Finite Group Databasebeta

← #28559563

Subgroups — #28559563

Order 15104.

576 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21434669C211yesmaximal, characteristic
2#21433248C211yesmaximal, characteristic, complemented
3#21433244C211yesmaximal, characteristic, complemented
4#21422968C211yesmaximal, characteristic, complemented
5#21422962C211yesmaximal, characteristic, complemented
6#21422959C211yesmaximal, characteristic, complemented
7#21422939C211yesmaximal, characteristic, complemented
8#21422936C211yesmaximal, characteristic, complemented
9#21422935C211yesmaximal, characteristic, complemented
10#21422930C211yesmaximal, characteristic, complemented
11#21422850C211yesmaximal, characteristic, complemented
12#21422560C211yesmaximal, characteristic, complemented
13#21422560C211yesmaximal, characteristic, complemented
14#21422387C211yesmaximal, characteristic, complemented
15C59×#1587C211yesmaximal, characteristic, complemented
16#16837939C2211yescharacteristic
17#16837939C2211yescharacteristic
18#16837803C411yescharacteristic
19#16837787C411yescharacteristic
20#16837758C411yescharacteristic
21#16837758C411yescharacteristic
22#16837640C411yescharacteristic
23#16837639C411yescharacteristic
24#16837634C411yescharacteristic
25#16837634C411yescharacteristic
26#16837533C2211yescharacteristic
27Q8×C59⋊C8C2211yescharacteristic
28C4×#11745671C2211yescharacteristic
29C4×#11745671C2211yescharacteristic
30C4×D472C2211yescharacteristic
31#16837481—21no—
32#16837481C2211yescharacteristic
33#16837479—21no—
34#16837479C2211yescharacteristic
35#16837475—21no—
36#16837472—21no—
37C8×D236C2211yescharacteristic
38#16837467C2211yescharacteristic
39#16837464—21no—
40#16837461—21no—
41#16837453C2211yescharacteristic
42#16837453C2211yescharacteristic
43#16837427—21no—
44#16837427—21no—
45#16837424C2211yescharacteristic
46#16837424C2211yescharacteristic
47C4×C8×D59C2211yescharacteristic
48#16837153C2211yescharacteristic
49#16837152C2211yescharacteristic
50#16837152C2211yescharacteristic
51Q8⋊(C59⋊C8)C2211yescharacteristic
52Q8⋊(C59⋊C8)C2211yescharacteristic
53#16837131C2211yescharacteristic
54#16837131C2211yescharacteristic
55#16837129C2211yescharacteristic
56#16837129C2211yescharacteristic
57#16837124C2211yescharacteristic
58#16837124C2211yescharacteristic
59#16837123C2211yescharacteristic
60C59×#446C2211yescharacteristic
61C8×Q8×C59C2211yescharacteristic
62C4×Q16×C59C2211yescharacteristic
63C59×#334C2211yescharacteristic
64C59×Q8⋊C8C2211yescharacteristic
65C59×Q8⋊C8C2211yescharacteristic
66C59×#322C2211yescharacteristic
67C2×#11745671C2×C411yescharacteristic
68C2×#11745671C2×C411yescharacteristic
69C2×D472C2×C411yescharacteristic
70C2×#11745659—21no—
71C2×#11745659—21no—
72C2×#11745659—21no—
73C2×#11745659—21no—
74C2×C8×D59—21no—
75C2×C8×D59—21no—
76C2×C8×D59C2×C411yescharacteristic
77C2×C8×D59C2×C411yescharacteristic
