Finite Group Databasebeta

← #28604169

Subgroups — #28604169

Order 15104.

1670 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837474C211yesmaximal, characteristic, complemented
2C2×#16837403C211yesmaximal, characteristic, complemented
3C22×#14273648C211yesmaximal, characteristic, complemented
4D4×C4⋊Dic59C211yesmaximal, characteristic, complemented
5#21425029C211yesmaximal, characteristic, complemented
6#21424913C211yesmaximal, characteristic, complemented
7#21424535C211yesmaximal, characteristic, complemented
8#21424520C211yesmaximal, characteristic, complemented
9#21424414C211yesmaximal, characteristic, complemented
10#21424404C211yesmaximal, characteristic, complemented
11#21424096C211yesmaximal, characteristic, complemented
12#21424036C211yesmaximal, characteristic, complemented
13#21424027C211yesmaximal, characteristic, complemented
14#21423921C211yesmaximal, characteristic, complemented
15C2×C59×#546C211yesmaximal, characteristic
16C22×#11745664C2211yescharacteristic, complemented
17C23×C59⋊C8C2211yescharacteristic
18C2×D4×Dic59—21no—
19C22×C4⋊Dic59C2211yescharacteristic
20C22×C4⋊Dic59C2211yescharacteristic, complemented
21#16837474—24no—
22C2×C4⋊(C59⋊C8)C2211yescharacteristic, complemented
23#16837403—24no—
24C2×#14273651C2211yescharacteristic, complemented
25C2×#14273651C2211yescharacteristic, complemented
26C2×#14273651C2211yescharacteristic, complemented
27C2×#14273651C2211yescharacteristic, complemented
28C2×#14273648—24no—
29C2×#14273648C2211yescharacteristic
30C2×#14273648C2211yescharacteristic
31C2×#14273648C2211yescharacteristic
32C2×#14273648C2211yescharacteristic
33C2×#14273648C2211yescharacteristic
34C2×#14273648C2211yescharacteristic
35C2×#14273648C2211yescharacteristic
36C2×#14273648C2211yescharacteristic
37C2×C22⋊(C59⋊C8)C2211yescharacteristic
38C2×C22⋊(C59⋊C8)C2211yescharacteristic, complemented
39C2×#14273638C2211yescharacteristic, complemented
40#16837301—21no—
41#16837277—21no—
42#16837277—21no—
43#16837272C2211yescharacteristic, complemented
44#16837262C2211yescharacteristic
45#16837262C2211yescharacteristic, complemented
46C4×C4⋊Dic59C2211yescharacteristic, complemented
47#16837164C2211yescharacteristic, complemented
48#16837164C2211yescharacteristic, complemented
49#16837164C2211yescharacteristic, complemented
50#16837164C2211yescharacteristic, complemented
51C22×#41×C59C2211yescharacteristic
52C23×D4×C59C2211yescharacteristic
53C59×#546—24no—
54C59×#546C418yescomplemented
55C2×#124×C59C2211yescharacteristic
56C2×#123×C59—21no—
57C2×C22⋊Q8×C59C2211yescharacteristic
58C2×#121×C59—21no—
59C2×#121×C59C2211yescharacteristic
