Finite Group Databasebeta

← C2×#20288483 #28292266

Subgroups — C2×#20288483 #28292266

Order 13568.

11210 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133265C211yesmaximal, characteristic, complemented
2C22×#13133264C211yesmaximal, characteristic, complemented
3#20288483C2132yesmaximal, direct product factor
4C2×#16811292C211yesmaximal, characteristic, complemented
5C2×#16811291C213yesmaximal, complemented
6C2×Q8×C22⋊D53C211yesmaximal, characteristic, complemented
7C2×#16811286C213yesmaximal, complemented
8C2×#16811285C211yesmaximal, characteristic, complemented
9C2×#16811282C213yesmaximal, complemented
10C2×#16811281C213yesmaximal, complemented
11C2×#16811203C213yesmaximal, complemented
12C2×#16811202C213yesmaximal, complemented
13C2×#16811172C213yesmaximal, complemented
14C2×#16811170C213yesmaximal, complemented
15C2×C4×Q8×D53C211yesmaximal, characteristic, complemented
16C2×C53×#548C211yesmaximal, characteristic, complemented
17C2×#13133265—216no—
18C2×#13133265C22116yescomplemented
19C2×#13133264—216no—
20C2×#13133264C22116yescomplemented
21C22×#11719949C2213yes—
22C22×#11719949C2211yescharacteristic
23C22×#11719945C2213yes—
24C22×#11719945C2213yes—
25C22×#11719945C2213yes—
26C22×#11719947C2213yes—
27C22×#11719947C2213yes—
28C23×Dic106C2213yes—
29C22×Q8×D53C2213yes—
30C22×Q8×D53C2211yescharacteristic
31C22×Q8×D53C2211yescharacteristic
32#16811292C22116yescomplemented
33#16811291C22148yescomplemented
34Q8×C22⋊D53C22116yescomplemented
35#16811286C22148yescomplemented
36#16811285C22116yescomplemented
37#16811282C22148yescomplemented
38#16811281C22148yescomplemented
39#16811203C22148yescomplemented
40#16811202C22148yescomplemented
41#16811172C22148yescomplemented
42#16811170C22148yescomplemented
43C2×#13133216C2213yes—
44C2×#13133215C2213yes—
45C2×#13133213C2213yes—
46C2×#13133213C2213yes—
47C2×#13133205C2213yes—
48C2×#13133203C2213yes—
49C2×#13133203C2213yes—
50C2×#13133197C2213yes—
51C2×#13133196C2213yes—
52C2×#13133195C2216yes—
53C2×#13133194C2216yes—
54C2×#13133193C2213yes—
55C2×#13133192C2213yes—
56C2×#13133192C2213yes—
57C2×#13133191C2213yes—
58C2×#13133190C2216yes—
59C2×#13133190C2216yes—
60C2×#13133190C2211yescharacteristic
61C2×#13133190C2213yes—
62C2×#13133189C2216yes—
63C2×#13133188C2213yes—
64C2×#13133188C2213yes—
65C2×Q8×Dic53C2211yescharacteristic
66C2×C4×Dic106C2213yes—
67C2×#13133182C2213yes—
68C4×Q8×D53C22116yescomplemented
69C2×C4×D212C2213yes—
70C2×C4×C22⋊D53C2213yes—
71C2×C4×C22⋊D53C2213yes—
72C2×#13133177C2216yes—
73C2×#13133177C2216yes—
74C2×C4⋊C4×D53C2213yes—
75C2×C42×D53C2213yes—
76C22×#41×C53C2211yescharacteristic
77C23×Q8×C53C2211yescharacteristic
78C53×#548C22116yescomplemented
79C2×#124×C53C2213yes—
80C2×C22⋊Q8×C53C2213yes—
81C2×#121×C53C2213yes—
