Finite Group Databasebeta

← #28656699

Subgroups — #28656699

Order 15104.

680 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21427894C211yesmaximal, characteristic
2#21425587C211yesmaximal, characteristic, complemented
3#21425337C211yesmaximal, characteristic
4#21425244C211yesmaximal, characteristic, complemented
5#21425239C211yesmaximal, characteristic
6#21425028C211yesmaximal, characteristic
7#21424792C211yesmaximal, characteristic
8#21424737C211yesmaximal, characteristic, complemented
9#21424716C211yesmaximal, characteristic
10#21424716C211yesmaximal, characteristic
11#21424688C211yesmaximal, characteristic, complemented
12#21424662C211yesmaximal, characteristic, complemented
13#21424349C211yesmaximal, characteristic, complemented
14#21423929C211yesmaximal, characteristic, complemented
15C59×#2370C211yesmaximal, characteristic, complemented
16C2×#14273715C2211yescharacteristic
17C2×C4×Dic118C2211yescharacteristic
18C2×#14273660C2211yescharacteristic
19C2×#14273660C2211yescharacteristic
20C2×C4⋊(C59⋊C8)C2211yescharacteristic
21C2×#14273650C2211yescharacteristic
22C2×#14273650C2211yescharacteristic
23C2×#14273650C2211yescharacteristic
24C2×#14273650C2211yescharacteristic
25C2×#14273647C2211yescharacteristic
26C2×#14273647C2211yescharacteristic
27C2×#14273647C2211yescharacteristic
28C2×#14273647C2211yescharacteristic
29C2×#14273638C2211yescharacteristic
30#16837337—21no—
31#16837331—21no—
32#16837308C2211yescharacteristic
33#16837304C2211yescharacteristic
34#16837304C2211yescharacteristic
35#16837300C2211yescharacteristic
36#16837292—21no—
37#16837291—21no—
38#16837164C2211yescharacteristic
39#16837164C2211yescharacteristic
40#16837164C2211yescharacteristic
41#16837164C2211yescharacteristic
42#16837164C2211yescharacteristic
43#16837164C2211yescharacteristic
44#16837157C2211yescharacteristic
45#16837157C2211yescharacteristic
46#16837157C2211yescharacteristic
47#16837157C2211yescharacteristic
48C2×#125×C59C2211yescharacteristic
49C59×#389—21no—
50C59×#389C2211yescharacteristic
51C59×#389C2211yescharacteristic
52C59×#387—21no—
53C59×#387—21no—
54C4×C4⋊C4×C59—21no—
55C4×C4⋊C4×C59C2211yescharacteristic
56C4×C4⋊C4×C59C2211yescharacteristic
57C4×C4⋊C4×C59C2211yescharacteristic
58C4×C4⋊C4×C59C2211yescharacteristic
59C22×Dic118C2311yescharacteristic
60C22×D236C2311yescharacteristic
61C22×C59⋊C8C2311yescharacteristic
62C22×C59⋊C8C2311yescharacteristic
63C22×C59⋊C8C2311yescharacteristic
64C22×C59⋊C8C2311yescharacteristic
65#14273715—22no—
66#14273715—41no—
67C4×Dic118—22no—
68C4×Dic118—41no—
69C2×C4⋊Dic59C2311yescharacteristic
70C2×C4⋊Dic59C2311yescharacteristic
71C2×Dic59⋊C4—21no—
72C2×Dic59⋊C4—21no—
73C2×(C2×D59)⋊C4—21no—
