Finite Group Databasebeta

← #28761713

Subgroups — #28761713

Order 15104.

2930 conjugacy classes of subgroups.

The subgroup lattice has 1150 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273705C211yesmaximal, characteristic, complemented
2C2×C4×D4×D59C211yesmaximal, characteristic
3#21432431C212yesmaximal, complemented
4#21432382C212yesmaximal, complemented
5#21429914C212yesmaximal, complemented
6#21429906C212yesmaximal, complemented
7#21429445C211yesmaximal, characteristic, complemented
8#21429443C211yesmaximal, characteristic, complemented
9#21429439C211yesmaximal, characteristic, complemented
10#21429281C212yesmaximal, complemented
11#21429275C212yesmaximal, complemented
12#21428412C211yesmaximal, characteristic, complemented
13#21428410C211yesmaximal, characteristic, complemented
14#21427542C212yesmaximal, complemented
15#21427540C212yesmaximal, complemented
16#21427460C211yesmaximal, characteristic, complemented
17#21427458C211yesmaximal, characteristic, complemented
18#21426707C211yesmaximal, characteristic, complemented
19#21426707C211yesmaximal, characteristic, complemented
20#21426670C211yesmaximal, characteristic
21#21426670C211yesmaximal, characteristic
22#380×D59C211yesmaximal, characteristic, complemented
23C59×#2579C211yesmaximal, characteristic, complemented
24C23×Dic118C2211yescharacteristic, complemented
25C22×D4×D59C2211yescharacteristic
26C23×C4×D59C2211yescharacteristic
27C23×C4×D59C2211yescharacteristic
28C2×#14273705—28no—
29C2×#14273705C2212yes—
30C2×#14273705C2212yes—
31C2×#14273705C2212yescomplemented
32C2×#14273705C2212yescomplemented
33C2×#14273705C2212yescomplemented
34C2×#14273704C2212yescomplemented
35C2×C4×D236C2211yescharacteristic
36C2×D4×Dic59C2211yescharacteristic
37C2×#14273689C2211yescharacteristic
38C2×C4×C22⋊D59C2211yescharacteristic
39C2×C4×C22⋊D59C2211yescharacteristic
40C2×(C22⋊D59)⋊C4C2211yescharacteristic
41C2×(C22⋊D59)⋊C4C2211yescharacteristic
42C4×D4×D59—28no—
43C22×Dic59⋊C4C2211yescharacteristic, complemented
44C22×Dic59⋊C4C2211yescharacteristic, complemented
45C2×C4⋊C4×D59C2211yescharacteristic
46C2×C4⋊C4×D59C2212yescomplemented
47C22×(C2×D59)⋊C4C2211yescharacteristic
48C22×(C2×D59)⋊C4C2211yescharacteristic
49C2×C22⋊C4×D59C2211yescharacteristic
50C2×C22⋊C4×D59C2211yescharacteristic
51C2×C22⋊C4×D59C2211yescharacteristic
52C2×C22⋊C4×D59C2211yescharacteristic
53C2×C42×D59C2211yescharacteristic
54#16837344C2212yescomplemented
55#16837343C2212yescomplemented
56#16837338C2212yescomplemented
57#16837337C2212yescomplemented
58#16837335C2212yescomplemented
59#16837335C2212yescomplemented
60#16837332C2212yescomplemented
61#16837325C2212yescomplemented
62#16837324C2212yescomplemented
63#16837324C2212yescomplemented
64#16837323C2212yescomplemented
65#16837322C2212yescomplemented
66#16837315C2212yescomplemented
67#16837314C2212yescomplemented
68#16837306C2212yescomplemented
69#16837306C2212yescomplemented
70#16837299C2212yescomplemented
71#16837297C2212yescomplemented
72#16837287C2212yescomplemented
73#16837286C2212yescomplemented
74#16837283C2212yescomplemented
75#16837282C2211yescharacteristic
76#16837282C2211yescharacteristic
77#16837281C2211yescharacteristic
78#16837281C2211yescharacteristic
79#16837280C2212yes—
80#16837280C2212yes—
81#16837279C2211yescharacteristic
82#16837279C2211yescharacteristic
83#16837278C2212yes—
84#16837278C2212yes—
85#16837277C2211yescharacteristic, complemented
86#16837277C2211yescharacteristic, complemented
87#16837276C2212yes—
88#16837276C2212yes—
89#16837276C2212yescomplemented