78#14273722—21no—
79#14273722—21no—
80#14273718C2×C411yescharacteristic
81#14273718C2×C411yescharacteristic
82#14273716C2×C411yescharacteristic
83#14273716C2×C411yescharacteristic
84#14273712—21no—
85#14273712—21no—
86#14273703C2×C411yescharacteristic
87#14273703C2×C411yescharacteristic
88#14273702C2×C411yescharacteristic
89#14273702C2×C411yescharacteristic
90C4×D236—21no—
91C4×D236—21no—
92C4×D236C2311yescharacteristic
93C4×D236C2311yescharacteristic
94#14273684—21no—
95#14273684—21no—
96C42×D59C2311yescharacteristic
97#14273661C2×C411yescharacteristic
98#14273658C2×C411yescharacteristic
99#14273658C2×C411yescharacteristic
100C4⋊(C59⋊C8)—21no—
101C4⋊(C59⋊C8)—21no—
102C4⋊(C59⋊C8)C2311yescharacteristic
103C4⋊(C59⋊C8)C2311yescharacteristic
104Dic59⋊C8—21no—
105Dic59⋊C8—21no—
106Dic59⋊C8—21no—
107Dic59⋊C8D411yescharacteristic
108Dic59⋊C8D411yescharacteristic
109#14273651C2×C411yescharacteristic
110#14273651C2×C411yescharacteristic
111#14273649C2×C411yescharacteristic
112#14273649C2×C411yescharacteristic
113#14273647C2×C411yescharacteristic
114#14273647C2×C411yescharacteristic
115(C2×D59)⋊C8—21no—
116(C2×D59)⋊C8—21no—
117(C2×D59)⋊C8—21no—
118(C2×D59)⋊C8—21no—
119(C2×D59)⋊C8—21no—
120(C2×D59)⋊C8D411yescharacteristic
121(C2×D59)⋊C8D411yescharacteristic
122#14273638—21no—
123C4×C59⋊C8—21no—
124C4×C59⋊C8C2311yescharacteristic
125C4×C59⋊C8C2311yescharacteristic
126C4×C59⋊C8C2311yescharacteristic
127C8×Dic59C2×C411yescharacteristic
128C8×Dic59C2×C411yescharacteristic
129C2×Q16×C59C2×C411yescharacteristic
130C4×Q8×C59C2311yescharacteristic
131C4×Q8×C59C2311yescharacteristic
132#107×C59C2×C411yescharacteristic
133C4⋊C8×C59—21no—
134C4⋊C8×C59—21no—
135C4⋊C8×C59C2311yescharacteristic
136C4⋊C8×C59C2311yescharacteristic
137#103×C59C2×C411yescharacteristic
138#103×C59C2×C411yescharacteristic
139#97×C59—21no—
140C4×C8×C59—21no—
141C4×C8×C59C2311yescharacteristic
142C4×C8×C59C2311yescharacteristic
143C4×C8×C59C2311yescharacteristic
144C2×Q8×C59C22×C411yescharacteristic
145C2×Q8×C59C22×C411yescharacteristic
146C2×D236—21no—
147C2×D236—21no—
148C2×D236C22×C411yescharacteristic
149C2×D236C22×C411yescharacteristic
150C2×C4×D59—21no—
151C2×C4×D59—21no—
152C2×C4×D59C22×C411yescharacteristic
153C2×C4×D59C2×D411yescharacteristic
154C2×C4×D59#4111yescharacteristic
155Q16×C59—41no—
156C2×C8×C59—21no—
157C2×C8×C59—21no—
158C2×C8×C59—21no—
159C2×C8×C59C22×C411yescharacteristic
160C2×C8×C59C22×C411yescharacteristic
161C2×C8×C59C2×D411yescharacteristic
162C2×C8×C59C2×D411yescharacteristic
163C4⋊C4×C59—21no—
164C4⋊C4×C59—21no—
165C4⋊C4×C59C22×C411yescharacteristic
166C4⋊C4×C59C22×C411yescharacteristic
167C42×C59—21no—
168C42×C59—21no—
169C42×C59C2411yescharacteristic
170#11745671—41no—
171#11745671—41no—
172(C2×D59)⋊C4—21no—
173(C2×D59)⋊C4—21no—
174(C2×D59)⋊C4—21no—
175(C2×D59)⋊C4—21no—
176(C2×D59)⋊C4—21no—
177(C2×D59)⋊C4—21no—
178(C2×D59)⋊C4—21no—
