Finite Group Databasebeta

← #28608946

Subgroups — #28608946

Order 15104.

1302 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837553C211yesmaximal, characteristic
2C2×#16837499C211yesmaximal, characteristic, complemented
3#21427101C211yesmaximal, characteristic, complemented
4D4×C22⋊Dic59C211yesmaximal, characteristic
5#21424978C211yesmaximal, characteristic, complemented
6#21424790C211yesmaximal, characteristic, complemented
7#21424719C211yesmaximal, characteristic, complemented
8#21424519C211yesmaximal, characteristic, complemented
9#21424448C211yesmaximal, characteristic, complemented
10#21424428C211yesmaximal, characteristic, complemented
11#21424341C211yesmaximal, characteristic, complemented
12#21424284C211yesmaximal, characteristic, complemented
13#21423923C211yesmaximal, characteristic, complemented
14#21423872C211yesmaximal, characteristic, complemented
15C22×#102×C59C211yesmaximal, characteristic
16C22×#11745670C2211yescharacteristic
17C22×#11745670C2211yescharacteristic
18C2×#14273706C2211yescharacteristic
19C2×#14273692C2211yescharacteristic, complemented
20C2×D4×Dic59C2211yescharacteristic
21C2×D4×Dic59C2211yescharacteristic
22C22×C22⋊Dic59—21no—
23#16837553C418yescomplemented
24#16837499—24no—
25C2×#14273660C2211yescharacteristic, complemented
26C2×#14273660C2211yescharacteristic, complemented
27C2×#14273652C2211yescharacteristic, complemented
28C2×#14273652C2211yescharacteristic, complemented
29C2×#14273648C2211yescharacteristic
30C2×#14273648C2211yescharacteristic
31C2×C22⋊(C59⋊C8)C2211yescharacteristic
32C2×#14273637C2211yescharacteristic, complemented
33C2×#14273637C2211yescharacteristic, complemented
34#16837307C2211yescharacteristic, complemented
35#16837305C2211yescharacteristic
36#16837305C2211yescharacteristic
37#16837298C2211yescharacteristic, complemented
38#16837297—21no—
39#16837283—21no—
40#16837282—21no—
41#16837282—21no—
42#16837275—21no—
43#16837262C2211yescharacteristic
44#16837258—21no—
45C4⋊C4×Dic59C2211yescharacteristic, complemented
46C4×C22⋊Dic59—21no—
47C4×C22⋊Dic59C2211yescharacteristic
48#16837165C2211yescharacteristic, complemented
49#16837165C2211yescharacteristic, complemented
50#16837164C2211yescharacteristic, complemented
51#16837164C2211yescharacteristic, complemented
52#16837156C2211yescharacteristic, complemented
53#16837156C2211yescharacteristic, complemented
54C23×D4×C59C2211yescharacteristic
55C23×C8×C59C2211yescharacteristic
56C22×C4⋊C4×C59C2211yescharacteristic
57C2×#102×C59—24no—
58C2×#102×C59C2211yescharacteristic
59C2×#102×C59C2211yescharacteristic
60C2×#102×C59C2211yescharacteristic
