Finite Group Databasebeta

← C2×#20288204 #28291053

Subgroups — C2×#20288204 #28291053

Order 13568.

12314 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#11719949C211yesmaximal, characteristic, complemented
2C22×#41×D53C211yesmaximal, characteristic, complemented
3#20288204C2132yesmaximal, direct product factor
4C2×#16811292C211yesmaximal, characteristic, complemented
5C2×Q8×C22⋊D53C211yesmaximal, characteristic, complemented
6C2×#16811285C211yesmaximal, characteristic, complemented
7C2×#16811275C213yesmaximal, complemented
8C2×#16811269C213yesmaximal, complemented
9C2×#16811266C213yesmaximal, complemented
10C2×#16811257C213yesmaximal, complemented
11C2×#16811172C213yesmaximal, complemented
12C2×#16811136C213yesmaximal, complemented
13C2×#16811133C213yesmaximal, complemented
14C2×C4×#11719949C211yesmaximal, characteristic, complemented
15C2×C4×D4×D53C213yesmaximal, complemented
16C2×C53×#548C211yesmaximal, characteristic, complemented
17C22×#11719949—216no—
18C22×#11719949C2211yescharacteristic
19C22×#11719949C2213yescomplemented
20C22×#11719949C2211yescharacteristic, complemented
21C22×#11719949C2213yescomplemented
22C22×#11719949C22116yescomplemented
23C22×#11719945C2213yescomplemented
24C22×#11719947C2213yescomplemented
25C2×#41×D53—216no—
26C2×#41×D53C22116yescomplemented
27C22×Q8×D53C2211yescharacteristic, complemented
28C23×D212C2213yescomplemented
29C22×D4×D53C2213yes—
30C22×D4×D53C2213yescomplemented
31C23×C4×D53C2213yescomplemented
32C23×C4×D53C2213yescomplemented
33#16811292C22116yescomplemented
34Q8×C22⋊D53C22116yescomplemented
35#16811285C22116yescomplemented
36#16811275C22148yescomplemented
37#16811269C22148yescomplemented
38#16811266C22148yescomplemented
39#16811257C22148yescomplemented
40#16811172C22148yescomplemented
41C2×#13133215C2213yescomplemented
42C2×#13133213C2213yescomplemented
43C2×#13133205C2213yescomplemented
44#16811136C22148yescomplemented
45#16811133C22148yescomplemented
46C2×#13133202C2216yescomplemented
47C2×#13133199C2216yescomplemented
48C2×#13133197C2213yescomplemented
49C2×#13133196C2213yescomplemented
50C2×#13133193C2213yescomplemented
51C2×#13133192C2213yescomplemented
52C2×#13133191C2213yescomplemented
53C2×#13133190C2216yescomplemented
54C2×#13133190C2216yescomplemented
55C2×#13133188C2213yescomplemented
56C2×#13133187C2216yescomplemented
57C2×#13133185C2216yescomplemented
58C4×#11719949C22116yescomplemented
59C2×Q8×Dic53C2211yescharacteristic, complemented
60C2×C4×D212C2213yescomplemented
61C2×C4×D212C2213yescomplemented
62C2×D4×Dic53C2213yescomplemented
63C2×#13133179C2213yescomplemented
64C2×#13133179C2213yescomplemented
65C2×C4×C22⋊D53C2213yes—
66C2×C4×C22⋊D53C2213yescomplemented
67C2×#13133177C2211yescharacteristic
68C2×#13133177C2213yescomplemented
69C2×#13133177C2216yescomplemented
70C4×D4×D53C22148yescomplemented
71C2×#13133175C2213yescomplemented
72C2×C4⋊C4×D53C2213yescomplemented
73C2×C22⋊C4×D53C2213yescomplemented
74C2×C22⋊C4×D53C2213yescomplemented
75C2×C42×D53C2213yescomplemented
76C22×#41×C53C2211yescharacteristic, complemented
