Finite Group Databasebeta

← #28559836

Subgroups — #28559836

Order 15104.

592 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21434161C211yesmaximal, characteristic
2#21433113C211yesmaximal, characteristic
3#21433045C211yesmaximal, characteristic, complemented
4#21423001C211yesmaximal, characteristic, complemented
5#21422983C211yesmaximal, characteristic, complemented
6#21422971C211yesmaximal, characteristic, complemented
7#21422970C211yesmaximal, characteristic, complemented
8#21422949C211yesmaximal, characteristic, complemented
9#21422936C211yesmaximal, characteristic, complemented
10#21422912C211yesmaximal, characteristic, complemented
11#21422900C211yesmaximal, characteristic, complemented
12#21422882C211yesmaximal, characteristic, complemented
13#21422484C211yesmaximal, characteristic
14#21422391C211yesmaximal, characteristic, complemented
15C59×#1497C211yesmaximal, characteristic, complemented
16C4×#11745685C2211yescharacteristic
17#16837740C411yescharacteristic
18#16837740C411yescharacteristic
19#16837684C411yescharacteristic
20#16837679C411yescharacteristic
21#16837609C411yescharacteristic
22#16837604C411yescharacteristic
23#16837562C411yescharacteristic
24#16837562C411yescharacteristic
25#16837533—21no—
26#16837533—21no—
27#16837533C2211yescharacteristic
28#16837533C2211yescharacteristic
29Q8×C59⋊C8C2211yescharacteristic
30Q8×C59⋊C8C2211yescharacteristic
31#16837526C2211yescharacteristic
32#16837526C2211yescharacteristic
33C4×#11745672C2211yescharacteristic
34C4×#11745672C2211yescharacteristic
35C4×#11745671C2211yescharacteristic
36C4×#11745671C2211yescharacteristic
37#16837479C2211yescharacteristic
38#16837479C2211yescharacteristic
39#16837477—21no—
40#16837477—21no—
41#16837457—21no—
42#16837455C2211yescharacteristic
43#16837429—21no—
44C2×C4⋊(C59⋊C8)C2211yescharacteristic
45#16837358—21no—
46C4×#11745664C2211yescharacteristic
47#16837354—21no—
48#16837154C2211yescharacteristic
49#16837154C2211yescharacteristic
50#16837152C2211yescharacteristic
51#16837152C2211yescharacteristic
52#16837134C2211yescharacteristic
53#16837134C2211yescharacteristic
54#16837131C2211yescharacteristic
55#16837131C2211yescharacteristic
56#16837124C2211yescharacteristic
57#16837124C2211yescharacteristic
58#16837123C2211yescharacteristic
59C8×C59⋊C8C2211yescharacteristic
60C59×#533C2211yescharacteristic
61C59×#432C2211yescharacteristic
62C59×#431C2211yescharacteristic
63C59×Q8⋊C8C2211yescharacteristic
64C59×Q8⋊C8C2211yescharacteristic
65C59×Q8⋊C8C2211yescharacteristic
66C59×Q8⋊C8C2211yescharacteristic
67C2×#11745685C2×C411yescharacteristic
68C2×#11745672C2×C411yescharacteristic
69C2×#11745672C2×C411yescharacteristic
70C2×#11745671C2×C411yescharacteristic
71C2×#11745671C2×C411yescharacteristic
72C2×#11745664D411yescharacteristic
