Finite Group Databasebeta

← #27311468

Subgroups — #27311468

Order 13568.

1866 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133194C211yesmaximal, characteristic
2C2×#16810528C211yesmaximal, characteristic, complemented
3C2×#16810516C211yesmaximal, characteristic
4C2×#16810484C211yesmaximal, characteristic
5#20272985C211yesmaximal, characteristic, complemented
6#20272984C211yesmaximal, characteristic, complemented
7#20272969C211yesmaximal, characteristic, complemented
8#20272965C211yesmaximal, characteristic, complemented
9#20272962C211yesmaximal, characteristic
10#20272962C211yesmaximal, characteristic
11#20272950C211yesmaximal, characteristic, complemented
12#20272948C211yesmaximal, characteristic, complemented
13#20272945C211yesmaximal, characteristic, complemented
14#20272937C211yesmaximal, characteristic
15C2×C53×#388C211yesmaximal, characteristic
16C23×Dic106C2211yescharacteristic
17C24×Dic53C2211yescharacteristic
18C2×#13133194—24no—
19C2×#13133194—24no—
20C2×#13133194C418yescomplemented
21C22×C4⋊Dic53C2211yescharacteristic
22C22×C4⋊Dic53C2211yescharacteristic
23C22×#11719919C2211yescharacteristic
24C22×#11719919C2211yescharacteristic
25C22×C22⋊Dic53C2211yescharacteristic
26C22×C22⋊Dic53C2211yescharacteristic
27C22×C22⋊Dic53C2211yescharacteristic
28C22×C4×Dic53C2211yescharacteristic
29#16810528—24no—
30#16810516—24no—
31#16810484—24no—
32C2×#13133124C2211yescharacteristic
33C2×#13133124C2211yescharacteristic
34C2×#13133124C2211yescharacteristic
35C2×#13133124C2211yescharacteristic
36C2×#13133124C2211yescharacteristic
37C2×#13133124C2211yescharacteristic
38C2×#13133124C2211yescharacteristic
39C2×#13133124C2211yescharacteristic
40C2×#13133124C2211yescharacteristic
41C2×#13133124C2211yescharacteristic
42C2×#13133124C2211yescharacteristic
43C2×#13133124C2211yescharacteristic
44C2×#13133124C2211yescharacteristic
45C2×#13133124C2211yescharacteristic
46C2×#13133124C2211yescharacteristic
47C2×#13133124C2211yescharacteristic
48C2×#13133124C2211yescharacteristic
49C2×#13133124C2211yescharacteristic
50C22×C4⋊C4×C53C2211yescharacteristic
51C22×C22⋊C4×C53C2211yescharacteristic
52C22×C22⋊C4×C53C2211yescharacteristic
53C22×C22⋊C4×C53C2211yescharacteristic
54C22×C42×C53C2211yescharacteristic
55C53×#388—24no—
56C2×#95×C53C2211yescharacteristic
57C2×#95×C53C2211yescharacteristic
58C22×Dic106—22no—
59C22×Dic106—22no—
60C22×Dic106—22no—
61C22×Dic106—22no—
62C22×Dic106—41no—
63C22×Dic106—41no—
64C22×Dic106C2×C414yes—
65C23×Dic53—22no—
66C23×Dic53—22no—
67C23×Dic53—22no—
68C23×Dic53—22no—
69C23×Dic53—41no—
70C23×Dic53—41no—
71C23×Dic53C2×C414yes—
72C23×Dic53C2311yescharacteristic
73C23×Dic53C2311yescharacteristic
74C23×Dic53C2311yescharacteristic