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—
85C24×D53C2313yes—
86C2×#11719949—28no—
87C2×#11719949—2128no—
88C2×#11719949—224no—
89C2×#11719949—224no—
90C2×#11719949D4116yescomplemented
91C2×#11719949C2318yes—
92C2×#11719949C23124yescomplemented
93C2×#11719949C2318yescomplemented
94C2×#11719949C23124yescomplemented
95C2×#11719945—224no—
96C2×#11719945C23124yescomplemented
97C2×#11719947—224no—
98C2×#11719947C23124yescomplemented
99#41×D53—2128no—
100C22×Dic106C2313yes—
101C2×Q8×D53—28no—
102C2×Q8×D53C2318yescomplemented
103C22×D212—224no—
104C22×D212C2313yes—
105C22×D212C2316yes—
106C22×D212C2313yes—
107C22×D212C2313yes—
108C22×D212C23124yescomplemented
109C22×C22⋊D53C2313yes—
110C22×C22⋊D53C2316yes—
111C22×C22⋊D53C2316yes—
112C22×C22⋊D53C2311yescharacteristic
113C2×D4×D53—224no—
114C2×D4×D53—224no—
115C2×D4×D53C23124yes—
116C2×D4×D53C23124yescomplemented
117C23×Dic53C2311yescharacteristic
118C23×Dic53C2313yes—
119C22×C4×D53—224no—
120C22×C4×D53—224no—
121C22×C4×D53C2313yes—
122C22×C4×D53C2313yes—
123C22×C4×D53C2313yes—
124C22×C4×D53C2311yescharacteristic
125C22×C4×D53C2313yes—
126C22×C4×D53C2313yes—
127C22×C4×D53C2313yes—
128C22×C4×D53C2313yes—
129C22×C4×D53C2313yes—
130C22×C4×D53C23124yescomplemented
131C22×C4×D53C23124yescomplemented
132#13133215C23124yescomplemented
133#13133213C23124yescomplemented
134#13133205C23124yescomplemented
135#13133202C23148yescomplemented
136#13133199C23148yescomplemented
137#13133197C23124yescomplemented
138#13133196C23124yescomplemented
139#13133193C23124yescomplemented
140#13133192C23124yescomplemented
141#13133191C23124yescomplemented
142#13133190C23148yescomplemented
143#13133190C23148yescomplemented
144#13133188C23124yescomplemented
145#13133187C23148yescomplemented
146#13133185C23148yescomplemented
147Q8×Dic53C2318yescomplemented
148C4×D212C23124yescomplemented
149C4×D212C23124yescomplemented
150D4×Dic53C23124yescomplemented
151#13133179C23124yescomplemented
152#13133179C23124yescomplemented
153C4×C22⋊D53C23124yes—
154C4×C22⋊D53C23124yescomplemented
155#13133177C2318yes—
156#13133177C23124yescomplemented
157#13133177C23148yescomplemented
158#13133175C23124yescomplemented
159C2×C4⋊Dic53C2313yes—
160C2×C4⋊Dic53C2313yes—
161C2×#11719919C2311yescharacteristic
162C2×#11719919C2313yes—
163C2×#11719919C2316yes—
164C4⋊C4×D53C23124yescomplemented
165C2×C22⋊Dic53C2313yes—
166C2×C22⋊Dic53C2313yes—
167C2×#11719921C2311yescharacteristic
168C2×#11719921C2313yes—
169C2×#11719921C2313yes—
170C2×#11719921C2313yes—
171C2×#11719921C2316yes—
172C2×#11719921C2316yes—
173C22⋊C4×D53C23124yescomplemented
174C22⋊C4×D53C23124yescomplemented
175C2×C4×Dic53C2311yescharacteristic
176C2×C4×Dic53C2313yes—
177C2×C4×Dic53C2313yes—
178C42×D53C23124yescomplemented
179C2×#41×C53—28no—
180C2×#41×C53C2318yescomplemented
181C22×Q8×C53—28no—
182C22×Q8×C53C2313yes—
183C22×Q8×C53C2311yescharacteristic
184C22×Q8×C53C2318yescomplemented
185C22×D4×C53C2313yes—
186C22×D4×C53C2313yes—
187C23×C4×C53C2313yes—
188C23×C4×C53C2313yes—
189#124×C53C23124yescomplemented
190C22⋊Q8×C53C23124yescomplemented
