Finite Group Databasebeta

← D59×#2364 #28748265

Subgroups — D59×#2364 #28748265

Order 15104.

4262 conjugacy classes of subgroups.

The subgroup lattice has 1086 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#121×D59C211yesmaximal, characteristic
2C2×C4×D4×D59C212yesmaximal, complemented
3#21427148C211yesmaximal, characteristic, complemented
4#21427147C212yesmaximal, complemented
5#21427146C211yesmaximal, characteristic, complemented
6#21427145C212yesmaximal, complemented
7#21427144C212yesmaximal, complemented
8#21427143C211yesmaximal, characteristic, complemented
9#21427142C212yesmaximal, complemented
10#21427141C212yesmaximal, complemented
11#21427140C212yesmaximal, complemented
12#388×D59C212yesmaximal, complemented
13#387×D59C212yesmaximal, complemented
14#386×D59C212yesmaximal, complemented
15#386×D59C212yesmaximal, complemented
16C4×C22⋊C4×D59C211yesmaximal, characteristic, complemented
17C4×C22⋊C4×D59C212yesmaximal, complemented
18C2×#95×D59C211yesmaximal, characteristic, complemented
19C59×#2364C211yesmaximal, characteristic, complemented
20C22×D4×D59C2212yes—
21C22×D4×D59C2211yescharacteristic
22C23×C4×D59C2212yes—
23C23×C4×D59C2212yes—
24C23×C4×D59C2211yescharacteristic
25C2×#14273702C2211yescharacteristic
26C2×#14273701C2211yescharacteristic
27C2×#14273700C2212yes—
28C2×#14273699C2212yes—
29C2×#14273698C2211yescharacteristic
30#121×D59C4116yescomplemented
31C2×C4×D236C2212yescomplemented
32C2×D4×Dic59C2212yescomplemented
33C2×#14273689C2212yescomplemented
34C2×C4×C22⋊D59C2212yescomplemented
35C2×C4×C22⋊D59C2212yescomplemented
36C2×(C22⋊D59)⋊C4C2212yescomplemented
37C2×(C22⋊D59)⋊C4C2212yescomplemented
38C4×D4×D59—216no—
39C2×C4⋊C4×D59C2212yes—
40C2×C4⋊C4×D59C2211yescharacteristic
41C2×C22⋊C4×D59C2212yes—
42C2×C22⋊C4×D59C2211yescharacteristic
43C2×C22⋊C4×D59C2212yes—
44C2×C22⋊C4×D59C2212yes—
45C2×C22⋊C4×D59C2212yes—
46C2×C22⋊C4×D59C2211yescharacteristic
47C2×C42×D59C2212yes—
48C2×C42×D59C2212yes—
49#16837296C2212yescomplemented
50#16837295C2212yescomplemented
51#16837294C2212yescomplemented
52#16837293C2212yescomplemented
53#16837292C2212yescomplemented
54#16837291C2212yescomplemented
55#16837290C2212yescomplemented
56#16837289C2212yescomplemented
57#16837288C2212yescomplemented
58#16837287C2212yescomplemented
59#16837286C2212yescomplemented
60#16837285C2212yescomplemented
61#16837284C2212yescomplemented
62#16837283C2212yescomplemented
63#16837282C2212yescomplemented
64#16837282C2212yescomplemented
65#16837281C2212yescomplemented
66#16837281C2212yescomplemented
67#16837280C2212yescomplemented
68#16837280C2212yescomplemented
69#16837280C2212yescomplemented
70#16837280C2212yescomplemented
71#16837279C2212yescomplemented
72#16837279C2212yescomplemented
73#16837278C2212yescomplemented
74#16837278C2212yescomplemented
75#16837278C2212yescomplemented
76#16837278C2212yescomplemented
77C22⋊C4×Dic59C2212yescomplemented
78C22⋊C4×Dic59C2211yescharacteristic, complemented
79C22⋊C4×Dic59C2211yescharacteristic, complemented
80C22⋊C4×Dic59C2212yescomplemented
81C4×(C2×D59)⋊C4C2212yescomplemented
82C4×(C2×D59)⋊C4C2212yescomplemented
83C4×(C2×D59)⋊C4C2212yescomplemented
84C4×C22⋊Dic59C2212yescomplemented
85C4×C22⋊Dic59C2211yescharacteristic, complemented
86#16837249C2212yescomplemented
87#16837249C2212yescomplemented
88#16837249C2212yescomplemented
89C2×C59⋊#95C2212yescomplemented
90C2×C59⋊#95C2211yescharacteristic, complemented
91#95×D59C2212yes—
92#95×D59C2212yes—
93#95×D59C2212yes—
94#95×D59C2212yes—
