Finite Group Databasebeta

← #28647643

Subgroups — #28647643

Order 15104.

750 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21429129C211yesmaximal, characteristic, complemented
2#21427044C211yesmaximal, characteristic
3#21425622C211yesmaximal, characteristic
4#21425484C211yesmaximal, characteristic
5#21425480C211yesmaximal, characteristic
6#21424852C211yesmaximal, characteristic, complemented
7#21424851C211yesmaximal, characteristic, complemented
8#21424851C211yesmaximal, characteristic, complemented
9#21424813C211yesmaximal, characteristic, complemented
10#21424669C211yesmaximal, characteristic, complemented
11#21424668C211yesmaximal, characteristic, complemented
12#21424254C211yesmaximal, characteristic, complemented
13#21424094C211yesmaximal, characteristic
14#102×Dic59C211yesmaximal, characteristic
15C59×#2093C211yesmaximal, characteristic
16C2×#14273717—21no—
17C2×D4×Dic59C2211yescharacteristic
18C2×#14273683—21no—
19C2×#14273661C2211yescharacteristic
20C2×#14273660C2211yescharacteristic
21C2×#14273660C2211yescharacteristic
22C2×#14273660C2211yescharacteristic
23C2×C4⋊(C59⋊C8)C2211yescharacteristic
24C2×Dic59⋊C8C2211yescharacteristic
25C2×Dic59⋊C8C2211yescharacteristic
26C2×#14273648C2211yescharacteristic
27C2×#14273648C2211yescharacteristic
28C2×C8×Dic59C2211yescharacteristic
29#16837335—21no—
30#16837333—21no—
31#16837305C2211yescharacteristic
32#16837301C2211yescharacteristic
33#16837300C2211yescharacteristic
34#16837297—21no—
35#16837296—21no—
36#16837290—21no—
37#16837271C2211yescharacteristic
38#16837271C2211yescharacteristic
39#16837271C2211yescharacteristic
40#16837260—21no—
41C4⋊C4×Dic59C2211yescharacteristic
42C4⋊C4×Dic59C2211yescharacteristic
43C4×Dic59⋊C4C2211yescharacteristic
44C4×C4⋊Dic59C2211yescharacteristic
45#16837165C2211yescharacteristic
46#16837165C2211yescharacteristic
47#16837165C2211yescharacteristic
48#16837164C2211yescharacteristic
49#16837164C2211yescharacteristic
50#16837164C2211yescharacteristic
51#16837156C2211yescharacteristic
52C2×#107×C59C2211yescharacteristic
53C2×#107×C59C2211yescharacteristic
54C2×#102×C59C2211yescharacteristic
55C2×#102×C59C2211yescharacteristic
56C59×#390C2211yescharacteristic
57C59×#384C2211yescharacteristic
58C59×#336C2211yescharacteristic
59C23×Dic59—21no—
60C22×C59⋊C8C2311yescharacteristic
61C22×C59⋊C8C2311yescharacteristic
62#14273717—44no—
63D4×Dic59—22no—
64D4×Dic59Q814yes—
65#14273683—44no—
66C2×C4⋊Dic59—21no—
67C2×C4⋊Dic59C2311yescharacteristic
68C2×C4⋊Dic59C2311yescharacteristic
69C2×C4⋊Dic59C2311yescharacteristic
70C2×C4⋊Dic59C2311yescharacteristic
71C2×Dic59⋊C4—21no—
72C2×Dic59⋊C4—21no—
73C2×Dic59⋊C4—21no—
74C2×Dic59⋊C4—21no—
75C2×Dic59⋊C4—21no—
