Finite Group Databasebeta

← #28609467

Subgroups — #28609467

Order 15104.

1020 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21433314C211yesmaximal, characteristic
2C2×#16837517C211yesmaximal, characteristic, complemented
3#21432817C211yesmaximal, characteristic, complemented
4C2×#16837419C211yesmaximal, characteristic, complemented
5#21424988C211yesmaximal, characteristic, complemented
6#21424803C211yesmaximal, characteristic, complemented
7#21424741C211yesmaximal, characteristic, complemented
8#21424542C211yesmaximal, characteristic, complemented
9#21424426C211yesmaximal, characteristic, complemented
10#21424423C211yesmaximal, characteristic, complemented
11#21424371C211yesmaximal, characteristic, complemented
12#21424300C211yesmaximal, characteristic, complemented
13#21423938C211yesmaximal, characteristic, complemented
14#21423864C211yesmaximal, characteristic, complemented
15C59×#2880C211yesmaximal, characteristic, complemented
16C2×#14273747C2211yescharacteristic
17C2×#14273747C2211yescharacteristic
18C2×#14273733C2211yescharacteristic, complemented
19C22×#11745664C2211yescharacteristic
20#16837913C2211yescharacteristic
21C2×#14273686C2211yescharacteristic
22#16837564C411yescharacteristic, complemented
23#16837564C411yescharacteristic, complemented
24#16837558C411yescharacteristic, complemented
25#16837553C411yescharacteristic, complemented
26#16837547C411yescharacteristic, complemented
27#16837547C411yescharacteristic, complemented
28#16837541C411yescharacteristic, complemented
29#16837536C411yescharacteristic, complemented
30#16837517—24no—
31#16837477—21no—
32#16837476—21no—
33#16837470—21no—
34(C22⋊D59)⋊C8—21no—
35C2×#14273662C2211yescharacteristic, complemented
36C2×#14273662C2211yescharacteristic, complemented
37#16837428C2211yescharacteristic, complemented
38#16837419—24no—
39C2×#14273654C2211yescharacteristic
40C2×#14273654C2211yescharacteristic
41C2×#14273654C2211yescharacteristic
42C2×#14273654C2211yescharacteristic
43C2×#14273653C2211yescharacteristic, complemented
44C2×#14273653C2211yescharacteristic, complemented
45#16837398C2211yescharacteristic
46#16837398C2211yescharacteristic
47#16837368C2211yescharacteristic, complemented
48C2×C22⋊(C59⋊C8)C2211yescharacteristic
49#16837357C2211yescharacteristic, complemented
50C2×#14273637C2211yescharacteristic, complemented
51C2×C8×Dic59C2211yescharacteristic, complemented
52#16837166C2211yescharacteristic, complemented
53#16837166C2211yescharacteristic, complemented
54#16837163C2211yescharacteristic, complemented
55#16837163C2211yescharacteristic, complemented
56#16837156C2211yescharacteristic, complemented
57#16837156C2211yescharacteristic, complemented
58C22×#41×C59C2211yescharacteristic
59C2×#131×C59C2211yescharacteristic
60C2×#131×C59C2211yescharacteristic
61C59×#408—21no—
62C59×#408—21no—
63C59×#408C2211yescharacteristic
64C59×#408C2211yescharacteristic
65C59×#407—21no—