191#121×C53C23124yescomplemented
192C4×Q8×C53C2318yescomplemented
193C4×D4×C53C23124yescomplemented
194C2×C4⋊C4×C53C2313yes—
195C2×C4⋊C4×C53C2313yes—
196C2×C22⋊C4×C53C2311yescharacteristic
197C2×C22⋊C4×C53C2313yes—
198C2×C22⋊C4×C53C2316yes—
199C2×C42×C53C2313yes—
200C24×C53C2413yes—
201C24×C53C2411yescharacteristic
202C23×D53—212no—
203C23×D53—212no—
204C23×D53—212no—
205C23×D53—212no—
206C23×D53—46no—
207C23×D53—46no—
208C23×D53C2413yes—
209C23×D53C24112yes—
210C23×D53C24112yes—
211C23×D53C2413yes—
212C23×D53C2411yescharacteristic
213#41×C53—232no—
214C2×Q8×C53—232no—
215C2×Q8×C53—212no—
216C2×Q8×C53C2×D418yescomplemented
217C2×Q8×C53C24112yes—
218C2×Q8×C53C2414yes—
219C2×D4×C53—212no—
220C2×D4×C53—212no—
221C2×D4×C53C24112yes—
222C2×D4×C53C24112yes—
223C22×C4×C53—212no—
224C22×C4×C53—212no—
225C22×C4×C53C2411yescharacteristic
226C22×C4×C53C2413yes—
227C22×C4×C53C2413yes—
228C22×C4×C53C2411yescharacteristic
229C22×C4×C53C24112yes—
230C22×C4×C53C24112yes—
231C22×C4×C53C2413yes—
232C2×C22⋊D53—224no—
233C2×C22⋊D53—212no—
234C2×C22⋊D53—412no—
235C2×C22⋊D53#4118yescomplemented
236C2×C22⋊D53C24112yes—
237C2×C22⋊D53C24124yes—
238C2×C22⋊D53C24124yes—
239C2×C22⋊D53C2414yes—
240C22×Dic53—24no—
241C22×Dic53—212no—
242C22×Dic53C2413yes—
243C22×Dic53C2413yes—
244C22×Dic53C2411yescharacteristic
245C22×Dic53C2414yes—
246C22×Dic53C24112yes—
247C22×Dic53C2411yescharacteristic
248C22×Dic53C2411yescharacteristic
249#11719949—232no—
250#11719949—296no—
251#11719949—296no—
252#11719949C2×D4164yescomplemented
253Q8×D53—232no—
254#11719947—296no—
255D4×D53—296no—
256D4×D53—296no—
257#11719945—296no—
258C2×D212—224no—
259C2×D212—212no—
260C2×D212—212no—
261C2×D212—296no—
262C2×D212C2×D4124yescomplemented
263C2×D212C24112yes—
264C2×D212C24124yes—
265C2×D212C24112yes—
266C2×D212C24112yes—
267C2×C4×D53—212no—
268C2×C4×D53—212no—
269C2×C4×D53—212no—
270C2×C4×D53—212no—
271C2×C4×D53—24no—
272C2×C4×D53—212no—
273C2×C4×D53—212no—
274C2×C4×D53—296no—
275C2×C4×D53—296no—
276C2×C4×D53—46no—
277C2×C4×D53C2×D4124yescomplemented
278C2×C4×D53C24112yes—
279C2×C4×D53C24112yes—
280C2×C4×D53C24112yes—
281C2×C4×D53C2414yes—
282C2×C4×D53C24112yes—
283C2×C4×D53C24112yes—
284C2×C4×D53C24112yes—
285C2×C4×D53C24112yes—
286C2×C4×D53C24112yes—
287C2×Dic106—212no—
288C2×Dic106C24112yes—
289C4⋊C4×C53C24112yes—
290C4⋊C4×C53C24112yes—
291C22⋊C4×C53C2414yes—
292C22⋊C4×C53C24112yes—
293C22⋊C4×C53C24124yes—
294C42×C53C24112yes—
295C22⋊Dic53C24112yes—
296C22⋊Dic53C24112yes—
297#11719921C2414yes—
298#11719921C24112yes—
299#11719921C24112yes—
300#11719921C24112yes—
301#11719921C24124yes—
302#11719921C24124yes—
303C4⋊Dic53C24112yes—
304C4⋊Dic53C24112yes—
305#11719919C2414yes—
306#11719919C24112yes—
307#11719919C24124yes—
308C4×Dic53C2414yes—
309C4×Dic53C24112yes—
310C4×Dic53C24112yes—
311C23×C53—22no—
312C23×C53—22no—
313C23×C53—26no—
314C23×C53—26no—
315C23×C53—26no—
316C23×C53C2×#4114yescomplemented
317C23×C53C2516yes—
318C23×C53C2512yes—
319C23×C53C2511yescharacteristic
320C22×D53—22no—
321C22×D53—26no—
322C22×D53—26no—
323C22×D53—22no—
