Finite Group Databasebeta

← #27542852

Subgroups — #27542852

Order 13568.

3134 conjugacy classes of subgroups.

The subgroup lattice has 1184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811136C211yesmaximal, characteristic
2C2×C4×#11719949C211yesmaximal, characteristic, complemented
3C2×#117×D53C211yesmaximal, characteristic, complemented
4#20277409C211yesmaximal, characteristic, complemented
5#20277408C211yesmaximal, characteristic, complemented
6#20277406C211yesmaximal, characteristic, complemented
7#20277404C211yesmaximal, characteristic, complemented
8#20277400C211yesmaximal, characteristic, complemented
9#20277399C211yesmaximal, characteristic, complemented
10#20277391C211yesmaximal, characteristic, complemented
11#20277388C212yesmaximal, complemented
12#20277379C212yesmaximal, complemented
13#20277377C212yesmaximal, complemented
14#20277368C212yesmaximal, complemented
15#20277204C211yesmaximal, characteristic, complemented
16#20277196C211yesmaximal, characteristic, complemented
17#20277175C212yesmaximal, complemented
18#20277173C212yesmaximal, complemented
19#20277157C212yesmaximal, complemented
20#20277153C212yesmaximal, complemented
21#20277097C211yesmaximal, characteristic, complemented
22C4×#13133175C211yesmaximal, characteristic, complemented
23C53×#2323C211yesmaximal, characteristic, complemented
24C22×#11719949C2211yescharacteristic
25C23×C4×D53C2211yescharacteristic
26#16811136C4116yescomplemented
27C2×#13133202C2212yes—
28C2×#13133193C2211yescharacteristic
29C2×#13133192C2211yescharacteristic
30C2×#13133191C2211yescharacteristic
31C2×#13133187C2212yes—
32C4×#11719949—28no—
33C2×Q8×Dic53C2211yescharacteristic, complemented
34C2×C4×D212C2212yes—
35C2×C4×D212C2211yescharacteristic, complemented
36C2×#13133179C2212yes—
37C2×#13133179C2212yes—
38C2×#13133179C2211yescharacteristic, complemented
39C2×#13133177C2212yes—
40C2×#13133176C2211yescharacteristic
41C2×#13133175C2211yescharacteristic
42C2×#13133175C2211yescharacteristic
43C2×#13133175C2211yescharacteristic
44C2×#13133175C2211yescharacteristic
45C2×#13133175C2211yescharacteristic
46C2×#13133175C2212yescomplemented
47C2×#13133174C2211yescharacteristic
48C2×#13133174C2211yescharacteristic
49C2×#13133173C2211yescharacteristic
50C2×#13133173C2211yescharacteristic
51#117×D53—28no—
52C2×C4⋊C4×D53C2211yescharacteristic
53C2×C4⋊C4×D53C2211yescharacteristic
54C2×C22⋊C4×D53C2211yescharacteristic
55C2×C22⋊C4×D53C2211yescharacteristic
56C2×C42×D53C2211yescharacteristic
57C2×C42×D53C2211yescharacteristic
58C2×C42×D53C2212yescomplemented
59#16810530C2211yescharacteristic, complemented
60#16810525C2212yes—
61#16810525C2211yescharacteristic, complemented
62#16810524C2212yes—
63#16810524C2211yescharacteristic, complemented
64#16810523C2212yes—
65#16810523C2212yes—
66#16810522C2212yescomplemented
67#16810522C2211yescharacteristic, complemented
68#16810521C2211yescharacteristic, complemented
69#16810520C2212yescomplemented
70#16810519C2211yescharacteristic, complemented
71#16810518C2212yescomplemented
72#16810516C2212yes—
73#16810516C2212yes—
74#16810515C2212yes—
75#16810515C2212yescomplemented
76#16810514C2212yes—
77#16810514C2212yescomplemented
78#16810513C2212yes—
79#16810513C2212yescomplemented
80#16810512C2212yes—
81#16810512C2212yescomplemented
82#16810509C2212yescomplemented
83#16810507C2212yescomplemented
84#16810505C2212yescomplemented
85#16810501C2212yes—
86#16810501C2212yes—
87#16810501C2212yes—
88#16810501C2212yes—
89#16810499C2212yes—
90#16810499C2212yes—
91#16810497C2212yes—
92#16810497C2212yescomplemented
93#16810497C2212yescomplemented
94#16810494C2212yes—
95#16810494C2212yescomplemented
