Finite Group Databasebeta

← #28749096

Subgroups — #28749096

Order 15104.

3102 conjugacy classes of subgroups.

The subgroup lattice has 1122 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#124×D59C211yesmaximal, characteristic
2C2×#16837878C211yesmaximal, characteristic, complemented
3C2×#16837874C211yesmaximal, characteristic
4#21427172C211yesmaximal, characteristic, complemented
5#21427171C211yesmaximal, characteristic, complemented
6#21427169C211yesmaximal, characteristic, complemented
7#21427167C211yesmaximal, characteristic, complemented
8#21427166C211yesmaximal, characteristic, complemented
9#21427165C211yesmaximal, characteristic, complemented
10#21427163C211yesmaximal, characteristic, complemented
11#21426944C212yesmaximal, complemented
12#21426943C212yesmaximal, complemented
13#21426940C212yesmaximal, complemented
14#21426939C212yesmaximal, complemented
15#21426805C212yesmaximal, complemented
16#21426802C212yesmaximal, complemented
17#21426679C211yesmaximal, characteristic, complemented
18#21426675C211yesmaximal, characteristic
19#21426637C212yesmaximal, complemented
20C4×#14273713C212yesmaximal, complemented
21#21426500C211yesmaximal, characteristic, complemented
22C4×#14273685C211yesmaximal, characteristic, complemented
23C59×#2367C211yesmaximal, characteristic, complemented
24C22×Q8×D59C2211yescharacteristic
25C22×D4×D59C2211yescharacteristic
26C2×#14273716C2211yescharacteristic
27C2×#14273715C2211yescharacteristic
28C2×#14273714C2211yescharacteristic
29C2×#14273713C2212yes—
30C2×#14273713C2212yes—
31#124×D59C4116yescomplemented
32#16837878—28no—
33#16837874—28no—
34C2×Q8×Dic59C2211yescharacteristic, complemented
35C2×C4×Dic118C2212yescomplemented
36C2×C4×Dic118C2211yescharacteristic, complemented
37C2×#14273692C2212yescomplemented
38C2×#14273692C2211yescharacteristic, complemented
39C2×C4×D236C2211yescharacteristic
40C2×D4×Dic59C2211yescharacteristic
41C2×#14273689C2211yescharacteristic
42C2×C4×C22⋊D59C2212yes—
43C2×(C22⋊D59)⋊C4C2212yes—
44C2×#14273685C2212yes—
45C2×#14273685C2211yescharacteristic
46C2×#14273685C2211yescharacteristic
47C2×#14273684C2211yescharacteristic
48C2×#14273684C2211yescharacteristic
49C2×#14273684C2212yes—
50C22×(C2×D59)⋊C4C2212yes—
51C2×C22⋊C4×D59C2212yes—
52C2×C22⋊C4×D59C2212yes—
53C2×C22⋊C4×D59C2212yes—
54C2×C42×D59C2211yescharacteristic
55#16837309C2211yescharacteristic, complemented
56#16837308C2211yescharacteristic, complemented
57#16837307C2211yescharacteristic, complemented
58#16837306C2212yescomplemented
59#16837306C2212yescomplemented
60#16837305C2211yescharacteristic
61#16837304C2211yescharacteristic
62#16837303C2211yescharacteristic
63#16837302C2212yes—
64#16837302C2212yes—
65#16837296C2212yescomplemented
66#16837296C2212yescomplemented
67#16837295C2212yescomplemented
68#16837295C2212yescomplemented
69#16837294C2212yescomplemented
70#16837294C2212yescomplemented
71#16837293C2212yescomplemented
72#16837293C2212yescomplemented
73#16837292C2212yescomplemented
74#16837292C2212yescomplemented
75#16837291C2212yescomplemented
76#16837291C2212yescomplemented
77#16837290C2212yescomplemented
78#16837290C2212yescomplemented
79#16837277C2212yescomplemented
80#16837276C2212yescomplemented
81#16837276C2212yescomplemented
82#16837275C2212yescomplemented
83#16837274C2212yescomplemented
84#16837273C2212yescomplemented
85#16837273C2212yescomplemented
86#16837271C2211yescharacteristic, complemented
87#16837271C2211yescharacteristic, complemented
88#16837266C2211yescharacteristic, complemented
89#16837266C2211yescharacteristic, complemented
90#16837264C2212yes—