324C22×D53—26no—
325C22×D53—26no—
326C22×D53—224no—
327C22×D53—26no—
328C22×D53—224no—
329C22×D53—224no—
330C22×D53—224no—
331C22×D53—412no—
332C22×D53—412no—
333C22×D53—448no—
334C22×D53—448no—
335C22×D53C22×D4112yes—
336C22×D53C2×#4114yescomplemented
337C22×D53C2516yes—
338C22×D53C2516yes—
339C22×D53C2512yes—
340Q8×C53—224no—
341Q8×C53C22×D4116yescomplemented
342D4×C53—224no—
343D4×C53—224no—
344C2×C4×C53—22no—
345C2×C4×C53—26no—
346C2×C4×C53—26no—
347C2×C4×C53—22no—
348C2×C4×C53—224no—
349C2×C4×C53—224no—
350C2×C4×C53C22×D4112yes—
351C2×C4×C53C2512yes—
352C2×C4×C53C2512yes—
353C2×C4×C53C2516yes—
354C2×C4×C53C2516yes—
355C2×C4×C53C2516yes—
356C22⋊D53—248no—
357C22⋊D53—224no—
358C22⋊D53—424no—
359C22⋊D53C2×#41116yescomplemented
360C2×Dic53—26no—
361C2×Dic53—22no—
362C2×Dic53—26no—
363C2×Dic53—28no—
364C2×Dic53—224no—
365C2×Dic53C22×D414yes—
366C2×Dic53C2×#4114yescomplemented
367C2×Dic53C2516yes—
368C2×Dic53C2512yes—
369C2×Dic53C2516yes—
370C2×Dic53C2512yes—
371C2×Dic53C2512yes—
372D212—248no—
373D212—224no—
374D212—224no—
375D212C22×D4148yescomplemented
376C4×D53—224no—
377C4×D53—224no—
378C4×D53—224no—
379C4×D53—224no—
380C4×D53—28no—
381C4×D53—224no—
382C4×D53—224no—
383C4×D53—412no—
384C4×D53C22×D4148yescomplemented
385Dic106—224no—
386C2×D4×#41—531nomaximal, Sylow
387C22×C53—22no—
388C22×C53—22no—
389C22×C53—28no—
390C22×C53—26no—
391C22×C53—26no—
392C22×C53—26no—
393C22×C53—412no—
394C22×C53C23×D412yes—
395C22×C53C22×#4112yes—
396C22×C53C22×#4114yescomplemented
397C22×C53#58512yes—
398C22×C53C2611yescharacteristic
399C2×D53—22no—
400C2×D53—26no—
401C2×D53—26no—
402C2×D53—22no—
403C2×D53—28no—
404C2×D53—224no—
405C2×D53—26no—
406C2×D53—26no—
407C2×D53—26no—
408C2×D53—448no—
409C2×D53—448no—
410C2×D53—412no—
411C2×D53C23×D4112yes—
412C2×D53C22×#4114yescomplemented
413C4×C53—22no—
414C4×C53—26no—
415C4×C53—26no—
416C4×C53—22no—
417C4×C53C23×D4112yes—
418Dic53—26no—
419Dic53—22no—
420Dic53—26no—
421Dic53C23×D414yes—
422Dic53C22×#4114yescomplemented
423C23×#41—531no—
424C23×#41—531no—
425D4×#41—5332no—
426C2×#550—531no—
427C2×D4×Q8—531no—
428C2×#548—531no—
429C2×#548D5311yescharacteristic, complemented
430C2×#547—533no—
431C2×#546—533no—
432C2×#546—533no—
433C2×D42—533no—
434C2×#532—533no—
435C2×#525—533no—
436C2×#525—533no—
437C2×C4×#41—531no—
438C22×C4×D4—533no—
439C2×C53—24no—
440C2×C53—46no—
441C2×C53D4×#4114yescomplemented
442C2×C53C24×D411yescharacteristic
443C2×C53C23×#4111yescharacteristic
444C2×C53C2×#58511yescharacteristic
445D53—24no—
446D53—212no—
447D53—46no—
448C22×#41—5316no—
449C22×#41—531no—
450C22×#41—533no—
451C22×#41—533no—
452C22×#41—531no—
453C22×#41—5316no—
454C22×#41—533no—
455C22×#41—533no—
456C22×#41—10616no—
457C22×#41—10616no—
458C22×#41C2×D5311yescharacteristic, complemented
459C23×Q8—531no—
460C23×Q8C2×D5311yescharacteristic, complemented
461C23×D4—533no—
462C23×D4—533no—
463C23×D4—533no—
464C24×C4—533no—
465C24×C4—533no—
466#550—5316no—
467D4×Q8—5316no—
468#548—5316no—
469#548C2×D53116yescomplemented
470#547—5348no—
471#546—5348no—
472#546—5348no—
473D42—5348no—
