Finite Group Databasebeta

← #27289608

Subgroups — #27289608

Order 13568.

1350 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811104C211yesmaximal, characteristic
2C22×#13133143C211yesmaximal, characteristic
3C2×#16810625C211yesmaximal, characteristic
4#20274435C211yesmaximal, characteristic, complemented
5C2×#16810384C211yesmaximal, characteristic, complemented
6#20272944C211yesmaximal, characteristic, complemented
7C2×C53×#343C211yesmaximal, characteristic, complemented
8C22×#11719945C2211yescharacteristic
9#16811104—22no—
10#16811104—22no—
11#16811104—22no—
12#16811104C414yescomplemented
13C2×#13133182—21no—
14C2×#13133179—21no—
15C2×C4×C22⋊D53—22no—
16C2×#13133176C2211yescharacteristic
17C2×#13133175—21no—
18C22×C4⋊Dic53C2211yescharacteristic
19C2×C4⋊C4×D53—21no—
20C22×C4×Dic53C2211yescharacteristic
21C2×#13133143—22no—
22C2×#13133143—22no—
23C2×#13133143C414yescomplemented
24#16810625—22no—
25#16810625C414yescomplemented
26C2×#13133142—21no—
27C2×#13133139—21no—
28C2×#13133124—22no—
29#16810386—21no—
30#16810386—21no—
31#16810384—22no—
32C22×M16×C53C2211yescharacteristic
33C22×M16×C53C2211yescharacteristic
34C22×C4⋊C4×C53C2211yescharacteristic
35C53×#343—22no—
36C2×#11719945—21no—
37C2×#11719945—21no—
38C2×#11719945—21no—
39C2×#11719945—21no—
40C2×#11719945—21no—
41C2×#11719945—21no—
42C2×#11719945C2×C412yes—
43C2×#11719945C2×C412yes—
44C2×#11719945C2×C412yes—
45C2×#11719945D412yes—
46C2×#11719945D412yes—
47C2×#11719945Q812yes—
48C22×Dic106D411yescharacteristic
49C22×D212D411yescharacteristic
50C22×C22⋊D53—21no—
51C23×Dic53—21no—
52C23×Dic53—21no—
53C22×C4×D53—21no—
54C22×C4×D53—22no—
55#13133182—24no—
56#13133182—24no—
57#13133179—24no—
58#13133179—24no—
59C4×C22⋊D53—28no—
60C4×C22⋊D53—28no—
61#13133176—21no—
62#13133176—21no—
63#13133176C2×C412yes—
64#13133176D412yes—
65#13133175—24no—
66#13133175—24no—
67C2×C4⋊Dic53—21no—
68C2×C4⋊Dic53—21no—
69C2×C4⋊Dic53—21no—
70C2×C4⋊Dic53—21no—
71C2×C4⋊Dic53—21no—
72C2×C4⋊Dic53C2×C412yescomplemented
73C2×C4⋊Dic53D411yescharacteristic
74C2×C4⋊Dic53D411yescharacteristic
75C2×#11719919—22no—
76C4⋊C4×D53—24no—
77C4⋊C4×D53—24no—
78C2×C22⋊Dic53—21no—
79C2×#11719921—22no—
80C2×C4×Dic53—22no—
81C2×C4×Dic53—21no—
82C2×C4×Dic53—21no—
83C2×C4×Dic53—21no—
84C2×C4×Dic53—21no—
85C2×C4×Dic53—21no—
86C2×C4×Dic53—21no—
87C2×C4×Dic53C2×C412yescomplemented
88#13133143—28no—
89#13133142—24no—
90#13133139—24no—
91#13133124—44no—
92C23×C4×C53D412yes—
93C23×C4×C53C2311yescharacteristic
94C2×M16×C53—21no—
95C2×M16×C53—21no—
96C2×M16×C53—21no—
97C2×M16×C53—21no—
98C2×M16×C53—21no—
