Finite Group Databasebeta

← #28556218

Subgroups — #28556218

Order 15104.

1060 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21438128C211yesmaximal, characteristic
2#21426729C211yesmaximal, characteristic, complemented
3#21422674C211yesmaximal, characteristic, complemented
4#21422665C211yesmaximal, characteristic, complemented
5#21422657C211yesmaximal, characteristic, complemented
6#21422653C211yesmaximal, characteristic, complemented
7#21422644C211yesmaximal, characteristic, complemented
8#21422640C211yesmaximal, characteristic, complemented
9#21422635C211yesmaximal, characteristic, complemented
10#21422626C211yesmaximal, characteristic, complemented
11#21422613C211yesmaximal, characteristic, complemented
12#21422601C211yesmaximal, characteristic, complemented
13#21422588C211yesmaximal, characteristic, complemented
14C2×#16837137C211yesmaximal, characteristic, complemented
15C59×#2974C211yesmaximal, characteristic, complemented
16#16838117C411yescharacteristic, complemented
17#16838109C411yescharacteristic, complemented
18#16838100—21no—
19#16838098C411yescharacteristic, complemented
20#16838098C411yescharacteristic, complemented
21#16838073C411yescharacteristic, complemented
22#16838048C411yescharacteristic, complemented
23#16838048C411yescharacteristic, complemented
24#16838042—21no—
25#16838042—21no—
26D4×D236C411yescharacteristic, complemented
27D4×C22⋊D59—21no—
28#16838003—21no—
29#16837985—21no—
30#16837985—21no—
31#16837952C2211yescharacteristic
32#16837936C2211yescharacteristic
33#16837913C2211yescharacteristic
34#16837913C2211yescharacteristic
35C2×#14273701C2211yescharacteristic
36C2×#14273701C2211yescharacteristic
37#16837874—21no—
38#16837295—21no—
39#16837288—21no—
40#16837282—21no—
41#16837277—21no—
42#16837270C2211yescharacteristic, complemented
43#16837268C2211yescharacteristic, complemented
44#16837265C2211yescharacteristic, complemented
45#16837262C2211yescharacteristic, complemented
46C4×C22⋊Dic59C2211yescharacteristic, complemented
47C2×C59⋊#95C2211yescharacteristic, complemented
48#16837140C2211yescharacteristic, complemented
49#16837140C2211yescharacteristic, complemented
50#16837140C2211yescharacteristic, complemented
51#16837140C2211yescharacteristic, complemented
52#16837137C2211yescharacteristic
53#16837137C2211yescharacteristic
54#16837137C2211yescharacteristic
55#16837137C2211yescharacteristic
56#16837137C2211yescharacteristic, complemented
57#16837137C2211yescharacteristic, complemented
58#16837137C2211yescharacteristic, complemented
59#16837137C2211yescharacteristic, complemented
60#16837137C2211yescharacteristic, complemented
61#16837137C2211yescharacteristic, complemented
62#16837137C2211yescharacteristic, complemented
63#16837137C2211yescharacteristic, complemented
64C2×C4×D4×C59C2211yescharacteristic
65C59×#436—21no—
66C59×#435—21no—
67C59×#435—21no—
68C8×D4×C59—21no—
69C59×#432C2211yescharacteristic, complemented
70C59×#431C2211yescharacteristic, complemented
71C59×#407C2211yescharacteristic, complemented
72C59×#407C2211yescharacteristic, complemented
73C2×C22⋊C8×C59C2211yescharacteristic, complemented
74C2×C22⋊C8×C59C2211yescharacteristic, complemented
75C2×#11745685—21no—
