Finite Group Databasebeta

← C2×#20288372 #28292335

Subgroups — C2×#20288372 #28292335

Order 13568.

11510 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133265C211yesmaximal, characteristic, complemented
2C22×#41×D53C211yesmaximal, characteristic, complemented
3#20288372C2132yesmaximal, direct product factor
4C2×#16811295C211yesmaximal, characteristic, complemented
5C2×#16811294C213yesmaximal, complemented
6C2×#16811292C211yesmaximal, characteristic, complemented
7C2×#16811291C213yesmaximal, complemented
8C2×#16811284C211yesmaximal, characteristic, complemented
9C2×#16811283C213yesmaximal, complemented
10C2×#16811281C213yesmaximal, complemented
11C2×#16811191C213yesmaximal, complemented
12C2×#16811189C213yesmaximal, complemented
13C2×#16811136C213yesmaximal, complemented
14C2×#16811132C213yesmaximal, complemented
15C2×#16811099C211yesmaximal, characteristic, complemented
16C2×C53×#548C211yesmaximal, characteristic, complemented
17C2×#13133265—216no—
18C2×#13133265C22116yescomplemented
19C22×#11719949C2213yes—
20C22×#11719949C2211yescharacteristic
21C22×#11719949C2211yescharacteristic, complemented
22C22×#11719945C2213yes—
23C22×#11719945C2213yes—
24C22×#11719945C2213yescomplemented
25C22×#11719947C2213yes—
26C2×#41×D53—216no—
27C2×#41×D53C22116yescomplemented
28C22×Q8×D53C2211yescharacteristic
29C22×Q8×D53C2213yescomplemented
30C22×D4×D53C2213yes—
31C23×C4×D53C2213yes—
32#16811295C22116yescomplemented
33#16811294C22148yescomplemented
34#16811292C22116yescomplemented
35#16811291C22148yescomplemented
36#16811284C22116yescomplemented
37#16811283C22148yescomplemented
38#16811281C22148yescomplemented
39#16811191C22148yescomplemented
40#16811189C22148yescomplemented
41C2×#13133214C2213yescomplemented
42C2×#13133213C2216yescomplemented
43C2×#13133213C2213yescomplemented
44C2×#13133206C2213yescomplemented
45C2×#13133203C2216yescomplemented
46#16811136C22148yescomplemented
47#16811132C22148yescomplemented
48C2×#13133202C2213yes—
49C2×#13133199C2211yescharacteristic
50C2×#13133195C2213yescomplemented
51C2×#13133194C2213yescomplemented
52C2×#13133193C2213yescomplemented
53C2×#13133192C2213yescomplemented
54C2×#13133192C2213yescomplemented
55C2×#13133191C2213yescomplemented
56C2×#13133191C2213yescomplemented
57C2×#13133190C2216yescomplemented
58C2×#13133190C2216yescomplemented
59C2×#13133190C2213yescomplemented
60C2×#13133189C2213yescomplemented
61C2×#13133188C2213yescomplemented
62C2×#13133187C2216yes—
63C2×#13133187C2213yes—
64C2×#13133185C2213yes—
65#16811099C22116yescomplemented
66C2×Q8×Dic53C2211yescharacteristic, complemented
67C2×C4×Dic106C2213yescomplemented
68C2×#13133182C2213yescomplemented
69C2×C4×D212C2213yescomplemented
70C2×#13133179C2216yescomplemented
71C2×C4×C22⋊D53C2213yescomplemented
72C2×C4×C22⋊D53C2213yescomplemented
73C2×#13133177C2216yescomplemented