95#95×D59C2211yescharacteristic
96#95×D59C2211yescharacteristic
97#95×D59C2211yescharacteristic, complemented
98#95×D59C2212yescomplemented
99#95×D59C2211yescharacteristic, complemented
100C2×#121×C59C2211yescharacteristic
101C2×C4×D4×C59C2212yescomplemented
102C59×#388C2212yescomplemented
103C59×#387C2212yescomplemented
104C59×#386C2212yescomplemented
105C59×#386C2212yescomplemented
106C4×C22⋊C4×C59C2211yescharacteristic, complemented
107C4×C22⋊C4×C59C2212yescomplemented
108C2×#95×C59C2211yescharacteristic, complemented
109C24×D59C2312yes—
110C24×D59C2311yescharacteristic
111C22×D236C2312yes—
112C22×D236C2311yescharacteristic
113C22×C22⋊D59C2312yes—
114C22×C22⋊D59C2312yes—
115C22×C22⋊D59C2312yes—
116C2×D4×D59—28no—
117C2×D4×D59—28no—
118C2×D4×D59—44no—
119C2×D4×D59C2×C4116yescomplemented
120C2×D4×D59C2×C418yescomplemented
121C23×Dic59C2312yes—
122C23×Dic59C2312yes—
123C23×Dic59C2311yescharacteristic
124C22×C4×D59—28no—
125C22×C4×D59—28no—
126C22×C4×D59—28no—
127C22×C4×D59—28no—
128C22×C4×D59—44no—
129C22×C4×D59—44no—
130C22×C4×D59—44no—
131C22×C4×D59C2×C418yescomplemented
132C22×C4×D59C2312yes—
133C22×C4×D59C2312yes—
134C22×C4×D59C2312yes—
135C22×C4×D59C2312yes—
136C22×C4×D59C2312yes—
137C22×C4×D59C2312yes—
138C22×C4×D59C2311yescharacteristic
139C22×C4×D59C2311yescharacteristic
140C22×C4×D59C2312yes—
141C22×C4×D59C2312yes—
142C22×C4×D59C2312yes—
143C22×C4×D59C2311yescharacteristic
144C22×C4×D59C2311yescharacteristic
145#14273702C2×C418yescomplemented
146#14273701C2×C418yescomplemented
147#14273700C2×C4116yescomplemented
148#14273699C2×C4116yescomplemented
149#14273698C2×C418yescomplemented
150C4×D236—28no—
151D4×Dic59—28no—
152#14273689—28no—
153C4×C22⋊D59—28no—
154C4×C22⋊D59—28no—
155(C22⋊D59)⋊C4—28no—
156(C22⋊D59)⋊C4—28no—
157C2×C4⋊Dic59C2312yes—
158C2×C4⋊Dic59C2311yescharacteristic
159C2×Dic59⋊C4C2312yes—
160C2×Dic59⋊C4C2312yes—
161C2×Dic59⋊C4C2312yes—
162C4⋊C4×D59—28no—
163C4⋊C4×D59C2×C418yescomplemented
164C2×C22⋊Dic59C2312yes—
165C2×C22⋊Dic59C2311yescharacteristic
166C2×C22⋊Dic59C2312yes—
167C2×C22⋊Dic59C2312yes—
168C2×C22⋊Dic59C2312yes—
169C2×C22⋊Dic59C2311yescharacteristic
170C2×(C2×D59)⋊C4C2312yes—
171C2×(C2×D59)⋊C4C2312yes—
172C2×(C2×D59)⋊C4C2312yes—
173C2×(C2×D59)⋊C4C2312yes—
174C2×(C2×D59)⋊C4C2312yes—
175C2×(C2×D59)⋊C4C2312yes—
176C2×(C2×D59)⋊C4C2312yes—
177C2×(C2×D59)⋊C4C2312yes—
178C2×(C2×D59)⋊C4C2312yes—
179C2×(C2×D59)⋊C4C2312yes—
180C22⋊C4×D59—24no—
181C22⋊C4×D59—28no—
182C22⋊C4×D59—28no—
183C22⋊C4×D59—44no—
184C22⋊C4×D59C2×C4116yescomplemented
185C22⋊C4×D59D418yescomplemented
186C2×C4×Dic59C2312yes—
187C2×C4×Dic59C2312yes—
188C2×C4×Dic59C2312yes—
189C2×C4×Dic59C2312yes—
190C2×C4×Dic59C2312yes—
191C2×C4×Dic59C2312yes—
192C42×D59—28no—
193C42×D59—44no—
194C59⋊#95C2312yes—
195C59⋊#95C2311yescharacteristic
196C59⋊#95C2312yes—
197C59⋊#95C2312yes—
198C59⋊#95C2312yes—
199C59⋊#95C2312yes—
200C59⋊#95C2311yescharacteristic
201C59⋊#95C2312yes—
202C59⋊#95C2312yes—
203C59⋊#95C2312yes—
204C59⋊#95C2312yes—
205C59⋊#95C2312yes—
206C59⋊#95C2312yes—
207C59⋊#95C2312yes—
208C59⋊#95C2312yes—
209C59⋊#95C2312yes—
210C22×D4×C59C2312yes—
211C22×D4×C59C2311yescharacteristic
212C23×C4×C59C2312yes—
213C23×C4×C59C2312yes—
214C23×C4×C59C2311yescharacteristic
215#121×C59C2×C418yescomplemented
216C4×D4×C59—28no—
217C2×C4⋊C4×C59C2312yes—
218C2×C4⋊C4×C59C2311yescharacteristic
219C2×C22⋊C4×C59C2312yes—
220C2×C22⋊C4×C59C2311yescharacteristic
221C2×C22⋊C4×C59C2312yes—
222C2×C22⋊C4×C59C2312yes—
223C2×C22⋊C4×C59C2312yes—