61C2×#102×C59C2211yescharacteristic
62C22×Dic118C2311yescharacteristic
63C23×Dic59—21no—
64C23×Dic59—21no—
65C2×#11745670—22no—
66C2×#11745670—22no—
67C2×#11745670—41no—
68C2×#11745670—41no—
69C2×#11745670C2×C414yescomplemented
70C2×#11745670C2×C414yescomplemented
71C22×C59⋊C8C2311yescharacteristic
72C22×C59⋊C8C2311yescharacteristic
73#14273706—22no—
74#14273706C2×C414yescomplemented
75#14273692—22no—
76#14273692—41no—
77D4×Dic59—22no—
78D4×Dic59—22no—
79D4×Dic59—41no—
80D4×Dic59—41no—
81C2×C4⋊Dic59C2311yescharacteristic
82C2×C4⋊Dic59C2311yescharacteristic
83C2×C4⋊Dic59C2311yescharacteristic
84C2×Dic59⋊C4—21no—
85C2×Dic59⋊C4—21no—
86C2×Dic59⋊C4—21no—
87C2×C22⋊Dic59—21no—
88C2×C22⋊Dic59—21no—
89C2×C22⋊Dic59—21no—
90C2×C22⋊Dic59—21no—
91C2×C22⋊Dic59—21no—
92C2×C22⋊Dic59—21no—
93C2×C22⋊Dic59—21no—
94C2×C22⋊Dic59—21no—
95C2×C22⋊Dic59—44no—
96C2×C22⋊Dic59D411yescharacteristic
97C2×C22⋊Dic59D411yescharacteristic
98C2×C4×Dic59—21no—
99C2×C4×Dic59—21no—
100C2×C4×Dic59C2311yescharacteristic
101C2×C4×Dic59C2311yescharacteristic
102#14273660—22no—
103#14273660—41no—
104#14273652—22no—
105#14273652—41no—
106#14273648C2×C414yescomplemented
107#14273648C2×C414yescomplemented
108C22⋊(C59⋊C8)C2×C414yescomplemented
109#14273637—22no—
110#14273637—41no—
111C59⋊#95—21no—
112C59⋊#95—21no—
113C59⋊#95—21no—
114C59⋊#95—21no—
115C59⋊#95—21no—
116C59⋊#95D411yescharacteristic
117C59⋊#95D411yescharacteristic
118C25×C59—21no—
119C22×D4×C59—22no—
120C22×D4×C59—22no—
121C22×D4×C59—21no—
122C22×D4×C59—22no—
123C22×D4×C59—41no—
124C22×D4×C59—41no—
125C22×D4×C59C2×C414yes—
126C22×D4×C59C2311yescharacteristic
127C22×D4×C59C2311yescharacteristic
128C23×C4×C59—21no—
129C23×C4×C59C2311yescharacteristic
130C22×C8×C59—22no—
131C22×C8×C59—22no—
132C22×C8×C59—41no—
133C22×C8×C59C2311yescharacteristic
134C22×C8×C59C2311yescharacteristic
135C2×C4⋊C4×C59—22no—
136C2×C4⋊C4×C59—21no—
137C2×C4⋊C4×C59—41no—
138C2×C4⋊C4×C59C2311yescharacteristic
139C2×C4⋊C4×C59C2311yescharacteristic
140#102×C59—22no—
141#102×C59—22no—
142#102×C59—22no—
143#102×C59D414yes—
144C24×C59—21no—
145C24×C59—21no—
146C24×C59—24no—
147C24×C59—42no—
148C24×C59—42no—
149C24×C59—42no—
150C24×C59—42no—
151C24×C59—81no—
152C24×C59—81no—
153C24×C59C2×D411yescharacteristic
154C2×D4×C59—28no—
155C2×D4×C59—24no—
156C2×D4×C59—21no—
157C2×D4×C59—21no—
158C2×D4×C59—21no—
159C2×D4×C59—21no—
160C2×D4×C59—21no—
161C2×D4×C59—21no—
162C2×D4×C59—21no—
163C2×D4×C59—21no—
164C2×D4×C59—44no—
165C2×D4×C59—44no—
166C2×D4×C59—44no—
167C2×D4×C59—42no—
168C2×D4×C59—42no—
169C2×D4×C59C22×C412yes—
170C2×D4×C59C22×C412yes—
171C2×D4×C59C2×D412yes—
172C2×D4×C59#4112yes—