76C2×#11745685C2×C411yescharacteristic
77C2×#11745685C2×C411yescharacteristic, complemented
78C22×D236C2×C411yescharacteristic
79C22×D236C2×C411yescharacteristic, complemented
80C22×C22⋊D59—21no—
81C22×C22⋊D59—21no—
82C2×D4×D59—21no—
83C23×Dic59—21no—
84#14273727C2×C411yescharacteristic, complemented
85#14273724C2×C411yescharacteristic, complemented
86#14273723—21no—
87#14273722—21no—
88#14273722—21no—
89#14273721—21no—
90#14273719C2×C411yescharacteristic, complemented
91#14273718—21no—
92#14273715—21no—
93#14273715C2×C411yescharacteristic, complemented
94#14273713—21no—
95#14273713—21no—
96#14273712—21no—
97#14273712—21no—
98#14273710—21no—
99#14273710—21no—
100#14273710—21no—
101#14273709—21no—
102#14273709—21no—
103#14273706C2×C411yescharacteristic
104#14273706C2×C411yescharacteristic, complemented
105#14273706C2311yescharacteristic
106#14273704—21no—
107#14273704—21no—
108#14273702—21no—
109#14273701—21no—
110#14273701—21no—
111#14273701—21no—
112#14273701—21no—
113#14273701—21no—
114#14273701C2×C411yescharacteristic
115#14273701C2×C411yescharacteristic
116#14273701C2×C411yescharacteristic
117#14273701C2×C411yescharacteristic, complemented
118#14273701C2×C411yescharacteristic, complemented
119#14273701C2×C411yescharacteristic, complemented
120#14273701C2311yescharacteristic
121#14273701C2311yescharacteristic
122#14273701C2311yescharacteristic
123#14273700—21no—
124#14273700—21no—
125#14273700—21no—
126#14273700—21no—
127#14273699—21no—
128#14273699—21no—
129#14273698—21no—
130#14273697—21no—
131#14273697—21no—
132#14273696—21no—
133#14273696—21no—
134#14273695—21no—
135#14273695—21no—
136C4×Dic118C2×C411yescharacteristic, complemented
137C4×D236—21no—
138C4×D236C2×C411yescharacteristic, complemented
139C4×D236C2×C411yescharacteristic, complemented
140C4×D236C2×C411yescharacteristic, complemented
141D4×Dic59—21no—
142#14273689—21no—
143C4×C22⋊D59—21no—
144C4×C22⋊D59—21no—
145C4×C22⋊D59—21no—
146C4×C22⋊D59—21no—
147C4×C22⋊D59—21no—
148(C22⋊D59)⋊C4—21no—
149(C22⋊D59)⋊C4—21no—
150#14273686C2×C411yescharacteristic
151#14273686C2×C411yescharacteristic, complemented
152#14273685—21no—
153#14273684—21no—
154C2×C4⋊Dic59—21no—
155C2×C4⋊Dic59—21no—
156C2×C4⋊Dic59C2×C411yescharacteristic
157C2×C4⋊Dic59C2×C411yescharacteristic, complemented
158C2×C22⋊Dic59—21no—
159C2×C22⋊Dic59—21no—
160C2×C22⋊Dic59—21no—
161C2×(C2×D59)⋊C4—21no—
162C2×(C2×D59)⋊C4—21no—
163C22⋊C4×D59—21no—
164C22⋊C4×D59—21no—
165C2×C4×Dic59—21no—
166C59⋊#95—21no—
167C59⋊#95—21no—
168C59⋊#95—21no—
169C59⋊#95—21no—
170C59⋊#95—21no—
171C59⋊#95C2311yescharacteristic
172C59⋊#95C2311yescharacteristic
173C59⋊#95C2311yescharacteristic
174C59⋊#95C2311yescharacteristic
175C22×D4×C59D411yescharacteristic
176C23×C4×C59C2311yescharacteristic
177C23×C4×C59C2311yescharacteristic
178C2×M16×C59—21no—
179C2×M16×C59—21no—
180C22×C8×C59—21no—
181C22×C8×C59—21no—
182C4×D4×C59C2×C411yescharacteristic
183C4×D4×C59C2×C411yescharacteristic
184C4×D4×C59C2×C411yescharacteristic
185C4×D4×C59C2×C411yescharacteristic
186C4×D4×C59D411yescharacteristic
187C4×D4×C59D411yescharacteristic
188C4×D4×C59D411yescharacteristic
189C4×D4×C59D411yescharacteristic
190C2×C4⋊C4×C59D411yescharacteristic