474#532—5348no—
475C2×C4⋊Q8—533no—
476C2×#127—533no—
477C2×#124—533no—
478C2×#124C2×D5313yescomplemented
479#525—5348no—
480#525—5348no—
481C2×#123—536no—
482C2×#123—536no—
483C2×C22⋊Q8—533no—
484C2×C22⋊Q8—533no—
485C2×C22⋊Q8—533no—
486C2×C22⋊Q8C2×D5313yescomplemented
487C2×#121—533no—
488C2×#121—533no—
489C2×#121—533no—
490C2×#121—536no—
491C2×#121—536no—
492C2×#121C2×D5313yescomplemented
493C2×#120—536no—
494C2×#120—536no—
495C4×#41—5316no—
496C2×C4×Q8—531no—
497C2×C4×Q8C2×D5311yescharacteristic, complemented
498C2×C4×D4—533no—
499C2×C4×D4—533no—
500C2×C4×D4—533no—
501C2×C4×D4—5348no—
502C2×C4×D4—533no—
503C2×C4×D4—533no—
504C2×C4×D4—531no—
505C2×C4×D4—533no—
506C2×C4×D4—536no—
507C2×C4×D4—533no—
508C2×C4×D4—533no—
509C2×C4×D4C2×D5313yescomplemented
510C2×#117—533no—
511C22×C4⋊C4—533no—
512C22×C22⋊C4—533no—
513C22×C22⋊C4—533no—
514C22×C42—533no—
515C53C2×D4×#4111yescharacteristic, complemented, Sylow
516C25—533no—
517C25—533no—
518C2×#41—28no—
519C2×#41—5316no—
520C2×#41—538no—
521C2×#41—5324no—
522C2×#41—5324no—
523C2×#41—538no—
524C2×#41—5324no—
525C2×#41—5324no—
526C2×#41—10624no—
527C2×#41—10624no—
528C2×#41—10624no—
529C2×#41—10624no—
530C2×#41—106128no—
531C2×#41—106128no—
532C2×#41—1068no—
533C2×#41C22×D5318yescomplemented
534C22×Q8—28no—
535C22×Q8—538no—
536C22×Q8—533no—
537C22×Q8—1068no—
538C22×Q8C22×D5313yes—
539C22×Q8C22×D5311yescharacteristic
540C22×Q8C22×D5318yescomplemented
541C22×D4—531no—
542C22×D4—533no—
543C22×D4—536no—
544C22×D4—536no—
545C22×D4—5324no—
546C22×D4—5324no—
547C22×D4—533no—
548C22×D4—533no—
549C22×D4—536no—
550C22×D4—533no—
551C22×D4—5324no—
552C22×D4—10624no—
553C22×D4—10624no—
554C22×D4—10624no—
555C22×D4C22×D5313yes—
556C22×D4C22×D5313yes—
557C23×C4—533no—
558C23×C4—531no—
559C23×C4—533no—
560C23×C4—533no—
561C23×C4—533no—
562C23×C4—533no—
563C23×C4—531no—
564C23×C4—533no—
565C23×C4—533no—
566C23×C4—533no—
567C23×C4—5324no—
568C23×C4—5324no—
569C23×C4—533no—
570C23×C4—10624no—
571C23×C4—10624no—
572C23×C4C22×D5313yes—
573C23×C4C22×D5313yes—
574C4⋊Q8—5324no—
575#127—5324no—
576#124—5324no—
577#124C22×D53124yescomplemented
578#123—5348no—
579#123—5348no—
580C22⋊Q8—5324no—
581C22⋊Q8—5324no—
582C22⋊Q8—5324no—
583C22⋊Q8C22×D53124yescomplemented
584#121—5324no—
585#121—5324no—
586#121—5324no—
587#121—5348no—
588#121—5348no—
589#121C22×D53124yescomplemented
590#120—5348no—
591#120—5348no—
592C4×Q8—538no—
593C4×Q8C22×D5318yescomplemented
594C4×D4—5324no—
595C4×D4—5324no—
596C4×D4—5324no—
597C4×D4—5324no—
598C4×D4—5324no—
599C4×D4—538no—
600C4×D4—5324no—
601C4×D4—5348no—
602C4×D4—5324no—
603C4×D4—5324no—
604C4×D4C22×D53124yescomplemented
605#117—5324no—
606C2×C4⋊C4—531no—
607C2×C4⋊C4—533no—
608C2×C4⋊C4—533no—
609C2×C4⋊C4—533no—
610C2×C4⋊C4—536no—
611C2×C4⋊C4—5324no—
612C2×C4⋊C4C22×D5313yes—
613C2×C4⋊C4C22×D5313yes—
614C2×C22⋊C4—533no—
615C2×C22⋊C4—533no—
616C2×C22⋊C4—531no—
617C2×C22⋊C4—533no—
618C2×C22⋊C4—533no—
619C2×C22⋊C4—533no—
620C2×C22⋊C4—536no—
621C2×C22⋊C4—536no—
622C2×C22⋊C4—5324no—
623C2×C22⋊C4—5324no—
624C2×C22⋊C4C22×D5311yescharacteristic