99C2×M16×C53—21no—
100C2×M16×C53—21no—
101C2×M16×C53—21no—
102C2×M16×C53—21no—
103C2×M16×C53—21no—
104C2×M16×C53C2×C412yescomplemented
105C2×M16×C53C2×C412yescomplemented
106C22×C8×C53—21no—
107C22×C8×C53—21no—
108C2×C4⋊C4×C53—21no—
109C2×C4⋊C4×C53—21no—
110C2×C4⋊C4×C53—21no—
111C2×C4⋊C4×C53—21no—
112C2×C4⋊C4×C53C2×C412yes—
113C2×C4⋊C4×C53D412yes—
114C24×C53C2×D411yescharacteristic
115C23×D53—21no—
116C22×C4×C53—22no—
117C22×C4×C53—22no—
118C22×C4×C53—42no—
119C22×C4×C53—42no—
120C22×C4×C53C22⋊C414yes—
121C22×C4×C53C22×C411yescharacteristic
122C22×C4×C53C22×C411yescharacteristic
123C22×C4×C53C22×C411yescharacteristic
124C22×C4×C53C2×D411yescharacteristic
125C22×C4×C53C2×D411yescharacteristic
126C22×C4×C53C2×D411yescharacteristic
127C22×C4×C53C2×D411yescharacteristic
128C22×C4×C53C2×D411yescharacteristic
129C22×C4×C53C2×D411yescharacteristic
130C22×C4×C53C2×Q811yescharacteristic
131C22×C4×C53#4111yescharacteristic
132C22×C4×C53#4111yescharacteristic
133C22×C4×C53#4111yescharacteristic
134C22×C4×C53#4111yescharacteristic
135C2×C22⋊D53—22no—
136C2×C22⋊D53—22no—
137C2×C22⋊D53—22no—
138C2×C22⋊D53—22no—
139C2×C22⋊D53—22no—
140C2×C22⋊D53—22no—
141C22×Dic53—21no—
142C22×Dic53—22no—
143C22×Dic53—22no—
144C22×Dic53—22no—
145C22×Dic53—21no—
146C22×Dic53—21no—
147C22×Dic53—22no—
148C22×Dic53—41no—
149C22×Dic53—41no—
150C22×Dic53—41no—
151C22×Dic53—41no—
152C22×Dic53—42no—
153C22×Dic53—42no—
154C22×Dic53—41no—
155C22×Dic53—41no—
156#11719945—22no—
157#11719945—22no—
158#11719945—22no—
159#11719945—22no—
160#11719945—22no—
161#11719945—22no—
162#11719945—22no—
163#11719945—22no—
164#11719945—22no—
165#11719945—22no—
166#11719945—22no—
167#11719945—22no—
168#11719945C4214yes—
169#11719945C22⋊C414yes—
170#11719945C4⋊C414yes—
171#11719945C4⋊C414yes—
172C2×D212—21no—
173C2×D212—21no—
174C2×D212—21no—
175C2×D212C22⋊C412yes—
176C2×D212C22⋊C412yes—
177C2×D212C4⋊C412yes—
178C2×C4×D53—22no—
179C2×C4×D53—22no—
180C2×C4×D53—22no—
181C2×C4×D53—22no—
182C2×C4×D53—22no—
183C2×C4×D53—22no—
184C2×C4×D53—28no—
185C2×C4×D53—82no—
186C2×C4×D53—82no—
187C2×Dic106—21no—
188C2×Dic106—21no—
189C2×Dic106—21no—
190C2×Dic106C22⋊C412yes—
191C2×Dic106C22⋊C412yes—
192C2×Dic106C4⋊C412yes—
193M16×C53—22no—
194M16×C53—22no—
195M16×C53—22no—
196M16×C53—22no—
197M16×C53—41no—
198M16×C53—41no—
199M16×C53—41no—
200M16×C53—41no—
201C2×C8×C53—22no—
202C2×C8×C53—22no—
203C2×C8×C53—41no—
204C2×C8×C53—41no—
205C2×C8×C53—41no—
206C2×C8×C53—41no—
207C4⋊C4×C53—22no—
208C4⋊C4×C53—22no—
209C4⋊C4×C53—22no—
210C4⋊C4×C53—22no—
211C22⋊Dic53—22no—
212C22⋊Dic53—22no—
