Finite Group Databasebeta

← #27412302

Subgroups — #27412302

Order 13568.

1188 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811157C211yesmaximal, characteristic
2C2×C4×#11719925C211yesmaximal, characteristic, complemented
3C2×C4×#11719924C211yesmaximal, characteristic, complemented
4#20276053C211yesmaximal, characteristic, complemented
5#20275956C211yesmaximal, characteristic, complemented
6#20275911C211yesmaximal, characteristic, complemented
7#20275897C211yesmaximal, characteristic
8#20275866C211yesmaximal, characteristic, complemented
9#20275808C211yesmaximal, characteristic, complemented
10#20275723C211yesmaximal, characteristic, complemented
11#20275716C211yesmaximal, characteristic
12C4×#13133140C211yesmaximal, characteristic, complemented
13C4×#13133137C211yesmaximal, characteristic, complemented
14C4×C22⋊#88322C211yesmaximal, characteristic, complemented
15C4×C22⋊Q8×C53C211yesmaximal, characteristic, complemented
16C22×#11719925C2211yescharacteristic
17C22×#11719924C2211yescharacteristic
18#16811157—24no—
19#16811157—24no—
20C2×#13133211—21no—
21C2×#13133209C2211yescharacteristic
22C2×#13133205C2211yescharacteristic
23C2×#13133200—21no—
24C2×#13133196C2211yescharacteristic
25C2×#13133191C2211yescharacteristic
26C2×C4×Dic106C2211yescharacteristic
27C2×C4×D212C2211yescharacteristic
28C2×C4×C22⋊D53—21no—
29C2×#13133174—21no—
30C4×#11719925—24no—
31C4×#11719924—24no—
32C2×#13133150C2211yescharacteristic
33C2×#13133148C2211yescharacteristic
34C2×#13133141C2211yescharacteristic
35C2×#13133141C2211yescharacteristic
36C2×#13133140C2211yescharacteristic
37C2×#13133140C2211yescharacteristic
38C2×#13133140C2211yescharacteristic
39C2×#13133137C2211yescharacteristic
40C2×#13133137C2211yescharacteristic
41C2×#13133137C2211yescharacteristic
42C2×C22⋊#88322C2211yescharacteristic
43C2×C22⋊#88322C2211yescharacteristic
44C2×C4×#88322C2211yescharacteristic
45C2×C4×#88322C2211yescharacteristic
46#16810385C2211yescharacteristic
47#16810385C2211yescharacteristic
48#16810385C2211yescharacteristic
49#16810385C2211yescharacteristic
50#16810378C2211yescharacteristic
51#16810378C2211yescharacteristic
52C2×C22⋊Q8×C53C2211yescharacteristic
53C2×C4×Q8×C53C2211yescharacteristic
54C22×C42×C53C2211yescharacteristic
55C53×#391C2211yescharacteristic
56C53×#389C2211yescharacteristic
57C53×#387—21no—
58C53×#385—21no—
59C53×#380C2211yescharacteristic
60C4×C4⋊C4×C53—21no—
61C4×C4⋊C4×C53C2211yescharacteristic
62C4×C22⋊C4×C53—21no—
63C22×Dic106C2311yescharacteristic
64C22×D212C2311yescharacteristic
65C22×C22⋊D53—21no—
66C22×C4×D53—21no—
67C2×#11719925—22no—
68C2×#11719925—22no—
69C2×#11719925—22no—
70C2×#11719924—22no—
71C2×#11719924—22no—
72C2×#11719924—22no—
73C22×#88322C2311yescharacteristic
74C22×#88322C2311yescharacteristic
