Finite Group Databasebeta

← #28625732

Subgroups — #28625732

Order 15104.

1678 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837636C211yesmaximal, characteristic, complemented
2C2×#16837633C211yesmaximal, characteristic, complemented
3C2×#16837547C211yesmaximal, characteristic, complemented
4C22×C22⋊(C59⋊C8)C211yesmaximal, characteristic, complemented
5#21432378C211yesmaximal, characteristic, complemented
6#21425296C211yesmaximal, characteristic, complemented
7#21425282C211yesmaximal, characteristic, complemented
8#21425097C211yesmaximal, characteristic, complemented
9#21425092C211yesmaximal, characteristic, complemented
10#21424525C211yesmaximal, characteristic, complemented
11#21424520C211yesmaximal, characteristic, complemented
12#21424418C211yesmaximal, characteristic, complemented
13#21424295C211yesmaximal, characteristic, complemented
14#21424036C211yesmaximal, characteristic, complemented
15C2×C59×#525C211yesmaximal, characteristic, complemented
16C22×#11745671C2211yescharacteristic, complemented
17C22×#11745669C2211yescharacteristic, complemented
18C23×C59⋊C8C2211yescharacteristic
19C23×C59⋊C8C2211yescharacteristic
20C2×#14273701C2211yescharacteristic
21C2×#14273701C2211yescharacteristic
22C2×#14273701C2211yescharacteristic
23C2×#14273696—21no—
24#16837636—24no—
25#16837633—24no—
26#16837547—24no—
27C2×#14273660C2211yescharacteristic, complemented
28C2×#14273658C2211yescharacteristic, complemented
29C2×#14273651C2211yescharacteristic, complemented
30C2×#14273651C2211yescharacteristic, complemented
31C2×#14273651C2211yescharacteristic, complemented
32C2×#14273648C2211yescharacteristic, complemented
33C2×#14273648C2211yescharacteristic, complemented
34C2×#14273648C2211yescharacteristic, complemented
35C2×#14273647C2211yescharacteristic, complemented
36C2×#14273647C2211yescharacteristic, complemented
37C2×C22⋊(C59⋊C8)—24no—
38C2×C22⋊(C59⋊C8)C2211yescharacteristic
39C2×C22⋊(C59⋊C8)C2211yescharacteristic
40C2×C22⋊(C59⋊C8)C2211yescharacteristic
41C2×C22⋊(C59⋊C8)C2211yescharacteristic
42#16837281—21no—
43#16837281—21no—
44#16837281—21no—
45#16837262C2211yescharacteristic
46#16837262C2211yescharacteristic
47#16837262C2211yescharacteristic
48#16837164C2211yescharacteristic, complemented
49#16837164C2211yescharacteristic, complemented
50#16837164C2211yescharacteristic, complemented
51#16837164C2211yescharacteristic, complemented
52C22×#41×C59C2211yescharacteristic
53C24×C4×C59C2211yescharacteristic
54C59×#525—24no—
55C59×#525—24no—
56C2×#123×C59—21no—
57C2×C22⋊Q8×C59C2211yescharacteristic
58C2×C22⋊Q8×C59C2211yescharacteristic
59C2×#121×C59C2211yescharacteristic
