Finite Group Databasebeta

← #27400347

Subgroups — #27400347

Order 13568.

1226 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811321C211yesmaximal, characteristic
2C2×#16810686C211yesmaximal, characteristic, complemented
3#20277646C211yesmaximal, characteristic, complemented
4#20275678C211yesmaximal, characteristic, complemented
5#20275669C211yesmaximal, characteristic, complemented
6#20275142C211yesmaximal, characteristic, complemented
7#20275141C211yesmaximal, characteristic, complemented
8#20275036C211yesmaximal, characteristic, complemented
9#20275030C211yesmaximal, characteristic, complemented
10#20274809C211yesmaximal, characteristic, complemented
11#20274724C211yesmaximal, characteristic, complemented
12#20274529C211yesmaximal, characteristic, complemented
13#20274430C211yesmaximal, characteristic, complemented
14C2×#16810385C211yesmaximal, characteristic, complemented
15C53×#1824C211yesmaximal, characteristic, complemented
16C23×#88322C2211yescharacteristic
17C22×C8×D53C2211yescharacteristic
18#16811321—24no—
19#16811321C418yescomplemented
20C2×#13133212—21no—
21C2×#13133208C2211yescharacteristic
22C2×#13133202—21no—
23C2×#13133192C2211yescharacteristic
24C2×#13133191—21no—
25C2×#13133191C2211yescharacteristic
26C2×#13133179C2211yescharacteristic
27C2×C4×C22⋊D53—21no—
28C2×C4×C22⋊D53C2211yescharacteristic
29C2×#13133175C2211yescharacteristic
30C2×#13133175C2211yescharacteristic
31C22×C4⋊Dic53C2211yescharacteristic
32#16810686—24no—
33C2×#13133146C2211yescharacteristic
34C2×#13133139C2211yescharacteristic
35C2×#13133139C2211yescharacteristic
36C2×#13133137C2211yescharacteristic
37C2×#13133137C2211yescharacteristic
38C2×#13133129C2211yescharacteristic
39C2×C8×Dic53C2211yescharacteristic
40#16810515—21no—
41#16810510—21no—
42#16810500—21no—
43#16810488C2211yescharacteristic
44#16810480C2211yescharacteristic
45C4⋊C4×Dic53C2211yescharacteristic
46C22⋊C4×Dic53—21no—
47#16810386C2211yescharacteristic
48#16810386C2211yescharacteristic
49#16810385C2211yescharacteristic
50#16810385C2211yescharacteristic
51#16810385C2211yescharacteristic
52#16810385C2211yescharacteristic
53#16810385C2211yescharacteristic
54#16810385C2211yescharacteristic
55C22×C4⋊C4×C53C2211yescharacteristic
56C2×C22⋊C8×C53C2211yescharacteristic
57C53×#380C2211yescharacteristic
58C53×#340C2211yescharacteristic
59C53×#340C2211yescharacteristic
60C53×#340C2211yescharacteristic
61C53×#340C2211yescharacteristic
62C22×D212—21no—
63C22×D212C2311yescharacteristic
64C22×C22⋊D53—21no—
65C22×C22⋊D53D411yescharacteristic
66C23×Dic53—21no—
67C22×C4×D53—21no—
68C22×C4×D53C2311yescharacteristic
69C22×#88322—22no—
70C22×#88322—22no—
71C22×#88322—41no—
72C22×#88322C2311yescharacteristic
73C22×#88322C2311yescharacteristic
74C2×C8×D53—22no—
75C2×C8×D53—22no—
76C2×C8×D53—41no—
77#13133212—28no—
78#13133208—22no—
79#13133208C2×C414yescomplemented