60C2×#120×C59—21no—
61C2×C4×D4×C59C2211yescharacteristic
62C2×C4×D4×C59C2211yescharacteristic
63C22×C22⋊C4×C59—21no—
64C23×Dic59—21no—
65C23×Dic59—21no—
66C2×#11745664—22no—
67C2×#11745664—22no—
68C2×#11745664—41no—
69C22×C59⋊C8—22no—
70C22×C59⋊C8—22no—
71C22×C59⋊C8—41no—
72C22×C59⋊C8C2311yescharacteristic
73C22×C59⋊C8C2311yescharacteristic
74C22×C59⋊C8C2311yescharacteristic
75C22×C59⋊C8C2311yescharacteristic
76D4×Dic59—44no—
77C2×C4⋊Dic59—22no—
78C2×C4⋊Dic59—22no—
79C2×C4⋊Dic59—21no—
80C2×C4⋊Dic59—21no—
81C2×C4⋊Dic59—21no—
82C2×C4⋊Dic59—21no—
83C2×C4⋊Dic59—41no—
84C2×C4⋊Dic59—41no—
85C2×C4⋊Dic59C2311yescharacteristic
86C2×C4⋊Dic59C2311yescharacteristic
87C2×C4⋊Dic59C2311yescharacteristic
88C2×C4⋊Dic59C2311yescharacteristic
89C2×C22⋊Dic59—21no—
90C2×C22⋊Dic59—21no—
91C2×C4×Dic59—21no—
92C4⋊(C59⋊C8)—22no—
93#14273651—22no—
94#14273651—22no—
95#14273651—41no—
96#14273651—41no—
97#14273648—22no—
98#14273648—22no—
99#14273648—22no—
100#14273648—22no—
101#14273648—22no—
102#14273648—41no—
103#14273648—41no—
104#14273648D414yescomplemented
105C22⋊(C59⋊C8)—22no—
106C22⋊(C59⋊C8)—22no—
107#14273638—22no—
108C59⋊#95—21no—
109C59⋊#95—21no—
110C59⋊#95—21no—
111C25×C59—21no—
112C2×#41×C59—22no—
113C2×#41×C59—22no—
114C2×#41×C59—22no—
115C2×#41×C59—41no—
116C2×#41×C59—41no—
117C2×#41×C59C2×C414yescomplemented
118C22×Q8×C59C2311yescharacteristic
119C22×D4×C59—22no—
120C22×D4×C59—22no—
121C22×D4×C59—21no—
122C22×D4×C59—21no—
123C22×D4×C59—21no—
124C22×D4×C59—22no—
125C22×D4×C59—41no—
126C22×D4×C59—41no—
127C22×D4×C59C2×C414yescomplemented
128C22×D4×C59D411yescharacteristic
129C22×D4×C59C2311yescharacteristic
130C22×D4×C59C2311yescharacteristic
131C23×C4×C59—21no—
132C23×C4×C59—21no—
133C23×C4×C59C2311yescharacteristic
134C23×C4×C59C2311yescharacteristic
135#124×C59—22no—
136#124×C59C2×C414yescomplemented
137#123×C59—28no—
138C22⋊Q8×C59—22no—
139C22⋊Q8×C59C2×C414yescomplemented
140#121×C59—22no—
141#121×C59—28no—
142#121×C59C2×C414yescomplemented
143#120×C59—28no—
144C4×D4×C59—22no—
145C4×D4×C59C2×C414yes—
146C4×D4×C59C2×C414yescomplemented
147C4×D4×C59D414yes—
148C2×C4⋊C4×C59—21no—
149C2×C4⋊C4×C59D411yescharacteristic
150C2×C4⋊C4×C59C2311yescharacteristic
151C2×C22⋊C4×C59—21no—
152C2×C22⋊C4×C59—21no—
153C2×C22⋊C4×C59—21no—
154C2×C22⋊C4×C59—21no—
155C2×C22⋊C4×C59—21no—
156C2×C22⋊C4×C59—28no—
157C2×C22⋊C4×C59D411yescharacteristic
158C2×C22⋊C4×C59D411yescharacteristic
159C2×C42×C59C2311yescharacteristic
160C24×C59—21no—
161C24×C59—21no—
162C24×C59—24no—
163C24×C59—42no—
164C24×C59—42no—
165C24×C59—42no—
166C24×C59—42no—
167C24×C59—81no—