173C22×C4×C59—21no—
174C22×C4×C59—21no—
175C22×C4×C59—21no—
176C22×C4×C59—21no—
177C22×C4×C59—21no—
178C22×C4×C59—21no—
179C22×C4×C59—42no—
180C22×C4×C59—42no—
181C22×C4×C59—81no—
182C22×C4×C59C22×C412yes—
183C22×C4×C59C2×D411yescharacteristic
184C22×C4×C59#4112yes—
185C22×C4×C59C2411yescharacteristic
186C22×Dic59—21no—
187C22×Dic59—21no—
188C22×Dic59—21no—
189C22×Dic59—21no—
190C22×Dic59—42no—
191C22×Dic59—42no—
192C22×Dic59—42no—
193C22×Dic59—42no—
194C22×Dic59—81no—
195C22×Dic59—81no—
196C22×Dic59C2×D411yescharacteristic
197C22×Dic59C2×D411yescharacteristic
198C22×Dic59C2×D411yescharacteristic
199C22×Dic59C2×D411yescharacteristic
200C2×Dic118—21no—
201C2×Dic118—21no—
202C2×Dic118—21no—
203C2×Dic118—21no—
204C2×Dic118—21no—
205C2×Dic118C22×C412yes—
206C2×C8×C59—21no—
207C2×C8×C59—21no—
208C2×C8×C59—21no—
209C2×C8×C59—21no—
210C2×C8×C59—21no—
211C2×C8×C59—44no—
212C2×C8×C59C2×D412yes—
213C4⋊C4×C59—21no—
214C4⋊C4×C59—21no—
215C4⋊C4×C59—21no—
216C4⋊C4×C59—42no—
217C4⋊C4×C59C2×D412yes—
218C22⋊Dic59—24no—
219C22⋊Dic59—22no—
220C22⋊Dic59—22no—
221C22⋊Dic59—42no—
222C22⋊Dic59—42no—
223C22⋊Dic59—42no—
224C22⋊Dic59—42no—
225C22⋊Dic59—42no—
226C22⋊Dic59—81no—
227C22⋊Dic59—81no—
228#11745670—28no—
229#11745670—44no—
230C4⋊Dic59—21no—
231C4⋊Dic59—21no—
232C4⋊Dic59—21no—
233C4⋊Dic59—21no—
234C4⋊Dic59—21no—
235C4⋊Dic59C22×C412yes—
236Dic59⋊C4—24no—
237Dic59⋊C4—42no—
238Dic59⋊C4—81no—
239C4×Dic59—21no—
240C4×Dic59—21no—
241C4×Dic59—21no—
242C4×Dic59—21no—
243C4×Dic59—42no—
244C4×Dic59—81no—
245C2×C59⋊C8—21no—
246C2×C59⋊C8—21no—
247C2×C59⋊C8—21no—
248C2×C59⋊C8—21no—
249C2×C59⋊C8C22×C412yes—
250C2×C59⋊C8C22×C412yes—
251C23×C59—21no—
252C23×C59—21no—
253C23×C59—21no—
254C23×C59—21no—
255C23×C59—22no—
256C23×C59—22no—
257C23×C59—22no—
258C23×C59—22no—
259C23×C59—48no—
260C23×C59—41no—
261C23×C59—41no—
262C23×C59—41no—
263C23×C59—41no—
264C23×C59—41no—
265C23×C59—41no—
266C23×C59—41no—
267C23×C59—41no—
268C23×C59—41no—
269C23×C59—41no—
270C23×C59—48no—
271C23×C59—84no—
272C23×C59—84no—
273C23×C59—84no—
274C23×C59—84no—
275C23×C59—84no—
276C23×C59C4×D412yes—
277C23×C59AGL(1,ℤ/8)12yes—
278C23×C59#13712yes—
279C23×C59C22×D411yescharacteristic
280D4×C59—22no—
281D4×C59—22no—
282D4×C59—22no—
283D4×C59—22no—
284D4×C59—22no—
285D4×C59—48no—
286D4×C59—41no—
287D4×C59—41no—
288D4×C59C4×D414yes—
289C2×C4×C59—21no—
290C2×C4×C59—21no—
291C2×C4×C59—22no—
292C2×C4×C59—22no—
293C2×C4×C59—22no—
294C2×C4×C59—22no—
295C2×C4×C59—22no—
296C2×C4×C59—41no—
297C2×C4×C59—41no—
298C2×C4×C59—41no—
299C2×C4×C59—41no—
300C2×C4×C59—41no—
301C2×C4×C59—84no—
302C2×C4×C59C4×D412yes—
