Finite Group Databasebeta

← #29453866

Subgroups — #29453866

Order 15104.

1908 conjugacy classes of subgroups.

The subgroup lattice has 1166 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21437388C211yesmaximal, characteristic
2#21433253C212yesmaximal, complemented
3#21433249C212yesmaximal, complemented
4#21433242C212yesmaximal, complemented
5#21433238C212yesmaximal, complemented
6#21433224C212yesmaximal, complemented
7#21433216C212yesmaximal, complemented
8#21433208C212yesmaximal, complemented
9#21433203C212yesmaximal, complemented
10#21433029C211yesmaximal, characteristic, complemented
11#21433028C211yesmaximal, characteristic, complemented
12#21432823C211yesmaximal, characteristic, complemented
13#21432821C211yesmaximal, characteristic, complemented
14#21432817C211yesmaximal, characteristic, complemented
15#21432806C211yesmaximal, characteristic, complemented
16#21432804C211yesmaximal, characteristic, complemented
17#21432760C211yesmaximal, characteristic, complemented
18#21432758C211yesmaximal, characteristic, complemented
19C2×#16837452C211yesmaximal, characteristic, complemented
20#21432663C211yesmaximal, characteristic, complemented
21#21432662C211yesmaximal, characteristic, complemented
22C2×#16837425C211yesmaximal, characteristic, complemented
23C59×#2933C211yesmaximal, characteristic, complemented
24C2×#14273735C2211yescharacteristic
25C2×#14273734C2211yescharacteristic
26C2×#14273733C2211yescharacteristic
27C22×#11745664C2211yescharacteristic
28#16837955C2211yescharacteristic
29#16837954C411yescharacteristic
30#16837954C411yescharacteristic
31#16837948C2211yescharacteristic
32#16837947C411yescharacteristic
33#16837947C411yescharacteristic
34#16837938C411yescharacteristic
35#16837938C411yescharacteristic
36#16837933C411yescharacteristic
37#16837933C411yescharacteristic
38#16837932C2212yes—
39#16837932C2212yes—
40#16837929C412yes—
41#16837929C412yes—
42#16837913C2211yescharacteristic
43#16837908C412yes—
44#16837908C412yes—
45#41×Dic59C2211yescharacteristic
46#16837870C2211yescharacteristic
47C4×#11745687C2212yes—
48C4×#11745687C2212yes—
49C22×C4×Dic59C2211yescharacteristic
50#16837531C2212yescomplemented
51#16837531C2212yescomplemented
52#16837530C2212yescomplemented
53#16837530C2212yescomplemented
54C8×Dic118C2212yescomplemented
55C8×Dic118C2212yescomplemented
56#16837526C2212yescomplemented
57#16837526C2212yescomplemented
58#16837480C2212yes—
59#16837478C2212yes—
60#16837478C2212yescomplemented
61#16837478C2212yescomplemented
62#16837477C2212yes—
63#16837477C2212yescomplemented
64#16837477C2212yescomplemented
65#16837476C2212yes—
66#16837474C2212yes—
67#16837474C2212yes—
68#16837473C2212yes—
69#16837471C2212yes—
70#16837470C2212yes—
71D4×C59⋊C8C2212yes—
72C8×C22⋊D59C2212yes—
73C8×C22⋊D59C2212yescomplemented
74C8×C22⋊D59C2212yescomplemented
75(C22⋊D59)⋊C8C2212yes—
76(C22⋊D59)⋊C8C2212yescomplemented
77(C22⋊D59)⋊C8C2212yescomplemented
78#16837464C2212yescomplemented
79#16837461C2212yescomplemented
80#16837460C2212yescomplemented
81#16837460C2212yescomplemented
82#16837457C2212yescomplemented
83#16837456C2212yescomplemented
84#16837453C2212yescomplemented
85#16837452C2211yescharacteristic
86#16837452C2211yescharacteristic
87#16837452C2211yescharacteristic
88#16837452C2211yescharacteristic
89#16837452C2211yescharacteristic
90#16837452C2211yescharacteristic
91#16837452C2211yescharacteristic
92#16837452C2211yescharacteristic
93#16837452C2212yescomplemented
94#16837430C2211yescharacteristic
95#16837430C2212yescomplemented
96#16837429C2211yescharacteristic
97#16837428C2211yescharacteristic
98#16837428C2212yescomplemented
99#16837427C2212yescomplemented
100#16837427C2212yescomplemented
