Finite Group Databasebeta

← #28606064

Subgroups — #28606064

Order 15104.

888 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21432756C211yesmaximal, characteristic, complemented
2#21432615C211yesmaximal, characteristic
3#21432545C211yesmaximal, characteristic
4#21424804C211yesmaximal, characteristic, complemented
5#21424797C211yesmaximal, characteristic, complemented
6#21424747C211yesmaximal, characteristic, complemented
7#21424747C211yesmaximal, characteristic, complemented
8#21424369C211yesmaximal, characteristic, complemented
9#21424369C211yesmaximal, characteristic, complemented
10#21424196C211yesmaximal, characteristic, complemented
11#21424136C211yesmaximal, characteristic, complemented
12#21423941C211yesmaximal, characteristic, complemented
13#21423934C211yesmaximal, characteristic, complemented
14#21423880C211yesmaximal, characteristic, complemented
15C59×#1789C211yesmaximal, characteristic
16C2×#14273734C2211yescharacteristic
17C2×#14273734C2211yescharacteristic
18C22×#11745664C2211yescharacteristic
19C2×#14273686C2211yescharacteristic
20#16837460—21no—
21#16837460—21no—
22#16837456—21no—
23#16837452—21no—
24C2×#14273662C2211yescharacteristic, complemented
25C2×#14273662C2211yescharacteristic, complemented
26#16837430C2211yescharacteristic, complemented
27#16837430C2211yescharacteristic, complemented
28#16837411C411yescharacteristic, complemented
29#16837411C411yescharacteristic, complemented
30#16837407C411yescharacteristic, complemented
31#16837407C411yescharacteristic, complemented
32#16837403C411yescharacteristic, complemented
33#16837403C411yescharacteristic, complemented
34#16837403C411yescharacteristic, complemented
35#16837403C411yescharacteristic, complemented
36#16837398C2211yescharacteristic
37#16837398C2211yescharacteristic
38#16837398C2211yescharacteristic
39#16837398C2211yescharacteristic
40#16837369—21no—
41#16837369—21no—
42#16837369C2211yescharacteristic
43#16837369C2211yescharacteristic
44#16837366—21no—
45#16837366C2211yescharacteristic
46C2×C22⋊(C59⋊C8)—21no—
47C2×C22⋊(C59⋊C8)C2211yescharacteristic
48#16837360C2211yescharacteristic, complemented
49#16837360C2211yescharacteristic, complemented
50C2×#14273638C2211yescharacteristic, complemented
51C2×C4×C59⋊C8C2211yescharacteristic, complemented
52#16837166C2211yescharacteristic, complemented
53#16837166C2211yescharacteristic, complemented
54#16837162C2211yescharacteristic, complemented
55#16837162C2211yescharacteristic, complemented
56#16837162C2211yescharacteristic, complemented
57#16837162C2211yescharacteristic, complemented
58#16837157C2211yescharacteristic, complemented
59#16837157C2211yescharacteristic, complemented
60C22×#41×C59C2211yescharacteristic
61C2×#104×C59C2211yescharacteristic
62C2×#104×C59C2211yescharacteristic
63C2×#104×C59C2211yescharacteristic
64C2×#104×C59C2211yescharacteristic
65C59×#407C2211yescharacteristic
66C4×C22⋊C4×C59C2211yescharacteristic
67#14273734—22no—
68#14273734—22no—
69#14273734—41no—
70#14273734—41no—
71C2×#11745664—21no—
72C2×#11745664—21no—
73C2×#11745664—41no—
74C2×#11745664—41no—
75C2×#11745664C2×C411yescharacteristic
76C2×#11745664C2×C411yescharacteristic
