Finite Group Databasebeta

← #28600840

Subgroups — #28600840

Order 15104.

784 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837699C211yesmaximal, characteristic
2#21426560C211yesmaximal, characteristic
3#21425054C211yesmaximal, characteristic, complemented
4#21424862C211yesmaximal, characteristic, complemented
5#21424836C211yesmaximal, characteristic, complemented
6#21424831C211yesmaximal, characteristic, complemented
7#21424792C211yesmaximal, characteristic
8#21424792C211yesmaximal, characteristic
9#21424723C211yesmaximal, characteristic
10#21424716C211yesmaximal, characteristic
11#21424674C211yesmaximal, characteristic, complemented
12#21424667C211yesmaximal, characteristic, complemented
13#21424103C211yesmaximal, characteristic
14#21423949C211yesmaximal, characteristic, complemented
15C4×#125×C59C211yesmaximal, characteristic, complemented
16C2×C4×D236C2211yescharacteristic
17C2×#14273684—21no—
18#16837699C418yescomplemented
19C2×#14273660C2211yescharacteristic
20C2×#14273660C2211yescharacteristic
21C2×#14273658C2211yescharacteristic
22C2×#14273658C2211yescharacteristic
23C2×C4⋊(C59⋊C8)C2211yescharacteristic
24C2×C4⋊(C59⋊C8)C2211yescharacteristic
25C2×#14273647C2211yescharacteristic
26C2×#14273647C2211yescharacteristic
27C2×#14273647C2211yescharacteristic
28C2×#14273647C2211yescharacteristic
29C2×#14273638C2211yescharacteristic
30C2×#14273638C2211yescharacteristic
31#16837304C2211yescharacteristic
32#16837304C2211yescharacteristic
33#16837300C2211yescharacteristic
34#16837300C2211yescharacteristic
35#16837293—21no—
36#16837293—21no—
37C4×C4⋊Dic59C2211yescharacteristic
38C4×(C2×D59)⋊C4—21no—
39#16837164C2211yescharacteristic
40#16837164C2211yescharacteristic
41#16837164C2211yescharacteristic
42#16837164C2211yescharacteristic
43#16837164C2211yescharacteristic
44#16837164C2211yescharacteristic
45#16837164C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837157C2211yescharacteristic
48#16837157C2211yescharacteristic
49C2×#125×C59C2211yescharacteristic
50C59×#389C2211yescharacteristic
51C59×#389C2211yescharacteristic
52C59×#387—21no—
53C59×#387—21no—
54C59×#382C2211yescharacteristic
55C4×C4⋊C4×C59—21no—
56C4×C4⋊C4×C59—21no—
57C4×C4⋊C4×C59C2211yescharacteristic
58C4×C4⋊C4×C59C2211yescharacteristic
59C43×C59C2211yescharacteristic
60C22×D236C2311yescharacteristic
61C22×C4×D59—21no—
62C22×C59⋊C8C2311yescharacteristic
63C22×C59⋊C8C2311yescharacteristic
64C22×C59⋊C8C2311yescharacteristic
65C22×C59⋊C8C2311yescharacteristic
66C4×D236—22no—
67C4×D236C2×C414yes—
68#14273684—44no—
69C2×C4⋊Dic59C2311yescharacteristic
70C2×C4⋊Dic59C2311yescharacteristic
71C2×C4⋊Dic59C2311yescharacteristic
72C2×Dic59⋊C4—21no—
73C2×Dic59⋊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—41no—
81#14273660C2×C414yes—
82#14273658—41no—
83#14273658C2×C414yes—
84C4⋊(C59⋊C8)—22no—
85C4⋊(C59⋊C8)C2×C414yes—
86#14273647—41no—
87#14273647—41no—
88#14273647C2×C414yes—
89#14273647C2×C414yes—
90#14273638—41no—
91#14273638—41no—
92C59⋊#95—21no—
93C59⋊#95—21no—
94C59⋊#95—21no—
95#125×C59—22no—
96#125×C59C2×C414yes—
97C2×C4⋊C4×C59—21no—
98C2×C4⋊C4×C59—21no—
99C2×C4⋊C4×C59—21no—
100C2×C4⋊C4×C59—21no—
101C2×C4⋊C4×C59C2311yescharacteristic
102C2×C4⋊C4×C59C2311yescharacteristic
103C2×C4⋊C4×C59C2311yescharacteristic
104C2×C4⋊C4×C59C2311yescharacteristic
