Finite Group Databasebeta

← #28597806

Subgroups — #28597806

Order 15104.

1390 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837369C211yesmaximal, characteristic, complemented
2#21426688C211yesmaximal, characteristic, complemented
3#21424535C211yesmaximal, characteristic, complemented
4#21424530C211yesmaximal, characteristic, complemented
5#21424525C211yesmaximal, characteristic, complemented
6#21424520C211yesmaximal, characteristic, complemented
7#21424419C211yesmaximal, characteristic, complemented
8#21424414C211yesmaximal, characteristic, complemented
9#21424409C211yesmaximal, characteristic, complemented
10#21424404C211yesmaximal, characteristic, complemented
11#21424186C211yesmaximal, characteristic, complemented
12#21424182C211yesmaximal, characteristic, complemented
13#21424036C211yesmaximal, characteristic, complemented
14#21424036C211yesmaximal, characteristic, complemented
15C2×C59×#537C211yesmaximal, characteristic
16C22×#11745664C2211yescharacteristic
17C23×C59⋊C8C2211yescharacteristic
18C2×#14273686C2211yescharacteristic
19C22×C4⋊Dic59C2211yescharacteristic
20C2×#14273651C2211yescharacteristic
21C2×#14273651C2211yescharacteristic
22C2×#14273651C2211yescharacteristic
23C2×#14273651C2211yescharacteristic
24C2×#14273648C2211yescharacteristic
25C2×#14273648C2211yescharacteristic
26C2×#14273648C2211yescharacteristic
27C2×#14273648C2211yescharacteristic
28#16837369—24no—
29C2×C22⋊(C59⋊C8)C2211yescharacteristic
30C2×C22⋊(C59⋊C8)C2211yescharacteristic
31C2×C22⋊(C59⋊C8)C2211yescharacteristic
32C2×C22⋊(C59⋊C8)C2211yescharacteristic
33#16837309—21no—
34#16837305—21no—
35#16837282—21no—
36#16837282—21no—
37#16837262C2211yescharacteristic
38#16837262C2211yescharacteristic
39#16837262C2211yescharacteristic
40#16837262C2211yescharacteristic
41#16837164C2211yescharacteristic
42#16837164C2211yescharacteristic
43#16837164C2211yescharacteristic
44#16837164C2211yescharacteristic
45#16837164C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837164C2211yescharacteristic
48#16837164C2211yescharacteristic
49C22×#41×C59C2211yescharacteristic
50C22×#41×C59C2211yescharacteristic
51C59×#537—24no—
52C59×#537C418yescomplemented
53C2×C22⋊Q8×C59—21no—
54C2×C22⋊Q8×C59C2211yescharacteristic
55C2×C22⋊Q8×C59C2211yescharacteristic
56C2×#121×C59—21no—
57C2×#121×C59—21no—
58C2×#121×C59—21no—
59C2×#121×C59C2211yescharacteristic
60C2×#121×C59C2211yescharacteristic
61C22×C4⋊C4×C59C2211yescharacteristic
62C23×Dic59—21no—
63C2×#11745664—22no—
64C2×#11745664—41no—
65C2×#11745664—41no—
66C22×C59⋊C8—22no—
67C22×C59⋊C8—41no—
68C22×C59⋊C8—41no—
69C22×C59⋊C8C2311yescharacteristic
70C22×C59⋊C8C2311yescharacteristic