213#11719921—28no—
214C4⋊Dic53—21no—
215C4⋊Dic53—21no—
216C4⋊Dic53—22no—
217C4⋊Dic53—22no—
218C4⋊Dic53—41no—
219C4⋊Dic53—41no—
220C4⋊Dic53C22⋊C412yes—
221C4⋊Dic53C22⋊C412yes—
222#11719919—28no—
223C4×Dic53—28no—
224C4×Dic53—22no—
225C4×Dic53—22no—
226C4×Dic53—22no—
227C4×Dic53—22no—
228C4×Dic53—41no—
229C4×Dic53—41no—
230C23×C53—21no—
231C23×C53—21no—
232C23×C53—21no—
233C23×C53—21no—
234C23×C53C2×C22⋊C411yescharacteristic
235C23×C53C4×D411yescharacteristic
236C23×C53C4×D411yescharacteristic
237C23×C53#12011yescharacteristic
238C23×C53#12011yescharacteristic
239C23×C53#12111yescharacteristic
240C23×C53C22⋊Q811yescharacteristic
241C22×D53—22no—
242C22×D53—22no—
243C22×D53—22no—
244C22×D53—41no—
245C22×D53—41no—
246C22×D53—41no—
247C22×D53—41no—
248C2×C4×C53—24no—
249C2×C4×C53—42no—
250C2×C4×C53—42no—
251C2×C4×C53—44no—
252C2×C4×C53—82no—
253C2×C4×C53C2×C4211yescharacteristic
254C2×C4×C53C2×C22⋊C411yescharacteristic
255C2×C4×C53C2×C22⋊C411yescharacteristic
256C2×C4×C53C2×C22⋊C411yescharacteristic
257C2×C4×C53C2×C22⋊C411yescharacteristic
258C2×C4×C53C2×C4⋊C411yescharacteristic
259C2×C4×C53C2×C4⋊C411yescharacteristic
260C2×C4×C53C2×C4⋊C411yescharacteristic
261C2×C4×C53#11711yescharacteristic
262C2×C4×C53#11711yescharacteristic
263C2×C4×C53C4×D411yescharacteristic
264C2×C4×C53C4×D411yescharacteristic
265C2×C4×C53C4×D411yescharacteristic
266C2×C4×C53C4×D411yescharacteristic
267C2×C4×C53C4×D411yescharacteristic
268C2×C4×C53C4×D411yescharacteristic
269C2×C4×C53#12011yescharacteristic
270C2×C4×C53#12011yescharacteristic
271C2×C4×C53#12111yescharacteristic
272C2×C4×C53#12111yescharacteristic
273C2×C4×C53#12111yescharacteristic
274C2×C4×C53C22⋊Q811yescharacteristic
275C2×C4×C53C22⋊Q811yescharacteristic
276C2×C4×C53C22⋊Q811yescharacteristic
277C2×C4×C53#12311yescharacteristic
278C2×C4×C53#12311yescharacteristic
279C2×C4×C53#12311yescharacteristic
280C2×C4×C53#12311yescharacteristic
281C22⋊D53—24no—
282C22⋊D53—24no—
283C22⋊D53—24no—
284C22⋊D53—24no—
285C2×Dic53—22no—
286C2×Dic53—22no—
287C2×Dic53—22no—
288C2×Dic53—24no—
289C2×Dic53—22no—
290C2×Dic53—22no—
291C2×Dic53—42no—
292C2×Dic53—42no—
293C2×Dic53—42no—
294C2×Dic53—42no—
295C2×Dic53—42no—
296C2×Dic53—42no—
297C2×Dic53—41no—
298C2×Dic53—41no—
299C2×Dic53—41no—
300C2×Dic53—41no—
301C2×Dic53—44no—
302C2×Dic53—42no—
303C2×Dic53—82no—
304C2×Dic53—81no—
305C2×Dic53—81no—
306D212—22no—
307D212—22no—
308D212—22no—
309D212#9514yescomplemented
310C4×D53—24no—
311C4×D53—24no—
312C4×D53—24no—
313C4×D53—24no—
314C4×D53—88no—
315Dic106—22no—
316Dic106—22no—
317Dic106—22no—