625C2×C22⋊C4C22×D5313yes—
626C2×C22⋊C4C22×D5316yes—
627C2×C42—533no—
628C2×C42—531no—
629C2×C42—533no—
630C2×C42—5324no—
631C2×C42C22×D5313yes—
632C24—531no—
633C24—533no—
634C24—533no—
635C24—5312no—
636C24—5312no—
637C24—10612no—
638C24—10612no—
639C24—10612no—
640C24—10612no—
641C24—2126no—
642C24—2126no—
643C24C23×D5313yes—
644C24C23×D5311yescharacteristic
645#41—232no—
646#41—5364no—
647#41—10696no—
648#41—10696no—
649#41—10696no—
650#41—10696no—
651#41—10632no—
652C2×Q8—232no—
653C2×Q8—212no—
654C2×Q8—5312no—
655C2×Q8—10632no—
656C2×Q8—10612no—
657C2×Q8D4×D5318yescomplemented
658C2×Q8C23×D53112yes—
659C2×Q8C23×D5314yes—
660C2×D4—212no—
661C2×D4—212no—
662C2×D4—538no—
663C2×D4—534no—
664C2×D4—5312no—
665C2×D4—5324no—
666C2×D4—5324no—
667C2×D4—5324no—
668C2×D4—5312no—
669C2×D4—5312no—
670C2×D4—5324no—
671C2×D4—5312no—
672C2×D4—10696no—
673C2×D4—10612no—
674C2×D4—10624no—
675C2×D4—10612no—
676C2×D4—10696no—
677C2×D4—10696no—
678C2×D4—10624no—
679C2×D4—10612no—
680C2×D4—21212no—
681C2×D4C23×D53112yes—
682C2×D4C23×D53112yes—
683C22×C4—212no—
684C22×C4—212no—
685C22×C4—531no—
686C22×C4—531no—
687C22×C4—5324no—
688C22×C4—5312no—
689C22×C4—534no—
690C22×C4—5312no—
691C22×C4—533no—
692C22×C4—531no—
693C22×C4—533no—
694C22×C4—5312no—
695C22×C4—5312no—
696C22×C4—5312no—
697C22×C4—534no—
698C22×C4—5312no—
699C22×C4—5312no—
700C22×C4—5312no—
701C22×C4—5312no—
702C22×C4—1064no—
703C22×C4—10612no—
704C22×C4—10696no—
705C22×C4—10696no—
706C22×C4—10612no—
707C22×C4—10612no—
708C22×C4—10612no—
709C22×C4—1064no—
710C22×C4—10612no—
711C22×C4—10612no—
712C22×C4—10612no—
713C22×C4—2126no—
714C22×C4C23×D53112yes—
715C22×C4C23×D53112yes—
716C22×C4C23×D5311yescharacteristic
717C22×C4C23×D5313yes—
718C22×C4C23×D5311yescharacteristic
719C22×C4C23×D5313yes—
720C22×C4C23×D5313yes—
721C4⋊C4—534no—
722C4⋊C4—5312no—
723C4⋊C4—5312no—
724C4⋊C4—5312no—
725C4⋊C4—5324no—
726C4⋊C4C23×D53112yes—
727C4⋊C4C23×D53112yes—
728C22⋊C4—5312no—
729C22⋊C4—5312no—
730C22⋊C4—534no—
731C22⋊C4—5312no—
732C22⋊C4—5312no—
733C22⋊C4—5312no—
734C22⋊C4—5324no—
735C22⋊C4—5324no—
736C22⋊C4C23×D5314yes—
737C22⋊C4C23×D53112yes—
738C22⋊C4C23×D53124yes—
739C42—534no—
740C42—5312no—
741C42—5312no—
742C42C23×D53112yes—
743C23—22no—
744C23—22no—
745C23—26no—
746C23—26no—
747C23—26no—
748C23—5312no—
749C23—534no—
750C23—532no—
751C23—536no—
752C23—536no—
753C23—10624no—
754C23—10624no—
755C23—10624no—
756C23—1062no—
757C23—1066no—
758C23—1066no—
759C23—1062no—
760C23—1066no—
761C23—1066no—
762C23—10624no—
763C23—1066no—
764C23—21212no—
765C23—21212no—
766C23—21248no—
767C23—21248no—
768C23#41×D5314yescomplemented
769C23C24×D5316yes—
770C23C24×D5312yes—
771C23C24×D5311yescharacteristic
772Q8—224no—
773Q8—10624no—
774Q8C2×D4×D53116yescomplemented
775D4—224no—
776D4—224no—
777D4—5316no—
778D4—5348no—
779D4—10624no—
780D4—10648no—
781D4—10624no—
782D4—10648no—
783D4—10624no—
784D4—21224no—
785C2×C4—22no—
786C2×C4—26no—
787C2×C4—26no—
788C2×C4—22no—
789C2×C4—224no—
790C2×C4—224no—
791C2×C4—534no—
792C2×C4—534no—
793C2×C4—532no—
794C2×C4—532no—
795C2×C4—5348no—