303C2×C4×C59C23×C411yescharacteristic
304C2×C4×C59C22×D411yescharacteristic
305C2×C4×C59C2×#4111yescharacteristic
306C2×C4×C59C2×#4111yescharacteristic
307C2×C4×C59H(5,𝔽2)11yescharacteristic
308C2×C4×C59H(5,𝔽2)11yescharacteristic
309C2×Dic59—22no—
310C2×Dic59—22no—
311C2×Dic59—21no—
312C2×Dic59—21no—
313C2×Dic59—21no—
314C2×Dic59—21no—
315C2×Dic59—21no—
316C2×Dic59—21no—
317C2×Dic59—21no—
318C2×Dic59—21no—
319C2×Dic59—21no—
320C2×Dic59—21no—
321C2×Dic59—21no—
322C2×Dic59—21no—
323C2×Dic59—41no—
324C2×Dic59—41no—
325C2×Dic59—41no—
326C2×Dic59—41no—
327C2×Dic59—41no—
328C2×Dic59—41no—
329C2×Dic59—41no—
330C2×Dic59—41no—
331C2×Dic59—41no—
332C2×Dic59—41no—
333C2×Dic59—84no—
334C2×Dic59—84no—
335Dic118—22no—
336Dic118—22no—
337Dic118—41no—
338Dic118—41no—
339C8×C59—22no—
340C8×C59—41no—
341C59⋊C8—22no—
342C59⋊C8—22no—
343#22854—591nomaximal, Sylow
344C22×C59—22no—
345C22×C59—22no—
346C22×C59—22no—
347C22×C59—22no—
348C22×C59—22no—
349C22×C59—22no—
350C22×C59—24no—
351C22×C59—42no—
352C22×C59—42no—
353C22×C59—42no—
354C22×C59—42no—
355C22×C59—42no—
356C22×C59—42no—
357C22×C59—42no—
358C22×C59—42no—
359C22×C59—42no—
360C22×C59—816no—
361C22×C59—81no—
362C22×C59—81no—
363C22×C59—81no—
364C22×C59—81no—
365C22×C59#44014yescomplemented
366C22×C59C2×C4×D411yescharacteristic
367C22×C59D4211yescharacteristic
368C22×C59#54611yescharacteristic
369C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
370C22×C59C2×#13711yescharacteristic
371C22×C59#57611yescharacteristic
372C22×C59#57711yescharacteristic
373C4×C59—22no—
374C4×C59—42no—
375C4×C59—81no—
376C4×C59C2×C4×D411yescharacteristic
377C4×C59#51811yescharacteristic
378C4×C59#54611yescharacteristic
379C4×C59#55111yescharacteristic
380Dic59—42no—
381Dic59—42no—
382Dic59—41no—
383Dic59—41no—
384Dic59—41no—
385Dic59—41no—
386Dic59—81no—
387Dic59—81no—
388C2×#450—591no—
389C2×#440—591no—
390C22×#102D5911yescharacteristic
391#2360—591no—
392D4×C22⋊C4—591no—
393#1973—591no—
394#1936—591no—
395#1925—591no—
396#1892—591no—
397#1880—591no—
398#1877—591no—
399#1862—591no—
400#1852—591no—
401#1762—591no—
402#1752—591no—
403C2×C59—24no—
404C2×C59—44no—
405C2×C59—82no—
406C2×C59#235811yescharacteristic
407C2×C59C2×#44011yescharacteristic
408C2×C59#294611yescharacteristic
409C2×C59#326411yescharacteristic
410C2×C59#326611yescharacteristic
411C2×C59#331011yescharacteristic
412C2×C59#331411yescharacteristic
413C23×D4C2×D5911yescharacteristic
414C22×SD16—591no—
415C22×SD16—591no—
416C23×C8C2×D5911yescharacteristic
417C2×C22⋊Q8—591no—
418C2×C4×Q8—591no—
419C2×C4×D4—591no—
420C2×C4×D4—591no—
421C22×C4⋊C4C2×D5911yescharacteristic
422C22×C22⋊C4—1181no—