224C2×C22⋊C4×C59C2311yescharacteristic
225C2×C42×C59C2312yes—
226C2×C42×C59C2312yes—
227#95×C59C2311yescharacteristic
228#95×C59C2312yes—
229#95×C59C2311yescharacteristic
230#95×C59C2312yes—
231#95×C59C2312yes—
232#95×C59C2312yes—
233C24×C59C2412yes—
234C24×C59C2411yescharacteristic
235C23×D59—24no—
236C23×D59—24no—
237C23×D59—24no—
238C23×D59—24no—
239C23×D59—24no—
240C23×D59—24no—
241C23×D59—24no—
242C23×D59—24no—
243C23×D59C22×C418yes—
244C23×D59C22×C414yes—
245C23×D59C2×D414yes—
246C23×D59#4114yes—
247C23×D59C2412yes—
248C23×D59C2411yescharacteristic
249C23×D59C2411yescharacteristic
250C2×D4×C59—24no—
251C2×D4×C59—24no—
252C2×D4×C59—42no—
253C2×D4×C59C22×C418yescomplemented
254C2×D4×C59C22×C414yescomplemented
255C22×C4×C59—24no—
256C22×C4×C59—24no—
257C22×C4×C59—24no—
258C22×C4×C59—24no—
259C22×C4×C59—42no—
260C22×C4×C59—42no—
261C22×C4×C59—42no—
262C22×C4×C59C22×C414yescomplemented
263C22×C4×C59C2412yes—
264C22×C4×C59C2412yes—
265C22×C4×C59C2411yescharacteristic
266C22×C4×C59C2411yescharacteristic
267C22×C4×C59C2412yes—
268C22×C4×C59C2412yes—
269C22×C4×C59C2412yes—
270C2×C22⋊D59—24no—
271C2×C22⋊D59—24no—
272C2×C22⋊D59—24no—
273C2×C22⋊D59—24no—
274C2×C22⋊D59—42no—
275C2×C22⋊D59—42no—
276C2×C22⋊D59C22×C418yescomplemented
277C2×C22⋊D59C22×C418yescomplemented
278C2×C22⋊D59C22×C418yescomplemented
279C22×Dic59—24no—
280C22×Dic59—24no—
281C22×Dic59—24no—
282C22×Dic59—24no—
283C22×Dic59—42no—
284C22×Dic59—42no—
285C22×Dic59—42no—
286C22×Dic59C22×C414yescomplemented
287C22×Dic59C2412yes—
288C22×Dic59C2412yes—
289C22×Dic59C2411yescharacteristic
290C22×Dic59C2411yescharacteristic
291C22×Dic59C2412yes—
292C22×Dic59C2412yes—
293C22×Dic59C2412yes—
294D4×D59—264no—
295D4×D59—416no—
296C2×D236—24no—
297C2×D236—24no—
298C2×D236—42no—
299C2×D236C22×C418yescomplemented
300C2×D236C22×C414yescomplemented
301C2×C4×D59—24no—
302C2×C4×D59—24no—
303C2×C4×D59—24no—
304C2×C4×D59—24no—
305C2×C4×D59—24no—
306C2×C4×D59—24no—
307C2×C4×D59—24no—
308C2×C4×D59—24no—
309C2×C4×D59—24no—
310C2×C4×D59—24no—
311C2×C4×D59—24no—
312C2×C4×D59—24no—
313C2×C4×D59—24no—
314C2×C4×D59—24no—
315C2×C4×D59—24no—
316C2×C4×D59—24no—
317C2×C4×D59—24no—
318C2×C4×D59—24no—
319C2×C4×D59—24no—
320C2×C4×D59—24no—
321C2×C4×D59—24no—
322C2×C4×D59—24no—
323C2×C4×D59—416no—
324C2×C4×D59—432no—
325C2×C4×D59—432no—
326C2×C4×D59—42no—
327C2×C4×D59—42no—
328C2×C4×D59—42no—
329C2×C4×D59—42no—
330C2×C4×D59—42no—
331C2×C4×D59—42no—
332C2×C4×D59C22×C414yes—
333C2×C4×D59C22×C418yes—
334C2×C4×D59C22×C414yes—
335C2×C4×D59C22×C414yescomplemented
336C2×C4×D59C22×C414yescomplemented
337C2×C4×D59C2×D418yes—
338C2×C4×D59#4118yes—
339C4⋊C4×C59—24no—
340C4⋊C4×C59C22×C414yescomplemented
341C22⋊C4×C59—22no—
342C22⋊C4×C59—24no—
343C22⋊C4×C59—24no—
344C22⋊C4×C59—42no—
345C22⋊C4×C59C22×C418yescomplemented
346C22⋊C4×C59C2×D414yescomplemented
347C42×C59—24no—
348C42×C59—42no—
349C22⋊Dic59—22no—
350C22⋊Dic59—24no—
351C22⋊Dic59—24no—
352C22⋊Dic59—42no—
353C22⋊Dic59C22×C418yescomplemented
354C22⋊Dic59C2×D414yescomplemented
355(C2×D59)⋊C4—24no—
356(C2×D59)⋊C4—24no—
357(C2×D59)⋊C4—24no—
358(C2×D59)⋊C4—24no—
359(C2×D59)⋊C4—24no—
360(C2×D59)⋊C4—42no—
361(C2×D59)⋊C4—42no—
362(C2×D59)⋊C4C22×C418yescomplemented
363(C2×D59)⋊C4C22×C418yescomplemented
364(C2×D59)⋊C4C2×D418yescomplemented
365C4⋊Dic59—24no—
366C4⋊Dic59C22×C414yescomplemented
367Dic59⋊C4—24no—
368Dic59⋊C4—24no—
369Dic59⋊C4C22×C418yescomplemented
370C4×Dic59—24no—
371C4×Dic59—24no—
372C4×Dic59—24no—
373C4×Dic59—42no—