96#16810494C2212yescomplemented
97#16810485C2212yes—
98#16810483C2211yescharacteristic
99#16810480C2211yescharacteristic
100#16810480C2211yescharacteristic
101#16810478C2212yes—
102C4⋊C4×Dic53C2211yescharacteristic, complemented
103C4⋊C4×Dic53C2211yescharacteristic, complemented
104C4⋊C4×Dic53C2212yescomplemented
105C4×C4⋊Dic53C2211yescharacteristic, complemented
106#16810474C2212yescomplemented
107C22⋊C4×Dic53C2212yes—
108C4×#11719921C2212yes—
109#16810470C2212yes—
110#16810470C2212yes—
111#16810470C2212yescomplemented
112#16810470C2212yescomplemented
113#16810468C2212yescomplemented
114C42×Dic53C2212yescomplemented
115C2×C22⋊Q8×C53C2211yescharacteristic
116C2×C4×Q8×C53C2211yescharacteristic, complemented
117C2×#117×C53C2211yescharacteristic
118C53×#391C2211yescharacteristic, complemented
119C53×#389C2212yescomplemented
120C53×#389C2211yescharacteristic, complemented
121C53×#388C2212yes—
122C53×#388C2212yes—
123C53×#387C2212yescomplemented
124C53×#380C2211yescharacteristic
125C4×C4⋊C4×C53C2211yescharacteristic, complemented
126C24×D53C2311yescharacteristic
127C2×#11719949—24no—
128C2×#11719949—24no—
129C2×#11719949C2×C418yes—
130C22×D212C2312yes—
131C22×D212C2311yescharacteristic
132C22×D212C2312yes—
133C22×C22⋊D53C2312yes—
134C23×Dic53C2311yescharacteristic
135C22×C4×D53—24no—
136C22×C4×D53—24no—
137C22×C4×D53C2×C418yescomplemented
138C22×C4×D53C2312yes—
139C22×C4×D53C2311yescharacteristic
140C22×C4×D53C2311yescharacteristic
141C22×C4×D53C2311yescharacteristic
142C22×C4×D53C2311yescharacteristic
143C22×C4×D53C2312yes—
144C22×C4×D53C2312yes—
145C22×C4×D53C2311yescharacteristic
146C22×C4×D53C2311yescharacteristic
147C22×C4×D53C2311yescharacteristic
148C22×C4×D53C2311yescharacteristic
149#13133202C2×C4116yescomplemented
150#13133193C2×C418yescomplemented
151#13133192C2×C418yescomplemented
152#13133191C2×C418yescomplemented
153#13133187C2×C4116yescomplemented
154Q8×Dic53—24no—
155C4×D212—24no—
156C4×D212—28no—
157#13133179—24no—
158#13133179—28no—
159#13133179C2×C4116yescomplemented
160#13133177C2×C4116yescomplemented
161#13133176—24no—
162#13133175—24no—
163#13133175—24no—
164#13133175—28no—
165#13133175—24no—
166#13133175—24no—
167#13133175C2×C418yescomplemented
168#13133174—24no—
169#13133174—24no—
170#13133173—24no—
171#13133173—24no—
172C2×C4⋊Dic53C2311yescharacteristic
173C2×C4⋊Dic53C2312yes—
174C2×C4⋊Dic53C2311yescharacteristic
175C2×C4⋊Dic53C2311yescharacteristic
176C2×C4⋊Dic53C2311yescharacteristic
177C2×C4⋊Dic53C2312yes—
178C2×C4⋊Dic53C2311yescharacteristic
179C2×#11719919C2311yescharacteristic
180C2×#11719919C2311yescharacteristic
181C2×#11719919C2311yescharacteristic
182C2×#11719919C2311yescharacteristic
183C2×#11719919C2312yes—
184C2×#11719919C2312yes—
185C2×#11719919C2312yes—
186C4⋊C4×D53—24no—
187C4⋊C4×D53—24no—
188C2×C22⋊Dic53C2311yescharacteristic
189C2×C22⋊Dic53C2311yescharacteristic
190C2×C22⋊Dic53C2312yes—
191C2×#11719921C2312yes—
192C2×#11719921C2311yescharacteristic
193C2×#11719921C2311yescharacteristic
194C2×#11719921C2312yes—
195C2×#11719921C2312yes—
196C2×#11719921C2311yescharacteristic
197C2×#11719921C2312yes—
198C2×#11719921C2311yescharacteristic
199C2×#11719921C2312yes—
200C2×#11719921C2312yes—
201C2×#11719921C2312yes—
202C2×#11719921C2312yes—
203C2×#11719921C2312yes—
204C2×#11719921C2312yes—
205C2×#11719921C2312yes—
206C2×#11719921C2312yes—
207C2×#11719921C2312yes—
208C2×#11719921C2312yes—
209C22⋊C4×D53—24no—
210C22⋊C4×D53—24no—
211C2×C4×Dic53C2312yes—
212C2×C4×Dic53C2311yescharacteristic
213C2×C4×Dic53C2311yescharacteristic
214C2×C4×Dic53C2311yescharacteristic
215C2×C4×Dic53C2312yes—
216C2×C4×Dic53C2312yes—
217C2×C4×Dic53C2312yes—
218C2×C4×Dic53C2312yes—