90#16837275C2211yescharacteristic, complemented
91#16837275C2211yescharacteristic, complemented
92#16837275C2212yescomplemented
93#16837274C2211yescharacteristic, complemented
94#16837274C2211yescharacteristic, complemented
95#16837273C2212yes—
96#16837273C2212yes—
97#16837273C2212yescomplemented
98#16837264C2212yes—
99#16837264C2212yes—
100#16837262C2211yescharacteristic, complemented
101#16837261C2212yes—
102#16837261C2212yescomplemented
103#16837261C2212yescomplemented
104#16837261C2212yescomplemented
105#16837260C2211yescharacteristic, complemented
106#16837260C2211yescharacteristic, complemented
107#16837260C2212yescomplemented
108#16837259C2212yes—
109#16837259C2212yescomplemented
110#16837259C2212yescomplemented
111#16837257C2212yes—
112#16837257C2212yes—
113#95×D59C2212yescomplemented
114C2×C4×D4×C59C2211yescharacteristic
115C22×C4⋊C4×C59C2211yescharacteristic, complemented
116C59×#398C2212yescomplemented
117C59×#396C2212yescomplemented
118C59×#387C2212yescomplemented
119C59×#386C2211yescharacteristic
120C59×#386C2211yescharacteristic
121C59×#385C2211yescharacteristic, complemented
122C59×#385C2211yescharacteristic, complemented
123C59×#385C2212yescomplemented
124C59×#380C2211yescharacteristic, complemented
125C24×D59C2311yescharacteristic
126C24×D59C2311yescharacteristic
127C22×Dic118—24no—
128C22×Dic118—44no—
129C22×Dic118C2312yes—
130C22×Dic118C2312yes—
131C22×D236C2311yescharacteristic
132C22×C22⋊D59C2311yescharacteristic
133C22×C22⋊D59C2311yescharacteristic
134C2×D4×D59—24no—
135C2×D4×D59—24no—
136C2×D4×D59Q818yescomplemented
137C23×Dic59C2311yescharacteristic
138C23×Dic59C2311yescharacteristic
139C23×Dic59C2311yescharacteristic
140C23×Dic59C2311yescharacteristic
141C22×C4×D59—24no—
142C22×C4×D59—44no—
143C22×C4×D59—44no—
144C22×C4×D59D418yes—
145C22×C4×D59C2311yescharacteristic
146C22×C4×D59C2311yescharacteristic
147C22×C4×D59C2311yescharacteristic
148C22×C4×D59C2311yescharacteristic
149C22×C4×D59C2311yescharacteristic
150C22×C4×D59C2311yescharacteristic
151C22×C4×D59C2312yes—
152C22×C4×D59C2312yes—
153C22×C4×D59C2311yescharacteristic
154C22×C4×D59C2311yescharacteristic
155C22×C4×D59C2311yescharacteristic
156#14273705—28no—
157#14273705—28no—
158#14273705—28no—
159#14273705—28no—
160#14273705—44no—
161#14273704—44no—
162C4×D236—24no—
163D4×Dic59—24no—
164#14273689—24no—
165C4×C22⋊D59—24no—
166C4×C22⋊D59—24no—
167(C22⋊D59)⋊C4—24no—
168(C22⋊D59)⋊C4—24no—
169C2×C4⋊Dic59C2311yescharacteristic
170C2×C4⋊Dic59C2312yes—
171C2×C4⋊Dic59C2312yes—
172C2×C4⋊Dic59C2312yes—
173C2×Dic59⋊C4—24no—
174C2×Dic59⋊C4—24no—
175C2×Dic59⋊C4C2312yes—
176C2×Dic59⋊C4C2312yes—
177C2×Dic59⋊C4C2312yes—
178C2×Dic59⋊C4C2312yes—
179C2×Dic59⋊C4C2312yes—
180C2×Dic59⋊C4C2312yes—
181C2×Dic59⋊C4C2311yescharacteristic
182C2×Dic59⋊C4C2311yescharacteristic
183C2×Dic59⋊C4C2312yes—
184C2×Dic59⋊C4C2312yes—
185C2×Dic59⋊C4C2312yes—
186C2×Dic59⋊C4C2312yes—
187C4⋊C4×D59—24no—
188C4⋊C4×D59—44no—
189C2×C22⋊Dic59C2311yescharacteristic
190C2×C22⋊Dic59C2311yescharacteristic
191C2×C22⋊Dic59C2311yescharacteristic
192C2×C22⋊Dic59C2311yescharacteristic
193C2×C22⋊Dic59C2312yes—
194C2×C22⋊Dic59C2312yes—
195C2×(C2×D59)⋊C4—24no—
196C2×(C2×D59)⋊C4—24no—
197C2×(C2×D59)⋊C4C2312yes—
198C2×(C2×D59)⋊C4C2312yes—
199C2×(C2×D59)⋊C4C2312yes—
200C2×(C2×D59)⋊C4C2312yes—
201C2×(C2×D59)⋊C4C2312yes—
202C2×(C2×D59)⋊C4C2312yes—
203C2×(C2×D59)⋊C4C2311yescharacteristic
204C2×(C2×D59)⋊C4C2311yescharacteristic
205C2×(C2×D59)⋊C4C2311yescharacteristic
206C2×(C2×D59)⋊C4C2311yescharacteristic
207C2×(C2×D59)⋊C4C2312yes—