796C2×C4—536no—
797C2×C4—532no—
798C2×C4—536no—
799C2×C4—1068no—
800C2×C4—10624no—
801C2×C4—10624no—
802C2×C4—10624no—
803C2×C4—10624no—
804C2×C4—1068no—
805C2×C4—10624no—
806C2×C4—1062no—
807C2×C4—1066no—
808C2×C4—1066no—
809C2×C4—10624no—
810C2×C4—10624no—
811C2×C4—21212no—
812C2×C4C2×D4×D53112yes—
813C2×C4C24×D5312yes—
814C2×C4C24×D5316yes—
815C2×C4C24×D5312yes—
816C2×C4C24×D5316yes—
817C2×C4C24×D5316yes—
818C22—28no—
819C22—22no—
820C22—22no—
821C22—26no—
822C22—26no—
823C22—26no—
824C22—412no—
825C22—5312no—
826C22—534no—
827C22—1068no—
828C22—10624no—
829C22—1062no—
830C22—1066no—
831C22—1066no—
832C22—1062no—
833C22—1066no—
834C22—1066no—
835C22—1066no—
836C22—21248no—
837C22—21248no—
838C22—21212no—
839C22C22×D4×D5312yes—
840C22C2×#41×D5312yes—
841C22C2×#41×D5314yescomplemented
842C22#1681146012yes—
843C22C25×D5311yescharacteristic
844C4—22no—
845C4—26no—
846C4—26no—
847C4—22no—
848C4—534no—
849C4—534no—
850C4—1062no—
851C4—1066no—
852C4—1066no—
853C4C22×D4×D53112yes—
854C2—24no—
855C2—46no—
856C2—1064no—
857C2—10612no—
858C2—2126no—
859C2#2028820414yesdirect product factor
860C2C23×D4×D5311yescharacteristic
861C2C22×#41×D5311yescharacteristic
862C2C2×#1681146011yescharacteristic
subgroupG/H
centerC23C24×D53
commutator, cosocleC22×C53C26
FrattiniC22C25×D53
FittingC2×C53×#548C2
socleC23×C53C25
hypercenterC2×#548D53
hypocenterC53C2×D4×#41
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C23×#11719949C2semidirect
2. C22×#41×D53C2semidirect
3. #20288204C2direct (N × H)
4. C2×#16811292C2semidirect
5. C2×Q8×C22⋊D53C2semidirect
6. C2×#16811285C2semidirect
7. C2×#16811275C2semidirect
8. C2×#16811269C2semidirect
9. C2×#16811266C2semidirect
10. C2×#16811257C2semidirect
11. C2×#16811172C2semidirect
12. C2×#16811136C2semidirect
13. C2×#16811133C2semidirect
14. C2×C4×#11719949C2semidirect
15. C2×C4×D4×D53C2semidirect
16. C2×C53×#548C2semidirect
19. C22×#11719949C22semidirect
20. C22×#11719949C22semidirect
21. C22×#11719949C22semidirect
22. C22×#11719949C22semidirect
23. C22×#11719945C22semidirect
24. C22×#11719947C22semidirect
26. C2×#41×D53C22semidirect
27. C22×Q8×D53C22semidirect
28. C23×D212C22semidirect
30. C22×D4×D53C22semidirect
31. C23×C4×D53C22semidirect
32. C23×C4×D53C22semidirect
33. #16811292C22semidirect
34. Q8×C22⋊D53C22semidirect
35. #16811285C22semidirect
36. #16811275C22semidirect
37. #16811269C22semidirect
38. #16811266C22semidirect
39. #16811257C22semidirect
40. #16811172C22semidirect
41. C2×#13133215C22semidirect
42. C2×#13133213C22semidirect
43. C2×#13133205C22semidirect
44. #16811136C22semidirect
45. #16811133C22semidirect
46. C2×#13133202C22semidirect
47. C2×#13133199C22semidirect
48. C2×#13133197C22semidirect
49. C2×#13133196C22semidirect
50. C2×#13133193C22semidirect
51. C2×#13133192C22semidirect
52. C2×#13133191C22semidirect
53. C2×#13133190C22semidirect
54. C2×#13133190C22semidirect
55. C2×#13133188C22semidirect
56. C2×#13133187C22semidirect
57. C2×#13133185C22semidirect
58. C4×#11719949C22semidirect
59. C2×Q8×Dic53C22semidirect
60. C2×C4×D212C22semidirect