66C59×#407C2211yescharacteristic
67C2×C22⋊C8×C59—21no—
68C2×C22⋊C8×C59C2211yescharacteristic
69C2×#11745685C2311yescharacteristic
70#14273747—22no—
71#14273747—22no—
72#14273747—41no—
73#14273747—41no—
74C2×#11745672C2×C411yescharacteristic
75C2×#11745672C2×C411yescharacteristic
76C2×#11745670C2×C411yescharacteristic
77C2×#11745670C2×C411yescharacteristic
78C2×#11745671C2×C411yescharacteristic
79C2×#11745671C2×C411yescharacteristic
80C2×#11745669C2×C411yescharacteristic
81C2×#11745669C2×C411yescharacteristic
82#14273733—22no—
83#14273733—41no—
84C2×#11745664—21no—
85C2×#11745664—22no—
86C2×#11745664—41no—
87C2×#11745664C2311yescharacteristic
88C2×#11745664C2311yescharacteristic
89C2×#11745659—21no—
90C22×C59⋊C8—21no—
91C22×C59⋊C8C2311yescharacteristic
92C22×C59⋊C8C2311yescharacteristic
93C2×C8×D59—21no—
94#14273710—21no—
95#14273706C2×C411yescharacteristic
96#14273706C2×C411yescharacteristic
97#14273701C2×C411yescharacteristic
98#14273701C2×C411yescharacteristic
99#14273696—21no—
100C4×C22⋊D59—21no—
101C4×C22⋊D59—21no—
102#14273686—22no—
103#14273686—41no—
104#14273686C2311yescharacteristic
105C2×C4⋊Dic59—21no—
106C2×C22⋊Dic59—21no—
107C2×C4×Dic59C2311yescharacteristic
108C2×C4×Dic59C2311yescharacteristic
109#14273662—22no—
110#14273662—41no—
111Dic59⋊C8—21no—
112Dic59⋊C8—21no—
113#14273654—22no—
114#14273654—22no—
115#14273654—22no—
116#14273654D414yescomplemented
117#14273653—22no—
118#14273653—41no—
119#14273651C2×C411yescharacteristic
120#14273651C2×C411yescharacteristic
121#14273651C2×C411yescharacteristic
122#14273651C2×C411yescharacteristic
123#14273648C2×C411yescharacteristic
124#14273648C2×C411yescharacteristic
125#14273648C2×C411yescharacteristic
126#14273648C2×C411yescharacteristic
127C22⋊(C59⋊C8)C2×C411yescharacteristic
128C22⋊(C59⋊C8)C2×C411yescharacteristic
129C22⋊(C59⋊C8)C2×C411yescharacteristic
130C22⋊(C59⋊C8)C2×C411yescharacteristic
131(C2×D59)⋊C8—21no—
132(C2×D59)⋊C8—21no—
133#14273637—21no—
134#14273637—41no—
135C8×Dic59—21no—
136C8×Dic59—22no—
137C2×#41×C59—21no—
138C2×#41×C59—21no—
139C2×#41×C59—22no—
140C2×#41×C59—22no—
141C2×#41×C59—41no—
142C2×#41×C59—41no—
143C2×#41×C59C2×C411yescharacteristic
144C2×#41×C59C2×C411yescharacteristic
145C2×#41×C59C2311yescharacteristic
146C2×#41×C59C2311yescharacteristic
147C22×Q8×C59C2×C411yescharacteristic
148C22×D4×C59—21no—
149C22×D4×C59C2×C411yescharacteristic
150C23×C4×C59—21no—
151C23×C4×C59C2311yescharacteristic
152#131×C59—22no—
153#131×C59—22no—
154#131×C59—41no—
155#131×C59—41no—
156C2×M16×C59—21no—
157C2×M16×C59—21no—
158C2×M16×C59C2311yescharacteristic
159C2×M16×C59C2311yescharacteristic
160C22×C8×C59—21no—
161C22×C8×C59—21no—
162C22×C8×C59C2311yescharacteristic
163C22×C8×C59C2311yescharacteristic
164C22⋊C8×C59—21no—
165C22⋊C8×C59—21no—
166C22⋊C8×C59—21no—
167C22⋊C8×C59—21no—
168C22⋊C8×C59—21no—
169C22⋊C8×C59—21no—
170C22⋊C8×C59D411yescharacteristic
171C22⋊C8×C59D411yescharacteristic