80#13133202—28no—
81#13133192—22no—
82#13133192C2×C414yescomplemented
83#13133191—22no—
84#13133191—28no—
85#13133191C2×C414yes—
86#13133179—22no—
87#13133179C2×C414yescomplemented
88C4×C22⋊D53—28no—
89C4×C22⋊D53C2×C414yes—
90C4×C22⋊D53D414yes—
91#13133175—22no—
92#13133175—22no—
93#13133175—41no—
94#13133175C2×C414yescomplemented
95C2×C4⋊Dic53—21no—
96C2×C4⋊Dic53—21no—
97C2×C4⋊Dic53—22no—
98C2×C4⋊Dic53—41no—
99C2×C4⋊Dic53C2311yescharacteristic
100C2×C4⋊Dic53C2311yescharacteristic
101C2×C4⋊Dic53C2311yescharacteristic
102C2×#11719919—21no—
103C2×#11719919D411yescharacteristic
104C2×C22⋊Dic53D411yescharacteristic
105C2×#11719921—21no—
106C2×#11719921—21no—
107C2×#11719921—21no—
108C2×#11719921—21no—
109C2×#11719921—21no—
110C2×#11719921—21no—
111C2×#11719921D411yescharacteristic
112C2×C4×Dic53—21no—
113C2×C4×Dic53—21no—
114C2×C4×Dic53—21no—
115C2×C4×Dic53C2311yescharacteristic
116#13133146—22no—
117#13133139—22no—
118#13133139—41no—
119#13133137—22no—
120#13133137—41no—
121#13133129—22no—
122C8×Dic53—22no—
123#13133124—21no—
124#13133124—21no—
125#13133124—21no—
126#13133124—21no—
127C23×C4×C53—21no—
128C23×C4×C53C2311yescharacteristic
129C22×C8×C53C2311yescharacteristic
130C22×C8×C53C2311yescharacteristic
131C2×C4⋊C4×C53—22no—
132C2×C4⋊C4×C53—21no—
133C2×C4⋊C4×C53C2×C414yes—
134C2×C4⋊C4×C53C2311yescharacteristic
135C2×C4⋊C4×C53C2311yescharacteristic
136C2×C4⋊C4×C53C2311yescharacteristic
137C2×C4⋊C4×C53C2311yescharacteristic
138C2×C22⋊C4×C53—21no—
139C22⋊C8×C53—22no—
140#95×C53—21no—
141C24×C53C2×D411yescharacteristic
142C23×D53—21no—
143C23×D53C2×D411yescharacteristic
144C22×C4×C53—21no—
145C22×C4×C53—21no—
146C22×C4×C53—21no—
147C22×C4×C53—21no—
148C22×C4×C53—21no—
149C22×C4×C53—21no—
150C22×C4×C53—24no—
151C22×C4×C53—21no—
152C22×C4×C53—21no—
153C22×C4×C53—81no—
154C22×C4×C53—81no—
155C22×C4×C53C22×C412yes—
156C22×C4×C53C2×D411yescharacteristic
157C22×C4×C53C2×D412yes—
158C22×C4×C53C2411yescharacteristic
159C2×C22⋊D53—22no—
160C2×C22⋊D53—22no—
161C2×C22⋊D53—24no—
162C2×C22⋊D53—42no—
163C2×C22⋊D53—42no—
164C2×C22⋊D53C22⋊C414yes—
165C22×Dic53—21no—
166C22×Dic53—21no—
167C22×Dic53—21no—
168C22×Dic53—42no—
169C22×Dic53—42no—
170C22×Dic53—81no—
171C22×Dic53C2×D411yescharacteristic
172C22×Dic53C2×D411yescharacteristic
173C22×Dic53C2×D411yescharacteristic
174C2×D212—21no—
175C2×D212—21no—
176C2×D212—21no—
177C2×D212—21no—
178C2×D212—21no—
179C2×D212—24no—
180C2×D212—81no—
181C2×D212—81no—
182C2×D212C22×C412yes—
183C2×C4×D53—21no—
184C2×C4×D53—21no—
185C2×C4×D53—21no—
186C2×C4×D53—21no—
187C2×C4×D53—24no—
188C2×C4×D53—81no—
189C2×C4×D53—81no—
190C2×C4×D53C22×C412yes—
191C2×C4×D53C2×D412yes—
192C2×C8×C53—21no—
193C2×C8×C53—21no—
194C2×C8×C53—21no—
195C2×C8×C53—21no—
196C2×C8×C53—21no—
197C2×C8×C53—21no—
198C4⋊C4×C53—24no—
199C4⋊C4×C53—21no—
200C4⋊C4×C53—21no—
201C4⋊C4×C53—21no—
