Finite Group Databasebeta

← #28604244

Subgroups — #28604244

Order 15104.

1598 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837474C211yesmaximal, characteristic, complemented
2C2×#16837407C211yesmaximal, characteristic, complemented
3C2×#16837398C211yesmaximal, characteristic, complemented
4#21427045C211yesmaximal, characteristic, complemented
5#21425029C211yesmaximal, characteristic, complemented
6#21424913C211yesmaximal, characteristic, complemented
7#21424530C211yesmaximal, characteristic, complemented
8#21424525C211yesmaximal, characteristic, complemented
9#21424419C211yesmaximal, characteristic, complemented
10#21424409C211yesmaximal, characteristic, complemented
11#21424096C211yesmaximal, characteristic, complemented
12#21424036C211yesmaximal, characteristic, complemented
13#21424027C211yesmaximal, characteristic, complemented
14#21423921C211yesmaximal, characteristic, complemented
15C2×C59×#546C211yesmaximal, characteristic
16C22×#11745664C2211yescharacteristic
17C23×C59⋊C8C2211yescharacteristic, complemented
18C2×#14273686C2211yescharacteristic
19C2×#14273686C2211yescharacteristic, complemented
20#16837474—24no—
21C2×C4⋊(C59⋊C8)C2211yescharacteristic, complemented
22#16837407—24no—
23#16837398—24no—
24C2×#14273651C2211yescharacteristic, complemented
25C2×#14273651C2211yescharacteristic, complemented
26C2×#14273651C2211yescharacteristic, complemented
27C2×#14273651C2211yescharacteristic, complemented
28C2×#14273648C2211yescharacteristic
29C2×#14273648C2211yescharacteristic
30C2×#14273648C2211yescharacteristic
31C2×#14273648C2211yescharacteristic
32C2×#14273648C2211yescharacteristic
33C2×#14273648C2211yescharacteristic
34C2×#14273648C2211yescharacteristic
35C2×#14273648C2211yescharacteristic
36C2×C22⋊(C59⋊C8)C2211yescharacteristic
37C2×C22⋊(C59⋊C8)C2211yescharacteristic, complemented
38C2×#14273638C2211yescharacteristic, complemented
39#16837305—21no—
40#16837295—21no—
41#16837295—21no—
42#16837272C2211yescharacteristic, complemented
43#16837262C2211yescharacteristic
44#16837262C2211yescharacteristic, complemented
45C4⋊C4×Dic59—21no—
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—
64C2×#11745664—22no—
65C2×#11745664—22no—
66C2×#11745664—41no—
67C22×C59⋊C8—22no—
68C22×C59⋊C8—22no—
69C22×C59⋊C8—41no—
70C22×C59⋊C8C2311yescharacteristic
71C22×C59⋊C8C2311yescharacteristic
72C22×C59⋊C8C2311yescharacteristic
73C22×C59⋊C8C2311yescharacteristic
74#14273686—22no—
75#14273686—22no—
76#14273686—41no—
77#14273686—41no—
78C2×C4⋊Dic59—21no—
79C2×C4⋊Dic59—21no—
80C2×C4⋊Dic59C2311yescharacteristic
81C2×C4⋊Dic59C2311yescharacteristic
82C2×C4⋊Dic59C2311yescharacteristic
83C2×C4⋊Dic59C2311yescharacteristic
84C2×C22⋊Dic59—21no—