168C24×C59—81no—
169C24×C59C2×D411yescharacteristic
170C24×C59C2×D411yescharacteristic
171#41×C59—28no—
172#41×C59—44no—
173#41×C59—44no—
174#41×C59—44no—
175C2×Q8×C59—21no—
176C2×Q8×C59—21no—
177C2×Q8×C59—21no—
178C2×Q8×C59—21no—
179C2×Q8×C59—21no—
180C2×Q8×C59C22×C412yes—
181C2×D4×C59—22no—
182C2×D4×C59—22no—
183C2×D4×C59—28no—
184C2×D4×C59—24no—
185C2×D4×C59—24no—
186C2×D4×C59—24no—
187C2×D4×C59—21no—
188C2×D4×C59—21no—
189C2×D4×C59—21no—
190C2×D4×C59—21no—
191C2×D4×C59—21no—
192C2×D4×C59—21no—
193C2×D4×C59—21no—
194C2×D4×C59—21no—
195C2×D4×C59—44no—
196C2×D4×C59—44no—
197C2×D4×C59—44no—
198C2×D4×C59—42no—
199C2×D4×C59—42no—
200C2×D4×C59—42no—
201C2×D4×C59—42no—
202C2×D4×C59—81no—
203C2×D4×C59—81no—
204C2×D4×C59C22⋊C414yes—
205C2×D4×C59C22×C412yes—
206C2×D4×C59C22×C412yes—
207C2×D4×C59C2×D412yes—
208C2×D4×C59#4112yes—
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—21no—
218C22×C4×C59—21no—
219C22×C4×C59—24no—
220C22×C4×C59—24no—
221C22×C4×C59—42no—
222C22×C4×C59—42no—
223C22×C4×C59—81no—
224C22×C4×C59—81no—
225C22×C4×C59C22×C412yes—
226C22×C4×C59C22×C412yes—
227C22×C4×C59C2×D411yescharacteristic
228C22×C4×C59C2×D411yescharacteristic
229C22×C4×C59C2×D411yescharacteristic
230C22×C4×C59C2×D411yescharacteristic
231C22×C4×C59C2×D412yes—
232C22×C4×C59C2×D412yes—
233C22×C4×C59C2411yescharacteristic
234C22×Dic59—21no—
235C22×Dic59—21no—
236C22×Dic59—21no—
237C22×Dic59—21no—
238C22×Dic59—42no—
239C22×Dic59—42no—
240C22×Dic59—42no—
241C22×Dic59—42no—
242C22×Dic59—81no—
243C22×Dic59—81no—
244C4⋊C4×C59—24no—
245C4⋊C4×C59—21no—
246C4⋊C4×C59C22⋊C414yes—
247C4⋊C4×C59C22×C412yes—
248C22⋊C4×C59—24no—
249C22⋊C4×C59—24no—
250C22⋊C4×C59—24no—
251C22⋊C4×C59—24no—
252C22⋊C4×C59—24no—
253C22⋊C4×C59C22⋊C414yes—
254C22⋊C4×C59C22⋊C414yes—
255C42×C59C22×C412yes—
256C42×C59C2×D412yes—
257C22⋊Dic59—42no—
258C22⋊Dic59—42no—
259C4⋊Dic59—21no—
260C4⋊Dic59—21no—
261C4⋊Dic59—21no—
262C4⋊Dic59—21no—
263C4⋊Dic59—21no—
264C4⋊Dic59—21no—
265C4⋊Dic59—21no—
266C4⋊Dic59—42no—
267C4⋊Dic59—42no—
268C4⋊Dic59—42no—
269C4⋊Dic59—81no—
270C4⋊Dic59C2×D412yes—
271C4×Dic59—42no—
272#11745664—44no—
273C2×C59⋊C8—21no—
274C2×C59⋊C8—21no—
275C2×C59⋊C8—21no—
276C2×C59⋊C8—21no—
277C2×C59⋊C8—21no—
278C2×C59⋊C8—21no—
279C2×C59⋊C8—21no—
280C2×C59⋊C8—21no—
281C2×C59⋊C8—21no—
282C2×C59⋊C8—21no—
283C2×C59⋊C8—21no—
284C2×C59⋊C8—44no—
285C2×C59⋊C8C2×D412yes—
286C23×C59—21no—
287C23×C59—21no—
288C23×C59—21no—
289C23×C59—21no—
290C23×C59—22no—
291C23×C59—21no—
292C23×C59—22no—
293C23×C59—21no—
294C23×C59—22no—
295C23×C59—21no—
296C23×C59—21no—
297C23×C59—21no—
298C23×C59—21no—
299C23×C59—22no—