172C22⋊C8×C59D411yescharacteristic
173C22⋊C8×C59D411yescharacteristic
174C24×C59—21no—
175C24×C59#4111yescharacteristic
176#41×C59—21no—
177#41×C59—21no—
178#41×C59—22no—
179#41×C59—22no—
180#41×C59—21no—
181#41×C59—21no—
182#41×C59—21no—
183#41×C59—21no—
184#41×C59—42no—
185#41×C59—42no—
186#41×C59—41no—
187#41×C59—41no—
188#41×C59—42no—
189#41×C59—42no—
190#41×C59C2×D412yes—
191#41×C59#4112yes—
192C2×Q8×C59—21no—
193C2×Q8×C59—22no—
194C2×Q8×C59—41no—
195C2×Q8×C59C22×C411yescharacteristic
196C2×Q8×C59C22×C411yescharacteristic
197C2×D4×C59—21no—
198C2×D4×C59—22no—
199C2×D4×C59—21no—
200C2×D4×C59—21no—
201C2×D4×C59—21no—
202C2×D4×C59—21no—
203C2×D4×C59—41no—
204C2×D4×C59—42no—
205C2×D4×C59—42no—
206C2×D4×C59C22×C411yescharacteristic
207C2×D4×C59C22×C411yescharacteristic
208C22×C4×C59—21no—
209C22×C4×C59—21no—
210C22×C4×C59—21no—
211C22×C4×C59—21no—
212C22×C4×C59—21no—
213C22×C4×C59—21no—
214C22×C4×C59—21no—
215C22×C4×C59—21no—
216C22×C4×C59—21no—
217C22×C4×C59—42no—
218C22×C4×C59—42no—
219C22×C4×C59C22×C411yescharacteristic
220C22×C4×C59C22×C411yescharacteristic
221C22×C4×C59C2×D411yescharacteristic
222C22×C4×C59C2×D411yescharacteristic
223C22×C4×C59#4111yescharacteristic
224C22×C4×C59C2411yescharacteristic
225C2×C22⋊D59—21no—
226C2×C22⋊D59—21no—
227C2×C22⋊D59—21no—
228C22×Dic59—21no—
229C22×Dic59—21no—
230#11745685—21no—
231#11745685—21no—
232#11745685—21no—
233#11745685—21no—
234C2×D236C22×C411yescharacteristic
235C2×C4×D59—21no—
236C2×Dic118C22×C411yescharacteristic
237M16×C59—21no—
238M16×C59—21no—
239M16×C59—21no—
240M16×C59—21no—
241M16×C59—42no—
242M16×C59—42no—
243C2×C8×C59—21no—
244C2×C8×C59—21no—
245C2×C8×C59—21no—
246C2×C8×C59—21no—
247C2×C8×C59—21no—
248C2×C8×C59—21no—
249C2×C8×C59—42no—
250C2×C8×C59—42no—
251C2×C8×C59C2×D411yescharacteristic
252C2×C8×C59C2×D411yescharacteristic
253C2×C8×C59C2×D411yescharacteristic
254C2×C8×C59C2×D411yescharacteristic
255C22⋊Dic59—21no—
256C22⋊Dic59—21no—
257C22⋊Dic59—21no—
258C22⋊Dic59—42no—
259#11745672—22no—
260#11745672—41no—
261#11745671—22no—
262#11745671—41no—
263#11745670—22no—
264#11745670—41no—
265#11745669—22no—
266#11745669—41no—
267(C2×D59)⋊C4—21no—
268(C2×D59)⋊C4—21no—
269C4⋊Dic59—42no—
270C4⋊Dic59C22×C411yescharacteristic
271C4⋊Dic59C22×C411yescharacteristic
272Dic59⋊C4—21no—
273Dic59⋊C4—21no—
274C4×Dic59—21no—
275C4×Dic59—21no—
276C4×Dic59—21no—
277C4×Dic59—21no—
278C4×Dic59C2×D412yes—
279#11745664—21no—
280#11745664—21no—
281#11745664—21no—
282#11745664—42no—
283#11745664C2×D412yes—
284C2×C59⋊C8—21no—
285C2×C59⋊C8—21no—
286C2×C59⋊C8—21no—
287C2×C59⋊C8—21no—
288C2×C59⋊C8—21no—
289C2×C59⋊C8—21no—
290C2×C59⋊C8—42no—
291C2×C59⋊C8C22×C411yescharacteristic
292C2×C59⋊C8C22×C411yescharacteristic
293C2×C59⋊C8C22×C411yescharacteristic
294C2×C59⋊C8C22×C411yescharacteristic
295#11745659—42no—
296C8×D59—42no—
297C23×C59—21no—
298C23×C59—21no—
299C23×C59—21no—
300C23×C59—21no—
301C23×C59—41no—