85C2×C22⋊Dic59—21no—
86C2×C22⋊Dic59—21no—
87C2×C22⋊Dic59—21no—
88C2×C4×Dic59—21no—
89C2×C4×Dic59—21no—
90C2×C4×Dic59—21no—
91C4⋊(C59⋊C8)—22no—
92#14273651—22no—
93#14273651—22no—
94#14273651—41no—
95#14273651—41no—
96#14273648—22no—
97#14273648—22no—
98#14273648—22no—
99#14273648—22no—
100#14273648—22no—
101#14273648—41no—
102#14273648—41no—
103#14273648D414yescomplemented
104C22⋊(C59⋊C8)—22no—
105C22⋊(C59⋊C8)—22no—
106#14273638—22no—
107C59⋊#95—21no—
108C59⋊#95—21no—
109C59⋊#95—21no—
110C25×C59—21no—
111C2×#41×C59—22no—
112C2×#41×C59—22no—
113C2×#41×C59—22no—
114C2×#41×C59—41no—
115C2×#41×C59—41no—
116C2×#41×C59C2×C414yes—
117C22×Q8×C59C2311yescharacteristic
118C22×D4×C59—22no—
119C22×D4×C59—22no—
120C22×D4×C59—21no—
121C22×D4×C59—21no—
122C22×D4×C59—21no—
123C22×D4×C59—22no—
124C22×D4×C59—41no—
125C22×D4×C59—41no—
126C22×D4×C59C2×C414yes—
127C22×D4×C59D411yescharacteristic
128C22×D4×C59C2311yescharacteristic
129C22×D4×C59C2311yescharacteristic
130C23×C4×C59—21no—
131C23×C4×C59—21no—
132C23×C4×C59C2311yescharacteristic
133C23×C4×C59C2311yescharacteristic
134#124×C59—22no—
135#124×C59C2×C414yes—
136#123×C59—28no—
137C22⋊Q8×C59—22no—
138C22⋊Q8×C59C2×C414yes—
139#121×C59—22no—
140#121×C59—28no—
141#121×C59C2×C414yes—
142#120×C59—28no—
143C4×D4×C59—22no—
144C4×D4×C59C2×C414yes—
145C4×D4×C59C2×C414yes—
146C4×D4×C59D414yes—
147C2×C4⋊C4×C59—21no—
148C2×C4⋊C4×C59D411yescharacteristic
149C2×C4⋊C4×C59C2311yescharacteristic
150C2×C22⋊C4×C59—21no—
151C2×C22⋊C4×C59—21no—
152C2×C22⋊C4×C59—21no—
153C2×C22⋊C4×C59—21no—
154C2×C22⋊C4×C59—21no—
155C2×C22⋊C4×C59—28no—
156C2×C22⋊C4×C59D411yescharacteristic
157C2×C22⋊C4×C59D411yescharacteristic
158C2×C42×C59C2311yescharacteristic
159C24×C59—21no—
160C24×C59—21no—
161C24×C59—24no—
162C24×C59—42no—
163C24×C59—42no—
164C24×C59—42no—
165C24×C59—42no—
166C24×C59—81no—
167C24×C59—81no—
168C24×C59C2×D411yescharacteristic
169C24×C59C2×D411yescharacteristic
170#41×C59—28no—
171#41×C59—44no—
172#41×C59—44no—
173#41×C59—44no—
174C2×Q8×C59—21no—
175C2×Q8×C59—21no—
176C2×Q8×C59—21no—
177C2×Q8×C59—21no—
178C2×Q8×C59—21no—
179C2×Q8×C59C22×C412yes—
180C2×D4×C59—28no—
181C2×D4×C59—24no—
182C2×D4×C59—24no—
183C2×D4×C59—24no—
184C2×D4×C59—21no—
185C2×D4×C59—21no—
186C2×D4×C59—21no—
187C2×D4×C59—21no—
188C2×D4×C59—21no—
189C2×D4×C59—21no—
190C2×D4×C59—21no—
191C2×D4×C59—21no—
192C2×D4×C59—44no—
193C2×D4×C59—44no—
194C2×D4×C59—44no—
195C2×D4×C59—41no—
196C2×D4×C59—41no—
197C2×D4×C59—42no—
198C2×D4×C59—42no—
199C2×D4×C59—42no—
200C2×D4×C59—42no—
201C2×D4×C59—81no—
202C2×D4×C59—81no—
203C2×D4×C59C22⋊C414yes—
204C2×D4×C59C22×C412yes—
205C2×D4×C59C22×C412yes—
206C2×D4×C59C2×D412yes—
207C2×D4×C59#4112yes—