60C2×#121×C59C2211yescharacteristic
61C2×#120×C59—21no—
62C2×C4×D4×C59—21no—
63C2×C4×D4×C59—21no—
64C2×#117×C59C2211yescharacteristic
65C22×D236C2311yescharacteristic
66C22×C22⋊D59—21no—
67C22×C22⋊D59—21no—
68C22×C22⋊D59—21no—
69C2×#11745671—22no—
70C2×#11745671—22no—
71C2×#11745671—41no—
72C2×#11745669—22no—
73C2×#11745669—22no—
74C2×#11745669—41no—
75C22×C59⋊C8—22no—
76C22×C59⋊C8—22no—
77C22×C59⋊C8—22no—
78C22×C59⋊C8—22no—
79C22×C59⋊C8—41no—
80C22×C59⋊C8—41no—
81C22×C59⋊C8C2311yescharacteristic
82C22×C59⋊C8C2311yescharacteristic
83C22×C59⋊C8C2311yescharacteristic
84C22×C59⋊C8C2311yescharacteristic
85#14273701—22no—
86#14273701—22no—
87#14273701—22no—
88#14273701—22no—
89#14273701—41no—
90#14273701—41no—
91#14273696—44no—
92C2×C4⋊Dic59C2311yescharacteristic
93C2×C4⋊Dic59C2311yescharacteristic
94C2×C4⋊Dic59C2311yescharacteristic
95C2×C22⋊Dic59—21no—
96C2×C22⋊Dic59—21no—
97C2×C22⋊Dic59—21no—
98C2×(C2×D59)⋊C4—21no—
99C2×(C2×D59)⋊C4—21no—
100C2×(C2×D59)⋊C4—21no—
101#14273660—22no—
102#14273658—22no—
103#14273651—22no—
104#14273651—22no—
105#14273651—41no—
106#14273648—22no—
107#14273648—22no—
108#14273648—41no—
109#14273647—22no—
110#14273647—22no—
111C22⋊(C59⋊C8)—22no—
112C22⋊(C59⋊C8)—22no—
113C22⋊(C59⋊C8)—22no—
114C22⋊(C59⋊C8)D414yescomplemented
115C59⋊#95—21no—
116C59⋊#95—21no—
117C59⋊#95—21no—
118C25×C59D411yescharacteristic
119C2×#41×C59—22no—
120C2×#41×C59—22no—
121C2×#41×C59—22no—
122C2×#41×C59—22no—
123C2×#41×C59—41no—
124C2×#41×C59—41no—
125C22×Q8×C59C2311yescharacteristic
126C22×D4×C59—21no—
127C22×D4×C59—21no—
128C22×D4×C59—21no—
129C22×D4×C59C2311yescharacteristic
130C23×C4×C59—21no—
131C23×C4×C59—22no—
132C23×C4×C59—22no—
133C23×C4×C59—22no—
134C23×C4×C59—22no—
135C23×C4×C59—41no—
136C23×C4×C59—41no—
137C23×C4×C59D411yescharacteristic
138C23×C4×C59D411yescharacteristic
139C23×C4×C59D411yescharacteristic
140C23×C4×C59C2311yescharacteristic
141C23×C4×C59C2311yescharacteristic
142C23×C4×C59C2311yescharacteristic
143#123×C59—28no—
144C22⋊Q8×C59—22no—
145C22⋊Q8×C59—22no—
146C22⋊Q8×C59—22no—
147C22⋊Q8×C59D414yescomplemented
148#121×C59—22no—
149#121×C59—22no—
150#121×C59—22no—
151#121×C59D414yescomplemented
152#120×C59—28no—
153C4×D4×C59—28no—
154C4×D4×C59—28no—
155#117×C59—22no—
156#117×C59—22no—
157C2×C4⋊C4×C59—21no—
158C2×C4⋊C4×C59—21no—
159C2×C4⋊C4×C59C2311yescharacteristic
160C2×C4⋊C4×C59C2311yescharacteristic
161C2×C22⋊C4×C59—21no—
162C2×C22⋊C4×C59—21no—
163C2×C22⋊C4×C59—21no—
164C2×C22⋊C4×C59—21no—
165C2×C22⋊C4×C59—21no—
166C2×C42×C59—21no—
167C24×C59—22no—
168C24×C59—22no—
169C24×C59—22no—
170C24×C59—22no—
171C24×C59—22no—
172C24×C59—21no—
173C24×C59—41no—