374C4×Dic59—42no—
375C4×Dic59—42no—
376C23×C59—22no—
377C23×C59—22no—
378C23×C59—22no—
379C23×C59—22no—
380C23×C59—22no—
381C23×C59—22no—
382C23×C59—22no—
383C23×C59—22no—
384C23×C59C23×C414yes—
385C23×C59C23×C412yes—
386C23×C59C22×D412yes—
387C23×C59C2×#4112yes—
388C23×C59C2511yescharacteristic
389C22×D59—22no—
390C22×D59—22no—
391C22×D59—28no—
392C22×D59—28no—
393C22×D59—216no—
394C22×D59—216no—
395C22×D59—22no—
396C22×D59—22no—
397C22×D59—22no—
398C22×D59—22no—
399C22×D59—22no—
400C22×D59—22no—
401C22×D59—216no—
402C22×D59—216no—
403C22×D59—216no—
404C22×D59—48no—
405C22×D59—48no—
406C22×D59—48no—
407C22×D59—48no—
408C22×D59C4×D4116yes—
409C22×D59C23×C414yes—
410C22×D59C23×C412yes—
411C22×D59C23×C412yes—
412C22×D59C22×D412yes—
413C22×D59C22×D412yes—
414C22×D59C2×#4112yes—
415C22×D59C2×#4112yes—
416C22×D59C2×#4114yes—
417C22×D59H(5,𝔽2)14yes—
418D4×C59—216no—
419D4×C59—44no—
420C2×C4×C59—22no—
421C2×C4×C59—22no—
422C2×C4×C59—22no—
423C2×C4×C59—22no—
424C2×C4×C59—22no—
425C2×C4×C59—22no—
426C2×C4×C59—22no—
427C2×C4×C59—22no—
428C2×C4×C59—22no—
429C2×C4×C59—22no—
430C2×C4×C59—22no—
431C2×C4×C59—22no—
432C2×C4×C59—22no—
433C2×C4×C59—22no—
434C2×C4×C59—44no—
435C2×C4×C59—48no—
436C2×C4×C59—48no—
437C2×C4×C59C23×C414yes—
438C2×C4×C59C23×C412yes—
439C2×C4×C59C23×C412yes—
440C2×C4×C59C22×D414yes—
441C2×C4×C59C2×#4114yes—
442C22⋊D59—216no—
443C22⋊D59—216no—
444C22⋊D59—48no—
445C2×Dic59—22no—
446C2×Dic59—22no—
447C2×Dic59—22no—
448C2×Dic59—22no—
449C2×Dic59—22no—
450C2×Dic59—22no—
451C2×Dic59—22no—
452C2×Dic59—22no—
453C2×Dic59—22no—
454C2×Dic59—22no—
455C2×Dic59—22no—
456C2×Dic59—22no—
457C2×Dic59—22no—
458C2×Dic59—22no—
459C2×Dic59—44no—
460C2×Dic59—48no—
461C2×Dic59—48no—
462C2×Dic59C23×C412yes—
463C2×Dic59C23×C414yes—
464C2×Dic59C23×C412yes—
465C2×Dic59C22×D414yes—
466C2×Dic59C2×#4114yes—
467D236—216no—
468D236—44no—
469C4×D59—216no—
470C4×D59—28no—
471C4×D59—28no—
472C4×D59—216no—
473C4×D59—216no—
474C4×D59—44no—
475C4×D59—44no—
476C4×D59—48no—
477C4×D59—48no—
478C4×D59—48no—
479C4×D59—48no—
480C4×D59—48no—
481C4×D59—48no—
482C2×#2364—591nomaximal, Sylow
483C22×C59—22no—
484C22×C59—22no—
485C22×C59—24no—
486C22×C59—24no—
487C22×C59—24no—
488C22×C59—24no—
489C22×C59—24no—
490C22×C59—42no—
491C22×C59—42no—
492C22×C59—42no—
493C22×C59—42no—
494C22×C59C2×C4×D414yes—
495C22×C59C24×C411yescharacteristic
496C22×C59C23×D411yescharacteristic
497C22×C59C22×#4111yescharacteristic
498C22×C59C22×#4112yes—
499C22×C59C2×H(5,𝔽2)12yes—
500C2×D59—22no—
501C2×D59—22no—
502C2×D59—24no—
503C2×D59—24no—
504C2×D59—232no—
505C2×D59—24no—
506C2×D59—24no—
507C2×D59—24no—
508C2×D59—42no—
509C2×D59—42no—
510C2×D59—42no—
511C2×D59—42no—
512C2×D59—432no—
513C2×D59C2×C4×D414yes—
514C2×D59C2×C4×D414yes—
515C2×D59C4×#4114yes—
516C2×D59#51814yes—
517C2×D59#54618yes—
518C2×D59#55318yes—
519C4×C59—24no—
520C4×C59—22no—
521C4×C59—22no—
522C4×C59—24no—
523C4×C59—24no—
524C4×C59—42no—
525C4×C59—42no—
526Dic59—24no—
527Dic59—22no—
528Dic59—22no—
529Dic59—24no—
530Dic59—24no—
531Dic59—42no—
532Dic59—42no—
533C22×#121—591no—
534C22×C4×D4—592no—
535#2364—592no—
536#2364—592no—
537#2364—592no—
538#2364—592no—
539#2364—591no—
540#2364—592no—
541#2364—591no—
542#2364—591no—
543#2364—592no—
544#2364D5911yescharacteristic, direct product factor
545C2×#388—592no—
546C2×#387—592no—
547C2×#386—592no—
548C2×#386—592no—
549C2×C4×C22⋊C4—591no—
550C2×C4×C22⋊C4—592no—
551C22×#95—591no—
552C2×C59—24no—
553C2×C59—44no—
554C2×C59C22×C4×D411yescharacteristic