77C2×#11745664C2×C411yescharacteristic
78C2×#11745664C2×C411yescharacteristic
79C2×#11745664C2311yescharacteristic
80C2×#11745664C2311yescharacteristic
81C22×C59⋊C8—21no—
82C22×C59⋊C8—21no—
83C22×C59⋊C8C2311yescharacteristic
84C22×C59⋊C8C2311yescharacteristic
85C22×C59⋊C8C2311yescharacteristic
86C22×C59⋊C8C2311yescharacteristic
87#14273686—21no—
88#14273686—21no—
89#14273686C2×C411yescharacteristic
90#14273686C2×C411yescharacteristic
91#14273686C2311yescharacteristic
92#14273686C2311yescharacteristic
93C2×C4⋊Dic59C2×C411yescharacteristic
94C2×C4⋊Dic59C2×C411yescharacteristic
95C2×C22⋊Dic59—21no—
96C2×C4×Dic59—21no—
97#14273662—41no—
98#14273662—41no—
99Dic59⋊C8—21no—
100Dic59⋊C8—21no—
101Dic59⋊C8—21no—
102Dic59⋊C8—21no—
103#14273651C2×C411yescharacteristic
104#14273651C2×C411yescharacteristic
105#14273651C2×C411yescharacteristic
106#14273651C2×C411yescharacteristic
107#14273651C2×C411yescharacteristic
108#14273651C2×C411yescharacteristic
109#14273651C2×C411yescharacteristic
110#14273651C2×C411yescharacteristic
111#14273648C2×C411yescharacteristic
112#14273648C2×C411yescharacteristic
113#14273648C2×C411yescharacteristic
114#14273648C2×C411yescharacteristic
115#14273648C2×C411yescharacteristic
116#14273648C2×C411yescharacteristic
117#14273648C2×C411yescharacteristic
118#14273648C2×C411yescharacteristic
119C22⋊(C59⋊C8)—21no—
120C22⋊(C59⋊C8)—21no—
121C22⋊(C59⋊C8)—21no—
122C22⋊(C59⋊C8)—21no—
123C22⋊(C59⋊C8)—21no—
124C22⋊(C59⋊C8)—21no—
125C22⋊(C59⋊C8)D411yescharacteristic
126C22⋊(C59⋊C8)D411yescharacteristic
127C22⋊(C59⋊C8)D411yescharacteristic
128C22⋊(C59⋊C8)D411yescharacteristic
129#14273638—41no—
130#14273637—21no—
131#14273637—21no—
132C4×C59⋊C8—41no—
133C8×Dic59—21no—
134C8×Dic59—21no—
135C2×#41×C59—21no—
136C2×#41×C59—21no—
137C2×#41×C59—22no—
138C2×#41×C59—22no—
139C2×#41×C59—41no—
140C2×#41×C59—41no—
141C2×#41×C59C2×C411yescharacteristic
142C2×#41×C59C2×C411yescharacteristic
143C2×#41×C59C2311yescharacteristic
144C2×#41×C59C2311yescharacteristic
145C22×Q8×C59C2×C411yescharacteristic
146C22×D4×C59—21no—
147C22×D4×C59C2×C411yescharacteristic
148C23×C4×C59—21no—
149C23×C4×C59C2311yescharacteristic
150C2×M16×C59C2311yescharacteristic
151C2×M16×C59C2311yescharacteristic
152C2×C22⋊C4×C59—21no—
153C2×C42×C59C2311yescharacteristic
154C2×C42×C59C2311yescharacteristic
155#104×C59—22no—
156#104×C59—22no—
157#104×C59—41no—
158#104×C59—41no—
159C22⋊C8×C59—21no—
160C22⋊C8×C59—21no—
161#95×C59—21no—
162C24×C59—21no—
163C24×C59#4111yescharacteristic
164#41×C59—21no—
165#41×C59—21no—
166#41×C59—22no—
167#41×C59—22no—
168#41×C59—21no—
169#41×C59—21no—
170#41×C59—21no—
171#41×C59—21no—
172#41×C59—42no—
173#41×C59—42no—
174#41×C59—41no—
175#41×C59—41no—
176#41×C59—42no—
177#41×C59—42no—
178#41×C59#4112yes—
179#41×C59#4112yes—
180C2×Q8×C59—21no—
181C2×Q8×C59—22no—
182C2×Q8×C59—41no—
183C2×Q8×C59C22×C411yescharacteristic
184C2×Q8×C59C22×C411yescharacteristic
185C2×D4×C59—21no—
186C2×D4×C59—22no—
187C2×D4×C59—21no—
188C2×D4×C59—21no—
189C2×D4×C59—21no—
190C2×D4×C59—21no—
191C2×D4×C59—41no—
192C2×D4×C59—42no—
193C2×D4×C59—42no—
194C2×D4×C59C22×C411yescharacteristic