91#16837264C2212yes—
92#16837261C2211yescharacteristic
93#16837261C2211yescharacteristic
94#16837259C2211yescharacteristic
95#16837259C2211yescharacteristic
96#16837257C2212yes—
97#16837257C2212yes—
98C4⋊C4×Dic59C2211yescharacteristic, complemented
99C4⋊C4×Dic59C2211yescharacteristic, complemented
100C4×Dic59⋊C4C2211yescharacteristic, complemented
101C4×Dic59⋊C4C2211yescharacteristic, complemented
102C4×C4⋊Dic59C2211yescharacteristic, complemented
103C4×C4⋊Dic59C2211yescharacteristic, complemented
104C22⋊C4×Dic59C2212yescomplemented
105C22⋊C4×Dic59C2212yescomplemented
106C4×(C2×D59)⋊C4C2212yes—
107C4×(C2×D59)⋊C4C2212yescomplemented
108C4×(C2×D59)⋊C4C2212yescomplemented
109C4×C22⋊Dic59C2212yescomplemented
110#16837249C2212yes—
111#16837249C2212yescomplemented
112#16837249C2212yescomplemented
113#16837247C2212yescomplemented
114C42×Dic59C2212yescomplemented
115C2×#124×C59C2211yescharacteristic
116C2×C4×Q8×C59C2211yescharacteristic, complemented
117C2×C4×D4×C59C2211yescharacteristic
118C59×#391C2211yescharacteristic, complemented
119C59×#390C2211yescharacteristic
120C59×#388C2212yescomplemented
121C59×#388C2212yescomplemented
122C59×#385C2212yescomplemented
123C4×C4⋊C4×C59C2211yescharacteristic, complemented
124C4×C4⋊C4×C59C2211yescharacteristic, complemented
125C4×C22⋊C4×C59C2212yescomplemented
126C24×D59C2312yes—
127C22×Dic118C2312yes—
128C22×Dic118C2311yescharacteristic
129C2×Q8×D59—24no—
130C2×Q8×D59—24no—
131C2×Q8×D59C2×C418yescomplemented
132C22×D236C2311yescharacteristic
133C22×C22⋊D59C2312yes—
134C2×D4×D59—24no—
135C2×D4×D59—24no—
136C2×D4×D59C2×C418yes—
137C23×Dic59C2312yes—
138C22×C4×D59C2312yes—
139C22×C4×D59C2312yes—
140C22×C4×D59C2312yes—
141C22×C4×D59C2311yescharacteristic
142C22×C4×D59C2311yescharacteristic
143C22×C4×D59C2311yescharacteristic
144#14273716C2×C418yescomplemented
145#14273715C2×C418yescomplemented
146#14273714C2×C418yescomplemented
147#14273713C2×C4116yescomplemented
148#14273713C2×C4116yescomplemented
149Q8×Dic59—24no—
150C4×Dic118—24no—
151C4×Dic118—28no—
152#14273692—24no—
153#14273692—28no—
154C4×D236—24no—
155D4×Dic59—24no—
156#14273689—24no—
157C4×C22⋊D59—28no—
158(C22⋊D59)⋊C4—28no—
159#14273685—24no—
160#14273685—28no—
161#14273685D418yes—
162#14273684—24no—
163#14273684—24no—
164#14273684—28no—
165C2×C4⋊Dic59C2311yescharacteristic
166C2×C4⋊Dic59C2312yes—
167C2×C4⋊Dic59C2311yescharacteristic
168C2×C4⋊Dic59C2311yescharacteristic
169C2×C4⋊Dic59C2311yescharacteristic
170C2×Dic59⋊C4C2311yescharacteristic
171C2×Dic59⋊C4C2311yescharacteristic
172C2×Dic59⋊C4C2311yescharacteristic
173C2×Dic59⋊C4C2311yescharacteristic
174C2×Dic59⋊C4C2312yes—
175C2×Dic59⋊C4C2312yes—
176C2×Dic59⋊C4C2311yescharacteristic
177C2×Dic59⋊C4C2311yescharacteristic
178C2×Dic59⋊C4C2311yescharacteristic
179C2×Dic59⋊C4C2311yescharacteristic
180C2×C22⋊Dic59C2312yes—
181C2×C22⋊Dic59C2312yes—
182C2×C22⋊Dic59C2312yes—
183C2×C22⋊Dic59C2312yes—
184C2×C22⋊Dic59C2312yes—
185C2×(C2×D59)⋊C4—28no—
186C2×(C2×D59)⋊C4C2312yes—
187C2×(C2×D59)⋊C4C2311yescharacteristic
188C2×(C2×D59)⋊C4C2311yescharacteristic
189C2×(C2×D59)⋊C4C2311yescharacteristic
190C2×(C2×D59)⋊C4C2311yescharacteristic
191C2×(C2×D59)⋊C4C2312yes—
192C2×(C2×D59)⋊C4C2312yes—
193C2×(C2×D59)⋊C4C2312yes—
194C2×(C2×D59)⋊C4C2312yes—
195C2×(C2×D59)⋊C4C2312yes—
196C2×(C2×D59)⋊C4C2312yes—
197C2×(C2×D59)⋊C4C2312yes—
198C2×(C2×D59)⋊C4C2312yes—
199C2×(C2×D59)⋊C4C2312yes—
200C2×(C2×D59)⋊C4C2312yes—
201C2×(C2×D59)⋊C4C2312yes—
202C22⋊C4×D59—28no—
203C22⋊C4×D59C2×C4116yescomplemented
204C22⋊C4×D59C2×C4116yescomplemented
205C2×C4×Dic59C2312yes—
206C2×C4×Dic59C2312yes—
207C2×C4×Dic59C2312yes—