105C2×C42×C59—21no—
106C2×C42×C59—21no—
107C2×C42×C59D411yescharacteristic
108C2×C42×C59D411yescharacteristic
109C2×C42×C59D411yescharacteristic
110C2×C42×C59D411yescharacteristic
111C2×C42×C59C2311yescharacteristic
112C2×C42×C59C2311yescharacteristic
113C2×C42×C59C2311yescharacteristic
114#95×C59—21no—
115#95×C59—21no—
116#95×C59—21no—
117#95×C59—21no—
118#95×C59—21no—
119#95×C59—21no—
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×D236C22×C412yes—
141C2×C4×D59—24no—
142C2×C4×D59—42no—
143C2×C4×D59—42no—
144C4⋊C4×C59—24no—
145C4⋊C4×C59—24no—
146C4⋊C4×C59—21no—
147C4⋊C4×C59—21no—
148C4⋊C4×C59—21no—
149C4⋊C4×C59—21no—
150C4⋊C4×C59—21no—
151C4⋊C4×C59—21no—
152C4⋊C4×C59—42no—
153C4⋊C4×C59—42no—
154C4⋊C4×C59C22×C412yes—
155C4⋊C4×C59C22×C412yes—
156C42×C59—22no—
157C42×C59—21no—
158C42×C59—21no—
159C42×C59—21no—
160C42×C59—21no—
161C42×C59—41no—
162C42×C59—41no—
163C42×C59—41no—
164C42×C59—42no—
165C42×C59—42no—
166C42×C59C22×C412yes—
167C42×C59#4112yes—
168(C2×D59)⋊C4—24no—
169(C2×D59)⋊C4—42no—
170(C2×D59)⋊C4—42no—
171(C2×D59)⋊C4—42no—
172(C2×D59)⋊C4—42no—
173C4⋊Dic59—21no—
174C4⋊Dic59—21no—
175C4⋊Dic59—21no—
176C4⋊Dic59—21no—
177C4⋊Dic59—21no—
178C4⋊Dic59C22×C412yes—
179Dic59⋊C4—42no—
180Dic59⋊C4—42no—
181C4×Dic59—42no—
182C2×C59⋊C8—21no—
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⋊C8C22×C412yes—
193C2×C59⋊C8C22×C412yes—
194C23×C59C22×D411yescharacteristic
195C22×D59—22no—
196C22×D59—41no—
197C22×D59—41no—
198C22×D59—41no—
199C22×D59—41no—
200C22×D59—41no—
201C22×D59—41no—
202C2×C4×C59—21no—
203C2×C4×C59—21no—
204C2×C4×C59—21no—
205C2×C4×C59—21no—
206C2×C4×C59—21no—
207C2×C4×C59—21no—
208C2×C4×C59—22no—
209C2×C4×C59—22no—
210C2×C4×C59—21no—
211C2×C4×C59—21no—
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—41no—
220C2×C4×C59—41no—
221C2×C4×C59—41no—
222C2×C4×C59—41no—
223C2×C4×C59—41no—
224C2×C4×C59—41no—
225C2×C4×C59—41no—
226C2×C4×C59—41no—
227C2×C4×C59—41no—
228C2×C4×C59—41no—
229C2×C4×C59C4×D412yes—
230C2×C4×C59C4×D412yes—
231C2×C4×C59AGL(1,ℤ/8)12yes—
232C2×C4×C59C23×C411yescharacteristic
233C2×C4×C59C2×#4111yescharacteristic
234C2×C4×C59H(5,𝔽2)11yescharacteristic
235C2×C4×C592−1+411yescharacteristic
236C2×C4×C592−1+411yescharacteristic
237C2×C4×C592−1+411yescharacteristic
238C2×Dic59—22no—
239C2×Dic59—41no—
240C2×Dic59—41no—
241C2×Dic59—41no—
242C2×Dic59—41no—
243C2×Dic59—41no—
244C2×Dic59—41no—
245C2×Dic59—41no—
246C2×Dic59—41no—
247D236—22no—
248D236—22no—
249D236—41no—
250D236—41no—
251C4×D59—48no—
252C59⋊C8—22no—
253C59⋊C8—22no—
254C59⋊C8—41no—
255C59⋊C8—41no—
256#22120—591nomaximal, Sylow
257C22×C59C2×C4×D411yescharacteristic
258C22×C59#53611yescharacteristic
259C22×C59#53711yescharacteristic
260C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
261C22×C59#57511yescharacteristic
262C22×C59#57511yescharacteristic
263C22×C59#57511yescharacteristic
264C2×D59—42no—
265C2×D59—42no—
266C2×D59—42no—
267C2×D59—81no—
268C2×D59—81no—
269C2×D59—81no—
270C2×D59—81no—
271C4×C59—22no—
272C4×C59—22no—
273C4×C59—22no—
274C4×C59—42no—
275C4×C59—42no—
276C4×C59—41no—
277C4×C59—41no—
278C4×C59—41no—
279C4×C59—81no—
280C4×C59—81no—
281C4×C59#51911yescharacteristic
282C4×C59#52011yescharacteristic
283C4×C59#54111yescharacteristic
284C4×C59#54211yescharacteristic
285Dic59—42no—
