Finite Group Databasebeta

← #28629954

Subgroups — #28629954

Order 15104.

868 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837699C211yesmaximal, characteristic, complemented
2C2×#16837459C211yesmaximal, characteristic, complemented
3C4×#14273701C211yesmaximal, characteristic
4#21425533C211yesmaximal, characteristic, complemented
5#21425522C211yesmaximal, characteristic, complemented
6#21425285C211yesmaximal, characteristic
7#21425278C211yesmaximal, characteristic
8#21425054C211yesmaximal, characteristic, complemented
9#21424862C211yesmaximal, characteristic, complemented
10#21424836C211yesmaximal, characteristic, complemented
11#21424831C211yesmaximal, characteristic, complemented
12#21424792C211yesmaximal, characteristic, complemented
13#21424792C211yesmaximal, characteristic, complemented
14#21424103C211yesmaximal, characteristic, complemented
15C59×#2851C211yesmaximal, characteristic, complemented
16C2×#14273701C2211yescharacteristic
17C2×C4×D236C2211yescharacteristic
18C2×C4×C22⋊D59—21no—
19#16837699—24no—
20#16837459—24no—
21C2×#14273660C2211yescharacteristic
22C2×#14273660C2211yescharacteristic
23C2×#14273658C2211yescharacteristic
24C2×#14273658C2211yescharacteristic
25C2×C4⋊(C59⋊C8)C2211yescharacteristic
26C2×C4⋊(C59⋊C8)C2211yescharacteristic
27C2×#14273647C2211yescharacteristic
28C2×#14273647C2211yescharacteristic
29C2×#14273647C2211yescharacteristic
30C2×#14273647C2211yescharacteristic
31C2×C22⋊(C59⋊C8)C2211yescharacteristic
32C2×C22⋊(C59⋊C8)C2211yescharacteristic
33C2×#14273638C2211yescharacteristic
34C2×#14273638C2211yescharacteristic
35#16837304C2211yescharacteristic
36#16837300C2211yescharacteristic
37#16837293—21no—
38#16837281—21no—
39#16837262C2211yescharacteristic
40C4×C4⋊Dic59C2211yescharacteristic
41C4×(C2×D59)⋊C4—21no—
42#16837164C2211yescharacteristic
43#16837164C2211yescharacteristic
44#16837164C2211yescharacteristic
45#16837164C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837164C2211yescharacteristic
48#16837164C2211yescharacteristic
49#16837164C2211yescharacteristic
50C2×#125×C59C2211yescharacteristic
51C22×C42×C59C2211yescharacteristic
52C59×#389C2211yescharacteristic
53C59×#389C2211yescharacteristic
54C59×#387—21no—
55C59×#387—21no—
56C59×#385—21no—
57C59×#385—21no—
58C59×#382C2211yescharacteristic
59C59×#380C2211yescharacteristic
60C59×#380C2211yescharacteristic
61C22×D236C2311yescharacteristic
62C22×C22⋊D59—21no—
63C22×C4×D59—21no—
64C22×C59⋊C8C2311yescharacteristic
65C22×C59⋊C8C2311yescharacteristic
66C22×C59⋊C8C2311yescharacteristic
67C22×C59⋊C8C2311yescharacteristic
68#14273701—22no—
69#14273701—22no—
70C4×D236—22no—
71C4×D236—22no—
72C4×C22⋊D59—44no—
73C2×C4⋊Dic59C2311yescharacteristic
74C2×C4⋊Dic59C2311yescharacteristic
75C2×C4⋊Dic59C2311yescharacteristic
76C2×Dic59⋊C4—21no—
77C2×C22⋊Dic59—21no—
78C2×(C2×D59)⋊C4—21no—
79C2×(C2×D59)⋊C4—21no—
80C2×(C2×D59)⋊C4—21no—
81C2×(C2×D59)⋊C4—21no—
82C2×C4×Dic59—21no—
83#14273660—22no—
84#14273660—22no—
85#14273658—22no—