75C22×#88322C2311yescharacteristic
76C22×#88322C2311yescharacteristic
77#13133211—28no—
78#13133209—22no—
79#13133209—22no—
80#13133205—22no—
81#13133205—22no—
82#13133200—28no—
83#13133196—22no—
84#13133196—22no—
85#13133191—22no—
86#13133191—22no—
87C4×Dic106—22no—
88C4×Dic106D414yes—
89C4×D212—22no—
90C4×D212D414yes—
91C4×C22⋊D53—28no—
92#13133174—28no—
93C2×C4⋊Dic53C2311yescharacteristic
94C2×C4⋊Dic53C2311yescharacteristic
95C2×#11719919—21no—
96C2×#11719919—21no—
97C2×#11719919—21no—
98C2×#11719919—21no—
99C2×C22⋊Dic53—21no—
100C2×#11719921—21no—
101C2×#11719921—21no—
102C2×#11719921—21no—
103C2×#11719921—21no—
104C2×C4×Dic53—21no—
105#13133150—22no—
106#13133148—22no—
107#13133141—22no—
108#13133141—22no—
109#13133140—22no—
110#13133140—22no—
111#13133140—22no—
112#13133137—22no—
113#13133137—22no—
114#13133137—22no—
115C22⋊#88322—22no—
116C22⋊#88322—22no—
117C4×#88322—22no—
118C4×#88322—22no—
119C22×Q8×C53C2311yescharacteristic
120C23×C4×C53D411yescharacteristic
121C23×C4×C53D411yescharacteristic
122C23×C4×C53C2311yescharacteristic
123C22⋊Q8×C53—22no—
124C22⋊Q8×C53—22no—
125C4×Q8×C53—22no—
126C4×Q8×C53—22no—
127C2×C4⋊C4×C53—21no—
128C2×C4⋊C4×C53—21no—
129C2×C4⋊C4×C53—21no—
130C2×C4⋊C4×C53C2311yescharacteristic
131C2×C4⋊C4×C53C2311yescharacteristic
132C2×C4⋊C4×C53C2311yescharacteristic
133C2×C22⋊C4×C53—21no—
134C2×C22⋊C4×C53—21no—
135C2×C42×C53—22no—
136C2×C42×C53—22no—
137C2×C42×C53—21no—
138C2×C42×C53—21no—
139C2×C42×C53D411yescharacteristic
140C2×C42×C53D411yescharacteristic
141C2×C42×C53C2311yescharacteristic
142C2×C42×C53C2311yescharacteristic
143#95×C53—21no—
144#95×C53—21no—
145#95×C53—21no—
146#95×C53—21no—
147#95×C53—21no—
148C24×C53C2×D411yescharacteristic
149C23×D53—21no—
150C2×Q8×C53—21no—
151C2×Q8×C53—21no—
152C2×Q8×C53—21no—
153C2×Q8×C53—21no—
154C2×Q8×C53—21no—
155C2×Q8×C53#4112yes—
156C22×C4×C53—22no—
157C22×C4×C53—21no—
158C22×C4×C53—21no—
159C22×C4×C53—22no—
160C22×C4×C53—22no—
161C22×C4×C53—22no—
162C22×C4×C53—22no—
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—41no—
172C22×C4×C53C2×D411yescharacteristic
173C22×C4×C53C2×D411yescharacteristic
174C22×C4×C53C2×D411yescharacteristic
175C22×C4×C53C2×D411yescharacteristic
176C22×C4×C53C2×D411yescharacteristic
177C22×C4×C53C2411yescharacteristic
178C2×C22⋊D53—24no—
179C2×C22⋊D53—42no—
180C2×C22⋊D53—42no—
181C22×Dic53—21no—
182C22×Dic53—21no—
183C22×Dic53—21no—
184C2×D212—21no—
185C2×D212—21no—
186C2×D212—21no—
187C2×D212—21no—
188C2×D212—21no—
189C2×D212C2×D412yes—
190C2×C4×D53—24no—
191C2×C4×D53—42no—
192C2×C4×D53—42no—
193C2×Dic106—21no—
194C2×Dic106—21no—
195C2×Dic106—21no—
196C2×Dic106—21no—
197C2×Dic106—21no—
198C2×Dic106C2×D412yes—
199C4⋊C4×C53—24no—
200C4⋊C4×C53—21no—
201C4⋊C4×C53—21no—
202C4⋊C4×C53—21no—