191C2×C22⋊C4×C59D411yescharacteristic
192C2×C22⋊C4×C59D411yescharacteristic
193C2×C42×C59C2311yescharacteristic
194C4⋊C8×C59—21no—
195C4⋊C8×C59—21no—
196C22⋊C8×C59—21no—
197C22⋊C8×C59—21no—
198C22⋊C8×C59—21no—
199C22⋊C8×C59—21no—
200C22⋊C8×C59C2311yescharacteristic
201C22⋊C8×C59C2311yescharacteristic
202C22⋊C8×C59C2311yescharacteristic
203C22⋊C8×C59C2311yescharacteristic
204#97×C59—21no—
205C4×C8×C59—21no—
206C24×C59C2×D411yescharacteristic
207C24×C59C2×D411yescharacteristic
208C23×D59—21no—
209C23×D59—21no—
210C2×D4×C59—42no—
211C2×D4×C59C22⋊C411yescharacteristic
212C2×D4×C59C22⋊C411yescharacteristic
213C2×D4×C59C22⋊C411yescharacteristic
214C2×D4×C59C22⋊C411yescharacteristic
215C22×C4×C59—81no—
216C22×C4×C59—81no—
217C22×C4×C59C22×C411yescharacteristic
218C22×C4×C59C22×C411yescharacteristic
219C22×C4×C59C22×C411yescharacteristic
220C22×C4×C59C22×C411yescharacteristic
221C22×C4×C59C2×D411yescharacteristic
222C22×C4×C59C2×D411yescharacteristic
223C22×C4×C59C2×D411yescharacteristic
224C22×C4×C59C2×D411yescharacteristic
225C22×C4×C59C2×D411yescharacteristic
226C22×C4×C59C2×D411yescharacteristic
227C22×C4×C59C2×D411yescharacteristic
228C22×C4×C59C2×D411yescharacteristic
229C22×C4×C59C2411yescharacteristic
230C2×C22⋊D59—21no—
231C2×C22⋊D59—21no—
232C2×C22⋊D59—21no—
233C2×C22⋊D59—21no—
234C2×C22⋊D59—21no—
235C2×C22⋊D59—21no—
236C2×C22⋊D59—21no—
237C2×C22⋊D59—21no—
238C2×C22⋊D59—21no—
239C2×C22⋊D59—21no—
240C2×C22⋊D59—21no—
241C2×C22⋊D59—81no—
242C2×C22⋊D59—81no—
243C2×C22⋊D59—81no—
244C2×C22⋊D59—81no—
245C22×Dic59—21no—
246C22×Dic59—21no—
247C22×Dic59—21no—
248C22×Dic59—21no—
249C22×Dic59—21no—
250C22×Dic59—21no—
251C22×Dic59—42no—
252C22×Dic59—81no—
253C22×Dic59—81no—
254D4×D59—44no—
255#11745685—81no—
256#11745685—81no—
257#11745685—81no—
258#11745685—81no—
259C2×D236—21no—
260C2×D236—21no—
261C2×D236—21no—
262C2×D236—21no—
263C2×D236—81no—
264C2×D236—81no—
265C2×D236C22×C411yescharacteristic
266C2×D236C22×C411yescharacteristic
267C2×D236C22×C411yescharacteristic
268C2×C4×D59—21no—
269C2×C4×D59—21no—
270C2×C4×D59—21no—
271C2×C4×D59—21no—
272C2×C4×D59—21no—
273C2×Dic118—21no—
274C2×Dic118C22×C411yescharacteristic
275M16×C59—81no—
276M16×C59—81no—
277C2×C8×C59—21no—
278C2×C8×C59—21no—
279C2×C8×C59—21no—
280C2×C8×C59—21no—
281C2×C8×C59—81no—
282C2×C8×C59—81no—
283C4⋊C4×C59C22⋊C411yescharacteristic
284C4⋊C4×C59C22⋊C411yescharacteristic
285C4⋊C4×C59C22⋊C411yescharacteristic
286C4⋊C4×C59C22⋊C411yescharacteristic
287C22⋊C4×C59C22⋊C411yescharacteristic
288C22⋊C4×C59C22⋊C411yescharacteristic
289C22⋊C4×C59C22⋊C411yescharacteristic
290C22⋊C4×C59C22⋊C411yescharacteristic
291C22⋊C4×C59C22⋊C411yescharacteristic
292C22⋊C4×C59C22⋊C411yescharacteristic
293C22⋊C4×C59C22⋊C411yescharacteristic
294C22⋊C4×C59C22⋊C411yescharacteristic
295C42×C59C22×C411yescharacteristic
296C42×C59C22×C411yescharacteristic
297C42×C59C2×D411yescharacteristic
298C42×C59C2×D411yescharacteristic
299C22⋊Dic59—21no—
300C22⋊Dic59—21no—
301C22⋊Dic59—21no—
302C22⋊Dic59—21no—
303C22⋊Dic59—21no—
304C22⋊Dic59—42no—
305C22⋊Dic59—81no—
306C22⋊Dic59—81no—
307(C2×D59)⋊C4—21no—
308(C2×D59)⋊C4—21no—
309(C2×D59)⋊C4—21no—
310(C2×D59)⋊C4—21no—
311(C2×D59)⋊C4—21no—