423#450—598no—
424#440—1184no—
425C2×#107—591no—
426C2×#107—591no—
427C2×#103—591no—
428C2×#103—591no—
429C2×#102—24no—
430C2×#102—591no—
431C2×#102—591no—
432C2×#102C2×D5911yescharacteristic
433C2×#102C2×D5911yescharacteristic
434C2×#102C2×D5911yescharacteristic
435C2×#102C2×D5911yescharacteristic
436C2×C22⋊C8—591no—
437C2×#97—591no—
438C2×#97—591no—
439#391—591no—
440#390—591no—
441#390—591no—
442#389—591no—
443#389—1181no—
444#387—1181no—
445#386—1181no—
446#386—1181no—
447#385—1181no—
448#380—591no—
449#379—1181no—
450C4×C4⋊C4—591no—
451C4×C22⋊C4—591no—
452C4×C22⋊C4—1181no—
453#340—591no—
454#340—591no—
455#340—591no—
456#340—591no—
457#336—591no—
458#336—591no—
459C59#2285411yescharacteristic, complemented, Sylow
460C25—21no—
461C22×Q8—591no—
462C22×D4—22no—
463C22×D4—22no—
464C22×D4—21no—
465C22×D4—22no—
466C22×D4—41no—
467C22×D4—41no—
468C22×D4C4×D5914yes—
469C22×D4C22×D5911yescharacteristic
470C22×D4C22×D5911yescharacteristic
471C23×C4—21no—
472C23×C4—1181no—
473C23×C4—1181no—
474C23×C4C22×D5911yescharacteristic
475C2×SD16—594no—
476C2×SD16—594no—
477C2×SD16—1182no—
478C2×SD16—1182no—
479C2×SD16—2361no—
480C2×SD16—2361no—
481C22×C8—22no—
482C22×C8—22no—
483C22×C8—41no—
484C22×C8—591no—
485C22×C8—591no—
486C22×C8C22×D5911yescharacteristic
487C22×C8C22×D5911yescharacteristic
488C22⋊Q8—594no—
489C22⋊Q8—1182no—
490C4×Q8—1182no—
491C4×Q8—2361no—
492C4×D4—1182no—
493C4×D4—1182no—
494C4×D4—2361no—
495C4×D4—2361no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—41no—
499C2×C4⋊C4—591no—
500C2×C4⋊C4—591no—
501C2×C4⋊C4—591no—
502C2×C4⋊C4—1181no—
503C2×C4⋊C4—1181no—
504C2×C4⋊C4—1181no—
505C2×C4⋊C4C22×D5911yescharacteristic
506C2×C4⋊C4C22×D5911yescharacteristic
507C2×C22⋊C4—591no—
508C2×C22⋊C4—591no—
509C2×C22⋊C4—1181no—
510C2×C22⋊C4—1181no—
511C2×C22⋊C4—1181no—
512C2×C22⋊C4—1181no—
513C2×C22⋊C4—1181no—
514C2×C22⋊C4—1181no—
515C2×C22⋊C4—1181no—
516C2×C22⋊C4—1181no—
517C2×C22⋊C4—2364no—
518C2×C42—591no—
519C2×C42—591no—
520C2×C42—1181no—
521C2×C42—1181no—
522#107—1182no—
523#107—2361no—
524#103—1182no—
525#103—2361no—
526#102—22no—
527#102—22no—
528#102—22no—
529#102—594no—
530#102—594no—
531#102C22⋊D5914yes—
532C22⋊C8—594no—
533#97—1182no—
534#97—2361no—
535#95—591no—
536#95—591no—
537#95—1181no—
538#95—1181no—
539#95—1181no—
540#95—1181no—
541#95—1181no—
542C24—21no—
543C24—21no—
544C24—24no—
545C24—42no—
546C24—42no—
547C24—42no—
548C24—42no—
549C24—81no—
550C24—81no—
551C24D4×D5911yescharacteristic
552C2×Q8—592no—
553C2×Q8—1181no—
554C2×Q8—1181no—
555C2×Q8—1181no—
556C2×Q8—1181no—
557C2×Q8—1181no—
558C2×D4—28no—