71C22×C59⋊C8C2311yescharacteristic
72C22×C59⋊C8C2311yescharacteristic
73#14273686—41no—
74#14273686—41no—
75C2×C4⋊Dic59—21no—
76C2×C4⋊Dic59—41no—
77C2×C4⋊Dic59—41no—
78C2×C4⋊Dic59C2311yescharacteristic
79C2×C4⋊Dic59C2311yescharacteristic
80C2×C4⋊Dic59C2311yescharacteristic
81C2×C4⋊Dic59C2311yescharacteristic
82C2×C22⋊Dic59—21no—
83C2×C22⋊Dic59—21no—
84C2×C22⋊Dic59—21no—
85C2×C22⋊Dic59—21no—
86C2×C22⋊Dic59—21no—
87C2×C4×Dic59—21no—
88#14273651—41no—
89#14273651—41no—
90#14273651—41no—
91#14273651—41no—
92#14273648—41no—
93#14273648—41no—
94#14273648—41no—
95#14273648—41no—
96C22⋊(C59⋊C8)—22no—
97C22⋊(C59⋊C8)—22no—
98C22⋊(C59⋊C8)—22no—
99C22⋊(C59⋊C8)—22no—
100C59⋊#95—21no—
101C59⋊#95—21no—
102C59⋊#95—21no—
103C59⋊#95—21no—
104C2×#41×C59—22no—
105C2×#41×C59—41no—
106C2×#41×C59—41no—
107C2×#41×C59—41no—
108C2×#41×C59—41no—
109C2×#41×C59—41no—
110C2×#41×C59—41no—
111C2×#41×C59—41no—
112C2×#41×C59—41no—
113C2×#41×C59C2×C414yes—
114C2×#41×C59C2×C414yescomplemented
115C2×#41×C59D414yes—
116C22×Q8×C59D411yescharacteristic
117C22×Q8×C59C2311yescharacteristic
118C22×D4×C59—21no—
119C22×D4×C59—21no—
120C22×D4×C59—21no—
121C22×D4×C59D411yescharacteristic
122C22×D4×C59D411yescharacteristic
123C22×D4×C59D411yescharacteristic
124C22×D4×C59C2311yescharacteristic
125C23×C4×C59—21no—
126C23×C4×C59—21no—
127C23×C4×C59C2311yescharacteristic
128C23×C4×C59C2311yescharacteristic
129C23×C4×C59C2311yescharacteristic
130C22⋊Q8×C59—28no—
131C22⋊Q8×C59—22no—
132C22⋊Q8×C59—22no—
133C22⋊Q8×C59C2×C414yes—
134C22⋊Q8×C59C2×C414yescomplemented
135#121×C59—28no—
136#121×C59—28no—
137#121×C59—28no—
138#121×C59—22no—
139#121×C59—22no—
140#121×C59C2×C414yes—
141#121×C59C2×C414yescomplemented
142C2×C4⋊C4×C59—21no—
143C2×C4⋊C4×C59—22no—
144C2×C4⋊C4×C59—21no—
145C2×C4⋊C4×C59—21no—
146C2×C4⋊C4×C59C2×C414yescomplemented
147C2×C4⋊C4×C59C2311yescharacteristic
148C2×C4⋊C4×C59C2311yescharacteristic
149C2×C22⋊C4×C59—21no—
150C2×C22⋊C4×C59—21no—
151C2×C22⋊C4×C59—21no—
152C2×C22⋊C4×C59—21no—
153C24×C59—21no—
154C24×C59C2×D411yescharacteristic
155C24×C59C2×D411yescharacteristic
156C24×C59C2×D411yescharacteristic
157#41×C59—44no—
158#41×C59—44no—
159#41×C59—44no—
160#41×C59—44no—
161#41×C59—44no—
162#41×C59—44no—
163#41×C59—44no—
164#41×C59—44no—
165C2×Q8×C59—21no—
166C2×Q8×C59—21no—
167C2×Q8×C59—21no—
168C2×Q8×C59—21no—
169C2×Q8×C59—21no—
170C2×Q8×C59—41no—
171C2×Q8×C59—41no—
172C2×Q8×C59C22⋊C414yes—
173C2×Q8×C59C22×C412yes—
174C2×D4×C59—24no—
175C2×D4×C59—24no—
176C2×D4×C59—24no—
177C2×D4×C59—21no—
178C2×D4×C59—21no—
179C2×D4×C59—21no—
180C2×D4×C59—21no—
181C2×D4×C59—21no—
182C2×D4×C59—41no—
183C2×D4×C59—41no—
184C2×D4×C59—41no—