555C2×C59C2×C4×#4111yescharacteristic
556C2×C59C2×#51811yescharacteristic
557C2×C59C2×#54612yes—
558C2×C59C2×#55312yes—
559D59—24no—
560D59—44no—
561D59#236418yesdirect product factor
562C23×D4—592no—
563C23×D4—591no—
564C24×C4—591no—
565C24×C4—592no—
566C24×C4—592no—
567C2×#121—591no—
568C2×#121—592no—
569C2×#121—591no—
570C2×#121—5916no—
571C2×#121—591no—
572C2×#121—592no—
573C2×#121C2×D5911yescharacteristic
574C2×C4×D4—592no—
575C2×C4×D4—592no—
576C2×C4×D4—592no—
577C2×C4×D4—592no—
578C2×C4×D4—592no—
579C2×C4×D4—592no—
580C2×C4×D4—592no—
581C2×C4×D4—11816no—
582C2×C4×D4C2×D5912yescomplemented
583C22×C4⋊C4—591no—
584C22×C4⋊C4—592no—
585C22×C22⋊C4—591no—
586C22×C22⋊C4—592no—
587C22×C22⋊C4—592no—
588C22×C22⋊C4—592no—
589C22×C22⋊C4—591no—
590C22×C22⋊C4—592no—
591C22×C42—592no—
592C22×C42—592no—
593#388—592no—
594#388—592no—
595#388—592no—
596#388—592no—
597#388—592no—
598#388—592no—
599#388—592no—
600#388C2×D5912yescomplemented
601#387—592no—
602#387—592no—
603#387—592no—
604#387—592no—
605#387—592no—
606#387—592no—
607#387—592no—
608#387C2×D5912yescomplemented
609#386—592no—
610#386—592no—
611#386—592no—
612#386—592no—
613#386—592no—
614#386—592no—
615#386—592no—
616#386—592no—
617#386—592no—
618#386—592no—
619#386—592no—
620#386—592no—
621#386—592no—
622#386—592no—
623#386C2×D5912yescomplemented
624#386C2×D5912yescomplemented
625C4×C22⋊C4—592no—
626C4×C22⋊C4—591no—
627C4×C22⋊C4—592no—
628C4×C22⋊C4—592no—
629C4×C22⋊C4—591no—
630C4×C22⋊C4—591no—
631C4×C22⋊C4—592no—
632C4×C22⋊C4—592no—
633C4×C22⋊C4—592no—
634C4×C22⋊C4—592no—
635C4×C22⋊C4—592no—
636C4×C22⋊C4—592no—
637C4×C22⋊C4C2×D5912yescomplemented
638C4×C22⋊C4C2×D5911yescharacteristic, complemented
639C2×#95—592no—
640C2×#95—591no—
641C2×#95—591no—
642C2×#95—592no—
643C2×#95—591no—
644C2×#95—591no—
645C2×#95—592no—
646C2×#95—591no—
647C2×#95—592no—
648C2×#95—592no—
649C2×#95—592no—
650C2×#95C2×D5911yescharacteristic, complemented
651C59C2×#236411yescharacteristic, complemented, Sylow
652C25—591no—
653C25—592no—
654C22×D4—592no—
655C22×D4—592no—
656C22×D4—592no—
657C22×D4—5916no—
658C22×D4—598no—
659C22×D4—592no—
660C22×D4—591no—
661C22×D4—1188no—
662C22×D4—1188no—
663C22×D4—2364no—
664C22×D4C22×D5912yes—
665C22×D4C22×D5911yescharacteristic
666C23×C4—591no—
667C23×C4—592no—
668C23×C4—591no—
669C23×C4—592no—
670C23×C4—592no—
671C23×C4—591no—
672C23×C4—598no—
673C23×C4—591no—
674C23×C4—591no—
675C23×C4—592no—
676C23×C4—592no—
677C23×C4—592no—
678C23×C4—592no—
679C23×C4—592no—
680C23×C4—592no—
681C23×C4—592no—
682C23×C4—592no—
683C23×C4—1188no—
684C23×C4—1188no—
685C23×C4—1188no—
686C23×C4—1188no—
687C23×C4—2364no—
688C23×C4—2364no—
689C23×C4—2364no—
690C23×C4C22×D5912yes—
691C23×C4C22×D5912yes—
692C23×C4C22×D5911yescharacteristic
693#121—598no—
694#121—5916no—
695#121—598no—
696#121—598no—
697#121—5916no—
698#121C4×D5918yescomplemented
699C4×D4—28no—
700C4×D4—1188no—
701C4×D4—1188no—
702C4×D4—1188no—
703C4×D4—1188no—
704C4×D4—1188no—
705C4×D4—1188no—
706C4×D4—1188no—
707C2×C4⋊C4—592no—
708C2×C4⋊C4—591no—
709C2×C4⋊C4—598no—
710C2×C4⋊C4—592no—
711C2×C4⋊C4—592no—
712C2×C4⋊C4—592no—
713C2×C4⋊C4—1188no—
714C2×C4⋊C4C22×D5912yes—
715C2×C4⋊C4C22×D5911yescharacteristic
716C2×C22⋊C4—591no—
717C2×C22⋊C4—592no—
718C2×C22⋊C4—592no—
719C2×C22⋊C4—592no—
720C2×C22⋊C4—592no—
721C2×C22⋊C4—5916no—
722C2×C22⋊C4—598no—
723C2×C22⋊C4—592no—
724C2×C22⋊C4—592no—
725C2×C22⋊C4—591no—
726C2×C22⋊C4—592no—
727C2×C22⋊C4—592no—
728C2×C22⋊C4—592no—
729C2×C22⋊C4—592no—
730C2×C22⋊C4—592no—