203C4⋊C4×C53—21no—
204C4⋊C4×C53—21no—
205C4⋊C4×C53—42no—
206C4⋊C4×C53—42no—
207C4⋊C4×C53#4112yes—
208C22⋊C4×C53—24no—
209C22⋊C4×C53—42no—
210C42×C53—22no—
211C42×C53—22no—
212C42×C53—21no—
213C42×C53—21no—
214C42×C53—42no—
215C42×C53—42no—
216C42×C53C2×D412yes—
217C42×C53C2×D412yes—
218C22⋊Dic53—24no—
219#11719925—28no—
220#11719924—28no—
221#11719921—24no—
222#11719921—24no—
223#11719921—24no—
224#11719921—24no—
225C4⋊Dic53—21no—
226C4⋊Dic53—21no—
227C4⋊Dic53C2×D412yes—
228C4⋊Dic53C2×D412yes—
229#11719919—24no—
230#11719919—24no—
231#11719919—24no—
232#11719919—24no—
233C4×Dic53—24no—
234C2×#88322—21no—
235C2×#88322—21no—
236C2×#88322—21no—
237C2×#88322—21no—
238C2×#88322—21no—
239C2×#88322—21no—
240C2×#88322—21no—
241C2×#88322—21no—
242C2×#88322—21no—
243C2×#88322—21no—
244C2×#88322#4112yes—
245C2×#88322#4112yes—
246C23×C53—21no—
247C23×C53—21no—
248C23×C53—21no—
249C23×C53—21no—
250C23×C53—21no—
251C23×C53—21no—
252C23×C53#13512yes—
253C23×C53C22×D411yescharacteristic
254C22×D53—22no—
255C22×D53—41no—
256C22×D53—41no—
257C22×D53—41no—
258C22×D53—41no—
259C22×D53—41no—
260C22×D53—41no—
261Q8×C53—22no—
262Q8×C53—22no—
263Q8×C53—41no—
264Q8×C53—41no—
265C2×C4×C53—21no—
266C2×C4×C53—21no—
267C2×C4×C53—21no—
268C2×C4×C53—21no—
269C2×C4×C53—21no—
270C2×C4×C53—21no—
271C2×C4×C53—22no—
272C2×C4×C53—22no—
273C2×C4×C53—21no—
274C2×C4×C53—21no—
275C2×C4×C53—21no—
276C2×C4×C53—21no—
277C2×C4×C53—21no—
278C2×C4×C53—44no—
279C2×C4×C53—41no—
280C2×C4×C53—41no—
281C2×C4×C53—41no—
282C2×C4×C53—41no—
283C2×C4×C53—41no—
284C2×C4×C53—41no—
285C2×C4×C53—41no—
286C2×C4×C53—41no—
287C2×C4×C53—44no—
288C2×C4×C53—41no—
289C2×C4×C53—41no—
290C2×C4×C53—41no—
291C2×C4×C53—41no—
292C2×C4×C53—41no—
293C2×C4×C53—41no—
294C2×C4×C53#12012yes—
295C2×C4×C53#12012yes—
296C2×C4×C53#13512yes—
297C2×C4×C53#13712yes—
298C2×C4×C53C22×D411yescharacteristic
299C2×C4×C53C22×D411yescharacteristic
300C2×C4×C53C2×#4111yescharacteristic
301C2×C4×C53C2×#4111yescharacteristic
302C2×C4×C53C2×#4111yescharacteristic
303C2×C4×C53C2×#4111yescharacteristic
304C22⋊D53—48no—
305C2×Dic53—22no—
306C2×Dic53—22no—
307C2×Dic53—22no—
308C2×Dic53—41no—
309C2×Dic53—41no—
310C2×Dic53—41no—
311C2×Dic53—41no—
312C2×Dic53—41no—
313C2×Dic53—41no—
314D212—22no—
315D212—22no—
316D212—41no—
317D212—41no—
318C4×D53—48no—
319Dic106—22no—
320Dic106—22no—
321Dic106—41no—
322Dic106—41no—
323#88322—22no—
324#88322—22no—
325#88322—41no—
326#88322—41no—
327#23572—531nomaximal, Sylow
328C22×C53—22no—
329C22×C53—22no—
330C22×C53—22no—
331C22×C53—41no—
332C22×C53—41no—
333C22×C53—41no—
334C22×C53—41no—
335C22×C53C2×#12011yescharacteristic
336C22×C53#52511yescharacteristic
337C22×C53#53211yescharacteristic
338C22×C53C2×#13511yescharacteristic
339C22×C53C2×#13511yescharacteristic