76C2×Dic59⋊C4—21no—
77C2×Dic59⋊C4—21no—
78C2×Dic59⋊C4D411yescharacteristic
79C2×Dic59⋊C4D411yescharacteristic
80C2×C22⋊Dic59—21no—
81C2×C22⋊Dic59—21no—
82C2×C22⋊Dic59—21no—
83C2×C4×Dic59—21no—
84C2×C4×Dic59—21no—
85C2×C4×Dic59—21no—
86C2×C4×Dic59C2311yescharacteristic
87C2×C4×Dic59C2311yescharacteristic
88#14273661—22no—
89#14273660—41no—
90#14273660—41no—
91#14273660—41no—
92C4⋊(C59⋊C8)—22no—
93Dic59⋊C8—22no—
94Dic59⋊C8—22no—
95#14273648—22no—
96#14273648—41no—
97C8×Dic59—22no—
98C59⋊#95—21no—
99C59⋊#95—21no—
100C59⋊#95—21no—
101C59⋊#95—21no—
102C59⋊#95—21no—
103C59⋊#95D411yescharacteristic
104C59⋊#95D411yescharacteristic
105C22×D4×C59C2311yescharacteristic
106C22×C8×C59C2311yescharacteristic
107C22×C8×C59C2311yescharacteristic
108C2×C4⋊C4×C59—21no—
109C2×C4⋊C4×C59—21no—
110C2×C4⋊C4×C59C2311yescharacteristic
111C2×C4⋊C4×C59C2311yescharacteristic
112C2×C4⋊C4×C59C2311yescharacteristic
113C2×C22⋊C4×C59—21no—
114C2×C22⋊C4×C59—21no—
115C2×C42×C59C2311yescharacteristic
116#107×C59—22no—
117#107×C59—41no—
118#102×C59—22no—
119#102×C59—41no—
120C24×C59—21no—
121C2×D4×C59—21no—
122C2×D4×C59—21no—
123C2×D4×C59—21no—
124C2×D4×C59—21no—
125C2×D4×C59—21no—
126C2×D4×C59C2×Q812yes—
127C22×C4×C59—21no—
128C22×C4×C59—21no—
129C22×C4×C59—21no—
130C22×C4×C59C2×D411yescharacteristic
131C22×C4×C59C2×D411yescharacteristic
132C22×C4×C59C2411yescharacteristic
133C22×Dic59—21no—
134C22×Dic59—24no—
135C22×Dic59—21no—
136C22×Dic59—21no—
137C22×Dic59—21no—
138C22×Dic59—42no—
139C22×Dic59—42no—
140C22×Dic59C2×D411yescharacteristic
141C22×Dic59C2×D411yescharacteristic
142C22×Dic59C2×D411yescharacteristic
143C22×Dic59C2×D411yescharacteristic
144C2×C8×C59—21no—
145C2×C8×C59—21no—
146C2×C8×C59—21no—
147C2×C8×C59—21no—
148C2×C8×C59—21no—
149C2×C8×C59#4112yes—
150C4⋊C4×C59—21no—
151C4⋊C4×C59—21no—
152C4⋊C4×C59—21no—
153C4⋊C4×C59—21no—
154C4⋊C4×C59—21no—
155C4⋊C4×C59—21no—
156C4⋊C4×C59—42no—
157C4⋊C4×C59—81no—
158C22⋊C4×C59—42no—
159C22⋊C4×C59—81no—
160C42×C59—21no—
161C42×C59—21no—
162C22⋊Dic59—24no—
163C22⋊Dic59—42no—
164C22⋊Dic59—81no—
165C4⋊Dic59—21no—
166C4⋊Dic59—21no—
167C4⋊Dic59—21no—
168C4⋊Dic59—21no—
169C4⋊Dic59—21no—
170C4⋊Dic59—21no—
171C4⋊Dic59—21no—
172C4⋊Dic59—42no—
173C4⋊Dic59C2×Q812yes—
174Dic59⋊C4—22no—
175Dic59⋊C4—42no—
176Dic59⋊C4—42no—
177Dic59⋊C4—42no—
178Dic59⋊C4—42no—
179Dic59⋊C4—81no—
180Dic59⋊C4—81no—
181Dic59⋊C4—81no—
182Dic59⋊C4D814yes—
183C4×Dic59—21no—
184C4×Dic59—21no—
185C4×Dic59—42no—
186C4×Dic59—42no—
187C4×Dic59—42no—
188C4×Dic59C2×Q812yes—
189C4×Dic59#4112yes—
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×C59—22no—
197C23×C59—41no—
198C23×C59—41no—
199C23×C59—41no—
200C23×C59—41no—
201C23×C59—41no—
202C23×C59—41no—