174C24×C59—41no—
175C24×C59C2×D411yescharacteristic
176C24×C59C2×D411yescharacteristic
177C24×C59C2×D411yescharacteristic
178C23×D59—21no—
179#41×C59—44no—
180#41×C59—44no—
181#41×C59—44no—
182#41×C59—44no—
183C2×Q8×C59—21no—
184C2×Q8×C59—21no—
185C2×Q8×C59—21no—
186C2×Q8×C59—21no—
187C2×Q8×C59—21no—
188C2×Q8×C59C2×D412yes—
189C2×D4×C59—24no—
190C2×D4×C59—24no—
191C2×D4×C59—24no—
192C2×D4×C59—21no—
193C2×D4×C59—21no—
194C2×D4×C59—21no—
195C2×D4×C59—21no—
196C2×D4×C59—21no—
197C2×D4×C59—42no—
198C2×D4×C59—42no—
199C2×D4×C59—42no—
200C2×D4×C59—42no—
201C2×D4×C59—42no—
202C2×D4×C59—42no—
203C2×D4×C59C2×D412yes—
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—24no—
213C22×C4×C59—22no—
214C22×C4×C59—22no—
215C22×C4×C59—21no—
216C22×C4×C59—21no—
217C22×C4×C59—21no—
218C22×C4×C59—22no—
219C22×C4×C59—22no—
220C22×C4×C59—22no—
221C22×C4×C59—22no—
222C22×C4×C59—21no—
223C22×C4×C59—21no—
224C22×C4×C59—21no—
225C22×C4×C59—21no—
226C22×C4×C59—21no—
227C22×C4×C59—21no—
228C22×C4×C59—41no—
229C22×C4×C59—41no—
230C22×C4×C59—41no—
231C22×C4×C59—44no—
232C22×C4×C59—44no—
233C22×C4×C59—44no—
234C22×C4×C59—44no—
235C22×C4×C59—42no—
236C22×C4×C59—42no—
237C22×C4×C59C2×D411yescharacteristic
238C22×C4×C59C2×D411yescharacteristic
239C22×C4×C59C2×D412yes—
240C22×C4×C59C2×D412yes—
241C22×C4×C59C2×D411yescharacteristic
242C22×C4×C59C2×D412yes—
243C22×C4×C59#4112yes—
244C22×C4×C59C2411yescharacteristic
245C2×C22⋊D59—42no—
246C2×C22⋊D59—42no—
247C2×C22⋊D59—42no—
248C2×C22⋊D59—42no—
249C2×C22⋊D59—42no—
250C2×C22⋊D59—42no—
251C2×C22⋊D59—42no—
252C2×C22⋊D59—42no—
253C2×C22⋊D59—42no—
254C22×Dic59—21no—
255C22×Dic59—21no—
256C22×Dic59—21no—
257C2×D236—21no—
258C2×D236—21no—
259C2×D236—21no—
260C2×D236—21no—
261C2×D236—21no—
262C2×D236—21no—
263C4⋊C4×C59—24no—
264C4⋊C4×C59—24no—
265C4⋊C4×C59—21no—
266C4⋊C4×C59—21no—
267C4⋊C4×C59C2×D412yes—
268C4⋊C4×C59C2×D412yes—
269C22⋊C4×C59—24no—
270C22⋊C4×C59—24no—
271C22⋊C4×C59—24no—
272C22⋊C4×C59—24no—
273C22⋊C4×C59—24no—
274C42×C59—24no—
275C22⋊Dic59—42no—
276C22⋊Dic59—42no—
277C22⋊Dic59—42no—
278#11745671—44no—
279#11745669—44no—
280(C2×D59)⋊C4—42no—
281(C2×D59)⋊C4—42no—
282(C2×D59)⋊C4—42no—
283C4⋊Dic59—21no—
284C4⋊Dic59—21no—
285C4⋊Dic59—21no—
286C4⋊Dic59—21no—
287C4⋊Dic59—21no—
288C4⋊Dic59—21no—
289C2×C59⋊C8—21no—
290C2×C59⋊C8—21no—
291C2×C59⋊C8—21no—
292C2×C59⋊C8—21no—
293C2×C59⋊C8—21no—
294C2×C59⋊C8—21no—
295C2×C59⋊C8—21no—
296C2×C59⋊C8—21no—
297C2×C59⋊C8—21no—
298C2×C59⋊C8—21no—
299C2×C59⋊C8—44no—
300C2×C59⋊C8—44no—
301C2×C59⋊C8C2×D412yes—
302C2×C59⋊C8C2×D412yes—
303C23×C59—21no—
304C23×C59—21no—
305C23×C59—21no—
306C23×C59—21no—
307C23×C59—28no—
308C23×C59—21no—