185C2×D4×C59—41no—
186C2×D4×C59—41no—
187C2×D4×C59—41no—
188C2×D4×C59—42no—
189C2×D4×C59—42no—
190C2×D4×C59—81no—
191C2×D4×C59—81no—
192C2×D4×C59—81no—
193C2×D4×C59—81no—
194C2×D4×C59C22⋊C414yes—
195C2×D4×C59C22⋊C414yes—
196C2×D4×C59C22⋊C414yes—
197C2×D4×C59C22×C412yes—
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—21no—
208C22×C4×C59—21no—
209C22×C4×C59—21no—
210C22×C4×C59—21no—
211C22×C4×C59—21no—
212C22×C4×C59—21no—
213C22×C4×C59—24no—
214C22×C4×C59—24no—
215C22×C4×C59—42no—
216C22×C4×C59—42no—
217C22×C4×C59—81no—
218C22×C4×C59—81no—
219C22×C4×C59C22×C412yes—
220C22×C4×C59C22×C412yes—
221C22×C4×C59C22×C412yes—
222C22×C4×C59C2×D411yescharacteristic
223C22×C4×C59C2×D411yescharacteristic
224C22×C4×C59C2×D411yescharacteristic
225C22×C4×C59C2×D412yes—
226C22×C4×C59C2×D412yes—
227C22×C4×C59C2×D412yes—
228C22×C4×C59C2411yescharacteristic
229C22×Dic59—21no—
230C22×Dic59—21no—
231C22×Dic59—21no—
232C22×Dic59—21no—
233C22×Dic59—42no—
234C22×Dic59—81no—
235C22×Dic59—81no—
236C4⋊C4×C59—24no—
237C4⋊C4×C59—24no—
238C4⋊C4×C59—24no—
239C4⋊C4×C59—21no—
240C4⋊C4×C59—21no—
241C4⋊C4×C59C22×C412yes—
242C4⋊C4×C59C22×C412yes—
243C22⋊C4×C59—24no—
244C22⋊C4×C59—24no—
245C22⋊C4×C59—24no—
246C22⋊C4×C59—24no—
247C22⋊Dic59—42no—
248C22⋊Dic59—81no—
249C22⋊Dic59—81no—
250C22⋊Dic59—81no—
251C22⋊Dic59—81no—
252C4⋊Dic59—21no—
253C4⋊Dic59—21no—
254C4⋊Dic59—21no—
255C4⋊Dic59—21no—
256C4⋊Dic59—21no—
257C4⋊Dic59—21no—
258C4⋊Dic59—21no—
259C4⋊Dic59—21no—
260C4⋊Dic59—42no—
261C4×Dic59—42no—
262#11745664—44no—
263C2×C59⋊C8—21no—
264C2×C59⋊C8—21no—
265C2×C59⋊C8—21no—
266C2×C59⋊C8—21no—
267C2×C59⋊C8—21no—
268C2×C59⋊C8—21no—
269C2×C59⋊C8—21no—
270C2×C59⋊C8—21no—
271C2×C59⋊C8—21no—
272C2×C59⋊C8—21no—
273C2×C59⋊C8—21no—
274C2×C59⋊C8—21no—
275C2×C59⋊C8—44no—
276C23×C59—21no—
277C23×C59—21no—
278C23×C59—21no—
279C23×C59—21no—
280C23×C59—21no—
281C23×C59—21no—
282C23×C59—21no—
283C23×C59—21no—
284C23×C59—21no—
285C23×C59—21no—
286C23×C59—21no—
287C23×C59—21no—
288C23×C59—21no—
289C23×C59—21no—
290C23×C59—21no—
291C23×C59—21no—
292C23×C59—21no—
293C23×C59—21no—
294C23×C59—22no—
295C23×C59—41no—
296C23×C59—41no—
297C23×C59—41no—
298C23×C59—41no—
299C23×C59—41no—
300C23×C59—41no—
301C23×C59C2×C22⋊C412yes—
302C23×C59C2×C22⋊C412yes—
303C23×C59C2×C22⋊C412yes—
304C23×C59C22×D411yescharacteristic
305Q8×C59—22no—
306Q8×C59—22no—
307Q8×C59—44no—
308Q8×C59—41no—
309Q8×C59—41no—
310D4×C59—22no—
311D4×C59—22no—
312D4×C59—44no—
313D4×C59—44no—
314D4×C59—44no—
315D4×C59—48no—
316D4×C59—41no—
317D4×C59—41no—
318D4×C59—84no—
319D4×C59—84no—
320C2×C4×C59—21no—
321C2×C4×C59—21no—
322C2×C4×C59—21no—
323C2×C4×C59—21no—
324C2×C4×C59—21no—