731C2×C22⋊C4—592no—
732C2×C22⋊C4—592no—
733C2×C22⋊C4—592no—
734C2×C22⋊C4—1188no—
735C2×C22⋊C4—1188no—
736C2×C22⋊C4—1184no—
737C2×C22⋊C4—2364no—
738C2×C22⋊C4C22×D5912yes—
739C2×C22⋊C4C22×D5911yescharacteristic
740C2×C22⋊C4C22×D5912yes—
741C2×C22⋊C4C22×D5912yes—
742C2×C22⋊C4C22×D5912yes—
743C2×C22⋊C4C22×D5911yescharacteristic
744C2×C42—592no—
745C2×C42—592no—
746C2×C42—592no—
747C2×C42—592no—
748C2×C42—592no—
749C2×C42—592no—
750C2×C42—1188no—
751C2×C42—2364no—
752C2×C42C22×D5912yes—
753C2×C42C22×D5912yes—
754#95—591no—
755#95—592no—
756#95—592no—
757#95—592no—
758#95—592no—
759#95—592no—
760#95—591no—
761#95—592no—
762#95—592no—
763#95—592no—
764#95—592no—
765#95—592no—
766#95—592no—
767#95—592no—
768#95—592no—
769#95—592no—
770#95C22×D5911yescharacteristic
771#95C22×D5912yes—
772#95C22×D5911yescharacteristic
773#95C22×D5912yes—
774#95C22×D5912yes—
775#95C22×D5912yes—
776C24—591no—
777C24—594no—
778C24—594no—
779C24—594no—
780C24—591no—
781C24—598no—
782C24—592no—
783C24—1184no—
784C24—1184no—
785C24—1184no—
786C24—1184no—
787C24—1184no—
788C24—1184no—
789C24—1184no—
790C24—1184no—
791C24C23×D5912yes—
792C24C23×D5911yescharacteristic
793C2×D4—24no—
794C2×D4—24no—
795C2×D4—42no—
796C2×D4—598no—
797C2×D4—598no—
798C2×D4—598no—
799C2×D4—598no—
800C2×D4—594no—
801C2×D4—1184no—
802C2×D4—1184no—
803C2×D4—11864no—
804C2×D4—1184no—
805C2×D4—1184no—
806C2×D4—1184no—
807C2×D4—1184no—
808C2×D4—2362no—
809C2×D4—23616no—
810C2×D4—2362no—
811C2×D4—2362no—
812C2×D4C2×C4×D5918yescomplemented
813C2×D4C2×C4×D5914yescomplemented
814C22×C4—24no—
815C22×C4—24no—
816C22×C4—24no—
817C22×C4—24no—
818C22×C4—42no—
819C22×C4—42no—
820C22×C4—42no—
821C22×C4—591no—
822C22×C4—592no—
823C22×C4—591no—
824C22×C4—592no—
825C22×C4—592no—
826C22×C4—594no—
827C22×C4—594no—
828C22×C4—598no—
829C22×C4—594no—
830C22×C4—598no—
831C22×C4—598no—
832C22×C4—594no—
833C22×C4—594no—
834C22×C4—592no—
835C22×C4—592no—
836C22×C4—1184no—
837C22×C4—1184no—
838C22×C4—1184no—
839C22×C4—1184no—
840C22×C4—1184no—
841C22×C4—1184no—
842C22×C4—1184no—
843C22×C4—1184no—
844C22×C4—1184no—
845C22×C4—1184no—
846C22×C4—1184no—
847C22×C4—1184no—
848C22×C4—1184no—
849C22×C4—1184no—
850C22×C4—1184no—
851C22×C4—1184no—
852C22×C4—1184no—
853C22×C4—1184no—
854C22×C4—1184no—
855C22×C4—1184no—
856C22×C4—1184no—
857C22×C4—1184no—
858C22×C4—1184no—
859C22×C4—1184no—
860C22×C4—1184no—
861C22×C4—1184no—
862C22×C4—2362no—
863C22×C4—2362no—
864C22×C4—2362no—
865C22×C4—2362no—
866C22×C4—2362no—
867C22×C4—2362no—
868C22×C4—23616no—
869C22×C4—23632no—
870C22×C4—23632no—
871C22×C4—2362no—
872C22×C4—2362no—
873C22×C4—2362no—
874C22×C4C2×C4×D5914yescomplemented
875C22×C4C23×D5912yes—
876C22×C4C23×D5912yes—
877C22×C4C23×D5911yescharacteristic
878C22×C4C23×D5911yescharacteristic
879C22×C4C23×D5912yes—
880C22×C4C23×D5912yes—
881C22×C4C23×D5912yes—
882C4⋊C4—24no—
883C4⋊C4—598no—
884C4⋊C4—594no—
885C4⋊C4—1184no—
886C4⋊C4—1184no—
887C4⋊C4—1184no—
888C4⋊C4C2×C4×D5914yescomplemented
889C22⋊C4—22no—
890C22⋊C4—24no—
891C22⋊C4—24no—
892C22⋊C4—42no—
893C22⋊C4—598no—
894C22⋊C4—594no—
895C22⋊C4—598no—
896C22⋊C4—598no—
897C22⋊C4—598no—
898C22⋊C4—1184no—
899C22⋊C4—1184no—
900C22⋊C4—1184no—
901C22⋊C4—1184no—
902C22⋊C4—1184no—
903C22⋊C4—1182no—
904C22⋊C4—1184no—
905C22⋊C4—1184no—
906C22⋊C4—2362no—
907C22⋊C4—2362no—
908C22⋊C4—2362no—
909C22⋊C4C2×C4×D5918yescomplemented
910C22⋊C4D4×D5914yescomplemented
911C42—24no—
912C42—42no—
913C42—1184no—
914C42—1184no—
915C42—1184no—
916C42—2362no—