312(C2×D59)⋊C4—21no—
313(C2×D59)⋊C4—21no—
314(C2×D59)⋊C4—21no—
315(C2×D59)⋊C4—21no—
316(C2×D59)⋊C4—21no—
317(C2×D59)⋊C4—21no—
318(C2×D59)⋊C4—21no—
319(C2×D59)⋊C4—21no—
320(C2×D59)⋊C4—21no—
321C4⋊Dic59—21no—
322C4⋊Dic59—21no—
323C4⋊Dic59—21no—
324C4⋊Dic59—81no—
325C4⋊Dic59—81no—
326C4⋊Dic59C22×C411yescharacteristic
327C4⋊Dic59C22×C411yescharacteristic
328C4⋊Dic59C22×C411yescharacteristic
329C4⋊Dic59C22×C411yescharacteristic
330Dic59⋊C4—21no—
331Dic59⋊C4—21no—
332Dic59⋊C4—21no—
333Dic59⋊C4—21no—
334Dic59⋊C4—21no—
335Dic59⋊C4—21no—
336C4×Dic59—21no—
337C4×Dic59—21no—
338C4×Dic59—21no—
339C4×Dic59—81no—
340C23×C59—21no—
341C23×C59—21no—
342C23×C59—22no—
343C23×C59—21no—
344C23×C59—21no—
345C23×C59—41no—
346C23×C59—41no—
347C23×C59—41no—
348C23×C59C2×C22⋊C411yescharacteristic
349C23×C59C2×C22⋊C411yescharacteristic
350C23×C59C2×C22⋊C411yescharacteristic
351C23×C59C2×C22⋊C411yescharacteristic
352C23×C59C22×D411yescharacteristic
353C22×D59—21no—
354C22×D59—21no—
355C22×D59—21no—
356C22×D59—42no—
357C22×D59—42no—
358C22×D59—81no—
359C22×D59—81no—
360C22×D59—81no—
361C22×D59—81no—
362D4×C59—22no—
363D4×C59—22no—
364D4×C59—41no—
365D4×C59—41no—
366C2×C4×C59—21no—
367C2×C4×C59—21no—
368C2×C4×C59—41no—
369C2×C4×C59—41no—
370C2×C4×C59—41no—
371C2×C4×C59—41no—
372C2×C4×C59—41no—
373C2×C4×C59—41no—
374C2×C4×C59—41no—
375C2×C4×C59—41no—
376C2×C4×C59—41no—
377C2×C4×C59—41no—
378C2×C4×C59—41no—
379C2×C4×C59—41no—
380C2×C4×C59C2×C22⋊C411yescharacteristic
381C2×C4×C59C2×C22⋊C411yescharacteristic
382C2×C4×C59C2×C22⋊C411yescharacteristic
383C2×C4×C59C2×C22⋊C411yescharacteristic
384C2×C4×C59C2×C22⋊C411yescharacteristic
385C2×C4×C59C2×C22⋊C411yescharacteristic
386C2×C4×C59C2×C22⋊C411yescharacteristic
387C2×C4×C59C2×C22⋊C411yescharacteristic
388C2×C4×C59C23×C411yescharacteristic
389C2×C4×C59C22×D411yescharacteristic
390C22⋊D59—42no—
391C22⋊D59—41no—
392C22⋊D59—41no—
393C22⋊D59—41no—
394C22⋊D59—41no—
395C22⋊D59—41no—
396C22⋊D59—41no—
397C22⋊D59—42no—
398C22⋊D59—81no—
399C22⋊D59—81no—
400C22⋊D59—81no—
401C22⋊D59—81no—
402C22⋊D59—81no—
403C22⋊D59—81no—
404C2×Dic59—21no—
405C2×Dic59—21no—
406C2×Dic59—21no—
407C2×Dic59—21no—
408C2×Dic59—21no—
409C2×Dic59—41no—
410C2×Dic59—41no—
411C2×Dic59—41no—
412C2×Dic59—41no—
413C2×Dic59—41no—
414C2×Dic59—41no—
415C2×Dic59—41no—
416C2×Dic59—41no—
417C2×Dic59—41no—
418C2×Dic59—41no—
419C2×Dic59—41no—
420C2×Dic59—41no—
421C2×Dic59—81no—
422C2×Dic59—81no—
423C2×Dic59—84no—
424D236—41no—
425D236—41no—
426D236—41no—
427D236—42no—
428D236—81no—
429D236—81no—
430D236—81no—
431C4×D59—42no—
432C4×D59—81no—
433C4×D59—81no—
434C4×D59—81no—
435C4×D59—81no—
436Dic118—41no—
437Dic118—81no—
438C8×C59—41no—
439C8×C59—41no—
440C8×C59—41no—
441C8×C59—41no—
442#17597—591nomaximal, Sylow
443C22×C59—21no—
444C22×C59—21no—
445C22×C59—21no—
446C22×C59—21no—
447C22×C59—21no—
448C22×C59—21no—
449C22×C59—21no—
450C22×C59—21no—
451C22×C59—21no—
452C22×C59—21no—
453C22×C59—21no—
454C22×C59—21no—
455C22×C59—21no—
456C22×C59—42no—
457C22×C59—42no—
458C22×C59—81no—
459C22×C59—81no—
460C22×C59#42112yes—
461C22×C59C22×C22⋊C411yescharacteristic
462C22×C59#57611yescharacteristic
463C22×C59#57711yescharacteristic
464C2×D59—41no—
465C2×D59—41no—