325C2×C4×C59—21no—
326C2×C4×C59—22no—
327C2×C4×C59—22no—
328C2×C4×C59—22no—
329C2×C4×C59—22no—
330C2×C4×C59—22no—
331C2×C4×C59—22no—
332C2×C4×C59—22no—
333C2×C4×C59—22no—
334C2×C4×C59—22no—
335C2×C4×C59—22no—
336C2×C4×C59—22no—
337C2×C4×C59—22no—
338C2×C4×C59—22no—
339C2×C4×C59—22no—
340C2×C4×C59—22no—
341C2×C4×C59—48no—
342C2×C4×C59—41no—
343C2×C4×C59—41no—
344C2×C4×C59—41no—
345C2×C4×C59—41no—
346C2×C4×C59—41no—
347C2×C4×C59—41no—
348C2×C4×C59—84no—
349C2×C4×C59C2×C22⋊C412yes—
350C2×C4×C59C2×C22⋊C412yes—
351C2×C4×C59C2×C22⋊C412yes—
352C2×C4×C59C23×C411yescharacteristic
353C2×C4×C59C22×D411yescharacteristic
354C2×C4×C59H(5,𝔽2)11yescharacteristic
355C2×C4×C59H(5,𝔽2)11yescharacteristic
356C2×C4×C59H(5,𝔽2)11yescharacteristic
357C2×C4×C59H(5,𝔽2)11yescharacteristic
358C2×Dic59—41no—
359C2×Dic59—41no—
360C2×Dic59—41no—
361C2×Dic59—41no—
362C2×Dic59—41no—
363C2×Dic59—41no—
364C2×Dic59—41no—
365C2×Dic59—41no—
366C2×Dic59—41no—
367C2×Dic59—41no—
368C2×Dic59—41no—
369C2×Dic59—41no—
370C2×Dic59—84no—
371C59⋊C8—41no—
372C59⋊C8—41no—
373C59⋊C8—41no—
374C59⋊C8—41no—
375#21772—591nomaximal, Sylow
376C22×C59—22no—
377C22×C59—22no—
378C22×C59—22no—
379C22×C59—22no—
380C22×C59—22no—
381C22×C59—22no—
382C22×C59—22no—
383C22×C59—22no—
384C22×C59—22no—
385C22×C59—41no—
386C22×C59—41no—
387C22×C59—41no—
388C22×C59—41no—
389C22×C59—41no—
390C22×C59—41no—
391C22×C59—41no—
392C22×C59—41no—
393C22×C59—41no—
394C22×C59—41no—
395C22×C59—41no—
396C22×C59—41no—
397C22×C59—42no—
398C22×C59—42no—
399C22×C59—42no—
400C22×C59—81no—
401C22×C59—81no—
402C22×C59—81no—
403C22×C59—81no—
404C22×C59C22×C22⋊C411yescharacteristic
405C22×C59#53411yescharacteristic
406C22×C59#53411yescharacteristic
407C22×C59#57611yescharacteristic
408C22×C59#57711yescharacteristic
409C22×C59#57711yescharacteristic
410C22×C59#57811yescharacteristic
411C4×C59—22no—
412C4×C59—22no—
413C4×C59—22no—
414C4×C59—42no—
415C4×C59—42no—
416C4×C59—42no—
417C4×C59#51811yescharacteristic
418C4×C59#51811yescharacteristic
419C4×C59#53411yescharacteristic
420C4×C59#53411yescharacteristic
421Dic59—81no—
422Dic59—81no—
423Dic59—81no—
424Dic59—81no—
425C2×#537D5911yescharacteristic
426C2×#408—591no—
427#2311—591no—
428#1895—591no—
429#1894—591no—
430#1893—591no—
431#1892—591no—
432#1875—591no—
433#1874—591no—
434#1873—591no—
435#1872—591no—
436#1824—591no—
437#1823—591no—
438#1788—591no—
439#1788—591no—
440C2×C59—42no—
441C2×C59—42no—
442C2×C59—42no—
443C2×C59—82no—
444C2×C59#230811yescharacteristic
445C2×C59#289711yescharacteristic
446C2×C59#289811yescharacteristic
447C2×C59#319811yescharacteristic
448C2×C59#320111yescharacteristic
449C2×C59#320311yescharacteristic