286Dic59—81no—
287Dic59—81no—
288C2×#478—591no—
289C4×#125D5911yescharacteristic, complemented
290#2293—591no—
291#1989—591no—
292#1949—591no—
293#1944—591no—
294#1943—591no—
295#1936—591no—
296#1936—591no—
297#1926—591no—
298#1925—591no—
299#1919—591no—
300#1918—591no—
301#1804—591no—
302#1767—591no—
303C2×C59#232311yescharacteristic
304C2×C59#294311yescharacteristic
305C2×C59C4×AGL(1,ℤ/8)11yescharacteristic
306C2×C59#323411yescharacteristic
307C2×C59#324011yescharacteristic
308C2×C59#325111yescharacteristic
309C2×C59#325611yescharacteristic
310D59—82no—
311C2×#125C2×D5911yescharacteristic
312C2×C4×D4—591no—
313C2×#117—1181no—
314#478—598no—
315C2×#107—591no—
316C2×#107—591no—
317C2×#106—591no—
318C2×#106—591no—
319C2×C4⋊C8—591no—
320C2×C4⋊C8—591no—
321C2×#102—591no—
322C2×#102—591no—
323C2×#102—591no—
324C2×#102—591no—
325C2×#97—591no—
326C2×#97—591no—
327#390—591no—
328#390—591no—
329#389—591no—
330#389—591no—
331#389C2×D5911yescharacteristic
332#389C2×D5911yescharacteristic
333#388—1181no—
334#388—1181no—
335#387—21no—
336#387—21no—
337#382C2×D5911yescharacteristic
338C4×C4⋊C4—21no—
339C4×C4⋊C4—21no—
340C4×C4⋊C4—591no—
341C4×C4⋊C4C2×D5911yescharacteristic
342C4×C4⋊C4C2×D5911yescharacteristic
343C4×C22⋊C4—1181no—
344C43C2×D5911yescharacteristic
345#340—591no—
346#340—591no—
347#340—591no—
348#340—591no—
349#340—591no—
350#340—591no—
351#340—591no—
352#340—591no—
353#336—591no—
354#336—591no—
355C59#2212011yescharacteristic, complemented, Sylow
356C22×D4—591no—
357C23×C4—1181no—
358C22×C8—591no—
359C22×C8—591no—
360C22×C8—591no—
361C22×C8—591no—
362#125—22no—
363#125C4×D5914yes—
364C4×D4—594no—
365C4×D4—1182no—
366#117—2364no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—591no—
372C2×C4⋊C4—591no—
373C2×C4⋊C4—591no—
374C2×C4⋊C4—1181no—
375C2×C4⋊C4—1181no—
376C2×C4⋊C4C22×D5911yescharacteristic
377C2×C4⋊C4C22×D5911yescharacteristic
378C2×C4⋊C4C22×D5911yescharacteristic
379C2×C4⋊C4C22×D5911yescharacteristic
380C2×C22⋊C4—1181no—
381C2×C22⋊C4—1181no—
382C2×C22⋊C4—1181no—
383C2×C22⋊C4—1181no—
384C2×C22⋊C4—1181no—
385C2×C42—21no—
386C2×C42—21no—
387C2×C42—1181no—
388C2×C42C22⋊D5911yescharacteristic
389C2×C42C22⋊D5911yescharacteristic
390C2×C42C22⋊D5911yescharacteristic
391C2×C42C22⋊D5911yescharacteristic
392C2×C42C22×D5911yescharacteristic
393C2×C42C22×D5911yescharacteristic
394C2×C42C22×D5911yescharacteristic
395#107—594no—
396#107—2361no—
397#106—594no—
398#106—2361no—
399C4⋊C8—594no—
400C4⋊C8—1182no—
401#102—594no—
402#102—594no—
403#102—2361no—
404#102—2361no—
405#97—2361no—
406#97—2361no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—1181no—
414#95—1181no—
415#95—1181no—
416C24—1181no—
417C2×D4—592no—
418C2×D4—1181no—
419C2×D4—1181no—
420C2×D4—1181no—
421C2×D4—1181no—
422C2×D4—1181no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—1181no—
428C22×C4—1184no—
429C22×C4—1181no—
430C22×C4—1181no—
431C22×C4—2362no—
432C22×C4—2362no—
433C22×C4C2×C22⋊D5911yescharacteristic
434C22×C4C2×C22⋊D5911yescharacteristic
435C22×C4C2×C22⋊D5911yescharacteristic
436C22×C4C2×C22⋊D5911yescharacteristic
437C22×C4C2×C22⋊D5911yescharacteristic
438C22×C4C2×C22⋊D5911yescharacteristic
439C22×C4C23×D5911yescharacteristic
440C2×C8—592no—
441C2×C8—592no—
442C2×C8—1181no—
443C2×C8—1181no—
444C2×C8—1181no—
445C2×C8—1181no—