202C4⋊C4×C53—21no—
203C4⋊C4×C53—21no—
204C4⋊C4×C53—21no—
205C4⋊C4×C53C22×C412yes—
206C4⋊C4×C53C22×C412yes—
207C22⋊C4×C53—42no—
208C22⋊Dic53C22⋊C414yes—
209#11719921—24no—
210#11719921—24no—
211#11719921—24no—
212#11719921—24no—
213#11719921—42no—
214#11719921—81no—
215#11719921C22⋊C414yes—
216C4⋊Dic53—21no—
217C4⋊Dic53—21no—
218C4⋊Dic53—24no—
219C4⋊Dic53—21no—
220C4⋊Dic53—21no—
221C4⋊Dic53—42no—
222C4⋊Dic53C22×C412yes—
223C4⋊Dic53#4112yes—
224#11719919—24no—
225#11719919C22⋊C414yes—
226C4×Dic53—24no—
227C4×Dic53—42no—
228C4×Dic53—81no—
229C4×Dic53C22×C412yes—
230C4×Dic53C2×D412yes—
231C2×#88322—21no—
232C2×#88322—21no—
233C2×#88322—21no—
234C2×#88322—21no—
235C2×#88322—21no—
236C2×#88322—44no—
237C2×#88322#4112yes—
238C8×D53—44no—
239C23×C53—21no—
240C23×C53—21no—
241C23×C53—21no—
242C23×C53—21no—
243C23×C53C2×C22⋊C412yes—
244C23×C53#13512yes—
245C23×C53#13512yes—
246C23×C53C22×D411yescharacteristic
247C22×D53—21no—
248C22×D53—21no—
249C22×D53—21no—
250C22×D53—21no—
251C22×D53—21no—
252C22×D53—21no—
253C22×D53—22no—
254C22×D53—41no—
255C22×D53—41no—
256C22×D53—41no—
257C22×D53—41no—
258C22×D53—41no—
259C22×D53—41no—
260C22×D53C2×C22⋊C412yes—
261C2×C4×C53—21no—
262C2×C4×C53—21no—
263C2×C4×C53—22no—
264C2×C4×C53—22no—
265C2×C4×C53—22no—
266C2×C4×C53—22no—
267C2×C4×C53—22no—
268C2×C4×C53—22no—
269C2×C4×C53—41no—
270C2×C4×C53—41no—
271C2×C4×C53—41no—
272C2×C4×C53—41no—
273C2×C4×C53—41no—
274C2×C4×C53—41no—
275C2×C4×C53—41no—
276C2×C4×C53—41no—
277C2×C4×C53—41no—
278C2×C4×C53—41no—
279C2×C4×C53—84no—
280C2×C4×C53C2×C22⋊C412yes—
281C2×C4×C53C23×C411yescharacteristic
282C2×C4×C53C22×D411yescharacteristic
283C2×C4×C53C2×#4111yescharacteristic
284C2×C4×C53C2×#4111yescharacteristic
285C2×C4×C53H(5,𝔽2)11yescharacteristic
286C2×C4×C532−1+411yescharacteristic
287C22⋊D53—28no—
288C22⋊D53—48no—
289C2×Dic53—21no—
290C2×Dic53—21no—
291C2×Dic53—21no—
292C2×Dic53—21no—
293C2×Dic53—21no—
294C2×Dic53—21no—
295C2×Dic53—22no—
296C2×Dic53—22no—
297C2×Dic53—41no—
298C2×Dic53—41no—
299C2×Dic53—41no—
300C2×Dic53—41no—
301C2×Dic53—41no—
302C2×Dic53—41no—
303C2×Dic53—41no—
304C2×Dic53—84no—
305C2×Dic53C2×C22⋊C412yes—
306C2×Dic53C2×C22⋊C412yes—
307C2×Dic53C2×C22⋊C412yes—
308D212—22no—
309D212—22no—
310D212—41no—
311D212—41no—
312D212—84no—
313C4×D53—22no—
314C4×D53—22no—
315C4×D53—22no—
316C4×D53—22no—
317C4×D53—84no—
318C8×C53—41no—
319C8×C53—41no—
320#88322—22no—
321#88322—41no—
322#22488—531nomaximal, Sylow
323C22×C53—22no—
324C22×C53—22no—
325C22×C53—22no—
326C22×C53—22no—
327C22×C53—22no—
328C22×C53—22no—
329C22×C53#41614yes—
330C22×C53C22×C22⋊C411yescharacteristic
331C22×C53#54611yescharacteristic
332C22×C53#54711yescharacteristic
333C22×C53C2×#13511yescharacteristic
334C22×C53C2×#13511yescharacteristic
335C22×C53#57611yescharacteristic
336C22×C53#57711yescharacteristic
337C2×D53—22no—
338C2×D53—22no—
339C2×D53—22no—