309C23×C59—21no—
310C23×C59—21no—
311C23×C59—21no—
312C23×C59—21no—
313C23×C59—21no—
314C23×C59—21no—
315C23×C59—21no—
316C23×C59—21no—
317C23×C59—21no—
318C23×C59—21no—
319C23×C59—21no—
320C23×C59—22no—
321C23×C59—44no—
322C23×C59—44no—
323C23×C59—44no—
324C23×C59—44no—
325C23×C59—44no—
326C23×C59—44no—
327C23×C59—41no—
328C23×C59—41no—
329C23×C59—41no—
330C23×C59—41no—
331C23×C59—41no—
332C23×C59—41no—
333C23×C59#12012yes—
334C23×C59#12112yes—
335C23×C59#13512yes—
336C23×C59#13512yes—
337C23×C59AGL(1,ℤ/8)12yes—
338C23×C59C22×D411yescharacteristic
339C22×D59—41no—
340C22×D59—41no—
341C22×D59—41no—
342C22×D59—41no—
343C22×D59—41no—
344C22×D59—41no—
345C22×D59—41no—
346Q8×C59—22no—
347Q8×C59—22no—
348Q8×C59—41no—
349Q8×C59—41no—
350D4×C59—22no—
351D4×C59—22no—
352D4×C59—48no—
353D4×C59—48no—
354D4×C59—48no—
355D4×C59—41no—
356D4×C59—41no—
357C2×C4×C59—21no—
358C2×C4×C59—21no—
359C2×C4×C59—21no—
360C2×C4×C59—21no—
361C2×C4×C59—22no—
362C2×C4×C59—22no—
363C2×C4×C59—22no—
364C2×C4×C59—22no—
365C2×C4×C59—22no—
366C2×C4×C59—22no—
367C2×C4×C59—22no—
368C2×C4×C59—22no—
369C2×C4×C59—22no—
370C2×C4×C59—22no—
371C2×C4×C59—21no—
372C2×C4×C59—22no—
373C2×C4×C59—21no—
374C2×C4×C59—21no—
375C2×C4×C59—44no—
376C2×C4×C59—44no—
377C2×C4×C59—44no—
378C2×C4×C59—48no—
379C2×C4×C59—41no—
380C2×C4×C59—41no—
381C2×C4×C59—41no—
382C2×C4×C59—41no—
383C2×C4×C59—41no—
384C2×C4×C59—41no—
385C2×C4×C59—41no—
386C2×C4×C59—41no—
387C2×C4×C59—41no—
388C2×C4×C59—41no—
389C2×C4×C59#12012yes—
390C2×C4×C59#12112yes—
391C2×C4×C59C22×D411yescharacteristic
392C2×C4×C59C22×D411yescharacteristic
393C2×C4×C59C22×D411yescharacteristic
394C2×C4×C59C2×#4111yescharacteristic
395C2×C4×C59H(5,𝔽2)11yescharacteristic
396C2×C4×C59H(5,𝔽2)11yescharacteristic
397C22⋊D59—84no—
398C22⋊D59—84no—
399C22⋊D59—84no—
400C2×Dic59—41no—
401C2×Dic59—41no—
402C2×Dic59—41no—
403C2×Dic59—41no—
404C2×Dic59—41no—
405C2×Dic59—41no—
406C2×Dic59—41no—
407C2×Dic59—41no—
408C2×Dic59—41no—
409D236—41no—
410D236—41no—
411D236—41no—
412D236—41no—
413C59⋊C8—22no—
414C59⋊C8—22no—
415C59⋊C8—41no—
416C59⋊C8—41no—
417#24382—591nomaximal, Sylow
418C22×C59—22no—
419C22×C59—22no—
420C22×C59—22no—
421C22×C59—22no—
422C22×C59—22no—
423C22×C59—22no—
424C22×C59—22no—
425C22×C59—22no—
426C22×C59—22no—
427C22×C59—22no—
428C22×C59—22no—
429C22×C59—22no—
430C22×C59—416no—
431C22×C59—41no—
432C22×C59—41no—
433C22×C59—41no—
434C22×C59—41no—
435C22×C59—41no—
436C22×C59—41no—
437C22×C59—41no—
438C22×C59—41no—
439C22×C59—42no—
440C22×C59—42no—
441C22×C59—42no—
442C22×C59—81no—
443C22×C59—81no—
444C22×C59—81no—
445C22×C59—81no—
446C22×C59#44914yescomplemented