74C2×#13133175C2213yes—
75C2×#13133174C2213yes—
76C22×#41×C53C2211yescharacteristic
77C23×Q8×C53C2211yescharacteristic, complemented
78C53×#548C22116yescomplemented
79C2×#124×C53C2213yescomplemented
80C2×C22⋊Q8×C53C2213yescomplemented
81C2×#121×C53C2213yescomplemented
82C2×C4×Q8×C53C2211yescharacteristic, complemented
83C2×C4×D4×C53C2213yescomplemented
84C24×D53C2313yes—
85#13133265—2128no—
86C2×#11719949—28no—
87C2×#11719949—28no—
88C2×#11719949—224no—
89C2×#11719949C2318yes—
90C2×#11719949C23124yes—
91C2×#11719949C2318yescomplemented
92C2×#11719945—224no—
93C2×#11719945—224no—
94C2×#11719945—224no—
95C2×#11719945C23124yes—
96C2×#11719945C23124yes—
97C2×#11719945C23124yescomplemented
98C2×#11719947—224no—
99C2×#11719947C23124yes—
100#41×D53—2128no—
101C22×Dic106C2313yes—
102C22×Dic106C2313yes—
103C2×Q8×D53—224no—
104C2×Q8×D53D4116yescomplemented
105C2×Q8×D53C2318yes—
106C2×Q8×D53C23124yescomplemented
107C22×D212C2313yes—
108C22×D212C2313yes—
109C22×D212C2313yes—
110C22×D212C2316yes—
111C22×D212C2313yes—
112C22×C22⋊D53C2311yescharacteristic
113C22×C22⋊D53C2313yes—
114C22×C22⋊D53C2316yes—
115C22×C22⋊D53C2316yes—
116C22×C22⋊D53C2313yes—
117C22×C22⋊D53C2313yes—
118C2×D4×D53—224no—
119C2×D4×D53C23124yes—
120C23×Dic53C2313yes—
121C22×C4×D53—224no—
122C22×C4×D53C2316yes—
123C22×C4×D53C2313yes—
124C22×C4×D53C2313yes—
125C22×C4×D53C2313yes—
126C22×C4×D53C2311yescharacteristic
127C22×C4×D53C23124yes—
128C22×C4×D53C2313yes—
129#13133214C23124yescomplemented
130#13133213C23124yescomplemented
131#13133213C23148yescomplemented
132#13133206C23124yescomplemented
133#13133203C23148yescomplemented
134#13133202C23124yes—
135#13133199C2318yes—
136#13133195C23124yescomplemented
137#13133194C23124yescomplemented
138#13133193C23124yescomplemented
139#13133192C23124yescomplemented
140#13133192C23124yescomplemented
141#13133191C23124yescomplemented
142#13133191C23124yescomplemented
143#13133190C23148yescomplemented
144#13133190C23148yescomplemented
145#13133190C23124yescomplemented
146#13133189C23124yescomplemented
147#13133188C23124yescomplemented
148#13133187C23124yes—
149#13133187C23148yes—
150#13133185C23124yes—
151Q8×Dic53C2318yescomplemented
152C4×Dic106C23124yescomplemented
153#13133182C23124yescomplemented
154C4×D212C23124yescomplemented
155#13133179C23148yescomplemented
156C4×C22⋊D53C23124yescomplemented
157C4×C22⋊D53C23124yescomplemented
158#13133177C23148yescomplemented
159#13133175C23124yes—
160#13133174C23124yes—
161C2×C4⋊Dic53C2313yes—
162C2×C4⋊Dic53C2311yescharacteristic
163C2×#11719919C2313yes—
164C2×#11719919C2313yes—
165C2×#11719919C2313yes—
166C2×#11719919C2311yescharacteristic
167C2×C22⋊Dic53C2311yescharacteristic
168C2×C22⋊Dic53C2313yes—
169C2×#11719921C2311yescharacteristic
170C2×#11719921C2313yes—
171C2×#11719921C2313yes—
172C2×#11719921C2313yes—
173C2×#11719921C2313yes—