86#14273658—22no—
87C4⋊(C59⋊C8)—22no—
88C4⋊(C59⋊C8)D414yescomplemented
89#14273647—22no—
90#14273647—22no—
91#14273647—22no—
92#14273647—22no—
93C22⋊(C59⋊C8)—22no—
94C22⋊(C59⋊C8)—22no—
95#14273638—22no—
96#14273638—22no—
97C59⋊#95—21no—
98C59⋊#95—21no—
99C59⋊#95—21no—
100C23×C4×C59D411yescharacteristic
101C23×C4×C59D411yescharacteristic
102C23×C4×C59C2311yescharacteristic
103#125×C59—22no—
104#125×C59—22no—
105C2×C4⋊C4×C59—21no—
106C2×C4⋊C4×C59—21no—
107C2×C4⋊C4×C59—21no—
108C2×C4⋊C4×C59—21no—
109C2×C4⋊C4×C59C2311yescharacteristic
110C2×C4⋊C4×C59C2311yescharacteristic
111C2×C4⋊C4×C59C2311yescharacteristic
112C2×C4⋊C4×C59C2311yescharacteristic
113C2×C22⋊C4×C59—21no—
114C2×C22⋊C4×C59—21no—
115C2×C42×C59—22no—
116C2×C42×C59—22no—
117C2×C42×C59D411yescharacteristic
118C2×C42×C59D411yescharacteristic
119C2×C42×C59C2311yescharacteristic
120C2×C42×C59C2311yescharacteristic
121#95×C59—21no—
122#95×C59—21no—
123#95×C59—21no—
124#95×C59—21no—
125#95×C59—21no—
126#95×C59—21no—
127C24×C59C2×D411yescharacteristic
128C23×D59—21no—
129C22×C4×C59—22no—
130C22×C4×C59—22no—
131C22×C4×C59—22no—
132C22×C4×C59—21no—
133C22×C4×C59—21no—
134C22×C4×C59—21no—
135C22×C4×C59—21no—
136C22×C4×C59—21no—
137C22×C4×C59—21no—
138C22×C4×C59—21no—
139C22×C4×C59—21no—
140C22×C4×C59—21no—
141C22×C4×C59—21no—
142C22×C4×C59—41no—
143C22×C4×C59—41no—
144C22×C4×C59—41no—
145C22×C4×C59C2×D411yescharacteristic
146C22×C4×C59C2×D411yescharacteristic
147C22×C4×C59C2×D411yescharacteristic
148C22×C4×C59C2×D411yescharacteristic
149C22×C4×C59C2×D411yescharacteristic
150C22×C4×C59C2411yescharacteristic
151C2×C22⋊D59—24no—
152C2×C22⋊D59—42no—
153C2×C22⋊D59—42no—
154C22×Dic59—21no—
155C22×Dic59—21no—
156C22×Dic59—21no—
157C2×D236—21no—
158C2×D236—21no—
159C2×D236—21no—
160C2×D236—21no—
161C2×D236—21no—
162C2×D236#4112yes—
163C2×C4×D59—42no—
164C2×C4×D59—42no—
165C2×C4×D59—42no—
166C4⋊C4×C59—21no—
167C4⋊C4×C59—21no—
168C4⋊C4×C59—21no—
169C4⋊C4×C59—21no—
170C4⋊C4×C59—21no—
171C4⋊C4×C59—21no—
172C4⋊C4×C59—21no—
173C4⋊C4×C59—21no—
174C4⋊C4×C59—42no—
175C4⋊C4×C59—42no—
176C4⋊C4×C59—42no—
177C4⋊C4×C59—42no—
178C22⋊C4×C59—42no—
179C22⋊C4×C59—42no—
180C42×C59—22no—
181C42×C59—22no—
182C42×C59—21no—
183C42×C59—21no—
184C42×C59C2×D412yes—
185C42×C59#4112yes—
186C22⋊Dic59—42no—
187(C2×D59)⋊C4—24no—
188(C2×D59)⋊C4—42no—
189(C2×D59)⋊C4—42no—
190(C2×D59)⋊C4—42no—
191C4⋊Dic59—21no—
192C4⋊Dic59—21no—
193C4⋊Dic59—21no—
194C4⋊Dic59—21no—
195C4⋊Dic59—21no—
196C4⋊Dic59#4112yes—
197Dic59⋊C4—42no—
198C4×Dic59—42no—
199C2×C59⋊C8—21no—
200C2×C59⋊C8—21no—
201C2×C59⋊C8—21no—
202C2×C59⋊C8—21no—
203C2×C59⋊C8—21no—
204C2×C59⋊C8—21no—
205C2×C59⋊C8—21no—
206C2×C59⋊C8—21no—
207C2×C59⋊C8—21no—
208C2×C59⋊C8—21no—
209C2×C59⋊C8C2×D412yes—
210C2×C59⋊C8C2×D412yes—
211C23×C59—21no—
212C23×C59—21no—
213C23×C59—21no—
214C23×C59—21no—
215C23×C59—21no—
216C23×C59—21no—
217C23×C59AGL(1,ℤ/8)12yes—
218C23×C59C22×D411yescharacteristic
219C22×D59—22no—
220C22×D59—41no—
221C22×D59—41no—
222C22×D59—41no—
223C22×D59—41no—