101#16837425C2211yescharacteristic
102#16837425C2211yescharacteristic
103#16837425C2212yes—
104#16837425C2212yes—
105#16837425C2211yescharacteristic
106#16837425C2211yescharacteristic
107#16837425C2212yescomplemented
108#16837424C2212yescomplemented
109C2×Dic59⋊C8C2212yes—
110C2×Dic59⋊C8C2212yes—
111C2×Dic59⋊C8C2211yescharacteristic
112C2×Dic59⋊C8C2211yescharacteristic
113C2×Dic59⋊C8C2212yescomplemented
114C4⋊C8×D59C2212yescomplemented
115#16837370C2211yescharacteristic
116#16837369C2211yescharacteristic
117#16837368C2211yescharacteristic
118C2×C22⋊(C59⋊C8)C2211yescharacteristic
119#16837360C2211yescharacteristic
120#16837358C2211yescharacteristic
121#16837357C2211yescharacteristic
122C2×C8×Dic59C2211yescharacteristic
123C2×C8×Dic59C2211yescharacteristic
124C2×#131×C59C2211yescharacteristic
125C22×M16×C59C2211yescharacteristic
126C59×#525C2211yescharacteristic
127C59×#436C2212yes—
128C59×#435C2212yes—
129C59×#435C2212yes—
130C8×D4×C59C2212yes—
131C59×#424C2211yescharacteristic
132C59×#408C2211yescharacteristic
133C2×C22⋊C8×C59C2211yescharacteristic
134C59×#405C2211yescharacteristic
135C2×#11745685C2311yescharacteristic
136C2×#11745687C2×C412yes—
137C2×#11745687C2×C412yes—
138C23×Dic59C2×C411yescharacteristic
139C23×Dic59C2×C411yescharacteristic
140#14273735—42no—
141#14273734—42no—
142#14273733—42no—
143C2×#11745664—42no—
144C2×#11745664C2311yescharacteristic
145C2×#11745664C2311yescharacteristic
146C2×#11745664C2312yes—
147C2×#11745664C2312yes—
148C2×#11745659C2312yes—
149C2×#11745659C2312yes—
150C22×C59⋊C8C2311yescharacteristic
151C22×C59⋊C8C2311yescharacteristic
152C22×C59⋊C8C2312yes—
153C22×C59⋊C8C2312yes—
154C2×C8×D59C2312yes—
155C2×C8×D59C2312yes—
156#14273726C2×C411yescharacteristic
157#14273726C2×C411yescharacteristic
158#14273725C2×C411yescharacteristic
159#14273723C2×C411yescharacteristic
160#14273722C2×C412yes—
161#14273722C2×C412yes—
162#14273720C2×C412yes—
163#14273720C2×C412yes—
164#14273718C2×C411yescharacteristic
165#14273718C2×C411yescharacteristic
166#14273717C2×C412yes—
167#14273717C2×C412yes—
168#14273716C2×C411yescharacteristic
169#14273714C2×C411yescharacteristic
170#14273713C2×C412yes—
171#14273713C2×C412yes—
172#14273711C2×C412yes—
173#14273711C2×C412yes—
174#14273710C2×C412yes—
175#14273708C2×C412yes—
176#14273708C2×C412yes—
177#14273706C2×C411yescharacteristic
178#14273706C2×C411yescharacteristic
179#14273704C2×C412yes—
180#14273704C2×C412yes—
181#14273704C2×C412yes—
182#14273704C2×C412yes—
183#14273701C2×C411yescharacteristic
184#14273701C2×C411yescharacteristic
185#14273699C2×C412yes—
186#14273699C2×C412yes—
187#14273699C2×C412yes—
188#14273699C2×C412yes—
189#14273696C2×C412yes—
190Q8×Dic59C2×C411yescharacteristic
191Q8×Dic59C2×C411yescharacteristic
192C4×Dic118C2312yes—
193C4×Dic118C2312yes—
194#14273692C2×C412yes—
195#14273692C2×C412yes—
196#14273692C2×C411yescharacteristic
197#14273692C2×C411yescharacteristic
198D4×Dic59C2×C412yes—
199D4×Dic59C2×C412yes—
200D4×Dic59C2×C412yes—
201D4×Dic59C2×C412yes—
202D4×Dic59C2×C411yescharacteristic
203D4×Dic59C2×C411yescharacteristic
204#14273689C2×C411yescharacteristic
205#14273689C2×C411yescharacteristic
206C4×C22⋊D59C2312yes—
207C4×C22⋊D59C2312yes—
208C4×C22⋊D59C2312yes—
209C4×C22⋊D59C2312yes—
210(C22⋊D59)⋊C4C2×C412yes—
211(C22⋊D59)⋊C4C2×C412yes—
212(C22⋊D59)⋊C4C2×C412yes—
213(C22⋊D59)⋊C4C2×C412yes—
214(C22⋊D59)⋊C4C2×C412yes—
215(C22⋊D59)⋊C4C2×C412yes—
216#14273686C2311yescharacteristic
217#14273686C2312yes—
218#14273685C2×C412yes—
219#14273685C2×C412yes—
220#14273684C2312yes—
221#14273683C2×C412yes—
222#14273683C2×C412yes—
223#14273683C2×C412yes—
224#14273683C2×C412yes—
225C2×C4×Dic59C2×C411yescharacteristic