203C23×C59C22×D411yescharacteristic
204D4×C59—22no—
205D4×C59—22no—
206D4×C59—41no—
207D4×C59—41no—
208C2×C4×C59—21no—
209C2×C4×C59—21no—
210C2×C4×C59—21no—
211C2×C4×C59—21no—
212C2×C4×C59—21no—
213C2×C4×C59—41no—
214C2×C4×C59—41no—
215C2×C4×C59—41no—
216C2×C4×C59—41no—
217C2×C4×C59—41no—
218C2×C4×C59—41no—
219C2×C4×C59—41no—
220C2×C4×C59—41no—
221C2×C4×C59—41no—
222C2×C4×C59C2×D812yes—
223C2×C4×C59C22×Q811yescharacteristic
224C2×C4×C59C2×#4111yescharacteristic
225C2×C4×C59C2×#4111yescharacteristic
226C2×C4×C59C2×#4111yescharacteristic
227C2×C4×C59H(5,𝔽2)11yescharacteristic
228C2×C4×C592−1+411yescharacteristic
229C2×Dic59—21no—
230C2×Dic59—21no—
231C2×Dic59—21no—
232C2×Dic59—21no—
233C2×Dic59—22no—
234C2×Dic59—21no—
235C2×Dic59—21no—
236C2×Dic59—21no—
237C2×Dic59—41no—
238C2×Dic59—41no—
239C2×Dic59—48no—
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—
249C2×Dic59C22⋊Q812yes—
250C2×Dic59C22⋊Q812yes—
251C2×Dic59C2×D812yes—
252C2×Dic59C2×D812yes—
253C2×Dic59#13712yes—
254C8×C59—22no—
255C8×C59—41no—
256C59⋊C8—22no—
257C59⋊C8—41no—
258#26086—591nomaximal, Sylow
259C22×C59—42no—
260C22×C59—42no—
261C22×C59—42no—
262C22×C59—81no—
263C22×C59—81no—
264C22×C59—81no—
265C22×C59—81no—
266C22×C59C2×C22⋊Q811yescharacteristic
267C22×C59#54711yescharacteristic
268C22×C59#55011yescharacteristic
269C22×C59C22×D811yescharacteristic
270C22×C59C2×#13711yescharacteristic
271C22×C59#57611yescharacteristic
272C22×C59#57811yescharacteristic
273C4×C59—22no—
274C4×C59—41no—
275C4×C59—81no—
276C4×C59—81no—
277C4×C59—81no—
278C4×C59#53311yescharacteristic
279C4×C59#54411yescharacteristic
280C4×C59#55211yescharacteristic
281C4×C59#55311yescharacteristic
282Dic59—22no—
283Dic59—22no—
284Dic59—41no—
285Dic59—42no—
286Dic59—81no—
287Dic59—81no—
288Dic59—81no—
289Dic59#47414yes—
290#2552—591no—
291#2354—591no—
292#2093—591no—
293#2093D5911yescharacteristic
294#2067—591no—
295#2067—591no—
296#1947—591no—
297#1947—591no—
298#1947—591no—
299#1939—591no—
300#1918—591no—
301#1918—591no—
302#1845—591no—
303#1802—591no—
304C4×#102—591no—
305C2×C59—82no—
306C2×C59#244111yescharacteristic
307C2×C59C2×#47411yescharacteristic
308C2×C59#308311yescharacteristic
309C2×C59#333411yescharacteristic
310C2×C59#335711yescharacteristic
311C2×C59#339111yescharacteristic
312C2×C59#339811yescharacteristic
313C2×#125—1181no—
314C2×C4×D4—591no—
315C2×#117—1181no—
316C2×#107—591no—
317C2×#107—591no—
318C2×#107—591no—
319C2×#107—591no—
320C2×#107C2×D5911yescharacteristic
321C2×#107C2×D5911yescharacteristic
322C2×C4⋊C8—591no—
323C2×C4⋊C8—591no—
324C2×C4⋊C8—591no—
325C2×#102—591no—
326C2×#102—591no—
327C2×#102C2×D5911yescharacteristic
328C2×#102C2×D5911yescharacteristic
329C2×C4×C8—591no—
330#398—1181no—