75C23×Dic53C2311yescharacteristic
76C23×Dic53C2311yescharacteristic
77C23×Dic53C2311yescharacteristic
78C23×Dic53C2311yescharacteristic
79C23×Dic53C2311yescharacteristic
80#13133194—232no—
81C2×C4⋊Dic53—22no—
82C2×C4⋊Dic53—22no—
83C2×C4⋊Dic53—22no—
84C2×C4⋊Dic53—22no—
85C2×C4⋊Dic53—41no—
86C2×C4⋊Dic53C2×C414yes—
87C2×#11719919—22no—
88C2×#11719919—22no—
89C2×#11719919—22no—
90C2×#11719919—22no—
91C2×#11719919C2×C414yes—
92C2×#11719919C2×C414yes—
93C2×C22⋊Dic53—22no—
94C2×C22⋊Dic53—22no—
95C2×C22⋊Dic53—22no—
96C2×C22⋊Dic53—22no—
97C2×C22⋊Dic53—22no—
98C2×C22⋊Dic53—22no—
99C2×C22⋊Dic53—41no—
100C2×C22⋊Dic53—41no—
101C2×C22⋊Dic53C2×C414yes—
102C2×C4×Dic53—22no—
103C2×C4×Dic53—22no—
104C2×C4×Dic53—41no—
105#13133124—22no—
106#13133124—22no—
107#13133124—22no—
108#13133124—22no—
109#13133124—22no—
110#13133124—22no—
111#13133124—22no—
112#13133124—22no—
113#13133124—22no—
114#13133124—22no—
115#13133124—22no—
116#13133124—41no—
117#13133124—41no—
118#13133124—41no—
119#13133124—41no—
120#13133124—41no—
121#13133124—41no—
122#13133124D414yes—
123C25×C53C2311yescharacteristic
124C23×C4×C53C2311yescharacteristic
125C23×C4×C53C2311yescharacteristic
126C23×C4×C53C2311yescharacteristic
127C23×C4×C53C2311yescharacteristic
128C23×C4×C53C2311yescharacteristic
129C23×C4×C53C2311yescharacteristic
130C2×C4⋊C4×C53—22no—
131C2×C4⋊C4×C53—22no—
132C2×C4⋊C4×C53—41no—
133C2×C22⋊C4×C53—22no—
134C2×C22⋊C4×C53—22no—
135C2×C22⋊C4×C53—22no—
136C2×C22⋊C4×C53—22no—
137C2×C22⋊C4×C53—41no—
138C2×C22⋊C4×C53—41no—
139C2×C22⋊C4×C53C2×C414yes—
140C2×C22⋊C4×C53D414yes—
141C2×C22⋊C4×C53D414yes—
142C2×C42×C53—22no—
143C2×C42×C53—22no—
144C2×C42×C53—41no—
145#95×C53—22no—
146#95×C53—22no—
147C24×C53—21no—
148C24×C53—21no—
149C24×C53—21no—
150C24×C53—21no—
151C24×C53—21no—
152C24×C53—21no—
153C24×C53—21no—
154C24×C53—21no—
155C24×C53—21no—
156C24×C53—21no—
157C24×C53—21no—
158C24×C53—21no—
159C24×C53C22×C412yes—
160C24×C53C2×D412yes—
161C24×C53C2×D412yes—
162C24×C53C2411yescharacteristic
163C22×C4×C53—21no—
164C22×C4×C53—21no—
165C22×C4×C53—21no—
166C22×C4×C53—21no—
167C22×C4×C53—21no—
168C22×C4×C53—21no—
169C22×C4×C53—21no—
170C22×C4×C53—21no—
171C22×C4×C53—21no—
172C22×C4×C53—21no—
173C22×C4×C53—21no—
174C22×C4×C53—21no—
175C22×C4×C53—21no—
176C22×C4×C53—21no—
177C22×C4×C53—21no—
178C22×C4×C53—21no—
179C22×C4×C53—21no—
180C22×C4×C53—21no—
181C22×C4×C53—21no—
182C22×C4×C53—21no—
183C22×C4×C53—21no—
184C22×C4×C53—21no—
185C22×C4×C53—21no—
186C22×C4×C53—21no—
187C22×C4×C53—21no—
188C22×C4×C53—21no—
189C22×C4×C53—21no—
190C22×C4×C53—21no—
191C22×C4×C53—21no—
192C22×C4×C53—21no—
193C22×C4×C53—21no—
194C22×C4×C53—21no—
195C22×C4×C53—21no—
196C22×C4×C53—21no—
197C22×C4×C53C22×C412yes—
198C22×C4×C53C22×C412yes—