226C2×C4×Dic59C2×C411yescharacteristic
227C2×C4×Dic59C2×C411yescharacteristic
228C2×C4×Dic59C2×C411yescharacteristic
229C2×C4×Dic59C2×C411yescharacteristic
230C2×C4×Dic59C2×C411yescharacteristic
231C2×C4×Dic59C2311yescharacteristic
232C2×C4×Dic59C2311yescharacteristic
233C2×C4×Dic59C2311yescharacteristic
234C2×C4×Dic59C2311yescharacteristic
235C2×C4×Dic59C2312yes—
236C2×C4×Dic59C2311yescharacteristic
237C2×C4×Dic59C2311yescharacteristic
238C42×D59C2312yes—
239C4⋊(C59⋊C8)C2312yes—
240C4⋊(C59⋊C8)C2312yes—
241Dic59⋊C8C2311yescharacteristic
242Dic59⋊C8C2312yes—
243Dic59⋊C8C2312yes—
244Dic59⋊C8C2311yescharacteristic
245Dic59⋊C8C2312yes—
246Dic59⋊C8C2312yes—
247Dic59⋊C8C2312yes—
248Dic59⋊C8C2312yes—
249Dic59⋊C8C2312yes—
250Dic59⋊C8C2312yes—
251Dic59⋊C8C2311yescharacteristic
252Dic59⋊C8C2311yescharacteristic
253Dic59⋊C8C2311yescharacteristic
254Dic59⋊C8C2311yescharacteristic
255Dic59⋊C8C2311yescharacteristic
256Dic59⋊C8C2311yescharacteristic
257Dic59⋊C8C2312yes—
258Dic59⋊C8C2312yes—
259Dic59⋊C8C2312yes—
260Dic59⋊C8C2312yes—
261C22⋊(C59⋊C8)C2311yescharacteristic
262C22⋊(C59⋊C8)C2311yescharacteristic
263C22⋊(C59⋊C8)C2311yescharacteristic
264C22⋊(C59⋊C8)C2311yescharacteristic
265C22⋊(C59⋊C8)C2312yes—
266C22⋊(C59⋊C8)C2312yes—
267(C2×D59)⋊C8C2312yes—
268(C2×D59)⋊C8C2312yes—
269(C2×D59)⋊C8C2312yes—
270(C2×D59)⋊C8C2312yes—
271#14273638C2312yes—
272#14273637C2312yes—
273#14273637C2312yes—
274C4×C59⋊C8C2312yes—
275C8×Dic59C2311yescharacteristic
276C8×Dic59C2311yescharacteristic
277C8×Dic59C2311yescharacteristic
278C8×Dic59C2311yescharacteristic
279C8×Dic59C2311yescharacteristic
280C8×Dic59C2311yescharacteristic
281C8×Dic59C2311yescharacteristic
282C8×Dic59C2311yescharacteristic
283C8×Dic59C2312yes—
284C8×Dic59C2312yes—
285C2×#41×C59C2311yescharacteristic
286C23×C4×C59C2311yescharacteristic
287#131×C59—42no—
288C2×M16×C59—42no—
289C2×M16×C59C2311yescharacteristic
290C2×M16×C59C2311yescharacteristic
291C2×M16×C59C2312yes—
292C2×M16×C59C2312yes—
293C22×C8×C59C2311yescharacteristic
294C22×C8×C59C2311yescharacteristic
295C22×C8×C59C2312yes—
296C22×C8×C59C2312yes—
297#123×C59C2×C412yes—
298C22⋊Q8×C59C2×C411yescharacteristic
299C22⋊Q8×C59C2×C411yescharacteristic
300#121×C59C2×C411yescharacteristic
301#121×C59C2×C411yescharacteristic
302#120×C59C2×C412yes—
303C4×D4×C59C2312yes—
304C4×D4×C59C2312yes—
305#117×C59C2311yescharacteristic
306C4⋊C8×C59C2312yes—
307C4⋊C8×C59C2312yes—
308C22⋊C8×C59C2311yescharacteristic
309C22⋊C8×C59C2311yescharacteristic
310C22⋊C8×C59C2311yescharacteristic
311C22⋊C8×C59C2311yescharacteristic
312C22⋊C8×C59C2312yes—
313C22⋊C8×C59C2312yes—
314#97×C59C2312yes—
315C4×C8×C59C2312yes—
316C24×C59C22×C411yescharacteristic
317#41×C59—22no—
318#41×C59—22no—
319C2×Q8×C59C22×C411yescharacteristic
320C2×D4×C59C22×C412yes—
321C2×D4×C59C22×C412yes—
322C2×D4×C59C22×C411yescharacteristic
323C2×D4×C59C22×C412yes—
324C22×C4×C59—22no—
325C22×C4×C59—22no—
326C22×C4×C59C22×C411yescharacteristic
327C22×C4×C59C22×C411yescharacteristic
328C22×C4×C59C22×C411yescharacteristic
329C22×C4×C59C2411yescharacteristic
330C22×C4×C59C2412yes—
331C22×C4×C59C2411yescharacteristic
332C22×C4×C59C2411yescharacteristic
333C2×C22⋊D59C22×C412yes—
334C2×C22⋊D59C22×C412yes—
335C2×C22⋊D59C22×C412yes—
336C2×C22⋊D59C22×C412yes—
337C2×C22⋊D59C22×C412yes—
338C22×Dic59—24no—
339C22×Dic59—42no—
340C22×Dic59C22×C411yescharacteristic
341C22×Dic59C22×C411yescharacteristic
342C22×Dic59C22×C411yescharacteristic
343C22×Dic59C22×C411yescharacteristic
344C22×Dic59C22×C411yescharacteristic
345C22×Dic59C22×C411yescharacteristic
346C22×Dic59C22×C411yescharacteristic
347C22×Dic59C22×C411yescharacteristic
348C22×Dic59C22×C412yes—