331#398—1181no—
332#390—591no—
333#390C2×D5911yescharacteristic
334#389—591no—
335#389—591no—
336#389—1181no—
337#388—1181no—
338#388—1181no—
339#384—591no—
340#384—591no—
341#384—591no—
342#384C2×D5911yescharacteristic
343#380—1181no—
344C4×C4⋊C4—591no—
345C4×C4⋊C4—591no—
346C4×C4⋊C4—591no—
347C4×C4⋊C4—591no—
348#340—591no—
349#340—591no—
350#340—591no—
351#340—591no—
352#340—591no—
353#340—591no—
354#336—591no—
355#336C2×D5911yescharacteristic
356C59#2608611yescharacteristic, complemented, Sylow
357C22×D4C22×D5911yescharacteristic
358C23×C4—1181no—
359C22×C8—591no—
360C22×C8—591no—
361C22×C8C22×D5911yescharacteristic
362C22×C8C22×D5911yescharacteristic
363#125—2364no—
364C4×D4—594no—
365C4×D4—1182no—
366#117—2364no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—591no—
370C2×C4⋊C4—591no—
371C2×C4⋊C4—591no—
372C2×C4⋊C4—591no—
373C2×C4⋊C4—591no—
374C2×C4⋊C4—591no—
375C2×C4⋊C4—1181no—
376C2×C4⋊C4—1181no—
377C2×C4⋊C4—1181no—
378C2×C4⋊C4—1181no—
379C2×C4⋊C4—1181no—
380C2×C4⋊C4—1181no—
381C2×C4⋊C4—1181no—
382C2×C4⋊C4—1181no—
383C2×C4⋊C4C22×D5911yescharacteristic
384C2×C4⋊C4C22×D5911yescharacteristic
385C2×C4⋊C4C22×D5911yescharacteristic
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—1181no—
389C2×C22⋊C4—1181no—
390C2×C22⋊C4—1181no—
391C2×C42—591no—
392C2×C42—591no—
393C2×C42—1181no—
394C2×C42—1181no—
395C2×C42—1181no—
396C2×C42C22×D5911yescharacteristic
397#107—22no—
398#107—41no—
399#107—1182no—
400#107—2361no—
401#107—2361no—
402#107—2361no—
403C4⋊C8—1182no—
404C4⋊C8—1182no—
405C4⋊C8—1182no—
406#102—22no—
407#102—41no—
408#102—1182no—
409#102—2361no—
410C4×C8—1182no—
411#95—591no—
412#95—591no—
413#95—1181no—
414#95—1181no—
415#95—1181no—
416#95—1181no—
417#95—1181no—
418C24—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4Q8×D5912yes—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—591no—
429C22×C4—591no—
430C22×C4—591no—
431C22×C4—591no—
432C22×C4—1184no—
433C22×C4—1181no—
434C22×C4—1181no—
435C22×C4—1181no—
436C22×C4—1181no—
437C22×C4—2362no—
438C22×C4—2362no—
439C22×C4D4×D5911yescharacteristic
440C22×C4D4×D5911yescharacteristic
441C22×C4C23×D5911yescharacteristic
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—592no—
448C2×C8—1181no—
449C2×C8—1181no—
450C2×C8—1181no—
451C2×C8—1181no—
452C2×C8—1181no—
453C2×C8#1174568712yes—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—42no—
461C4⋊C4—81no—
462C4⋊C4—594no—
463C4⋊C4—592no—
464C4⋊C4—1182no—
465C4⋊C4—1181no—
466C4⋊C4—1181no—
467C4⋊C4—1181no—
468C4⋊C4—1181no—
469C4⋊C4—1181no—
470C4⋊C4—1181no—
471C4⋊C4—1181no—
472C4⋊C4—4721no—
473C4⋊C4—4721no—
474C4⋊C4—4721no—
475C4⋊C4—2362no—
476C4⋊C4—2362no—
477C4⋊C4—2362no—
478C4⋊C4—2362no—
479C4⋊C4—2362no—