300C23×C59—48no—
301C23×C59—41no—
302C23×C59—41no—
303C23×C59—41no—
304C23×C59—41no—
305C23×C59—41no—
306C23×C59—41no—
307C23×C59—41no—
308C23×C59—41no—
309C23×C59—41no—
310C23×C59—41no—
311C23×C59—48no—
312C23×C59—84no—
313C23×C59—84no—
314C23×C59—84no—
315C23×C59—84no—
316C23×C59—84no—
317C23×C59C2×C22⋊C412yes—
318C23×C59C2×C22⋊C412yes—
319C23×C59AGL(1,ℤ/8)12yes—
320C23×C59#13712yes—
321C23×C59C22×D411yescharacteristic
322Q8×C59—22no—
323Q8×C59—22no—
324Q8×C59—41no—
325Q8×C59—41no—
326D4×C59—28no—
327D4×C59—22no—
328D4×C59—22no—
329D4×C59—22no—
330D4×C59—22no—
331D4×C59—22no—
332D4×C59—48no—
333D4×C59—48no—
334D4×C59—41no—
335D4×C59—41no—
336D4×C59—84no—
337D4×C59C4×D414yescomplemented
338C2×C4×C59—21no—
339C2×C4×C59—21no—
340C2×C4×C59—21no—
341C2×C4×C59—21no—
342C2×C4×C59—21no—
343C2×C4×C59—21no—
344C2×C4×C59—21no—
345C2×C4×C59—21no—
346C2×C4×C59—22no—
347C2×C4×C59—22no—
348C2×C4×C59—22no—
349C2×C4×C59—22no—
350C2×C4×C59—22no—
351C2×C4×C59—22no—
352C2×C4×C59—22no—
353C2×C4×C59—22no—
354C2×C4×C59—22no—
355C2×C4×C59—22no—
356C2×C4×C59—48no—
357C2×C4×C59—41no—
358C2×C4×C59—41no—
359C2×C4×C59—41no—
360C2×C4×C59—41no—
361C2×C4×C59—84no—
362C2×C4×C59C2×C22⋊C412yes—
363C2×C4×C59C2×C22⋊C412yes—
364C2×C4×C59C2×C22⋊C412yes—
365C2×C4×C59C2×C22⋊C412yes—
366C2×C4×C59C23×C411yescharacteristic
367C2×C4×C59C22×D411yescharacteristic
368C2×C4×C59C22×D411yescharacteristic
369C2×C4×C59C2×#4111yescharacteristic
370C2×C4×C59H(5,𝔽2)11yescharacteristic
371C2×C4×C59H(5,𝔽2)11yescharacteristic
372C2×Dic59—22no—
373C2×Dic59—41no—
374C2×Dic59—41no—
375C2×Dic59—41no—
376C2×Dic59—41no—
377C2×Dic59—41no—
378C2×Dic59—41no—
379C2×Dic59—41no—
380C2×Dic59—41no—
381C2×Dic59—41no—
382C2×Dic59—41no—
383C2×Dic59—41no—
384C2×Dic59—84no—
385C2×Dic59—84no—
386C59⋊C8—22no—
387C59⋊C8—41no—
388C59⋊C8—41no—
389C59⋊C8—41no—
390#22419—591nomaximal, Sylow
391C22×C59—22no—
392C22×C59—22no—
393C22×C59—22no—
394C22×C59—22no—
395C22×C59—22no—
396C22×C59—22no—
397C22×C59—22no—
398C22×C59—24no—
399C22×C59—22no—
400C22×C59—22no—
401C22×C59—42no—
402C22×C59—42no—
403C22×C59—41no—
404C22×C59—42no—
405C22×C59—41no—
406C22×C59—42no—
407C22×C59—41no—
408C22×C59—42no—
409C22×C59—41no—
410C22×C59—42no—
411C22×C59—42no—
412C22×C59—42no—
413C22×C59—42no—
414C22×C59—816no—
415C22×C59—81no—
416C22×C59—81no—
417C22×C59—81no—
418C22×C59—81no—
419C22×C59#41714yescomplemented
420C22×C59C22×C22⋊C411yescharacteristic
421C22×C59D4211yescharacteristic
422C22×C59#54611yescharacteristic
423C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
424C22×C59C2×#13711yescharacteristic
425C22×C59#57611yescharacteristic