318Dic106#9514yescomplemented
319C8×C53—42no—
320C8×C53—42no—
321#10781—531nomaximal, Sylow
322C22×C53—21no—
323C22×C53—21no—
324C22×C53—21no—
325C22×C53—21no—
326C22×C53—21no—
327C22×C53—21no—
328C22×C53—21no—
329C22×C53—21no—
330C22×C53—21no—
331C22×C53—21no—
332C22×C53—21no—
333C22×C53—21no—
334C22×C53C4×C22⋊C411yescharacteristic
335C22×C53#37911yescharacteristic
336C22×C53#38011yescharacteristic
337C22×C53#38511yescharacteristic
338C22×C53#38511yescharacteristic
339C22×C53#38611yescharacteristic
340C22×C53#38611yescharacteristic
341C22×C53#45311yescharacteristic
342C22×C53#45411yescharacteristic
343C22×C53#45511yescharacteristic
344C22×C53#45611yescharacteristic
345C2×D53—24no—
346C2×D53—42no—
347C2×D53—42no—
348C2×D53—42no—
349C2×D53—42no—
350C2×D53—42no—
351C2×D53—42no—
352C4×C53—44no—
353C4×C53C2×#9511yescharacteristic
354C4×C53C4×C22⋊C411yescharacteristic
355C4×C53#38011yescharacteristic
356C4×C53#38111yescharacteristic
357C4×C53#38511yescharacteristic
358C4×C53#38511yescharacteristic
359C4×C53#38611yescharacteristic
360C4×C53#38611yescharacteristic
361Dic53—24no—
362Dic53—44no—
363Dic53—42no—
364Dic53—42no—
365Dic53—82no—
366C2×#520—531no—
367C22×#104—531no—
368C2×#417—531no—
369C2×#343D5311yescharacteristic, complemented
370#1736—531no—
371C2×#339—531no—
372C4⋊#95—531no—
373C2×C53—21no—
374C2×C53—21no—
375C2×C53—21no—
376C2×C53—21no—
377C2×C53C22⋊#9511yescharacteristic
378C2×C53#179211yescharacteristic
379C2×C53#179311yescharacteristic
380C2×C53#185911yescharacteristic
381C2×C53#186011yescharacteristic
382C2×C53#188211yescharacteristic
383C2×C53#188311yescharacteristic
384D53—44no—
385C22×#41—531no—
386C22×M16C2×D5311yescharacteristic
387C22×M16C2×D5311yescharacteristic
388#520—534no—
389#520—1062no—
390#520—1062no—
391#520—1062no—
392C2×C4×Q8—1061no—
393C2×C4×D4—1061no—
394C2×C4×D4—1062no—
395C2×#117—531no—
396C2×#117—1061no—
397C22×C4⋊C4—531no—
398C22×C4⋊C4—1061no—
399C22×C4⋊C4C2×D5311yescharacteristic
400C22×C42—531no—
401C2×#104—534no—
402C2×#104—1062no—
403C2×#104—1062no—
404#417—534no—
405#417—1062no—
406C2×#103—1061no—
407C2×#102—1061no—
408C2×#95—1062no—
409#343—22no—
410#340—1061no—
411#340—1061no—
412#339—1062no—
413C53#1078111yescharacteristic, complemented, Sylow
414C2×#41—532no—
415C2×#41—532no—
416C2×#41—532no—
417C2×#41—532no—
418C2×#41—532no—
419C2×#41—532no—
420C2×#41—1061no—
421C2×#41—1061no—
422C2×#41—1061no—
423C2×#41—1061no—
424C2×#41—1061no—
425C2×#41—1061no—
426C22×Q8—531no—
427C22×D4—531no—
428C22×D4—1061no—
429C23×C4—1062no—
430C23×C4—1061no—
431C23×C4—1061no—
432C23×C4—1061no—