208C2×(C2×D59)⋊C4C2312yes—
209C2×(C2×D59)⋊C4C2312yes—
210C2×(C2×D59)⋊C4C2312yes—
211C22⋊C4×D59—24no—
212C22⋊C4×D59—24no—
213C22⋊C4×D59—24no—
214C22⋊C4×D59—24no—
215C2×C4×Dic59C2311yescharacteristic
216C2×C4×Dic59C2311yescharacteristic
217C2×C4×Dic59C2311yescharacteristic
218C42×D59—24no—
219C59⋊#95C2312yes—
220C59⋊#95C2312yes—
221C59⋊#95C2312yes—
222C59⋊#95C2312yes—
223C59⋊#95C2312yes—
224C59⋊#95C2312yes—
225C59⋊#95C2312yes—
226C59⋊#95C2312yes—
227C59⋊#95C2312yes—
228C59⋊#95C2312yes—
229C59⋊#95C2312yes—
230C59⋊#95C2312yes—
231C59⋊#95C2312yes—
232C59⋊#95C2312yes—
233C59⋊#95C2312yes—
234C22×D4×C59C2311yescharacteristic
235C23×C4×C59C2311yescharacteristic
236C23×C4×C59C2311yescharacteristic
237C23×C4×C59C2311yescharacteristic
238C23×C4×C59C2311yescharacteristic
239C4×D4×C59—24no—
240C2×C4⋊C4×C59—24no—
241C2×C4⋊C4×C59C2312yes—
242C2×C4⋊C4×C59C2312yes—
243C2×C4⋊C4×C59C2311yescharacteristic
244C2×C4⋊C4×C59C2312yes—
245C2×C4⋊C4×C59C2312yes—
246C2×C4⋊C4×C59C2312yes—
247C2×C22⋊C4×C59C2311yescharacteristic
248C2×C22⋊C4×C59C2311yescharacteristic
249C2×C22⋊C4×C59C2311yescharacteristic
250C2×C22⋊C4×C59C2311yescharacteristic
251C2×C22⋊C4×C59C2312yes—
252C2×C22⋊C4×C59C2312yes—
253C2×C42×C59C2311yescharacteristic
254#95×C59C2312yes—
255#95×C59C2312yes—
256#95×C59C2312yes—
257#95×C59C2312yes—
258#95×C59C2312yes—
259C24×C59C2411yescharacteristic
260C24×C59C2411yescharacteristic
261C23×D59—22no—
262C23×D59—22no—
263C23×D59—42no—
264C23×D59—42no—
265C23×D59—42no—
266C23×D59—42no—
267C23×D59C2×D414yes—
268C23×D59C2×Q814yes—
269C23×D59C2×Q814yescomplemented
270C23×D59#4114yes—
271C23×D59C2411yescharacteristic
272C23×D59C2411yescharacteristic
273C23×D59C2411yescharacteristic
274C2×D4×C59—22no—
275C2×D4×C59—22no—
276C2×D4×C59C2×Q814yes—
277C22×C4×C59—22no—
278C22×C4×C59—22no—
279C22×C4×C59—22no—
280C22×C4×C59—42no—
281C22×C4×C59—42no—
282C22×C4×C59—42no—
283C22×C4×C59—42no—
284C22×C4×C59C2×D414yes—
285C22×C4×C59C2412yes—
286C22×C4×C59C2412yes—
287C22×C4×C59C2411yescharacteristic
288C22×C4×C59C2412yes—
289C22×C4×C59C2412yes—
290C22×C4×C59C2411yescharacteristic
291C22×C4×C59C2411yescharacteristic
292C22×C4×C59C2411yescharacteristic
293C22×C4×C59C2411yescharacteristic
294C2×C22⋊D59—22no—
295C2×C22⋊D59—22no—
296C2×C22⋊D59—22no—
297C2×C22⋊D59—22no—
298C2×C22⋊D59C2×Q814yes—
299C2×C22⋊D59C2×Q814yescomplemented
300C22×Dic59—24no—
301C22×Dic59—22no—
302C22×Dic59—22no—
303C22×Dic59—22no—
304C22×Dic59—24no—
305C22×Dic59—42no—
306C22×Dic59—42no—
307C22×Dic59C2×D414yes—
308C22×Dic59C2412yes—
309C22×Dic59C2412yes—
310C22×Dic59C2411yescharacteristic
311C22×Dic59C2412yes—
312C22×Dic59C2412yes—
313C22×Dic59C2411yescharacteristic
314C22×Dic59C2411yescharacteristic
315C22×Dic59C2411yescharacteristic
316C22×Dic59C2411yescharacteristic
317D4×D59—232no—
318C2×D236—22no—
319C2×D236—22no—
320C2×D236C2×Q814yescomplemented
321C2×C4×D59—22no—
322C2×C4×D59—22no—
323C2×C4×D59—24no—
324C2×C4×D59—24no—
325C2×C4×D59—22no—
326C2×C4×D59—22no—
327C2×C4×D59—22no—
328C2×C4×D59—22no—
329C2×C4×D59—24no—
330C2×C4×D59—24no—
331C2×C4×D59—24no—
332C2×C4×D59—416no—
333C2×C4×D59—416no—
334C2×C4×D59—42no—
335C2×C4×D59—42no—
336C2×C4×D59—42no—
337C2×C4×D59—42no—
338C2×C4×D59—42no—
339C2×C4×D59—42no—
340C2×C4×D59—42no—
341C2×C4×D59—42no—
342C2×C4×D59—42no—
343C2×C4×D59C2×D414yes—
344C2×C4×D59C2×D414yes—
345C2×C4×D59C2×D414yes—
346C2×C4×D59C2×D414yes—
347C2×C4×D59C2×Q814yescomplemented
348C2×Dic118—24no—
349C2×Dic118—24no—
350C2×Dic118—24no—
351C2×Dic118—24no—
352C2×Dic118—42no—
353C2×Dic118—42no—
354C2×Dic118—416no—
355C4⋊C4×C59—24no—