426C22×C59#57711yescharacteristic
427C4×C59—22no—
428C4×C59—22no—
429C4×C59—22no—
430C4×C59—22no—
431C4×C59—42no—
432C4×C59—42no—
433C4×C59C2×C4×D411yescharacteristic
434C4×C59#51811yescharacteristic
435C4×C59D4211yescharacteristic
436C4×C59#54611yescharacteristic
437Dic59—42no—
438Dic59—81no—
439Dic59—81no—
440Dic59—81no—
441C2×#546D5911yescharacteristic
442C2×#435—591no—
443C2×#417—591no—
444C22×#102—591no—
445D4×C4⋊C4—591no—
446#1983—591no—
447#1959—591no—
448#1895—591no—
449#1892—591no—
450#1874—591no—
451#1872—591no—
452#1802—591no—
453#1788—591no—
454#1786—591no—
455#1762—591no—
456C2×C59—24no—
457C2×C59—42no—
458C2×C59—44no—
459C2×C59—82no—
460C2×C59D4×C22⋊C411yescharacteristic
461C2×C59C2×#41711yescharacteristic
462C2×C59#289711yescharacteristic
463C2×C59#326411yescharacteristic
464C2×C59#326611yescharacteristic
465C2×C59#330611yescharacteristic
466C2×C59#331411yescharacteristic
467C22×#41C2×D5911yescharacteristic
468C23×D4C2×D5911yescharacteristic
469C22×M16—591no—
470C23×C8—591no—
471#546—24no—
472#546Dic5918yescomplemented
473C2×#124C2×D5911yescharacteristic
474C2×#123—21no—
475C2×C22⋊Q8C2×D5911yescharacteristic
476C2×#121—21no—
477C2×#121C2×D5911yescharacteristic
478C2×#120—21no—
479C2×C4×D4—1181no—
480C2×C4×D4C2×D5911yescharacteristic
481C2×C4×D4C2×D5911yescharacteristic
482C22×C4⋊C4—591no—
483C22×C4⋊C4—591no—
484C22×C22⋊C4—21no—
485#435—1184no—
486C2×C4⋊C8—591no—
487#417—1184no—
488C2×#103—591no—
489C2×#103—591no—
490C2×#103—591no—
491C2×#103—591no—
492C2×#102—591no—
493C2×#102—591no—
494C2×#102—591no—
495C2×#102—591no—
496C2×#102—591no—
497C2×#102—591no—
498C2×#102—591no—
499C2×#102—591no—
500C2×#102—1184no—
501C2×C22⋊C8—591no—
502C2×C22⋊C8—591no—
503C2×#97—591no—
504#389—1181no—
505#385—1181no—
506#385—1181no—
507#384—591no—
508#380—591no—
509#380—591no—
510C4×C4⋊C4—591no—
511#340—591no—
512#340—591no—
513#340—591no—
514#340—591no—
515C59#2241911yescharacteristic, complemented, Sylow
516C25—21no—
517C2×#41—22no—
518C2×#41—22no—
519C2×#41—22no—
520C2×#41—41no—
521C2×#41—41no—
522C2×#41C2×Dic5914yescomplemented
523C22×Q8C22×D5911yescharacteristic
524C22×D4—22no—
525C22×D4—22no—
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—22no—
530C22×D4—41no—
531C22×D4—41no—
532C22×D4C2×Dic5914yescomplemented
533C22×D4C22⋊D5911yescharacteristic
534C22×D4C22×D5911yescharacteristic
535C22×D4C22×D5911yescharacteristic
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—1181no—
539C23×C4—1181no—
540C23×C4C22×D5911yescharacteristic
541C23×C4C22×D5911yescharacteristic
542C2×M16—1182no—
543C2×M16—1182no—
544C2×M16—2361no—
545C22×C8—591no—