447C22×C59C2×#12011yescharacteristic
448C22×C59C2×#12111yescharacteristic
449C22×C59#53411yescharacteristic
450C22×C59C2×#13511yescharacteristic
451C22×C59C2×#13511yescharacteristic
452C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
453C22×C59#57511yescharacteristic
454C2×D59—81no—
455C2×D59—81no—
456C2×D59—81no—
457C2×D59—81no—
458C2×D59—81no—
459C2×D59—81no—
460C2×D59—81no—
461C4×C59—22no—
462C4×C59—22no—
463C4×C59—41no—
464C4×C59—42no—
465C4×C59—42no—
466C4×C59—42no—
467C4×C59D4211yescharacteristic
468C4×C59D4211yescharacteristic
469C4×C59#54611yescharacteristic
470C4×C59#54611yescharacteristic
471Dic59—81no—
472Dic59—81no—
473Dic59—81no—
474C2×#525D5911yescharacteristic, complemented
475C2×#466—591no—
476C2×#465—591no—
477C2×#449—591no—
478C22×C22⋊C8—591no—
479#2847—591no—
480#2036—591no—
481#2034—591no—
482#2000—591no—
483#1999—591no—
484#1893—591no—
485#1892—591no—
486#1875—591no—
487#1854—591no—
488#1788—591no—
489C2×C59—24no—
490C2×C59—42no—
491C2×C59—42no—
492C2×C59—82no—
493C2×C59#241011yescharacteristic
494C2×C59C2×#44911yescharacteristic
495C2×C59#300211yescharacteristic
496C2×C59#305011yescharacteristic
497C2×C59#305511yescharacteristic
498C2×C59#318811yescharacteristic
499C2×C59#319111yescharacteristic
500D59—161no—
501C22×#41C2×D5911yescharacteristic
502C24×C4C2×D5911yescharacteristic
503C22×SD16—591no—
504C22×D8—591no—
505C23×C8—591no—
506C23×C8—591no—
507#525—24no—
508#525—24no—
509C2×#123—21no—
510C2×C22⋊Q8C2×D5911yescharacteristic
511C2×C22⋊Q8C2×D5911yescharacteristic
512C2×#121—591no—
513C2×#121—591no—
514C2×#121—591no—
515C2×#121C2×D5911yescharacteristic
516C2×#121C2×D5911yescharacteristic
517C2×#120—21no—
518C2×#120—1181no—
519C2×C4×D4—21no—
520C2×C4×D4—21no—
521C2×#117C2×D5911yescharacteristic
522#466—1184no—
523#465—1184no—
524#449—1184no—
525C2×#107—591no—
526C2×#106—591no—
527C2×#103—591no—
528C2×#103—591no—
529C2×#103—591no—
530C2×#102—591no—
531C2×#102—591no—
532C2×#102—591no—
533C2×#102—591no—
534C2×#102—591no—
535C2×C22⋊C8—591no—
536C2×C22⋊C8—591no—
537C2×C22⋊C8—591no—
538C2×C22⋊C8—591no—
539C2×C22⋊C8—1184no—
540#386—1181no—
541#386—1181no—
542#386—1181no—
543#380—591no—
544#380—591no—
545#380—591no—
546#340—591no—
547#340—591no—
548#340—591no—
549#340—591no—
550C59#2438211yescharacteristic, complemented, Sylow
551C25C22⋊D5911yescharacteristic
552C2×#41—22no—
553C2×#41—22no—
554C2×#41—22no—
555C2×#41—22no—
556C2×#41—41no—
557C2×#41—41no—
558C22×Q8C22×D5911yescharacteristic
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4—591no—
563C22×D4—1181no—
564C22×D4—1181no—
565C22×D4—1181no—
566C22×D4C22×D5911yescharacteristic
567C23×C4—22no—
568C23×C4—22no—
