Finite Group Databasebeta

← #28611829

Subgroups — #28611829

Order 15104.

774 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837699C211yesmaximal, characteristic
2#21427067C211yesmaximal, characteristic
3#21425062C211yesmaximal, characteristic, complemented
4#21424864C211yesmaximal, characteristic, complemented
5#21424778C211yesmaximal, characteristic
6#21424778C211yesmaximal, characteristic
7#21424723C211yesmaximal, characteristic
8#21424716C211yesmaximal, characteristic
9#21424685C211yesmaximal, characteristic, complemented
10#21424671C211yesmaximal, characteristic, complemented
11C4×#14273660C211yesmaximal, characteristic, complemented
12C4×#14273658C211yesmaximal, characteristic, complemented
13C4⋊C4×C59⋊C8C211yesmaximal, characteristic, complemented
14C4×#14273647C211yesmaximal, characteristic
15C59×#2370C211yesmaximal, characteristic, complemented
16C2×C4×D236C2211yescharacteristic
17#16837699C418yescomplemented
18C2×#14273660C2211yescharacteristic
19C2×#14273660C2211yescharacteristic
20C2×#14273658C2211yescharacteristic
21C2×#14273658C2211yescharacteristic
22C2×C4⋊(C59⋊C8)C2211yescharacteristic
23C2×#14273647C2211yescharacteristic
24C2×#14273647C2211yescharacteristic
25C2×#14273647C2211yescharacteristic
26C2×#14273647C2211yescharacteristic
27C2×C4×C59⋊C8C2211yescharacteristic
28C2×C4×C59⋊C8C2211yescharacteristic
29C2×C4×C59⋊C8C2211yescharacteristic
30#16837304C2211yescharacteristic
31#16837304C2211yescharacteristic
32#16837292—21no—
33#16837292—21no—
34#16837268C2211yescharacteristic
35#16837264—21no—
36C4×C4⋊Dic59C2211yescharacteristic
37C4×C4⋊Dic59C2211yescharacteristic
38#16837249—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×#389—21no—
51C59×#389C2211yescharacteristic
52C59×#389C2211yescharacteristic
53C59×#387—21no—
54C59×#387—21no—
55C4×C4⋊C4×C59—21no—
56C4×C4⋊C4×C59C2211yescharacteristic
57C4×C4⋊C4×C59C2211yescharacteristic
58C4×C4⋊C4×C59C2211yescharacteristic
59C4×C4⋊C4×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—
68C2×C4⋊Dic59C2311yescharacteristic
69C2×C4⋊Dic59C2311yescharacteristic
70C2×C4⋊Dic59C2311yescharacteristic
71C2×(C2×D59)⋊C4—21no—
72C2×(C2×D59)⋊C4—21no—
73C2×(C2×D59)⋊C4—21no—
74C2×(C2×D59)⋊C4—21no—
75C2×(C2×D59)⋊C4—21no—
76C2×C4×Dic59—21no—
77C2×C4×Dic59—21no—
78#14273660—22no—
79#14273660C2×C414yes—
80#14273658—22no—
81#14273658C2×C414yes—
82C4⋊(C59⋊C8)C2×C414yes—
83#14273647—22no—
84#14273647—22no—
85#14273647C2×C414yes—
86#14273647C2×C414yes—
87C4×C59⋊C8—22no—
88C4×C59⋊C8—22no—
89C4×C59⋊C8—22no—
90C59⋊#95—21no—
91C59⋊#95—21no—
92C59⋊#95—21no—
93C59⋊#95—21no—
94#125×C59—22no—
95#125×C59C2×C414yes—
96C2×C4⋊C4×C59—21no—
97C2×C4⋊C4×C59—21no—
98C2×C4⋊C4×C59—21no—
99C2×C4⋊C4×C59—21no—
100C2×C4⋊C4×C59D411yescharacteristic
101C2×C4⋊C4×C59D411yescharacteristic
102C2×C4⋊C4×C59C2311yescharacteristic
103C2×C4⋊C4×C59C2311yescharacteristic
104C2×C4⋊C4×C59C2311yescharacteristic
105C2×C4⋊C4×C59C2311yescharacteristic
106C2×C42×C59—21no—
107C2×C42×C59—21no—
108C2×C42×C59—21no—
109C2×C42×C59C2311yescharacteristic
110C2×C42×C59C2311yescharacteristic
111C2×C42×C59C2311yescharacteristic
112#95×C59—21no—
113#95×C59—21no—
114#95×C59—21no—
115#95×C59—21no—
116#95×C59—21no—
117#95×C59D411yescharacteristic
118#95×C59D411yescharacteristic