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—21no—
218C22×C4×C59—24no—
219C22×C4×C59—24no—
220C22×C4×C59—42no—
221C22×C4×C59—42no—
222C22×C4×C59—81no—
223C22×C4×C59—81no—
224C22×C4×C59C22×C412yes—
225C22×C4×C59C22×C412yes—
226C22×C4×C59C2×D411yescharacteristic
227C22×C4×C59C2×D411yescharacteristic
228C22×C4×C59C2×D411yescharacteristic
229C22×C4×C59C2×D411yescharacteristic
230C22×C4×C59C2×D412yes—
231C22×C4×C59C2×D412yes—
232C22×C4×C59C2411yescharacteristic
233C22×Dic59—21no—
234C22×Dic59—21no—
235C22×Dic59—21no—
236C22×Dic59—21no—
237C4⋊C4×C59—24no—
238C4⋊C4×C59—21no—
239C4⋊C4×C59C22⋊C414yes—
240C4⋊C4×C59C22×C412yes—
241C22⋊C4×C59—24no—
242C22⋊C4×C59—24no—
243C22⋊C4×C59—24no—
244C22⋊C4×C59—24no—
245C22⋊C4×C59—24no—
246C22⋊C4×C59C22⋊C414yes—
247C22⋊C4×C59C22⋊C414yes—
248C42×C59C22×C412yes—
249C42×C59C2×D412yes—
250C22⋊Dic59—42no—
251C22⋊Dic59—42no—
252C22⋊Dic59—81no—
253C22⋊Dic59—81no—
254C4⋊Dic59—21no—
255C4⋊Dic59—21no—
256C4⋊Dic59—21no—
257C4⋊Dic59—21no—
258C4⋊Dic59—21no—
259C4⋊Dic59—21no—
260C4⋊Dic59—21no—
261C4⋊Dic59—42no—
262C4⋊Dic59—81no—
263C4⋊Dic59C2×D412yes—
264C4×Dic59—42no—
265C4×Dic59—42no—
266C4×Dic59—42no—
267#11745664—44no—
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—21no—
276C2×C59⋊C8—21no—
277C2×C59⋊C8—21no—
278C2×C59⋊C8—21no—
279C2×C59⋊C8—44no—
280C2×C59⋊C8C2×D412yes—
281C23×C59—22no—
282C23×C59—21no—
283C23×C59—21no—
284C23×C59—22no—
285C23×C59—21no—
286C23×C59—21no—
287C23×C59—22no—
288C23×C59—21no—
289C23×C59—21no—
290C23×C59—21no—
291C23×C59—21no—
292C23×C59—21no—
293C23×C59—21no—
294C23×C59—21no—
295C23×C59—21no—
296C23×C59—22no—
297C23×C59—48no—
298C23×C59—48no—
299C23×C59—41no—
300C23×C59—41no—
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—84no—
310C23×C59—84no—
311C23×C59—84no—
312C23×C59—84no—
313C23×C59—84no—
314C23×C59C2×C22⋊C412yes—
315C23×C59C2×C22⋊C412yes—
316C23×C59C22×D411yescharacteristic
317Q8×C59—22no—
318Q8×C59—22no—
319Q8×C59—41no—
320Q8×C59—41no—
321D4×C59—22no—
322D4×C59—22no—
323D4×C59—22no—
324D4×C59—22no—
325D4×C59—22no—
326D4×C59—44no—
327D4×C59—48no—
328D4×C59—48no—
329D4×C59—41no—
330D4×C59—41no—
331D4×C59—84no—
332D4×C59C4×D414yes—
333C2×C4×C59—21no—
334C2×C4×C59—21no—
335C2×C4×C59—21no—
336C2×C4×C59—21no—
337C2×C4×C59—21no—
338C2×C4×C59—21no—
339C2×C4×C59—21no—
340C2×C4×C59—21no—
341C2×C4×C59—22no—
342C2×C4×C59—22no—
343C2×C4×C59—22no—
344C2×C4×C59—22no—
345C2×C4×C59—22no—
346C2×C4×C59—22no—
347C2×C4×C59—22no—
348C2×C4×C59—22no—
349C2×C4×C59—22no—
350C2×C4×C59—22no—
351C2×C4×C59—48no—
352C2×C4×C59—41no—
353C2×C4×C59—41no—
354C2×C4×C59—41no—
355C2×C4×C59—41no—
356C2×C4×C59—84no—
357C2×C4×C59C2×C22⋊C412yes—
358C2×C4×C59C2×C22⋊C412yes—
359C2×C4×C59C2×C22⋊C412yes—