546C22×C8—591no—
547C22×C8—591no—
548C22×C8—591no—
549C22×C8—1182no—
550C22×C8—1182no—
551C22×C8—2361no—
552#124—22no—
553#124C2×Dic5914yescomplemented
554#123—28no—
555C22⋊Q8—22no—
556C22⋊Q8C2×Dic5914yescomplemented
557#121—22no—
558#121—28no—
559#121C2×Dic5914yescomplemented
560#120—28no—
561C4×D4—22no—
562C4×D4—2364no—
563C4×D4C2×Dic5914yes—
564C4×D4C2×Dic5914yescomplemented
565C4×D4C22⋊D5914yes—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—591no—
568C2×C4⋊C4—591no—
569C2×C4⋊C4—591no—
570C2×C4⋊C4—591no—
571C2×C4⋊C4—1182no—
572C2×C4⋊C4—1182no—
573C2×C4⋊C4—1181no—
574C2×C4⋊C4—1181no—
575C2×C4⋊C4—1181no—
576C2×C4⋊C4—1181no—
577C2×C4⋊C4—2361no—
578C2×C4⋊C4—2361no—
579C2×C4⋊C4C22⋊D5911yescharacteristic
580C2×C4⋊C4C22×D5911yescharacteristic
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—28no—
587C2×C22⋊C4—1181no—
588C2×C22⋊C4—1181no—
589C2×C22⋊C4C22⋊D5911yescharacteristic
590C2×C22⋊C4C22⋊D5911yescharacteristic
591C2×C42—1181no—
592C2×C42C22×D5911yescharacteristic
593C4⋊C8—1182no—
594#103—1182no—
595#103—1182no—
596#103—2361no—
597#103—2361no—
598#102—594no—
599#102—1182no—
600#102—1182no—
601#102—1182no—
602#102—1182no—
603#102—1182no—
604#102—2361no—
605#102—2361no—
606C22⋊C8—1182no—
607C22⋊C8—1182no—
608#97—1182no—
609#95—1181no—
610#95—1181no—
611#95—1181no—
612C24—21no—
613C24—21no—
614C24—24no—
615C24—42no—
616C24—42no—
617C24—42no—
618C24—42no—
619C24—81no—
620C24—81no—
621C24C2×C22⋊D5911yescharacteristic
622C24C2×C22⋊D5911yescharacteristic
623#41—28no—
624#41—44no—
625#41—44no—
626#41—44no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8C22×Dic5912yes—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—28no—
636C2×D4—24no—
637C2×D4—24no—
638C2×D4—24no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—44no—
648C2×D4—44no—
649C2×D4—44no—
650C2×D4—42no—
651C2×D4—42no—
652C2×D4—42no—
653C2×D4—42no—
654C2×D4—81no—
655C2×D4—81no—
656C2×D4C22⋊Dic5914yes—
657C2×D4D4×D5912yes—
658C2×D4#1174568712yes—
659C2×D4C22×Dic5912yes—
660C2×D4C22×Dic5912yes—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—24no—
672C22×C4—24no—
673C22×C4—42no—
674C22×C4—42no—
675C22×C4—81no—
676C22×C4—81no—
677C22×C4—1181no—
678C22×C4—1181no—
679C22×C4—1181no—
680C22×C4—1181no—
681C22×C4—4721no—
682C22×C4—4721no—
683C22×C4—2362no—
684C22×C4—2362no—
685C22×C4—2362no—
686C22×C4—2362no—
687C22×C4C22×Dic5912yes—
688C22×C4C22×Dic5912yes—
689C22×C4C2×C22⋊D5911yescharacteristic
690C22×C4C2×C22⋊D5911yescharacteristic
691C22×C4C2×C22⋊D5911yescharacteristic
692C22×C4C2×C22⋊D5911yescharacteristic
693C22×C4C2×C22⋊D5912yes—
694C22×C4C2×C22⋊D5912yes—