349C22×Dic59C22×C411yescharacteristic
350C22×Dic59C22×C411yescharacteristic
351C22×Dic59C22×C411yescharacteristic
352C22×Dic59C22×C412yes—
353C22×Dic59C22×C411yescharacteristic
354#11745687—28no—
355#11745687—44no—
356#11745685—22no—
357#11745685—22no—
358C2×D236C22×C411yescharacteristic
359C2×C4×D59C22×C412yes—
360C2×C4×D59C22×C412yes—
361C2×C4×D59C2412yes—
362C2×Dic118C22×C411yescharacteristic
363C2×Dic118C22×C412yes—
364C2×Dic118C22×C412yes—
365M16×C59—22no—
366M16×C59—22no—
367M16×C59—42no—
368M16×C59—42no—
369C2×C8×C59—22no—
370C2×C8×C59—22no—
371C2×C8×C59—42no—
372C2×C8×C59—42no—
373C2×C8×C59C2411yescharacteristic
374C2×C8×C59C2412yes—
375C2×C8×C59C2411yescharacteristic
376C2×C8×C59C2411yescharacteristic
377C2×C8×C59C2411yescharacteristic
378C2×C8×C59C2412yes—
379C4⋊C4×C59C22×C411yescharacteristic
380C4⋊C4×C59C22×C411yescharacteristic
381C4⋊C4×C59C22×C412yes—
382C4⋊C4×C59C22×C412yes—
383C22⋊C4×C59C22×C412yes—
384C22⋊C4×C59C22×C412yes—
385C22⋊C4×C59C22×C412yes—
386C22⋊C4×C59C22×C412yes—
387C22⋊C4×C59C22×C412yes—
388C42×C59C2412yes—
389C22⋊Dic59C22×C412yes—
390C22⋊Dic59C22×C412yes—
391C22⋊Dic59C22×C412yes—
392C22⋊Dic59C22×C412yes—
393C22⋊Dic59C22×C412yes—
394C22⋊Dic59C22×C412yes—
395C22⋊Dic59C22×C412yes—
396(C2×D59)⋊C4C22×C412yes—
397(C2×D59)⋊C4C22×C412yes—
398(C2×D59)⋊C4C22×C412yes—
399(C2×D59)⋊C4C22×C412yes—
400(C2×D59)⋊C4C22×C412yes—
401(C2×D59)⋊C4C22×C412yes—
402C4⋊Dic59C22×C412yes—
403C4⋊Dic59C22×C412yes—
404C4⋊Dic59C22×C411yescharacteristic
405C4⋊Dic59C22×C411yescharacteristic
406C4⋊Dic59C22×C412yes—
407C4⋊Dic59C22×C412yes—
408Dic59⋊C4C22×C412yes—
409Dic59⋊C4C22×C412yes—
410Dic59⋊C4C22×C412yes—
411Dic59⋊C4C22×C412yes—
412Dic59⋊C4C22×C412yes—
413Dic59⋊C4C22×C412yes—
414Dic59⋊C4C22×C412yes—
415Dic59⋊C4C22×C412yes—
416Dic59⋊C4C22×C412yes—
417Dic59⋊C4C22×C412yes—
418C4×Dic59C22×C412yes—
419C4×Dic59C22×C412yes—
420C4×Dic59C22×C411yescharacteristic
421C4×Dic59C22×C411yescharacteristic
422C4×Dic59C22×C411yescharacteristic
423C4×Dic59C22×C411yescharacteristic
424C4×Dic59C22×C411yescharacteristic
425C4×Dic59C22×C411yescharacteristic
426C4×Dic59C22×C411yescharacteristic
427C4×Dic59C22×C411yescharacteristic
428C4×Dic59C22×C411yescharacteristic
429C4×Dic59C22×C411yescharacteristic
430C4×Dic59C22×C411yescharacteristic
431C4×Dic59C22×C411yescharacteristic
432C4×Dic59C22×C412yes—
433C4×Dic59C22×C412yes—
434C4×Dic59C2411yescharacteristic
435C4×Dic59C2411yescharacteristic
436C4×Dic59C2412yes—
437C4×Dic59C2411yescharacteristic
438C4×Dic59C2411yescharacteristic
439#11745664—22no—
440#11745664—22no—
441#11745664—42no—
442#11745664—42no—
443C2×C59⋊C8—22no—
444C2×C59⋊C8—22no—
445C2×C59⋊C8—42no—
446C2×C59⋊C8—42no—
447C2×C59⋊C8C2411yescharacteristic
448C2×C59⋊C8C2411yescharacteristic
449C2×C59⋊C8C2411yescharacteristic
450C2×C59⋊C8C2411yescharacteristic
451C2×C59⋊C8C2412yes—
452C2×C59⋊C8C2412yes—
453#11745659—42no—
454#11745659—42no—
455C8×D59—42no—
456C8×D59—42no—
457C23×C59—22no—
458C23×C59—22no—
459C23×C59—41no—
460C23×C59C23×C412yes—
461C23×C59C23×C411yescharacteristic
462C23×C59C23×C411yescharacteristic
463C23×C59C23×C411yescharacteristic
464C22×D59C23×C412yes—
465Q8×C59—22no—
466D4×C59—24no—
467D4×C59—24no—
468D4×C59—22no—
469D4×C59—42no—
470C2×C4×C59—22no—
471C2×C4×C59—22no—
472C2×C4×C59—22no—
473C2×C4×C59—21no—
474C2×C4×C59—22no—
475C2×C4×C59—21no—
476C2×C4×C59—21no—
477C2×C4×C59—21no—
478C2×C4×C59—22no—
479C2×C4×C59C23×C411yescharacteristic
480C2×C4×C59C23×C411yescharacteristic
481C2×C4×C59C23×C412yes—
482C2×C4×C59C23×C412yes—
483C2×C4×C59C23×C412yes—
484C2×C4×C59C23×C411yescharacteristic
485C2×C4×C59H(5,𝔽2)12yes—
486C2×C4×C592−1+412yes—
487C2×C4×C59C2511yescharacteristic
488C22⋊D59—24no—
489C22⋊D59—24no—