174C2×#11719921C2316yes—
175C2×#11719921C2313yes—
176C2×C4×Dic53C2313yes—
177C2×C4×Dic53C2316yes—
178C2×#41×C53—28no—
179C2×#41×C53C2318yes—
180C22×Q8×C53—28no—
181C22×Q8×C53C2313yes—
182C22×Q8×C53C2311yescharacteristic
183C22×Q8×C53C2318yescomplemented
184C22×D4×C53C2313yes—
185C22×D4×C53C2313yes—
186C23×C4×C53C2313yes—
187C23×C4×C53C2313yes—
188#124×C53C23124yescomplemented
189C22⋊Q8×C53C23124yescomplemented
190#121×C53C23124yescomplemented
191C4×Q8×C53C2318yescomplemented
192C4×D4×C53C23124yescomplemented
193C2×C4⋊C4×C53C2313yes—
194C2×C4⋊C4×C53C2313yes—
195C2×C22⋊C4×C53C2311yescharacteristic
196C2×C22⋊C4×C53C2313yes—
197C2×C22⋊C4×C53C2316yes—
198C2×C42×C53C2313yes—
199C24×C53C2413yes—
200C24×C53C2411yescharacteristic
201C23×D53—212no—
202C23×D53—46no—
203C23×D53—46no—
204C23×D53C2413yes—
205C23×D53C2413yes—
206C23×D53C2411yescharacteristic
207C23×D53C24112yes—
208#41×C53—232no—
209C2×Q8×C53—232no—
210C2×Q8×C53—212no—
211C2×Q8×C53C2×D418yes—
212C2×Q8×C53C24112yes—
213C2×Q8×C53C2414yes—
214C2×D4×C53—212no—
215C2×D4×C53—46no—
216C2×D4×C53C24112yes—
217C2×D4×C53C24112yes—
218C22×C4×C53—212no—
219C22×C4×C53—212no—
220C22×C4×C53C2411yescharacteristic
221C22×C4×C53C2413yes—
222C22×C4×C53C2413yes—
223C22×C4×C53C2411yescharacteristic
224C22×C4×C53C24112yes—
225C22×C4×C53C24112yes—
226C22×C4×C53C2413yes—
227C2×C22⋊D53—24no—
228C2×C22⋊D53—224no—
229C2×C22⋊D53—212no—
230C2×C22⋊D53—46no—
231C2×C22⋊D53—412no—
232C2×C22⋊D53—46no—
233C2×C22⋊D53C2414yes—
234C2×C22⋊D53C24112yes—
235C2×C22⋊D53C24124yes—
236C2×C22⋊D53C24124yes—
237C2×C22⋊D53C24112yes—
238C2×C22⋊D53C24112yes—
239C22×Dic53—212no—
240C22×Dic53C2411yescharacteristic
241C22×Dic53C2413yes—
242C22×Dic53C2411yescharacteristic
243C22×Dic53C2411yescharacteristic
244C22×Dic53C24112yes—
245C22×Dic53C2413yes—
246#11719949—232no—
247#11719949—232no—
248#11719949—296no—
249Q8×D53—296no—
250Q8×D53C2×D4164yescomplemented
251#11719947—296no—
252D4×D53—296no—
253#11719945—296no—
254#11719945—296no—
255#11719945—296no—
256C2×D212—212no—
257C2×D212—212no—
258C2×D212—212no—
259C2×D212—46no—
260C2×D212—412no—
261C2×D212C24112yes—
262C2×D212C24112yes—
263C2×D212C24112yes—
264C2×D212C24124yes—
265C2×D212C24112yes—
266C2×C4×D53—24no—
267C2×C4×D53—212no—
268C2×C4×D53—212no—
269C2×C4×D53—212no—
270C2×C4×D53—224no—
271C2×C4×D53—296no—
272C2×C4×D53C2×D4124yes—
273C2×C4×D53C24124yes—
274C2×C4×D53C24112yes—
275C2×C4×D53C24112yes—
276C2×C4×D53C24112yes—
277C2×C4×D53C2414yes—
278C2×C4×D53C24112yes—
279C2×Dic106—212no—
280C2×Dic106C2×D4124yes—
281C2×Dic106C24112yes—
282C2×Dic106C24112yes—
283C4⋊C4×C53C24112yes—
284C4⋊C4×C53C24112yes—
285C22⋊C4×C53C2414yes—
286C22⋊C4×C53C24112yes—
287C22⋊C4×C53C24124yes—
288C42×C53C24112yes—
289C22⋊Dic53C2414yes—
290C22⋊Dic53C24112yes—
291#11719921C2414yes—
292#11719921C24112yes—
293#11719921C24112yes—
294#11719921C24112yes—