450C2×C59#320411yescharacteristic
451C22×#41C2×D5911yescharacteristic
452C22×#41C2×D5911yescharacteristic
453C22×M16—591no—
454C23×C8—591no—
455#537—24no—
456#537Dic5918yescomplemented
457C2×C22⋊Q8—21no—
458C2×C22⋊Q8C2×D5911yescharacteristic
459C2×C22⋊Q8C2×D5911yescharacteristic
460C2×#121—21no—
461C2×#121—21no—
462C2×#121—21no—
463C2×#121C2×D5911yescharacteristic
464C2×#121C2×D5911yescharacteristic
465C2×#117—591no—
466C22×C4⋊C4—591no—
467C22×C4⋊C4C2×D5911yescharacteristic
468C2×#103—591no—
469C2×#103—591no—
470C2×#103—591no—
471C2×#103—591no—
472C2×#102—591no—
473C2×#102—591no—
474C2×#102—591no—
475C2×#102—591no—
476#408—1184no—
477C2×C22⋊C8—591no—
478C2×C22⋊C8—591no—
479C2×C22⋊C8—591no—
480C2×C22⋊C8—591no—
481#391—1181no—
482#390—1181no—
483#386—1181no—
484#386—1181no—
485#380—591no—
486#380—591no—
487#380—591no—
488#380—591no—
489#340—591no—
490#340—591no—
491#340—591no—
492#340—591no—
493#340—591no—
494#340—591no—
495#340—591no—
496#340—591no—
497C59#2177211yescharacteristic, complemented, Sylow
498C2×#41—22no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41—41no—
507C2×#41C2×Dic5914yes—
508C2×#41C2×Dic5914yescomplemented
509C2×#41C22⋊D5914yes—
510C22×Q8C22⋊D5911yescharacteristic
511C22×Q8C22×D5911yescharacteristic
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4C22⋊D5911yescharacteristic
516C22×D4C22⋊D5911yescharacteristic
517C22×D4C22⋊D5911yescharacteristic
518C22×D4C22×D5911yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—1181no—
522C23×C4C22×D5911yescharacteristic
523C23×C4C22×D5911yescharacteristic
524C23×C4C22×D5911yescharacteristic
525C2×M16—1182no—
526C2×M16—2361no—
527C2×M16—2361no—
528C22×C8—591no—
529C22×C8—591no—
530C22×C8—591no—
531C22×C8—591no—
532C22×C8—1182no—
533C22×C8—2361no—
534C22×C8—2361no—
535C22⋊Q8—28no—
536C22⋊Q8—22no—
537C22⋊Q8—22no—
538C22⋊Q8C2×Dic5914yes—
539C22⋊Q8C2×Dic5914yescomplemented
540#121—28no—
541#121—28no—
542#121—28no—
543#121—22no—
544#121—22no—
545#121C2×Dic5914yes—
546#121C2×Dic5914yescomplemented
547#117—2361no—
548#117—2361no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—22no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—591no—
554C2×C4⋊C4—591no—
555C2×C4⋊C4—591no—
556C2×C4⋊C4—591no—
557C2×C4⋊C4—1181no—
558C2×C4⋊C4—2361no—
559C2×C4⋊C4—2361no—
560C2×C4⋊C4C2×Dic5914yescomplemented
561C2×C4⋊C4C22×D5911yescharacteristic
562C2×C4⋊C4C22×D5911yescharacteristic
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—1181no—
568C2×C22⋊C4—1181no—
569C2×C22⋊C4—1181no—
570C2×C22⋊C4—1181no—
571C2×C22⋊C4—1181no—
572C2×C42—1181no—
573#103—2361no—
574#103—2361no—
575#103—2361no—
576#103—2361no—
577#102—2361no—