82C2×C4×Q8×C53C2211yescharacteristic
83C2×C4×D4×C53C2213yes—
84#13133265—2128no—
85#13133264—2128no—
86C2×#11719949—28no—
87C2×#11719949—224no—
88C2×#11719949C2318yes—
89C2×#11719949C23124yes—
90C2×#11719945—224no—
91C2×#11719945—224no—
92C2×#11719945—224no—
93C2×#11719945C23124yes—
94C2×#11719945C23124yes—
95C2×#11719945C23124yes—
96C2×#11719947—224no—
97C2×#11719947—224no—
98C2×#11719947C23124yes—
99C2×#11719947C23124yes—
100C22×Dic106—224no—
101C22×Dic106C23124yes—
102C22×Dic106C2313yes—
103C22×Dic106C2313yes—
104C22×Dic106C2313yes—
105C22×Dic106C2313yes—
106C2×Q8×D53—28no—
107C2×Q8×D53—224no—
108C2×Q8×D53D4116yescomplemented
109C2×Q8×D53C23124yes—
110C2×Q8×D53C2318yes—
111C2×Q8×D53C2318yes—
112C22×D212C2313yes—
113C22×D212C2311yescharacteristic
114C22×D212C2313yes—
115C22×D212C2313yes—
116C22×C22⋊D53C2313yes—
117C22×C22⋊D53C2311yescharacteristic
118C22×C22⋊D53C2311yescharacteristic
119C22×C22⋊D53C2313yes—
120C22×C22⋊D53C2313yes—
121C22×C22⋊D53C2313yes—
122C22×C22⋊D53C2316yes—
123C23×Dic53C2316yes—
124C22×C4×D53C2311yescharacteristic
125C22×C4×D53C2316yes—
126C22×C4×D53C2313yes—
127C22×C4×D53C2313yes—
128C22×C4×D53C2313yes—
129C22×C4×D53C2313yes—
130#13133216C23124yes—
131#13133215C23124yes—
132#13133213C23124yes—
133#13133213C23124yes—
134#13133205C23124yes—
135#13133203C23124yes—
136#13133203C23124yes—
137#13133197C23124yes—
138#13133196C23124yes—
139#13133195C23148yes—
140#13133194C23148yes—
141#13133193C23124yes—
142#13133192C23124yes—
143#13133192C23124yes—
144#13133191C23124yes—
145#13133190C23148yes—
146#13133190C2318yes—
147#13133190C23124yes—
148#13133190C23148yes—
149#13133189C23148yes—
150#13133188C23124yes—
151#13133188C23124yes—
152Q8×Dic53C2318yes—
153C4×Dic106C23124yes—
154#13133182C23124yes—
155C4×D212C23124yes—
156C4×C22⋊D53C23124yes—
157C4×C22⋊D53C23124yes—
158#13133177C23148yes—
159#13133177C23148yes—
160C2×C4⋊Dic53C2313yes—
161C2×C4⋊Dic53C2313yes—
162C2×#11719919C2316yes—
163C2×#11719919C2313yes—
164C2×#11719919C2316yes—
165C2×#11719919C2311yescharacteristic
166C4⋊C4×D53C23124yes—
167C2×C22⋊Dic53C2313yes—
168C2×C22⋊Dic53C2313yes—
169C2×#11719921C2313yes—
170C2×#11719921C2316yes—
171C2×#11719921C2313yes—
172C2×#11719921C2313yes—
173C2×#11719921C2311yescharacteristic
174C2×C4×Dic53C2313yes—
175C2×C4×Dic53C2313yes—
176C2×C4×Dic53C2313yes—
177C42×D53C23124yes—
178C2×#41×C53—28no—
179C2×#41×C53C2318yes—
180C22×Q8×C53—28no—
181C22×Q8×C53C2318yes—
182C22×Q8×C53C2313yes—
183C22×Q8×C53C2311yescharacteristic
184C22×D4×C53C2313yes—
185C22×D4×C53C2313yes—
186C23×C4×C53C2313yes—
187C23×C4×C53C2313yes—
188#124×C53C23124yes—
189C22⋊Q8×C53C23124yes—
190#121×C53C23124yes—
191C4×Q8×C53C2318yes—
192C4×D4×C53C23124yes—
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×D53C2413yes—