208C2×C4×Dic59C2312yes—
209C2×C4×Dic59C2311yescharacteristic
210C2×C4×Dic59C2311yescharacteristic
211C2×C4×Dic59C2312yes—
212C2×C4×Dic59C2312yes—
213C2×C4×Dic59C2312yes—
214C2×C4×Dic59C2311yescharacteristic
215C2×C4×Dic59C2311yescharacteristic
216C2×C4×Dic59C2311yescharacteristic
217C2×C4×Dic59C2312yes—
218C42×D59C2×C418yescomplemented
219C59⋊#95C2312yes—
220C59⋊#95C2312yes—
221C59⋊#95C2312yes—
222C59⋊#95C2311yescharacteristic
223C59⋊#95C2312yes—
224C59⋊#95C2311yescharacteristic
225C59⋊#95C2312yes—
226C59⋊#95C2311yescharacteristic
227C59⋊#95C2311yescharacteristic
228C59⋊#95C2312yes—
229C59⋊#95C2312yes—
230C59⋊#95C2311yescharacteristic
231C59⋊#95C2311yescharacteristic
232C59⋊#95C2312yes—
233C59⋊#95C2312yes—
234C22×Q8×C59C2311yescharacteristic
235C22×D4×C59C2311yescharacteristic
236C23×C4×C59C2312yes—
237#124×C59C2×C418yescomplemented
238C4×Q8×C59—24no—
239C4×D4×C59—24no—
240C2×C4⋊C4×C59C2311yescharacteristic
241C2×C4⋊C4×C59C2312yes—
242C2×C4⋊C4×C59C2311yescharacteristic
243C2×C4⋊C4×C59C2311yescharacteristic
244C2×C4⋊C4×C59C2311yescharacteristic
245C2×C22⋊C4×C59C2312yes—
246C2×C22⋊C4×C59C2312yes—
247C2×C22⋊C4×C59C2312yes—
248C2×C22⋊C4×C59C2312yes—
249C2×C22⋊C4×C59C2312yes—
250C2×C42×C59C2312yes—
251C2×C42×C59C2311yescharacteristic
252C2×C42×C59C2311yescharacteristic
253C2×C42×C59C2312yes—
254C2×C42×C59C2311yescharacteristic
255#95×C59C2311yescharacteristic
256#95×C59C2312yes—
257#95×C59C2312yes—
258#95×C59C2311yescharacteristic
259#95×C59C2312yes—
260C24×C59C2412yes—
261C23×D59—24no—
262C23×D59—24no—
263C23×D59—42no—
264C23×D59—42no—
265C23×D59—42no—
266C23×D59—42no—
267C23×D59C22×C418yes—
268C23×D59C2412yes—
269C23×D59C2411yescharacteristic
270C2×Q8×C59—22no—
271C2×Q8×C59—22no—
272C2×Q8×C59C22×C414yes—
273C2×D4×C59—22no—
274C2×D4×C59—22no—
275C2×D4×C59C22×C414yes—
276C22×C4×C59—24no—
277C22×C4×C59—42no—
278C22×C4×C59—42no—
279C22×C4×C59C2412yes—
280C22×C4×C59C2411yescharacteristic
281C22×C4×C59C2411yescharacteristic
282C22×C4×C59C2411yescharacteristic
283C22×C4×C59C2411yescharacteristic
284C22×C4×C59C2411yescharacteristic
285C22×C4×C59C2411yescharacteristic
286C22×C4×C59C2412yes—
287C22×C4×C59C2412yes—
288C22×C4×C59C2411yescharacteristic
289C2×C22⋊D59—24no—
290C2×C22⋊D59—24no—
291C2×C22⋊D59C22×C418yes—
292C22×Dic59—24no—
293C22×Dic59—42no—
294C22×Dic59—42no—
295C22×Dic59C2412yes—
296C22×Dic59C2411yescharacteristic
297C22×Dic59C2411yescharacteristic
298C22×Dic59C2411yescharacteristic
299C22×Dic59C2411yescharacteristic
300C22×Dic59C2411yescharacteristic
301C22×Dic59C2411yescharacteristic
302C22×Dic59C2412yes—
303C22×Dic59C2412yes—
304C22×Dic59C2411yescharacteristic
305Q8×D59—232no—
306D4×D59—232no—
307C2×D236—22no—
308C2×D236—22no—
309C2×D236C22×C414yes—
310C2×C4×D59—24no—
311C2×C4×D59—24no—
312C2×C4×D59—24no—
313C2×C4×D59—24no—
314C2×C4×D59—41no—
315C2×C4×D59—41no—
316C2×C4×D59—41no—
317C2×C4×D59—41no—
318C2×C4×D59—42no—
319C2×C4×D59—42no—
320C2×C4×D59—42no—
321C2×C4×D59—42no—
322C2×C4×D59C22×C418yes—
323C2×C4×D59C22×C414yes—
324C2×C4×D59C22×C414yes—
325C2×C4×D59C22×C414yes—
326C2×C4×D59C2×D414yes—
327C2×C4×D59#4114yes—
328C2×Dic118—22no—
329C2×Dic118—22no—
330C2×Dic118—24no—
331C2×Dic118—24no—
332C2×Dic118C22×C418yes—
333C2×Dic118C22×C414yes—
334C4⋊C4×C59—24no—
335C4⋊C4×C59—22no—
336C4⋊C4×C59—41no—
337C4⋊C4×C59—41no—
338C4⋊C4×C59C2×D414yes—
339C22⋊C4×C59—24no—
340C22⋊C4×C59—42no—
341C22⋊C4×C59—42no—
342C22⋊C4×C59C22×C418yes—
343C22⋊C4×C59C22×C418yes—
344C42×C59—22no—
345C42×C59—24no—
346C42×C59—22no—
347C42×C59—42no—
348C42×C59C22×C414yes—
349C22⋊Dic59—24no—
350C22⋊Dic59—42no—
351C22⋊Dic59—42no—