179(C2×D59)⋊C4—21no—
180(C2×D59)⋊C4—21no—
181(C2×D59)⋊C4—21no—
182C4⋊Dic59—21no—
183C4⋊Dic59—21no—
184C4⋊Dic59C22×C411yescharacteristic
185C4⋊Dic59C22×C411yescharacteristic
186Dic59⋊C4—21no—
187Dic59⋊C4—21no—
188Dic59⋊C4—21no—
189Dic59⋊C4—21no—
190C4×Dic59C22×C411yescharacteristic
191C4×Dic59C2×D411yescharacteristic
192C4×Dic59#4111yescharacteristic
193C2×C59⋊C8—21no—
194C2×C59⋊C8—21no—
195C2×C59⋊C8—21no—
196C2×C59⋊C8C22×C411yescharacteristic
197C2×C59⋊C8C22×C411yescharacteristic
198C2×C59⋊C8C2×D411yescharacteristic
199C2×C59⋊C8C2×D411yescharacteristic
200D472—41no—
201#11745659—81no—
202#11745659—81no—
203#11745659—81no—
204#11745659—81no—
205C8×D59—41no—
206C8×D59—41no—
207C8×D59—81no—
208C8×D59—81no—
209C22×D59—21no—
210C22×D59—21no—
211C22×D59C4×D411yescharacteristic
212Q8×C59—21no—
213Q8×C59—21no—
214Q8×C59—21no—
215Q8×C59—21no—
216C2×C4×C59—21no—
217C2×C4×C59—21no—
218C2×C4×C59—21no—
219C2×C4×C59—21no—
220C2×C4×C59C23×C411yescharacteristic
221C2×C4×C59C22×D411yescharacteristic
222C2×C4×C59C2×#4111yescharacteristic
223C2×Dic59—21no—
224C2×Dic59—21no—
225C2×Dic59C4×D411yescharacteristic
226C2×Dic59C4×D411yescharacteristic
227C2×Dic59C4×D411yescharacteristic
228D236—21no—
229D236—21no—
230D236—21no—
231D236—21no—
232D236—81no—
233D236—81no—
234C4×D59—21no—
235C4×D59—21no—
236C4×D59—21no—
237C4×D59—21no—
238C4×D59—41no—
239C4×D59—41no—
240C4×D59—41no—
241C4×D59—41no—
242C4×D59—41no—
243C8×C59—21no—
244C8×C59—21no—
245C8×C59—21no—
246C8×C59—21no—
247C8×C59—41no—
248C8×C59—41no—
249C8×C59—41no—
250C59⋊C8—21no—
251C59⋊C8—21no—
252C59⋊C8—21no—
253C59⋊C8—21no—
254C59⋊C8—41no—
255C59⋊C8—41no—
256C59⋊C8—41no—
257#17993—591nomaximal, Sylow
258C22×C59C2×C4×D411yescharacteristic
259C2×D59—21no—
260C2×D59—21no—
261C2×D59—21no—
262C2×D59—41no—
263C2×D59—41no—
264C2×D59—41no—
265C2×D59—41no—
266C2×D59—41no—
267C2×D59—41no—
268C4×C59—21no—
269C4×C59—41no—
270C4×C59—41no—
271C4×C59—41no—
272C4×C59—41no—
273C4×C59#56811yescharacteristic
274C4×C59#56811yescharacteristic
275C4×C59#57711yescharacteristic
276C4×C59#57711yescharacteristic
277Dic59—21no—
278Dic59—21no—
279Dic59—21no—
280Dic59—41no—
281Dic59—41no—
282#3168—591no—
283#2993—591no—
284#2993—591no—
285#1587—591no—
286#1587D5911yescharacteristic, complemented
287#1586—591no—
288#1586—591no—
289#1583—591no—
290#1583—591no—
291#1582—591no—
292#1582—591no—
293#1566—591no—
294#1495—591no—
295#1495—591no—
296#1452—591no—
297C2×C59#293211yescharacteristic
298C2×C59#295211yescharacteristic
299C2×C59#295711yescharacteristic
300D59—41no—
301D59—81no—
302D59—81no—
303#529—591no—
304#529—591no—
305#499—591no—
306#495—591no—
307#488—591no—
308#488—591no—
309#467—591no—
310#466—591no—
311#465—591no—
312#465—591no—
313#446—591no—
314#446C2×D5911yescharacteristic
315C8×Q8—591no—
316C8×Q8C2×D5911yescharacteristic
317C4×Q16C2×D5911yescharacteristic
318C4×SD16—591no—