295#11719921C24112yes—
296#11719921C24124yes—
297#11719921C24112yes—
298C4⋊Dic53C24112yes—
299C4⋊Dic53C2414yes—
300#11719919C24112yes—
301#11719919C24112yes—
302#11719919C24112yes—
303#11719919C2414yes—
304C4×Dic53C24112yes—
305C4×Dic53C24124yes—
306C23×C53—26no—
307C23×C53—22no—
308C23×C53—22no—
309C23×C53—26no—
310C23×C53—26no—
311C23×C53—22no—
312C23×C53C2516yes—
313C23×C53C2512yes—
314C23×C53C2511yescharacteristic
315C22×D53—22no—
316C22×D53—22no—
317C22×D53—26no—
318C22×D53—26no—
319C22×D53—26no—
320C22×D53—26no—
321C22×D53—26no—
322C22×D53—26no—
323C22×D53—224no—
324C22×D53—412no—
325C22×D53—412no—
326C22×D53—448no—
327C22×D53C22×D414yes—
328C22×D53C2516yes—
329C22×D53C2516yes—
330C22×D53C2512yes—
331Q8×C53—224no—
332Q8×C53C22×D4116yes—
333D4×C53—224no—
334D4×C53—412no—
335C2×C4×C53—26no—
336C2×C4×C53—22no—
337C2×C4×C53—22no—
338C2×C4×C53—26no—
339C2×C4×C53—224no—
340C2×C4×C53—224no—
341C2×C4×C53C22×D4112yes—
342C2×C4×C53C2516yes—
343C2×C4×C53C2512yes—
344C2×C4×C53C2512yes—
345C2×C4×C53C2516yes—
346C2×C4×C53C2516yes—
347C22⋊D53—28no—
348C22⋊D53—224no—
349C22⋊D53—248no—
350C22⋊D53—412no—
351C22⋊D53—424no—
352C22⋊D53—412no—
353C2×Dic53—22no—
354C2×Dic53—22no—
355C2×Dic53—22no—
356C2×Dic53—26no—
357C2×Dic53—224no—
358C2×Dic53C22×D4112yes—
359C2×Dic53C2512yes—
360C2×Dic53C2512yes—
361C2×Dic53C2512yes—
362C2×Dic53C2516yes—
363C2×Dic53C2516yes—
364D212—224no—
365D212—224no—
366D212—224no—
367D212—412no—
368D212—424no—
369C4×D53—28no—
370C4×D53—224no—
371C4×D53—224no—
372C4×D53—224no—
373C4×D53—248no—
374C4×D53C22×D4148yes—
375Dic106—224no—
376Dic106C22×D4148yes—
377C2×#3487—531nomaximal, Sylow
378C22×C53—26no—
379C22×C53—22no—
380C22×C53—22no—
381C22×C53—26no—
382C22×C53—26no—
383C22×C53—22no—
384C22×C53—412no—
385C22×C53—44no—
386C22×C53C23×D412yes—
387C22×C53#58512yes—
388C22×C53#58512yes—
389C22×C53C2611yescharacteristic
390C2×D53—22no—
391C2×D53—22no—
392C2×D53—28no—
393C2×D53—26no—
394C2×D53—26no—
395C2×D53—26no—
396C2×D53—26no—
397C2×D53—26no—
398C2×D53—26no—
399C2×D53—448no—
400C2×D53—412no—
401C2×D53—412no—
402C2×D53C23×D414yes—
403C4×C53—26no—
404C4×C53—22no—
405C4×C53—22no—
406C4×C53—26no—
407C4×C53C23×D4112yes—
408Dic53—22no—
409Dic53—22no—
410Dic53—22no—
411Dic53—26no—
412Dic53C23×D4112yes—
413C22×2−1+4—531no—
414C23×#41—531no—
415#3487—5332no—
416C2×#550—531no—
417C2×#550—533no—
418C2×#550—531no—
419C2×#550—533no—
420C2×#548—531no—
421C2×#548—533no—
422C2×#548—533no—
423C2×#548D5311yescharacteristic, complemented
424C2×#535—533no—
425C2×#535—533no—
426C2×#525—533no—
427C2×#525—533no—
428C2×#519—531no—
429C2×C53—46no—
430C2×C53—42no—
431C2×C53#348714yescomplemented
432C2×C53C24×D411yescharacteristic
433C2×C53C2×#58511yescharacteristic
434C2×C53C2×#58511yescharacteristic
435D53—24no—
436D53—46no—
437D53—46no—
438C2×2−1+4—5316no—
439C2×2−1+4—10616no—
440C22×#41—5316no—