466C2×D59—41no—
467C2×D59—41no—
468C2×D59—41no—
469C2×D59—41no—
470C2×D59—41no—
471C2×D59—41no—
472C2×D59—41no—
473C2×D59—162no—
474C2×D59—162no—
475C4×C59—21no—
476C4×C59—21no—
477C4×C59—21no—
478C4×C59—21no—
479C4×C59—21no—
480C4×C59—21no—
481C4×C59—21no—
482C4×C59—21no—
483C4×C59—21no—
484C4×C59—21no—
485Dic59—41no—
486Dic59—41no—
487Dic59—41no—
488Dic59—41no—
489Dic59—41no—
490Dic59—81no—
491Dic59—81no—
492Dic59—81no—
493Dic59—81no—
494#3519—591no—
495#2974D5911yescharacteristic, complemented
496#2318—591no—
497#1521—591no—
498#1519—591no—
499#1517—591no—
500#1516—591no—
501#1514—591no—
502#1513—591no—
503#1512—591no—
504#1510—591no—
505#1507—591no—
506#1504—591no—
507#1501—591no—
508C2×#327—591no—
509C2×C59—21no—
510C2×C59—21no—
511C2×C59—22no—
512C2×C59—41no—
513C2×C59—41no—
514C2×C59—41no—
515C2×C59#288311yescharacteristic
516C2×C59#289711yescharacteristic
517C2×C59C2×#42111yescharacteristic
518D59—81no—
519D59—81no—
520D59—81no—
521#555—591no—
522#554—591no—
523#553—591no—
524#553—591no—
525#553—1181no—
526#550—591no—
527#546—591no—
528#546—591no—
529#546—1181no—
530#546—1181no—
531D42—591no—
532D42—1181no—
533#540—1181no—
534#538—1181no—
535#538—1181no—
536#532—591no—
537#529—591no—
538#525—591no—
539#525—591no—
540C2×#121—591no—
541C2×#121—591no—
542#518—1181no—
543C2×C4×D4C2×D5911yescharacteristic
544#436—21no—
545#435—21no—
546#435—21no—
547C8×D4—21no—
548#432C2×D5911yescharacteristic, complemented
549#431C2×D5911yescharacteristic, complemented
550#407C2×D5911yescharacteristic, complemented
551#407C2×D5911yescharacteristic, complemented
552C2×C22⋊C8C2×D5911yescharacteristic, complemented
553C2×C22⋊C8C2×D5911yescharacteristic, complemented
554#388—1181no—
555#387—1181no—
556#386—1181no—
557#385—1181no—
558#383—591no—
559#382—591no—
560#381—591no—
561#380—591no—
562C4×C22⋊C4—591no—
563C2×#95—591no—
564#328—591no—
565#328—591no—
566#328—591no—
567#328—591no—
568#327—591no—
569#327—591no—
570#327—591no—
571#327—591no—
572#327—591no—
573#327—591no—
574#327—591no—
575#327—591no—
576#327—591no—
577#327—591no—
578#327—591no—
579#327—591no—
580C59#1759711yescharacteristic, complemented, Sylow
581C2×#41—591no—
582C2×#41—591no—
583C2×#41—1181no—
584C22×D4—591no—
585C22×D4—591no—
586C22×D4—1181no—
587C22×D4—1181no—
588C22×D4—1181no—
589C22×D4D23611yescharacteristic
590C23×C4—1181no—
591C23×C4C22×D5911yescharacteristic
592C23×C4C22×D5911yescharacteristic
593C2×M16—21no—
594C2×M16—21no—
595C22×C8—21no—
596C22×C8—21no—
597C4⋊Q8—591no—
598#127—591no—
599#127—1181no—
600#126—1181no—
601#126—1181no—
602#126—1181no—
603#125—591no—
604#125—1181no—
605#124—591no—
606#124—1181no—
607#124—1181no—
608#124—1181no—
609#123—1181no—
610#123—1181no—
611#123—1181no—
612#123—1181no—
613#123—1181no—
614#123—1181no—
615#123—1181no—
616C22⋊Q8—591no—
617C22⋊Q8—591no—
618C22⋊Q8—591no—
619C22⋊Q8—1181no—
620C22⋊Q8—1181no—
621#121—591no—
622#121—591no—
623#121—591no—
624#121—591no—
625#121—591no—
626#121—591no—
627#121—591no—
628#121—591no—
629#121—591no—
630#121—1181no—
631#121—1181no—
632#121—1181no—
633#121—1181no—
634#121—1181no—
635#121—1181no—
636#121—1181no—
637#121—1181no—
638#121—1181no—
639#121—1181no—
640#121—1181no—
641#121—1181no—