199C22×C4×C53C2×D412yes—
200C22×C4×C53C2×D412yes—
201C22×C4×C53C2×D412yes—
202C22×C4×C53C2×D412yes—
203C22×C4×C53C2×D412yes—
204C22×C4×C53#4112yes—
205C22×Dic53—21no—
206C22×Dic53—21no—
207C22×Dic53—21no—
208C22×Dic53—21no—
209C22×Dic53—28no—
210C22×Dic53—21no—
211C22×Dic53—21no—
212C22×Dic53—21no—
213C22×Dic53—21no—
214C22×Dic53—21no—
215C22×Dic53—21no—
216C22×Dic53—21no—
217C22×Dic53—21no—
218C22×Dic53—21no—
219C22×Dic53—21no—
220C22×Dic53—21no—
221C22×Dic53—21no—
222C22×Dic53—21no—
223C22×Dic53—21no—
224C22×Dic53—21no—
225C22×Dic53—21no—
226C22×Dic53—21no—
227C22×Dic53—21no—
228C22×Dic53—21no—
229C22×Dic53—21no—
230C22×Dic53—21no—
231C22×Dic53—21no—
232C22×Dic53—21no—
233C22×Dic53—21no—
234C22×Dic53—21no—
235C22×Dic53—21no—
236C22×Dic53—21no—
237C22×Dic53—21no—
238C22×Dic53—21no—
239C22×Dic53—21no—
240C22×Dic53—28no—
241C22×Dic53—21no—
242C22×Dic53—21no—
243C22×Dic53—21no—
244C22×Dic53—21no—
245C22×Dic53—21no—
246C22×Dic53—21no—
247C22×Dic53—21no—
248C22×Dic53—21no—
249C22×Dic53—21no—
250C22×Dic53—21no—
251C22×Dic53—21no—
252C22×Dic53—21no—
253C22×Dic53—21no—
254C22×Dic53—21no—
255C22×Dic53—44no—
256C22×Dic53—44no—
257C22×Dic53—44no—
258C22×Dic53—44no—
259C22×Dic53—44no—
260C22×Dic53C22×C412yes—
261C22×Dic53C22×C412yes—
262C22×Dic53C22×C412yes—
263C22×Dic53C22×C412yes—
264C22×Dic53C2×D412yes—
265C22×Dic53C2×D412yes—
266C22×Dic53#4112yes—
267C22×Dic53#4112yes—
268C2×Dic106—28no—
269C2×Dic106—28no—
270C2×Dic106—44no—
271C2×Dic106—44no—
272C2×Dic106—44no—
273C2×Dic106—44no—
274C2×Dic106—44no—
275C4⋊C4×C53—44no—
276C22⋊C4×C53—44no—
277C22⋊C4×C53—44no—
278C22⋊C4×C53C22⋊C4116yes—
279C42×C53—44no—
280C22⋊Dic53—28no—
281C22⋊Dic53—44no—
282C22⋊Dic53—44no—
283C4⋊Dic53—28no—
284C4⋊Dic53—44no—
285#11719919—28no—
286#11719919—28no—
287C4×Dic53—44no—
288C23×C53—22no—
289C23×C53—22no—
290C23×C53—22no—
291C23×C53—22no—
292C23×C53—22no—
293C23×C53—22no—
294C23×C53—22no—
295C23×C53—22no—
296C23×C53—22no—
297C23×C53—22no—
298C23×C53—22no—
299C23×C53—22no—
300C23×C53—22no—
301C23×C53—22no—
302C23×C53—22no—
303C23×C53—22no—
304C23×C53—22no—
305C23×C53—22no—
306C23×C53—41no—
307C23×C53—41no—
308C23×C53—41no—
309C23×C53—41no—
310C23×C53—41no—
311C23×C53—41no—
312C23×C53—41no—
313C23×C53—41no—
314C23×C53—41no—
315C23×C53—41no—
316C23×C53—41no—
317C23×C53—41no—
318C23×C53—41no—
319C23×C53—41no—
320C23×C53—41no—
321C23×C53—41no—
322C23×C53C2×C22⋊C414yes—
323C23×C53C23×C411yescharacteristic
324C23×C53C22×D411yescharacteristic
325C23×C53C22×D411yescharacteristic
326C23×C53C22×D411yescharacteristic
327C23×C53C2×#4111yescharacteristic
328C23×C53C2×#4111yescharacteristic
329C23×C53C2×#4111yescharacteristic
330C23×C53H(5,𝔽2)11yescharacteristic
331C23×C53H(5,𝔽2)11yescharacteristic