202C23×D53C2411yescharacteristic
203C23×D53C2411yescharacteristic
204#41×C53—232no—
205C2×Q8×C53—232no—
206C2×Q8×C53—212no—
207C2×Q8×C53C2×D418yes—
208C2×Q8×C53C24112yes—
209C2×Q8×C53C2414yes—
210C2×D4×C53—212no—
211C2×D4×C53—46no—
212C2×D4×C53C24112yes—
213C2×D4×C53C24112yes—
214C22×C4×C53—212no—
215C22×C4×C53—212no—
216C22×C4×C53C2411yescharacteristic
217C22×C4×C53C2413yes—
218C22×C4×C53C2413yes—
219C22×C4×C53C2411yescharacteristic
220C22×C4×C53C24112yes—
221C22×C4×C53C24112yes—
222C22×C4×C53C2413yes—
223C2×C22⋊D53—212no—
224C2×C22⋊D53—24no—
225C2×C22⋊D53—212no—
226C2×C22⋊D53—212no—
227C2×C22⋊D53—212no—
228C2×C22⋊D53—24no—
229C2×C22⋊D53—412no—
230C2×C22⋊D53C24112yes—
231C2×C22⋊D53C2414yes—
232C2×C22⋊D53C2414yes—
233C2×C22⋊D53C24112yes—
234C2×C22⋊D53C24112yes—
235C2×C22⋊D53C24112yes—
236C2×C22⋊D53C24124yes—
237C22×Dic53—224no—
238C22×Dic53C2413yes—
239C22×Dic53C2413yes—
240C22×Dic53C2411yescharacteristic
241C22×Dic53C24124yes—
242C22×Dic53C2413yes—
243C22×Dic53C2411yescharacteristic
244#11719949—232no—
245#11719949—296no—
246Q8×D53—232no—
247Q8×D53—296no—
248Q8×D53C2×D4164yescomplemented
249#11719947—296no—
250#11719947—296no—
251#11719945—296no—
252#11719945—296no—
253#11719945—296no—
254C2×D212—24no—
255C2×D212—212no—
256C2×D212—212no—
257C2×D212—46no—
258C2×D212C24112yes—
259C2×D212C2414yes—
260C2×D212C24112yes—
261C2×D212C24112yes—
262C2×C4×D53—212no—
263C2×C4×D53—212no—
264C2×C4×D53—224no—
265C2×C4×D53—24no—
266C2×C4×D53—46no—
267C2×C4×D53C2×D4124yes—
268C2×C4×D53C2414yes—
269C2×C4×D53C24124yes—
270C2×C4×D53C24112yes—
271C2×C4×D53C24112yes—
272C2×C4×D53C24112yes—
273C2×C4×D53C24112yes—
274C2×Dic106—212no—
275C2×Dic106—212no—
276C2×Dic106—212no—
277C2×Dic106—296no—
278C2×Dic106C2×D4124yes—
279C2×Dic106C24112yes—
280C2×Dic106C24112yes—
281C2×Dic106C24112yes—
282C2×Dic106C24112yes—
283C4⋊C4×C53C24112yes—
284C4⋊C4×C53C24112yes—
285C22⋊C4×C53C2414yes—
286C22⋊C4×C53C24112yes—
287C22⋊C4×C53C24124yes—
288C42×C53C24112yes—
289C22⋊Dic53C24112yes—
290C22⋊Dic53C24112yes—
291#11719921C24112yes—
292#11719921C24124yes—
293#11719921C24112yes—
294#11719921C24112yes—
295#11719921C2414yes—
296C4⋊Dic53C24112yes—
297C4⋊Dic53C24112yes—
298#11719919C24124yes—
299#11719919C24112yes—
300#11719919C24124yes—
301#11719919C2414yes—
302C4×Dic53C24112yes—
303C4×Dic53C24112yes—
304C4×Dic53C24112yes—
305C23×C53—26no—
306C23×C53—22no—
307C23×C53—26no—
308C23×C53—22no—
309C23×C53—26no—
310C23×C53—22no—
311C23×C53C2516yes—
312C23×C53C2512yes—
313C23×C53C2511yescharacteristic
314C22×D53—22no—
315C22×D53—22no—
316C22×D53—26no—
317C22×D53—22no—
318C22×D53—26no—
319C22×D53—22no—
320C22×D53—22no—
321C22×D53—26no—
322C22×D53C22×D414yes—
323C22×D53C2516yes—
324C22×D53C2512yes—
325C22×D53C2512yes—
326Q8×C53—224no—
327Q8×C53C22×D4116yes—
328D4×C53—224no—