340C22×C53C2×#13711yescharacteristic
341C22×C53#57511yescharacteristic
342C2×D53—42no—
343C2×D53—42no—
344C2×D53—42no—
345C2×D53—81no—
346C2×D53—81no—
347C2×D53—81no—
348C2×D53—81no—
349C4×C53—22no—
350C4×C53—42no—
351C4×C53—41no—
352C4×C53—42no—
353C4×C53—41no—
354C4×C53—41no—
355C4×C53—81no—
356C4×C53—81no—
357C4×C53#45214yes—
358C4×C53#52511yescharacteristic
359C4×C53#52511yescharacteristic
360C4×C53#53211yescharacteristic
361C4×C53#53211yescharacteristic
362Dic53—42no—
363Dic53—42no—
364Dic53—42no—
365C2×#529—531no—
366C2×C4×Q16—531no—
367C2×C4×SD16—531no—
368C4×C22⋊Q8D5311yescharacteristic, complemented
369#2059—531no—
370#2042—531no—
371#2035—531no—
372#2033—531no—
373#2026—531no—
374#2015—531no—
375#2001—531no—
376#2000—531no—
377C4×#103—531no—
378C4×#102—531no—
379C4×C22⋊C8—531no—
380C2×C53—42no—
381C2×C53#238811yescharacteristic
382C2×C53C2×#45211yescharacteristic
383C2×C53#300211yescharacteristic
384C2×C53#310211yescharacteristic
385C2×C53#310811yescharacteristic
386C2×C53#316811yescharacteristic
387C2×C53#317211yescharacteristic
388D53—82no—
389C22×Q16—531no—
390C22×SD16—531no—
391#529—1064no—
392#529—1064no—
393C2×#126—1061no—
394C2×#125—531no—
395C2×#124—531no—
396C2×#123—1061no—
397C2×C22⋊Q8—531no—
398C2×C22⋊Q8C2×D5311yescharacteristic
399C2×#121—531no—
400C2×C4×Q8—531no—
401C2×C4×Q8C2×D5311yescharacteristic
402C2×C4×D4—531no—
403C2×C4×D4—1061no—
404C2×#117—1061no—
405C22×C42C2×D5311yescharacteristic
406C4×Q16—1064no—
407C4×SD16—1064no—
408C2×#107—531no—
409C2×#106—531no—
410C2×#103—531no—
411C2×#103—531no—
412C2×#103—531no—
413C2×#103—531no—
414C2×#103—531no—
415C2×#102—531no—
416C2×#102—531no—
417C2×#102—531no—
418C2×C22⋊C8—531no—
419C2×C22⋊C8—531no—
420C2×C4×C8—531no—
421C2×C4×C8—531no—
422#391C2×D5311yescharacteristic
423#389C2×D5311yescharacteristic
424#387—21no—
425#385—21no—
426#380C2×D5311yescharacteristic
427C4×C4⋊C4—21no—
428C4×C4⋊C4C2×D5311yescharacteristic
429C4×C22⋊C4—21no—
430#340—531no—
431#340—531no—
432#340—531no—
433#340—531no—
434#336—531no—
435#336—531no—
436C53#2357211yescharacteristic, complemented, Sylow
437C22×Q8—531no—
438C22×Q8C22×D5311yescharacteristic
439C22×D4—531no—
440C22×D4—1061no—
441C23×C4—1061no—
442C23×C4C22⋊D5311yescharacteristic
443C23×C4C22⋊D5311yescharacteristic
444C23×C4C22×D5311yescharacteristic
445C2×Q16—1062no—
446C2×Q16—1062no—
447C2×Q16—1062no—
448C2×SD16—1062no—
449C2×SD16—1062no—
450C2×SD16—1062no—
451C22×C8—531no—
452C22×C8—531no—
453C22×C8—531no—
454C22×C8—531no—
455#126—1068no—
456#125—1062no—
457#125—1062no—
458#124—1062no—
459#124—1062no—
460#123—1068no—
461C22⋊Q8—22no—
462C22⋊Q8—22no—
463C22⋊Q8—1062no—
464C22⋊Q8—1062no—
465#121—1062no—
466#121—1062no—
467C4×Q8—22no—
468C4×Q8—22no—
469C4×Q8—534no—
470C4×Q8—1062no—