340C2×D53—41no—
341C2×D53—41no—
342C2×D53—41no—
343C2×D53—41no—
344C2×D53—42no—
345C2×D53—42no—
346C2×D53—42no—
347C2×D53—81no—
348C2×D53—81no—
349C2×D53—81no—
350C2×D53—81no—
351C4×C53—22no—
352C4×C53—42no—
353C4×C53—42no—
354C4×C53—81no—
355C4×C53—81no—
356C4×C53C4×#4111yescharacteristic
357C4×C53#52011yescharacteristic
358C4×C53#54611yescharacteristic
359C4×C53#54711yescharacteristic
360Dic53—22no—
361Dic53—22no—
362Dic53—22no—
363Dic53—42no—
364Dic53—42no—
365Dic53—81no—
366C2×#553—531no—
367C2×C8×D4—531no—
368#2352—531no—
369#1991—531no—
370#1989—531no—
371#1893—531no—
372#1893—531no—
373#1875—531no—
374#1874—531no—
375#1825—531no—
376#1824D5311yescharacteristic, complemented
377#1804—531no—
378C4×#102—531no—
379#1735—531no—
380C2×#340—531no—
381C2×C53—24no—
382C2×C53#233911yescharacteristic
383C2×C53C2×#41611yescharacteristic
384C2×C53#289711yescharacteristic
385C2×C53#329711yescharacteristic
386C2×C53#330111yescharacteristic
387C2×C53#333711yescharacteristic
388C2×C53#333911yescharacteristic
389D53—42no—
390D53—82no—
391C23×C8—531no—
392C23×C8—531no—
393#553—538no—
394#553—1064no—
395C2×#126—1061no—
396C2×#125—531no—
397C2×#123—1061no—
398C2×#121—531no—
399C2×#121—531no—
400C2×#121—1061no—
401C2×C4×D4—531no—
402C2×C4×D4—531no—
403C2×C4×D4—1061no—
404C2×#117—531no—
405C2×#117—531no—
406C22×C4⋊C4—531no—
407C22×C4⋊C4C2×D5311yescharacteristic
408C8×D4—1064no—
409C2×C4⋊C8—531no—
410C2×#102—531no—
411C2×#102—531no—
412C2×#102—531no—
413C2×#102—531no—
414C2×C22⋊C8—531no—
415C2×C22⋊C8C2×D5311yescharacteristic
416C2×C4×C8—531no—
417#388—1061no—
418#387—1061no—
419#386—1061no—
420#382—531no—
421#380—531no—
422#380C2×D5311yescharacteristic
423C4×C4⋊C4—531no—
424C4×C22⋊C4—1061no—
425#340—531no—
426#340—531no—
427#340—531no—
428#340—531no—
429#340—531no—
430#340—531no—
431#340—531no—
432#340—531no—
433#340C2×D5311yescharacteristic
434#340C2×D5311yescharacteristic
435#340C2×D5311yescharacteristic
436#340C2×D5311yescharacteristic
437C53#2248811yescharacteristic, complemented, Sylow
438C22×D4—531no—
439C22×D4—531no—
440C22×D4—1061no—
441C22×D4—1061no—
442C23×C4—21no—
443C23×C4—531no—
444C23×C4—1061no—
445C23×C4—1061no—
446C23×C4C22×D5311yescharacteristic
447C22×C8—531no—
448C22×C8—531no—
449C22×C8—1062no—
450C22×C8—1062no—
451C22×C8—1062no—
452C22×C8—1062no—
453C22×C8—2121no—
454C22×C8—2121no—
455C22×C8C22×D5311yescharacteristic
456C22×C8C22×D5311yescharacteristic
457#126—1068no—
458#125—534no—
459#125—1062no—
460#123—1068no—
461#121—534no—
462#121—534no—
463#121—1062no—
464#121—1068no—
465#121—1062no—
466C4×D4—534no—
467C4×D4—534no—
468C4×D4—534no—
469C4×D4—1062no—
470C4×D4—1068no—
471#117—534no—
472#117—1062no—
473#117—1062no—
474#117—2121no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—531no—
478C2×C4⋊C4—531no—
479C2×C4⋊C4—531no—
480C2×C4⋊C4—531no—
481C2×C4⋊C4—1062no—
482C2×C4⋊C4—1061no—