195C2×D4×C59C22×C411yescharacteristic
196C22×C4×C59—21no—
197C22×C4×C59—21no—
198C22×C4×C59—21no—
199C22×C4×C59—21no—
200C22×C4×C59—21no—
201C22×C4×C59—21no—
202C22×C4×C59—21no—
203C22×C4×C59—21no—
204C22×C4×C59—21no—
205C22×C4×C59—21no—
206C22×C4×C59—21no—
207C22×C4×C59—42no—
208C22×C4×C59—42no—
209C22×C4×C59C22×C411yescharacteristic
210C22×C4×C59C22×C411yescharacteristic
211C22×C4×C59C2×D411yescharacteristic
212C22×C4×C59C2×D411yescharacteristic
213C22×C4×C59#4111yescharacteristic
214C22×C4×C59C2411yescharacteristic
215C22×Dic59—21no—
216C22×Dic59—21no—
217M16×C59—21no—
218M16×C59—21no—
219M16×C59—21no—
220M16×C59—21no—
221C2×C8×C59—21no—
222C2×C8×C59—21no—
223C22⋊C4×C59—42no—
224C42×C59—21no—
225C42×C59—21no—
226C42×C59—21no—
227C42×C59—21no—
228C22⋊Dic59—21no—
229C22⋊Dic59—21no—
230C22⋊Dic59—21no—
231C22⋊Dic59—21no—
232C4⋊Dic59—21no—
233C4⋊Dic59—21no—
234C4⋊Dic59C22×C411yescharacteristic
235C4⋊Dic59C22×C411yescharacteristic
236C4⋊Dic59C22×C411yescharacteristic
237C4⋊Dic59C22×C411yescharacteristic
238C4×Dic59—21no—
239C4×Dic59—21no—
240C4×Dic59—21no—
241C4×Dic59—21no—
242#11745664—21no—
243#11745664—21no—
244#11745664—21no—
245#11745664—21no—
246#11745664—41no—
247#11745664—41no—
248#11745664—41no—
249#11745664—41no—
250#11745664—42no—
251#11745664—42no—
252C2×C59⋊C8—21no—
253C2×C59⋊C8—21no—
254C2×C59⋊C8—21no—
255C2×C59⋊C8—21no—
256C2×C59⋊C8—21no—
257C2×C59⋊C8—21no—
258C2×C59⋊C8—21no—
259C2×C59⋊C8—21no—
260C2×C59⋊C8—21no—
261C2×C59⋊C8—21no—
262C2×C59⋊C8—42no—
263C2×C59⋊C8—42no—
264C2×C59⋊C8C22×C411yescharacteristic
265C2×C59⋊C8C22×C411yescharacteristic
266C2×C59⋊C8C22×C411yescharacteristic
267C2×C59⋊C8C22×C411yescharacteristic
268C2×C59⋊C8C2×D411yescharacteristic
269C2×C59⋊C8C2×D411yescharacteristic
270C2×C59⋊C8C2×D411yescharacteristic
271C2×C59⋊C8C2×D411yescharacteristic
272C23×C59—21no—
273C23×C59—21no—
274C23×C59—21no—
275C23×C59—21no—
276C23×C59—41no—
277C23×C59—41no—
278C23×C59—42no—
279C23×C59—42no—
280C23×C59—81no—
281C23×C59C4×D411yescharacteristic
282C23×C59C4×D411yescharacteristic
283C23×C59C2×#4111yescharacteristic
284Q8×C59—21no—
285Q8×C59—21no—
286Q8×C59—21no—
287Q8×C59—42no—
288Q8×C59#11712yes—
289D4×C59—22no—
290D4×C59—22no—
291D4×C59—21no—
292D4×C59—21no—
293D4×C59—21no—
294D4×C59—42no—
295D4×C59—42no—
296D4×C59—42no—
297D4×C59—41no—
298D4×C59—41no—
299D4×C59#11712yes—
300C2×C4×C59—21no—
301C2×C4×C59—21no—
302C2×C4×C59—21no—
303C2×C4×C59—21no—
304C2×C4×C59—21no—
305C2×C4×C59—21no—
306C2×C4×C59—21no—
307C2×C4×C59—22no—
308C2×C4×C59—22no—
309C2×C4×C59—21no—
310C2×C4×C59—21no—
311C2×C4×C59—21no—
312C2×C4×C59—21no—
313C2×C4×C59—22no—
314C2×C4×C59—21no—
315C2×C4×C59—42no—
316C2×C4×C59—42no—
317C2×C4×C59—42no—
318C2×C4×C59—41no—
319C2×C4×C59—41no—
320C2×C4×C59—41no—
321C2×C4×C59—41no—
322C2×C4×C59—41no—
323C2×C4×C59—41no—
324C2×C4×C59—41no—
325C2×C4×C59C4×D411yescharacteristic
326C2×C4×C59C4×D411yescharacteristic
327C2×C4×C59C23×C411yescharacteristic
328C2×C4×C59C22×D411yescharacteristic
329C2×C4×C59C2×#4111yescharacteristic
330C2×C4×C59C2×#4111yescharacteristic
331C2×C4×C59H(5,𝔽2)11yescharacteristic
332C2×C4×C59H(5,𝔽2)11yescharacteristic
333C2×Dic59—21no—
334C2×Dic59—21no—