73C2×#11745664D411yescharacteristic
74C2×#11745659—21no—
75C2×#11745659—21no—
76C22×C59⋊C8—21no—
77C4×Dic118C2×C411yescharacteristic
78C4×Dic118C2311yescharacteristic
79C4×D236C2×C411yescharacteristic
80C4×D236C2311yescharacteristic
81C4×C22⋊D59—21no—
82C4×C22⋊D59—21no—
83#14273686C2×C411yescharacteristic
84#14273684—21no—
85C42×D59—21no—
86#14273660C2×C411yescharacteristic
87#14273660C2×C411yescharacteristic
88#14273658C2×C411yescharacteristic
89#14273658C2×C411yescharacteristic
90C4⋊(C59⋊C8)—21no—
91C4⋊(C59⋊C8)—21no—
92C4⋊(C59⋊C8)—21no—
93C4⋊(C59⋊C8)—21no—
94C4⋊(C59⋊C8)—21no—
95C4⋊(C59⋊C8)C2×C411yescharacteristic
96C4⋊(C59⋊C8)C2×C411yescharacteristic
97C4⋊(C59⋊C8)C2311yescharacteristic
98C4⋊(C59⋊C8)C2311yescharacteristic
99Dic59⋊C8—21no—
100Dic59⋊C8—21no—
101#14273651C2×C411yescharacteristic
102#14273651C2×C411yescharacteristic
103#14273651C2×C411yescharacteristic
104#14273651C2×C411yescharacteristic
105#14273650C2×C411yescharacteristic
106#14273650C2×C411yescharacteristic
107#14273647C2×C411yescharacteristic
108#14273647C2×C411yescharacteristic
109C22⋊(C59⋊C8)C2×C411yescharacteristic
110C22⋊(C59⋊C8)C2×C411yescharacteristic
111(C2×D59)⋊C8—21no—
112(C2×D59)⋊C8—21no—
113#14273638—21no—
114#14273638—21no—
115#14273638D411yescharacteristic
116#14273638D411yescharacteristic
117C4×C59⋊C8—21no—
118C4×C59⋊C8—21no—
119C4×C59⋊C8C2311yescharacteristic
120C4×C59⋊C8C2311yescharacteristic
121C4×C59⋊C8C2311yescharacteristic
122C4×C59⋊C8C2311yescharacteristic
123C8×Dic59—21no—
124C8×Dic59—21no—
125C4⋊Q8×C59C2×C411yescharacteristic
126C4⋊Q8×C59C2×C411yescharacteristic
127#125×C59—21no—
128C22⋊Q8×C59—21no—
129C22⋊Q8×C59C2×C411yescharacteristic
130C22⋊Q8×C59C2×C411yescharacteristic
131C4×Q8×C59—21no—
132C4×Q8×C59C2311yescharacteristic
133C4×Q8×C59C2311yescharacteristic
134#117×C59—21no—
135C2×C42×C59C2311yescharacteristic
136C4⋊C8×C59—21no—
137C4⋊C8×C59C2311yescharacteristic
138C4⋊C8×C59C2311yescharacteristic
139C22⋊C8×C59—21no—
140C22⋊C8×C59—21no—
141#97×C59—21no—
142C4×C8×C59C2311yescharacteristic
143C4×C8×C59C2311yescharacteristic
144C2×Q8×C59—21no—
145C2×Q8×C59C22×C411yescharacteristic
146C2×Q8×C59C22×C411yescharacteristic
147C22×C4×C59C22×C411yescharacteristic
148C22×C4×C59C2×D411yescharacteristic
149C22×C4×C59#4111yescharacteristic
150C2×C22⋊D59—21no—
151#11745685—22no—
152#11745685—41no—
153C2×D236C22×C411yescharacteristic
154C2×C4×D59—21no—
155C2×C4×D59—21no—
156C2×C4×D59—21no—
157C2×Dic118C22×C411yescharacteristic
158C2×C8×C59—21no—
159C2×C8×C59—21no—
160C2×C8×C59—21no—
161C2×C8×C59—21no—
162C4⋊C4×C59—21no—
163C4⋊C4×C59—21no—
164C4⋊C4×C59—21no—
165C4⋊C4×C59—21no—
166C4⋊C4×C59—21no—
167C4⋊C4×C59—21no—
168C4⋊C4×C59—21no—
169C4⋊C4×C59C22×C411yescharacteristic
170C4⋊C4×C59C22×C411yescharacteristic
171C22⋊C4×C59—21no—
172C22⋊C4×C59—21no—