483C2×C4⋊C4—1061no—
484C2×C4⋊C4—1061no—
485C2×C4⋊C4—2121no—
486C2×C4⋊C4C4×D5314yes—
487C2×C4⋊C4C22×D5311yescharacteristic
488C2×C4⋊C4C22×D5311yescharacteristic
489C2×C4⋊C4C22×D5311yescharacteristic
490C2×C4⋊C4C22×D5311yescharacteristic
491C2×C22⋊C4—21no—
492C2×C22⋊C4—531no—
493C2×C22⋊C4—531no—
494C2×C22⋊C4—1061no—
495C2×C22⋊C4—1061no—
496C2×C22⋊C4—1061no—
497C2×C22⋊C4—1061no—
498C2×C22⋊C4—1061no—
499C2×C22⋊C4—1061no—
500C2×C42—531no—
501C2×C42—1061no—
502C2×C42—1061no—
503C2×C42—1061no—
504C4⋊C8—1062no—
505#102—1062no—
506#102—1062no—
507#102—2121no—
508#102—2121no—
509C22⋊C8—22no—
510C22⋊C8—1062no—
511C4×C8—1062no—
512#95—21no—
513#95—1061no—
514#95—1061no—
515#95—1061no—
516#95—1061no—
517C24—531no—
518C24—1061no—
519C24D4×D5311yescharacteristic
520C2×D4—534no—
521C2×D4—532no—
522C2×D4—1064no—
523C2×D4—1062no—
524C2×D4—1062no—
525C2×D4—1064no—
526C2×D4—1061no—
527C2×D4—1061no—
528C2×D4—1061no—
529C2×D4—1061no—
530C2×D4—1061no—
531C2×D4—4241no—
532C2×D4—4241no—
533C2×D4—2122no—
534C2×D4—2122no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—24no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—81no—
545C22×C4—81no—
546C22×C4—531no—
547C22×C4—531no—
548C22×C4—531no—
549C22×C4—532no—
550C22×C4—532no—
551C22×C4—1064no—
552C22×C4—1061no—
553C22×C4—1061no—
554C22×C4—1061no—
555C22×C4—1061no—
556C22×C4—1061no—
557C22×C4—1061no—
558C22×C4—1061no—
559C22×C4—4241no—
560C22×C4—4241no—
561C22×C4—4241no—
562C22×C4—2122no—
563C22×C4—2122no—
564C22×C4C2×C4×D5312yes—
565C22×C4D4×D5311yescharacteristic
566C22×C4D4×D5312yes—
567C22×C4C23×D5311yescharacteristic
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—532no—
575C2×C8—1061no—
576C2×C8—1061no—
577C2×C8—1061no—
578C2×C8—1061no—
579C2×C8—1061no—
580C2×C8—2124no—
581C2×C8—2124no—
582C4⋊C4—24no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—534no—
590C4⋊C4—532no—
591C4⋊C4—532no—
592C4⋊C4—1064no—
593C4⋊C4—1064no—
594C4⋊C4—1061no—
595C4⋊C4—1061no—
596C4⋊C4—1061no—
597C4⋊C4—1061no—
598C4⋊C4—2122no—
599C4⋊C4C2×C4×D5312yes—
600C4⋊C4C2×C4×D5312yes—
601C22⋊C4—42no—
602C22⋊C4—534no—
603C22⋊C4—534no—
604C22⋊C4—1064no—
605C22⋊C4—1064no—
606C22⋊C4—1064no—
607C22⋊C4—1064no—
608C22⋊C4—4241no—
609C22⋊C4—2122no—
610C42—532no—
611C42—532no—
612C42—1064no—
613C42—4241no—
614C42—2122no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—532no—
620C23—1061no—
621C23—1061no—
622C23—1061no—
623C23—1061no—
624C23—1061no—
625C23—1061no—
626C23—1062no—
627C23—2121no—
628C23—2121no—
629C23—2121no—
630C23—2121no—
631C23—2121no—
632C23—2121no—
633C23C22⋊C4×D5312yes—
634C23#1313323812yes—
635C23#1313324012yes—
636C23C2×D4×D5311yescharacteristic
637D4—1068no—
638D4—1062no—
639D4—1062no—
640D4—4244no—
641D4—2128no—
642D4—2121no—
643D4—2121no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—84no—
663C2×C4—532no—
664C2×C4—532no—
665C2×C4—532no—
666C2×C4—1061no—