335C2×Dic59—21no—
336C2×Dic59—21no—
337C2×Dic59—42no—
338C2×Dic59—81no—
339C8×C59—41no—
340C8×C59—41no—
341C59⋊C8—21no—
342C59⋊C8—21no—
343C59⋊C8—21no—
344C59⋊C8—21no—
345C59⋊C8—21no—
346C59⋊C8—21no—
347C59⋊C8—21no—
348C59⋊C8—21no—
349C59⋊C8—41no—
350C59⋊C8—41no—
351#22588—591nomaximal, Sylow
352C22×C59—21no—
353C22×C59—21no—
354C22×C59—21no—
355C22×C59—21no—
356C22×C59—22no—
357C22×C59—21no—
358C22×C59—21no—
359C22×C59—21no—
360C22×C59—21no—
361C22×C59—41no—
362C22×C59—41no—
363C22×C59—41no—
364C22×C59—41no—
365C22×C59—41no—
366C22×C59—81no—
367C22×C59—81no—
368C22×C59—84no—
369C22×C59C2×C4×D411yescharacteristic
370C22×C59#55111yescharacteristic
371C22×C59#55111yescharacteristic
372C4×C59—21no—
373C4×C59—21no—
374C4×C59—22no—
375C4×C59—42no—
376C4×C59—41no—
377C4×C59—81no—
378C4×C59C2×#11711yescharacteristic
379C4×C59#51811yescharacteristic
380C4×C59#54611yescharacteristic
381C4×C59#54611yescharacteristic
382Dic59—41no—
383Dic59—41no—
384Dic59—41no—
385Dic59—41no—
386#2924—591no—
387#2896—591no—
388#2880—591no—
389#1938—591no—
390#1937—591no—
391#1929—591no—
392#1929—591no—
393#1866—591no—
394#1866—591no—
395#1826—591no—
396#1811—591no—
397#1789D5911yescharacteristic
398#1765—591no—
399#1764—591no—
400#1753—591no—
401C2×C59—21no—
402C2×C59—21no—
403C2×C59—41no—
404C2×C59—41no—
405C2×C59—42no—
406C2×C59—81no—
407C2×C59#234211yescharacteristic
408C2×C59#295511yescharacteristic
409C2×C59#295611yescharacteristic
410C22×#41C2×D5911yescharacteristic
411C2×#131—591no—
412C2×#131—591no—
413C22×M16—591no—
414C2×#117—591no—
415#433—1181no—
416#433—1181no—
417#432—1181no—
418#431—1181no—
419C2×#108—591no—
420C2×#108—591no—
421#424—591no—
422#424—591no—
423C2×#104C2×D5911yescharacteristic
424C2×#104C2×D5911yescharacteristic
425C2×#104C2×D5911yescharacteristic
426C2×#104C2×D5911yescharacteristic
427#419—591no—
428#419—591no—
429#418—591no—
430#418—591no—
431#417—591no—
432#417—591no—
433#417—591no—
434#417—591no—
435#416—591no—
436#416—591no—
437#416—591no—
438#416—591no—
439#408—591no—
440#408—591no—
441#408—1181no—
442#408—1181no—
443#407—591no—
444#407—1181no—
445#407C2×D5911yescharacteristic
446C2×C22⋊C8—591no—
447C2×C22⋊C8—1181no—
448#405—591no—
449#405—591no—
450C2×#97—591no—
451C2×C4×C8—591no—
452C4×C22⋊C4C2×D5911yescharacteristic
453#341—591no—
454#341—591no—
455#339—591no—
456#339—591no—
457#339—591no—
458#339—591no—
459#336—591no—
460#336—591no—
461C59#2258811yescharacteristic, complemented, Sylow
462C2×#41—21no—
463C2×#41—21no—
464C2×#41—22no—
465C2×#41—22no—
466C2×#41—41no—
467C2×#41—41no—
468C2×#41C4×D5911yescharacteristic
469C2×#41C4×D5911yescharacteristic
470C2×#41C22×D5911yescharacteristic
471C2×#41C22×D5911yescharacteristic
472C22×Q8C4×D5911yescharacteristic
473C22×D4—21no—
474C22×D4C4×D5911yescharacteristic
475C23×C4—21no—
476C23×C4C22×D5911yescharacteristic
477#131—1182no—
478#131—1182no—
479#131—2361no—
480#131—2361no—
481C2×M16—591no—
482C2×M16—591no—
483C2×M16—591no—
484C2×M16—591no—
485C2×M16—591no—
486C2×M16—591no—
487C2×M16—1181no—
488C2×M16—1181no—
489C2×M16—2361no—
490C2×M16—2361no—
491C2×M16C22×D5911yescharacteristic
492C2×M16C22×D5911yescharacteristic