695C22×C4C23×D5911yescharacteristic
696M16—2364no—
697C2×C8—592no—
698C2×C8—1181no—
699C2×C8—1181no—
700C2×C8—1181no—
701C2×C8—1181no—
702C2×C8—1181no—
703C2×C8—1181no—
704C2×C8—1181no—
705C2×C8—1181no—
706C2×C8—1181no—
707C2×C8—1181no—
708C2×C8—1181no—
709C2×C8—2364no—
710C4⋊C4—24no—
711C4⋊C4—21no—
712C4⋊C4—592no—
713C4⋊C4—1181no—
714C4⋊C4—1181no—
715C4⋊C4—1181no—
716C4⋊C4—1181no—
717C4⋊C4—1181no—
718C4⋊C4—1181no—
719C4⋊C4—1181no—
720C4⋊C4—4721no—
721C4⋊C4—2362no—
722C4⋊C4—2362no—
723C4⋊C4—2362no—
724C4⋊C4C22⋊Dic5914yes—
725C4⋊C4C22×Dic5912yes—
726C22⋊C4—24no—
727C22⋊C4—24no—
728C22⋊C4—24no—
729C22⋊C4—24no—
730C22⋊C4—24no—
731C22⋊C4—2362no—
732C22⋊C4—2362no—
733C22⋊C4C22⋊Dic5914yes—
734C22⋊C4C22⋊Dic5914yes—
735C42—2362no—
736C42C22×Dic5912yes—
737C42C2×C22⋊D5912yes—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—22no—
748C23—21no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—48no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—48no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—84no—
765C23—84no—
766C23—84no—
767C23—84no—
768C23—84no—
769C23C2×C22⋊Dic5912yes—
770C23C2×C22⋊Dic5912yes—
771C23#1427375212yes—
772C23#1427375712yes—
773C23C22×C22⋊D5911yescharacteristic
774Q8—22no—
775Q8—22no—
776Q8—41no—
777Q8—41no—
778D4—28no—
779D4—22no—
780D4—22no—
781D4—22no—
782D4—22no—
783D4—22no—
784D4—48no—
785D4—48no—
786D4—41no—
787D4—41no—
788D4—84no—
789D4D4×Dic5914yescomplemented
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—48no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—84no—
814C2×C4—1182no—
815C2×C4—4724no—
816C2×C4—4724no—
817C2×C4—2361no—
818C2×C4—2361no—
819C2×C4—2361no—
820C2×C4—2361no—
821C2×C4—2361no—
822C2×C4—2361no—
823C2×C4—2361no—
824C2×C4—2361no—
825C2×C4—2361no—
826C2×C4—2361no—
827C2×C4—2361no—
828C2×C4C2×C22⋊Dic5912yes—
829C2×C4C2×C22⋊Dic5912yes—
830C2×C4C2×C22⋊Dic5912yes—
831C2×C4C2×C22⋊Dic5912yes—
832C2×C4C23×Dic5911yescharacteristic
833C2×C4C2×D4×D5911yescharacteristic
834C2×C4C22×C22⋊D5911yescharacteristic
835C2×C4C2×#1174568711yescharacteristic
836C2×C4#1427377211yescharacteristic
837C2×C4#1427377211yescharacteristic
838C8—1182no—
839C8—2361no—
840C8—2361no—
841C8—2361no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—24no—
852C22—41no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—41no—
857C22—42no—
858C22—41no—
859C22—42no—
860C22—41no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—816no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22#1683740314yescomplemented
871C22C22×C22⋊Dic5911yescharacteristic
872C22D4×C22⋊D5911yescharacteristic
873C22#1683804611yescharacteristic