433C23×C4D21212yes—
434C23×C4C22×D5311yescharacteristic
435C2×M16—21no—
436C2×M16—21no—
437C2×M16—21no—
438C2×M16—21no—
439C2×M16—21no—
440C2×M16—21no—
441C2×M16—21no—
442C2×M16—21no—
443C2×M16—21no—
444C2×M16—21no—
445C2×M16C4×D5312yescomplemented
446C2×M16C4×D5312yescomplemented
447C22×C8—21no—
448C22×C8—21no—
449C4×Q8—1064no—
450C4×Q8—1064no—
451C4×D4—1064no—
452C4×D4—1064no—
453C4×D4—1068no—
454C4×D4—1068no—
455#117—532no—
456#117—532no—
457#117—1064no—
458#117—1064no—
459#117—1061no—
460#117—1061no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—531no—
466C2×C4⋊C4—531no—
467C2×C4⋊C4—532no—
468C2×C4⋊C4—1064no—
469C2×C4⋊C4—1064no—
470C2×C4⋊C4—1062no—
471C2×C4⋊C4—1061no—
472C2×C4⋊C4—1061no—
473C2×C4⋊C4—1061no—
474C2×C4⋊C4—1061no—
475C2×C4⋊C4—1061no—
476C2×C4⋊C4C4×D5312yes—
477C2×C4⋊C4C22⋊D5312yes—
478C2×C22⋊C4—1062no—
479C2×C22⋊C4—1061no—
480C2×C42—532no—
481C2×C42—1062no—
482C2×C42—1061no—
483C2×C42—1061no—
484C2×C42—1061no—
485C2×C42—1061no—
486C2×C42—1061no—
487C2×C42—1061no—
488#104—1068no—
489#103—1064no—
490#102—1064no—
491#95—2124no—
492C24—1061no—
493C24C2×D21211yescharacteristic
494#41—534no—
495#41—534no—
496#41—534no—
497#41—534no—
498#41—1062no—
499#41—1062no—
500#41—1062no—
501#41—1062no—
502#41—1062no—
503#41—1062no—
504#41—1062no—
505#41—1062no—
506#41—1062no—
507#41—1062no—
508#41—1062no—
509#41—1062no—
510C2×Q8—532no—
511C2×Q8—532no—
512C2×Q8—532no—
513C2×Q8—1061no—
514C2×Q8—1061no—
515C2×Q8—1061no—
516C2×D4—532no—
517C2×D4—532no—
518C2×D4—532no—
519C2×D4—1062no—
520C2×D4—1062no—
521C2×D4—1062no—
522C2×D4—1062no—
523C2×D4—1062no—
524C2×D4—1062no—
525C2×D4—1061no—
526C2×D4—1061no—
527C2×D4—1061no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—1068no—
533C22×C4—1061no—
534C22×C4—1062no—
535C22×C4—1062no—
536C22×C4—1062no—
537C22×C4—1062no—
538C22×C4—1062no—
539C22×C4—1062no—
540C22×C4—1062no—
541C22×C4—1062no—
542C22×C4—1062no—
543C22×C4—1061no—
544C22×C4—1061no—
545C22×C4—1062no—
546C22×C4—4242no—
547C22×C4—4242no—
548C22×C4—2122no—
549C22×C4—2122no—
550C22×C4—2121no—
551C22×C4—2121no—
552C22×C4—2121no—
553C22×C4—2121no—
554C22×C4—2121no—
555C22×C4—2121no—
556C22×C4#1171992114yes—
557C22×C4C2×C4×D5311yescharacteristic
558C22×C4C2×C4×D5311yescharacteristic
559C22×C4C2×C4×D5311yescharacteristic
560C22×C4#1171994511yescharacteristic
561C22×C4#1171994511yescharacteristic
562C22×C4D4×D5311yescharacteristic
563C22×C4D4×D5311yescharacteristic
564C22×C4D4×D5311yescharacteristic
565C22×C4D4×D5311yescharacteristic
566C22×C4D4×D5311yescharacteristic
567C22×C4#1171994711yescharacteristic