493C22×C8—591no—
494C22×C8—591no—
495C22×C8—591no—
496C22×C8—591no—
497C22×C8—1181no—
498C22×C8—1181no—
499#117—591no—
500#117—591no—
501#117—591no—
502#117—591no—
503#117—1181no—
504#117—1181no—
505C2×C4⋊C4—591no—
506C2×C4⋊C4—591no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—1181no—
509C2×C42—1181no—
510C2×C42C22×D5911yescharacteristic
511C2×C42C22×D5911yescharacteristic
512#108—2361no—
513#108—2361no—
514C4⋊C8—1181no—
515C4⋊C8—1181no—
516C4⋊C8—1181no—
517C4⋊C8—1181no—
518#104—22no—
519#104—22no—
520#104—41no—
521#104—41no—
522#103—591no—
523#103—591no—
524#103—591no—
525#103—591no—
526#103—591no—
527#103—591no—
528#103—591no—
529#103—591no—
530#102—591no—
531#102—591no—
532#102—591no—
533#102—591no—
534#102—591no—
535#102—591no—
536#102—591no—
537#102—591no—
538C22⋊C8—21no—
539C22⋊C8—21no—
540C22⋊C8—591no—
541C22⋊C8—591no—
542C22⋊C8—591no—
543C22⋊C8—591no—
544C22⋊C8—1181no—
545C22⋊C8—1181no—
546C22⋊C8—1181no—
547C22⋊C8—1181no—
548C22⋊C8—1181no—
549C22⋊C8—1181no—
550#97—1181no—
551#97—1181no—
552#97—2361no—
553C4×C8—1181no—
554C4×C8—1181no—
555C4×C8—2361no—
556#95—21no—
557C24—21no—
558C24#1174568711yescharacteristic
559#41—21no—
560#41—21no—
561#41—22no—
562#41—22no—
563#41—21no—
564#41—21no—
565#41—21no—
566#41—21no—
567#41—42no—
568#41—42no—
569#41—41no—
570#41—41no—
571#41—42no—
572#41—42no—
573#41#1174568712yes—
574#41#1174568712yes—
575C2×Q8—21no—
576C2×Q8—22no—
577C2×Q8—41no—
578C2×Q8C2×C4×D5911yescharacteristic
579C2×Q8C2×C4×D5911yescharacteristic
580C2×D4—21no—
581C2×D4—22no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—41no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4C2×C4×D5911yescharacteristic
590C2×D4C2×C4×D5911yescharacteristic
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—1181no—
605C22×C4—1181no—
606C22×C4C2×C4×D5911yescharacteristic
607C22×C4C2×C4×D5911yescharacteristic
608C22×C4D4×D5911yescharacteristic
609C22×C4D4×D5911yescharacteristic
610C22×C4#1174568711yescharacteristic
611C22×C4C23×D5911yescharacteristic
612M16—21no—
613M16—21no—
614M16—21no—
615M16—21no—
616M16—1181no—
617M16—1181no—
618M16—1181no—
619M16—1181no—
620M16—2361no—
621M16—2361no—
622M16—2361no—
623M16—2361no—
624M16—2362no—
625M16—2362no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—591no—
629C2×C8—591no—
630C2×C8—591no—
631C2×C8—591no—
632C2×C8—591no—
633C2×C8—591no—
634C2×C8—591no—
635C2×C8—591no—
636C2×C8—1181no—
637C2×C8—1181no—
638C2×C8—1181no—
639C2×C8—1181no—
640C2×C8—1181no—
641C2×C8—1181no—
642C2×C8—1181no—
643C2×C8—1181no—
644C2×C8—1181no—
645C2×C8—1181no—
646C2×C8—2362no—
647C2×C8—2362no—
648C4⋊C4—591no—
649C4⋊C4—591no—
650C4⋊C4—591no—
651C4⋊C4—591no—
652C4⋊C4—1181no—
653C4⋊C4—1181no—
654C22⋊C4—42no—
655C22⋊C4—1181no—
656C22⋊C4—1181no—
657C22⋊C4—1181no—
658C22⋊C4—1181no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42—1181no—
664C42—1181no—
665C42—1181no—
666C42—1181no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—41no—
672C23—41no—
673C23—42no—
674C23—42no—
675C23—81no—
676C23(C22⋊D59)⋊C411yescharacteristic
677C23(C22⋊D59)⋊C411yescharacteristic
678C23C2×#1174568711yescharacteristic
679Q8—21no—
680Q8—21no—
681Q8—21no—