74C2×(C2×D59)⋊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—
80#14273660—22no—
81#14273660—41no—
82C4⋊(C59⋊C8)—41no—
83#14273650—22no—
84#14273650—22no—
85#14273650—22no—
86#14273650—22no—
87#14273647—22no—
88#14273647—22no—
89#14273647—22no—
90#14273647—41no—
91#14273638—41no—
92C59⋊#95—21no—
93C59⋊#95—21no—
94C59⋊#95—21no—
95#125×C59—22no—
96#125×C59—22no—
97C2×C4⋊C4×C59—21no—
98C2×C4⋊C4×C59—21no—
99C2×C4⋊C4×C59—21no—
100C2×C4⋊C4×C59—21no—
101C2×C4⋊C4×C59D411yescharacteristic
102C2×C4⋊C4×C59D411yescharacteristic
103C2×C4⋊C4×C59C2311yescharacteristic
104C2×C4⋊C4×C59C2311yescharacteristic
105C2×C4⋊C4×C59C2311yescharacteristic
106C2×C4⋊C4×C59C2311yescharacteristic
107C2×C42×C59—21no—
108C2×C42×C59—21no—
109C2×C42×C59—21no—
110C2×C42×C59C2311yescharacteristic
111C2×C42×C59C2311yescharacteristic
112C2×C42×C59C2311yescharacteristic
113#95×C59—21no—
114#95×C59—21no—
115#95×C59—21no—
116#95×C59—21no—
117#95×C59—21no—
118#95×C59D411yescharacteristic
119#95×C59D411yescharacteristic
120C23×D59—21no—
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×C59C2×D411yescharacteristic
128C22×C4×C59C2×D411yescharacteristic
129C22×C4×C59C2×D411yescharacteristic
130C22×C4×C59C2×D411yescharacteristic
131C22×C4×C59C2411yescharacteristic
132C22×Dic59—21no—
133C22×Dic59—21no—
134C22×Dic59—21no—
135C2×D236—21no—
136C2×D236—21no—
137C2×D236—21no—
138C2×D236—21no—
139C2×D236—21no—
140C2×D236—21no—
141C2×Dic118—21no—
142C2×Dic118—21no—
143C2×Dic118—21no—
144C2×Dic118—21no—
145C2×Dic118—21no—
146C2×Dic118#4112yes—
147C4⋊C4×C59—24no—
148C4⋊C4×C59—24no—
149C4⋊C4×C59—21no—
150C4⋊C4×C59—21no—
151C4⋊C4×C59—21no—
152C4⋊C4×C59—21no—
153C4⋊C4×C59—21no—
154C4⋊C4×C59—41no—
155C4⋊C4×C59—41no—
156C4⋊C4×C59—42no—
157C4⋊C4×C59—81no—
158C4⋊C4×C59#4112yes—
159C4⋊C4×C59#4112yes—
160C4⋊C4×C59#4112yes—
161C42×C59—21no—
162C42×C59—21no—
163C42×C59—21no—
164C42×C59—21no—
165C42×C59—21no—
166C42×C59—21no—
167C42×C59—42no—
168C42×C59—81no—
169C42×C59—81no—
170(C2×D59)⋊C4—42no—
171(C2×D59)⋊C4—42no—
172(C2×D59)⋊C4—42no—
173(C2×D59)⋊C4—42no—
174(C2×D59)⋊C4—81no—
175(C2×D59)⋊C4—81no—
176C4⋊Dic59—21no—
177C4⋊Dic59—21no—
178C4⋊Dic59—21no—
179C4⋊Dic59—21no—
180Dic59⋊C4—42no—
181Dic59⋊C4—81no—
182C4×Dic59—42no—
183C2×C59⋊C8—21no—
184C2×C59⋊C8—21no—
185C2×C59⋊C8—21no—
186C2×C59⋊C8—21no—
187C2×C59⋊C8—21no—
188C2×C59⋊C8—21no—
189C2×C59⋊C8—21no—
190C2×C59⋊C8—21no—
191C2×C59⋊C8—21no—
192C2×C59⋊C8—21no—
193C2×C59⋊C8—21no—
194C2×C59⋊C8—21no—
195C23×C59C22×D411yescharacteristic
196C22×D59—41no—
197C22×D59—41no—
198C22×D59—41no—
199C22×D59—41no—
200C22×D59—41no—
201C22×D59—41no—
202C22×D59—41no—
203C2×C4×C59—21no—
204C2×C4×C59—21no—
205C2×C4×C59—22no—
206C2×C4×C59—22no—
207C2×C4×C59—21no—