352C22⋊Dic59C22×C418yes—
353C22⋊Dic59C22×C418yes—
354(C2×D59)⋊C4—22no—
355(C2×D59)⋊C4—22no—
356(C2×D59)⋊C4—22no—
357(C2×D59)⋊C4—22no—
358(C2×D59)⋊C4—24no—
359(C2×D59)⋊C4—24no—
360(C2×D59)⋊C4—24no—
361(C2×D59)⋊C4—42no—
362(C2×D59)⋊C4—42no—
363(C2×D59)⋊C4—42no—
364(C2×D59)⋊C4—42no—
365(C2×D59)⋊C4C22×C418yes—
366(C2×D59)⋊C4C22×C418yes—
367(C2×D59)⋊C4C22×C418yes—
368(C2×D59)⋊C4C22×C418yes—
369(C2×D59)⋊C4C2×D418yes—
370C4⋊Dic59—22no—
371C4⋊Dic59—24no—
372C4⋊Dic59—41no—
373C4⋊Dic59—41no—
374C4⋊Dic59C2×D414yes—
375Dic59⋊C4—24no—
376Dic59⋊C4—22no—
377Dic59⋊C4—22no—
378Dic59⋊C4—22no—
379Dic59⋊C4—24no—
380Dic59⋊C4—22no—
381Dic59⋊C4—41no—
382Dic59⋊C4—41no—
383Dic59⋊C4—41no—
384Dic59⋊C4—41no—
385C4×Dic59—22no—
386C4×Dic59—22no—
387C4×Dic59—24no—
388C4×Dic59—24no—
389C4×Dic59—24no—
390C4×Dic59—24no—
391C4×Dic59—42no—
392C4×Dic59—42no—
393C4×Dic59—42no—
394C4×Dic59C22×C414yes—
395C4×Dic59C22×C414yes—
396C4×Dic59C22×C414yes—
397C4×Dic59C2×D418yes—
398C23×C59—22no—
399C23×C59—22no—
400C23×C59—22no—
401C23×C59—22no—
402C23×C59—22no—
403C23×C59—22no—
404C23×C59C23×C414yes—
405C23×C59C2511yescharacteristic
406C22×D59—21no—
407C22×D59—21no—
408C22×D59—21no—
409C22×D59—21no—
410C22×D59—22no—
411C22×D59—22no—
412C22×D59—22no—
413C22×D59—22no—
414C22×D59—22no—
415C22×D59—22no—
416C22×D59—216no—
417C22×D59—48no—
418C22×D59—48no—
419C22×D59—84no—
420C22×D59—84no—
421C22×D59—84no—
422C22×D59—84no—
423C22×D59C23×C414yes—
424C22×D59C23×C412yes—
425C22×D59C22×D412yes—
426C22×D59C2×#4112yes—
427Q8×C59—28no—
428D4×C59—28no—
429C2×C4×C59—22no—
430C2×C4×C59—22no—
431C2×C4×C59—21no—
432C2×C4×C59—22no—
433C2×C4×C59—21no—
434C2×C4×C59—21no—
435C2×C4×C59—21no—
436C2×C4×C59—22no—
437C2×C4×C59—21no—
438C2×C4×C59—21no—
439C2×C4×C59—21no—
440C2×C4×C59—21no—
441C2×C4×C59—22no—
442C2×C4×C59—22no—
443C2×C4×C59—21no—
444C2×C4×C59—21no—
445C2×C4×C59—21no—
446C2×C4×C59—21no—
447C2×C4×C59—21no—
448C2×C4×C59—22no—
449C2×C4×C59—21no—
450C2×C4×C59—21no—
451C2×C4×C59—21no—
452C2×C4×C59—84no—
453C2×C4×C59C23×C412yes—
454C2×C4×C59C23×C412yes—
455C2×C4×C59C23×C414yes—
456C2×C4×C59C23×C412yes—
457C2×C4×C59C22×D414yes—
458C2×C4×C59C22×D412yes—
459C2×C4×C59C2×#4112yes—
460C22⋊D59—216no—
461C2×Dic59—22no—
462C2×Dic59—22no—
463C2×Dic59—21no—
464C2×Dic59—21no—
465C2×Dic59—22no—
466C2×Dic59—22no—
467C2×Dic59—21no—
468C2×Dic59—21no—
469C2×Dic59—21no—
470C2×Dic59—21no—
471C2×Dic59—21no—
472C2×Dic59—21no—
473C2×Dic59—22no—
474C2×Dic59—22no—
475C2×Dic59—22no—
476C2×Dic59—21no—
477C2×Dic59—21no—
478C2×Dic59—21no—
479C2×Dic59—21no—
480C2×Dic59—21no—
481C2×Dic59—21no—
482C2×Dic59—21no—
483C2×Dic59—21no—
484C2×Dic59—84no—
485C2×Dic59C23×C412yes—
486C2×Dic59C23×C412yes—
487C2×Dic59C23×C414yes—
488C2×Dic59C23×C412yes—
489C2×Dic59C22×D414yes—
490C2×Dic59C22×D412yes—
491C2×Dic59C2×#4112yes—
492D236—28no—
493C4×D59—216no—
494C4×D59—44no—
495C4×D59—44no—
496C4×D59—84no—
497C4×D59—84no—
498C4×D59C4×D4116yes—
499Dic118—28no—
500Dic118—216no—
501#34211—591nomaximal, Sylow
502C22×C59—24no—
503C22×C59—24no—
504C22×C59—24no—
505C22×C59—42no—
506C22×C59—42no—
507C22×C59—42no—
508C22×C59—42no—
509C22×C59C24×C411yescharacteristic
510C22×C59C23×D411yescharacteristic
511C22×C59C22×#4111yescharacteristic
512C22×C59#58511yescharacteristic
513C22×C59#58511yescharacteristic
514C22×C59#58511yescharacteristic
515C22×C59#58511yescharacteristic
516C2×D59—22no—
517C2×D59—22no—
518C2×D59—22no—
519C2×D59—22no—
520C2×D59—22no—
521C2×D59—22no—
522C2×D59—24no—
523C2×D59—24no—
524C2×D59—24no—
525C2×D59—42no—
526C2×D59—42no—
527C2×D59—42no—
528C2×D59—42no—
529C2×D59—816no—
530C2×D59C2×C4×D414yes—
531C4×C59—24no—