446C2×C8—1181no—
447C2×C8—1181no—
448C2×C8—1181no—
449C2×C8—1181no—
450C2×C8—1181no—
451C2×C8—1181no—
452C4⋊C4—24no—
453C4⋊C4—24no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—42no—
461C4⋊C4—42no—
462C4⋊C4—592no—
463C4⋊C4—1181no—
464C4⋊C4—1181no—
465C4⋊C4—1181no—
466C4⋊C4—1181no—
467C4⋊C4—1181no—
468C4⋊C4—2362no—
469C4⋊C4—2362no—
470C4⋊C4C2×C4×D5912yes—
471C4⋊C4C2×C4×D5912yes—
472C22⋊C4—1184no—
473C22⋊C4—2362no—
474C22⋊C4—2362no—
475C22⋊C4—2362no—
476C22⋊C4—2362no—
477C42—22no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—41no—
483C42—41no—
484C42—41no—
485C42—42no—
486C42—42no—
487C42—2362no—
488C42C2×C4×D5912yes—
489C42#1174568512yes—
490C23—1182no—
491C23—2361no—
492C23—2361no—
493C23—2361no—
494C23—2361no—
495C23—2361no—
496C23—2361no—
497C23C22×C22⋊D5911yescharacteristic
498D4—1182no—
499D4—1182no—
500D4—2361no—
501D4—2361no—
502C2×C4—21no—
503C2×C4—21no—
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—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—1182no—
530C2×C4—2368no—
531C2×C4—2361no—
532C2×C4—2361no—
533C2×C4—2361no—
534C2×C4—2361no—
535C2×C4—2361no—
536C2×C4—2361no—
537C2×C4—2361no—
538C2×C4—2361no—
539C2×C4C4×C22⋊D5912yes—
540C2×C4C4×C22⋊D5912yes—
541C2×C4#1427375212yes—
542C2×C4C22×C4×D5911yescharacteristic
543C2×C4C2×#1174568511yescharacteristic
544C2×C4#1427377311yescharacteristic
545C2×C4#1427377411yescharacteristic
546C2×C4#1427377511yescharacteristic
547C2×C4#1427377511yescharacteristic
548C8—1182no—
549C8—1182no—
550C8—2361no—
551C8—2361no—
552C22—4721no—
553C22—4721no—
554C22—4721no—
555C22—4721no—
556C22—2362no—
557C22—2362no—
558C22—2362no—
559C22C2×C4×C22⋊D5911yescharacteristic
560C22#1683797611yescharacteristic
561C22#1683798011yescharacteristic
562C22C2×#1427375211yescharacteristic
563C22#1683820011yescharacteristic
564C22#1683820011yescharacteristic
565C22#1683820011yescharacteristic
566C4—22no—
567C4—22no—
568C4—22no—
569C4—42no—
570C4—41no—
571C4—42no—
572C4—41no—
573C4—41no—
574C4—81no—
575C4—81no—
576C4—4721no—
577C4—4721no—
578C4—2362no—
579C4#1683787811yescharacteristic
580C4#1683788411yescharacteristic
581C4#1683801011yescharacteristic
582C4#1683802411yescharacteristic
583C2—4722no—
584C2#2142677211yescharacteristic
585C2#2143289411yescharacteristic
586C2C4×#1427375211yescharacteristic
587C2#2143528611yescharacteristic
588C2#2143533611yescharacteristic
589C2#2143545811yescharacteristic
590C2#2143549211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC4×#125×C59C2
socleC23×C59C22×D4
prime radicalC22×D236C23
cosocleC22×C4×C59C24
hypercenterC4×#125D59
hypocenterC59#22120
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C43 ◁ C4×#125

Complements

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

NH ≅ G/Ntype
3. #21425054C2semidirect
4. #21424862C2semidirect
5. #21424836C2semidirect
6. #21424831C2semidirect
11. #21424674C2semidirect
12. #21424667C2semidirect
14. #21423949C2semidirect
15. C4×#125×C59C2semidirect
18. #16837699C4semidirect
289. C4×#125D59semidirect
355. C59#22120semidirect

Maximal subgroups

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

subgroupindex
C2×#168376992
#214265602
#214250542
#214248622
#214248362
#214248312
#214247922
#214247232
#214247162
#214246742
#214246672
#214241032
#214239492
C4×#125×C592
#2212059