208C2×C4×C59—21no—
209C2×C4×C59—21no—
210C2×C4×C59—21no—
211C2×C4×C59—22no—
212C2×C4×C59—21no—
213C2×C4×C59—21no—
214C2×C4×C59—21no—
215C2×C4×C59—21no—
216C2×C4×C59—21no—
217C2×C4×C59—21no—
218C2×C4×C59—21no—
219C2×C4×C59—21no—
220C2×C4×C59—21no—
221C2×C4×C59—21no—
222C2×C4×C59—21no—
223C2×C4×C59—21no—
224C2×C4×C59—41no—
225C2×C4×C59—41no—
226C2×C4×C59—41no—
227C2×C4×C59—41no—
228C2×C4×C59—41no—
229C2×C4×C59—41no—
230C2×C4×C59—41no—
231C2×C4×C59—41no—
232C2×C4×C59—41no—
233C2×C4×C59C2×#4111yescharacteristic
234C2×C4×C59C2×#4111yescharacteristic
235C2×C4×C59C2×#4111yescharacteristic
236C2×C4×C59C2×#4111yescharacteristic
237C2×C4×C59H(5,𝔽2)11yescharacteristic
238C2×C4×C592−1+411yescharacteristic
239C2×Dic59—22no—
240C2×Dic59—41no—
241C2×Dic59—41no—
242C2×Dic59—41no—
243C2×Dic59—41no—
244C2×Dic59—41no—
245C2×Dic59—41no—
246C2×Dic59—41no—
247C2×Dic59—41no—
248D236—41no—
249D236—41no—
250D236—41no—
251D236—41no—
252Dic118—22no—
253Dic118—22no—
254Dic118—41no—
255Dic118—41no—
256C59⋊C8—41no—
257C59⋊C8—41no—
258C59⋊C8—41no—
259C59⋊C8—41no—
260#26719—591nomaximal, Sylow
261C22×C59#52511yescharacteristic
262C22×C59#54611yescharacteristic
263C22×C59#54811yescharacteristic
264C22×C59#57511yescharacteristic
265C22×C59#57511yescharacteristic
266C22×C59#57611yescharacteristic
267C22×C59#57811yescharacteristic
268C2×D59—81no—
269C2×D59—81no—
270C2×D59—81no—
271C2×D59—81no—
272C2×D59—81no—
273C2×D59—81no—
274C2×D59—81no—
275C4×C59—41no—
276C4×C59—42no—
277C4×C59—42no—
278C4×C59—41no—
279C4×C59—42no—
280C4×C59—41no—
281C4×C59—41no—
282C4×C59—41no—
283C4×C59—41no—
284C4×C59—81no—
285C4×C59#52911yescharacteristic
286C4×C59#54211yescharacteristic
287C4×C59#55211yescharacteristic
288C4×C59#55911yescharacteristic
289Dic59—42no—
290Dic59—81no—
291Dic59—81no—
292#2448—591no—
293#2370D5911yescharacteristic, complemented
294#2086—591no—
295#2042—591no—
296#2026—591no—
297#2025—591no—
298#1983—591no—
299#1936—591no—
300#1928—591no—
301#1925—591no—
302#1925—591no—
303#1921—591no—
304#1917—591no—
305#1863—591no—
306#1763—591no—
307C2×C59#245811yescharacteristic
308C2×C59#311111yescharacteristic
309C2×C59#312411yescharacteristic
310C2×C59#330911yescharacteristic
311C2×C59#332711yescharacteristic
312C2×C59#337011yescharacteristic
313C2×C59#337711yescharacteristic
314D59—161no—
315C2×#125C2×D5911yescharacteristic
316C2×#124—591no—
317C2×C4×Q8—591no—
318C2×#107—591no—
319C2×#107—591no—
320C2×C4⋊C8—591no—
321C2×#103—591no—
322C2×#103—591no—
323C2×#103—591no—
324C2×#103—591no—
325C2×#102—591no—
326C2×#102—591no—
327C2×#102—591no—
328C2×#102—591no—
329C2×#97—591no—
330#399—1181no—
331#397—1181no—
332#391—591no—
333#390—591no—
334#390—591no—
335#389—21no—
336#389—591no—
