×D59#13512yes—
204C2×C4×C59—21no—
205C2×C4×C59—21no—
206C2×C4×C59—22no—
207C2×C4×C59—41no—
208C2×C4×C59—41no—
209C2×C4×C59—41no—
210C2×C4×C59—41no—
211C2×C4×C59—41no—
212C2×C4×C59—41no—
213C2×C4×C59—41no—
214C2×C4×C59—41no—
215C2×C4×C59—41no—
216C2×C4×C59—41no—
217C2×C4×C59—41no—
218C2×C4×C59#12312yes—
219C2×C4×C59#12312yes—
220C2×C4×C59#13512yes—
221C2×C4×C59#13712yes—
222C2×C4×C59C2×#4111yescharacteristic
223C2×C4×C59C2×#4111yescharacteristic
224C2×C4×C59C2×#4111yescharacteristic
225C2×C4×C59C2×#4111yescharacteristic
226C2×C4×C59C2×#4111yescharacteristic
227C2×C4×C59C2×#4111yescharacteristic
228C2×Dic59—21no—
229C2×Dic59—21no—
230C2×Dic59—21no—
231C2×Dic59—21no—
232C2×Dic59—22no—
233C2×Dic59—21no—
234C2×Dic59—21no—
235C2×Dic59—21no—
236C2×Dic59—21no—
237C2×Dic59—21no—
238C2×Dic59—41no—
239C2×Dic59—41no—
240C2×Dic59—41no—
241C2×Dic59—41no—
242C2×Dic59—41no—
243C2×Dic59—41no—
244C2×Dic59—41no—
245C2×Dic59—41no—
246C2×Dic59—41no—
247C2×Dic59—41no—
248C2×Dic59—41no—
249C4×D59—44no—
250C4×D59—41no—
251C4×D59—41no—
252C4×D59—41no—
253C4×D59—41no—
254C4×D59—44no—
255Dic118—22no—
256Dic118—22no—
257Dic118—41no—
258Dic118—41no—
259C8×C59—22no—
260C8×C59—41no—
261C59⋊C8—22no—
262C59⋊C8—41no—
263#23759—591nomaximal, Sylow
264C22×C59C2×#12311yescharacteristic
265C22×C59#52511yescharacteristic
266C22×C59#53211yescharacteristic
267C22×C59C2×#13511yescharacteristic
268C22×C59C2×#13511yescharacteristic
269C22×C59C2×#13711yescharacteristic
270C22×C59#57511yescharacteristic
271C2×D59—22no—
272C2×D59—22no—
273C2×D59—22no—
274C2×D59—41no—
275C2×D59—41no—
276C2×D59—41no—
277C2×D59—41no—
278C4×C59—22no—
279C4×C59—42no—
280C4×C59—81no—
281C4×C59—81no—
282C4×C59—81no—
283C4×C59#48514yes—
284C4×C59#52911yescharacteristic
285C4×C59#52911yescharacteristic
286C4×C59#52911yescharacteristic
287C4×C59#52911yescharacteristic
288Dic59—41no—
289Dic59—41no—
290Dic59—42no—
291Dic59—41no—
292Dic59—81no—
293Dic59—81no—
294Dic59—81no—
295C4×C22⋊Q8—591no—
296#2283—591no—
297#2101—591no—
298#2097—591no—
299#2085—591no—
300#2077—591no—
301#2075—591no—
302#2074—591no—
303#2036—591no—
304#2035—591no—
305C4×#107—591no—
306C4×#106D5911yescharacteristic, complemented
307C4×#103—591no—
308C4×#103—591no—
309C4×C22⋊C8—591no—
310C2×C59#239511yescharacteristic
311C2×C59C2×#48511yescharacteristic
312C2×C59#309111yescharacteristic
313C2×C59#310211yescharacteristic
314C2×C59#310811yescharacteristic
315C2×C59#316811yescharacteristic
316C2×C59#317211yescharacteristic
317D59—42no—
318C2×C22⋊Q8—591no—
319C2×C4×Q8—591no—
320C22×C42—591no—
321C2×#107—591no—
322C2×#107—591no—
323C2×#106C2×D5911yescharacteristic
324C2×#106C2×D5911yescharacteristic
325C2×#103—591no—
326C2×#103—591no—
327C2×#103—591no—
328C2×#103—591no—
329C2×C22⋊C8—591no—
330C2×C22⋊C8—591no—
331C2×C4×C8—591no—
332C2×C4×C8C2×D5911yescharacteristic
333#391—591no—
334#389—591no—
335#387—1181no—
336#385—1181no—
337#383—1181no—
338#382—591no—