642#121—1181no—
643#120—1181no—
644#120—1181no—
645#120—1181no—
646#120—1181no—
647#120—1181no—
648#120—1181no—
649C4×Q8—591no—
650C4×D4—591no—
651C4×D4—591no—
652C4×D4—591no—
653C4×D4—1181no—
654C4×D4—1181no—
655C4×D4—1181no—
656C4×D4—1181no—
657C4×D4—1181no—
658C4×D4—1181no—
659C4×D4—1181no—
660C4×D4—1181no—
661C4×D4—1181no—
662C4×D4—1181no—
663C4×D4C4×D5911yescharacteristic
664C4×D4C4×D5911yescharacteristic
665C4×D4C4×D5911yescharacteristic
666C4×D4C4×D5911yescharacteristic
667C4×D4C22⋊D5911yescharacteristic
668C4×D4C22⋊D5911yescharacteristic
669C4×D4C22⋊D5911yescharacteristic
670C4×D4C22⋊D5911yescharacteristic
671#117—591no—
672#117—591no—
673#117—1181no—
674#117—1181no—
675C2×C4⋊C4—591no—
676C2×C4⋊C4—591no—
677C2×C4⋊C4—1181no—
678C2×C4⋊C4—1181no—
679C2×C4⋊C4D23611yescharacteristic
680C2×C22⋊C4—1181no—
681C2×C22⋊C4—1181no—
682C2×C22⋊C4—1181no—
683C2×C22⋊C4—1181no—
684C2×C22⋊C4—1181no—
685C2×C22⋊C4—1181no—
686C2×C22⋊C4—1181no—
687C2×C22⋊C4D23611yescharacteristic
688C2×C22⋊C4D23611yescharacteristic
689C2×C42—1181no—
690C2×C42C22×D5911yescharacteristic
691C4⋊C8—21no—
692C4⋊C8—21no—
693C22⋊C8—21no—
694C22⋊C8—21no—
695C22⋊C8—21no—
696C22⋊C8—21no—
697C22⋊C8C22×D5911yescharacteristic
698C22⋊C8C22×D5911yescharacteristic
699C22⋊C8C22×D5911yescharacteristic
700C22⋊C8C22×D5911yescharacteristic
701#97—21no—
702C4×C8—21no—
703#95—591no—
704#95—591no—
705#95—591no—
706#95—591no—
707#95—1181no—
708#95—1181no—
709#95—1181no—
710#95—1181no—
711#95—1181no—
712C24—1181no—
713C24—1181no—
714C24C2×D23611yescharacteristic
715C24C2×D23611yescharacteristic
716#41—4721no—
717#41—4721no—
718#41—4721no—
719#41—4721no—
720C2×Q8—591no—
721C2×Q8—1181no—
722C2×D4—42no—
723C2×D4—591no—
724C2×D4—591no—
725C2×D4—591no—
726C2×D4—1181no—
727C2×D4—1181no—
728C2×D4—1181no—
729C2×D4—1181no—
730C2×D4—1181no—
731C2×D4—1181no—
732C2×D4—1181no—
733C2×D4—1181no—
734C2×D4—1181no—
735C2×D4—1181no—
736C2×D4—1181no—
737C2×D4—1181no—
738C2×D4—1181no—
739C2×D4—1181no—
740C2×D4—1181no—
741C2×D4—4721no—
742C2×D4—4721no—
743C2×D4—4721no—
744C2×D4—4721no—
745C2×D4—4721no—
746C2×D4—4721no—
747C2×D4—2364no—
748C2×D4(C2×D59)⋊C411yescharacteristic
749C2×D4(C2×D59)⋊C411yescharacteristic
750C2×D4(C2×D59)⋊C411yescharacteristic
751C2×D4(C2×D59)⋊C411yescharacteristic
752C22×C4—81no—
753C22×C4—81no—
754C22×C4—1181no—
755C22×C4—1181no—
756C22×C4—1181no—
757C22×C4—1181no—
758C22×C4—1181no—
759C22×C4—1181no—
760C22×C4—1181no—
761C22×C4—1181no—
762C22×C4—1181no—
763C22×C4—1181no—
764C22×C4—1181no—
765C22×C4—4721no—
766C22×C4—4721no—
767C22×C4—2362no—
768C22×C4C2×C4×D5911yescharacteristic
769C22×C4C2×C4×D5911yescharacteristic
770C22×C4C2×C4×D5911yescharacteristic
771C22×C4C2×C4×D5911yescharacteristic
772C22×C4C2×D23611yescharacteristic
773C22×C4C2×D23611yescharacteristic
774C22×C4C2×D23611yescharacteristic
775C22×C4C2×D23611yescharacteristic
776C22×C4C2×C22⋊D5911yescharacteristic
777C22×C4C2×C22⋊D5911yescharacteristic
778C22×C4C2×C22⋊D5911yescharacteristic
779C22×C4C2×C22⋊D5911yescharacteristic
780C22×C4C23×D5911yescharacteristic
781M16—81no—
782M16—81no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—81no—
788C2×C8—81no—
789C4⋊C4—591no—
790C4⋊C4—591no—
791C4⋊C4—591no—