332C23×C53H(5,𝔽2)11yescharacteristic
333C23×C532−1+411yescharacteristic
334C23×C532−1+411yescharacteristic
335C23×C532−1+411yescharacteristic
336C23×C532−1+411yescharacteristic
337C23×C532−1+411yescharacteristic
338C2×C4×C53—22no—
339C2×C4×C53—22no—
340C2×C4×C53—22no—
341C2×C4×C53—22no—
342C2×C4×C53—22no—
343C2×C4×C53—22no—
344C2×C4×C53—22no—
345C2×C4×C53—22no—
346C2×C4×C53—22no—
347C2×C4×C53—22no—
348C2×C4×C53—22no—
349C2×C4×C53—22no—
350C2×C4×C53—22no—
351C2×C4×C53—22no—
352C2×C4×C53—22no—
353C2×C4×C53—22no—
354C2×C4×C53—22no—
355C2×C4×C53—22no—
356C2×C4×C53—41no—
357C2×C4×C53—41no—
358C2×C4×C53—41no—
359C2×C4×C53—41no—
360C2×C4×C53—41no—
361C2×C4×C53—41no—
362C2×C4×C53—41no—
363C2×C4×C53—41no—
364C2×C4×C53—41no—
365C2×C4×C53—41no—
366C2×C4×C53—41no—
367C2×C4×C53—41no—
368C2×C4×C53—41no—
369C2×C4×C53—41no—
370C2×C4×C53—41no—
371C2×C4×C53—41no—
372C2×C4×C53—41no—
373C2×C4×C53—41no—
374C2×C4×C53—41no—
375C2×C4×C53—41no—
376C2×C4×C53—41no—
377C2×C4×C53—41no—
378C2×C4×C53C2×C22⋊C414yes—
379C2×C4×C53C2×C22⋊C414yes—
380C2×Dic53—22no—
381C2×Dic53—22no—
382C2×Dic53—22no—
383C2×Dic53—22no—
384C2×Dic53—22no—
385C2×Dic53—22no—
386C2×Dic53—22no—
387C2×Dic53—22no—
388C2×Dic53—22no—
389C2×Dic53—22no—
390C2×Dic53—22no—
391C2×Dic53—22no—
392C2×Dic53—22no—
393C2×Dic53—22no—
394C2×Dic53—22no—
395C2×Dic53—22no—
396C2×Dic53—22no—
397C2×Dic53—22no—
398C2×Dic53—22no—
399C2×Dic53—22no—
400C2×Dic53—22no—
401C2×Dic53—416no—
402C2×Dic53—41no—
403C2×Dic53—41no—
404C2×Dic53—41no—
405C2×Dic53—41no—
406C2×Dic53—41no—
407C2×Dic53—41no—
408C2×Dic53—41no—
409C2×Dic53—41no—
410C2×Dic53—41no—
411C2×Dic53—41no—
412C2×Dic53—41no—
413C2×Dic53—41no—
414C2×Dic53—41no—
415C2×Dic53—41no—
416C2×Dic53—41no—
417C2×Dic53—41no—
418C2×Dic53—41no—
419C2×Dic53—41no—
420C2×Dic53—41no—
421C2×Dic53—41no—
422C2×Dic53—41no—
423C2×Dic53—41no—
424C2×Dic53—41no—
425C2×Dic53—41no—
426C2×Dic53—41no—
427C2×Dic53—41no—
428C2×Dic53—41no—
429C2×Dic53—41no—
430C2×Dic53—41no—
431C2×Dic53—41no—
432C2×Dic53—41no—
433C2×Dic53—41no—
434C2×Dic53—41no—
435C2×Dic53—41no—
436C2×Dic53C4×D414yes—
437Dic106—416no—
438#14364—531nomaximal, Sylow
439C22×C53—24no—
440C22×C53—24no—
441C22×C53—24no—
442C22×C53—42no—
443C22×C53—42no—
444C22×C53—42no—
445C22×C53—42no—
446C22×C53—42no—
447C22×C53—42no—
448C22×C53—42no—
449C22×C53—42no—
450C22×C53—42no—
451C22×C53—42no—
452C22×C53—42no—
453C22×C53—42no—
454C22×C53C22×C22⋊C411yescharacteristic
455C22×C53C2×C4×D411yescharacteristic
456C22×C53C4×#4111yescharacteristic
457C22×C53#51811yescharacteristic
458C22×C53#51911yescharacteristic
459C22×C53#51911yescharacteristic
460C22×C53#52011yescharacteristic
461C22×C53#53611yescharacteristic
462C22×C53#53611yescharacteristic
463C22×C53#53611yescharacteristic