490C22⋊D59—24no—
491C22⋊D59—24no—
492C22⋊D59—42no—
493C2×Dic59—22no—
494C2×Dic59—24no—
495C2×Dic59—22no—
496C2×Dic59—22no—
497C2×Dic59—22no—
498C2×Dic59—22no—
499C2×Dic59—22no—
500C2×Dic59—22no—
501C2×Dic59—22no—
502C2×Dic59—42no—
503C2×Dic59—41no—
504C2×Dic59—41no—
505C2×Dic59—41no—
506C2×Dic59#13114yescomplemented
507C2×Dic59C23×C411yescharacteristic
508C2×Dic59C23×C411yescharacteristic
509C2×Dic59C23×C411yescharacteristic
510C2×Dic59C23×C411yescharacteristic
511C2×Dic59C23×C411yescharacteristic
512C2×Dic59C23×C412yes—
513C2×Dic59C23×C412yes—
514C2×Dic59C23×C412yes—
515C2×Dic59C23×C411yescharacteristic
516C2×Dic59C23×C411yescharacteristic
517C2×Dic59C23×C411yescharacteristic
518D236—22no—
519C4×D59—22no—
520C4×D59—22no—
521C4×D59—24no—
522C4×D59—42no—
523Dic118—22no—
524Dic118—24no—
525Dic118—24no—
526C8×C59—21no—
527C8×C59—22no—
528C8×C59—21no—
529C8×C59—22no—
530C8×C59—21no—
531C8×C59—21no—
532C59⋊C8—21no—
533C59⋊C8—22no—
534C59⋊C8—21no—
535C59⋊C8—22no—
536C59⋊C8—21no—
537C59⋊C8—21no—
538#60268—591nomaximal, Sylow
539C22×C59—21no—
540C22×C59—21no—
541C22×C59—21no—
542C22×C59—21no—
543C22×C59—21no—
544C22×C59—22no—
545C22×C59—21no—
546C22×C59—22no—
547C22×C59—21no—
548C22×C59—22no—
549C22×C59—44no—
550C22×C59#52012yes—
551C22×C59C2×#13112yes—
552C22×C59C24×C411yescharacteristic
553C2×D59—22no—
554C2×D59—22no—
555C2×D59—22no—
556C4×C59—21no—
557C4×C59—21no—
558C4×C59—22no—
559C4×C59—22no—
560C4×C59—22no—
561C4×C59#52012yes—
562C4×C59C2×H(5,𝔽2)11yescharacteristic
563C4×C59C2×2−1+411yescharacteristic
564Dic59—22no—
565Dic59—22no—
566Dic59—21no—
567Dic59—21no—
568Dic59—22no—
569Dic59—21no—
570Dic59—21no—
571Dic59—21no—
572Dic59C2×#13112yes—
573Dic59C2×#13112yes—
574Dic59#56812yes—
575#3444—591no—
576#2994—592no—
577#2994—592no—
578#2993—592no—
579#2993—592no—
580#2991—592no—
581#2990—592no—
582#2989—592no—
583#2988—592no—
584#2960—591no—
585#2960—591no—
586#2933—591no—
587#2933—591no—
588#2933—591no—
589#2933D5911yescharacteristic, complemented
590#2931—591no—
591#2931—591no—
592#2925—591no—
593#2925—591no—
594C2×#431—591no—
595#2906—591no—
596#2906—591no—
597C2×#423—591no—
598C2×C59—22no—
599C2×C59—22no—
600C2×C59—42no—
601C2×C59—41no—
602C2×C59C2×#52011yescharacteristic
603C2×C59C22×#13111yescharacteristic
604C2×C59C2×#56811yescharacteristic
605D59—42no—
606C2×#131—591no—
607C2×#131—591no—
608C2×#131—591no—
609C2×#131C2×D5911yescharacteristic
610C22×M16—591no—
611C22×M16C2×D5911yescharacteristic
612#533—591no—
613#533—591no—
614#533—591no—
615#532—591no—
616#532—591no—
617#532—591no—
618#529—592no—
619#529—592no—
620#529—591no—
621#529—591no—
622#529—591no—
623#529—591no—
624#529—592no—
625#529—592no—
626#525—591no—
627#525—592no—
628#525—592no—
629#525C2×D5911yescharacteristic
630C4×#41—591no—
631C4×#41—592no—
632C4×#41—592no—
633C4×#41—591no—
634C22×C42—591no—
635#446—592no—
636#446—592no—
637#446—592no—
638#446—592no—
639C8×Q8—592no—
640C8×Q8—592no—
641C8×Q8—592no—
642C8×Q8—592no—
643#436—592no—
644#436—592no—
645#436—592no—
646#436—592no—
647#436—592no—
648#436—592no—
649#436—592no—
650#436C2×D5912yes—
651#435—592no—
652#435—592no—
653#435—592no—
654#435—592no—
655#435—592no—
656#435—592no—
657#435C2×D5912yes—
658#435C2×D5912yes—
659C8×D4—592no—
660C8×D4—592no—
661C8×D4—592no—
662C8×D4—592no—
663C8×D4—592no—
664C8×D4—592no—
665C8×D4—592no—
666C8×D4C2×D5912yes—
667#433—592no—
668#433—592no—
669#433—592no—
670#433—592no—
671#432—592no—
672#432—592no—
673#431—591no—
674#431—591no—
675#431—591no—
676#431—591no—
677#431—591no—
678#431—591no—
679#431—591no—
680#431—591no—
681#431—592no—
682#431—592no—
683#424—591no—
684#424—592no—
685#424—591no—
686#424—592no—
687#424—591no—
688#424—592no—