219C2×C4×Dic53C2312yes—
220C2×C4×Dic53C2312yes—
221C2×C4×Dic53C2311yescharacteristic
222C2×C4×Dic53C2311yescharacteristic
223C2×C4×Dic53C2311yescharacteristic
224C42×D53—28no—
225C42×D53—24no—
226C42×D53D418yescomplemented
227#13133124C2312yes—
228#13133124C2312yes—
229#13133124C2312yes—
230#13133124C2312yes—
231#13133124C2312yes—
232#13133124C2312yes—
233#13133124C2312yes—
234#13133124C2312yes—
235#13133124C2312yes—
236#13133124C2312yes—
237#13133124C2312yes—
238C22×Q8×C53C2311yescharacteristic
239C23×C4×C53C2311yescharacteristic
240C22⋊Q8×C53C2×C418yescomplemented
241C4×Q8×C53—24no—
242#117×C53—24no—
243C2×C4⋊C4×C53C2312yes—
244C2×C4⋊C4×C53C2311yescharacteristic
245C2×C4⋊C4×C53C2311yescharacteristic
246C2×C4⋊C4×C53C2311yescharacteristic
247C2×C4⋊C4×C53C2311yescharacteristic
248C2×C4⋊C4×C53C2312yes—
249C2×C4⋊C4×C53C2312yes—
250C2×C4⋊C4×C53C2311yescharacteristic
251C2×C22⋊C4×C53C2311yescharacteristic
252C2×C22⋊C4×C53C2311yescharacteristic
253C2×C22⋊C4×C53C2312yes—
254C2×C22⋊C4×C53C2312yes—
255C2×C42×C53C2312yes—
256C2×C42×C53C2311yescharacteristic
257C2×C42×C53C2312yes—
258C2×C42×C53C2311yescharacteristic
259#95×C53C2312yes—
260#95×C53C2312yes—
261#95×C53C2312yes—
262#95×C53C2312yes—
263#95×C53C2312yes—
264C24×C53C2411yescharacteristic
265C23×D53—22no—
266C23×D53—22no—
267C23×D53—41no—
268C23×D53—41no—
269C23×D53—41no—
270C23×D53—41no—
271C23×D53C22×C414yes—
272C23×D53C2411yescharacteristic
273C23×D53C2412yes—
274C23×D53C2411yescharacteristic
275C2×Q8×C53—22no—
276C2×Q8×C53—22no—
277C2×Q8×C53C22×C414yes—
278C22×C4×C53—22no—
279C22×C4×C53—22no—
280C22×C4×C53C22×C414yes—
281C22×C4×C53C2412yes—
282C22×C4×C53C2411yescharacteristic
283C22×C4×C53C2411yescharacteristic
284C22×C4×C53C2412yes—
285C22×C4×C53C2412yes—
286C22×C4×C53C2412yes—
287C22×C4×C53C2411yescharacteristic
288C22×C4×C53C2411yescharacteristic
289C22×C4×C53C2411yescharacteristic
290C22×C4×C53C2411yescharacteristic
291C2×C22⋊D53—42no—
292C2×C22⋊D53—42no—
293C2×C22⋊D53C22×C418yes—
294C22×Dic53—22no—
295C22×Dic53—22no—
296C22×Dic53C22×C414yes—
297C22×Dic53C2412yes—
298C22×Dic53C2411yescharacteristic
299C22×Dic53C2411yescharacteristic
300C22×Dic53C2412yes—
301C22×Dic53C2412yes—
302C22×Dic53C2411yescharacteristic
303C22×Dic53C2411yescharacteristic
304C22×Dic53C2411yescharacteristic
305C22×Dic53C2411yescharacteristic
306#11719949—232no—
307C2×D212—24no—
308C2×D212—24no—
309C2×D212—22no—
310C2×D212—22no—
311C2×D212—42no—
312C2×D212—42no—
313C2×D212C22×C418yes—
314C2×D212C22×C414yes—
315C2×D212C22×C418yes—
316C2×C4×D53—22no—
317C2×C4×D53—22no—
318C2×C4×D53—22no—
319C2×C4×D53—22no—
320C2×C4×D53—24no—
321C2×C4×D53—22no—
322C2×C4×D53—22no—
323C2×C4×D53—24no—
324C2×C4×D53—232no—
325C2×C4×D53—22no—
326C2×C4×D53—22no—
327C2×C4×D53—24no—
328C2×C4×D53—24no—
329C2×C4×D53—41no—
330C2×C4×D53—41no—
331C2×C4×D53—41no—
332C2×C4×D53—41no—
333C2×C4×D53—42no—
334C2×C4×D53—42no—
335C2×C4×D53—42no—
336C2×C4×D53—42no—
337C2×C4×D53—41no—
338C2×C4×D53—41no—
339C2×C4×D53—41no—
340C2×C4×D53—41no—
341C2×C4×D53C22×C418yes—
342C2×C4×D53C22×C414yes—
343C2×C4×D53C22×C414yes—
344C2×C4×D53C22×C414yes—
345C2×C4×D53C22×C414yes—
346C2×C4×D53C2×D414yes—
347C2×C4×D53C2×D414yes—
348C2×C4×D53C2×D414yes—
349C2×C4×D53#4114yes—
350C4⋊C4×C53—22no—
351C4⋊C4×C53—22no—
352C4⋊C4×C53—24no—
353C4⋊C4×C53—22no—
354C4⋊C4×C53—22no—
355C4⋊C4×C53—42no—
356C4⋊C4×C53C22×C414yes—
357C4⋊C4×C53C22×C418yes—
358C22⋊C4×C53—22no—
359C22⋊C4×C53—22no—
360C22⋊C4×C53—42no—
361C22⋊C4×C53C22×C418yes—
362C42×C53—22no—
363C42×C53—24no—
364C42×C53—42no—
365C42×C53C2×D414yes—
366C22⋊Dic53—22no—
367C22⋊Dic53—22no—
368C22⋊Dic53—42no—
369#11719921—24no—
370#11719921—24no—
371#11719921—22no—
372#11719921—22no—