441C22×#41—531no—
442C22×#41—533no—
443C22×#41—531no—
444C22×#41—533no—
445C22×#41—533no—
446C22×#41—533no—
447C22×#41—533no—
448C22×#41—10616no—
449C22×#41C2×D5311yescharacteristic
450C23×Q8—531no—
451C23×Q8—533no—
452C23×Q8C2×D5311yescharacteristic, complemented
453C23×D4—533no—
454C24×C4—533no—
455#550—5316no—
456#550—5348no—
457#550—5316no—
458#550—5348no—
459#548—5316no—
460#548—5348no—
461#548—5348no—
462#548C2×D53116yescomplemented
463#535—5348no—
464#535—5348no—
465C2×#127—536no—
466C2×#127—533no—
467C2×#127—533no—
468C2×#124—533no—
469C2×#124—536no—
470C2×#124C2×D5313yescomplemented
471#525—5348no—
472#525—5348no—
473C2×#123—533no—
474C2×#123—531no—
475C2×C22⋊Q8—533no—
476C2×C22⋊Q8—533no—
477C2×C22⋊Q8—533no—
478C2×C22⋊Q8C2×D5313yescomplemented
479C2×#121—533no—
480C2×#121—533no—
481C2×#121—533no—
482C2×#121—533no—
483C2×#121—533no—
484C2×#121—533no—
485C2×#121—533no—
486C2×#121—536no—
487C2×#121—536no—
488C2×#121C2×D5313yescomplemented
489C2×#120—533no—
490C2×#120—536no—
491C2×#120—533no—
492#519—5316no—
493C2×C4×Q8—531no—
494C2×C4×Q8—533no—
495C2×C4×Q8—533no—
496C2×C4×Q8C2×D5311yescharacteristic, complemented
497C2×C4×D4—533no—
498C2×C4×D4—533no—
499C2×C4×D4—536no—
500C2×C4×D4—536no—
501C2×C4×D4—533no—
502C2×C4×D4C2×D5313yescomplemented
503C2×#117—533no—
504C2×#117—533no—
505C53C2×#348711yescharacteristic, complemented, Sylow
506C25—533no—
5072−1+4—106128no—
508C2×#41—28no—
509C2×#41—5324no—
510C2×#41—538no—
511C2×#41—538no—
512C2×#41—5324no—
513C2×#41—5324no—
514C2×#41—5324no—
515C2×#41—5324no—
516C2×#41—10624no—
517C2×#41—10624no—
518C2×#41—10624no—
519C2×#41—10624no—
520C2×#41—10624no—
521C2×#41—106128no—
522C2×#41—1068no—
523C2×#41—1068no—
524C2×#41C22×D5318yes—
525C22×Q8—28no—
526C22×Q8—5316no—
527C22×Q8—538no—
528C22×Q8—5324no—
529C22×Q8—533no—
530C22×Q8—533no—
531C22×Q8—10624no—
532C22×Q8C22×D5313yes—
533C22×Q8C22×D5311yescharacteristic
534C22×Q8C22×D5318yescomplemented
535C22×D4—531no—
536C22×D4—536no—
537C22×D4—533no—
538C22×D4—533no—
539C22×D4—533no—
540C22×D4—536no—
541C22×D4—5324no—
542C22×D4—533no—
543C22×D4—533no—
544C22×D4—533no—
545C22×D4—536no—
546C22×D4—533no—
547C22×D4—10624no—
548C22×D4C22×D5313yes—
549C22×D4C22×D5313yes—
550C23×C4—533no—
551C23×C4—533no—
552C23×C4—536no—
553C23×C4—533no—
554C23×C4—533no—
555C23×C4—533no—
556C23×C4—531no—
557C23×C4—5324no—
558C23×C4—10624no—
559C23×C4C22×D5313yes—
560C23×C4C22×D5313yes—
561#127—5348no—
562#127—5324no—
563#127—5324no—
564#124—5324no—
565#124—5348no—
566#124C22×D53124yescomplemented
567#123—5324no—
568#123—538no—
569C22⋊Q8—5324no—
570C22⋊Q8—5324no—
571C22⋊Q8—5324no—
572C22⋊Q8C22×D53124yescomplemented
573#121—5324no—
574#121—5324no—
575#121—5324no—
576#121—5324no—
577#121—5324no—
578#121—5324no—
579#121—5324no—
580#121—5348no—
581#121—5348no—
582#121C22×D53124yescomplemented
583#120—5324no—
584#120—5348no—