360C2×C4×C59C2×C22⋊C412yes—
361C2×C4×C59C23×C411yescharacteristic
362C2×C4×C59C22×D411yescharacteristic
363C2×C4×C59C22×D411yescharacteristic
364C2×C4×C59C2×#4111yescharacteristic
365C2×C4×C59H(5,𝔽2)11yescharacteristic
366C2×C4×C59H(5,𝔽2)11yescharacteristic
367C2×Dic59—22no—
368C2×Dic59—41no—
369C2×Dic59—41no—
370C2×Dic59—41no—
371C2×Dic59—41no—
372C2×Dic59—41no—
373C2×Dic59—41no—
374C2×Dic59—41no—
375C2×Dic59—41no—
376C2×Dic59—41no—
377C2×Dic59—41no—
378C2×Dic59—41no—
379C59⋊C8—22no—
380C59⋊C8—41no—
381C59⋊C8—41no—
382C59⋊C8—41no—
383#22424—591nomaximal, Sylow
384C22×C59—22no—
385C22×C59—22no—
386C22×C59—24no—
387C22×C59—22no—
388C22×C59—22no—
389C22×C59—22no—
390C22×C59—22no—
391C22×C59—42no—
392C22×C59—42no—
393C22×C59—41no—
394C22×C59—41no—
395C22×C59—42no—
396C22×C59—41no—
397C22×C59—41no—
398C22×C59—42no—
399C22×C59—41no—
400C22×C59—41no—
401C22×C59—42no—
402C22×C59—41no—
403C22×C59—41no—
404C22×C59—42no—
405C22×C59—42no—
406C22×C59—42no—
407C22×C59—42no—
408C22×C59—816no—
409C22×C59—81no—
410C22×C59—81no—
411C22×C59—81no—
412C22×C59—81no—
413C22×C59C22×C22⋊C411yescharacteristic
414C22×C59D4211yescharacteristic
415C22×C59#54611yescharacteristic
416C22×C59#57511yescharacteristic
417C22×C59#57511yescharacteristic
418C22×C59#57611yescharacteristic
419C22×C59#57711yescharacteristic
420C4×C59—22no—
421C4×C59—22no—
422C4×C59—22no—
423C4×C59—22no—
424C4×C59—42no—
425C4×C59—42no—
426C4×C59C2×C4×D411yescharacteristic
427C4×C59#51811yescharacteristic
428C4×C59D4211yescharacteristic
429C4×C59#54611yescharacteristic
430Dic59—42no—
431Dic59—81no—
432Dic59—81no—
433Dic59—81no—
434C2×#546D5911yescharacteristic
435C2×#435—591no—
436C2×#418—591no—
437C2×#416—591no—
438#2354—591no—
439#1983—591no—
440#1959—591no—
441#1894—591no—
442#1893—591no—
443#1875—591no—
444#1873—591no—
445#1802—591no—
446#1788—591no—
447#1786—591no—
448#1762—591no—
449C2×C59—42no—
450C2×C59—42no—
451C2×C59—44no—
452C2×C59—82no—
453C2×C59D4×C22⋊C411yescharacteristic
454C2×C59#289611yescharacteristic
455C2×C59#289711yescharacteristic
456C2×C59#326711yescharacteristic
457C2×C59#326811yescharacteristic
458C2×C59#331111yescharacteristic
459C2×C59#331911yescharacteristic
460C22×#41C2×D5911yescharacteristic
461C23×D4C2×D5911yescharacteristic
462C22×M16—591no—
463C23×C8—591no—
464#546—24no—
465#546Dic5918yescomplemented
466C2×#124C2×D5911yescharacteristic
467C2×#123—21no—
468C2×C22⋊Q8C2×D5911yescharacteristic
469C2×#121—21no—
470C2×#121C2×D5911yescharacteristic
471C2×#120—21no—
472C2×C4×D4C2×D5911yescharacteristic
473C2×C4×D4C2×D5911yescharacteristic
474C2×#117—591no—
475C2×#117—591no—
476C22×C22⋊C4—21no—
477#435—1184no—
478C2×C4⋊C8—591no—
479#418—1184no—
480#416—1184no—
481C2×#103—591no—