568C22×C4Q8×D5311yescharacteristic
569C22×C4#1171994911yescharacteristic
570C22×C4C2×C22⋊D5311yescharacteristic
571M16—22no—
572M16—22no—
573M16—22no—
574M16—22no—
575M16—41no—
576M16—41no—
577M16—41no—
578M16—41no—
579C2×C8—22no—
580C2×C8—22no—
581C2×C8—41no—
582C2×C8—41no—
583C2×C8—41no—
584C2×C8—41no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—532no—
590C4⋊C4—532no—
591C4⋊C4—1068no—
592C4⋊C4—1061no—
593C4⋊C4—1061no—
594C4⋊C4—1062no—
595C4⋊C4—1062no—
596C4⋊C4—2121no—
597C4⋊C4—2121no—
598C22⋊C4—1068no—
599C22⋊C4—1062no—
600C22⋊C4—1062no—
601C42—1068no—
602C42—1062no—
603C42—1062no—
604C42—1062no—
605C42—1062no—
606C42—2121no—
607C42—2121no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—1062no—
613C23—1062no—
614C23—1062no—
615C23—2121no—
616C23—2121no—
617C23—2121no—
618C23—2121no—
619C23C2×#1171992111yescharacteristic
620C23C4×D21211yescharacteristic
621C23C4×D21211yescharacteristic
622C23#1313318711yescharacteristic
623C23#1313318711yescharacteristic
624C23#1313319211yescharacteristic
625C23#1313319711yescharacteristic
626Q8—534no—
627Q8—1062no—
628Q8—1062no—
629Q8—1062no—
630D4—534no—
631D4—1064no—
632D4—1064no—
633D4—1064no—
634D4—1064no—
635D4—1062no—
636D4—1062no—
637D4—1062no—
638C2×C4—24no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—44no—
642C2×C4—82no—
643C2×C4—1062no—
644C2×C4—1062no—
645C2×C4—1062no—
646C2×C4—1064no—
647C2×C4—1064no—
648C2×C4—1064no—
649C2×C4—1064no—
650C2×C4—1064no—
651C2×C4—1062no—
652C2×C4—1062no—
653C2×C4—4248no—
654C2×C4—4242no—
655C2×C4—4241no—
656C2×C4—4241no—
657C2×C4—2124no—
658C2×C4—2122no—
659C2×C4—2122no—
660C2×C4—2122no—
661C2×C4—2122no—
662C2×C4—2122no—
663C2×C4—2122no—
664C2×C4—2122no—
665C2×C4—2121no—
666C2×C4—2121no—
667C2×C4—2121no—
668C2×C4—2121no—
669C2×C4C42×D5311yescharacteristic
670C2×C4C22⋊C4×D5311yescharacteristic
671C2×C4C22⋊C4×D5311yescharacteristic
672C2×C4C22⋊C4×D5311yescharacteristic
673C2×C4C22⋊C4×D5311yescharacteristic
674C2×C4C4⋊C4×D5311yescharacteristic
675C2×C4C4⋊C4×D5311yescharacteristic
676C2×C4C4⋊C4×D5311yescharacteristic
677C2×C4#1313317411yescharacteristic
678C2×C4#1313317511yescharacteristic
679C2×C4#1313317711yescharacteristic
680C2×C4#1313317711yescharacteristic
681C2×C4C4×C22⋊D5311yescharacteristic
682C2×C4C4×C22⋊D5311yescharacteristic
683C2×C4#1313317911yescharacteristic
684C2×C4#1313317911yescharacteristic
685C2×C4#1313318511yescharacteristic
686C2×C4#1313318511yescharacteristic
687C2×C4#1313318811yescharacteristic
688C2×C4#1313319011yescharacteristic
689C2×C4#1313319011yescharacteristic
690C2×C4#1313319311yescharacteristic