329D4×C53—412no—
330C2×C4×C53—22no—
331C2×C4×C53—26no—
332C2×C4×C53—22no—
333C2×C4×C53—26no—
334C2×C4×C53—224no—
335C2×C4×C53—224no—
336C2×C4×C53C22×D4112yes—
337C2×C4×C53C2512yes—
338C2×C4×C53C2516yes—
339C2×C4×C53C2516yes—
340C2×C4×C53C2512yes—
341C2×C4×C53C2516yes—
342C22⋊D53—28no—
343C22⋊D53—224no—
344C22⋊D53—224no—
345C22⋊D53—224no—
346C22⋊D53—224no—
347C22⋊D53—28no—
348C22⋊D53—424no—
349C2×Dic53—22no—
350C2×Dic53—26no—
351C2×Dic53—26no—
352C2×Dic53—248no—
353C2×Dic53C22×D4112yes—
354C2×Dic532−1+414yescomplemented
355C2×Dic53C2512yes—
356C2×Dic53C2516yes—
357C2×Dic53C2516yes—
358C2×Dic53C2516yes—
359C2×Dic53C2512yes—
360D212—28no—
361D212—224no—
362D212—224no—
363D212—412no—
364C4×D53—224no—
365C4×D53—224no—
366C4×D53—248no—
367C4×D53—28no—
368C4×D53—412no—
369C4×D53C22×D4148yes—
370Dic106—224no—
371Dic106—224no—
372Dic106—224no—
373Dic106C22×D4148yes—
374C2×#3497—531nomaximal, Sylow
375C22×C53—26no—
376C22×C53—22no—
377C22×C53—26no—
378C22×C53—22no—
379C22×C53—26no—
380C22×C53—22no—
381C22×C53—412no—
382C22×C53—44no—
383C22×C53C23×D412yes—
384C22×C53C2×2−1+412yes—
385C22×C53#58512yes—
386C22×C53C2611yescharacteristic
387C2×D53—22no—
388C2×D53—22no—
389C2×D53—28no—
390C2×D53—26no—
391C2×D53—22no—
392C2×D53—26no—
393C2×D53—22no—
394C2×D53—22no—
395C2×D53—26no—
396C2×D53—412no—
397C2×D53—44no—
398C2×D53C23×D414yes—
399C4×C53—22no—
400C4×C53—26no—
401C4×C53—22no—
402C4×C53—26no—
403C4×C53C23×D4112yes—
404Dic53—22no—
405Dic53—26no—
406Dic53—26no—
407Dic53C23×D4112yes—
408Dic53C2×2−1+414yescomplemented
409C22×2−1+4—531no—
410C22×2−1+4—531no—
411#3497—5332no—
412C2×#550—531no—
413C2×#550—533no—
414C2×D4×Q8—531no—
415C2×D4×Q8—533no—
416C2×#548—533no—
417C2×#548—531no—
418C2×#548—533no—
419C2×#548D5311yescharacteristic, complemented
420C2×#537—533no—
421C2×#537—533no—
422C2×#532—533no—
423C2×#532—533no—
424C22×C4×Q8—531no—
425C2×C53—46no—
426C2×C53—42no—
427C2×C53#349714yescomplemented
428C2×C53C24×D411yescharacteristic
429C2×C53C22×2−1+411yescharacteristic
430C2×C53C2×#58511yescharacteristic
431D53—24no—
432D53—46no—
433D53—42no—
434C2×2−1+4—5316no—
435C2×2−1+4—5316no—
436C2×2−1+4—10616no—
437C2×2−1+4—10616no—
438C22×#41—533no—
439C22×#41—531no—
440C22×#41—533no—
441C22×#41—533no—
442C22×#41—533no—
443C22×#41—533no—
444C22×#41—533no—
445C22×#41C2×D5311yescharacteristic
446C23×Q8—531no—
447C23×Q8—533no—
448C23×Q8—531no—
449C23×Q8—533no—
450C23×Q8C2×D5311yescharacteristic
451#550—5316no—
452#550—5348no—
453D4×Q8—5316no—
454D4×Q8—5348no—
455#548—5348no—
456#548—5316no—
457#548—5348no—
458#548C2×D53116yescomplemented
459#537—5348no—
460#537—5348no—
461#532—5348no—
462#532—5348no—
463C2×C4⋊Q8—533no—
464C2×C4⋊Q8—533no—
465C2×#127—533no—
466C2×#127—533no—
467C2×#124—533no—
468C2×#124—533no—