480C22⋊C4—42no—
481C22⋊C4—81no—
482C22⋊C4—1184no—
483C22⋊C4—4721no—
484C22⋊C4—2362no—
485C42—21no—
486C42—21no—
487C42—592no—
488C42—592no—
489C42—1181no—
490C42—1181no—
491C42—2362no—
492C42—2362no—
493C42—2362no—
494C23—22no—
495C23—41no—
496C23—41no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23C2×D4×D5911yescharacteristic
502D4—22no—
503D4—22no—
504D4—41no—
505D4—41no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—592no—
521C2×C4—592no—
522C2×C4—592no—
523C2×C4—592no—
524C2×C4—592no—
525C2×C4—1181no—
526C2×C4—1181no—
527C2×C4—1181no—
528C2×C4—1181no—
529C2×C4—1182no—
530C2×C4—1181no—
531C2×C4—1181no—
532C2×C4—1181no—
533C2×C4—2368no—
534C2×C4—2361no—
535C2×C4—2361no—
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×C4D8×D5912yes—
546C2×C4C2×Q8×D5911yescharacteristic
547C2×C4#41×D5911yescharacteristic
548C2×C4#41×D5911yescharacteristic
549C2×C4C2×#1174568711yescharacteristic
550C2×C4#1427377211yescharacteristic
551C2×C4#1427377411yescharacteristic
552C8—22no—
553C8—41no—
554C8—1182no—
555C8—2361no—
556C22—42no—
557C22—42no—
558C22—42no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22C22⋊Q8×D5911yescharacteristic
564C22#1683805011yescharacteristic
565C22#1683807211yescharacteristic
566C22C2×D8×D5911yescharacteristic
567C22#137×D5911yescharacteristic
568C22#1683820311yescharacteristic
569C22#1683821811yescharacteristic
570C4—22no—
571C4—41no—
572C4—81no—
573C4—81no—
574C4—81no—
575C4—594no—
576C4—1182no—
577C4—1182no—
578C4—4721no—
579C4—4721no—
580C4—4721no—
581C4—2361no—
582C4—2362no—
583C4#1683795411yescharacteristic
584C4#1683803111yescharacteristic
585C4#1683808911yescharacteristic
586C4#1683809711yescharacteristic
587C2—82no—
588C2#2142780211yescharacteristic
589C2#474×D5911yescharacteristic
590C2#2143394211yescharacteristic
591C2#2143643811yescharacteristic
592C2#2143671511yescharacteristic
593C2#2143706911yescharacteristic
594C2#2143712411yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC59×#2093C2
socleC23×C59C22×D4
prime radicalC22×D4×C59C23
hypercenter#2093D59
hypocenterC59#26086
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2093

Complements

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

NH ≅ G/Ntype
1. #21429129C2semidirect
6. #21424852C2semidirect
7. #21424851C2semidirect
8. #21424851C2semidirect
9. #21424813C2semidirect
10. #21424669C2semidirect
11. #21424668C2semidirect
12. #21424254C2semidirect
356. C59#26086semidirect

Maximal subgroups

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

subgroupindex
#214291292
#214270442
#214256222
#214254842
#214254802
#214248522
#214248512
#214248132
#214246692
#214246682
#214242542
#214240942
#102×Dic592
C59×#20932
#2608659