691C2×C4#1313319511yescharacteristic
692C2×C4#1313319511yescharacteristic
693C2×C4#1313319911yescharacteristic
694C2×C4#1313319911yescharacteristic
695C2×C4#1313320211yescharacteristic
696C2×C4#1313320211yescharacteristic
697C8—42no—
698C8—42no—
699C22—21no—
700C22—21no—
701C22—21no—
702C22—21no—
703C22—21no—
704C22—21no—
705C22—21no—
706C22—21no—
707C22—21no—
708C22—21no—
709C22—21no—
710C22—21no—
711C22—1064no—
712C22—2122no—
713C22—2122no—
714C22—2122no—
715C22—2122no—
716C22—2122no—
717C22—2122no—
718C22C4×#1171992111yescharacteristic
719C22#1681047811yescharacteristic
720C22#1681048011yescharacteristic
721C22#1681049711yescharacteristic
722C22#1681049711yescharacteristic
723C22#1681050111yescharacteristic
724C22#1681050111yescharacteristic
725C22#1681079311yescharacteristic
726C22#1681079811yescharacteristic
727C22#1681080311yescharacteristic
728C22#1681080811yescharacteristic
729C4—44no—
730C4—1064no—
731C4—4242no—
732C4—2124no—
733C4—2122no—
734C4—2122no—
735C4#95×D5311yescharacteristic
736C4#1681047011yescharacteristic
737C4#1681048211yescharacteristic
738C4#1681048511yescharacteristic
739C4#1681049411yescharacteristic
740C4#1681049411yescharacteristic
741C4#1681049911yescharacteristic
742C4#1681049911yescharacteristic
743C2—21no—
744C2—21no—
745C2—21no—
746C2—21no—
747C2—2124no—
748C2#2027293611yescharacteristic
749C2#2027467111yescharacteristic
750C2#2027467611yescharacteristic
751C2#2027494411yescharacteristic
752C2#2027495111yescharacteristic
753C2#2027508311yescharacteristic
754C2#2027509011yescharacteristic
subgroupG/H
centerC23#13133187
commutatorC2×C4×C53C2×C42
FrattiniC23×C4C22×D53
FittingC2×C53×#343C2
socleC23×C53#120
prime radicalC22×#11719945C22
cosocleC23×C4×C53C23
hypercenterC2×#343D53
hypocenterC53#10781
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#343

Complements

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

NH ≅ G/Ntype
4. #20274435C2semidirect
5. C2×#16810384C2semidirect
6. #20272944C2semidirect
7. C2×C53×#343C2semidirect
12. #16811104C4semidirect
23. C2×#13133143C4semidirect
25. #16810625C4semidirect
72. C2×C4⋊Dic53C2×C4semidirect
87. C2×C4×Dic53C2×C4semidirect
104. C2×M16×C53C2×C4semidirect
105. C2×M16×C53C2×C4semidirect
309. D212#95semidirect
318. Dic106#95semidirect
369. C2×#343D53semidirect
413. C53#10781semidirect
445. C2×M16C4×D53semidirect
446. C2×M16C4×D53semidirect

Maximal subgroups

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

subgroupindex
C2×#168111042
C22×#131331432
C2×#168106252
#202744352
C2×#168103842
#202729442
C2×C53×#3432
#1078153