173C42×C59—21no—
174C42×C59—21no—
175C42×C59C22×C411yescharacteristic
176C42×C59C2×D411yescharacteristic
177C42×C59#4111yescharacteristic
178C42×C59C2411yescharacteristic
179C22⋊Dic59—21no—
180#11745672—22no—
181#11745672—22no—
182#11745671—41no—
183#11745671—41no—
184(C2×D59)⋊C4—21no—
185(C2×D59)⋊C4—21no—
186C4⋊Dic59C22×C411yescharacteristic
187C4⋊Dic59C22×C411yescharacteristic
188Dic59⋊C4—21no—
189Dic59⋊C4—21no—
190C4×Dic59—21no—
191C4×Dic59—21no—
192C4×Dic59—21no—
193#11745664—22no—
194#11745664—41no—
195C2×C59⋊C8—21no—
196C2×C59⋊C8—21no—
197C2×C59⋊C8—42no—
198C2×C59⋊C8C22×C411yescharacteristic
199C2×C59⋊C8C22×C411yescharacteristic
200C2×C59⋊C8C22×C411yescharacteristic
201C2×C59⋊C8C22×C411yescharacteristic
202C2×C59⋊C8C2×D411yescharacteristic
203C2×C59⋊C8C2×D411yescharacteristic
204C2×C59⋊C8C2×D411yescharacteristic
205C2×C59⋊C8C2×D411yescharacteristic
206#11745659—42no—
207#11745659—42no—
208C23×C59C4×D411yescharacteristic
209C22×D59—21no—
210Q8×C59—21no—
211Q8×C59—21no—
212Q8×C59—21no—
213Q8×C59—21no—
214Q8×C59—81no—
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—41no—
224C2×C4×C59C4×D411yescharacteristic
225C2×C4×C59C4×D411yescharacteristic
226C2×C4×C59C4×D411yescharacteristic
227C2×C4×C59C23×C411yescharacteristic
228C2×C4×C59C22×D411yescharacteristic
229C2×C4×C59C2×#4111yescharacteristic
230C22⋊D59—42no—
231C2×Dic59—21no—
232C2×Dic59—21no—
233C2×Dic59—21no—
234D236—21no—
235D236—21no—
236C4×D59—42no—
237C4×D59—41no—
238C4×D59—41no—
239C4×D59—81no—
240Dic118—21no—
241Dic118#13112yes—
242C8×C59—41no—
243C8×C59—41no—
244C8×C59—41no—
245C8×C59—41no—
246C59⋊C8—21no—
247C59⋊C8—21no—
248C59⋊C8—21no—
249C59⋊C8—21no—
250C59⋊C8—21no—
251C59⋊C8—21no—
252C59⋊C8—21no—
253C59⋊C8—41no—
254C59⋊C8—41no—
255C59⋊C8#13712yes—
256#18013—591nomaximal, Sylow
257C22×C59—21no—
258C22×C59—21no—
259C22×C59—21no—
260C22×C59C2×C4×D411yescharacteristic
261C2×D59—41no—
262C2×D59—41no—
263C2×D59—41no—
264C4×C59—21no—
265C4×C59—21no—
266C4×C59—21no—
267C4×C59—21no—
268C4×C59—41no—
269C4×C59—41no—
270C4×C59—41no—
271C4×C59—41no—
272C4×C59C2×#13111yescharacteristic
273C4×C59#56811yescharacteristic
274C4×C59C2×#13711yescharacteristic
275C4×C59#57511yescharacteristic
276Dic59—22no—
277Dic59—41no—
278Dic59—41no—
279#3107—591no—
280#2971—591no—
281#2962—591no—
282#1592—591no—
283#1590—591no—
284#1588—591no—
285#1587—591no—
286#1584—591no—
287#1583—591no—
288#1579—591no—
289C8×Q16—591no—
290#1573—591no—
291#1497D5911yescharacteristic, complemented
292#1477—591no—
293#1453—591no—
294C2×C59—41no—
295C2×C59#293311yescharacteristic
296C2×C59C4×#13711yescharacteristic
297C2×C59#295711yescharacteristic
298D59—81no—
299#533C2×D5911yescharacteristic
300C4×#41—591no—
301#485—591no—
302#485—591no—
303#475—591no—
304#474—591no—
305#462—591no—
306#461—591no—
307#452—591no—