569C23×C4—21no—
570C23×C4—22no—
571C23×C4—22no—
572C23×C4—41no—
573C23×C4—41no—
574C23×C4C22⋊D5911yescharacteristic
575C23×C4C22⋊D5911yescharacteristic
576C23×C4C22⋊D5911yescharacteristic
577C23×C4C22×D5911yescharacteristic
578C23×C4C22×D5911yescharacteristic
579C23×C4C22×D5911yescharacteristic
580C2×SD16—1182no—
581C2×SD16—1182no—
582C2×SD16—2361no—
583C2×D8—1182no—
584C2×D8—1182no—
585C2×D8—2361no—
586C22×C8—591no—
587C22×C8—591no—
588C22×C8—591no—
589C22×C8—591no—
590C22×C8—1182no—
591C22×C8—1182no—
592C22×C8—1182no—
593C22×C8—1182no—
594C22×C8—2361no—
595C22×C8—2361no—
596#123—28no—
597C22⋊Q8—22no—
598C22⋊Q8—22no—
599C22⋊Q8—22no—
600C22⋊Q8C22⋊D5914yescomplemented
601#121—22no—
602#121—22no—
603#121—22no—
604#121—1182no—
605#121—1182no—
606#121—1182no—
607#121—1182no—
608#121—2361no—
609#121—2361no—
610#121C22⋊D5914yescomplemented
611#120—28no—
612#120—2364no—
613C4×D4—28no—
614C4×D4—28no—
615#117—22no—
616#117—22no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—591no—
620C2×C4⋊C4—591no—
621C2×C4⋊C4—591no—
622C2×C4⋊C4C22×D5911yescharacteristic
623C2×C4⋊C4C22×D5911yescharacteristic
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—1181no—
630C2×C22⋊C4—1181no—
631C2×C22⋊C4—1181no—
632C2×C22⋊C4—1181no—
633C2×C22⋊C4—1181no—
634C2×C22⋊C4—1181no—
635C2×C42—21no—
636#107—1182no—
637#106—1182no—
638#103—1182no—
639#103—1182no—
640#103—2361no—
641#102—1182no—
642#102—1182no—
643#102—1182no—
644#102—1182no—
645#102—2361no—
646C22⋊C8—594no—
647C22⋊C8—1182no—
648C22⋊C8—1182no—
649C22⋊C8—1182no—
650#95—1181no—
651#95—1181no—
652#95—1181no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—21no—
659C24—41no—
660C24—41no—
661C24—1181no—
662C24C2×C22⋊D5911yescharacteristic
663C24C2×C22⋊D5911yescharacteristic
664C24C2×C22⋊D5911yescharacteristic
665#41—44no—
666#41—44no—
667#41—44no—
668#41—44no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8—21no—
672C2×Q8—21no—
673C2×Q8—21no—
674C2×Q8C2×C22⋊D5912yes—
675C2×D4—24no—
676C2×D4—24no—
677C2×D4—24no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—42no—
684C2×D4—42no—
685C2×D4—42no—
686C2×D4—42no—
687C2×D4—42no—
688C2×D4—42no—
689C2×D4—1181no—
690C2×D4—1181no—
691C2×D4—1181no—
692C2×D4—1181no—
693C2×D4—1181no—
694C2×D4—1181no—
695C2×D4—2362no—
696C2×D4—2362no—
697C2×D4—2362no—
698C2×D4—2362no—
699C2×D4—2362no—
700C2×D4—2362no—
701C2×D4—2362no—
702C2×D4—2362no—
703C2×D4—2362no—
704C2×D4C2×C22⋊D5912yes—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—24no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—41no—
730C22×C4—41no—
731C22×C4—41no—
732C22×C4—44no—
733C22×C4—44no—
734C22×C4—44no—
735C22×C4—44no—