874C22C2×#1427375211yescharacteristic
875C22C2×#1427375711yescharacteristic
876C22#1683820511yescharacteristic
877C22#1683821311yescharacteristic
878C4—22no—
879C4—22no—
880C4—22no—
881C4—22no—
882C4—42no—
883C4—42no—
884C4—4721no—
885C4—4721no—
886C4—4721no—
887C4—2362no—
888C4C2×D4×Dic5911yescharacteristic
889C4#1683787711yescharacteristic
890C4D4×C22⋊D5911yescharacteristic
891C4#1683804611yescharacteristic
892C2—24no—
893C2—42no—
894C2—44no—
895C2—82no—
896C2D4×C22⋊Dic5911yescharacteristic
897C2C2×#1683740311yescharacteristic
898C2#2143262211yescharacteristic
899C2#2143557711yescharacteristic
900C2#2143560211yescharacteristic
901C2#2143605711yescharacteristic
902C2#2143617711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
Fitting, prime radicalC2×C59×#546C2
socleC23×C59C22×D4
cosocleC22×C4×C59C24
hypercenterC2×#546D59
hypocenterC59#22419
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. C2×#16837474C2semidirect
2. C2×#16837403C2semidirect
3. C22×#14273648C2semidirect
4. D4×C4⋊Dic59C2semidirect
5. #21425029C2semidirect
6. #21424913C2semidirect
7. #21424535C2semidirect
8. #21424520C2semidirect
9. #21424414C2semidirect
10. #21424404C2semidirect
11. #21424096C2semidirect
12. #21424036C2semidirect
13. #21424027C2semidirect
14. #21423921C2semidirect
16. C22×#11745664C22semidirect
20. C22×C4⋊Dic59C22semidirect
22. C2×C4⋊(C59⋊C8)C22semidirect
24. C2×#14273651C22semidirect
25. C2×#14273651C22semidirect
26. C2×#14273651C22semidirect
27. C2×#14273651C22semidirect
38. C2×C22⋊(C59⋊C8)C22semidirect
39. C2×#14273638C22semidirect
43. #16837272C22semidirect
45. #16837262C22semidirect
46. C4×C4⋊Dic59C22semidirect
47. #16837164C22semidirect
48. #16837164C22semidirect
49. #16837164C22semidirect
50. #16837164C22semidirect
54. C59×#546C4semidirect
104. #14273648D4semidirect
117. C2×#41×C59C2×C4semidirect
127. C22×D4×C59C2×C4semidirect
136. #124×C59C2×C4semidirect
139. C22⋊Q8×C59C2×C4semidirect
142. #121×C59C2×C4semidirect
146. C4×D4×C59C2×C4semidirect
337. D4×C59C4×D4semidirect
419. C22×C59#417semidirect
472. #546Dic59semidirect
515. C59#22419semidirect
522. C2×#41C2×Dic59semidirect
532. C22×D4C2×Dic59semidirect
553. #124C2×Dic59semidirect
556. C22⋊Q8C2×Dic59semidirect
559. #121C2×Dic59semidirect
564. C4×D4C2×Dic59semidirect
789. D4D4×Dic59semidirect
870. C22#16837403semidirect

Maximal subgroups

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

subgroupindex
C2×#168374742
C2×#168374032
C22×#142736482
D4×C4⋊Dic592
#214250292
#214249132
#214245352
#214245202
#214244142
#214244042
#214240962
#214240362
#214240272
#214239212
C2×C59×#5462
#2241959