464C22×C53#53611yescharacteristic
465C22×C53#53611yescharacteristic
466C22×C53#53711yescharacteristic
467C22×C53#53911yescharacteristic
468C22×C53#53911yescharacteristic
469C22×C53#54111yescharacteristic
470C22×C53#54211yescharacteristic
471C22×C53#54211yescharacteristic
472C22×C53#54211yescharacteristic
473C22×C53D4211yescharacteristic
474C22×C53D4211yescharacteristic
475C22×C53#54611yescharacteristic
476C22×C53#54611yescharacteristic
477C22×C53#54611yescharacteristic
478C22×C53#54611yescharacteristic
479C22×C53#54711yescharacteristic
480C22×C53#54711yescharacteristic
481C22×C53#54711yescharacteristic
482C22×C53#54811yescharacteristic
483C22×C53#55211yescharacteristic
484C22×C53#55611yescharacteristic
485C22×C53#56211yescharacteristic
486C22×C53#56211yescharacteristic
487C22×C53#56311yescharacteristic
488C22×C53#56311yescharacteristic
489C4×C53—24no—
490C4×C53—24no—
491C4×C53—42no—
492C4×C53—42no—
493C4×C53—81no—
494C4×C53—81no—
495Dic53—24no—
496Dic53—42no—
497Dic53—42no—
498Dic53—42no—
499Dic53—42no—
500Dic53—42no—
501Dic53—81no—
502Dic53—81no—
503C22×C22⋊Q8—531no—
504C2×#391—531no—
505C2×#388—531no—
506C2×#388D5311yescharacteristic
507C2×#381—531no—
508#1446—531no—
509#1445—531no—
510#1441—531no—
511#1441—531no—
512#1440—531no—
513#1440—531no—
514#1436—531no—
515#1436—531no—
516C4⋊#95—531no—
517C22⋊#95—531no—
518C2×C53—44no—
519C2×C53#231011yescharacteristic
520C2×C53#232311yescharacteristic
521C2×C53#233211yescharacteristic
522C2×C53D4×C22⋊C411yescharacteristic
523C2×C53#233911yescharacteristic
524C2×C53#236211yescharacteristic
525C2×C53#237811yescharacteristic
526C2×C53#267211yescharacteristic
527C2×C53#267411yescharacteristic
528C2×C53#268011yescharacteristic
529C2×C53#268111yescharacteristic
530C2×C53#268711yescharacteristic
531C2×C53#268911yescharacteristic
532C2×C53#269811yescharacteristic
533C2×C53#270011yescharacteristic
534C23×Q8—531no—
535C24×C4—531no—
536C2×C22⋊Q8—538no—
537C2×C22⋊Q8—1064no—
538C2×C22⋊Q8—1064no—
539C22×C4⋊C4—531no—
540C22×C4⋊C4—531no—
541C22×C4⋊C4—531no—
542C22×C4⋊C4—531no—
543C22×C4⋊C4C2×D5311yescharacteristic
544C22×C22⋊C4—531no—
545C22×C22⋊C4—531no—
546C22×C22⋊C4—531no—
547C22×C22⋊C4C2×D5311yescharacteristic
548C22×C22⋊C4C2×D5311yescharacteristic
549C22×C22⋊C4C2×D5311yescharacteristic
550C22×C42—531no—
551C22×C42C2×D5311yescharacteristic
552#391—1064no—
553#388—24no—
554#388—1064no—
555#381—1064no—
556C2×#95—531no—
557C2×#95—531no—
558C2×#95—531no—
559C2×#95—531no—
560C2×#95—531no—
561C2×#95—531no—
562C2×#95—531no—
563C2×#95—531no—
564C2×#95—531no—
565C2×#95—531no—
566C2×#95—531no—
567C2×#95—531no—
568C2×#95—531no—
569C2×#95—531no—
570C2×#95—531no—
571C2×#95—531no—
572C2×#95—531no—
573C2×#95—531no—
574C2×#95C2×D5311yescharacteristic