917C42—2362no—
918C42—2362no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—592no—
928C23—592no—
929C23—594no—
930C23—592no—
931C23—594no—
932C23—592no—
933C23—592no—
934C23—592no—
935C23—5916no—
936C23—594no—
937C23—1188no—
938C23—11816no—
939C23—1188no—
940C23—11816no—
941C23—11816no—
942C23—11816no—
943C23—11816no—
944C23—1182no—
945C23—1182no—
946C23—1182no—
947C23—1182no—
948C23—1182no—
949C23—1182no—
950C23—1182no—
951C23—1182no—
952C23—2368no—
953C23—2368no—
954C23—2368no—
955C23—2368no—
956C23C22×C4×D5914yes—
957C23C22×C4×D5912yes—
958C23C2×D4×D5912yes—
959C23#41×D5912yes—
960C23C24×D5911yescharacteristic
961D4—216no—
962D4—44no—
963D4—11816no—
964D4—11816no—
965D4—11816no—
966D4—2364no—
967D4—2368no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—44no—
983C2×C4—48no—
984C2×C4—48no—
985C2×C4—592no—
986C2×C4—594no—
987C2×C4—592no—
988C2×C4—594no—
989C2×C4—594no—
990C2×C4—1188no—
991C2×C4—11816no—
992C2×C4—11816no—
993C2×C4—1188no—
994C2×C4—11816no—
995C2×C4—1182no—
996C2×C4—1182no—
997C2×C4—1182no—
998C2×C4—1182no—
999C2×C4—1182no—
1000C2×C4—1182no—
1001C2×C4—1182no—
1002C2×C4—1182no—
1003C2×C4—1182no—
1004C2×C4—1182no—
1005C2×C4—1182no—
1006C2×C4—1182no—
1007C2×C4—1182no—
1008C2×C4—1182no—
1009C2×C4—2364no—
1010C2×C4—2364no—
1011C2×C4—2368no—
1012C2×C4—2368no—
1013C2×C4—2368no—
1014C2×C4—2368no—
1015C2×C4—2368no—
1016C2×C4—2368no—
1017C2×C4—2364no—
1018C2×C4—2368no—
1019C2×C4—2368no—
1020C2×C4C22×C4×D5912yes—
1021C2×C4C22×C4×D5914yes—
1022C2×C4C22×C4×D5912yes—
1023C2×C4C2×D4×D5914yes—
1024C2×C4#41×D5914yes—
1025C22—22no—
1026C22—22no—
1027C22—24no—
1028C22—24no—
1029C22—24no—
1030C22—24no—
1031C22—24no—
1032C22—42no—
1033C22—42no—
1034C22—42no—
1035C22—42no—
1036C22—594no—
1037C22—594no—
1038C22—594no—
1039C22—598no—
1040C22—598no—
1041C22—594no—
1042C22—11832no—
1043C22—1182no—
1044C22—1182no—
1045C22—1184no—
1046C22—1184no—
1047C22—1184no—
1048C22—1184no—
1049C22—1184no—
1050C22—23632no—
1051C22—2362no—
1052C22—2362no—
1053C22—2362no—
1054C22—2362no—
1055C22C4×D4×D5914yes—
1056C22C23×C4×D5911yescharacteristic
1057C22C22×D4×D5911yescharacteristic
1058C22C2×#41×D5911yescharacteristic
1059C22C2×#41×D5912yes—
1060C22H(5,𝔽2)×D5912yes—
1061C4—24no—
1062C4—22no—
1063C4—22no—
1064C4—24no—
1065C4—24no—
1066C4—42no—
1067C4—42no—
1068C4—1184no—
1069C4—1182no—
1070C4—1182no—
1071C4—1184no—
1072C4—1184no—
1073C4—2362no—
1074C4—2362no—
1075C2—24no—
1076C2—44no—
1077C2—598no—
1078C2—1184no—
1079C2—2364no—
1080C2C2×C4×D4×D5911yescharacteristic
1081C2C4×#41×D5911yescharacteristic
1082C2#518×D5911yescharacteristic
1083C2#546×D5912yes—
1084C2#553×D5912yes—
subgroupG/H
center, FrattiniC23C24×D59
commutatorC22×C59C24×C4
FittingC59×#2364C2
socle, cosocleC23×C59C25
prime radicalC2×#121×D59C2
hypercenter#2364D59
hypocenterC59C2×#2364
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ #2364

Complements

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

NH ≅ G/Ntype
2. C2×C4×D4×D59C2semidirect
3. #21427148C2semidirect
4. #21427147C2semidirect
5. #21427146C2semidirect
6. #21427145C2semidirect
7. #21427144C2semidirect
8. #21427143C2semidirect
9. #21427142C2semidirect
10. #21427141C2semidirect
11. #21427140C2semidirect
12. #388×D59C2semidirect
13. #387×D59C2semidirect
14. #386×D59C2semidirect
15. #386×D59C2semidirect
16. C4×C22⋊C4×D59C2semidirect
17. C4×C22⋊C4×D59C2semidirect
18. C2×#95×D59C2semidirect
19. C59×#2364C2semidirect
30. #121×D59C4semidirect
31. C2×C4×D236C22semidirect
32. C2×D4×Dic59C22semidirect