471C4×D4—534no—
472C4×D4—1068no—
473C4×D4—1062no—
474#117—1068no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—531no—
479C2×C4⋊C4—531no—
480C2×C4⋊C4—1061no—
481C2×C4⋊C4—1061no—
482C2×C4⋊C4—1061no—
483C2×C4⋊C4—1061no—
484C2×C4⋊C4C22×D5311yescharacteristic
485C2×C4⋊C4C22×D5311yescharacteristic
486C2×C4⋊C4C22×D5311yescharacteristic
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—1061no—
490C2×C22⋊C4—1061no—
491C2×C22⋊C4—1061no—
492C2×C22⋊C4—1061no—
493C2×C22⋊C4—1061no—
494C2×C42—22no—
495C2×C42—22no—
496C2×C42—21no—
497C2×C42—21no—
498C2×C42—1061no—
499C2×C42C22⋊D5311yescharacteristic
500C2×C42C22⋊D5311yescharacteristic
501C2×C42C22×D5311yescharacteristic
502C2×C42C22×D5311yescharacteristic
503#107—1062no—
504#106—1062no—
505#103—1062no—
506#103—1062no—
507#103—1062no—
508#103—1062no—
509#103—1062no—
510#102—1062no—
511#102—1062no—
512#102—1062no—
513C22⋊C8—1062no—
514C22⋊C8—1062no—
515C4×C8—1062no—
516C4×C8—1062no—
517#95—21no—
518#95—21no—
519#95—21no—
520#95—21no—
521#95—21no—
522C24—1061no—
523C24C2×C22⋊D5311yescharacteristic
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—532no—
530C2×Q8—1061no—
531C2×Q8—1061no—
532C2×Q8—1061no—
533C2×Q8—1061no—
534C2×Q8—1061no—
535C2×Q8#1171994512yes—
536C2×D4—532no—
537C2×D4—1064no—
538C2×D4—1061no—
539C2×D4—1061no—
540C2×D4—1061no—
541C2×D4—1061no—
542C2×D4—1061no—
543C2×D4—2122no—
544C2×D4—2122no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—41no—
561C22×C4—1061no—
562C22×C4—1061no—
563C22×C4—1061no—
564C22×C4—1064no—
565C22×C4—2122no—
566C22×C4—2122no—
567C22×C4C2×C22⋊D5311yescharacteristic
568C22×C4C2×C22⋊D5311yescharacteristic
569C22×C4C2×C22⋊D5311yescharacteristic
570C22×C4C2×C22⋊D5311yescharacteristic
571C22×C4C2×C22⋊D5311yescharacteristic
572C22×C4C23×D5311yescharacteristic
573Q16—1068no—
574SD16—1068no—
575C2×C8—532no—
576C2×C8—532no—
577C2×C8—1061no—
578C2×C8—1061no—
579C2×C8—1061no—
580C2×C8—1061no—
581C2×C8—1061no—
582C2×C8—1061no—
583C2×C8—1061no—
584C2×C8—1061no—
585C2×C8—1061no—
586C2×C8—1061no—
587C4⋊C4—24no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—42no—
594C4⋊C4—42no—
595C4⋊C4—532no—
596C4⋊C4—532no—
597C4⋊C4—1064no—
598C4⋊C4—1064no—
599C4⋊C4—1064no—
600C4⋊C4—1064no—
601C4⋊C4—1061no—
602C4⋊C4—1061no—
603C4⋊C4#1171994512yes—
604C22⋊C4—24no—
605C22⋊C4—42no—
606C22⋊C4—1064no—
607C22⋊C4—1064no—
608C22⋊C4—1064no—
609C22⋊C4—1064no—
610C22⋊C4—1064no—
611C42—22no—
612C42—22no—
613C42—21no—
614C42—21no—
615C42—42no—
616C42—42no—
617C42—1064no—
618C42D4×D5312yes—
619C42D4×D5312yes—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—1062no—
627C23—2121no—
628C23—2121no—
629C23—2121no—
630C23—2121no—
631C23—2121no—
632C23—2121no—
633C23#1313323712yes—
634C23C22×C22⋊D5311yescharacteristic
635Q8—22no—
636Q8—22no—
637Q8—41no—