575C2×#95C2×D5311yescharacteristic
576C53#1436411yescharacteristic, complemented, Sylow
577C25C22×D5311yescharacteristic
578C22×Q8—534no—
579C22×Q8—1062no—
580C22×Q8—1062no—
581C22×Q8—1062no—
582C22×Q8—1062no—
583C22×Q8—2121no—
584C22×Q8—2121no—
585C23×C4—531no—
586C23×C4—531no—
587C23×C4—531no—
588C23×C4—531no—
589C23×C4—531no—
590C23×C4—531no—
591C23×C4—534no—
592C23×C4—531no—
593C23×C4—531no—
594C23×C4—1062no—
595C23×C4—1062no—
596C23×C4—1062no—
597C23×C4—1062no—
598C23×C4—2121no—
599C23×C4—2121no—
600C23×C4C22×D5311yescharacteristic
601C23×C4C22×D5311yescharacteristic
602C23×C4C22×D5311yescharacteristic
603C23×C4C22×D5311yescharacteristic
604C23×C4C22×D5311yescharacteristic
605C23×C4C22×D5311yescharacteristic
606C22⋊Q8—10632no—
607C2×C4⋊C4—22no—
608C2×C4⋊C4—22no—
609C2×C4⋊C4—41no—
610C2×C4⋊C4—534no—
611C2×C4⋊C4—534no—
612C2×C4⋊C4—534no—
613C2×C4⋊C4—1062no—
614C2×C4⋊C4—1062no—
615C2×C4⋊C4—1062no—
616C2×C4⋊C4—1062no—
617C2×C4⋊C4—1062no—
618C2×C4⋊C4—1062no—
619C2×C4⋊C4—1062no—
620C2×C4⋊C4—1062no—
621C2×C4⋊C4—2121no—
622C2×C22⋊C4—22no—
623C2×C22⋊C4—22no—
624C2×C22⋊C4—22no—
625C2×C22⋊C4—22no—
626C2×C22⋊C4—41no—
627C2×C22⋊C4—41no—
628C2×C22⋊C4—534no—
629C2×C22⋊C4—1062no—
630C2×C22⋊C4—1062no—
631C2×C22⋊C4—1062no—
632C2×C22⋊C4—1062no—
633C2×C22⋊C4—1062no—
634C2×C22⋊C4—1062no—
635C2×C22⋊C4—2121no—
636C2×C22⋊C4—2121no—
637C2×C22⋊C4C4×D5314yes—
638C2×C22⋊C4D21214yes—
639C2×C22⋊C4C22⋊D5314yes—
640C2×C42—22no—
641C2×C42—22no—
642C2×C42—41no—
643C2×C42—1062no—
644C2×C42—1062no—
645C2×C42—2121no—
646#95—22no—
647#95—22no—
648#95—534no—
649#95—1062no—
650#95—1062no—
651#95—1062no—
652#95—1062no—
653#95—1062no—
654#95—1062no—
655#95—1062no—
656#95—1062no—
657#95—1062no—
658#95—1062no—
659#95—1062no—
660#95—2121no—
661#95—2121no—
662#95—2121no—
663#95—2121no—
664#95—2121no—
665#95—2121no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24C2×C4×D5312yes—
679C24C2×D21212yes—
680C24C2×C22⋊D5312yes—
681C24C23×D5311yescharacteristic
682C2×Q8—1068no—
683C2×Q8—1068no—
684C2×Q8—2124no—
685C2×Q8—2124no—
686C2×Q8—2124no—
687C2×Q8—2124no—
688C2×Q8—2124no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—532no—
724C22×C4—532no—
725C22×C4—532no—
726C22×C4—532no—
727C22×C4—532no—
728C22×C4—532no—
729C22×C4—532no—
730C22×C4—532no—
731C22×C4—1068no—
732C22×C4—1061no—
733C22×C4—1061no—
734C22×C4—1061no—
735C22×C4—1061no—
736C22×C4—1068no—
737C22×C4—1061no—
738C22×C4—1061no—
739C22×C4—1061no—
740C22×C4—1061no—
741C22×C4—1061no—
742C22×C4—1061no—
743C22×C4—1061no—
744C22×C4—1061no—
745C22×C4—1061no—
746C22×C4—1061no—
747C22×C4—1061no—
748C22×C4—1061no—
749C22×C4—1061no—
750C22×C4—1061no—
751C22×C4—1061no—
752C22×C4—1061no—
753C22×C4—1061no—
754C22×C4—1061no—
755C22×C4—1061no—