308#452—591no—
309#446—591no—
310#446—591no—
311#446—1181no—
312#446—1181no—
313C8×Q8—591no—
314C8×Q8—591no—
315C8×Q8—591no—
316C8×Q8—591no—
317C4×Q16—591no—
318C4×Q16—591no—
319C4×SD16—591no—
320C4×SD16—591no—
321#436—591no—
322#436—591no—
323#436—1181no—
324#436—1181no—
325#432—1181no—
326#432C2×D5911yescharacteristic
327#431—591no—
328#431C2×D5911yescharacteristic
329#424—1181no—
330C2×C4⋊C8—591no—
331#405—1181no—
332C4×M16—591no—
333C4×M16—1181no—
334#335—591no—
335#335—591no—
336#334—591no—
337#334—591no—
338Q8⋊C8—591no—
339Q8⋊C8—591no—
340Q8⋊C8C2×D5911yescharacteristic
341Q8⋊C8C2×D5911yescharacteristic
342Q8⋊C8C2×D5911yescharacteristic
343Q8⋊C8C2×D5911yescharacteristic
344D4⋊C8—591no—
345D4⋊C8—591no—
346#322—591no—
347#322—591no—
348#322—591no—
349C82—591no—
350C59#1801311yescharacteristic, complemented, Sylow
351C2×#41—591no—
352C2×Q16—591no—
353C2×Q16—591no—
354C2×SD16—591no—
355C2×SD16—591no—
356C2×M16—591no—
357C2×M16—591no—
358C2×M16—1181no—
359C2×M16—1181no—
360C22×C8—1181no—
361C4⋊Q8C4×D5911yescharacteristic
362C4⋊Q8C4×D5911yescharacteristic
363#125—21no—
364C22⋊Q8—21no—
365C22⋊Q8C4×D5911yescharacteristic
366C22⋊Q8C4×D5911yescharacteristic
367C4×Q8—21no—
368C4×Q8—591no—
369C4×Q8—591no—
370C4×Q8C22×D5911yescharacteristic
371C4×Q8C22×D5911yescharacteristic
372C4×D4—591no—
373C4×D4—591no—
374C4×D4—1181no—
375C4×D4—1181no—
376#117—21no—
377#117—591no—
378#117—1181no—
379C2×C42—1181no—
380C2×C42C22×D5911yescharacteristic
381#107—591no—
382#107—591no—
383#106—591no—
384#106—591no—
385C4⋊C8—21no—
386C4⋊C8—591no—
387C4⋊C8—591no—
388C4⋊C8—591no—
389C4⋊C8—591no—
390C4⋊C8—1181no—
391C4⋊C8—1181no—
392C4⋊C8—1181no—
393C4⋊C8—1181no—
394C4⋊C8—1181no—
395C4⋊C8—1181no—
396C4⋊C8—1181no—
397C4⋊C8C22×D5911yescharacteristic
398C4⋊C8C22×D5911yescharacteristic
399#103—591no—
400#103—591no—
401#103—591no—
402#103—591no—
403#103—591no—
404#103—591no—
405#102—591no—
406#102—591no—
407C22⋊C8—21no—
408C22⋊C8—21no—
409C22⋊C8—591no—
410C22⋊C8—591no—
411C22⋊C8—1181no—
412C22⋊C8—1181no—
413#97—21no—
414#97—591no—
415#97—591no—
416#97—1181no—
417#97—1181no—
418C4×C8—591no—
419C4×C8—591no—
420C4×C8—591no—
421C4×C8—591no—
422C4×C8—1181no—
423C4×C8—1181no—
424C4×C8—1181no—
425C4×C8—1181no—
426C4×C8C22×D5911yescharacteristic
427C4×C8C22×D5911yescharacteristic
428#41—1182no—
429#41—2361no—
430C2×Q8—21no—
431C2×Q8—591no—
432C2×Q8C2×C4×D5911yescharacteristic
433C2×Q8C2×C4×D5911yescharacteristic
434C2×D4—591no—
435C2×D4—1181no—
436C22×C4—1181no—
437C22×C4—1181no—
438C22×C4—1181no—
439C22×C4C2×C4×D5911yescharacteristic
440C22×C4D4×D5911yescharacteristic
441C22×C4#1174568711yescharacteristic
442Q16—1182no—
443Q16—1182no—
444SD16—2361no—
445SD16—2361no—
446M16—1182no—
447M16—2362no—
448M16—2362no—
449M16—2361no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—591no—