224C22×D59—41no—
225C22×D59—41no—
226C2×C4×C59—21no—
227C2×C4×C59—21no—
228C2×C4×C59—21no—
229C2×C4×C59—21no—
230C2×C4×C59—21no—
231C2×C4×C59—21no—
232C2×C4×C59—21no—
233C2×C4×C59—21no—
234C2×C4×C59—21no—
235C2×C4×C59—21no—
236C2×C4×C59—21no—
237C2×C4×C59—21no—
238C2×C4×C59—21no—
239C2×C4×C59—44no—
240C2×C4×C59—44no—
241C2×C4×C59—41no—
242C2×C4×C59—41no—
243C2×C4×C59—41no—
244C2×C4×C59—41no—
245C2×C4×C59—41no—
246C2×C4×C59—41no—
247C2×C4×C59—41no—
248C2×C4×C59—41no—
249C2×C4×C59—41no—
250C2×C4×C59—41no—
251C2×C4×C59—41no—
252C2×C4×C59—41no—
253C2×C4×C59—41no—
254C2×C4×C59—41no—
255C2×C4×C59—41no—
256C2×C4×C59—41no—
257C2×C4×C59#12112yes—
258C2×C4×C59#12112yes—
259C2×C4×C59C22×D411yescharacteristic
260C2×C4×C59C2×#4111yescharacteristic
261C2×C4×C59C2×#4111yescharacteristic
262C2×C4×C59C2×#4111yescharacteristic
263C2×C4×C592−1+411yescharacteristic
264C2×C4×C592−1+411yescharacteristic
265C22⋊D59—48no—
266C2×Dic59—22no—
267C2×Dic59—41no—
268C2×Dic59—41no—
269C2×Dic59—41no—
270C2×Dic59—41no—
271C2×Dic59—41no—
272C2×Dic59—41no—
273C2×Dic59—41no—
274C2×Dic59—41no—
275D236—22no—
276D236—22no—
277D236—41no—
278D236—41no—
279C4×D59—84no—
280C59⋊C8—22no—
281C59⋊C8—22no—
282C59⋊C8—41no—
283C59⋊C8—41no—
284#24706—591nomaximal, Sylow
285C22×C59—22no—
286C22×C59—22no—
287C22×C59—22no—
288C22×C59—41no—
289C22×C59—41no—
290C22×C59—41no—
291C22×C59—41no—
292C22×C59C2×#12111yescharacteristic
293C22×C59#52511yescharacteristic
294C22×C59#53611yescharacteristic
295C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
296C22×C59#57511yescharacteristic
297C22×C59#57511yescharacteristic
298C22×C59#57511yescharacteristic
299C2×D59—42no—
300C2×D59—42no—
301C2×D59—42no—
302C2×D59—81no—
303C2×D59—81no—
304C2×D59—81no—
305C2×D59—81no—
306C4×C59—22no—
307C4×C59—22no—
308C4×C59—41no—
309C4×C59—41no—
310C4×C59—41no—
311C4×C59—81no—
312C4×C59—81no—
313C4×C59—81no—
314C4×C59—81no—
315C4×C59#54711yescharacteristic
316C4×C59#54811yescharacteristic
317C4×C59#55211yescharacteristic
318C4×C59#55611yescharacteristic
319Dic59—42no—
320Dic59—81no—
321Dic59—81no—
322C2×#478—591no—
323C2×#432—591no—
324#2851D5911yescharacteristic, complemented
325C4×#121—591no—
326#2077—591no—
327#2075—591no—
328#2034—591no—
329#2033—591no—
330#1989—591no—
331#1949—591no—
332#1944—591no—
333#1943—591no—
334#1936—591no—
335#1936—591no—
336#1804—591no—
337C2×C59—42no—
338C2×C59#241511yescharacteristic
339C2×C59#305411yescharacteristic
340C2×C59#305511yescharacteristic
341C2×C59#311111yescharacteristic
342C2×C59#311411yescharacteristic
343C2×C59#323411yescharacteristic
344C2×C59#324011yescharacteristic
345D59—82no—
346C2×#125C2×D5911yescharacteristic
347C2×#121—591no—
348C2×C4×D4—591no—
349C2×C4×D4—1181no—
350C22×C42C2×D5911yescharacteristic
351#478—1184no—
352#432—1184no—
353C2×#107—591no—
354C2×#107—591no—
355C2×#106—591no—
356C2×#106—591no—
357C2×C4⋊C8—591no—
358C2×C4⋊C8—591no—
359C2×#102—591no—
360C2×#102—591no—
361C2×#102—591no—
362C2×#102—591no—
363C2×C22⋊C8—591no—