373#11719921—24no—
374#11719921—22no—
375#11719921—22no—
376#11719921—24no—
377#11719921—42no—
378#11719921—42no—
379#11719921—42no—
380#11719921—42no—
381#11719921—42no—
382#11719921—42no—
383#11719921C22×C418yes—
384#11719921C22×C418yes—
385#11719921C22×C418yes—
386#11719921C22×C418yes—
387C4⋊Dic53—22no—
388C4⋊Dic53—22no—
389C4⋊Dic53—22no—
390C4⋊Dic53—22no—
391C4⋊Dic53—24no—
392C4⋊Dic53—42no—
393C4⋊Dic53C22×C414yes—
394#11719919—22no—
395#11719919—22no—
396#11719919—22no—
397#11719919—22no—
398#11719919—42no—
399#11719919—42no—
400#11719919C22×C418yes—
401C4×Dic53—22no—
402C4×Dic53—22no—
403C4×Dic53—22no—
404C4×Dic53—24no—
405C4×Dic53—24no—
406C4×Dic53—24no—
407C4×Dic53—42no—
408C4×Dic53—42no—
409C4×Dic53—42no—
410C4×Dic53C22×C418yes—
411C4×Dic53C2×D414yes—
412C4×Dic53C2×D414yes—
413C4×Dic53C2×D414yes—
414C23×C53—21no—
415C23×C53—21no—
416C23×C53—21no—
417C23×C53—21no—
418C23×C53—21no—
419C23×C53—21no—
420C23×C53C23×C412yes—
421C23×C53C2511yescharacteristic
422C22×D53—21no—
423C22×D53—21no—
424C22×D53—21no—
425C22×D53—21no—
426C22×D53—22no—
427C22×D53—21no—
428C22×D53—21no—
429C22×D53—22no—
430C22×D53—22no—
431C22×D53—22no—
432C22×D53—22no—
433C22×D53—22no—
434C22×D53—21no—
435C22×D53—21no—
436C22×D53—21no—
437C22×D53—21no—
438C22×D53—28no—
439C22×D53—44no—
440C22×D53—44no—
441C22×D53—44no—
442C22×D53—44no—
443C22×D53—44no—
444C22×D53—44no—
445C22×D53C23×C412yes—
446C22×D53C23×C414yes—
447C22×D53C23×C412yes—
448C22×D53C22×D412yes—
449C22×D53C2×#4112yes—
450Q8×C53—28no—
451C2×C4×C53—21no—
452C2×C4×C53—22no—
453C2×C4×C53—21no—
454C2×C4×C53—22no—
455C2×C4×C53—21no—
456C2×C4×C53—21no—
457C2×C4×C53—21no—
458C2×C4×C53—21no—
459C2×C4×C53—22no—
460C2×C4×C53—22no—
461C2×C4×C53—28no—
462C2×C4×C53—21no—
463C2×C4×C53—21no—
464C2×C4×C53—22no—
465C2×C4×C53—22no—
466C2×C4×C53—21no—
467C2×C4×C53—22no—
468C2×C4×C53—21no—
469C2×C4×C53—21no—
470C2×C4×C53—22no—
471C2×C4×C53—21no—
472C2×C4×C53—22no—
473C2×C4×C53—22no—
474C2×C4×C53C23×C412yes—
475C2×C4×C53C23×C414yes—
476C2×C4×C53C23×C414yes—
477C2×C4×C53C23×C412yes—
478C2×C4×C53C22×D412yes—
479C2×C4×C53C22×D412yes—
480C2×C4×C53C22×D412yes—
481C2×C4×C53C2×#4112yes—
482C22⋊D53—48no—
483C2×Dic53—21no—
484C2×Dic53—21no—
485C2×Dic53—21no—
486C2×Dic53—21no—
487C2×Dic53—21no—
488C2×Dic53—21no—
489C2×Dic53—22no—
490C2×Dic53—22no—
491C2×Dic53—28no—
492C2×Dic53—21no—
493C2×Dic53—21no—
494C2×Dic53—22no—
495C2×Dic53—22no—
496C2×Dic53—21no—
497C2×Dic53—22no—
498C2×Dic53—21no—
499C2×Dic53—22no—
500C2×Dic53—21no—
501C2×Dic53—21no—
502C2×Dic53—22no—
503C2×Dic53—22no—
504C2×Dic53C23×C412yes—
505C2×Dic53C23×C414yes—
506C2×Dic53C23×C412yes—
507C2×Dic53C22×D412yes—
508C2×Dic53C22×D412yes—
509C2×Dic53C22×D412yes—
510C2×Dic53C2×#4112yes—
511D212—216no—
512D212—28no—
513D212—48no—
514C4×D53—28no—
515C4×D53—28no—
516C4×D53—28no—
517C4×D53—216no—
518C4×D53—44no—
519C4×D53—44no—
520C4×D53—48no—
521C4×D53—48no—
522C4×D53—44no—
523C4×D53—44no—
524C4×D53C4×D4116yes—
525#34065—531nomaximal, Sylow
526C22×C53—22no—
527C22×C53—22no—
528C22×C53—22no—
529C22×C53—41no—
530C22×C53—41no—
531C22×C53—41no—
532C22×C53—41no—
533C22×C53C24×C411yescharacteristic
534C22×C53C23×D411yescharacteristic
535C22×C53C22×#4111yescharacteristic
536C22×C53#58511yescharacteristic
537C22×C53#58511yescharacteristic
538C22×C53#58511yescharacteristic
539C22×C53#58511yescharacteristic
540C2×D53—22no—
541C2×D53—22no—
542C2×D53—22no—
543C2×D53—22no—
544C2×D53—22no—
545C2×D53—22no—
546C2×D53—22no—
547C2×D53—24no—
548C2×D53—22no—
549C2×D53—24no—
550C2×D53—24no—
551C2×D53—22no—
552C2×D53—416no—
553C2×D53—42no—
554C2×D53—42no—
555C2×D53—41no—
556C2×D53—41no—
557C2×D53—42no—
558C2×D53—42no—
559C2×D53—41no—