578#102—2361no—
579#102—2361no—
580#102—2361no—
581C22⋊C8—1182no—
582C22⋊C8—1182no—
583C22⋊C8—1182no—
584C22⋊C8—1182no—
585#95—1181no—
586#95—1181no—
587#95—1181no—
588#95—1181no—
589C24—21no—
590C24C2×C22⋊D5911yescharacteristic
591C24C2×C22⋊D5911yescharacteristic
592C24C2×C22⋊D5911yescharacteristic
593#41—44no—
594#41—44no—
595#41—44no—
596#41—44no—
597#41—44no—
598#41—44no—
599#41—44no—
600#41—44no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—41no—
607C2×Q8—41no—
608C2×Q8C22⋊Dic5914yes—
609C2×Q8C22×Dic5912yes—
610C2×D4—24no—
611C2×D4—24no—
612C2×D4—24no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—41no—
619C2×D4—41no—
620C2×D4—41no—
621C2×D4—41no—
622C2×D4—41no—
623C2×D4—41no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—81no—
627C2×D4—81no—
628C2×D4—81no—
629C2×D4—81no—
630C2×D4C22⋊Dic5914yes—
631C2×D4C22⋊Dic5914yes—
632C2×D4C22⋊Dic5914yes—
633C2×D4C22×Dic5912yes—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—24no—
650C22×C4—24no—
651C22×C4—42no—
652C22×C4—42no—
653C22×C4—81no—
654C22×C4—81no—
655C22×C4—1181no—
656C22×C4—1181no—
657C22×C4—1181no—
658C22×C4—1181no—
659C22×C4—4721no—
660C22×C4—4721no—
661C22×C4—2362no—
662C22×C4C22×Dic5912yes—
663C22×C4C22×Dic5912yes—
664C22×C4C22×Dic5912yes—
665C22×C4C2×C22⋊D5911yescharacteristic
666C22×C4C2×C22⋊D5911yescharacteristic
667C22×C4C2×C22⋊D5911yescharacteristic
668C22×C4C2×C22⋊D5912yes—
669C22×C4C2×C22⋊D5912yes—
670C22×C4C2×C22⋊D5912yes—
671C22×C4C23×D5911yescharacteristic
672M16—2364no—
673C2×C8—1181no—
674C2×C8—1181no—
675C2×C8—1181no—
676C2×C8—1181no—
677C2×C8—1181no—
678C2×C8—1181no—
679C2×C8—1181no—
680C2×C8—1181no—
681C2×C8—1181no—
682C2×C8—1181no—
683C2×C8—1181no—
684C2×C8—1181no—
685C2×C8—2364no—
686C4⋊C4—24no—
687C4⋊C4—24no—
688C4⋊C4—24no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—1181no—
692C4⋊C4—1181no—
693C4⋊C4—1181no—
694C4⋊C4—1181no—
695C4⋊C4—1181no—
696C4⋊C4—1181no—
697C4⋊C4—1181no—
698C4⋊C4—1181no—
699C4⋊C4—2362no—
700C4⋊C4C22×Dic5912yes—
701C4⋊C4C22×Dic5912yes—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—24no—
705C22⋊C4—24no—
706C22⋊C4—4721no—
707C22⋊C4—4721no—
708C22⋊C4—4721no—
709C22⋊C4—4721no—
710C22⋊C4—2362no—
711C42—2362no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—22no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23C2×C22⋊Dic5912yes—
738C23C2×C22⋊Dic5912yes—
739C23C2×C22⋊Dic5912yes—
740C23C22×C22⋊D5911yescharacteristic
741Q8—22no—
742Q8—22no—
743Q8—44no—
744Q8—41no—
745Q8—41no—
746D4—22no—
747D4—22no—
748D4—44no—
749D4—44no—
750D4—44no—
751D4—48no—
752D4—41no—
753D4—41no—
754D4—84no—
755D4—84no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—48no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—84no—