482C2×#103—591no—
483C2×#103—591no—
484C2×#103—591no—
485C2×#102—591no—
486C2×#102—591no—
487C2×#102—591no—
488C2×#102—591no—
489C2×#102—591no—
490C2×#102—591no—
491C2×#102—591no—
492C2×#102—591no—
493C2×C22⋊C8—591no—
494C2×C22⋊C8—591no—
495C2×#97—591no—
496#390—1181no—
497#388—1181no—
498#388—1181no—
499#384—591no—
500#380—591no—
501#380—591no—
502C4×C4⋊C4—591no—
503C4×C4⋊C4—1181no—
504#340—591no—
505#340—591no—
506#340—591no—
507#340—591no—
508C59#2242411yescharacteristic, complemented, Sylow
509C25—21no—
510C2×#41—22no—
511C2×#41—22no—
512C2×#41—22no—
513C2×#41—41no—
514C2×#41—41no—
515C2×#41C2×Dic5914yes—
516C22×Q8C22×D5911yescharacteristic
517C22×D4—22no—
518C22×D4—22no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—22no—
523C22×D4—41no—
524C22×D4—41no—
525C22×D4C2×Dic5914yes—
526C22×D4C22⋊D5911yescharacteristic
527C22×D4C22×D5911yescharacteristic
528C22×D4C22×D5911yescharacteristic
529C23×C4—21no—
530C23×C4—21no—
531C23×C4C22×D5911yescharacteristic
532C23×C4C22×D5911yescharacteristic
533C2×M16—1182no—
534C2×M16—1182no—
535C2×M16—2361no—
536C22×C8—591no—
537C22×C8—591no—
538C22×C8—591no—
539C22×C8—591no—
540C22×C8—1182no—
541C22×C8—1182no—
542C22×C8—2361no—
543#124—22no—
544#124C2×Dic5914yes—
545#123—28no—
546C22⋊Q8—22no—
547C22⋊Q8C2×Dic5914yes—
548#121—22no—
549#121—28no—
550#121C2×Dic5914yes—
551#120—28no—
552C4×D4—22no—
553C4×D4C2×Dic5914yes—
554C4×D4C2×Dic5914yes—
555C4×D4C22⋊D5914yes—
556#117—1182no—
557#117—1182no—
558#117—2361no—
559#117—2361no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—591no—
562C2×C4⋊C4—591no—
563C2×C4⋊C4—591no—
564C2×C4⋊C4—591no—
565C2×C4⋊C4—1181no—
566C2×C4⋊C4—1181no—
567C2×C4⋊C4C22⋊D5911yescharacteristic
568C2×C4⋊C4C22×D5911yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—28no—
575C2×C22⋊C4—1181no—
576C2×C22⋊C4—1181no—
577C2×C22⋊C4—1181no—
578C2×C22⋊C4—1181no—
579C2×C22⋊C4C22⋊D5911yescharacteristic
580C2×C22⋊C4C22⋊D5911yescharacteristic
581C2×C42—1181no—
582C2×C42—1181no—
583C2×C42—1181no—
584C2×C42C22×D5911yescharacteristic
585C4⋊C8—1182no—
586#103—1182no—
587#103—1182no—
588#103—2361no—
589#103—2361no—
590#102—594no—
591#102—1182no—
592#102—1182no—
593#102—1182no—
594#102—1182no—
595#102—1182no—
596#102—2361no—
597#102—2361no—
598C22⋊C8—1182no—
599C22⋊C8—1182no—
600#97—1182no—
601#95—1181no—
602#95—1181no—
603#95—1181no—
604C24—21no—
605C24—21no—
606C24—24no—
607C24—42no—
608C24—42no—
609C24—42no—
610C24—42no—
611C24—81no—
612C24—81no—
613C24C2×C22⋊D5911yescharacteristic
614C24C2×C22⋊D5911yescharacteristic
615#41—28no—
616#41—44no—
617#41—44no—
618#41—44no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8C22×Dic5912yes—
625C2×D4—28no—
626C2×D4—24no—
627C2×D4—24no—