560C2×D53—41no—
561C2×D53C2×C4×D414yes—
562C4×C53—22no—
563C4×C53—24no—
564C4×C53—24no—
565C4×C53—22no—
566C4×C53—22no—
567C4×C53—42no—
568C4×C53—41no—
569C4×C53—41no—
570C4×C53—42no—
571C4×C53C2×C4×D414yes—
572Dic53—22no—
573Dic53—24no—
574Dic53—22no—
575Dic53—22no—
576Dic53—41no—
577Dic53—42no—
578Dic53—41no—
579Dic53—42no—
580Dic53C2×C4×D414yes—
581C2×#525—531no—
582C2×C4×#41—531no—
583C22×#117—531no—
584#2324—531no—
585#2324—531no—
586#2324—531no—
587#2324—531no—
588#2323—531no—
589#2323—531no—
590#2323—531no—
591#2323D5311yescharacteristic, complemented
592#2322—532no—
593#2322—532no—
594#2321—532no—
595#2321—532no—
596#2297—531no—
597#2296—531no—
598#2293—532no—
599#2293—532no—
600#2290—532no—
601#2290—532no—
602#2280—531no—
603C4×#117—531no—
604C2×C53—42no—
605C2×C53C22×C4×D411yescharacteristic
606C2×C53#342811yescharacteristic
607C2×C53#342811yescharacteristic
608C2×C53#344911yescharacteristic
609C2×C53#344911yescharacteristic
610C2×C53#345511yescharacteristic
611C2×C53#345511yescharacteristic
612D53—24no—
613D53—44no—
614D53—42no—
615C22×#41—531no—
616C24×C4—531no—
617#525—5316no—
618C2×#123—532no—
619C2×C22⋊Q8—531no—
620C2×C22⋊Q8C2×D5311yescharacteristic
621C2×#121—531no—
622C2×#121—531no—
623C2×#120—532no—
624C4×#41—1068no—
625C2×C4×Q8—531no—
626C2×C4×Q8C2×D5311yescharacteristic, complemented
627C2×C4×D4—532no—
628C2×C4×D4—532no—
629C2×C4×D4—531no—
630C2×C4×D4—532no—
631C2×C4×D4—532no—
632C2×C4×D4—531no—
633C2×#117—531no—
634C2×#117—531no—
635C2×#117—531no—
636C2×#117—531no—
637C2×#117—531no—
638C2×#117—531no—
639C2×#117—532no—
640C2×#117—531no—
641C2×#117—531no—
642C2×#117—531no—
643C2×#117—531no—
644C2×#117—1068no—
645C2×#117C2×D5311yescharacteristic
646C22×C4⋊C4—531no—
647C22×C4⋊C4—531no—
648C22×C22⋊C4—531no—
649C22×C22⋊C4—531no—
650C22×C42—531no—
651C22×C42—531no—
652C22×C42—532no—
653#391—531no—
654#391C2×D5311yescharacteristic, complemented
655#390—532no—
656#390—531no—
657#390—532no—
658#390—532no—
659#390—532no—
660#390—531no—
661#389—532no—
662#389—532no—
663#389—531no—
664#389—531no—
665#389—531no—
666#389—532no—
667#389C2×D5312yescomplemented
668#389C2×D5311yescharacteristic, complemented
669#388—532no—
670#388—532no—
671#388—532no—
672#388—532no—
673#388—532no—
674#388—532no—
675#388—532no—
676#388—532no—
677#388—532no—
678#388—532no—
679#388C2×D5312yes—
680#388C2×D5312yes—
681#387—532no—
682#387—532no—
683#387—532no—
684#387C2×D5312yescomplemented
685#386—532no—
686#386—532no—
687#386—532no—
688#386—532no—
689#386—532no—
690#386—532no—
691#385—532no—
692#385—532no—
693#385—532no—
694#385—532no—
695#385—532no—
696#385—532no—
697#381—532no—
698#380—531no—
699#380—531no—
700#380—531no—
701#380C2×D5311yescharacteristic
702#379—532no—
703C4×C4⋊C4—531no—
704C4×C4⋊C4—531no—
705C4×C4⋊C4—532no—
706C4×C4⋊C4—531no—
707C4×C4⋊C4—532no—
708C4×C4⋊C4C2×D5311yescharacteristic, complemented
709C4×C22⋊C4—532no—
710C4×C22⋊C4—532no—
711C4×C22⋊C4—532no—
712C4×C22⋊C4—532no—
713C4×C22⋊C4—532no—
714C4×C22⋊C4—532no—
715#376—532no—
716C43—532no—
717C53#3406511yescharacteristic, complemented, Sylow
718C25—531no—
719C2×#41—538no—
720C2×#41—1064no—
721C2×#41—1064no—
722C22×Q8C22×D5311yescharacteristic
723C22×D4—532no—
724C22×D4—532no—
725C22×D4—531no—
726C22×D4—532no—
727C23×C4—531no—
728C23×C4—531no—
729C23×C4—538no—
730C23×C4—531no—
731C23×C4—531no—
732C23×C4—531no—
733C23×C4—532no—
734C23×C4—531no—
735C23×C4—531no—
736C23×C4—531no—
737C23×C4—531no—
738C23×C4—532no—
739C23×C4—532no—
740C23×C4—1064no—
741C23×C4—1064no—
742C23×C4C22×D5311yescharacteristic
743#123—5316no—
744C22⋊Q8—538no—
745C22⋊Q8C4×D5318yescomplemented
746#121—538no—
747#121—538no—
748#120—5316no—
749C4×Q8—24no—