756C22×C4—1061no—
757C22×C4—1061no—
758C22×C4—1061no—
759C22×C4—1061no—
760C22×C4—1061no—
761C22×C4—1061no—
762C22×C4—1061no—
763C22×C4—1061no—
764C22×C4—1061no—
765C22×C4—1061no—
766C22×C4—1061no—
767C22×C4—1061no—
768C22×C4—1061no—
769C22×C4—1061no—
770C22×C4—1061no—
771C22×C4—1061no—
772C22×C4—1061no—
773C22×C4—1061no—
774C22×C4—1061no—
775C22×C4—1061no—
776C22×C4—1061no—
777C22×C4—1061no—
778C22×C4—1061no—
779C22×C4—1061no—
780C22×C4—1061no—
781C22×C4—2124no—
782C22×C4—2124no—
783C22×C4—2124no—
784C22×C4—2124no—
785C22×C4—2124no—
786C22×C4C2×C4×D5312yes—
787C22×C4C2×C4×D5312yes—
788C22×C4C2×D21212yes—
789C22×C4C2×D21212yes—
790C22×C4D4×D5312yes—
791C22×C4#1171994712yes—
792C22×C4C2×C22⋊D5312yes—
793C22×C4C2×C22⋊D5312yes—
794C4⋊C4—44no—
795C4⋊C4—1068no—
796C4⋊C4—1068no—
797C4⋊C4—1068no—
798C4⋊C4—2124no—
799C22⋊C4—44no—
800C22⋊C4—44no—
801C22⋊C4—1068no—
802C22⋊C4—2124no—
803C22⋊C4—2124no—
804C22⋊C4#11719921116yes—
805C42—44no—
806C42—2124no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23C2×#1171992114yes—
842C23C22×C4×D5311yescharacteristic
843C23C2×D4×D5311yescharacteristic
844C23C22×C22⋊D5311yescharacteristic
845C23C22×D21211yescharacteristic
846C23#41×D5311yescharacteristic
847C23#41×D5311yescharacteristic
848C23C2×#1171994711yescharacteristic
849C23#1313326211yescharacteristic
850C23#1313326211yescharacteristic
851C23#1313326311yescharacteristic
852C23#1313326411yescharacteristic
853C23#1313326411yescharacteristic
854C23#1313326411yescharacteristic
855C23#1313326411yescharacteristic
856C23#1313326411yescharacteristic
857Q8—21216no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—534no—
899C2×C4—1062no—
900C2×C4—1062no—
901C2×C4—1062no—
902C2×C4—1062no—
903C2×C4—1062no—
904C2×C4—1062no—
905C2×C4—1062no—
906C2×C4—1062no—
907C2×C4—1062no—
908C2×C4—1062no—
909C2×C4—1062no—
910C2×C4—1062no—
911C2×C4—1062no—
912C2×C4—1062no—
913C2×C4—1062no—
914C2×C4—1062no—
915C2×C4—1062no—
916C2×C4—1062no—
917C2×C4—1062no—
918C2×C4—1062no—
919C2×C4—1062no—
920C2×C4—21216no—
921C2×C4—2121no—
922C2×C4—2121no—
923C2×C4—2121no—
924C2×C4—2121no—
925C2×C4—2121no—
926C2×C4—2121no—
927C2×C4—2121no—
928C2×C4—2121no—
929C2×C4—2121no—
930C2×C4—2121no—
931C2×C4—2121no—
932C2×C4—2121no—
933C2×C4—2121no—
934C2×C4—2121no—
935C2×C4—2121no—
936C2×C4—2121no—
937C2×C4—2121no—
938C2×C4—2121no—
939C2×C4—2121no—
940C2×C4—2121no—
941C2×C4—2121no—
942C2×C4—2121no—
943C2×C4—2121no—
944C2×C4—2121no—
945C2×C4—2121no—
946C2×C4—2121no—
947C2×C4—2121no—
948C2×C4—2121no—
949C2×C4—2121no—
950C2×C4—2121no—
951C2×C4—2121no—
952C2×C4—2121no—
953C2×C4—2121no—
954C2×C4—2121no—
955C2×C4C2×#1171992114yes—
956C2×C4C2×#1171992114yes—
957C22—24no—
958C22—24no—