339#382—591no—
340#381—1181no—
341#380—591no—
342#380—591no—
343#380—591no—
344C4×C4⋊C4—591no—
345C4×C4⋊C4—1181no—
346C4×C4⋊C4C2×D5911yescharacteristic
347C4×C4⋊C4C2×D5911yescharacteristic
348C4×C22⋊C4—1181no—
349C4×C22⋊C4—1181no—
350#376—1181no—
351#340—591no—
352#340—591no—
353#340—591no—
354#340—591no—
355#340—591no—
356#340—591no—
357#340C2×D5911yescharacteristic
358#340C2×D5911yescharacteristic
359#336—591no—
360#336—591no—
361C59#2375911yescharacteristic, complemented, Sylow
362C22×Q8—591no—
363C23×C4—591no—
364C23×C4—591no—
365C23×C4—591no—
366C22×C8—591no—
367C22×C8—591no—
368C22×C8C22×D5911yescharacteristic
369C22×C8C22×D5911yescharacteristic
370C22⋊Q8—1182no—
371C22⋊Q8—1182no—
372C4×Q8—1182no—
373C4×Q8—1182no—
374C2×C4⋊C4—591no—
375C2×C4⋊C4—591no—
376C2×C4⋊C4—591no—
377C2×C4⋊C4—1181no—
378C2×C4⋊C4—1181no—
379C2×C4⋊C4—1181no—
380C2×C4⋊C4C22×D5911yescharacteristic
381C2×C4⋊C4C22×D5911yescharacteristic
382C2×C4⋊C4C22×D5911yescharacteristic
383C2×C4⋊C4C22×D5911yescharacteristic
384C2×C22⋊C4—1181no—
385C2×C22⋊C4—1181no—
386C2×C22⋊C4—1181no—
387C2×C22⋊C4—1181no—
388C2×C42—21no—
389C2×C42—21no—
390C2×C42—591no—
391C2×C42—591no—
392C2×C42—591no—
393C2×C42—1182no—
394C2×C42—1182no—
395C2×C42—1181no—
396C2×C42—1181no—
397C2×C42C22×D5911yescharacteristic
398#107—1182no—
399#107—1182no—
400#106—22no—
401#106—22no—
402#103—1182no—
403#103—1182no—
404#103—1182no—
405#103—1182no—
406C22⋊C8—1182no—
407C22⋊C8—1182no—
408C4×C8—22no—
409C4×C8—1182no—
410#95—21no—
411#95—21no—
412#95—1181no—
413#95—1181no—
414#95—1181no—
415#95—1181no—
416#95—1181no—
417#95—1181no—
418#95—1181no—
419#95—1181no—
420#95—1181no—
421#95—1181no—
422#95—1181no—
423C24—591no—
424C2×Q8—592no—
425C2×Q8—1181no—
426C2×Q8—1181no—
427C2×Q8—1181no—
428C2×Q8—1181no—
429C2×Q8—1181no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—591no—
435C22×C4—591no—
436C22×C4—591no—
437C22×C4—1182no—
438C22×C4—1181no—
439C22×C4—1182no—
440C22×C4—1182no—
441C22×C4—1182no—
442C22×C4—1182no—
443C22×C4—1181no—
444C22×C4—1181no—
445C22×C4—1181no—
446C22×C4—1181no—
447C22×C4—1181no—
448C22×C4—1181no—
449C22×C4—1181no—
450C22×C4—1181no—
451C22×C4—1181no—
452C22×C4—2361no—
453C22×C4D4×D5911yescharacteristic
454C22×C4D4×D5911yescharacteristic
455C22×C4C23×D5911yescharacteristic
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—592no—
462C2×C8—1181no—
463C2×C8—1181no—
464C2×C8—1181no—
465C2×C8—1181no—
466C2×C8—1181no—
467C2×C8#1174568512yes—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—1184no—
476C4⋊C4—1181no—
477C4⋊C4—1181no—
478C4⋊C4—1181no—
479C4⋊C4—1181no—
480C4⋊C4—1181no—
481C4⋊C4—1181no—
482C4⋊C4—2362no—
483C4⋊C4—2362no—
484C4⋊C4#1174568512yes—
485C22⋊C4—1184no—
486C22⋊C4—2362no—
487C22⋊C4—2362no—
488C22⋊C4—2362no—
489C42—42no—
490C42—42no—
491C42—1182no—
492C42—1182no—
493C42—1181no—
494C42—1181no—
495C42—2362no—
496C42—2362no—
497C42#1174568512yes—
498C42#1174568912yes—
499C23—592no—
500C23—1181no—