469C2×#124—533no—
470C2×#124C2×D5313yes—
471C2×C22⋊Q8—533no—
472C2×C22⋊Q8—533no—
473C2×C22⋊Q8—536no—
474C2×C22⋊Q8—533no—
475C2×C22⋊Q8—536no—
476C2×C22⋊Q8C2×D5313yes—
477C2×#121—533no—
478C2×#121—533no—
479C2×#121—536no—
480C2×#121—533no—
481C2×#121—533no—
482C2×#121—533no—
483C2×#121—533no—
484C2×#121—531no—
485C2×#121—536no—
486C2×#121—536no—
487C2×#121C2×D5313yes—
488C2×C4×Q8—531no—
489C2×C4×Q8—5316no—
490C2×C4×Q8—533no—
491C2×C4×Q8—533no—
492C2×C4×Q8C2×D5311yescharacteristic
493C2×C4×D4—533no—
494C2×C4×D4—533no—
495C2×C4×D4—536no—
496C2×C4×D4—536no—
497C2×C4×D4—533no—
498C2×C4×D4C2×D5313yes—
499C22×C4⋊C4—533no—
500C22×C42—533no—
501C53C2×#349711yescharacteristic, complemented, Sylow
5022−1+4—106128no—
5032−1+4—106128no—
504C2×#41—28no—
505C2×#41—5324no—
506C2×#41—538no—
507C2×#41—5324no—
508C2×#41—5324no—
509C2×#41—5324no—
510C2×#41—5324no—
511C2×#41—5324no—
512C2×#41—10624no—
513C2×#41—10624no—
514C2×#41—10624no—
515C2×#41—10624no—
516C2×#41—10624no—
517C2×#41—10624no—
518C2×#41—1068no—
519C2×#41C22×D5318yes—
520C22×Q8—28no—
521C22×Q8—5316no—
522C22×Q8—538no—
523C22×Q8—5324no—
524C22×Q8—538no—
525C22×Q8—533no—
526C22×Q8—533no—
527C22×Q8—533no—
528C22×Q8—533no—
529C22×Q8—5324no—
530C22×Q8—10624no—
531C22×Q8—10624no—
532C22×Q8—1068no—
533C22×Q8C22×D5313yes—
534C22×Q8C22×D5318yes—
535C22×Q8C22×D5311yescharacteristic
536C22×D4—531no—
537C22×D4—533no—
538C22×D4—531no—
539C22×D4—533no—
540C22×D4—533no—
541C22×D4—533no—
542C22×D4—536no—
543C22×D4—531no—
544C22×D4—533no—
545C22×D4—533no—
546C22×D4—533no—
547C22×D4C22×D5313yes—
548C22×D4C22×D5313yes—
549C23×C4—533no—
550C23×C4—536no—
551C23×C4—536no—
552C23×C4—533no—
553C23×C4—533no—
554C23×C4—531no—
555C23×C4—533no—
556C23×C4C22×D5313yes—
557C23×C4C22×D5313yes—
558C4⋊Q8—5324no—
559C4⋊Q8—5324no—
560#127—5324no—
561#127—5324no—
562#124—5324no—
563#124—5324no—
564#124—5324no—
565#124C22×D53124yes—
566C22⋊Q8—5324no—
567C22⋊Q8—5324no—
568C22⋊Q8—5348no—
569C22⋊Q8—5324no—
570C22⋊Q8—5348no—
571C22⋊Q8C22×D53124yes—
572#121—5324no—
573#121—5324no—
574#121—5348no—
575#121—5324no—
576#121—5324no—
577#121—5324no—
578#121—5324no—
579#121—538no—
580#121—5348no—
581#121—5348no—
582#121C22×D53124yes—
583C4×Q8—538no—
584C4×Q8—5324no—
585C4×Q8—5324no—
586C4×Q8C22×D5318yes—
587C4×D4—5324no—
588C4×D4—5324no—
589C4×D4—5348no—
590C4×D4—5348no—
591C4×D4—5324no—
592C4×D4C22×D53124yes—
593C2×C4⋊C4—536no—
594C2×C4⋊C4—533no—
595C2×C4⋊C4—531no—
596C2×C4⋊C4—533no—
597C2×C4⋊C4—536no—
598C2×C4⋊C4—533no—
599C2×C4⋊C4—5324no—
600C2×C4⋊C4C22×D5313yes—
601C2×C4⋊C4C22×D5313yes—
602C2×C22⋊C4—533no—
603C2×C22⋊C4—533no—
604C2×C22⋊C4—533no—
605C2×C22⋊C4—531no—
606C2×C22⋊C4—533no—
607C2×C22⋊C4—533no—
608C2×C22⋊C4—536no—
609C2×C22⋊C4C22×D5313yes—
610C2×C22⋊C4C22×D5316yes—
611C2×C22⋊C4C22×D5311yescharacteristic