356C4⋊C4×C59—24no—
357C4⋊C4×C59—22no—
358C4⋊C4×C59—42no—
359C4⋊C4×C59—42no—
360C4⋊C4×C59—42no—
361C22⋊C4×C59—22no—
362C22⋊C4×C59—22no—
363C22⋊C4×C59—22no—
364C22⋊C4×C59—22no—
365C22⋊C4×C59—42no—
366C22⋊C4×C59—42no—
367C42×C59—22no—
368C22⋊Dic59—22no—
369C22⋊Dic59—22no—
370C22⋊Dic59—22no—
371C22⋊Dic59—22no—
372C22⋊Dic59—42no—
373C22⋊Dic59—42no—
374(C2×D59)⋊C4—22no—
375(C2×D59)⋊C4—22no—
376(C2×D59)⋊C4—24no—
377(C2×D59)⋊C4—24no—
378(C2×D59)⋊C4—24no—
379(C2×D59)⋊C4—24no—
380(C2×D59)⋊C4—24no—
381(C2×D59)⋊C4—24no—
382(C2×D59)⋊C4—22no—
383(C2×D59)⋊C4—22no—
384(C2×D59)⋊C4—42no—
385(C2×D59)⋊C4—42no—
386(C2×D59)⋊C4—42no—
387(C2×D59)⋊C4—42no—
388C4⋊Dic59—22no—
389C4⋊Dic59—42no—
390C4⋊Dic59—42no—
391C4⋊Dic59—42no—
392Dic59⋊C4—22no—
393Dic59⋊C4—24no—
394Dic59⋊C4—24no—
395Dic59⋊C4—22no—
396Dic59⋊C4—24no—
397Dic59⋊C4—24no—
398Dic59⋊C4—24no—
399Dic59⋊C4—24no—
400Dic59⋊C4—42no—
401Dic59⋊C4—42no—
402Dic59⋊C4—42no—
403Dic59⋊C4—42no—
404C4×Dic59—22no—
405C4×Dic59—22no—
406C4×Dic59—22no—
407C23×C59—22no—
408C23×C59—22no—
409C23×C59—21no—
410C23×C59—21no—
411C23×C59—22no—
412C23×C59—22no—
413C23×C59C22×D412yes—
414C23×C59C22×Q812yes—
415C23×C59C22×Q812yes—
416C23×C59C2×#4112yes—
417C23×C59C2511yescharacteristic
418C22×D59—22no—
419C22×D59—22no—
420C22×D59—22no—
421C22×D59—22no—
422C22×D59—21no—
423C22×D59—21no—
424C22×D59—22no—
425C22×D59—22no—
426C22×D59—28no—
427C22×D59—44no—
428C22×D59—44no—
429C22×D59—48no—
430C22×D59—48no—
431C22×D59—48no—
432C22×D59—44no—
433C22×D59—44no—
434C22×D59—48no—
435C22×D59C22⋊Q8116yescomplemented
436C22×D59C22×D412yes—
437C22×D59C22×D412yes—
438C22×D59C22×Q812yes—
439C22×D59C22×Q812yes—
440C22×D59C22×Q812yes—
441C22×D59C2×#4112yes—
442C22×D59C2×#4112yes—
443D4×C59—28no—
444C2×C4×C59—21no—
445C2×C4×C59—21no—
446C2×C4×C59—22no—
447C2×C4×C59—22no—
448C2×C4×C59—21no—
449C2×C4×C59—22no—
450C2×C4×C59—21no—
451C2×C4×C59—22no—
452C2×C4×C59—22no—
453C2×C4×C59—22no—
454C2×C4×C59—22no—
455C2×C4×C59—22no—
456C2×C4×C59—22no—
457C2×C4×C59—22no—
458C2×C4×C59—22no—
459C2×C4×C59—22no—
460C2×C4×C59—22no—
461C2×C4×C59—22no—
462C2×C4×C59—22no—
463C2×C4×C59—22no—
464C2×C4×C59—44no—
465C2×C4×C59—44no—
466C2×C4×C59—44no—
467C2×C4×C59—44no—
468C2×C4×C59C22×D412yes—
469C2×C4×C59C22×D412yes—
470C2×C4×C59C22×Q812yes—
471C22⋊D59—28no—
472C22⋊D59—28no—
473C2×Dic59—21no—
474C2×Dic59—21no—
475C2×Dic59—22no—
476C2×Dic59—28no—
477C2×Dic59—21no—
478C2×Dic59—22no—
479C2×Dic59—22no—
480C2×Dic59—21no—
481C2×Dic59—22no—
482C2×Dic59—22no—
483C2×Dic59—22no—
484C2×Dic59—22no—
485C2×Dic59—22no—
486C2×Dic59—22no—
487C2×Dic59—22no—
488C2×Dic59—22no—
489C2×Dic59—22no—
490C2×Dic59—22no—
491C2×Dic59—22no—
492C2×Dic59—22no—
493C2×Dic59—44no—
494C2×Dic59—44no—
495C2×Dic59—44no—
496C2×Dic59C22×D412yes—
497C2×Dic59C22×D412yes—
498C2×Dic59C22×Q812yes—
499C2×Dic59H(5,𝔽2)14yes—
500D236—28no—
501C4×D59—28no—
502C4×D59—28no—
503C4×D59—28no—
504C4×D59—44no—
505C4×D59—44no—
506C4×D59—44no—
507C4×D59—44no—
508C4×D59—44no—
509C4×D59—44no—
510C4×D59—84no—
511C4×D59—84no—
512Dic118—48no—
513Dic118—48no—
514#35010—591nomaximal, Sylow
515C22×C59—22no—
516C22×C59—22no—
517C22×C59—24no—
518C22×C59—24no—
519C22×C59—22no—
520C22×C59—24no—
521C22×C59—41no—
522C22×C59—41no—
523C22×C59—42no—
524C22×C59C2×C22⋊Q814yes—
525C22×C59C23×D411yescharacteristic
526C22×C59C23×Q811yescharacteristic
527C22×C59C22×#4111yescharacteristic
528C22×C59C2×H(5,𝔽2)12yes—
529C22×C59#58512yes—
530C2×D59—22no—
531C2×D59—22no—
532C2×D59—22no—
533C2×D59—22no—
534C2×D59—24no—
535C2×D59—24no—
536C2×D59—24no—
537C2×D59—24no—
538C2×D59—22no—