638Q8—41no—
639Q8—1062no—
640Q8—1062no—
641Q8—2121no—
642Q8—2121no—
643D4—1062no—
644D4—1062no—
645D4—2128no—
646D4—2121no—
647D4—2121no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—44no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—44no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—1062no—
678C2×C4—1062no—
679C2×C4—1062no—
680C2×C4—2121no—
681C2×C4—2121no—
682C2×C4—2121no—
683C2×C4—2121no—
684C2×C4—2121no—
685C2×C4—2121no—
686C2×C4—2128no—
687C2×C4#1313318512yes—
688C2×C4#1313318512yes—
689C2×C4#1313323712yes—
690C2×C4#1313324812yes—
691C2×C4C2×D4×D5311yescharacteristic
692C2×C4C2×D4×D5311yescharacteristic
693C2×C4#41×D5311yescharacteristic
694C2×C4#41×D5311yescharacteristic
695C2×C4C2×#1171994511yescharacteristic
696C2×C4C2×#1171994511yescharacteristic
697C8—1062no—
698C8—1062no—
699C8—2121no—
700C8—2121no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—4241no—
709C22—4241no—
710C22—4241no—
711C22—4241no—
712C22—2122no—
713C22—2122no—
714C22—2122no—
715C22C2×#1313318511yescharacteristic
716C22#1681113411yescharacteristic
717C22#1681116911yescharacteristic
718C22C2×#1313323711yescharacteristic
719C22C2×#1313323711yescharacteristic
720C22C2×#1313324811yescharacteristic
721C22#1681142111yescharacteristic
722C4—22no—
723C4—41no—
724C4—41no—
725C4—42no—
726C4—41no—
727C4—42no—
728C4—81no—
729C4—81no—
730C4—2122no—
731C4—2122no—
732C4—2122no—
733C4#1681078314yes—
734C4#1681113211yescharacteristic
735C4#1681113211yescharacteristic
736C4#1681117011yescharacteristic
737C4#1681117011yescharacteristic
738C2—42no—
739C2—4242no—
740C2#2027793011yescharacteristic
741C2C2×#1681078311yescharacteristic
742C2#2028393111yescharacteristic
743C2#2028473311yescharacteristic
744C2#2028479511yescharacteristic
745C2#2028527911yescharacteristic
746C2#2028531511yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D53
commutator, cosocleC22×C4×C53C24
FrattiniC22×C4C23×D53
FittingC4×C22⋊Q8×C53C2
socleC23×C53C22×D4
prime radicalC2×#13133191C22
hypercenterC4×C22⋊Q8D53
hypocenterC53#23572
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11719925C2semidirect
3. C2×C4×#11719924C2semidirect
4. #20276053C2semidirect
5. #20275956C2semidirect
6. #20275911C2semidirect
8. #20275866C2semidirect
9. #20275808C2semidirect
10. #20275723C2semidirect
12. C4×#13133140C2semidirect
13. C4×#13133137C2semidirect
14. C4×C22⋊#88322C2semidirect
15. C4×C22⋊Q8×C53C2semidirect
368. C4×C22⋊Q8D53semidirect
436. C53#23572semidirect

Maximal subgroups

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

subgroupindex
C2×#168111572
C2×C4×#117199252
C2×C4×#117199242
#202760532
#202759562
#202759112
#202758972
#202758662
#202758082
#202757232
#202757162
C4×#131331402
C4×#131331372
C4×C22⋊#883222
C4×C22⋊Q8×C532
#2357253