302C23×C59—41no—
303C23×C59—42no—
304C23×C59—42no—
305C23×C59—81no—
306C23×C59C4×D411yescharacteristic
307C23×C59C4×D411yescharacteristic
308C23×C59C2×#4111yescharacteristic
309C22×D59—21no—
310Q8×C59—21no—
311Q8×C59—21no—
312Q8×C59—21no—
313Q8×C59—42no—
314Q8×C59C4×D412yes—
315D4×C59—22no—
316D4×C59—22no—
317D4×C59—21no—
318D4×C59—21no—
319D4×C59—21no—
320D4×C59—42no—
321D4×C59—42no—
322D4×C59—42no—
323D4×C59—41no—
324D4×C59—41no—
325D4×C59C4×D412yes—
326C2×C4×C59—21no—
327C2×C4×C59—21no—
328C2×C4×C59—21no—
329C2×C4×C59—21no—
330C2×C4×C59—21no—
331C2×C4×C59—21no—
332C2×C4×C59—21no—
333C2×C4×C59—21no—
334C2×C4×C59—21no—
335C2×C4×C59—22no—
336C2×C4×C59—22no—
337C2×C4×C59—21no—
338C2×C4×C59—21no—
339C2×C4×C59—21no—
340C2×C4×C59—42no—
341C2×C4×C59—42no—
342C2×C4×C59—42no—
343C2×C4×C59—41no—
344C2×C4×C59—41no—
345C2×C4×C59C4×D411yescharacteristic
346C2×C4×C59C4×D411yescharacteristic
347C2×C4×C59C23×C411yescharacteristic
348C2×C4×C59C22×D411yescharacteristic
349C2×C4×C59C22×D411yescharacteristic
350C2×C4×C59C2×#4111yescharacteristic
351C2×C4×C59H(5,𝔽2)11yescharacteristic
352C2×C4×C59H(5,𝔽2)11yescharacteristic
353C22⋊D59—42no—
354C22⋊D59—41no—
355C22⋊D59—41no—
356C22⋊D59—81no—
357C2×Dic59—21no—
358C2×Dic59—21no—
359C2×Dic59—21no—
360C2×Dic59—22no—
361C2×Dic59—41no—
362C2×Dic59—41no—
363C2×Dic59—41no—
364C2×Dic59—41no—
365C2×Dic59—41no—
366D236—21no—
367D236—21no—
368C4×D59—41no—
369C4×D59—41no—
370Dic118—21no—
371Dic118—21no—
372C8×C59—21no—
373C8×C59—21no—
374C8×C59—21no—
375C8×C59—21no—
376C8×C59—41no—
377C8×C59—41no—
378C59⋊C8—21no—
379C59⋊C8—21no—
380C59⋊C8—21no—
381C59⋊C8—21no—
382C59⋊C8—22no—
383C59⋊C8—41no—
384#22889—591nomaximal, Sylow
385C22×C59—21no—
386C22×C59—21no—
387C22×C59—21no—
388C22×C59—21no—
389C22×C59—22no—
390C22×C59—21no—
391C22×C59—21no—
392C22×C59—21no—
393C22×C59—21no—
394C22×C59—41no—
395C22×C59—41no—
396C22×C59—41no—
397C22×C59—41no—
398C22×C59—41no—
399C22×C59—81no—
400C22×C59—81no—
401C22×C59—84no—
402C22×C59C2×C4×D411yescharacteristic
403C22×C59#54611yescharacteristic
404C22×C59#55111yescharacteristic
405C2×D59—41no—
406C2×D59—41no—
407C2×D59—41no—
408C4×C59—21no—
409C4×C59—21no—
410C4×C59—22no—
411C4×C59—41no—
412C4×C59C2×C4×D411yescharacteristic
413C4×C59#51811yescharacteristic
414C4×C59D4211yescharacteristic
415C4×C59#54611yescharacteristic
416Dic59—42no—
417Dic59—41no—
418Dic59—41no—
419Dic59—41no—
420Dic59—81no—
421#3002—591no—
422C2×#443—591no—
423#2933—591no—
424C2×#421—591no—
425#2880D5911yescharacteristic, complemented
426#1975—591no—
427#1937—591no—
428#1929—591no—
429#1897—591no—
430#1876—591no—
431#1876—591no—
432#1866—591no—
433#1855—591no—
434#1765—591no—
435#1750—591no—
436C2×C59—21no—
437C2×C59—21no—
438C2×C59—41no—
439C2×C59—41no—
440C2×C59—42no—
441C2×C59—81no—
442C2×C59#235811yescharacteristic
443C2×C59#295511yescharacteristic
444C2×C59#295711yescharacteristic
445D59—81no—
446C22×#41C2×D5911yescharacteristic