792C4⋊C4—591no—
793C4⋊C4—1181no—
794C4⋊C4—1181no—
795C4⋊C4—1181no—
796C4⋊C4—1181no—
797C4⋊C4—1181no—
798C4⋊C4—1181no—
799C4⋊C4—1181no—
800C4⋊C4—1181no—
801C4⋊C4—1181no—
802C4⋊C4—4721no—
803C4⋊C4—4721no—
804C4⋊C4(C2×D59)⋊C411yescharacteristic
805C4⋊C4(C2×D59)⋊C411yescharacteristic
806C4⋊C4(C2×D59)⋊C411yescharacteristic
807C4⋊C4(C2×D59)⋊C411yescharacteristic
808C22⋊C4—1181no—
809C22⋊C4—1181no—
810C22⋊C4—1181no—
811C22⋊C4—1181no—
812C22⋊C4—1181no—
813C22⋊C4—1181no—
814C22⋊C4—1181no—
815C22⋊C4—1181no—
816C22⋊C4—1181no—
817C22⋊C4—1181no—
818C22⋊C4—1181no—
819C22⋊C4—1181no—
820C22⋊C4—1181no—
821C22⋊C4—1181no—
822C22⋊C4—1181no—
823C22⋊C4—1181no—
824C22⋊C4—1181no—
825C22⋊C4—1181no—
826C22⋊C4—1181no—
827C22⋊C4—4721no—
828C22⋊C4—4721no—
829C22⋊C4—2362no—
830C22⋊C4(C2×D59)⋊C411yescharacteristic
831C22⋊C4(C2×D59)⋊C411yescharacteristic
832C22⋊C4(C2×D59)⋊C411yescharacteristic
833C22⋊C4(C2×D59)⋊C411yescharacteristic
834C22⋊C4(C2×D59)⋊C411yescharacteristic
835C22⋊C4(C2×D59)⋊C411yescharacteristic
836C22⋊C4(C2×D59)⋊C411yescharacteristic
837C22⋊C4(C2×D59)⋊C411yescharacteristic
838C42—1181no—
839C42—1181no—
840C42—1181no—
841C42—4721no—
842C42C2×C4×D5911yescharacteristic
843C42C2×C4×D5911yescharacteristic
844C42C2×C22⋊D5911yescharacteristic
845C42C2×C22⋊D5911yescharacteristic
846C23—22no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—1181no—
855C23—1181no—
856C23—1181no—
857C23—4721no—
858C23—4721no—
859C23—4721no—
860C23—4721no—
861C23—2362no—
862C23—2362no—
863C23C2×(C2×D59)⋊C411yescharacteristic
864C23C2×(C2×D59)⋊C411yescharacteristic
865C23C2×(C2×D59)⋊C411yescharacteristic
866C23C2×(C2×D59)⋊C411yescharacteristic
867C23C22×D23611yescharacteristic
868Q8—4721no—
869Q8—2361no—
870D4—22no—
871D4—22no—
872D4—41no—
873D4—41no—
874D4—4721no—
875D4—4721no—
876D4—4721no—
877D4—4721no—
878D4—4721no—
879D4—4721no—
880D4—4721no—
881D4—4721no—
882D4—4721no—
883D4—2361no—
884D4—2361no—
885D4—2361no—
886D4—2362no—
887D4—2362no—
888D4—2362no—
889D4—2361no—
890D4—2361no—
891D4—2361no—
892D4—2361no—
893D4—2361no—
894D4—2361no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—1181no—
910C2×C4—1181no—
911C2×C4—1181no—
912C2×C4—1181no—
913C2×C4—1181no—
914C2×C4—4721no—
915C2×C4—4721no—
916C2×C4—4721no—
917C2×C4—4721no—
918C2×C4—4724no—
919C2×C4—4721no—
920C2×C4—4721no—
921C2×C4—2362no—
922C2×C4—2361no—
923C2×C4—2361no—
924C2×C4—2361no—
925C2×C4—2361no—
926C2×C4—2361no—
927C2×C4—2361no—
928C2×C4—2361no—
929C2×C4—2361no—
930C2×C4—2361no—
931C2×C4—2361no—
932C2×C4—2361no—
933C2×C4—2361no—
934C2×C4C2×(C2×D59)⋊C411yescharacteristic
935C2×C4C2×(C2×D59)⋊C411yescharacteristic
936C2×C4C2×(C2×D59)⋊C411yescharacteristic
937C2×C4C2×(C2×D59)⋊C411yescharacteristic
938C2×C4C2×(C2×D59)⋊C411yescharacteristic
939C2×C4C2×(C2×D59)⋊C411yescharacteristic
940C2×C4C2×(C2×D59)⋊C411yescharacteristic
941C2×C4C2×(C2×D59)⋊C411yescharacteristic
942C2×C4C22×C4×D5911yescharacteristic
943C2×C4C22×C22⋊D5911yescharacteristic
944C8—41no—
945C8—41no—
946C8—41no—
947C8—41no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—21no—
961C22—42no—
962C22—42no—
963C22—81no—
964C22—81no—
965C22—9442no—
966C22—9442no—
967C22—2361no—
968C22—2361no—
969C22—2361no—
970C22—2361no—
971C22—2361no—