539C2×D59—24no—
540C2×D59—416no—
541C2×D59—416no—
542C2×D59—41no—
543C2×D59—41no—
544C2×D59—42no—
545C2×D59C2×C22⋊Q814yes—
546C2×D59C2×C22⋊Q814yes—
547C4×C59—22no—
548C4×C59—22no—
549C4×C59—22no—
550C4×C59—42no—
551C4×C59—41no—
552C4×C59—41no—
553C4×C59—42no—
554C4×C59—42no—
555C4×C59—42no—
556Dic59—22no—
557Dic59—22no—
558Dic59—42no—
559Dic59—41no—
560Dic59—41no—
561Dic59—42no—
562Dic59—42no—
563Dic59—42no—
564Dic59#53414yes—
565C22×C22⋊Q8—591no—
566C22×C4×D4—591no—
567#2855—592no—
568#2848—592no—
569#2627—592no—
570#2626—592no—
571#2579—591no—
572#2579—591no—
573#2579—591no—
574#2579D5911yescharacteristic, complemented
575#2564—592no—
576#2564—592no—
577#2487—591no—
578#2487—591no—
579#2417—592no—
580#2417—592no—
581#2409—591no—
582#2409—591no—
583#2315—591no—
584#2315—591no—
585#2308—591no—
586#2308—591no—
587C2×#380—591no—
588C2×C59—24no—
589C2×C59—42no—
590C2×C59C22×C22⋊Q811yescharacteristic
591C2×C59C2×#53411yescharacteristic
592C2×C59#344911yescharacteristic
593C2×C59#350112yes—
594C2×C59#350512yes—
595D59—24no—
596D59—24no—
597D59—42no—
598C23×Q8—591no—
599C23×D4—591no—
600C24×C4—591no—
601C24×C4—591no—
602C2×C22⋊Q8—592no—
603C2×C22⋊Q8—592no—
604C2×C22⋊Q8—592no—
605C2×C22⋊Q8—592no—
606C2×C22⋊Q8—592no—
607C2×C22⋊Q8—592no—
608C2×C22⋊Q8—1188no—
609C2×C4×D4—591no—
610C2×C4×D4—591no—
611C2×C4×D4—591no—
612C2×C4×D4—591no—
613C2×C4×D4—591no—
614C2×C4×D4—591no—
615C2×C4×D4—591no—
616C2×C4×D4—1188no—
617C2×C4×D4C2×D5911yescharacteristic
618C22×C4⋊C4—591no—
619C22×C4⋊C4—591no—
620C22×C4⋊C4—591no—
621C22×C4⋊C4—592no—
622C22×C4⋊C4C2×D5911yescharacteristic, complemented
623C22×C22⋊C4—591no—
624C22×C22⋊C4—591no—
625C22×C22⋊C4—591no—
626C22×C22⋊C4—591no—
627C22×C22⋊C4—591no—
628C22×C22⋊C4—591no—
629C22×C42—591no—
630#400—592no—
631#400—592no—
632#399—592no—
633#399—592no—
634#398—592no—
635#398—592no—
636#398—592no—
637#398C2×D5912yescomplemented
638#396—592no—
639#396—592no—
640#396—592no—
641#396C2×D5912yescomplemented
642#395—592no—
643#395—592no—
644#393—592no—
645#393—592no—
646#391—592no—
647#391—592no—
648#389—592no—
649#389—592no—
650#387—592no—
651#387—592no—
652#387—592no—
653#387C2×D5912yescomplemented
654#386—591no—
655#386—591no—
656#386—591no—
657#386—591no—
658#386—592no—
659#386—592no—
660#386—591no—
661#386—591no—
662#386—592no—
663#386—592no—
664#386C2×D5911yescharacteristic
665#386C2×D5911yescharacteristic
666#385—592no—
667#385—591no—
668#385—591no—
669#385—592no—
670#385—592no—
671#385—592no—
672#385—591no—
673#385—591no—
674#385—591no—
675#385—591no—
676#385—592no—
677#385—592no—
678#385—592no—
679#385C2×D5912yescomplemented
680#385C2×D5911yescharacteristic, complemented
681#385C2×D5911yescharacteristic, complemented
682#381—592no—
683#381—592no—
684#380—591no—
685#380—592no—
686#380—592no—
687#380—592no—
688#380—592no—
689#380—591no—
690#380—591no—
691#380—592no—
692#380—592no—
693#380—592no—
694#380—592no—
695#380C2×D5911yescharacteristic, complemented
696#379—592no—
697#379—592no—
698C2×#95—592no—
699C59#3501011yescharacteristic, complemented, Sylow
700C25—591no—
701C25—591no—
702C22×Q8—592no—
703C22×Q8—592no—
704C22×Q8—1184no—
705C22×Q8—2364no—
706C22×D4—591no—
707C22×D4—591no—
708C22×D4—598no—
709C22×D4—591no—
710C22×D4—1184no—
711C22×D4—1184no—
712C22×D4C22×D5911yescharacteristic
713C23×C4—591no—
714C23×C4—591no—
715C23×C4—591no—
716C23×C4—591no—
717C23×C4—598no—
718C23×C4—591no—
719C23×C4—591no—
720C23×C4—591no—
721C23×C4—591no—
722C23×C4—591no—
723C23×C4—591no—
724C23×C4—591no—
725C23×C4—591no—
726C23×C4—592no—
727C23×C4—592no—