447C2×#135—591no—
448C2×#135—591no—
449C2×#131—591no—
450C2×#131C2×D5911yescharacteristic
451C2×#131C2×D5911yescharacteristic
452C22×M16—591no—
453#525—591no—
454C2×#117—591no—
455#452—591no—
456#452—591no—
457#451—591no—
458#450—591no—
459#449—591no—
460#449—591no—
461#448—591no—
462#447—591no—
463#443—1184no—
464#436—1181no—
465#435—1181no—
466#435—1181no—
467C8×D4—1181no—
468C2×#108—591no—
469C2×#108—591no—
470#424—591no—
471#421—1184no—
472C2×#104—591no—
473C2×#104—591no—
474C2×#104—591no—
475C2×#104—591no—
476C2×#104—591no—
477C2×#104—591no—
478#416—591no—
479#416—591no—
480#408—21no—
481#408—21no—
482#408—591no—
483#408C2×D5911yescharacteristic
484#408C2×D5911yescharacteristic
485#407—21no—
486#407C2×D5911yescharacteristic
487C2×C22⋊C8—21no—
488C2×C22⋊C8—591no—
489C2×C22⋊C8C2×D5911yescharacteristic
490#405—591no—
491C2×#97—591no—
492C2×C4×C8—591no—
493#341—591no—
494#341—591no—
495#339—591no—
496#339—591no—
497#336—591no—
498#336—591no—
499C59#2288911yescharacteristic, complemented, Sylow
500C2×#41—21no—
501C2×#41—21no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41—591no—
507C2×#41C4×D5911yescharacteristic
508C2×#41C4×D5911yescharacteristic
509C2×#41C22×D5911yescharacteristic
510C2×#41C22×D5911yescharacteristic
511C22×Q8C4×D5911yescharacteristic
512C22×D4—21no—
513C22×D4C4×D5911yescharacteristic
514C23×C4—21no—
515C23×C4C22×D5911yescharacteristic
516#135—1182no—
517#135—1182no—
518#135—2361no—
519#135—2361no—
520C2×Q16—591no—
521C2×Q16—591no—
522C2×SD16—591no—
523C2×SD16—591no—
524C2×SD16—591no—
525C2×SD16—591no—
526C2×D8—591no—
527C2×D8—591no—
528#131—22no—
529#131—22no—
530#131—41no—
531#131—41no—
532#131—1182no—
533#131—2361no—
534C2×M16—21no—
535C2×M16—21no—
536C2×M16—591no—
537C2×M16—591no—
538C2×M16—1181no—
539C2×M16—1181no—
540C2×M16—1182no—
541C2×M16—2361no—
542C2×M16C22×D5911yescharacteristic
543C2×M16C22×D5911yescharacteristic
544C22×C8—21no—
545C22×C8—21no—
546C22×C8—591no—
547C22×C8—591no—
548C22×C8—1181no—
549C22×C8—1181no—
550C22×C8C22×D5911yescharacteristic
551C22×C8C22×D5911yescharacteristic
552#123—1181no—
553C22⋊Q8—591no—
554C22⋊Q8—591no—
555#121—591no—
556#121—591no—
557#120—1181no—
558C4×D4—1181no—
559C4×D4—1181no—
560#117—591no—
561#117—1182no—
562#117—2361no—
563C2×C4⋊C4—1181no—
564C2×C22⋊C4—1181no—
565C2×C42—591no—
566C2×C42—591no—
567#108—1182no—
568#108—2361no—
569C4⋊C8—1181no—
570C4⋊C8—1181no—
571#104—594no—
572#104—1182no—
573#104—1182no—
574#104—1182no—
575#104—1182no—
576#104—2361no—
577#103—591no—
578#103—591no—
579#103—591no—
580#103—591no—
581#102—591no—
582#102—591no—
583#102—591no—
584#102—591no—
585C22⋊C8—21no—
586C22⋊C8—21no—
587C22⋊C8—21no—
588C22⋊C8—21no—
589C22⋊C8—21no—
590C22⋊C8—21no—
591C22⋊C8—591no—
592C22⋊C8—591no—
593C22⋊C8—591no—
594C22⋊C8—591no—
595C22⋊C8—1181no—
596C22⋊C8—1181no—
597C22⋊C8C22⋊D5911yescharacteristic
598C22⋊C8C22⋊D5911yescharacteristic
599C22⋊C8C22⋊D5911yescharacteristic