667C2×C4—1061no—
668C2×C4—1061no—
669C2×C4—1061no—
670C2×C4—1061no—
671C2×C4—1061no—
672C2×C4—1062no—
673C2×C4—1062no—
674C2×C4—1062no—
675C2×C4—1062no—
676C2×C4—1062no—
677C2×C4—1062no—
678C2×C4—4244no—
679C2×C4—4244no—
680C2×C4—2121no—
681C2×C4—2121no—
682C2×C4—2121no—
683C2×C4—2121no—
684C2×C4—2121no—
685C2×C4—2121no—
686C2×C4—2121no—
687C2×C4C22⋊C4×D5312yes—
688C2×C4C22×C4×D5311yescharacteristic
689C2×C4C2×D4×D5311yescharacteristic
690C2×C4#41×D5311yescharacteristic
691C2×C4#41×D5311yescharacteristic
692C2×C4#1313326311yescharacteristic
693C2×C4#1313326411yescharacteristic
694C8—41no—
695C8—41no—
696C8—1062no—
697C8—2121no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—1062no—
705C22—1062no—
706C22—1062no—
707C22—4241no—
708C22—4241no—
709C22—4241no—
710C22—4241no—
711C22—2122no—
712C22—2122no—
713C22—2122no—
714C22—2121no—
715C22—2121no—
716C22—2121no—
717C22—2121no—
718C22#1681061814yes—
719C22C2×C22⋊C4×D5311yescharacteristic
720C22#1681126511yescharacteristic
721C22#1681127111yescharacteristic
722C22C2×#1313323811yescharacteristic
723C22C2×#1313324011yescharacteristic
724C22#1681142711yescharacteristic
725C22#1681143311yescharacteristic
726C4—22no—
727C4—42no—
728C4—42no—
729C4—81no—
730C4—81no—
731C4—1062no—
732C4—1062no—
733C4—1062no—
734C4—4241no—
735C4—2122no—
736C4—2122no—
737C4#1681109111yescharacteristic
738C4#1681110311yescharacteristic
739C4#1681126511yescharacteristic
740C4#1681127111yescharacteristic
741C2—24no—
742C2—4242no—
743C2—2122no—
744C2#2027753911yescharacteristic
745C2C2×#1681061811yescharacteristic
746C2#2028324011yescharacteristic
747C2#2028656311yescharacteristic
748C2#2028661511yescharacteristic
749C2#2028709211yescharacteristic
750C2#2028711511yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1824C2
socleC23×C53C22×D4
prime radicalC2×#16811321C2
cosocleC22×C4×C53C24
hypercenter#1824D53
hypocenterC53#22488
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1824

Complements

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

NH ≅ G/Ntype
2. C2×#16810686C2semidirect
3. #20277646C2semidirect
4. #20275678C2semidirect
5. #20275669C2semidirect
6. #20275142C2semidirect
7. #20275141C2semidirect
8. #20275036C2semidirect
9. #20275030C2semidirect
10. #20274809C2semidirect
11. #20274724C2semidirect
12. #20274529C2semidirect
13. #20274430C2semidirect
14. C2×#16810385C2semidirect
15. C53×#1824C2semidirect
19. #16811321C4semidirect
79. #13133208C2×C4semidirect
82. #13133192C2×C4semidirect
87. #13133179C2×C4semidirect
94. #13133175C2×C4semidirect
376. #1824D53semidirect
437. C53#22488semidirect

Maximal subgroups

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

subgroupindex
C2×#168113212
C2×#168106862
#202776462
#202756782
#202756692
#202751422
#202751412
#202750362
#202750302
#202748092
#202747242
#202745292
#202744302
C2×#168103852
C53×#18242
#2248853