750C4×Q8—1064no—
751C4×D4—5316no—
752C4×D4—5316no—
753C4×D4—1068no—
754C4×D4—1064no—
755C4×D4—1068no—
756C4×D4—1064no—
757#117—24no—
758#117—538no—
759#117—1064no—
760#117—1064no—
761#117—1064no—
762#117—1064no—
763#117—1064no—
764#117—1068no—
765#117—1064no—
766#117—1064no—
767#117—1064no—
768#117—1064no—
769C2×C4⋊C4—531no—
770C2×C4⋊C4—532no—
771C2×C4⋊C4—531no—
772C2×C4⋊C4—531no—
773C2×C4⋊C4—531no—
774C2×C4⋊C4—531no—
775C2×C4⋊C4—531no—
776C2×C4⋊C4—531no—
777C2×C4⋊C4—531no—
778C2×C4⋊C4—532no—
779C2×C4⋊C4—531no—
780C2×C4⋊C4—532no—
781C2×C4⋊C4—532no—
782C2×C4⋊C4—532no—
783C2×C4⋊C4—1064no—
784C2×C4⋊C4—1064no—
785C2×C4⋊C4C22×D5311yescharacteristic
786C2×C4⋊C4C22×D5311yescharacteristic
787C2×C4⋊C4C22×D5311yescharacteristic
788C2×C4⋊C4C22×D5312yes—
789C2×C4⋊C4C22×D5311yescharacteristic
790C2×C4⋊C4C22×D5312yes—
791C2×C4⋊C4C22×D5311yescharacteristic
792C2×C4⋊C4C22×D5312yes—
793C2×C22⋊C4—532no—
794C2×C22⋊C4—532no—
795C2×C22⋊C4—532no—
796C2×C22⋊C4—532no—
797C2×C22⋊C4—531no—
798C2×C22⋊C4—531no—
799C2×C22⋊C4—531no—
800C2×C22⋊C4—531no—
801C2×C22⋊C4—531no—
802C2×C22⋊C4—531no—
803C2×C22⋊C4—532no—
804C2×C22⋊C4—532no—
805C2×C22⋊C4—532no—
806C2×C22⋊C4—532no—
807C2×C22⋊C4—532no—
808C2×C22⋊C4—532no—
809C2×C22⋊C4—532no—
810C2×C22⋊C4—532no—
811C2×C22⋊C4—532no—
812C2×C22⋊C4—532no—
813C2×C22⋊C4—532no—
814C2×C22⋊C4—1064no—
815C2×C22⋊C4—1064no—
816C2×C22⋊C4C22×D5311yescharacteristic
817C2×C22⋊C4C22×D5311yescharacteristic
818C2×C22⋊C4C22×D5312yes—
819C2×C22⋊C4C22×D5312yes—
820C2×C42—531no—
821C2×C42—531no—
822C2×C42—531no—
823C2×C42—532no—
824C2×C42—538no—
825C2×C42—531no—
826C2×C42—532no—
827C2×C42—531no—
828C2×C42—531no—
829C2×C42—532no—
830C2×C42—532no—
831C2×C42—532no—
832C2×C42—532no—
833C2×C42—532no—
834C2×C42—1068no—
835C2×C42—1064no—
836C2×C42C22×D5311yescharacteristic
837C2×C42C22×D5312yes—
838C2×C42C22×D5312yes—
839C2×C42C22×D5311yescharacteristic
840#95—532no—
841#95—532no—
842#95—532no—
843#95—532no—
844#95—532no—
845#95—532no—
846#95—532no—
847#95—532no—
848#95—532no—
849#95—532no—
850#95—532no—
851#95C22×D5312yes—
852#95C22×D5312yes—
853#95C22×D5312yes—
854#95C22×D5312yes—
855#95C22×D5312yes—
856C24—531no—
857C24—531no—
858C24—532no—
859C24—534no—
860C24—1062no—
861C24—1062no—
862C24—2121no—
863C24—2121no—
864C24—2121no—
865C24—2121no—
866C24C23×D5311yescharacteristic
867#41—10632no—
868C2×Q8—22no—
869C2×Q8—22no—
870C2×Q8C2×C4×D5314yes—
871C2×D4—538no—
872C2×D4—538no—
873C2×D4—534no—
874C2×D4—538no—
875C2×D4—1064no—
876C2×D4—1064no—
877C2×D4—1062no—
878C2×D4—1062no—
879C2×D4—2122no—
880C2×D4—2122no—
881C2×D4—2122no—
882C2×D4—2122no—
883C22×C4—22no—
884C22×C4—22no—
885C22×C4—531no—
886C22×C4—534no—
887C22×C4—534no—
888C22×C4—534no—
889C22×C4—534no—
890C22×C4—531no—
891C22×C4—532no—
892C22×C4—531no—
893C22×C4—531no—
894C22×C4—534no—
895C22×C4—538no—
896C22×C4—534no—
897C22×C4—534no—
898C22×C4—534no—
899C22×C4—534no—
900C22×C4—532no—
901C22×C4—531no—
902C22×C4—531no—
903C22×C4—532no—
904C22×C4—1064no—
905C22×C4—1062no—
906C22×C4—1062no—
907C22×C4—10632no—
908C22×C4—1064no—
909C22×C4—1064no—
910C22×C4—1062no—
911C22×C4—1062no—
912C22×C4—1062no—
913C22×C4—1062no—
914C22×C4—1062no—
915C22×C4—1062no—
916C22×C4—1062no—
917C22×C4—1062no—
918C22×C4—1064no—
919C22×C4—2121no—
920C22×C4—2121no—
921C22×C4—2121no—
922C22×C4—2121no—
923C22×C4—2122no—
924C22×C4—2122no—
925C22×C4—2122no—
926C22×C4—2121no—
927C22×C4—2121no—
928C22×C4—2121no—
929C22×C4—2122no—
930C22×C4—2121no—
931C22×C4C2×C4×D5314yes—
932C22×C4C23×D5312yes—
933C22×C4C23×D5311yescharacteristic
934C22×C4C23×D5312yes—
935C22×C4C23×D5311yescharacteristic
936C22×C4C23×D5312yes—
937C22×C4C23×D5312yes—
938C22×C4C23×D5311yescharacteristic