612C2×C42—533no—
613C2×C42—533no—
614C2×C42—533no—
615C2×C42—5324no—
616C2×C42C22×D5313yes—
617C24—531no—
618C24—531no—
619C24—533no—
620C24C23×D5311yescharacteristic
621C24C23×D5313yes—
622#41—232no—
623#41—10696no—
624#41—10696no—
625#41—10696no—
626#41—10696no—
627#41—10696no—
628#41—10696no—
629#41—10632no—
630C2×Q8—232no—
631C2×Q8—212no—
632C2×Q8—5364no—
633C2×Q8—5324no—
634C2×Q8—5312no—
635C2×Q8—5312no—
636C2×Q8—5312no—
637C2×Q8—5312no—
638C2×Q8—10612no—
639C2×Q8—10612no—
640C2×Q8—10696no—
641C2×Q8—10696no—
642C2×Q8—10632no—
643C2×Q8—10612no—
644C2×Q8D4×D5318yes—
645C2×Q8C23×D53112yes—
646C2×Q8C23×D5314yes—
647C2×D4—212no—
648C2×D4—46no—
649C2×D4—534no—
650C2×D4—5312no—
651C2×D4—534no—
652C2×D4—5312no—
653C2×D4—5312no—
654C2×D4—5312no—
655C2×D4—5324no—
656C2×D4—534no—
657C2×D4—5312no—
658C2×D4—5312no—
659C2×D4—5312no—
660C2×D4—1064no—
661C2×D4—10612no—
662C2×D4—1064no—
663C2×D4—10612no—
664C2×D4—10612no—
665C2×D4—10612no—
666C2×D4—1064no—
667C2×D4—10612no—
668C2×D4—10612no—
669C2×D4—2126no—
670C2×D4—21212no—
671C2×D4C23×D53112yes—
672C2×D4C23×D53112yes—
673C22×C4—212no—
674C22×C4—212no—
675C22×C4—531no—
676C22×C4—533no—
677C22×C4—5324no—
678C22×C4—5312no—
679C22×C4—5324no—
680C22×C4—533no—
681C22×C4—533no—
682C22×C4—531no—
683C22×C4—534no—
684C22×C4—5324no—
685C22×C4—5312no—
686C22×C4—5312no—
687C22×C4—5312no—
688C22×C4—1064no—
689C22×C4—10624no—
690C22×C4—10624no—
691C22×C4—10612no—
692C22×C4—10612no—
693C22×C4—2126no—
694C22×C4C23×D53112yes—
695C22×C4C23×D53112yes—
696C22×C4C23×D5311yescharacteristic
697C22×C4C23×D5313yes—
698C22×C4C23×D5311yescharacteristic
699C22×C4C23×D5313yes—
700C22×C4C23×D5313yes—
701C4⋊C4—5324no—
702C4⋊C4—5312no—
703C4⋊C4—534no—
704C4⋊C4—5312no—
705C4⋊C4—5324no—
706C4⋊C4—5312no—
707C4⋊C4C23×D53112yes—
708C4⋊C4C23×D53112yes—
709C22⋊C4—5312no—
710C22⋊C4—5312no—
711C22⋊C4—5312no—
712C22⋊C4—534no—
713C22⋊C4—5312no—
714C22⋊C4—5312no—
715C22⋊C4—5324no—
716C22⋊C4C23×D53112yes—
717C22⋊C4C23×D53124yes—
718C22⋊C4C23×D5314yes—
719C42—5312no—
720C42—5312no—
721C42—5312no—
722C42C23×D53112yes—
723C23—22no—
724C23—26no—
725C23—22no—
726C23—26no—
727C23—22no—
728C23—26no—
729C23—534no—
730C23—532no—
731C23—532no—
732C23—536no—
733C23—1062no—
734C23—1062no—
735C23—1066no—
736C23—1062no—
737C23—1062no—
738C23—1066no—
739C23—1062no—
740C23—1066no—
741C23C24×D5312yes—
742C23C24×D5316yes—
743C23C24×D5311yescharacteristic
744Q8—224no—
745Q8—5348no—
746Q8—10624no—
747Q8—10624no—
748Q8—10624no—
749Q8C2×D4×D53116yes—
750D4—224no—
751D4—412no—
752D4—1068no—
753D4—10624no—
754D4—1068no—
755D4—10624no—
756D4—10624no—
757D4—10624no—
758D4—1068no—
759D4—10624no—
760D4—10624no—
761D4—21212no—
762D4—21224no—
763C2×C4—22no—
764C2×C4—26no—
765C2×C4—22no—
766C2×C4—26no—
767C2×C4—224no—