364C2×C22⋊C8—591no—
365C2×#97—591no—
366C2×#97—591no—
367#390—591no—
368#389—591no—
369#389C2×D5911yescharacteristic
370#389C2×D5911yescharacteristic
371#388—1181no—
372#387—21no—
373#387—21no—
374#386—1181no—
375#385—21no—
376#385—21no—
377#382C2×D5911yescharacteristic
378#380—591no—
379#380C2×D5911yescharacteristic
380#380C2×D5911yescharacteristic
381C4×C4⋊C4—591no—
382C4×C22⋊C4—1181no—
383#340—591no—
384#340—591no—
385#340—591no—
386#340—591no—
387#340—591no—
388#340—591no—
389#340—591no—
390#340—591no—
391C59#2470611yescharacteristic, complemented, Sylow
392C22×D4—591no—
393C22×D4—1181no—
394C23×C4—1181no—
395C23×C4C22⋊D5911yescharacteristic
396C23×C4C22⋊D5911yescharacteristic
397C23×C4C22×D5911yescharacteristic
398C22×C8—591no—
399C22×C8—591no—
400C22×C8—591no—
401C22×C8—591no—
402#125—22no—
403#125—22no—
404#121—1182no—
405#121—1182no—
406C4×D4—1182no—
407C4×D4—1182no—
408C4×D4—2364no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—591no—
414C2×C4⋊C4—591no—
415C2×C4⋊C4—591no—
416C2×C4⋊C4—1181no—
417C2×C4⋊C4C22×D5911yescharacteristic
418C2×C4⋊C4C22×D5911yescharacteristic
419C2×C4⋊C4C22×D5911yescharacteristic
420C2×C4⋊C4C22×D5911yescharacteristic
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—1181no—
424C2×C22⋊C4—1181no—
425C2×C22⋊C4—1181no—
426C2×C22⋊C4—1181no—
427C2×C22⋊C4—1181no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—1181no—
431C2×C42C22⋊D5911yescharacteristic
432C2×C42C22⋊D5911yescharacteristic
433C2×C42C22×D5911yescharacteristic
434C2×C42C22×D5911yescharacteristic
435#107—1182no—
436#107—1182no—
437#106—1182no—
438#106—1182no—
439C4⋊C8—594no—
440C4⋊C8—1182no—
441#102—1182no—
442#102—1182no—
443#102—1182no—
444#102—1182no—
445C22⋊C8—1182no—
446C22⋊C8—1182no—
447#97—1182no—
448#97—1182no—
449#95—21no—
450#95—21no—
451#95—21no—
452#95—21no—
453#95—21no—
454#95—21no—
455#95—1181no—
456#95—1181no—
457#95—1181no—
458C24—1181no—
459C24C2×C22⋊D5911yescharacteristic
460C2×D4—592no—
461C2×D4—1184no—
462C2×D4—1181no—
463C2×D4—1181no—
464C2×D4—1181no—
465C2×D4—1181no—
466C2×D4—1181no—
467C2×D4—2362no—
468C2×D4—2362no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—1181no—
486C22×C4—1181no—
487C22×C4—1181no—
488C22×C4—2362no—
489C22×C4—2362no—
490C22×C4—2362no—
491C22×C4C2×C22⋊D5911yescharacteristic
492C22×C4C2×C22⋊D5911yescharacteristic
493C22×C4C2×C22⋊D5911yescharacteristic
494C22×C4C2×C22⋊D5911yescharacteristic
495C22×C4C2×C22⋊D5911yescharacteristic
496C22×C4C23×D5911yescharacteristic
497C2×C8—592no—
498C2×C8—592no—
499C2×C8—1181no—
500C2×C8—1181no—
501C2×C8—1181no—
502C2×C8—1181no—
503C2×C8—1181no—
504C2×C8—1181no—
505C2×C8—1181no—
506C2×C8—1181no—
507C2×C8—1181no—
508C2×C8—1181no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—42no—
518C4⋊C4—42no—
519C4⋊C4—42no—
520C4⋊C4—42no—
521C4⋊C4—592no—
522C4⋊C4—1181no—
523C4⋊C4—1181no—
524C4⋊C4—1181no—
525C4⋊C4—1181no—
526C4⋊C4—1181no—
527C4⋊C4—2362no—
528C22⋊C4—42no—
529C22⋊C4—42no—
530C22⋊C4—1184no—
531C22⋊C4—2362no—
532C22⋊C4—2362no—