119C23×D59—21no—
120C22×C4×C59—21no—
121C22×C4×C59—21no—
122C22×C4×C59—21no—
123C22×C4×C59—21no—
124C22×C4×C59C2×D411yescharacteristic
125C22×C4×C59C2×D411yescharacteristic
126C22×C4×C59C2×D411yescharacteristic
127C22×C4×C59C2×D411yescharacteristic
128C22×C4×C59C2×D411yescharacteristic
129C22×C4×C59C2×D411yescharacteristic
130C22×C4×C59C2411yescharacteristic
131C22×Dic59—21no—
132C22×Dic59—21no—
133C22×Dic59—21no—
134C2×D236—21no—
135C2×D236—21no—
136C2×D236—21no—
137C2×D236—21no—
138C2×D236—21no—
139C2×D236C22×C412yes—
140C2×C4×D59—24no—
141C2×C4×D59—81no—
142C2×C4×D59—81no—
143C4⋊C4×C59—24no—
144C4⋊C4×C59—24no—
145C4⋊C4×C59—22no—
146C4⋊C4×C59—22no—
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—81no—
154C4⋊C4×C59C22×C412yes—
155C4⋊C4×C59C22×C412yes—
156C4⋊C4×C59#4112yes—
157C42×C59—21no—
158C42×C59—21no—
159C42×C59—21no—
160C42×C59—21no—
161C42×C59—42no—
162C42×C59—81no—
163C42×C59—81no—
164C42×C59C22×C412yes—
165C42×C59#4112yes—
166(C2×D59)⋊C4—24no—
167(C2×D59)⋊C4—42no—
168(C2×D59)⋊C4—42no—
169(C2×D59)⋊C4—81no—
170(C2×D59)⋊C4—81no—
171C4⋊Dic59—21no—
172C4⋊Dic59—21no—
173C4⋊Dic59—21no—
174C4⋊Dic59—21no—
175C4⋊Dic59—21no—
176C4⋊Dic59C22×C412yes—
177C4×Dic59—81no—
178C4×Dic59—81no—
179C2×C59⋊C8—21no—
180C2×C59⋊C8—21no—
181C2×C59⋊C8—21no—
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⋊C8C22×C412yes—
189C2×C59⋊C8C22×C412yes—
190C2×C59⋊C8#4112yes—
191C23×C59C22×D411yescharacteristic
192C22×D59—22no—
193C22×D59—41no—
194C22×D59—41no—
195C22×D59—41no—
196C22×D59—41no—
197C22×D59—41no—
198C22×D59—41no—
199C2×C4×C59—21no—
200C2×C4×C59—21no—
201C2×C4×C59—21no—
202C2×C4×C59—21no—
203C2×C4×C59—21no—
204C2×C4×C59—21no—
205C2×C4×C59—21no—
206C2×C4×C59—21no—
207C2×C4×C59—22no—
208C2×C4×C59—22no—
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—41no—
217C2×C4×C59—41no—
218C2×C4×C59—41no—
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×C59C4×D412yes—
226C2×C4×C59C4×D412yes—
227C2×C4×C59#13512yes—
228C2×C4×C59#13512yes—
229C2×C4×C59C23×C411yescharacteristic
230C2×C4×C59C2×#4111yescharacteristic
231C2×C4×C59C2×#4111yescharacteristic
232C2×C4×C59C2×#4111yescharacteristic
233C2×C4×C592−1+411yescharacteristic
234C2×C4×C592−1+411yescharacteristic
235C2×Dic59—22no—
236C2×Dic59—41no—
237C2×Dic59—41no—
238C2×Dic59—41no—
239C2×Dic59—41no—
240C2×Dic59—41no—
241C2×Dic59—41no—
242C2×Dic59—41no—
243C2×Dic59—41no—
244D236—22no—
245D236—22no—
246D236—41no—
247D236—41no—
248C4×D59—84no—
249C59⋊C8—22no—
250C59⋊C8—22no—
251C59⋊C8—22no—
252C59⋊C8—41no—
253#23065—591nomaximal, Sylow
254C22×C59C2×C4×D411yescharacteristic
255C22×C59#54711yescharacteristic
256C22×C59#54811yescharacteristic
257C22×C59C2×#13511yescharacteristic
258C22×C59C2×#13511yescharacteristic
259C22×C59#57611yescharacteristic
260C22×C59#57711yescharacteristic
261C2×D59—42no—
262C2×D59—42no—
263C2×D59—42no—
264C2×D59—81no—
265C2×D59—81no—
266C2×D59—81no—
267C2×D59—81no—
268C4×C59—22no—
269C4×C59—22no—
270C4×C59—22no—
271C4×C59—22no—
272C4×C59—41no—
273C4×C59—41no—
274C4×C59—42no—
275C4×C59—42no—
276C4×C59—42no—
277C4×C59—81no—
278C4×C59C4×#4111yescharacteristic
279C4×C59#51911yescharacteristic
280C4×C59#55211yescharacteristic
281C4×C59#55611yescharacteristic
282Dic59—42no—
283Dic59—81no—
284Dic59—81no—
285C2×#478—591no—