736C22×C4—42no—
737C22×C4—42no—
738C22×C4—1181no—
739C22×C4—1181no—
740C22×C4—1181no—
741C22×C4D4×D5912yes—
742C22×C4#1174568712yes—
743C22×C4C2×C22⋊D5911yescharacteristic
744C22×C4C2×C22⋊D5911yescharacteristic
745C22×C4C2×C22⋊D5912yes—
746C22×C4C2×C22⋊D5912yes—
747C22×C4C2×C22⋊D5911yescharacteristic
748C22×C4C23×D5911yescharacteristic
749SD16—2364no—
750D8—2364no—
751C2×C8—592no—
752C2×C8—592no—
753C2×C8—1181no—
754C2×C8—1181no—
755C2×C8—1181no—
756C2×C8—1181no—
757C2×C8—1181no—
758C2×C8—1181no—
759C2×C8—1181no—
760C2×C8—1181no—
761C2×C8—1181no—
762C2×C8—1181no—
763C2×C8—2364no—
764C2×C8—2364no—
765C4⋊C4—24no—
766C4⋊C4—24no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—1181no—
770C4⋊C4—1181no—
771C4⋊C4—1181no—
772C4⋊C4—1181no—
773C4⋊C4—1181no—
774C4⋊C4—1181no—
775C4⋊C4C2×C22⋊D5912yes—
776C4⋊C4C2×C22⋊D5912yes—
777C22⋊C4—24no—
778C22⋊C4—24no—
779C22⋊C4—24no—
780C22⋊C4—24no—
781C22⋊C4—24no—
782C22⋊C4—2362no—
783C22⋊C4—2362no—
784C22⋊C4—2362no—
785C22⋊C4—2362no—
786C22⋊C4—2362no—
787C22⋊C4—2362no—
788C42—24no—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—28no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—21no—
802C23—21no—
803C23—21no—
804C23—21no—
805C23—21no—
806C23—22no—
807C23—44no—
808C23—44no—
809C23—44no—
810C23—44no—
811C23—44no—
812C23—44no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—2361no—
820C23—2361no—
821C23—2361no—
822C23—2361no—
823C23—2361no—
824C23—2361no—
825C23—2361no—
826C23#1427369612yes—
827C23#1427369912yes—
828C23#1427374712yes—
829C23#1427374712yes—
830C23#1427375212yes—
831C23C22×C22⋊D5911yescharacteristic
832Q8—22no—
833Q8—22no—
834Q8—41no—
835Q8—41no—
836D4—22no—
837D4—22no—
838D4—48no—
839D4—48no—
840D4—48no—
841D4—41no—
842D4—41no—
843D4—4724no—
844D4—4724no—
845D4—4724no—
846D4—2361no—
847D4—2361no—
848D4—2361no—
849D4—2361no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—21no—
865C2×C4—22no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—44no—
869C2×C4—44no—
870C2×C4—44no—
871C2×C4—48no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—2361no—
883C2×C4—2361no—
884C2×C4—2361no—
885C2×C4—2361no—
886C2×C4—2361no—
887C2×C4—2361no—
888C2×C4—2361no—
889C2×C4—2361no—
890C2×C4—2361no—
891C2×C4#1427369612yes—
892C2×C4#1427369912yes—
893C2×C4C2×D4×D5911yescharacteristic
894C2×C4C22×C22⋊D5911yescharacteristic
895C2×C4C22×C22⋊D5911yescharacteristic
896C2×C4C2×#1174568711yescharacteristic
897C2×C4#1427377211yescharacteristic
898C2×C4#1427377211yescharacteristic
899C8—1182no—
900C8—1182no—
901C8—2361no—
902C8—2361no—
903C22—22no—
904C22—22no—
905C22—22no—
906C22—22no—
907C22—22no—
908C22—22no—
909C22—22no—
910C22—22no—