682Q8—42no—
683Q8#1427368312yes—
684D4—22no—
685D4—22no—
686D4—21no—
687D4—21no—
688D4—21no—
689D4—42no—
690D4—42no—
691D4—42no—
692D4—41no—
693D4—41no—
694D4#1427368312yes—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—22no—
709C2×C4—21no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—1181no—
721C2×C4—1181no—
722C2×C4—1181no—
723C2×C4—1181no—
724C2×C4—4721no—
725C2×C4—2362no—
726C2×C4(C22⋊D59)⋊C411yescharacteristic
727C2×C4(C22⋊D59)⋊C411yescharacteristic
728C2×C4C22×C4×D5911yescharacteristic
729C2×C4C2×D4×D5911yescharacteristic
730C2×C4C2×#1174568711yescharacteristic
731C2×C4C2×#1174568711yescharacteristic
732C2×C4#1427377211yescharacteristic
733C2×C4#1427377211yescharacteristic
734C8—41no—
735C8—41no—
736C8—1181no—
737C8—1181no—
738C8—1181no—
739C8—1181no—
740C8—1181no—
741C8—1181no—
742C8—1181no—
743C8—1181no—
744C8—2361no—
745C8—2361no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—22no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—21no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—81no—
761C22—81no—
762C22—84no—
763C22C2×(C22⋊D59)⋊C411yescharacteristic
764C22#1683808311yescharacteristic
765C22#1683808311yescharacteristic
766C4—21no—
767C4—21no—
768C4—22no—
769C4—42no—
770C4—41no—
771C4—81no—
772C4—2361no—
773C4—2361no—
774C4—2361no—
775C4—2361no—
776C4C2×#1427368311yescharacteristic
777C4#1683787511yescharacteristic
778C4#1683803911yescharacteristic
779C4#1683803911yescharacteristic
780C2—21no—
781C2—21no—
782C2—41no—
783C2—41no—
784C2—42no—
785C2—81no—
786C2#2142694711yescharacteristic
787C2#2143299511yescharacteristic
788C2#2143300211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#1789C2
socleC22×C59C2×C4×D4
prime radicalC22×#41×C59C22
cosocleC22×C4×C59C24
hypercenter#1789D59
hypocenterC59#22588
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1789

Complements

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

NH ≅ G/Ntype
1. #21432756C2semidirect
4. #21424804C2semidirect
5. #21424797C2semidirect
6. #21424747C2semidirect
7. #21424747C2semidirect
8. #21424369C2semidirect
9. #21424369C2semidirect
10. #21424196C2semidirect
11. #21424136C2semidirect
12. #21423941C2semidirect
13. #21423934C2semidirect
14. #21423880C2semidirect
24. C2×#14273662C22semidirect
25. C2×#14273662C22semidirect
26. #16837430C22semidirect
27. #16837430C22semidirect
28. #16837411C4semidirect
29. #16837411C4semidirect
30. #16837407C4semidirect
31. #16837407C4semidirect
32. #16837403C4semidirect
33. #16837403C4semidirect
34. #16837403C4semidirect
35. #16837403C4semidirect
48. #16837360C22semidirect
49. #16837360C22semidirect
50. C2×#14273638C22semidirect
51. C2×C4×C59⋊C8C22semidirect
52. #16837166C22semidirect
53. #16837166C22semidirect
54. #16837162C22semidirect
55. #16837162C22semidirect
56. #16837162C22semidirect
57. #16837162C22semidirect
58. #16837157C22semidirect
59. #16837157C22semidirect
461. C59#22588semidirect

Maximal subgroups

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

subgroupindex
#214327562
#214326152
#214325452
#214248042
#214247972
#214247472
#214243692
#214241962
#214241362
#214239412
#214239342
#214238802
C59×#17892
#2258859