728C23×C4—591no—
729C23×C4—1184no—
730C23×C4—2364no—
731C23×C4—2364no—
732C23×C4C22×D5911yescharacteristic
733C23×C4C22×D5911yescharacteristic
734C23×C4C22×D5911yescharacteristic
735C23×C4C22×D5911yescharacteristic
736C22⋊Q8—1188no—
737C22⋊Q8—1188no—
738C22⋊Q8—1188no—
739C22⋊Q8—1188no—
740C22⋊Q8—2364no—
741C22⋊Q8—2364no—
742C4×D4—24no—
743C4×D4—1184no—
744C4×D4—1184no—
745C4×D4—1184no—
746C4×D4—1184no—
747C4×D4—1184no—
748C4×D4—1184no—
749C4×D4—1184no—
750C2×C4⋊C4—24no—
751C2×C4⋊C4—591no—
752C2×C4⋊C4—591no—
753C2×C4⋊C4—591no—
754C2×C4⋊C4—592no—
755C2×C4⋊C4—592no—
756C2×C4⋊C4—592no—
757C2×C4⋊C4—592no—
758C2×C4⋊C4—592no—
759C2×C4⋊C4—592no—
760C2×C4⋊C4—592no—
761C2×C4⋊C4—592no—
762C2×C4⋊C4—592no—
763C2×C4⋊C4—592no—
764C2×C4⋊C4—592no—
765C2×C4⋊C4—592no—
766C2×C4⋊C4—592no—
767C2×C4⋊C4—1184no—
768C2×C4⋊C4—1184no—
769C2×C4⋊C4—1184no—
770C2×C4⋊C4—2364no—
771C2×C4⋊C4C22×D5911yescharacteristic
772C2×C4⋊C4C22×D5912yes—
773C2×C4⋊C4C22×D5912yes—
774C2×C4⋊C4C22×D5912yes—
775C2×C4⋊C4C22×D5912yes—
776C2×C4⋊C4C22×D5912yes—
777C2×C22⋊C4—591no—
778C2×C22⋊C4—591no—
779C2×C22⋊C4—591no—
780C2×C22⋊C4—591no—
781C2×C22⋊C4—591no—
782C2×C22⋊C4—591no—
783C2×C22⋊C4—591no—
784C2×C22⋊C4—591no—
785C2×C22⋊C4—592no—
786C2×C22⋊C4—592no—
787C2×C22⋊C4—592no—
788C2×C22⋊C4—592no—
789C2×C22⋊C4—592no—
790C2×C22⋊C4—592no—
791C2×C22⋊C4—592no—
792C2×C22⋊C4—592no—
793C2×C22⋊C4—592no—
794C2×C22⋊C4—592no—
795C2×C22⋊C4—592no—
796C2×C22⋊C4—592no—
797C2×C22⋊C4—1184no—
798C2×C22⋊C4—1184no—
799C2×C22⋊C4—1184no—
800C2×C22⋊C4—1184no—
801C2×C22⋊C4—1184no—
802C2×C22⋊C4—1184no—
803C2×C22⋊C4C22×D5911yescharacteristic
804C2×C22⋊C4C22×D5911yescharacteristic
805C2×C22⋊C4C22×D5911yescharacteristic
806C2×C22⋊C4C22×D5911yescharacteristic
807C2×C22⋊C4C22×D5912yes—
808C2×C22⋊C4C22×D5912yes—
809C2×C42—591no—
810C2×C42—591no—
811C2×C42—591no—
812C2×C42—1184no—
813C2×C42C22×D5911yescharacteristic
814#95—592no—
815#95—592no—
816#95—592no—
817#95—592no—
818#95—592no—
819#95—592no—
820#95—592no—
821#95—592no—
822#95—592no—
823#95—592no—
824#95—592no—
825#95—592no—
826#95—592no—
827#95—592no—
828#95—592no—
829#95C22×D5912yes—
830#95C22×D5912yes—
831#95C22×D5912yes—
832#95C22×D5912yes—
833#95C22×D5912yes—
834C24—591no—
835C24—591no—
836C24—594no—
837C24—594no—
838C24—594no—
839C24—591no—
840C24—594no—
841C24—1182no—
842C24—1182no—
843C24—2362no—
844C24—2362no—
845C24—2362no—
846C24—2362no—
847C24C23×D5911yescharacteristic
848C24C23×D5911yescharacteristic
849C2×Q8—1184no—
850C2×Q8—1184no—
851C2×Q8—1184no—
852C2×Q8—1184no—
853C2×Q8—2362no—
854C2×Q8—2362no—
855C2×Q8—23616no—
856C2×D4—22no—
857C2×D4—22no—
858C2×D4—594no—
859C2×D4—594no—
860C2×D4—594no—
861C2×D4—1182no—
862C2×D4—1182no—
863C2×D4—11832no—
864C2×D4—1182no—
865C2×D4—1182no—
866C2×D4—1182no—
867C2×D4—1182no—
868C2×D4Q8×D5914yes—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—22no—
872C22×C4—42no—
873C22×C4—42no—
874C22×C4—42no—
875C22×C4—42no—
876C22×C4—591no—
877C22×C4—594no—
878C22×C4—591no—
879C22×C4—591no—
880C22×C4—594no—
881C22×C4—594no—
882C22×C4—594no—
883C22×C4—594no—
884C22×C4—594no—
885C22×C4—592no—
886C22×C4—592no—
887C22×C4—591no—
888C22×C4—592no—
889C22×C4—592no—
890C22×C4—591no—
891C22×C4—1184no—
892C22×C4—1184no—
893C22×C4—1182no—
894C22×C4—1184no—
895C22×C4—1182no—
896C22×C4—1182no—
897C22×C4—1184no—
898C22×C4—1184no—
899C22×C4—1182no—
900C22×C4—1182no—
901C22×C4—1184no—
902C22×C4—1182no—
903C22×C4—1184no—
904C22×C4—1182no—
905C22×C4—1182no—
906C22×C4—1182no—
907C22×C4—2362no—
908C22×C4—2362no—
909C22×C4—2362no—
910C22×C4—2362no—
911C22×C4—2362no—