689#424—592no—
690#424C2×D5911yescharacteristic
691#423—591no—
692#423—591no—
693#423—591no—
694#423—591no—
695#423—592no—
696#423—592no—
697#423—592no—
698#423—592no—
699C2×C4⋊C8—592no—
700C2×C4⋊C8—592no—
701C2×C4⋊C8—591no—
702C2×C4⋊C8—591no—
703C2×C4⋊C8—592no—
704C2×C4⋊C8—592no—
705#408—591no—
706#408—591no—
707#408—591no—
708#408C2×D5911yescharacteristic
709C2×C22⋊C8—591no—
710C2×C22⋊C8C2×D5911yescharacteristic
711#405—591no—
712#405—591no—
713#405—591no—
714#405C2×D5911yescharacteristic
715C2×C4×C8—591no—
716C2×C4×C8—591no—
717C59#6026811yescharacteristic, complemented, Sylow
718C2×#41—592no—
719C2×#41—592no—
720C2×#41—591no—
721C2×#41C22×D5911yescharacteristic
722C23×C4—591no—
723C23×C4—591no—
724C23×C4C22×D5911yescharacteristic
725#131—42no—
726#131—2362no—
727#131—2362no—
728#131—2362no—
729C2×M16—42no—
730C2×M16—591no—
731C2×M16—591no—
732C2×M16—592no—
733C2×M16—592no—
734C2×M16—592no—
735C2×M16—592no—
736C2×M16—2362no—
737C2×M16C22×D5911yescharacteristic
738C2×M16C22×D5911yescharacteristic
739C2×M16C22×D5912yes—
740C2×M16C22×D5912yes—
741C22×C8—591no—
742C22×C8—591no—
743C22×C8—592no—
744C22×C8—592no—
745C22×C8—592no—
746C22×C8—592no—
747C22×C8C22×D5911yescharacteristic
748C22×C8C22×D5911yescharacteristic
749C22×C8C22×D5912yes—
750C22×C8C22×D5912yes—
751C4⋊Q8—591no—
752C4⋊Q8—591no—
753C4⋊Q8—591no—
754#127—591no—
755#126—592no—
756#126—592no—
757#126—592no—
758#126—592no—
759#125—592no—
760#125—592no—
761#125—591no—
762#125—591no—
763#124—591no—
764#124—591no—
765#124—592no—
766#124—592no—
767#123—592no—
768#123—592no—
769#123—592no—
770#123—592no—
771#123—592no—
772#123C4×D5912yes—
773C22⋊Q8—591no—
774C22⋊Q8—591no—
775C22⋊Q8—592no—
776C22⋊Q8—592no—
777C22⋊Q8—592no—
778C22⋊Q8—592no—
779C22⋊Q8C4×D5911yescharacteristic
780C22⋊Q8C4×D5911yescharacteristic
781#121—592no—
782#121—592no—
783#121—592no—
784#121—592no—
785#121—591no—
786#121—591no—
787#121C4×D5911yescharacteristic
788#121C4×D5911yescharacteristic
789#120—592no—
790#120C4×D5912yes—
791C4×Q8—591no—
792C4×Q8—591no—
793C4×Q8—592no—
794C4×Q8—592no—
795C4×Q8—591no—
796C4×Q8—591no—
797C4×Q8—592no—
798C4×Q8—592no—
799C4×D4—592no—
800C4×D4—592no—
801C4×D4—592no—
802C4×D4—592no—
803C4×D4—591no—
804C4×D4—591no—
805C4×D4—592no—
806C4×D4—592no—
807C4×D4—592no—
808C4×D4—592no—
809C4×D4—591no—
810C4×D4—591no—
811C4×D4—592no—
812C4×D4—592no—
813C4×D4—592no—
814C4×D4—592no—
815C4×D4—592no—
816C4×D4—592no—
817C4×D4C22×D5912yes—
818C4×D4C22×D5912yes—
819#117—591no—
820#117—592no—
821#117—592no—
822#117—592no—
823#117—592no—
824#117—592no—
825#117—592no—
826#117—592no—
827#117—592no—
828#117C22×D5911yescharacteristic
829C2×C42—591no—
830C2×C42—591no—
831C2×C42—591no—
832C2×C42—591no—
833C2×C42—591no—
834C2×C42—591no—
835C2×C42—592no—
836C2×C42—591no—
837C2×C42—591no—
838C2×C42—591no—
839C2×C42—591no—
840C2×C42—591no—
841C2×C42—591no—
842C2×C42—592no—
843C4⋊C8—591no—
844C4⋊C8—592no—
845C4⋊C8—592no—
846C4⋊C8—591no—
847C4⋊C8—592no—
848C4⋊C8—592no—
849C4⋊C8—592no—
850C4⋊C8—592no—
851C4⋊C8—592no—
852C4⋊C8—592no—
853C4⋊C8—591no—
854C4⋊C8—591no—
855C4⋊C8—592no—
856C4⋊C8—592no—
857C4⋊C8—591no—
858C4⋊C8—591no—
859C4⋊C8—591no—
860C4⋊C8—591no—
861C4⋊C8—592no—
862C4⋊C8—592no—
863C4⋊C8—592no—
864C4⋊C8—592no—
865C4⋊C8C22×D5912yes—
866C4⋊C8C22×D5912yes—
867C22⋊C8—591no—
868C22⋊C8—591no—
869C22⋊C8—591no—
870C22⋊C8—591no—
871C22⋊C8—592no—
872C22⋊C8—592no—
873C22⋊C8—592no—
874C22⋊C8—592no—
875C22⋊C8—592no—
876C22⋊C8—592no—
877C22⋊C8C22×D5911yescharacteristic
878C22⋊C8C22×D5911yescharacteristic
879C22⋊C8C22×D5911yescharacteristic
880C22⋊C8C22×D5911yescharacteristic
881C22⋊C8C22×D5912yes—
882C22⋊C8C22×D5912yes—
883#97—592no—
884#97—592no—
885#97—592no—
886#97C22×D5912yes—