532C4×C59—22no—
533C4×C59—22no—
534C4×C59—24no—
535C4×C59—41no—
536C4×C59—41no—
537C4×C59—41no—
538C4×C59—41no—
539C4×C59—42no—
540C4×C59C2×C4×D414yes—
541Dic59—24no—
542Dic59—22no—
543Dic59—22no—
544Dic59—24no—
545Dic59—41no—
546Dic59—41no—
547Dic59—41no—
548Dic59—41no—
549Dic59—42no—
550Dic59C2×C4×D414yes—
551C22×#124—591no—
552C2×#519—591no—
553C2×#518—591no—
554#2367—591no—
555#2367—591no—
556#2367—591no—
557#2367—591no—
558#2367—591no—
559#2367—591no—
560#2367—591no—
561#2367D5911yescharacteristic, complemented
562#2342—592no—
563#2342—592no—
564#2342—592no—
565#2342—592no—
566#2326—592no—
567#2326—592no—
568#2310—591no—
569#2309—591no—
570C4×#124—592no—
571C4×#124—592no—
572#2285—591no—
573C4×#117—591no—
574C2×C59—44no—
575C2×C59C22×C4×D411yescharacteristic
576C2×C59#342811yescharacteristic
577C2×C59#342811yescharacteristic
578C2×C59#350011yescharacteristic
579C2×C59#350011yescharacteristic
580C2×C59#351011yescharacteristic
581C2×C59#351011yescharacteristic
582D59—24no—
583D59—44no—
584C23×Q8—591no—
585C23×D4—591no—
586C2×#124—591no—
587C2×#124—591no—
588C2×#124—5916no—
589C2×#124—592no—
590C2×#124—592no—
591C2×#124—591no—
592C2×#124C2×D5911yescharacteristic
593#519—1188no—
594#518—1188no—
595C2×C4×Q8—591no—
596C2×C4×Q8—592no—
597C2×C4×Q8—591no—
598C2×C4×Q8—592no—
599C2×C4×Q8—591no—
600C2×C4×Q8C2×D5911yescharacteristic, complemented
601C2×C4×D4—591no—
602C2×C4×D4—592no—
603C2×C4×D4—591no—
604C2×C4×D4—592no—
605C2×C4×D4—591no—
606C2×C4×D4C2×D5911yescharacteristic
607C2×#117—591no—
608C2×#117—591no—
609C2×#117—592no—
610C2×#117—591no—
611C2×#117—591no—
612C2×#117—592no—
613C22×C22⋊C4—592no—
614C22×C22⋊C4—592no—
615C22×C22⋊C4—592no—
616C22×C22⋊C4—592no—
617C22×C42—591no—
618#391—591no—
619#391—591no—
620#391—591no—
621#391—592no—
622#391—592no—
623#391C2×D5911yescharacteristic, complemented
624#390—591no—
625#390—591no—
626#390—592no—
627#390—592no—
628#390—591no—
629#390C2×D5911yescharacteristic
630#388—592no—
631#388—592no—
632#388—592no—
633#388—592no—
634#388—592no—
635#388—592no—
636#388—592no—
637#388—592no—
638#388—592no—
639#388—592no—
640#388—592no—
641#388—592no—
642#388—592no—
643#388—592no—
644#388C2×D5912yescomplemented
645#388C2×D5912yescomplemented
646#385—592no—
647#385—592no—
648#385—592no—
649#385—592no—
650#385—592no—
651#385—592no—
652#385—592no—
653#385C2×D5912yescomplemented
654#384—591no—
655#384—591no—
656#382—591no—
657#382—591no—
658#381—592no—
659#381—592no—
660#380—591no—
661#380—591no—
662#380—591no—
663#380—591no—
664#379—592no—
665#379—592no—
666C4×C4⋊C4—591no—
667C4×C4⋊C4—591no—
668C4×C4⋊C4—591no—
669C4×C4⋊C4—591no—
670C4×C4⋊C4—591no—
671C4×C4⋊C4—591no—
672C4×C4⋊C4C2×D5911yescharacteristic, complemented
673C4×C4⋊C4C2×D5911yescharacteristic, complemented
674C4×C22⋊C4—592no—
675C4×C22⋊C4—592no—
676C4×C22⋊C4—592no—
677C4×C22⋊C4—592no—
678C4×C22⋊C4—592no—
679C4×C22⋊C4—592no—
680C4×C22⋊C4—592no—
681C4×C22⋊C4—592no—
682C4×C22⋊C4—592no—
683C4×C22⋊C4C2×D5912yescomplemented
684#376—592no—
685C43—592no—
686C59#3421111yescharacteristic, complemented, Sylow
687C25—592no—
688C22×Q8—598no—
689C22×Q8—592no—
690C22×Q8—591no—
691C22×Q8—1184no—
692C22×Q8—1184no—
693C22×Q8C22×D5911yescharacteristic
694C22×D4—592no—
695C22×D4—598no—
696C22×D4—591no—
697C22×D4—1184no—
698C22×D4—1184no—
699C22×D4C22×D5911yescharacteristic
700C23×C4—591no—
701C23×C4—592no—
702C23×C4—591no—
703C23×C4—591no—
704C23×C4—592no—
705C23×C4—592no—
706C23×C4—592no—
707C23×C4C22×D5912yes—
708#124—598no—
709#124—598no—
710#124—5916no—
711#124—5916no—
712#124—598no—
713#124C4×D5918yescomplemented
714C4×Q8—24no—