972C22—2361no—
973C22—2361no—
974C22—2361no—
975C22—2361no—
976C22#1683741812yes—
977C22C22×(C2×D59)⋊C411yescharacteristic
978C22#1683820711yescharacteristic
979C22#1683821411yescharacteristic
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—21no—
987C4—21no—
988C4—21no—
989C4—21no—
990C4—4721no—
991C4—4721no—
992C4—4721no—
993C4—4721no—
994C4—2361no—
995C4—2361no—
996C4—2361no—
997C4—2361no—
998C4—2361no—
999C2—21no—
1000C2—21no—
1001C2—22no—
1002C2—41no—
1003C2—41no—
1004C2—41no—
1005C2—4721no—
1006C2—4721no—
1007C2—4721no—
1008C2#2143255611yescharacteristic
1009C2#2143262311yescharacteristic
1010C2C2×#1683741811yescharacteristic
subgroupG/H
centerC22C22×(C2×D59)⋊C4
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#2974C2
socleC22×C59C22×C22⋊C4
prime radical#21438128C2
cosocleC22×C4×C59C24
hypercenter#2974D59
hypocenterC59#17597
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2974

Complements

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

NH ≅ G/Ntype
2. #21426729C2semidirect
3. #21422674C2semidirect
4. #21422665C2semidirect
5. #21422657C2semidirect
6. #21422653C2semidirect
7. #21422644C2semidirect
8. #21422640C2semidirect
9. #21422635C2semidirect
10. #21422626C2semidirect
11. #21422613C2semidirect
12. #21422601C2semidirect
13. #21422588C2semidirect
14. C2×#16837137C2semidirect
15. C59×#2974C2semidirect
16. #16838117C4semidirect
17. #16838109C4semidirect
19. #16838098C4semidirect
20. #16838098C4semidirect
21. #16838073C4semidirect
22. #16838048C4semidirect
23. #16838048C4semidirect
26. D4×D236C4semidirect
42. #16837270C22semidirect
43. #16837268C22semidirect
44. #16837265C22semidirect
45. #16837262C22semidirect
46. C4×C22⋊Dic59C22semidirect
47. C2×C59⋊#95C22semidirect
48. #16837140C22semidirect
49. #16837140C22semidirect
50. #16837140C22semidirect
51. #16837140C22semidirect
56. #16837137C22semidirect
57. #16837137C22semidirect
58. #16837137C22semidirect
59. #16837137C22semidirect
60. #16837137C22semidirect
61. #16837137C22semidirect
62. #16837137C22semidirect
63. #16837137C22semidirect
69. C59×#432C22semidirect
70. C59×#431C22semidirect
71. C59×#407C22semidirect
72. C59×#407C22semidirect
73. C2×C22⋊C8×C59C22semidirect
74. C2×C22⋊C8×C59C22semidirect
77. C2×#11745685C2×C4semidirect
79. C22×D236C2×C4semidirect
84. #14273727C2×C4semidirect
85. #14273724C2×C4semidirect
90. #14273719C2×C4semidirect
93. #14273715C2×C4semidirect
104. #14273706C2×C4semidirect
117. #14273701C2×C4semidirect
118. #14273701C2×C4semidirect
119. #14273701C2×C4semidirect
136. C4×Dic118C2×C4semidirect
138. C4×D236C2×C4semidirect
139. C4×D236C2×C4semidirect
140. C4×D236C2×C4semidirect
151. #14273686C2×C4semidirect
157. C2×C4⋊Dic59C2×C4semidirect
495. #2974D59semidirect
548. #432C2×D59semidirect
549. #431C2×D59semidirect
550. #407C2×D59semidirect
551. #407C2×D59semidirect
552. C2×C22⋊C8C2×D59semidirect
553. C2×C22⋊C8C2×D59semidirect
580. C59#17597semidirect

Maximal subgroups

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

subgroupindex
#214381282
#214267292
#214226742
#214226652
#214226572
#214226532
#214226442
#214226402
#214226352
#214226262
#214226132
#214226012
#214225882
C2×#168371372
C59×#29742
#1759759