785C2×C4—4724no—
786C2×C4—2361no—
787C2×C4—2361no—
788C2×C4—2361no—
789C2×C4—2361no—
790C2×C4—2361no—
791C2×C4—2361no—
792C2×C4—2361no—
793C2×C4—2361no—
794C2×C4—2361no—
795C2×C4—2361no—
796C2×C4—2361no—
797C2×C4—2361no—
798C2×C4C2×C22⋊Dic5912yes—
799C2×C4C2×C22⋊Dic5912yes—
800C2×C4C2×C22⋊Dic5912yes—
801C2×C4C23×Dic5911yescharacteristic
802C2×C4C22×C22⋊D5911yescharacteristic
803C2×C4#1427377211yescharacteristic
804C2×C4#1427377211yescharacteristic
805C2×C4#1427377211yescharacteristic
806C2×C4#1427377211yescharacteristic
807C8—2361no—
808C8—2361no—
809C8—2361no—
810C8—2361no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22C22×C22⋊Dic5911yescharacteristic
840C22#1683796111yescharacteristic
841C22#1683796111yescharacteristic
842C22#1683820511yescharacteristic
843C22#1683821011yescharacteristic
844C22#1683821311yescharacteristic
845C22#1683821711yescharacteristic
846C4—22no—
847C4—22no—
848C4—22no—
849C4—42no—
850C4—42no—
851C4—42no—
852C4—4721no—
853C4—4721no—
854C4—4721no—
855C4—4721no—
856C4#1683787711yescharacteristic
857C4#1683787711yescharacteristic
858C4#1683796111yescharacteristic
859C4#1683796111yescharacteristic
860C2—42no—
861C2—42no—
862C2—42no—
863C2—82no—
864C2#2142667411yescharacteristic
865C2#2143262211yescharacteristic
866C2#2143262911yescharacteristic
867C2#2143494211yescharacteristic
868C2#2143497211yescharacteristic
869C2#2143499311yescharacteristic
870C2#2143500211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
Fitting, prime radicalC2×C59×#537C2
socleC23×C59C22×D4
cosocleC22×C4×C59C24
hypercenterC2×#537D59
hypocenterC59#21772
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. C2×#16837369C2semidirect
2. #21426688C2semidirect
3. #21424535C2semidirect
4. #21424530C2semidirect
5. #21424525C2semidirect
6. #21424520C2semidirect
7. #21424419C2semidirect
8. #21424414C2semidirect
9. #21424409C2semidirect
10. #21424404C2semidirect
11. #21424186C2semidirect
12. #21424182C2semidirect
13. #21424036C2semidirect
14. #21424036C2semidirect
52. C59×#537C4semidirect
114. C2×#41×C59C2×C4semidirect
134. C22⋊Q8×C59C2×C4semidirect
141. #121×C59C2×C4semidirect
146. C2×C4⋊C4×C59C2×C4semidirect
456. #537Dic59semidirect
497. C59#21772semidirect
508. C2×#41C2×Dic59semidirect
539. C22⋊Q8C2×Dic59semidirect
546. #121C2×Dic59semidirect
560. C2×C4⋊C4C2×Dic59semidirect

Maximal subgroups

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

subgroupindex
C2×#168373692
#214266882
#214245352
#214245302
#214245252
#214245202
#214244192
#214244142
#214244092
#214244042
#214241862
#214241822
#214240362
C2×C59×#5372
#2177259