715C4×Q8—1188no—
716C4×Q8—1184no—
717C4×Q8—1188no—
718C4×Q8—1184no—
719C4×Q8—1184no—
720C4×D4—24no—
721C4×D4—1184no—
722C4×D4—1188no—
723C4×D4—1188no—
724C4×D4—1184no—
725C4×D4—1184no—
726#117—598no—
727#117—1188no—
728#117—1184no—
729#117—1184no—
730#117—1188no—
731#117—1184no—
732C2×C4⋊C4—591no—
733C2×C4⋊C4—591no—
734C2×C4⋊C4—591no—
735C2×C4⋊C4—591no—
736C2×C4⋊C4—591no—
737C2×C4⋊C4—592no—
738C2×C4⋊C4—592no—
739C2×C4⋊C4—592no—
740C2×C4⋊C4—591no—
741C2×C4⋊C4—591no—
742C2×C4⋊C4—591no—
743C2×C4⋊C4—591no—
744C2×C4⋊C4—591no—
745C2×C4⋊C4—591no—
746C2×C4⋊C4—591no—
747C2×C4⋊C4C22×D5912yes—
748C2×C4⋊C4C22×D5911yescharacteristic
749C2×C4⋊C4C22×D5911yescharacteristic
750C2×C4⋊C4C22×D5911yescharacteristic
751C2×C4⋊C4C22×D5911yescharacteristic
752C2×C22⋊C4—592no—
753C2×C22⋊C4—592no—
754C2×C22⋊C4—592no—
755C2×C22⋊C4—592no—
756C2×C22⋊C4—592no—
757C2×C22⋊C4—592no—
758C2×C22⋊C4—592no—
759C2×C22⋊C4—5916no—
760C2×C22⋊C4—5916no—
761C2×C22⋊C4—592no—
762C2×C22⋊C4—591no—
763C2×C22⋊C4—591no—
764C2×C22⋊C4—592no—
765C2×C22⋊C4—592no—
766C2×C22⋊C4—591no—
767C2×C22⋊C4—591no—
768C2×C22⋊C4—592no—
769C2×C22⋊C4—592no—
770C2×C22⋊C4—592no—
771C2×C22⋊C4—592no—
772C2×C22⋊C4—592no—
773C2×C22⋊C4—592no—
774C2×C22⋊C4—592no—
775C2×C22⋊C4—1188no—
776C2×C22⋊C4—1188no—
777C2×C22⋊C4C22×D5912yes—
778C2×C22⋊C4C22×D5912yes—
779C2×C22⋊C4C22×D5912yes—
780C2×C22⋊C4C22×D5912yes—
781C2×C22⋊C4C22×D5912yes—
782C2×C42—592no—
783C2×C42—591no—
784C2×C42—591no—
785C2×C42—591no—
786C2×C42—598no—
787C2×C42—591no—
788C2×C42—592no—
789C2×C42—592no—
790C2×C42—592no—
791C2×C42—591no—
792C2×C42—592no—
793C2×C42—592no—
794C2×C42—592no—
795C2×C42—592no—
796C2×C42C22×D5911yescharacteristic
797C2×C42C22×D5912yes—
798C2×C42C22×D5911yescharacteristic
799C2×C42C22×D5912yes—
800C2×C42C22×D5911yescharacteristic
801#95—592no—
802#95—592no—
803#95—592no—
804#95—591no—
805#95—591no—
806#95—591no—
807#95—591no—
808#95—591no—
809#95—591no—
810#95—592no—
811#95—592no—
812#95—592no—
813#95—592no—
814#95—592no—
815#95—592no—
816#95C22×D5912yes—
817#95C22×D5911yescharacteristic
818#95C22×D5912yes—
819#95C22×D5911yescharacteristic
820#95C22×D5912yes—
821C24—591no—
822C24—592no—
823C24—598no—
824C24—1184no—
825C24—1184no—
826C24—2362no—
827C24—2362no—
828C24—2362no—
829C24—2362no—
830C24C23×D5912yes—
831C2×Q8—22no—
832C2×Q8—22no—
833C2×Q8—598no—
834C2×Q8—594no—
835C2×Q8—1184no—
836C2×Q8—1184no—
837C2×Q8—11832no—
838C2×Q8—1182no—
839C2×Q8—1182no—
840C2×Q8C2×C4×D5914yes—
841C2×D4—22no—
842C2×D4—22no—
843C2×D4—598no—
844C2×D4—594no—
845C2×D4—11832no—
846C2×D4—1184no—
847C2×D4—1184no—
848C2×D4—1182no—
849C2×D4—1182no—
850C2×D4C2×C4×D5914yes—
851C22×C4—24no—
852C22×C4—42no—
853C22×C4—42no—
854C22×C4—591no—
855C22×C4—594no—
856C22×C4—594no—
857C22×C4—594no—
858C22×C4—591no—
859C22×C4—591no—
860C22×C4—592no—
861C22×C4—592no—
862C22×C4—598no—
863C22×C4—594no—
864C22×C4—594no—
865C22×C4—592no—
866C22×C4—591no—
867C22×C4—591no—
868C22×C4—591no—
869C22×C4—591no—
870C22×C4—1184no—
871C22×C4—1184no—
872C22×C4—1184no—
873C22×C4—1184no—
874C22×C4—1184no—
875C22×C4—2362no—
876C22×C4—2362no—
877C22×C4—2362no—
878C22×C4—2362no—
879C22×C4—2361no—
880C22×C4—2361no—
881C22×C4—2361no—
882C22×C4—2361no—
883C22×C4—2362no—
884C22×C4—2362no—
885C22×C4C23×D5912yes—
886C22×C4C23×D5911yescharacteristic
887C22×C4C23×D5911yescharacteristic
888C22×C4C23×D5911yescharacteristic
889C22×C4C23×D5911yescharacteristic
890C22×C4C23×D5911yescharacteristic
891C22×C4C23×D5911yescharacteristic
892C22×C4C23×D5912yes—
893C22×C4C23×D5912yes—
894C22×C4C23×D5911yescharacteristic
895C4⋊C4—24no—
896C4⋊C4—22no—
897C4⋊C4—41no—
898C4⋊C4—41no—