628C2×D4—24no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—44no—
638C2×D4—44no—
639C2×D4—44no—
640C2×D4—41no—
641C2×D4—41no—
642C2×D4—42no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—81no—
647C2×D4—81no—
648C2×D4C22⋊Dic5914yes—
649C2×D4D4×D5912yes—
650C2×D4#1174568712yes—
651C2×D4C22×Dic5912yes—
652C2×D4C22×Dic5912yes—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—24no—
664C22×C4—24no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—81no—
668C22×C4—81no—
669C22×C4—1181no—
670C22×C4—1181no—
671C22×C4—1181no—
672C22×C4—1181no—
673C22×C4C22×Dic5912yes—
674C22×C4C22×Dic5912yes—
675C22×C4C2×C22⋊D5911yescharacteristic
676C22×C4C2×C22⋊D5911yescharacteristic
677C22×C4C2×C22⋊D5911yescharacteristic
678C22×C4C2×C22⋊D5911yescharacteristic
679C22×C4C2×C22⋊D5912yes—
680C22×C4C2×C22⋊D5912yes—
681C22×C4C23×D5911yescharacteristic
682M16—2364no—
683C2×C8—592no—
684C2×C8—1181no—
685C2×C8—1181no—
686C2×C8—1181no—
687C2×C8—1181no—
688C2×C8—1181no—
689C2×C8—1181no—
690C2×C8—1181no—
691C2×C8—1181no—
692C2×C8—1181no—
693C2×C8—1181no—
694C2×C8—1181no—
695C2×C8—2364no—
696C4⋊C4—24no—
697C4⋊C4—21no—
698C4⋊C4—592no—
699C4⋊C4—1181no—
700C4⋊C4—1181no—
701C4⋊C4—1181no—
702C4⋊C4—1181no—
703C4⋊C4—1181no—
704C4⋊C4—1181no—
705C4⋊C4—1181no—
706C4⋊C4—4721no—
707C4⋊C4—2362no—
708C4⋊C4C22⋊Dic5914yes—
709C4⋊C4C22×Dic5912yes—
710C22⋊C4—24no—
711C22⋊C4—24no—
712C22⋊C4—24no—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—4721no—
716C22⋊C4—4721no—
717C22⋊C4—2362no—
718C22⋊C4—2362no—
719C22⋊C4C22⋊Dic5914yes—
720C22⋊C4C22⋊Dic5914yes—
721C42—2362no—
722C42—2362no—
723C42—2362no—
724C42C22×Dic5912yes—
725C42C2×C22⋊D5912yes—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—22no—
737C23—21no—
738C23—21no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—48no—
743C23—48no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—84no—
755C23—84no—
756C23—84no—
757C23—84no—
758C23—84no—
759C23C2×C22⋊Dic5912yes—
760C23C2×C22⋊Dic5912yes—
761C23C22×C22⋊D5911yescharacteristic
762Q8—22no—
763Q8—22no—
764Q8—41no—
765Q8—41no—
766D4—22no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—44no—
772D4—48no—
773D4—48no—
774D4—41no—
775D4—41no—
776D4—84no—
777D4D4×Dic5914yes—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—48no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—84no—
802C2×C4—1182no—
803C2×C4—2361no—
804C2×C4—2361no—
805C2×C4—2361no—
806C2×C4—2361no—
807C2×C4—2361no—
808C2×C4—2361no—
809C2×C4—2361no—
810C2×C4—2361no—
811C2×C4—2361no—
812C2×C4—2361no—
813C2×C4—2361no—
814C2×C4C2×C22⋊Dic5912yes—
815C2×C4C2×C22⋊Dic5912yes—
816C2×C4C2×C22⋊Dic5912yes—
817C2×C4C2×C22⋊Dic5912yes—
818C2×C4C23×Dic5911yescharacteristic