585#120—5324no—
586C4×Q8—538no—
587C4×Q8—5324no—
588C4×Q8—5324no—
589C4×Q8C22×D5318yescomplemented
590C4×D4—5324no—
591C4×D4—5324no—
592C4×D4—5348no—
593C4×D4—5348no—
594C4×D4—5324no—
595C4×D4C22×D53124yescomplemented
596#117—5324no—
597#117—5324no—
598C2×C4⋊C4—533no—
599C2×C4⋊C4—533no—
600C2×C4⋊C4—533no—
601C2×C4⋊C4—531no—
602C2×C4⋊C4—533no—
603C2×C4⋊C4—531no—
604C2×C4⋊C4C22×D5313yes—
605C2×C4⋊C4C22×D5313yes—
606C2×C22⋊C4—531no—
607C2×C22⋊C4—533no—
608C2×C22⋊C4—533no—
609C2×C22⋊C4—531no—
610C2×C22⋊C4—533no—
611C2×C22⋊C4—533no—
612C2×C22⋊C4—533no—
613C2×C22⋊C4—536no—
614C2×C22⋊C4—533no—
615C2×C22⋊C4C22×D5316yes—
616C2×C22⋊C4C22×D5311yescharacteristic
617C2×C22⋊C4C22×D5313yes—
618C2×C42—536no—
619C2×C42—533no—
620C2×C42C22×D5313yes—
621C24—531no—
622C24—533no—
623C24—533no—
624C24—5312no—
625C24—10612no—
626C24—2126no—
627C24—2126no—
628C24C23×D5313yes—
629C24C23×D5311yescharacteristic
630#41—232no—
631#41—10696no—
632#41—10696no—
633#41—10696no—
634#41—10696no—
635#41—10696no—
636#41—10632no—
637#41—10632no—
638C2×Q8—232no—
639C2×Q8—212no—
640C2×Q8—5364no—
641C2×Q8—5324no—
642C2×Q8—5312no—
643C2×Q8—5312no—
644C2×Q8—10612no—
645C2×Q8—10696no—
646C2×Q8D4×D5318yes—
647C2×Q8C23×D53112yes—
648C2×Q8C23×D5314yes—
649C2×D4—212no—
650C2×D4—46no—
651C2×D4—534no—
652C2×D4—5324no—
653C2×D4—5312no—
654C2×D4—5312no—
655C2×D4—5324no—
656C2×D4—5312no—
657C2×D4—5312no—
658C2×D4—5312no—
659C2×D4—5312no—
660C2×D4—5324no—
661C2×D4—5312no—
662C2×D4—10612no—
663C2×D4—10696no—
664C2×D4—10624no—
665C2×D4—10612no—
666C2×D4—1064no—
667C2×D4—10612no—
668C2×D4—10612no—
669C2×D4—21212no—
670C2×D4—2126no—
671C2×D4—2126no—
672C2×D4—2126no—
673C2×D4—21212no—
674C2×D4C23×D53112yes—
675C2×D4C23×D53112yes—
676C22×C4—212no—
677C22×C4—212no—
678C22×C4—533no—
679C22×C4—5324no—
680C22×C4—5312no—
681C22×C4—5312no—
682C22×C4—531no—
683C22×C4—533no—
684C22×C4—531no—
685C22×C4—531no—
686C22×C4—5324no—
687C22×C4—5312no—
688C22×C4—5312no—
689C22×C4—5312no—
690C22×C4—534no—
691C22×C4—10612no—
692C22×C4—10696no—
693C22×C4—10624no—
694C22×C4—1064no—
695C22×C4—10612no—
696C22×C4—10612no—
697C22×C4—10612no—
698C22×C4C23×D53112yes—
699C22×C4C23×D53112yes—
700C22×C4C23×D5313yes—
701C22×C4C23×D5311yescharacteristic
702C22×C4C23×D5313yes—
703C22×C4C23×D5311yescharacteristic
704C22×C4C23×D5313yes—
705C4⋊C4—5312no—
706C4⋊C4—5312no—
707C4⋊C4—5312no—
708C4⋊C4—534no—
709C4⋊C4—5312no—
710C4⋊C4—534no—
711C4⋊C4C23×D53112yes—
712C4⋊C4C23×D53112yes—
713C22⋊C4—534no—
714C22⋊C4—5312no—
715C22⋊C4—5312no—
716C22⋊C4—534no—
717C22⋊C4—5312no—
718C22⋊C4—5312no—
719C22⋊C4—5312no—
720C22⋊C4—5324no—
721C22⋊C4—5312no—
722C22⋊C4C23×D53124yes—
723C22⋊C4C23×D5314yes—
724C22⋊C4C23×D53112yes—
725C42—5324no—
726C42—5312no—
727C42C23×D53112yes—
728C23—22no—
729C23—26no—
730C23—22no—
731C23—26no—
732C23—22no—
733C23—26no—
734C23—534no—
735C23—532no—