912C22×C4—2362no—
913C22×C4—2362no—
914C22×C4—2362no—
915C22×C4—2362no—
916C22×C4—23616no—
917C22×C4—23616no—
918C22×C4—2362no—
919C22×C4—2362no—
920C22×C4D4×D5914yes—
921C22×C4C23×D5912yes—
922C22×C4C23×D5912yes—
923C22×C4C23×D5911yescharacteristic
924C22×C4C23×D5912yes—
925C22×C4C23×D5912yes—
926C22×C4C23×D5911yescharacteristic
927C22×C4C23×D5911yescharacteristic
928C22×C4C23×D5911yescharacteristic
929C22×C4C23×D5911yescharacteristic
930C4⋊C4—24no—
931C4⋊C4—24no—
932C4⋊C4—22no—
933C4⋊C4—42no—
934C4⋊C4—42no—
935C4⋊C4—42no—
936C4⋊C4—1182no—
937C4⋊C4—1182no—
938C4⋊C4—1184no—
939C4⋊C4—1184no—
940C4⋊C4—1184no—
941C4⋊C4—1184no—
942C4⋊C4—1182no—
943C4⋊C4—1184no—
944C4⋊C4—1184no—
945C4⋊C4—2362no—
946C4⋊C4—2362no—
947C4⋊C4—2362no—
948C4⋊C4—2362no—
949C4⋊C4—2362no—
950C4⋊C4—2362no—
951C4⋊C4—2362no—
952C22⋊C4—22no—
953C22⋊C4—22no—
954C22⋊C4—22no—
955C22⋊C4—22no—
956C22⋊C4—42no—
957C22⋊C4—42no—
958C22⋊C4—1182no—
959C22⋊C4—1182no—
960C22⋊C4—1182no—
961C22⋊C4—1184no—
962C22⋊C4—1184no—
963C22⋊C4—1184no—
964C22⋊C4—1184no—
965C22⋊C4—1184no—
966C22⋊C4—1184no—
967C22⋊C4—1182no—
968C22⋊C4—1182no—
969C22⋊C4—1182no—
970C22⋊C4—1182no—
971C22⋊C4—1182no—
972C22⋊C4—2362no—
973C22⋊C4—2362no—
974C22⋊C4—2362no—
975C22⋊C4—2362no—
976C22⋊C4—2362no—
977C22⋊C4—2362no—
978C42—22no—
979C42—1182no—
980C42—1182no—
981C42—1182no—
982C23—22no—
983C23—22no—
984C23—21no—
985C23—21no—
986C23—22no—
987C23—22no—
988C23—592no—
989C23—592no—
990C23—592no—
991C23—592no—
992C23—592no—
993C23—592no—
994C23—5916no—
995C23—592no—
996C23—1188no—
997C23—1182no—
998C23—1182no—
999C23—1182no—
1000C23—1182no—
1001C23—1181no—
1002C23—1181no—
1003C23—1182no—
1004C23—1182no—
1005C23—2364no—
1006C23—2368no—
1007C23—2368no—
1008C23—2364no—
1009C23—2368no—
1010C23—2364no—
1011C23—2368no—
1012C23—2364no—
1013C23C2×D4×D5912yes—
1014C23C2×Q8×D5912yes—
1015C23C2×Q8×D5912yes—
1016C23#41×D5912yes—
1017C23C24×D5911yescharacteristic
1018Q8—2368no—
1019Q8—2368no—
1020D4—28no—
1021D4—1188no—
1022D4—1188no—
1023D4—1188no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—44no—
1045C2×C4—44no—
1046C2×C4—44no—
1047C2×C4—44no—
1048C2×C4—592no—
1049C2×C4—594no—
1050C2×C4—592no—
1051C2×C4—592no—
1052C2×C4—1188no—
1053C2×C4—1188no—
1054C2×C4—1188no—
1055C2×C4—1188no—
1056C2×C4—1181no—
1057C2×C4—1181no—
1058C2×C4—1182no—
1059C2×C4—1181no—
1060C2×C4—1182no—
1061C2×C4—1181no—
1062C2×C4—1182no—
1063C2×C4—1182no—
1064C2×C4—1182no—
1065C2×C4—1182no—
1066C2×C4—1182no—
1067C2×C4—1182no—
1068C2×C4—1182no—
1069C2×C4—1182no—
1070C2×C4—1182no—
1071C2×C4—1182no—
1072C2×C4—1182no—
1073C2×C4—1182no—
1074C2×C4—1182no—
1075C2×C4—4724no—
1076C2×C4—4724no—
1077C2×C4—2364no—
1078C2×C4—2364no—
1079C2×C4—2364no—
1080C2×C4—2364no—
1081C2×C4—2364no—
1082C2×C4—2364no—
1083C2×C4—2364no—
1084C2×C4—2364no—
1085C2×C4—2364no—
1086C2×C4C2×D4×D5912yes—
1087C2×C4C2×D4×D5912yes—
1088C2×C4C2×Q8×D5912yes—
1089C22—24no—
1090C22—22no—
1091C22—24no—
1092C22—22no—
1093C22—22no—
1094C22—24no—
1095C22—41no—
1096C22—42no—
1097C22—41no—
1098C22—594no—
1099C22—594no—
1100C22—1184no—
1101C22—1184no—
1102C22—1182no—
1103C22—1182no—
1104C22—1184no—
1105C22—1184no—
1106C22—1182no—
1107C22—1182no—
1108C22—1182no—
1109C22—1184no—
1110C22—23616no—
1111C22—23616no—
1112C22—2361no—
1113C22—2362no—
1114C22—2361no—
1115C22C22⋊Q8×D5914yes—
1116C22C22×D4×D5911yescharacteristic
1117C22C22×Q8×D5911yescharacteristic
1118C22C2×#41×D5911yescharacteristic
1119C22H(5,𝔽2)×D5912yes—
1120C22#1683823812yes—
1121C4—22no—
1122C4—22no—
1123C4—22no—
1124C4—41no—
1125C4—42no—
1126C4—42no—
1127C4—42no—