768C2×C4—224no—
769C2×C4—5312no—
770C2×C4—534no—
771C2×C4—532no—
772C2×C4—536no—
773C2×C4—5348no—
774C2×C4—536no—
775C2×C4—532no—
776C2×C4—536no—
777C2×C4—1068no—
778C2×C4—10648no—
779C2×C4—10648no—
780C2×C4—1062no—
781C2×C4—1066no—
782C2×C4—1066no—
783C2×C4—10624no—
784C2×C4—10624no—
785C2×C4—21212no—
786C2×C4C2×D4×D53112yes—
787C2×C4C24×D5312yes—
788C2×C4C24×D5316yes—
789C2×C4C24×D5312yes—
790C2×C4C24×D5316yes—
791C2×C4C24×D5316yes—
792C22—22no—
793C22—26no—
794C22—22no—
795C22—26no—
796C22—22no—
797C22—26no—
798C22—44no—
799C22—412no—
800C22—534no—
801C22—1068no—
802C22—1062no—
803C22—1062no—
804C22—1066no—
805C22—1062no—
806C22—1062no—
807C22—1066no—
808C22—1062no—
809C22—1066no—
810C22—21212no—
811C22—2124no—
812C22C22×D4×D5312yes—
813C222−1+4×D5312yes—
814C22#1681145912yes—
815C22C25×D5311yescharacteristic
816C4—22no—
817C4—26no—
818C4—22no—
819C4—26no—
820C4—5312no—
821C4—534no—
822C4—1066no—
823C4—1062no—
824C4—1066no—
825C4C22×D4×D53112yes—
826C2—42no—
827C2—46no—
828C2—1064no—
829C2—2126no—
830C2—2122no—
831C2#2028848314yesdirect product factor
832C2C23×D4×D5311yescharacteristic
833C2C2×2−1+4×D5311yescharacteristic
834C2C2×#1681145911yescharacteristic
subgroupG/H
centerC23C24×D53
commutator, cosocleC22×C53C26
FrattiniC22C25×D53
FittingC2×C53×#548C2
socleC23×C53C25
hypercenterC2×#548D53
hypocenterC53C2×#3497
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×#13133264C2semidirect
3. #20288483C2direct (N × H)
4. C2×#16811292C2semidirect
5. C2×#16811291C2semidirect
6. C2×Q8×C22⋊D53C2semidirect
7. C2×#16811286C2semidirect
8. C2×#16811285C2semidirect
9. C2×#16811282C2semidirect
10. C2×#16811281C2semidirect
11. C2×#16811203C2semidirect
12. C2×#16811202C2semidirect
13. C2×#16811172C2semidirect
14. C2×#16811170C2semidirect
15. C2×C4×Q8×D53C2semidirect
16. C2×C53×#548C2semidirect
18. C2×#13133265C22semidirect
20. C2×#13133264C22semidirect
32. #16811292C22semidirect
33. #16811291C22semidirect
34. Q8×C22⋊D53C22semidirect
35. #16811286C22semidirect
36. #16811285C22semidirect
37. #16811282C22semidirect
38. #16811281C22semidirect
39. #16811203C22semidirect
40. #16811202C22semidirect
41. #16811172C22semidirect
42. #16811170C22semidirect
68. C4×Q8×D53C22semidirect
78. C53×#548C22semidirect
108. C2×Q8×D53D4semidirect
248. Q8×D53C2×D4semidirect
354. C2×Dic532−1+4semidirect
408. Dic53C2×2−1+4semidirect
419. C2×#548D53semidirect
427. C2×C53#3497semidirect
458. #548C2×D53semidirect
501. C53C2×#3497semidirect
831. C2#20288483direct (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×#131332642
#202884832
C2×#168112922
C2×#168112912
C2×Q8×C22⋊D532
C2×#168112862
C2×#168112852
C2×#168112822
C2×#168112812
C2×#168112032
C2×#168112022
C2×#168111722
C2×#168111702
C2×C4×Q8×D532
C2×C53×#5482
C2×#349753