286#2370D5911yescharacteristic, complemented
287#2357—591no—
288#1991—591no—
289#1949—591no—
290#1934—591no—
291#1934—591no—
292#1926—591no—
293#1925—591no—
294#1921—591no—
295#1919—591no—
296C4×#107—591no—
297C4×#106—591no—
298C8×C4⋊C4—591no—
299C4×#102—591no—
300C2×C59#236211yescharacteristic
301C2×C59C4×#13511yescharacteristic
302C2×C59#294611yescharacteristic
303C2×C59#333711yescharacteristic
304C2×C59#333911yescharacteristic
305C2×C59#336111yescharacteristic
306C2×C59#336511yescharacteristic
307D59—82no—
308C2×#125C2×D5911yescharacteristic
309C2×C4×D4—591no—
310#478—598no—
311C2×#107—591no—
312C2×#107—591no—
313C2×#106—591no—
314C2×#106—591no—
315C2×C4⋊C8—591no—
316C2×#102—591no—
317C2×#102—591no—
318C2×#102—591no—
319C2×#102—591no—
320C2×C4×C8—591no—
321C2×C4×C8—591no—
322C2×C4×C8—591no—
323#390—591no—
324#390—591no—
325#389—21no—
326#389C2×D5911yescharacteristic
327#389C2×D5911yescharacteristic
328#388—1181no—
329#388—1181no—
330#387—21no—
331#387—21no—
332#382—591no—
333#381—1181no—
334C4×C4⋊C4—21no—
335C4×C4⋊C4—591no—
336C4×C4⋊C4—591no—
337C4×C4⋊C4C2×D5911yescharacteristic
338C4×C4⋊C4C2×D5911yescharacteristic
339C4×C4⋊C4C2×D5911yescharacteristic
340C4×C4⋊C4C2×D5911yescharacteristic
341C4×C22⋊C4—1181no—
342#340—591no—
343#340—591no—
344#340—591no—
345#340—591no—
346#340—591no—
347#340—591no—
348#340—591no—
349#340—591no—
350#336—591no—
351#336—591no—
352C59#2306511yescharacteristic, complemented, Sylow
353C22×D4—591no—
354C23×C4—1181no—
355C22×C8—591no—
356C22×C8—591no—
357C22×C8—591no—
358C22×C8—591no—
359#125—22no—
360#125C4×D5914yes—
361C4×D4—594no—
362C4×D4—1182no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—591no—
368C2×C4⋊C4—591no—
369C2×C4⋊C4—591no—
370C2×C4⋊C4C22⋊D5911yescharacteristic
371C2×C4⋊C4C22⋊D5911yescharacteristic
372C2×C4⋊C4C22×D5911yescharacteristic
373C2×C4⋊C4C22×D5911yescharacteristic
374C2×C4⋊C4C22×D5911yescharacteristic
375C2×C4⋊C4C22×D5911yescharacteristic
376C2×C22⋊C4—1181no—
377C2×C22⋊C4—1181no—
378C2×C22⋊C4—1181no—
379C2×C22⋊C4—1181no—
380C2×C22⋊C4—1181no—
381C2×C42—21no—
382C2×C42—21no—
383C2×C42—21no—
384C2×C42—1181no—
385C2×C42—1181no—
386C2×C42C22×D5911yescharacteristic
387C2×C42C22×D5911yescharacteristic
388C2×C42C22×D5911yescharacteristic
389#107—594no—
390#107—1182no—
391#106—594no—
392#106—1182no—
393C4⋊C8—594no—
394#102—594no—
395#102—594no—
396#102—1182no—
397#102—1182no—
398C4×C8—1182no—
399C4×C8—1182no—
400C4×C8—1182no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—1181no—
407#95—1181no—
408#95—1181no—
409#95—1181no—
410#95C22⋊D5911yescharacteristic
411#95C22⋊D5911yescharacteristic
412C24—1181no—
413C2×D4—592no—
414C2×D4—1181no—
415C2×D4—1181no—
416C2×D4—1181no—
417C2×D4—1181no—
418C2×D4—1181no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—1181no—
424C22×C4—1184no—
425C22×C4—1181no—
426C22×C4—1181no—
427C22×C4—4721no—
428C22×C4—4721no—
429C22×C4C2×C22⋊D5911yescharacteristic
430C22×C4C2×C22⋊D5911yescharacteristic
431C22×C4C2×C22⋊D5911yescharacteristic
432C22×C4C2×C22⋊D5911yescharacteristic
433C22×C4C2×C22⋊D5911yescharacteristic
434C22×C4C2×C22⋊D5911yescharacteristic
435C22×C4C23×D5911yescharacteristic
436C2×C8—592no—
437C2×C8—592no—
438C2×C8—592no—
439C2×C8—1181no—
440C2×C8—1181no—
441C2×C8—1181no—
442C2×C8—1181no—