337#389C2×D5911yescharacteristic
338#389C2×D5911yescharacteristic
339#388—1181no—
340#388—1181no—
341#387—21no—
342#387—21no—
343C4×C4⋊C4—21no—
344C4×C4⋊C4C2×D5911yescharacteristic
345C4×C4⋊C4C2×D5911yescharacteristic
346C4×C4⋊C4C2×D5911yescharacteristic
347C4×C4⋊C4C2×D5911yescharacteristic
348#340—591no—
349#340—591no—
350#340—591no—
351#340—591no—
352#340—591no—
353#340—591no—
354#336—591no—
355#336—591no—
356#336—591no—
357#336—591no—
358C59#2671911yescharacteristic, complemented, Sylow
359C22×Q8—591no—
360C22×D4—591no—
361C22×C8—591no—
362C22×C8—591no—
363C22×C8—591no—
364C22×C8—591no—
365#125—22no—
366#125—22no—
367#124—1182no—
368#124—2361no—
369C4×Q8—1182no—
370C4×Q8—2361no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—591no—
376C2×C4⋊C4—591no—
377C2×C4⋊C4—1181no—
378C2×C4⋊C4—1181no—
379C2×C4⋊C4C22⋊D5911yescharacteristic
380C2×C4⋊C4C22⋊D5911yescharacteristic
381C2×C4⋊C4C22×D5911yescharacteristic
382C2×C4⋊C4C22×D5911yescharacteristic
383C2×C4⋊C4C22×D5911yescharacteristic
384C2×C4⋊C4C22×D5911yescharacteristic
385C2×C22⋊C4—1181no—
386C2×C22⋊C4—1181no—
387C2×C22⋊C4—1181no—
388C2×C22⋊C4—1181no—
389C2×C22⋊C4—1181no—
390C2×C22⋊C4—1181no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42—21no—
394C2×C42—1181no—
395C2×C42C22×D5911yescharacteristic
396C2×C42C22×D5911yescharacteristic
397C2×C42C22×D5911yescharacteristic
398#107—1182no—
399#107—2361no—
400C4⋊C8—2361no—
401#103—1182no—
402#103—1182no—
403#103—1182no—
404#103—1182no—
405#102—1182no—
406#102—1182no—
407#102—1182no—
408#102—2361no—
409#97—2361no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—1181no—
416#95—1181no—
417#95—1181no—
418#95C22⋊D5911yescharacteristic
419#95C22⋊D5911yescharacteristic
420C24—1181no—
421C2×Q8—592no—
422C2×Q8—1181no—
423C2×Q8—1181no—
424C2×Q8—1181no—
425C2×Q8—1181no—
426C2×Q8—1181no—
427C2×D4—1181no—
428C2×D4—1181no—
429C2×D4—1181no—
430C2×D4—1181no—
431C2×D4—1181no—
432C2×D4—1181no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—1181no—
438C22×C4—1181no—
439C22×C4—1181no—
440C22×C4C2×C22⋊D5911yescharacteristic
441C22×C4C2×C22⋊D5911yescharacteristic
442C22×C4C2×C22⋊D5911yescharacteristic
443C22×C4C2×C22⋊D5911yescharacteristic
444C22×C4C2×C22⋊D5911yescharacteristic
445C22×C4C2×C22⋊D5911yescharacteristic
446C22×C4C23×D5911yescharacteristic
447C2×C8—1181no—
448C2×C8—1181no—
449C2×C8—1181no—
450C2×C8—1181no—
451C2×C8—1181no—
452C2×C8—1181no—
453C2×C8—1181no—
454C2×C8—1181no—
455C2×C8—1181no—
456C2×C8—1181no—
457C2×C8—1181no—
458C2×C8—1181no—
459C4⋊C4—24no—
460C4⋊C4—24no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4—42no—
469C4⋊C4—81no—
470C4⋊C4—1181no—
471C4⋊C4—1181no—
472C4⋊C4—1181no—
473C4⋊C4—1181no—
474C4⋊C4—4721no—