33. C2×#14273689C22semidirect
34. C2×C4×C22⋊D59C22semidirect
35. C2×C4×C22⋊D59C22semidirect
36. C2×(C22⋊D59)⋊C4C22semidirect
37. C2×(C22⋊D59)⋊C4C22semidirect
49. #16837296C22semidirect
50. #16837295C22semidirect
51. #16837294C22semidirect
52. #16837293C22semidirect
53. #16837292C22semidirect
54. #16837291C22semidirect
55. #16837290C22semidirect
56. #16837289C22semidirect
57. #16837288C22semidirect
58. #16837287C22semidirect
59. #16837286C22semidirect
60. #16837285C22semidirect
61. #16837284C22semidirect
62. #16837283C22semidirect
63. #16837282C22semidirect
64. #16837282C22semidirect
65. #16837281C22semidirect
66. #16837281C22semidirect
67. #16837280C22semidirect
68. #16837280C22semidirect
69. #16837280C22semidirect
70. #16837280C22semidirect
71. #16837279C22semidirect
72. #16837279C22semidirect
73. #16837278C22semidirect
74. #16837278C22semidirect
75. #16837278C22semidirect
76. #16837278C22semidirect
77. C22⋊C4×Dic59C22semidirect
78. C22⋊C4×Dic59C22semidirect
79. C22⋊C4×Dic59C22semidirect
80. C22⋊C4×Dic59C22semidirect
81. C4×(C2×D59)⋊C4C22semidirect
82. C4×(C2×D59)⋊C4C22semidirect
83. C4×(C2×D59)⋊C4C22semidirect
84. C4×C22⋊Dic59C22semidirect
85. C4×C22⋊Dic59C22semidirect
86. #16837249C22semidirect
87. #16837249C22semidirect
88. #16837249C22semidirect
89. C2×C59⋊#95C22semidirect
90. C2×C59⋊#95C22semidirect
97. #95×D59C22semidirect
98. #95×D59C22semidirect
99. #95×D59C22semidirect
101. C2×C4×D4×C59C22semidirect
102. C59×#388C22semidirect
103. C59×#387C22semidirect
104. C59×#386C22semidirect
105. C59×#386C22semidirect
106. C4×C22⋊C4×C59C22semidirect
107. C4×C22⋊C4×C59C22semidirect
108. C2×#95×C59C22semidirect
119. C2×D4×D59C2×C4semidirect
120. C2×D4×D59C2×C4semidirect
131. C22×C4×D59C2×C4semidirect
145. #14273702C2×C4semidirect
146. #14273701C2×C4semidirect
147. #14273700C2×C4semidirect
148. #14273699C2×C4semidirect
149. #14273698C2×C4semidirect
163. C4⋊C4×D59C2×C4semidirect
184. C22⋊C4×D59C2×C4semidirect
185. C22⋊C4×D59D4semidirect
215. #121×C59C2×C4semidirect
253. C2×D4×C59C22×C4semidirect
254. C2×D4×C59C22×C4semidirect
262. C22×C4×C59C22×C4semidirect
276. C2×C22⋊D59C22×C4semidirect
277. C2×C22⋊D59C22×C4semidirect
278. C2×C22⋊D59C22×C4semidirect
286. C22×Dic59C22×C4semidirect
299. C2×D236C22×C4semidirect
300. C2×D236C22×C4semidirect
335. C2×C4×D59C22×C4semidirect
336. C2×C4×D59C22×C4semidirect
340. C4⋊C4×C59C22×C4semidirect
345. C22⋊C4×C59C22×C4semidirect
346. C22⋊C4×C59C2×D4semidirect
353. C22⋊Dic59C22×C4semidirect
354. C22⋊Dic59C2×D4semidirect
362. (C2×D59)⋊C4C22×C4semidirect
363. (C2×D59)⋊C4C22×C4semidirect
364. (C2×D59)⋊C4C2×D4semidirect
366. C4⋊Dic59C22×C4semidirect
369. Dic59⋊C4C22×C4semidirect
544. #2364D59direct (N × H)
561. D59#2364direct (N × H)
582. C2×C4×D4C2×D59semidirect
600. #388C2×D59semidirect
608. #387C2×D59semidirect
623. #386C2×D59semidirect
624. #386C2×D59semidirect
637. C4×C22⋊C4C2×D59semidirect
638. C4×C22⋊C4C2×D59semidirect
650. C2×#95C2×D59semidirect
651. C59C2×#2364semidirect
698. #121C4×D59semidirect
812. C2×D4C2×C4×D59semidirect
813. C2×D4C2×C4×D59semidirect
874. C22×C4C2×C4×D59semidirect
888. C4⋊C4C2×C4×D59semidirect
909. C22⋊C4C2×C4×D59semidirect
910. C22⋊C4D4×D59semidirect

Maximal subgroups

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

subgroupindex
C2×#121×D592
C2×C4×D4×D592
#214271482
#214271472
#214271462
#214271452
#214271442
#214271432
#214271422
#214271412
#214271402
#388×D592
#387×D592
#386×D592
C4×C22⋊C4×D592
C2×#95×D592
C59×#23642
C2×#236459