600C22⋊C8C22⋊D5911yescharacteristic
601#97—1181no—
602#97—2361no—
603C4×C8—1182no—
604C4×C8—1181no—
605C24—21no—
606C24#1174568511yescharacteristic
607#41—21no—
608#41—21no—
609#41—22no—
610#41—22no—
611#41—21no—
612#41—21no—
613#41—21no—
614#41—21no—
615#41—42no—
616#41—42no—
617#41—41no—
618#41—41no—
619#41—42no—
620#41—42no—
621#41—1181no—
622#41—1181no—
623#41—1181no—
624#41—1181no—
625#41D4×D5912yes—
626#41#1174568712yes—
627C2×Q8—21no—
628C2×Q8—22no—
629C2×Q8—41no—
630C2×Q8—591no—
631C2×Q8C2×C4×D5911yescharacteristic
632C2×Q8C2×C4×D5911yescharacteristic
633C2×D4—21no—
634C2×D4—22no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—41no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—591no—
643C2×D4—1181no—
644C2×D4—1181no—
645C2×D4—1181no—
646C2×D4C2×C4×D5911yescharacteristic
647C2×D4C2×C4×D5911yescharacteristic
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4—1181no—
660C22×C4—1181no—
661C22×C4—1181no—
662C22×C4C2×C4×D5911yescharacteristic
663C22×C4C2×C4×D5911yescharacteristic
664C22×C4#1174568511yescharacteristic
665C22×C4C2×C22⋊D5911yescharacteristic
666C22×C4C2×C22⋊D5911yescharacteristic
667C22×C4C23×D5911yescharacteristic
668Q16—1182no—
669Q16—2361no—
670SD16—1182no—
671SD16—1182no—
672SD16—2361no—
673SD16—2361no—
674D8—1182no—
675D8—2361no—
676M16—21no—
677M16—21no—
678M16—21no—
679M16—21no—
680M16—42no—
681M16—42no—
682M16—592no—
683M16—1181no—
684M16—1181no—
685M16—1181no—
686M16—2362no—
687M16—2362no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—42no—
695C2×C8—42no—
696C2×C8—591no—
697C2×C8—591no—
698C2×C8—591no—
699C2×C8—591no—
700C2×C8—1181no—
701C2×C8—1181no—
702C2×C8—1181no—
703C2×C8—1181no—
704C2×C8—1181no—
705C2×C8—1181no—
706C2×C8—2362no—
707C2×C8—2362no—
708C2×C8C2×C22⋊D5911yescharacteristic
709C2×C8C2×C22⋊D5911yescharacteristic
710C2×C8C2×C22⋊D5911yescharacteristic
711C2×C8C2×C22⋊D5911yescharacteristic
712C4⋊C4—591no—
713C4⋊C4—591no—
714C4⋊C4—1181no—
715C4⋊C4—1181no—
716C4⋊C4—2362no—
717C22⋊C4—1181no—
718C22⋊C4—1181no—
719C22⋊C4—1181no—
720C22⋊C4—1181no—
721C22⋊C4—1181no—
722C22⋊C4—2362no—
723C42—592no—
724C42—1181no—
725C42—1181no—
726C42—1181no—
727C42—1181no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—41no—
733C23—41no—
734C23—42no—
735C23—42no—
736C23—81no—
737C23—1181no—
738C23C4×C22⋊D5911yescharacteristic
739C23C4×C22⋊D5911yescharacteristic
740C23C2×#1174568511yescharacteristic
741Q8—21no—
742Q8—21no—
743Q8—21no—
744Q8—42no—
745Q8—1181no—
746Q8—1181no—
747Q8(C22⋊D59)⋊C412yes—
748D4—22no—
749D4—22no—
750D4—21no—
751D4—21no—
752D4—21no—
753D4—42no—
754D4—42no—
755D4—42no—
756D4—41no—
757D4—41no—
758D4—1181no—
759D4—1181no—
760D4—4721no—
761D4—2362no—
762D4—2361no—
763D4—2361no—
764D4(C22⋊D59)⋊C412yes—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—1182no—
785C2×C4—1181no—
786C2×C4—1181no—
787C2×C4—1181no—
788C2×C4—2361no—
789C2×C4—2361no—
790C2×C4—2361no—
791C2×C4—2361no—
792C2×C4—2361no—