899C4⋊C4—594no—
900C4⋊C4—1182no—
901C4⋊C4—1182no—
902C4⋊C4—1182no—
903C4⋊C4—1184no—
904C4⋊C4—1182no—
905C4⋊C4—1184no—
906C4⋊C4—1184no—
907C4⋊C4—1182no—
908C4⋊C4—2361no—
909C4⋊C4—2361no—
910C4⋊C4—2361no—
911C4⋊C4—2361no—
912C4⋊C4—2361no—
913C4⋊C4—2361no—
914C4⋊C4D4×D5914yes—
915C22⋊C4—24no—
916C22⋊C4—42no—
917C22⋊C4—42no—
918C22⋊C4—598no—
919C22⋊C4—598no—
920C22⋊C4—598no—
921C22⋊C4—598no—
922C22⋊C4—598no—
923C22⋊C4—598no—
924C22⋊C4—598no—
925C22⋊C4—1184no—
926C22⋊C4—1182no—
927C22⋊C4—1182no—
928C22⋊C4—1182no—
929C22⋊C4—1182no—
930C22⋊C4—1184no—
931C22⋊C4—1184no—
932C22⋊C4—1184no—
933C22⋊C4—2362no—
934C22⋊C4—2362no—
935C22⋊C4—2362no—
936C22⋊C4—2362no—
937C22⋊C4—2362no—
938C22⋊C4—2362no—
939C22⋊C4C2×C4×D5918yes—
940C22⋊C4C2×C4×D5918yes—
941C42—22no—
942C42—24no—
943C42—22no—
944C42—42no—
945C42—594no—
946C42—594no—
947C42—594no—
948C42—598no—
949C42—1184no—
950C42—1184no—
951C42—1184no—
952C42—1182no—
953C42—1184no—
954C42—1182no—
955C42—2362no—
956C42—2362no—
957C42—2362no—
958C42C2×C4×D5914yes—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—592no—
966C23—592no—
967C23—592no—
968C23—594no—
969C23—11816no—
970C23—1181no—
971C23—1181no—
972C23—1181no—
973C23—1181no—
974C23—1182no—
975C23—1182no—
976C23—1182no—
977C23—1182no—
978C23—1182no—
979C23—1182no—
980C23—4724no—
981C23—4724no—
982C23—4724no—
983C23—4724no—
984C23—2368no—
985C23—2368no—
986C23C22×C4×D5914yes—
987C23C24×D5911yescharacteristic
988Q8—28no—
989Q8—11816no—
990Q8—1188no—
991D4—28no—
992D4—11816no—
993D4—1188no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—21no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—22no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—84no—
1018C2×C4—592no—
1019C2×C4—592no—
1020C2×C4—592no—
1021C2×C4—5916no—
1022C2×C4—592no—
1023C2×C4—592no—
1024C2×C4—594no—
1025C2×C4—594no—
1026C2×C4—11816no—
1027C2×C4—1182no—
1028C2×C4—1182no—
1029C2×C4—1181no—
1030C2×C4—1181no—
1031C2×C4—1181no—
1032C2×C4—1182no—
1033C2×C4—1182no—
1034C2×C4—1181no—
1035C2×C4—1181no—
1036C2×C4—1181no—
1037C2×C4—1181no—
1038C2×C4—1181no—
1039C2×C4—1182no—
1040C2×C4—1181no—
1041C2×C4—1181no—
1042C2×C4—1182no—
1043C2×C4—1181no—
1044C2×C4—1181no—
1045C2×C4—1181no—
1046C2×C4—1181no—
1047C2×C4—1182no—
1048C2×C4—1181no—
1049C2×C4—1181no—
1050C2×C4—4724no—
1051C2×C4—4724no—
1052C2×C4—4724no—
1053C2×C4—2364no—
1054C2×C4—2364no—
1055C2×C4C22×C4×D5912yes—
1056C2×C4C22×C4×D5912yes—
1057C2×C4C22×C4×D5914yes—
1058C2×C4C22×C4×D5912yes—
1059C2×C4C2×D4×D5914yes—
1060C2×C4C2×D4×D5912yes—
1061C2×C4#41×D5912yes—
1062C22—24no—
1063C22—24no—
1064C22—24no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—594no—
1070C22—1182no—
1071C22—1182no—
1072C22—1182no—
1073C22—1182no—
1074C22—1182no—
1075C22—1182no—
1076C22—1184no—
1077C22—1184no—
1078C22—1184no—
1079C22—47216no—
1080C22—2362no—
1081C22—2362no—
1082C22—2362no—
1083C22—2362no—
1084C22C23×C4×D5911yescharacteristic
1085C22C22×D4×D5911yescharacteristic
1086C22C2×#41×D5911yescharacteristic
1087C22#1683823711yescharacteristic
1088C22#1683823811yescharacteristic
1089C22#1683823811yescharacteristic
1090C22#1683823911yescharacteristic
1091C4—24no—
1092C4—22no—
1093C4—22no—
1094C4—24no—
1095C4—42no—
1096C4—41no—
1097C4—41no—
1098C4—41no—
1099C4—41no—
1100C4—594no—
1101C4—1184no—
1102C4—1182no—
1103C4—1182no—
1104C4—1184no—
1105C4—2362no—
1106C4—2361no—
1107C4—2361no—
1108C4—2361no—
1109C4—2361no—
1110C4C4×D4×D5914yes—
1111C2—44no—
1112C2—1184no—
1113C2—2364no—
1114C2C2×C4×D4×D5911yescharacteristic
1115C2#2143729511yescharacteristic
1116C2#2143729611yescharacteristic
1117C2#2143788211yescharacteristic