911C22—22no—
912C22—22no—
913C22—22no—
914C22—22no—
915C22—416no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—4721no—
932C22—4721no—
933C22—4721no—
934C22—4721no—
935C22—4721no—
936C22—4721no—
937C22—4721no—
938C22#1683754714yescomplemented
939C22C2×#1427369611yescharacteristic
940C22C2×#1427369911yescharacteristic
941C22#1683796111yescharacteristic
942C22C2×#1427374711yescharacteristic
943C22C2×#1427374711yescharacteristic
944C22C2×#1427375211yescharacteristic
945C22#1683820011yescharacteristic
946C4—22no—
947C4—22no—
948C4—41no—
949C4—42no—
950C4—42no—
951C4—42no—
952C4—4721no—
953C4—4721no—
954C4—4721no—
955C4D4×C22⋊D5911yescharacteristic
956C4D4×C22⋊D5911yescharacteristic
957C4#1683804611yescharacteristic
958C4#1683804611yescharacteristic
959C2—24no—
960C2—42no—
961C2—42no—
962C2—82no—
963C2—9441no—
964C2#2142747011yescharacteristic
965C2C2×#1683754711yescharacteristic
966C2#2143331411yescharacteristic
967C2#2143367411yescharacteristic
968C2#2143371711yescharacteristic
969C2#2143485711yescharacteristic
970C2#2143488411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC2×C59×#525C2
socleC23×C59C22×D4
hypercenterC2×#525D59
hypocenterC59#24382
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C2×#16837636C2semidirect
2. C2×#16837633C2semidirect
3. C2×#16837547C2semidirect
4. C22×C22⋊(C59⋊C8)C2semidirect
5. #21432378C2semidirect
6. #21425296C2semidirect
7. #21425282C2semidirect
8. #21425097C2semidirect
9. #21425092C2semidirect
10. #21424525C2semidirect
11. #21424520C2semidirect
12. #21424418C2semidirect
13. #21424295C2semidirect
14. #21424036C2semidirect
15. C2×C59×#525C2semidirect
16. C22×#11745671C22semidirect
17. C22×#11745669C22semidirect
27. C2×#14273660C22semidirect
28. C2×#14273658C22semidirect
29. C2×#14273651C22semidirect
30. C2×#14273651C22semidirect
31. C2×#14273651C22semidirect
32. C2×#14273648C22semidirect
33. C2×#14273648C22semidirect
34. C2×#14273648C22semidirect
35. C2×#14273647C22semidirect
36. C2×#14273647C22semidirect
48. #16837164C22semidirect
49. #16837164C22semidirect
50. #16837164C22semidirect
51. #16837164C22semidirect
114. C22⋊(C59⋊C8)D4semidirect
147. C22⋊Q8×C59D4semidirect
151. #121×C59D4semidirect
446. C22×C59#449semidirect
474. C2×#525D59semidirect
550. C59#24382semidirect
600. C22⋊Q8C22⋊D59semidirect
610. #121C22⋊D59semidirect
938. C22#16837547semidirect

Maximal subgroups

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

subgroupindex
C2×#168376362
C2×#168376332
C2×#168375472
C22×C22⋊(C59⋊C8)2
#214323782
#214252962
#214252822
#214250972
#214250922
#214245252
#214245202
#214244182
#214242952
#214240362
C2×C59×#5252
#2438259