959C22—24no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22C22×#1171992111yescharacteristic
973C22C4×D4×D5311yescharacteristic
974C22C4×#1171994711yescharacteristic
975C22#1681109511yescharacteristic
976C22#1681110011yescharacteristic
977C22#1681110011yescharacteristic
978C22#1681110211yescharacteristic
979C22#1681119311yescharacteristic
980C22#1681119411yescharacteristic
981C22#1681119411yescharacteristic
982C22#1681119911yescharacteristic
983C22#1681119911yescharacteristic
984C22#1681120011yescharacteristic
985C22#1681121411yescharacteristic
986C22#1681121711yescharacteristic
987C22#1681123011yescharacteristic
988C22#1681123711yescharacteristic
989C22#1681124011yescharacteristic
990C22#1681124111yescharacteristic
991C22D4×C22⋊D5311yescharacteristic
992C22D4×D21211yescharacteristic
993C22#1681126111yescharacteristic
994C22#1681126711yescharacteristic
995C22#1681126811yescharacteristic
996C22#1681126811yescharacteristic
997C22#1681127211yescharacteristic
998C22#1681127311yescharacteristic
999C22#1681127711yescharacteristic
1000C22#1681128111yescharacteristic
1001C22#1681131011yescharacteristic
1002C22#1681134011yescharacteristic
1003C22#1681136811yescharacteristic
1004C22#1681137011yescharacteristic
1005C22#1681137311yescharacteristic
1006C22#1681137511yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—42no—
1010C4—42no—
1011C4—81no—
1012C4—81no—
1013C4—1064no—
1014C4—4241no—
1015C4—4241no—
1016C4—2122no—
1017C4—2122no—
1018C4—2122no—
1019C4—2122no—
1020C4—2122no—
1021C2—44no—
1022C2#2027729911yescharacteristic
1023C2#2027739011yescharacteristic
1024C2#2027747211yescharacteristic
1025C2D4×#1171992111yescharacteristic
1026C2#2027754011yescharacteristic
1027C2#2027773911yescharacteristic
1028C2#2027787511yescharacteristic
1029C2#2028096011yescharacteristic
1030C2#2028099011yescharacteristic
1031C2#2028105311yescharacteristic
1032C2#2028106511yescharacteristic
1033C2#2028113011yescharacteristic
1034C2#2028116011yescharacteristic
1035C2#2028128711yescharacteristic
1036C2#2028131111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC2×C53×#388C2
socle, cosocleC24×C53C24
prime radicalC25×C53C23
hypercenterC2×#388D53
hypocenterC53#14364
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×#16810528C2semidirect
5. #20272985C2semidirect
6. #20272984C2semidirect
7. #20272969C2semidirect
8. #20272965C2semidirect
11. #20272950C2semidirect
12. #20272948C2semidirect
13. #20272945C2semidirect
20. C2×#13133194C4semidirect
576. C53#14364semidirect

Maximal subgroups

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

subgroupindex
C22×#131331942
C2×#168105282
C2×#168105162
C2×#168104842
#202729852
#202729842
#202729692
#202729652
#202729622
#202729502
#202729482
#202729452
#202729372
C2×C53×#3882
#1436453