455C2×C8—591no—
456C2×C8—591no—
457C2×C8—591no—
458C2×C8—591no—
459C2×C8—591no—
460C2×C8—591no—
461C2×C8—591no—
462C2×C8—1181no—
463C2×C8—1181no—
464C2×C8—2362no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—591no—
473C4⋊C4—591no—
474C4⋊C4—1181no—
475C4⋊C4—1181no—
476C4⋊C4C2×C4×D5911yescharacteristic
477C4⋊C4C2×C4×D5911yescharacteristic
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—1181no—
481C22⋊C4—1181no—
482C22⋊C4—1181no—
483C42—21no—
484C42—21no—
485C42—1181no—
486C42—1181no—
487C42—1181no—
488C42C2×C4×D5911yescharacteristic
489C42D4×D5911yescharacteristic
490C42#1174568711yescharacteristic
491C42C23×D5911yescharacteristic
492C23—1181no—
493C23(C22⋊D59)⋊C411yescharacteristic
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—21no—
498Q8—81no—
499Q8—592no—
500Q8—1181no—
501D4—1181no—
502D4—1181no—
503D4—2362no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—41no—
513C2×C4—1181no—
514C2×C4—1181no—
515C2×C4—1181no—
516C2×C4—4721no—
517C2×C4—2362no—
518C2×C4—2361no—
519C2×C4—2361no—
520C2×C4(C22⋊D59)⋊C411yescharacteristic
521C2×C4(C22⋊D59)⋊C411yescharacteristic
522C2×C4(C22⋊D59)⋊C411yescharacteristic
523C2×C4C22×C4×D5911yescharacteristic
524C2×C4C2×D4×D5911yescharacteristic
525C2×C4C2×#1174568711yescharacteristic
526C8—41no—
527C8—41no—
528C8—41no—
529C8—41no—
530C8—592no—
531C8—1181no—
532C8—1181no—
533C8—1181no—
534C8—1181no—
535C8—1181no—
536C8—1181no—
537C8—1181no—
538C8—2361no—
539C8—2361no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—2361no—
544C22—2361no—
545C22—2361no—
546C22C2×(C22⋊D59)⋊C411yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—1182no—
556C4—2361no—
557C4—2361no—
558C4#131×D5911yescharacteristic
559C4#1683816711yescharacteristic
560C4#137×D5911yescharacteristic
561C4#1683820111yescharacteristic
562C2—41no—
563C2—4721no—
564C2#2143282611yescharacteristic
565C2#2143291111yescharacteristic
566C2#2143300911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC42C23×D59
FittingC59×#1497C2
socleC22×C59C2×C4×D4
prime radicalC2×#11745685C2×C4
cosocleC42×C59C24
hypercenter#1497D59
hypocenterC59#18013
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1497

Complements

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

NH ≅ G/Ntype
3. #21433045C2semidirect
4. #21423001C2semidirect
5. #21422983C2semidirect
6. #21422971C2semidirect
7. #21422970C2semidirect
8. #21422949C2semidirect
9. #21422936C2semidirect
10. #21422912C2semidirect
11. #21422900C2semidirect
12. #21422882C2semidirect
14. #21422391C2semidirect
15. C59×#1497C2semidirect
291. #1497D59semidirect
350. C59#18013semidirect

Maximal subgroups

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

subgroupindex
#214341612
#214331132
#214330452
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