939C22×C4C23×D5311yescharacteristic
940C22×C4C23×D5311yescharacteristic
941C22×C4C23×D5311yescharacteristic
942C4⋊C4—22no—
943C4⋊C4—22no—
944C4⋊C4—24no—
945C4⋊C4—22no—
946C4⋊C4—22no—
947C4⋊C4—42no—
948C4⋊C4—534no—
949C4⋊C4—538no—
950C4⋊C4—1062no—
951C4⋊C4—1062no—
952C4⋊C4—1062no—
953C4⋊C4—1062no—
954C4⋊C4—1064no—
955C4⋊C4—1062no—
956C4⋊C4—1062no—
957C4⋊C4—1062no—
958C4⋊C4—1062no—
959C4⋊C4—2122no—
960C4⋊C4—2122no—
961C4⋊C4—2122no—
962C4⋊C4C2×C4×D5314yes—
963C4⋊C4C2×C4×D5318yes—
964C22⋊C4—22no—
965C22⋊C4—22no—
966C22⋊C4—42no—
967C22⋊C4—538no—
968C22⋊C4—538no—
969C22⋊C4—538no—
970C22⋊C4—538no—
971C22⋊C4—1062no—
972C22⋊C4—1062no—
973C22⋊C4—1064no—
974C22⋊C4—1064no—
975C22⋊C4—1064no—
976C22⋊C4—1062no—
977C22⋊C4—1062no—
978C22⋊C4—1062no—
979C22⋊C4—1062no—
980C22⋊C4—1064no—
981C22⋊C4—2122no—
982C22⋊C4—2122no—
983C22⋊C4—2122no—
984C22⋊C4—2122no—
985C22⋊C4—2122no—
986C22⋊C4—2122no—
987C22⋊C4—2122no—
988C22⋊C4C2×C4×D5318yes—
989C42—22no—
990C42—24no—
991C42—42no—
992C42—538no—
993C42—534no—
994C42—534no—
995C42—534no—
996C42—1062no—
997C42—1062no—
998C42—1064no—
999C42—1064no—
1000C42—1064no—
1001C42—1062no—
1002C42—2122no—
1003C42—2122no—
1004C42—2122no—
1005C42D4×D5314yes—
1006C23—21no—
1007C23—21no—
1008C23—21no—
1009C23—21no—
1010C23—21no—
1011C23—21no—
1012C23—532no—
1013C23—532no—
1014C23—532no—
1015C23—532no—
1016C23—534no—
1017C23—1068no—
1018C23—1061no—
1019C23—1061no—
1020C23—1061no—
1021C23—1061no—
1022C23—1061no—
1023C23—1062no—
1024C23—1061no—
1025C23—1062no—
1026C23—1062no—
1027C23—1061no—
1028C23—1061no—
1029C23—1061no—
1030C23—1062no—
1031C23—1062no—
1032C23—1062no—
1033C23—1061no—
1034C23—2124no—
1035C23—2124no—
1036C23—2124no—
1037C23—2124no—
1038C23—2124no—
1039C23—2124no—
1040C23C22×C4×D5312yes—
1041C23C24×D5311yescharacteristic
1042Q8—28no—
1043D4—10616no—
1044D4—1068no—
1045D4—2128no—
1046D4—2128no—
1047C2×C4—22no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—22no—
1051C2×C4—21no—
1052C2×C4—22no—
1053C2×C4—21no—
1054C2×C4—22no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—28no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—21no—
1065C2×C4—22no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—22no—
1069C2×C4—21no—
1070C2×C4—532no—
1071C2×C4—532no—
1072C2×C4—532no—
1073C2×C4—5316no—
1074C2×C4—534no—
1075C2×C4—532no—
1076C2×C4—532no—
1077C2×C4—532no—
1078C2×C4—1068no—
1079C2×C4—10616no—
1080C2×C4—1068no—
1081C2×C4—1068no—
1082C2×C4—1061no—
1083C2×C4—1061no—
1084C2×C4—1061no—
1085C2×C4—1061no—
1086C2×C4—1061no—
1087C2×C4—1062no—
1088C2×C4—1062no—
1089C2×C4—1061no—
1090C2×C4—1068no—
1091C2×C4—1061no—
1092C2×C4—1061no—
1093C2×C4—1062no—
1094C2×C4—1062no—
1095C2×C4—1061no—
1096C2×C4—1062no—
1097C2×C4—1062no—
1098C2×C4—1061no—
1099C2×C4—1062no—
1100C2×C4—1062no—
1101C2×C4—1061no—
1102C2×C4—1061no—
1103C2×C4—2124no—
1104C2×C4—2124no—
1105C2×C4—2128no—
1106C2×C4—2128no—
1107C2×C4—2124no—
1108C2×C4—2124no—
1109C2×C4C22×C4×D5314yes—
1110C2×C4C22×C4×D5312yes—
1111C2×C4C22×C4×D5314yes—
1112C2×C4C22×C4×D5312yes—
1113C2×C4C2×D4×D5312yes—
1114C2×C4C2×D4×D5312yes—
1115C2×C4C2×D4×D5312yes—
1116C2×C4#41×D5312yes—
1117C22—22no—
1118C22—22no—
1119C22—22no—
1120C22—41no—
1121C22—41no—
1122C22—41no—
1123C22—41no—
1124C22—534no—
1125C22—1062no—
1126C22—1062no—
1127C22—1062no—
1128C22—1062no—
1129C22—1062no—
1130C22—1062no—
1131C22—1062no—
1132C22—1064no—
1133C22—1062no—
1134C22—1064no—
1135C22—1064no—
1136C22—1062no—
1137C22—21216no—
1138C22—2122no—
1139C22—2121no—
1140C22—2122no—
1141C22—2121no—
1142C22—2121no—
1143C22—2122no—
1144C22—2121no—
1145C22—2122no—
1146C22C23×C4×D5311yescharacteristic
1147C22C22×D4×D5311yescharacteristic
1148C22C2×#41×D5311yescharacteristic