559C2×D4—24no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—44no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4C2×C4×D5912yes—
574C2×D4C2×C4×D5912yes—
575C2×D4#1174568512yes—
576C2×D4C2×C22⋊D5912yes—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—81no—
586C22×C4—591no—
587C22×C4—591no—
588C22×C4—591no—
589C22×C4—591no—
590C22×C4—1181no—
591C22×C4—1181no—
592C22×C4—1181no—
593C22×C4—1181no—
594C22×C4—4721no—
595C22×C4—4721no—
596C22×C4—2362no—
597C22×C4—2362no—
598C22×C4—2362no—
599C22×C4—2362no—
600C22×C4C2×C4×D5912yes—
601C22×C4D4×D5911yescharacteristic
602C22×C4#1174568712yes—
603C22×C4C23×D5911yescharacteristic
604SD16—1188no—
605SD16—2364no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—44no—
612C2×C8—592no—
613C2×C8—592no—
614C2×C8—1181no—
615C2×C8—1181no—
616C2×C8—1181no—
617C2×C8—1181no—
618C2×C8C2×C22⋊D5912yes—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—42no—
623C4⋊C4—592no—
624C4⋊C4—1184no—
625C4⋊C4—1181no—
626C4⋊C4—1181no—
627C4⋊C4—1181no—
628C4⋊C4—1181no—
629C4⋊C4—1181no—
630C4⋊C4—4721no—
631C4⋊C4—2362no—
632C4⋊C4C2×C22⋊D5912yes—
633C22⋊C4—1184no—
634C22⋊C4—1182no—
635C22⋊C4—1182no—
636C22⋊C4—4721no—
637C22⋊C4—4721no—
638C22⋊C4—2362no—
639C22⋊C4—2362no—
640C22⋊C4—2362no—
641C22⋊C4—2362no—
642C22⋊C4—2362no—
643C42—1181no—
644C42—1181no—
645C42—1181no—
646C42—1181no—
647C42—4721no—
648C42—2362no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—48no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—48no—
667C23—41no—
668C23—41no—
669C23—84no—
670C23—84no—
671C23—84no—
672C23—84no—
673C23—84no—
674C23(C22⋊D59)⋊C412yes—
675C23#1427375112yes—
676C23#1427375612yes—
677C23C2×D4×D5911yescharacteristic
678Q8—1182no—
679Q8—1182no—
680Q8—2361no—
681Q8—2361no—
682D4—22no—
683D4—22no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—48no—
688D4—41no—
689D4—41no—
690D4C4×C22⋊D5914yes—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—84no—
704C2×C4—1181no—
705C2×C4—1181no—
706C2×C4—1181no—
707C2×C4—1181no—
708C2×C4—1181no—
709C2×C4—1181no—
710C2×C4—1181no—
711C2×C4—1181no—
712C2×C4—1181no—
713C2×C4—1181no—
714C2×C4—1181no—
715C2×C4—1181no—
716C2×C4—1182no—
717C2×C4—1182no—
718C2×C4—4724no—
719C2×C4—4724no—
720C2×C4—2361no—
721C2×C4—2361no—
722C2×C4—2361no—
723C2×C4—2361no—
724C2×C4—2361no—
725C2×C4—2361no—
726C2×C4—2361no—
727C2×C4—2361no—
728C2×C4—2361no—
729C2×C4—2361no—
730C2×C4(C22⋊D59)⋊C412yes—
731C2×C4C22×C4×D5911yescharacteristic
732C2×C4C22×C22⋊D5911yescharacteristic
733C2×C4C2×#1174568711yescharacteristic
734C2×C4C2×#1174568511yescharacteristic
735C2×C4#1427377211yescharacteristic
736C2×C4#1427377211yescharacteristic
737C8—22no—