475C4⋊C4—2362no—
476C4⋊C4#1174568512yes—
477C4⋊C4#1174568512yes—
478C4⋊C4#1174568912yes—
479C22⋊C4—4721no—
480C22⋊C4—4721no—
481C22⋊C4—2362no—
482C22⋊C4—2362no—
483C22⋊C4—2362no—
484C22⋊C4—2362no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—21no—
491C42—42no—
492C42—81no—
493C42—81no—
494C42—2362no—
495C23—2361no—
496C23—2361no—
497C23—2361no—
498C23—2361no—
499C23—2361no—
500C23—2361no—
501C23—2361no—
502C23C22×C22⋊D5911yescharacteristic
503Q8—1182no—
504Q8—1182no—
505Q8—2361no—
506Q8—2361no—
507D4—2361no—
508D4—2361no—
509D4—2361no—
510D4—2361no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—22no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—1182no—
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#41×D5911yescharacteristic
551C2×C4C2×#1174568511yescharacteristic
552C2×C4C2×#1174568511yescharacteristic
553C2×C4C2×#1174568911yescharacteristic
554C2×C4#1427377311yescharacteristic
555C2×C4#1427377511yescharacteristic
556C8—2361no—
557C8—2361no—
558C8—2361no—
559C8—2361no—
560C22—4721no—
561C22—4721no—
562C22—4721no—
563C22—4721no—
564C22—4721no—
565C22—4721no—
566C22—4721no—
567C22#1683791311yescharacteristic
568C22#1683804011yescharacteristic
569C22#1683806311yescharacteristic
570C22#1683820011yescharacteristic
571C22#1683820011yescharacteristic
572C22#1683820511yescharacteristic
573C22#1683821711yescharacteristic
574C4—41no—
575C4—42no—
576C4—42no—
577C4—41no—
578C4—41no—
579C4—41no—
580C4—41no—
581C4—41no—
582C4—42no—
583C4—81no—
584C4—4721no—
585C4—4721no—
586C4—2362no—
587C4#1683793911yescharacteristic
588C4#1683802411yescharacteristic
589C4#1683809311yescharacteristic
590C4#1683813711yescharacteristic
591C2—9441no—
592C2#2142801211yescharacteristic
593C2#2143420511yescharacteristic
594C2#2143435811yescharacteristic
595C2#2143609611yescharacteristic
596C2#2143635811yescharacteristic
597C2#2143684911yescharacteristic
598C2#2143693811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC59×#2370C2
socleC23×C59C22×D4
prime radicalC22×D236C23
hypercenter#2370D59
hypocenterC59#26719
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2370

Complements

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

NH ≅ G/Ntype
2. #21425587C2semidirect
4. #21425244C2semidirect
8. #21424737C2semidirect
11. #21424688C2semidirect
12. #21424662C2semidirect
13. #21424349C2semidirect
14. #21423929C2semidirect
15. C59×#2370C2semidirect
293. #2370D59semidirect
358. C59#26719semidirect

Maximal subgroups

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

subgroupindex
#214278942
#214255872
#214253372
#214252442
#214252392
#214250282
#214247922
#214247372
#214247162
#214246882
#214246622
#214243492
#214239292
C59×#23702
#2671959