1149C22#1681145811yescharacteristic
1150C22#1681146011yescharacteristic
1151C22#1681146011yescharacteristic
1152C22#1681146011yescharacteristic
1153C4—22no—
1154C4—22no—
1155C4—22no—
1156C4—24no—
1157C4—24no—
1158C4—41no—
1159C4—42no—
1160C4—41no—
1161C4—42no—
1162C4—534no—
1163C4—1062no—
1164C4—1062no—
1165C4—1062no—
1166C4—1064no—
1167C4—2121no—
1168C4—2121no—
1169C4—2122no—
1170C4—2122no—
1171C4C4×D4×D5314yes—
1172C2—42no—
1173C2—1064no—
1174C2—2122no—
1175C2—2124no—
1176C2C2×C4×D4×D5311yescharacteristic
1177C2#2028791511yescharacteristic
1178C2#2028791711yescharacteristic
1179C2#2028804311yescharacteristic
1180C2#2028804711yescharacteristic
1181C2#2028810211yescharacteristic
1182C2#2028810611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D53
commutatorC22×C53C24×C4
FittingC53×#2323C2
socle, cosocleC23×C53C25
prime radicalC2×#16811136C2
hypercenter#2323D53
hypocenterC53#34065
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ #2323

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11719949C2semidirect
3. C2×#117×D53C2semidirect
4. #20277409C2semidirect
5. #20277408C2semidirect
6. #20277406C2semidirect
7. #20277404C2semidirect
8. #20277400C2semidirect
9. #20277399C2semidirect
10. #20277391C2semidirect
11. #20277388C2semidirect
12. #20277379C2semidirect
13. #20277377C2semidirect
14. #20277368C2semidirect
15. #20277204C2semidirect
16. #20277196C2semidirect
17. #20277175C2semidirect
18. #20277173C2semidirect
19. #20277157C2semidirect
20. #20277153C2semidirect
21. #20277097C2semidirect
22. C4×#13133175C2semidirect
23. C53×#2323C2semidirect
26. #16811136C4semidirect
33. C2×Q8×Dic53C22semidirect
35. C2×C4×D212C22semidirect
38. C2×#13133179C22semidirect
46. C2×#13133175C22semidirect
58. C2×C42×D53C22semidirect
59. #16810530C22semidirect
61. #16810525C22semidirect
63. #16810524C22semidirect
66. #16810522C22semidirect
67. #16810522C22semidirect
68. #16810521C22semidirect
69. #16810520C22semidirect
70. #16810519C22semidirect
71. #16810518C22semidirect
75. #16810515C22semidirect
77. #16810514C22semidirect
79. #16810513C22semidirect
81. #16810512C22semidirect
82. #16810509C22semidirect
83. #16810507C22semidirect
84. #16810505C22semidirect
92. #16810497C22semidirect
93. #16810497C22semidirect
95. #16810494C22semidirect
96. #16810494C22semidirect
102. C4⋊C4×Dic53C22semidirect
103. C4⋊C4×Dic53C22semidirect
104. C4⋊C4×Dic53C22semidirect
105. C4×C4⋊Dic53C22semidirect
106. #16810474C22semidirect
111. #16810470C22semidirect
112. #16810470C22semidirect
113. #16810468C22semidirect
114. C42×Dic53C22semidirect
116. C2×C4×Q8×C53C22semidirect
118. C53×#391C22semidirect
119. C53×#389C22semidirect
120. C53×#389C22semidirect
123. C53×#387C22semidirect
125. C4×C4⋊C4×C53C22semidirect
137. C22×C4×D53C2×C4semidirect
149. #13133202C2×C4semidirect
150. #13133193C2×C4semidirect
151. #13133192C2×C4semidirect
152. #13133191C2×C4semidirect
153. #13133187C2×C4semidirect
159. #13133179C2×C4semidirect
160. #13133177C2×C4semidirect
167. #13133175C2×C4semidirect
226. C42×D53D4semidirect
240. C22⋊Q8×C53C2×C4semidirect
591. #2323D53semidirect
626. C2×C4×Q8C2×D53semidirect
654. #391C2×D53semidirect
667. #389C2×D53semidirect
668. #389C2×D53semidirect
684. #387C2×D53semidirect
708. C4×C4⋊C4C2×D53semidirect
717. C53#34065semidirect
745. C22⋊Q8C4×D53semidirect

Maximal subgroups

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

subgroupindex
C2×#168111362
C2×C4×#117199492
C2×#117×D532
#202774092
#202774082
#202774062
#202774042
#202774002
#202773992
#202773912
#202773882
#202773792
#202773772
#202773682
#202772042
#202771962
#202771752
#202771732
#202771572
#202771532
#202770972
C4×#131331752
C53×#23232
#3406553