736C23—536no—
737C23—536no—
738C23—10624no—
739C23—1062no—
740C23—1062no—
741C23—1066no—
742C23—1066no—
743C23—1066no—
744C23—1066no—
745C23—1066no—
746C23—1066no—
747C23—21212no—
748C23—21212no—
749C23—21248no—
750C23C24×D5316yes—
751C23C24×D5312yes—
752C23C24×D5311yescharacteristic
753Q8—224no—
754Q8—5348no—
755Q8—10624no—
756Q8C2×D4×D53116yes—
757D4—224no—
758D4—412no—
759D4—10624no—
760D4—10648no—
761D4—10624no—
762D4—1068no—
763D4—10624no—
764D4—10624no—
765D4—21224no—
766D4—21212no—
767D4—21212no—
768D4—21212no—
769D4—21224no—
770C2×C4—22no—
771C2×C4—26no—
772C2×C4—26no—
773C2×C4—22no—
774C2×C4—224no—
775C2×C4—224no—
776C2×C4—5312no—
777C2×C4—536no—
778C2×C4—5348no—
779C2×C4—532no—
780C2×C4—536no—
781C2×C4—532no—
782C2×C4—532no—
783C2×C4—10624no—
784C2×C4—10648no—
785C2×C4—1068no—
786C2×C4—10624no—
787C2×C4—1062no—
788C2×C4—1062no—
789C2×C4—1062no—
790C2×C4—1066no—
791C2×C4—10624no—
792C2×C4—10624no—
793C2×C4C2×D4×D53112yes—
794C2×C4C24×D5316yes—
795C2×C4C24×D5312yes—
796C2×C4C24×D5316yes—
797C2×C4C24×D5312yes—
798C2×C4C24×D5316yes—
799C22—22no—
800C22—26no—
801C22—22no—
802C22—26no—
803C22—22no—
804C22—26no—
805C22—412no—
806C22—44no—
807C22—534no—
808C22—1068no—
809C22—1062no—
810C22—1062no—
811C22—1066no—
812C22—1066no—
813C22—1066no—
814C22—1066no—
815C22—1066no—
816C22—1066no—
817C22—21248no—
818C22—21212no—
819C22—21212no—
820C22C22×D4×D5312yes—
821C22#1681145912yes—
822C22#1681146012yes—
823C22C25×D5311yescharacteristic
824C4—22no—
825C4—26no—
826C4—26no—
827C4—22no—
828C4—5312no—
829C4—1062no—
830C4—1062no—
831C4—1062no—
832C4—1066no—
833C4C22×D4×D53112yes—
834C2—46no—
835C2—42no—
836C2—1064no—
837C2—2126no—
838C2—2126no—
839C2#2028837214yesdirect product factor
840C2C23×D4×D5311yescharacteristic
841C2C2×#1681145911yescharacteristic
842C2C2×#1681146011yescharacteristic
subgroupG/H
centerC23C24×D53
commutator, cosocleC22×C53C26
FrattiniC22C25×D53
FittingC2×C53×#548C2
socleC23×C53C25
hypercenterC2×#548D53
hypocenterC53C2×#3487
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×#13133265C2semidirect
2. C22×#41×D53C2semidirect
3. #20288372C2direct (N × H)
4. C2×#16811295C2semidirect
5. C2×#16811294C2semidirect
6. C2×#16811292C2semidirect
7. C2×#16811291C2semidirect
8. C2×#16811284C2semidirect
9. C2×#16811283C2semidirect
10. C2×#16811281C2semidirect
11. C2×#16811191C2semidirect
12. C2×#16811189C2semidirect
13. C2×#16811136C2semidirect
14. C2×#16811132C2semidirect
15. C2×#16811099C2semidirect
16. C2×C53×#548C2semidirect
18. C2×#13133265C22semidirect
21. C22×#11719949C22semidirect
24. C22×#11719945C22semidirect
27. C2×#41×D53C22semidirect
29. C22×Q8×D53C22semidirect
32. #16811295C22semidirect
33. #16811294C22semidirect
34. #16811292C22semidirect
35. #16811291C22semidirect
36. #16811284C22semidirect
37. #16811283C22semidirect
38. #16811281C22semidirect
39. #16811191C22semidirect