1128C4—42no—
1129C4—41no—
1130C4—594no—
1131C4—1182no—
1132C4—1182no—
1133C4—2361no—
1134C4—2362no—
1135C4—2362no—
1136C4—2362no—
1137C4—2361no—
1138C4—2362no—
1139C2—24no—
1140C2—42no—
1141C2—1184no—
1142C2—1184no—
1143C2—2362no—
1144C2C2×C22⋊Q8×D5911yescharacteristic
1145C2#534×D5911yescharacteristic
1146C2#2143742611yescharacteristic
1147C2#2143789512yes—
1148C2#2143792912yes—
subgroupG/H
center, FrattiniC23C24×D59
commutator, socle, cosocleC23×C59C25
FittingC59×#2579C2
prime radicalC22×D4×D59C22
hypercenter#2579D59
hypocenterC59#35010
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #2579

Complements

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

NH ≅ G/Ntype
1. C22×#14273705C2semidirect
3. #21432431C2semidirect
4. #21432382C2semidirect
5. #21429914C2semidirect
6. #21429906C2semidirect
7. #21429445C2semidirect
8. #21429443C2semidirect
9. #21429439C2semidirect
10. #21429281C2semidirect
11. #21429275C2semidirect
12. #21428412C2semidirect
13. #21428410C2semidirect
14. #21427542C2semidirect
15. #21427540C2semidirect
16. #21427460C2semidirect
17. #21427458C2semidirect
18. #21426707C2semidirect
19. #21426707C2semidirect
22. #380×D59C2semidirect
23. C59×#2579C2semidirect
24. C23×Dic118C22semidirect
31. C2×#14273705C22semidirect
32. C2×#14273705C22semidirect
33. C2×#14273705C22semidirect
34. C2×#14273704C22semidirect
43. C22×Dic59⋊C4C22semidirect
44. C22×Dic59⋊C4C22semidirect
46. C2×C4⋊C4×D59C22semidirect
54. #16837344C22semidirect
55. #16837343C22semidirect
56. #16837338C22semidirect
57. #16837337C22semidirect
58. #16837335C22semidirect
59. #16837335C22semidirect
60. #16837332C22semidirect
61. #16837325C22semidirect
62. #16837324C22semidirect
63. #16837324C22semidirect
64. #16837323C22semidirect
65. #16837322C22semidirect
66. #16837315C22semidirect
67. #16837314C22semidirect
68. #16837306C22semidirect
69. #16837306C22semidirect
70. #16837299C22semidirect
71. #16837297C22semidirect
72. #16837287C22semidirect
73. #16837286C22semidirect
74. #16837283C22semidirect
85. #16837277C22semidirect
86. #16837277C22semidirect
89. #16837276C22semidirect
90. #16837275C22semidirect
91. #16837275C22semidirect
92. #16837275C22semidirect
93. #16837274C22semidirect
94. #16837274C22semidirect
97. #16837273C22semidirect
100. #16837262C22semidirect
102. #16837261C22semidirect
103. #16837261C22semidirect
104. #16837261C22semidirect
105. #16837260C22semidirect
106. #16837260C22semidirect
107. #16837260C22semidirect
109. #16837259C22semidirect
110. #16837259C22semidirect
113. #95×D59C22semidirect
115. C22×C4⋊C4×C59C22semidirect
116. C59×#398C22semidirect
117. C59×#396C22semidirect
118. C59×#387C22semidirect
121. C59×#385C22semidirect
122. C59×#385C22semidirect
123. C59×#385C22semidirect
124. C59×#380C22semidirect
136. C2×D4×D59Q8semidirect
269. C23×D59C2×Q8semidirect
299. C2×C22⋊D59C2×Q8semidirect
320. C2×D236C2×Q8semidirect
347. C2×C4×D59C2×Q8semidirect
435. C22×D59C22⋊Q8semidirect
574. #2579D59semidirect
622. C22×C4⋊C4C2×D59semidirect
637. #398C2×D59semidirect
641. #396C2×D59semidirect
653. #387C2×D59semidirect
679. #385C2×D59semidirect
680. #385C2×D59semidirect
681. #385C2×D59semidirect
695. #380C2×D59semidirect
699. C59#35010semidirect

Maximal subgroups

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

subgroupindex
C22×#142737052
C2×C4×D4×D592
#214324312
#214323822
#214299142
#214299062
#214294452
#214294432
#214294392
#214292812
#214292752
#214284122
#214284102
#214275422
#214275402
#214274602
#214274582
#214267072
#214266702
#380×D592
C59×#25792
#3501059