319C4×SD16—591no—
320C4×D8—591no—
321#436—591no—
322#436—591no—
323#436—1181no—
324#436—1181no—
325#435—1181no—
326#435—1181no—
327C8×D4—591no—
328C8×D4—591no—
329#433—1181no—
330#433—1181no—
331#431—591no—
332#431—591no—
333#424—1181no—
334#424—1181no—
335#423—591no—
336#423—591no—
337C2×C4×C8—591no—
338#334—591no—
339#334—591no—
340#334—591no—
341#334C2×D5911yescharacteristic
342Q8⋊C8—591no—
343Q8⋊C8—591no—
344Q8⋊C8C2×D5911yescharacteristic
345Q8⋊C8C2×D5911yescharacteristic
346D4⋊C8—591no—
347D4⋊C8—591no—
348D4⋊C8—591no—
349D4⋊C8—591no—
350#322—591no—
351#322—591no—
352#322—591no—
353#322C2×D5911yescharacteristic
354C59#1799311yescharacteristic, complemented, Sylow
355C2×Q16C4×D5911yescharacteristic
356C2×SD16—591no—
357C2×SD16—591no—
358C2×D8—591no—
359C2×M16—1181no—
360C2×M16—1181no—
361C2×M16—1181no—
362C2×M16—1181no—
363C22×C8—591no—
364C22×C8—591no—
365C22×C8—1181no—
366C22×C8—1181no—
367#126—1181no—
368#126—1181no—
369#125—591no—
370#125—591no—
371#124—591no—
372#124—591no—
373#123—1181no—
374#123—1181no—
375C22⋊Q8—591no—
376C22⋊Q8—591no—
377#121—591no—
378#121—591no—
379C4×Q8C22×D5911yescharacteristic
380C4×Q8C22×D5911yescharacteristic
381C4×D4—591no—
382C4×D4—591no—
383C4×D4—1181no—
384C4×D4—1181no—
385#117—1181no—
386#117—1181no—
387C2×C42—591no—
388#107—591no—
389#107C4×D5911yescharacteristic
390#106—591no—
391#106—591no—
392C4⋊C8—21no—
393C4⋊C8—21no—
394C4⋊C8—591no—
395C4⋊C8—591no—
396C4⋊C8—591no—
397C4⋊C8—591no—
398C4⋊C8—1181no—
399C4⋊C8—1181no—
400C4⋊C8—1181no—
401C4⋊C8—1181no—
402C4⋊C8—1181no—
403C4⋊C8C22×D5911yescharacteristic
404C4⋊C8C22×D5911yescharacteristic
405#103—591no—
406#103—591no—
407#103C4×D5911yescharacteristic
408#103C4×D5911yescharacteristic
409#102—591no—
410#102—591no—
411#102—591no—
412#102—591no—
413C22⋊C8—591no—
414C22⋊C8—591no—
415C22⋊C8—1181no—
416C22⋊C8—1181no—
417C22⋊C8—1181no—
418C22⋊C8—1181no—
419C22⋊C8—1181no—
420#97—21no—
421#97—1181no—
422C4×C8—21no—
423C4×C8—591no—
424C4×C8—591no—
425C4×C8—591no—
426C4×C8—591no—
427C4×C8—591no—
428C4×C8—1181no—
429C4×C8C22×D5911yescharacteristic
430C4×C8C22×D5911yescharacteristic
431C4×C8C22×D5911yescharacteristic
432C2×Q8C2×C4×D5911yescharacteristic
433C2×Q8C2×C4×D5911yescharacteristic
434C2×D4—591no—
435C2×D4—591no—
436C2×D4—1181no—
437C2×D4—1181no—
438C22×C4—591no—
439C22×C4—591no—
440C22×C4—591no—
441C22×C4—1181no—
442C22×C4—1181no—
443Q16—41no—
444SD16—2361no—
445SD16—2361no—
446D8—2361no—
447M16—4721no—
448M16—4721no—
449M16—4721no—
450M16—4721no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—591no—
455C2×C8—591no—
456C2×C8—591no—
457C2×C8—591no—
458C2×C8—1181no—
459C2×C8—1181no—
460C2×C8—1181no—
461C2×C8—4721no—
462C2×C8—4721no—
463C2×C8—2361no—
464C2×C8—2361no—
465C2×C8C2×C4×D5911yescharacteristic
466C2×C8C2×C4×D5911yescharacteristic
467C2×C8D4×D5911yescharacteristic
468C2×C8D4×D5911yescharacteristic