40. #16811189C22semidirect
41. C2×#13133214C22semidirect
42. C2×#13133213C22semidirect
43. C2×#13133213C22semidirect
44. C2×#13133206C22semidirect
45. C2×#13133203C22semidirect
46. #16811136C22semidirect
47. #16811132C22semidirect
50. C2×#13133195C22semidirect
51. C2×#13133194C22semidirect
52. C2×#13133193C22semidirect
53. C2×#13133192C22semidirect
54. C2×#13133192C22semidirect
55. C2×#13133191C22semidirect
56. C2×#13133191C22semidirect
57. C2×#13133190C22semidirect
58. C2×#13133190C22semidirect
59. C2×#13133190C22semidirect
60. C2×#13133189C22semidirect
61. C2×#13133188C22semidirect
65. #16811099C22semidirect
66. C2×Q8×Dic53C22semidirect
67. C2×C4×Dic106C22semidirect
68. C2×#13133182C22semidirect
69. C2×C4×D212C22semidirect
70. C2×#13133179C22semidirect
71. C2×C4×C22⋊D53C22semidirect
72. C2×C4×C22⋊D53C22semidirect
73. C2×#13133177C22semidirect
77. C23×Q8×C53C22semidirect
78. C53×#548C22semidirect
79. C2×#124×C53C22semidirect
80. C2×C22⋊Q8×C53C22semidirect
81. C2×#121×C53C22semidirect
82. C2×C4×Q8×C53C22semidirect
83. C2×C4×D4×C53C22semidirect
91. C2×#11719949C23semidirect
97. C2×#11719945C23semidirect
104. C2×Q8×D53D4semidirect
106. C2×Q8×D53C23semidirect
129. #13133214C23semidirect
130. #13133213C23semidirect
131. #13133213C23semidirect
132. #13133206C23semidirect
133. #13133203C23semidirect
136. #13133195C23semidirect
137. #13133194C23semidirect
138. #13133193C23semidirect
139. #13133192C23semidirect
140. #13133192C23semidirect
141. #13133191C23semidirect
142. #13133191C23semidirect
143. #13133190C23semidirect
144. #13133190C23semidirect
145. #13133190C23semidirect
146. #13133189C23semidirect
147. #13133188C23semidirect
151. Q8×Dic53C23semidirect
152. C4×Dic106C23semidirect
153. #13133182C23semidirect
154. C4×D212C23semidirect
155. #13133179C23semidirect
156. C4×C22⋊D53C23semidirect
157. C4×C22⋊D53C23semidirect
158. #13133177C23semidirect
183. C22×Q8×C53C23semidirect
188. #124×C53C23semidirect
189. C22⋊Q8×C53C23semidirect
190. #121×C53C23semidirect
191. C4×Q8×C53C23semidirect
192. C4×D4×C53C23semidirect
250. Q8×D53C2×D4semidirect
423. C2×#548D53semidirect
431. C2×C53#3487semidirect
452. C23×Q8C2×D53semidirect
462. #548C2×D53semidirect
470. C2×#124C2×D53semidirect
478. C2×C22⋊Q8C2×D53semidirect
488. C2×#121C2×D53semidirect
496. C2×C4×Q8C2×D53semidirect
502. C2×C4×D4C2×D53semidirect
505. C53C2×#3487semidirect
534. C22×Q8C22×D53semidirect
566. #124C22×D53semidirect
572. C22⋊Q8C22×D53semidirect
582. #121C22×D53semidirect
589. C4×Q8C22×D53semidirect
595. C4×D4C22×D53semidirect
839. C2#20288372direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131332652
C22×#41×D532
#202883722
C2×#168112952
C2×#168112942
C2×#168112922
C2×#168112912
C2×#168112842
C2×#168112832
C2×#168112812
C2×#168111912
C2×#168111892
C2×#168111362
C2×#168111322
C2×#168110992
C2×C53×#5482
C2×#348753