501C23—1181no—
502C23—1181no—
503C23—1181no—
504C23—1181no—
505C23—1181no—
506C23C2×D4×D5911yescharacteristic
507Q8—1182no—
508Q8—1182no—
509Q8—2361no—
510Q8—2361no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—22no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—1181no—
526C2×C4—1181no—
527C2×C4—1181no—
528C2×C4—1182no—
529C2×C4—1181no—
530C2×C4—1181no—
531C2×C4—1181no—
532C2×C4—1181no—
533C2×C4—1181no—
534C2×C4—1181no—
535C2×C4—2364no—
536C2×C4—2361no—
537C2×C4—2361no—
538C2×C4—2361no—
539C2×C4—2361no—
540C2×C4—2361no—
541C2×C4—2361no—
542C2×C4—2361no—
543C2×C4—2361no—
544C2×C4—2361no—
545C2×C4—2361no—
546C2×C4—2361no—
547C2×C4—2361no—
548C2×C4—2361no—
549C2×C4—2361no—
550C2×C4—2361no—
551C2×C4—2364no—
552C2×C4#1427371212yes—
553C2×C4#1427371212yes—
554C2×C4#1427374812yes—
555C2×C4#1427375612yes—
556C2×C4#41×D5911yescharacteristic
557C2×C4#41×D5911yescharacteristic
558C2×C4C2×#1174568511yescharacteristic
559C2×C4C2×#1174568511yescharacteristic
560C2×C4C2×#1174568511yescharacteristic
561C2×C4C2×#1174568911yescharacteristic
562C8—22no—
563C8—41no—
564C8—1182no—
565C8—2361no—
566C22—1182no—
567C22—1182no—
568C22—1182no—
569C22—2361no—
570C22—2361no—
571C22—2361no—
572C22—2361no—
573C22C2×#1427371211yescharacteristic
574C22#1683791111yescharacteristic
575C22#1683794911yescharacteristic
576C22#135×D5911yescharacteristic
577C22C2×#1427374811yescharacteristic
578C22C2×#1427375611yescharacteristic
579C22#1683819911yescharacteristic
580C4—22no—
581C4—42no—
582C4—81no—
583C4—81no—
584C4—81no—
585C4—4721no—
586C4—4721no—
587C4—4721no—
588C4—2361no—
589C4—2361no—
590C4—2361no—
591C4—2362no—
592C4#1683774614yes—
593C4#1683793011yescharacteristic
594C4#1683793611yescharacteristic
595C4#1683793911yescharacteristic
596C4#1683793911yescharacteristic
597C2—2362no—
598C2#2142735911yescharacteristic
599C2C2×#1683774611yescharacteristic
600C2#2143401311yescharacteristic
601C2#2143411811yescharacteristic
602C2#2143417411yescharacteristic
603C2#2143466211yescharacteristic
604C2#2143469811yescharacteristic
subgroupG/H
centerC22×C4D4×D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC4×#106×C59C2
socleC23×C59C22×D4
prime radicalC23×D59C2×D4
hypercenterC4×#106D59
hypocenterC59#23759
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#106

Complements

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

NH ≅ G/Ntype
3. #21425669C2semidirect
4. #21425645C2semidirect
5. #21425581C2semidirect
8. #21425518C2semidirect
11. C4×#14273660C2semidirect
12. C4×#14273650C2semidirect
13. C4×#14273652C2semidirect
15. C4×#106×C59C2semidirect
306. C4×#106D59semidirect
361. C59#23759semidirect

Maximal subgroups

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

subgroupindex
C4×#142737072
#214264922
#214256692
#214256452
#214255812
#214255302
#214255232
#214255182
#214253022
#214252942
C4×#142736602
C4×#142736502
C4×#142736522
C4×(C2×D59)⋊C82
C4×#106×C592
#2375959