738C8—41no—
739C8—1182no—
740C8—1182no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—24no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—816no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22#1683749914yescomplemented
763C22C2×(C22⋊D59)⋊C411yescharacteristic
764C22D4×C22⋊D5911yescharacteristic
765C22#1683804211yescharacteristic
766C22C2×#1427375111yescharacteristic
767C22C2×#1427375611yescharacteristic
768C22#1683820311yescharacteristic
769C22#1683820811yescharacteristic
770C4—22no—
771C4—42no—
772C4—81no—
773C4—4721no—
774C4—4721no—
775C4—2361no—
776C4—2362no—
777C4—2362no—
778C4—2361no—
779C4—2361no—
780C4—2361no—
781C4C2×C4×C22⋊D5911yescharacteristic
782C4#1683787511yescharacteristic
783C4#1683804611yescharacteristic
784C4#1683807811yescharacteristic
785C2—24no—
786C2—44no—
787C2—82no—
788C2#2142707511yescharacteristic
789C2C2×#1683749911yescharacteristic
790C2#2143292211yescharacteristic
791C2#2143557611yescharacteristic
792C2#2143560611yescharacteristic
793C2#2143611311yescharacteristic
794C2#2143617311yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC22×#102×C59C2
socleC23×C59C22×D4
prime radicalC23×D4×C59C22
cosocleC22×C4×C59C24
hypercenterC22×#102D59
hypocenterC59#22854
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
2. C2×#16837499C2semidirect
3. #21427101C2semidirect
5. #21424978C2semidirect
6. #21424790C2semidirect
7. #21424719C2semidirect
8. #21424519C2semidirect
9. #21424448C2semidirect
10. #21424428C2semidirect
11. #21424341C2semidirect
12. #21424284C2semidirect
13. #21423923C2semidirect
14. #21423872C2semidirect
19. C2×#14273692C22semidirect
23. #16837553C4semidirect
25. C2×#14273660C22semidirect
26. C2×#14273660C22semidirect
27. C2×#14273652C22semidirect
28. C2×#14273652C22semidirect
32. C2×#14273637C22semidirect
33. C2×#14273637C22semidirect
34. #16837307C22semidirect
37. #16837298C22semidirect
45. C4⋊C4×Dic59C22semidirect
48. #16837165C22semidirect
49. #16837165C22semidirect
50. #16837164C22semidirect
51. #16837164C22semidirect
52. #16837156C22semidirect
53. #16837156C22semidirect
69. C2×#11745670C2×C4semidirect
70. C2×#11745670C2×C4semidirect
74. #14273706C2×C4semidirect
106. #14273648C2×C4semidirect
107. #14273648C2×C4semidirect
108. C22⋊(C59⋊C8)C2×C4semidirect
365. C22×C59#440semidirect
459. C59#22854semidirect
762. C22#16837499semidirect

Maximal subgroups

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

subgroupindex
C2×#168375532
C2×#168374992
#214271012
D4×C22⋊Dic592
#214249782
#214247902
#214247192
#214245192
#214244482
#214244282
#214243412
#214242842
#214239232
#214238722
C22×#102×C592
#2285459