793C2×C4—2361no—
794C2×C4—2361no—
795C2×C4C4×C22⋊D5911yescharacteristic
796C2×C4C4×C22⋊D5911yescharacteristic
797C2×C4C22×C4×D5911yescharacteristic
798C2×C4C2×D4×D5911yescharacteristic
799C2×C4C22×C22⋊D5911yescharacteristic
800C2×C4C2×#1174568711yescharacteristic
801C2×C4#1427377211yescharacteristic
802C2×C4#1427377211yescharacteristic
803C8—21no—
804C8—21no—
805C8—21no—
806C8—21no—
807C8—41no—
808C8—41no—
809C8—1182no—
810C8—1181no—
811C8—1181no—
812C8—1181no—
813C8—1181no—
814C8—2361no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—22no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—81no—
830C22—81no—
831C22—84no—
832C22—2361no—
833C22—2361no—
834C22—2361no—
835C22C2×C4×C22⋊D5911yescharacteristic
836C22#1683804211yescharacteristic
837C22#1683807811yescharacteristic
838C4—21no—
839C4—21no—
840C4—22no—
841C4—41no—
842C4—4721no—
843C4—2362no—
844C4—2361no—
845C4—2361no—
846C4—2361no—
847C4C2×(C22⋊D59)⋊C411yescharacteristic
848C4#1683787511yescharacteristic
849C4D4×C22⋊D5911yescharacteristic
850C4#1683804611yescharacteristic
851C2—21no—
852C2—21no—
853C2—41no—
854C2—41no—
855C2—42no—
856C2—81no—
857C2—4721no—
858C2#2142707511yescharacteristic
859C2#2143299711yescharacteristic
860C2#2143301111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#2880C2
socleC22×C59C2×C4×D4
prime radical#21433314C2
cosocleC22×C4×C59C24
hypercenter#2880D59
hypocenterC59#22889
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #2880

Complements

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

NH ≅ G/Ntype
2. C2×#16837517C2semidirect
3. #21432817C2semidirect
4. C2×#16837419C2semidirect
5. #21424988C2semidirect
6. #21424803C2semidirect
7. #21424741C2semidirect
8. #21424542C2semidirect
9. #21424426C2semidirect
10. #21424423C2semidirect
11. #21424371C2semidirect
12. #21424300C2semidirect
13. #21423938C2semidirect
14. #21423864C2semidirect
15. C59×#2880C2semidirect
18. C2×#14273733C22semidirect
22. #16837564C4semidirect
23. #16837564C4semidirect
24. #16837558C4semidirect
25. #16837553C4semidirect
26. #16837547C4semidirect
27. #16837547C4semidirect
28. #16837541C4semidirect
29. #16837536C4semidirect
35. C2×#14273662C22semidirect
36. C2×#14273662C22semidirect
37. #16837428C22semidirect
43. C2×#14273653C22semidirect
44. C2×#14273653C22semidirect
47. #16837368C22semidirect
49. #16837357C22semidirect
50. C2×#14273637C22semidirect
51. C2×C8×Dic59C22semidirect
52. #16837166C22semidirect
53. #16837166C22semidirect
54. #16837163C22semidirect
55. #16837163C22semidirect
56. #16837156C22semidirect
57. #16837156C22semidirect
116. #14273654D4semidirect
425. #2880D59semidirect
499. C59#22889semidirect

Maximal subgroups

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

subgroupindex
#214333142
C2×#168375172
#214328172
C2×#168374192
#214249882
#214248032
#214247412
#214245422
#214244262
#214244232
#214243712
#214243002
#214239382
#214238642
C59×#28802
#2288959