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—591no—
472C4⋊C4—591no—
473C4⋊C4—1181no—
474C4⋊C4—1181no—
475C4⋊C4—1181no—
476C4⋊C4—1181no—
477C4⋊C4—1181no—
478C4⋊C4—1181no—
479C4⋊C4C2×C4×D5911yescharacteristic
480C4⋊C4C2×C4×D5911yescharacteristic
481C22⋊C4—1181no—
482C22⋊C4—1181no—
483C22⋊C4—1181no—
484C22⋊C4—1181no—
485C22⋊C4—1181no—
486C22⋊C4—1181no—
487C22⋊C4—1181no—
488C22⋊C4—1181no—
489C22⋊C4—1181no—
490C22⋊C4—1181no—
491C42—21no—
492C42—21no—
493C42—591no—
494C42—591no—
495C42—591no—
496C42C23×D5911yescharacteristic
497C23—591no—
498C23—1181no—
499C23—1181no—
500Q8—21no—
501Q8—21no—
502Q8—21no—
503Q8—21no—
504D4—1181no—
505D4—1181no—
506D4—1181no—
507D4—1181no—
508D4—4721no—
509D4—4721no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—591no—
515C2×C4—591no—
516C2×C4—591no—
517C2×C4—1181no—
518C2×C4—1181no—
519C2×C4—1181no—
520C2×C4—1181no—
521C2×C4—1181no—
522C2×C4—1181no—
523C2×C4—2361no—
524C2×C4—2361no—
525C2×C4—2361no—
526C2×C4—2361no—
527C2×C4—2361no—
528C2×C4C22×C4×D5911yescharacteristic
529C2×C4C2×D4×D5911yescharacteristic
530C2×C4#41×D5911yescharacteristic
531C8—21no—
532C8—21no—
533C8—21no—
534C8—21no—
535C8—41no—
536C8—41no—
537C8—41no—
538C8—1181no—
539C8—1181no—
540C8—1181no—
541C8—1181no—
542C8—2361no—
543C8—2361no—
544C8—2361no—
545C22—1181no—
546C22—1181no—
547C22—1181no—
548C22—2361no—
549C22—2361no—
550C22—2361no—
551C22—2361no—
552C22—2361no—
553C22—2361no—
554C22C4×D4×D5911yescharacteristic
555C4—21no—
556C4—41no—
557C4—41no—
558C4—41no—
559C4—41no—
560C4—1181no—
561C4—1181no—
562C4—1181no—
563C4—2361no—
564C4—2361no—
565C4#1683816711yescharacteristic
566C4#1683816811yescharacteristic
567C4#1683821111yescharacteristic
568C4#1683821111yescharacteristic
569C2—4721no—
570C2—4721no—
571C2—2361no—
572C2#2143281011yescharacteristic
573C2#2143297611yescharacteristic
574C2#2143300811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC42C23×D59
FittingC59×#1587C2
socleC22×C59C2×C4×D4
prime radical#16837639C4
cosocleC42×C59C24
hypercenter#1587D59
hypocenterC59#17993
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1587

Complements

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

NH ≅ G/Ntype
2. #21433248C2semidirect
3. #21433244C2semidirect
4. #21422968C2semidirect
5. #21422962C2semidirect
6. #21422959C2semidirect
7. #21422939C2semidirect
8. #21422936C2semidirect
9. #21422935C2semidirect
10. #21422930C2semidirect
11. #21422850C2semidirect
12. #21422560C2semidirect
13. #21422560C2semidirect
14. #21422387C2semidirect
15. C59×#1587C2semidirect
286. #1587D59semidirect
354. C59#17993semidirect

Maximal subgroups

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

subgroupindex
#214346692
#214332482
#214332442
#214229682
#214229622
#214229592
#214229392
#214229362
#214229352
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C59×#15872
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