887C4×C8—591no—
888C4×C8—591no—
889C4×C8—591no—
890C4×C8—591no—
891C4×C8—591no—
892C4×C8—591no—
893C4×C8—591no—
894C4×C8—591no—
895C4×C8—592no—
896C4×C8—592no—
897C4×C8—592no—
898C4×C8C22×D5912yes—
899C24C2×C4×D5911yescharacteristic
900#41—22no—
901#41—22no—
902#41—1188no—
903#41—1182no—
904#41—1182no—
905#41—2364no—
906C2×Q8—592no—
907C2×Q8—592no—
908C2×Q8—591no—
909C2×Q8C2×C4×D5911yescharacteristic
910C2×D4—592no—
911C2×D4—592no—
912C2×D4—592no—
913C2×D4—592no—
914C2×D4—592no—
915C2×D4—591no—
916C2×D4C2×C4×D5912yes—
917C2×D4C2×C4×D5911yescharacteristic
918C2×D4C2×C4×D5912yes—
919C2×D4C2×C4×D5912yes—
920C22×C4—22no—
921C22×C4—22no—
922C22×C4—591no—
923C22×C4—591no—
924C22×C4—591no—
925C22×C4—591no—
926C22×C4—591no—
927C22×C4—591no—
928C22×C4—591no—
929C22×C4—591no—
930C22×C4—591no—
931C22×C4—592no—
932C22×C4—591no—
933C22×C4—591no—
934C22×C4—591no—
935C22×C4—592no—
936C22×C4—592no—
937C22×C4—592no—
938C22×C4—592no—
939C22×C4—1184no—
940C22×C4—2362no—
941C22×C4C2×C4×D5911yescharacteristic
942C22×C4C2×C4×D5911yescharacteristic
943C22×C4C2×C4×D5911yescharacteristic
944C22×C4C23×D5911yescharacteristic
945C22×C4C23×D5911yescharacteristic
946C22×C4C23×D5912yes—
947C22×C4C23×D5911yescharacteristic
948M16—22no—
949M16—22no—
950M16—42no—
951M16—42no—
952M16—1182no—
953M16—1182no—
954M16—2362no—
955M16—2362no—
956M16—2362no—
957M16—2362no—
958C2×C8—22no—
959C2×C8—22no—
960C2×C8—42no—
961C2×C8—42no—
962C2×C8—591no—
963C2×C8—591no—
964C2×C8—591no—
965C2×C8—591no—
966C2×C8—592no—
967C2×C8—592no—
968C2×C8—1182no—
969C2×C8—1182no—
970C2×C8—2362no—
971C2×C8—2362no—
972C2×C8—2362no—
973C2×C8—2362no—
974C2×C8C23×D5911yescharacteristic
975C2×C8C23×D5911yescharacteristic
976C2×C8C23×D5911yescharacteristic
977C2×C8C23×D5911yescharacteristic
978C2×C8C23×D5912yes—
979C2×C8C23×D5912yes—
980C4⋊C4—592no—
981C4⋊C4—592no—
982C4⋊C4—592no—
983C4⋊C4—592no—
984C4⋊C4—591no—
985C4⋊C4—591no—
986C4⋊C4—592no—
987C4⋊C4—592no—
988C4⋊C4—592no—
989C4⋊C4—592no—
990C4⋊C4—592no—
991C4⋊C4—592no—
992C4⋊C4—592no—
993C4⋊C4—592no—
994C4⋊C4—592no—
995C4⋊C4—592no—
996C4⋊C4C2×C4×D5912yes—
997C4⋊C4C2×C4×D5912yes—
998C4⋊C4C2×C4×D5911yescharacteristic
999C4⋊C4C2×C4×D5911yescharacteristic
1000C22⋊C4—592no—
1001C22⋊C4—592no—
1002C22⋊C4—592no—
1003C22⋊C4—592no—
1004C22⋊C4—592no—
1005C22⋊C4—592no—
1006C22⋊C4—592no—
1007C22⋊C4—592no—
1008C22⋊C4—592no—
1009C22⋊C4—592no—
1010C22⋊C4—592no—
1011C22⋊C4—592no—
1012C22⋊C4—592no—
1013C22⋊C4C2×C4×D5912yes—
1014C22⋊C4C2×C4×D5912yes—
1015C22⋊C4C2×C4×D5912yes—
1016C22⋊C4C2×C4×D5912yes—
1017C22⋊C4C2×C4×D5912yes—
1018C42—591no—
1019C42—591no—
1020C42—591no—
1021C42—591no—
1022C42—591no—
1023C42—591no—
1024C42—591no—
1025C42—591no—
1026C42—591no—
1027C42—591no—
1028C42—591no—
1029C42—591no—
1030C42—592no—
1031C42—592no—
1032C42—592no—
1033C42—592no—
1034C42—591no—
1035C42—591no—
1036C42—592no—
1037C42—591no—
1038C42—591no—
1039C42C23×D5912yes—
1040C23—22no—
1041C23—22no—
1042C23—41no—
1043C23—592no—
1044C23C22×C4×D5912yes—
1045C23C22×C4×D5911yescharacteristic
1046C23C22×C4×D5911yescharacteristic
1047C23C22×C4×D5911yescharacteristic
1048Q8—22no—
1049Q8—1184no—
1050Q8—1184no—
1051Q8—1182no—
1052D4—24no—
1053D4—24no—
1054D4—22no—
1055D4—42no—
1056D4—1184no—
1057D4—1184no—
1058D4—1184no—
1059D4—1184no—
1060D4—1182no—
1061D4—2362no—
1062C2×C4—22no—
1063C2×C4—21no—
1064C2×C4—22no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—594no—
1072C2×C4—591no—
1073C2×C4—591no—
1074C2×C4—591no—
1075C2×C4—591no—
1076C2×C4—591no—
1077C2×C4—591no—
1078C2×C4—591no—
1079C2×C4—591no—
1080C2×C4—592no—
1081C2×C4—592no—
1082C2×C4—592no—
1083C2×C4—1184no—
1084C2×C4—1182no—
1085C2×C4—1182no—
1086C2×C4—1182no—
1087C2×C4—1182no—