533C22⋊C4—2362no—
534C22⋊C4—2362no—
535C42—22no—
536C42—22no—
537C42—21no—
538C42—21no—
539C42—2362no—
540C42D4×D5912yes—
541C42#1174568712yes—
542C23—21no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—1182no—
549C23—2361no—
550C23—2361no—
551C23—2361no—
552C23—2361no—
553C23—2361no—
554C23—2361no—
555C23#1427375212yes—
556C23C22×C22⋊D5911yescharacteristic
557D4—1182no—
558D4—1182no—
559D4—2368no—
560D4—2361no—
561D4—2361no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—44no—
576C2×C4—44no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—1182no—
594C2×C4—4724no—
595C2×C4—2361no—
596C2×C4—2361no—
597C2×C4—2361no—
598C2×C4—2361no—
599C2×C4—2361no—
600C2×C4—2361no—
601C2×C4—2361no—
602C2×C4—2361no—
603C2×C4#1427369912yes—
604C2×C4#1427369912yes—
605C2×C4C2×D4×D5911yescharacteristic
606C2×C4#41×D5911yescharacteristic
607C2×C4#41×D5911yescharacteristic
608C2×C4C2×#1174568711yescharacteristic
609C2×C4#1427377511yescharacteristic
610C2×C4#1427377511yescharacteristic
611C8—1182no—
612C8—1182no—
613C8—2361no—
614C8—2361no—
615C22—22no—
616C22—22no—
617C22—22no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—4721no—
623C22—4721no—
624C22—4721no—
625C22—4721no—
626C22—2362no—
627C22—2362no—
628C22—2362no—
629C22C2×#1427369911yescharacteristic
630C22#1683790911yescharacteristic
631C22#1683797611yescharacteristic
632C22C2×#1427375211yescharacteristic
633C22#1683820011yescharacteristic
634C22#1683820011yescharacteristic
635C22#1683820011yescharacteristic
636C4—22no—
637C4—22no—
638C4—41no—
639C4—41no—
640C4—41no—
641C4—81no—
642C4—81no—
643C4—81no—
644C4—81no—
645C4—4721no—
646C4—4721no—
647C4—2362no—
648C4#1683805411yescharacteristic
649C4#1683806211yescharacteristic
650C4#1683808611yescharacteristic
651C4#1683812311yescharacteristic
652C2—42no—
653C2—4722no—
654C2#2142752611yescharacteristic
655C2#2143370211yescharacteristic
656C2#2143371711yescharacteristic
657C2#2143419911yescharacteristic
658C2#2143423011yescharacteristic
659C2#2143528611yescharacteristic
660C2#2143533611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC59×#2851C2
socleC23×C59C22×D4
prime radicalC2×#14273701C22
hypercenter#2851D59
hypocenterC59#24706
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2851

Complements

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

NH ≅ G/Ntype
1. C2×#16837699C2semidirect
2. C2×#16837459C2semidirect
4. #21425533C2semidirect
5. #21425522C2semidirect
8. #21425054C2semidirect
9. #21424862C2semidirect
10. #21424836C2semidirect
11. #21424831C2semidirect
12. #21424792C2semidirect
13. #21424792C2semidirect
14. #21424103C2semidirect
15. C59×#2851C2semidirect
88. C4⋊(C59⋊C8)D4semidirect
324. #2851D59semidirect
391. C59#24706semidirect

Maximal subgroups

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

subgroupindex
C2×#168376992
C2×#168374592
C4×#142737012
#214255332
#214255222
#214252852
#214252782
#214250542
#214248622
#214248362
#214248312
#214247922
#214241032
C59×#28512
#2470659