819C2×C4C2×D4×D5911yescharacteristic
820C2×C4C22×C22⋊D5911yescharacteristic
821C2×C4C2×#1174568711yescharacteristic
822C2×C4#1427377211yescharacteristic
823C2×C4#1427377211yescharacteristic
824C8—1182no—
825C8—2361no—
826C8—2361no—
827C8—2361no—
828C22—22no—
829C22—22no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—24no—
835C22—42no—
836C22—42no—
837C22—41no—
838C22—41no—
839C22—42no—
840C22—41no—
841C22—41no—
842C22—42no—
843C22—41no—
844C22—41no—
845C22—42no—
846C22—41no—
847C22—41no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—816no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22C22×C22⋊Dic5911yescharacteristic
858C22D4×C22⋊D5911yescharacteristic
859C22#1683804611yescharacteristic
860C22#1683820011yescharacteristic
861C22#1683820011yescharacteristic
862C22#1683820511yescharacteristic
863C22#1683821311yescharacteristic
864C4—22no—
865C4—22no—
866C4—22no—
867C4—22no—
868C4—42no—
869C4—42no—
870C4—4721no—
871C4—4721no—
872C4—4721no—
873C4—2362no—
874C4C2×D4×Dic5911yescharacteristic
875C4#1683787711yescharacteristic
876C4D4×C22⋊D5911yescharacteristic
877C4#1683804611yescharacteristic
878C2—42no—
879C2—42no—
880C2—44no—
881C2—82no—
882C2D4×C22⋊Dic5911yescharacteristic
883C2#2143261511yescharacteristic
884C2#2143262211yescharacteristic
885C2#2143561711yescharacteristic
886C2#2143563211yescharacteristic
887C2#2143613211yescharacteristic
888C2#2143625211yescharacteristic
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#22424
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×#16837407C2semidirect
3. C2×#16837398C2semidirect
4. #21427045C2semidirect
5. #21425029C2semidirect
6. #21424913C2semidirect
7. #21424530C2semidirect
8. #21424525C2semidirect
9. #21424419C2semidirect
10. #21424409C2semidirect
11. #21424096C2semidirect
12. #21424036C2semidirect
13. #21424027C2semidirect
14. #21423921C2semidirect
17. C23×C59⋊C8C22semidirect
19. C2×#14273686C22semidirect
21. C2×C4⋊(C59⋊C8)C22semidirect
24. C2×#14273651C22semidirect
25. C2×#14273651C22semidirect
26. C2×#14273651C22semidirect
27. C2×#14273651C22semidirect
37. C2×C22⋊(C59⋊C8)C22semidirect
38. C2×#14273638C22semidirect
42. #16837272C22semidirect
44. #16837262C22semidirect
46. C4×C4⋊Dic59C22semidirect
47. #16837164C22semidirect
48. #16837164C22semidirect
49. #16837164C22semidirect
50. #16837164C22semidirect
54. C59×#546C4semidirect
103. #14273648D4semidirect
465. #546Dic59semidirect
508. C59#22424semidirect

Maximal subgroups

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

subgroupindex
C2×#168374742
C2×#168374072
C2×#168373982
#214270452
#214250292
#214249132
#214245302
#214245252
#214244192
#214244092
#214240962
#214240362
#214240272
#214239212
C2×C59×#5462
#2242459