443C2×C8—1181no—
444C2×C8—1181no—
445C2×C8—1181no—
446C2×C8—1181no—
447C2×C8—1181no—
448C4⋊C4—24no—
449C4⋊C4—24no—
450C4⋊C4—22no—
451C4⋊C4—22no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—42no—
458C4⋊C4—81no—
459C4⋊C4—592no—
460C4⋊C4—1181no—
461C4⋊C4—1181no—
462C4⋊C4—1181no—
463C4⋊C4—1181no—
464C4⋊C4—1181no—
465C4⋊C4C2×C4×D5912yes—
466C4⋊C4C2×C4×D5912yes—
467C4⋊C4#1174568912yes—
468C22⋊C4—1184no—
469C22⋊C4—4721no—
470C22⋊C4—4721no—
471C22⋊C4—2362no—
472C22⋊C4—2362no—
473C42—21no—
474C42—21no—
475C42—21no—
476C42—21no—
477C42—42no—
478C42—81no—
479C42—81no—
480C42—4721no—
481C42—4721no—
482C42C2×C4×D5912yes—
483C42#1174568512yes—
484C23—1182no—
485C23—2361no—
486C23—2361no—
487C23—2361no—
488C23—2361no—
489C23—2361no—
490C23—2361no—
491C23C22×C22⋊D5911yescharacteristic
492D4—1182no—
493D4—1182no—
494D4—2361no—
495D4—2361no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
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—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—1182no—
523C2×C4—4724no—
524C2×C4—2361no—
525C2×C4—2361no—
526C2×C4—2361no—
527C2×C4—2361no—
528C2×C4—2361no—
529C2×C4—2361no—
530C2×C4—2361no—
531C2×C4—2361no—
532C2×C4C4×C22⋊D5912yes—
533C2×C4C4×C22⋊D5912yes—
534C2×C4#1427374712yes—
535C2×C4#1427374712yes—
536C2×C4C22×C4×D5911yescharacteristic
537C2×C4#41×D5911yescharacteristic
538C2×C4C2×#1174568511yescharacteristic
539C2×C4C2×#1174568911yescharacteristic
540C2×C4#1427377411yescharacteristic
541C2×C4#1427377511yescharacteristic
542C8—1182no—
543C8—1182no—
544C8—1182no—
545C8—2361no—
546C22—4721no—
547C22—4721no—
548C22—4721no—
549C22—4721no—
550C22—2362no—
551C22—2362no—
552C22—2362no—
553C22C2×C4×C22⋊D5911yescharacteristic
554C22#1683805111yescharacteristic
555C22#1683806311yescharacteristic
556C22C2×#1427374711yescharacteristic
557C22C2×#1427374711yescharacteristic
558C22#1683820511yescharacteristic
559C22#1683821011yescharacteristic
560C4—22no—
561C4—22no—
562C4—22no—
563C4—22no—
564C4—42no—
565C4—41no—
566C4—41no—
567C4—42no—
568C4—42no—
569C4—81no—
570C4—4721no—
571C4—4721no—
572C4—2362no—
573C4C4×#1174568911yescharacteristic
574C4#1683787811yescharacteristic
575C4#1683809311yescharacteristic
576C4#1683812511yescharacteristic
577C2—4722no—
578C2#2142711911yescharacteristic
579C2C4×#1427374711yescharacteristic
580C2#2143292411yescharacteristic
581C2#2143647511yescharacteristic
582C2#2143649211yescharacteristic
583C2#2143675611yescharacteristic
584C2#2143679211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#2370C2
socleC23×C59C22×D4
prime radicalC22×D236C23
cosocleC22×C4×C59C24
hypercenter#2370D59
hypocenterC59#23065
LCSG ▷ C2×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
3. #21425062C2semidirect
4. #21424864C2semidirect
9. #21424685C2semidirect
10. #21424671C2semidirect
11. C4×#14273660C2semidirect
12. C4×#14273658C2semidirect
13. C4⋊C4×C59⋊C8C2semidirect
15. C59×#2370C2semidirect
17. #16837699C4semidirect
286. #2370D59semidirect
352. C59#23065semidirect

Maximal subgroups

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

subgroupindex
C2×#168376992
#214270672
#214250622
#214248642
#214247782
#214247232
#214247162
#214246852
#214246712
C4×#142736602
C4×#142736582
C4⋊C4×C59⋊C82
C4×#142736472
C59×#23702
#2306559