1118C2#2143788711yescharacteristic
1119C2#2143798611yescharacteristic
1120C2#2143798911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D59
commutatorC22×C59C24×C4
FittingC59×#2367C2
socle, cosocleC23×C59C25
prime radicalC22×D4×D59C22
hypercenter#2367D59
hypocenterC59#34211
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ #2367

Complements

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

NH ≅ G/Ntype
2. C2×#16837878C2semidirect
4. #21427172C2semidirect
5. #21427171C2semidirect
6. #21427169C2semidirect
7. #21427167C2semidirect
8. #21427166C2semidirect
9. #21427165C2semidirect
10. #21427163C2semidirect
11. #21426944C2semidirect
12. #21426943C2semidirect
13. #21426940C2semidirect
14. #21426939C2semidirect
15. #21426805C2semidirect
16. #21426802C2semidirect
17. #21426679C2semidirect
19. #21426637C2semidirect
20. C4×#14273713C2semidirect
21. #21426500C2semidirect
22. C4×#14273685C2semidirect
23. C59×#2367C2semidirect
31. #124×D59C4semidirect
34. C2×Q8×Dic59C22semidirect
35. C2×C4×Dic118C22semidirect
36. C2×C4×Dic118C22semidirect
37. C2×#14273692C22semidirect
38. C2×#14273692C22semidirect
55. #16837309C22semidirect
56. #16837308C22semidirect
57. #16837307C22semidirect
58. #16837306C22semidirect
59. #16837306C22semidirect
65. #16837296C22semidirect
66. #16837296C22semidirect
67. #16837295C22semidirect
68. #16837295C22semidirect
69. #16837294C22semidirect
70. #16837294C22semidirect
71. #16837293C22semidirect
72. #16837293C22semidirect
73. #16837292C22semidirect
74. #16837292C22semidirect
75. #16837291C22semidirect
76. #16837291C22semidirect
77. #16837290C22semidirect
78. #16837290C22semidirect
79. #16837277C22semidirect
80. #16837276C22semidirect
81. #16837276C22semidirect
82. #16837275C22semidirect
83. #16837274C22semidirect
84. #16837273C22semidirect
85. #16837273C22semidirect
86. #16837271C22semidirect
87. #16837271C22semidirect
88. #16837266C22semidirect
89. #16837266C22semidirect
98. C4⋊C4×Dic59C22semidirect
99. C4⋊C4×Dic59C22semidirect
100. C4×Dic59⋊C4C22semidirect
101. C4×Dic59⋊C4C22semidirect
102. C4×C4⋊Dic59C22semidirect
103. C4×C4⋊Dic59C22semidirect
104. C22⋊C4×Dic59C22semidirect
105. C22⋊C4×Dic59C22semidirect
107. C4×(C2×D59)⋊C4C22semidirect
108. C4×(C2×D59)⋊C4C22semidirect
109. C4×C22⋊Dic59C22semidirect
111. #16837249C22semidirect
112. #16837249C22semidirect
113. #16837247C22semidirect
114. C42×Dic59C22semidirect
116. C2×C4×Q8×C59C22semidirect
118. C59×#391C22semidirect
120. C59×#388C22semidirect
121. C59×#388C22semidirect
122. C59×#385C22semidirect
123. C4×C4⋊C4×C59C22semidirect
124. C4×C4⋊C4×C59C22semidirect
125. C4×C22⋊C4×C59C22semidirect
131. C2×Q8×D59C2×C4semidirect
144. #14273716C2×C4semidirect
145. #14273715C2×C4semidirect
146. #14273714C2×C4semidirect
147. #14273713C2×C4semidirect
148. #14273713C2×C4semidirect
203. C22⋊C4×D59C2×C4semidirect
204. C22⋊C4×D59C2×C4semidirect
218. C42×D59C2×C4semidirect
237. #124×C59C2×C4semidirect
561. #2367D59semidirect
600. C2×C4×Q8C2×D59semidirect
623. #391C2×D59semidirect
644. #388C2×D59semidirect
645. #388C2×D59semidirect
653. #385C2×D59semidirect
672. C4×C4⋊C4C2×D59semidirect
673. C4×C4⋊C4C2×D59semidirect
683. C4×C22⋊C4C2×D59semidirect
686. C59#34211semidirect
713. #124C4×D59semidirect

Maximal subgroups

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

subgroupindex
C2×#124×D592
C2×#168378782
C2×#168378742
#214271722
#214271712
#214271692
#214271672
#214271662
#214271652
#214271632
#214269442
#214269432
#214269402
#214269392
#214268052
#214268022
#214266792
#214266752
#214266372
C4×#142737132
#214265002
C4×#142736852
C59×#23672
#3421159