1088C2×C4—1182no—
1089C2×C4—1182no—
1090C2×C4—1182no—
1091C2×C4—1184no—
1092C2×C4—1182no—
1093C2×C4—1182no—
1094C2×C4—1182no—
1095C2×C4—2362no—
1096C2×C4—2361no—
1097C2×C4—2361no—
1098C2×C4—2361no—
1099C2×C4—2362no—
1100C2×C4C22×C4×D5911yescharacteristic
1101C2×C4C22×C4×D5911yescharacteristic
1102C2×C4C22×C4×D5912yes—
1103C2×C4C22×C4×D5912yes—
1104C2×C4C22×C4×D5912yes—
1105C2×C4C22×C4×D5911yescharacteristic
1106C2×C4#1427377212yes—
1107C2×C4#1427377412yes—
1108C2×C4C24×D5911yescharacteristic
1109C8—21no—
1110C8—21no—
1111C8—22no—
1112C8—22no—
1113C8—21no—
1114C8—21no—
1115C8—1181no—
1116C8—1181no—
1117C8—1182no—
1118C8—1182no—
1119C8—1181no—
1120C8—1181no—
1121C22—21no—
1122C22—21no—
1123C22—21no—
1124C22—21no—
1125C22—21no—
1126C22—22no—
1127C22—21no—
1128C22—22no—
1129C22—21no—
1130C22—22no—
1131C22—44no—
1132C22—1182no—
1133C22—1182no—
1134C22—1182no—
1135C22#1683788112yes—
1136C22#131×D5912yes—
1137C22C23×C4×D5911yescharacteristic
1138C4—22no—
1139C4—22no—
1140C4—21no—
1141C4—21no—
1142C4—22no—
1143C4—592no—
1144C4—592no—
1145C4—592no—
1146C4—1181no—
1147C4—1181no—
1148C4—1182no—
1149C4—1181no—
1150C4—1181no—
1151C4—1181no—
1152C4—1182no—
1153C4—1182no—
1154C4#1683788112yes—
1155C4C2×#1427377211yescharacteristic
1156C4C2×#1427377411yescharacteristic
1157C2—22no—
1158C2—22no—
1159C2—41no—
1160C2—42no—
1161C2—2362no—
1162C2C2×#1683788111yescharacteristic
1163C2C2×#131×D5911yescharacteristic
1164C2#568×D5911yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D59
commutator, socleC22×C59C24×C4
FittingC59×#2933C2
prime radical#21437388C2
cosocleC2×C4×C59C25
hypercenter#2933D59
hypocenterC59#60268
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ #2933

Complements

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

NH ≅ G/Ntype
2. #21433253C2semidirect
3. #21433249C2semidirect
4. #21433242C2semidirect
5. #21433238C2semidirect
6. #21433224C2semidirect
7. #21433216C2semidirect
8. #21433208C2semidirect
9. #21433203C2semidirect
10. #21433029C2semidirect
11. #21433028C2semidirect
12. #21432823C2semidirect
13. #21432821C2semidirect
14. #21432817C2semidirect
15. #21432806C2semidirect
16. #21432804C2semidirect
17. #21432760C2semidirect
18. #21432758C2semidirect
19. C2×#16837452C2semidirect
20. #21432663C2semidirect
21. #21432662C2semidirect
22. C2×#16837425C2semidirect
23. C59×#2933C2semidirect
50. #16837531C22semidirect
51. #16837531C22semidirect
52. #16837530C22semidirect
53. #16837530C22semidirect
54. C8×Dic118C22semidirect
55. C8×Dic118C22semidirect
56. #16837526C22semidirect
57. #16837526C22semidirect
60. #16837478C22semidirect
61. #16837478C22semidirect
63. #16837477C22semidirect
64. #16837477C22semidirect
73. C8×C22⋊D59C22semidirect
74. C8×C22⋊D59C22semidirect
76. (C22⋊D59)⋊C8C22semidirect
77. (C22⋊D59)⋊C8C22semidirect
78. #16837464C22semidirect
79. #16837461C22semidirect
80. #16837460C22semidirect
81. #16837460C22semidirect
82. #16837457C22semidirect
83. #16837456C22semidirect
84. #16837453C22semidirect
93. #16837452C22semidirect
95. #16837430C22semidirect
98. #16837428C22semidirect
99. #16837427C22semidirect
100. #16837427C22semidirect
107. #16837425C22semidirect
108. #16837424C22semidirect
113. C2×Dic59⋊C8C22semidirect
114. C4⋊C8×D59C22semidirect
506. C2×Dic59#131semidirect
589. #2933D59semidirect
717. C59#60268semidirect

Maximal subgroups

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

subgroupindex
#214373882
#214332532
#214332492
#214332422
#214332382
#214332242
#214332162
#214332082
#214332032
#214330292
#214330282
#214328232
#214328212
#214328172
#214328062
#214328042
#214327602
#214327582
C2×#168374522
#214326632
#214326622
C2×#168374252
C59×#29332
#6026859