61. C2×C4×D212C22semidirect
62. C2×D4×Dic53C22semidirect
63. C2×#13133179C22semidirect
64. C2×#13133179C22semidirect
66. C2×C4×C22⋊D53C22semidirect
68. C2×#13133177C22semidirect
69. C2×#13133177C22semidirect
70. C4×D4×D53C22semidirect
71. C2×#13133175C22semidirect
72. C2×C4⋊C4×D53C22semidirect
73. C2×C22⋊C4×D53C22semidirect
74. C2×C22⋊C4×D53C22semidirect
75. C2×C42×D53C22semidirect
76. C22×#41×C53C22semidirect
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
90. C2×#11719949D4semidirect
92. C2×#11719949C23semidirect
93. C2×#11719949C23semidirect
94. C2×#11719949C23semidirect
96. C2×#11719945C23semidirect
98. C2×#11719947C23semidirect
102. C2×Q8×D53C23semidirect
108. C22×D212C23semidirect
116. C2×D4×D53C23semidirect
130. C22×C4×D53C23semidirect
131. C22×C4×D53C23semidirect
132. #13133215C23semidirect
133. #13133213C23semidirect
134. #13133205C23semidirect
135. #13133202C23semidirect
136. #13133199C23semidirect
137. #13133197C23semidirect
138. #13133196C23semidirect
139. #13133193C23semidirect
140. #13133192C23semidirect
141. #13133191C23semidirect
142. #13133190C23semidirect
143. #13133190C23semidirect
144. #13133188C23semidirect
145. #13133187C23semidirect
146. #13133185C23semidirect
147. Q8×Dic53C23semidirect
148. C4×D212C23semidirect
149. C4×D212C23semidirect
150. D4×Dic53C23semidirect
151. #13133179C23semidirect
152. #13133179C23semidirect
154. C4×C22⋊D53C23semidirect
156. #13133177C23semidirect
157. #13133177C23semidirect
158. #13133175C23semidirect
164. C4⋊C4×D53C23semidirect
173. C22⋊C4×D53C23semidirect
174. C22⋊C4×D53C23semidirect
178. C42×D53C23semidirect
180. C2×#41×C53C23semidirect
184. C22×Q8×C53C23semidirect
189. #124×C53C23semidirect
190. C22⋊Q8×C53C23semidirect
191. #121×C53C23semidirect
192. C4×Q8×C53C23semidirect
193. C4×D4×C53C23semidirect
216. C2×Q8×C53C2×D4semidirect
235. C2×C22⋊D53#41semidirect
252. #11719949C2×D4semidirect
262. C2×D212C2×D4semidirect
277. C2×C4×D53C2×D4semidirect
316. C23×C53C2×#41semidirect
336. C22×D53C2×#41semidirect
341. Q8×C53C22×D4semidirect
359. C22⋊D53C2×#41semidirect
366. C2×Dic53C2×#41semidirect
375. D212C22×D4semidirect
384. C4×D53C22×D4semidirect
396. C22×C53C22×#41semidirect
412. C2×D53C22×#41semidirect
422. Dic53C22×#41semidirect
429. C2×#548D53semidirect
441. C2×C53D4×#41semidirect
458. C22×#41C2×D53semidirect
460. C23×Q8C2×D53semidirect
469. #548C2×D53semidirect
478. C2×#124C2×D53semidirect
486. C2×C22⋊Q8C2×D53semidirect
492. C2×#121C2×D53semidirect
497. C2×C4×Q8C2×D53semidirect
509. C2×C4×D4C2×D53semidirect
515. C53C2×D4×#41semidirect
533. C2×#41C22×D53semidirect
540. C22×Q8C22×D53semidirect
577. #124C22×D53semidirect
583. C22⋊Q8C22×D53semidirect
589. #121C22×D53semidirect
593. C4×Q8C22×D53semidirect
604. C4×D4C22×D53semidirect
657. C2×Q8D4×D53semidirect
768. C23#41×D53semidirect
774. Q8C2×D4×D53semidirect
841. C22C2×#41×D53semidirect
859. C2#20288204direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#117199492
C22×#41×D532
#202882042
C2×#168112922
C2×Q8×C22⋊D532
C2×#168112852
C2×#168112752
C2×#168112692
C2×#168112662
C2×#168112572
C2×#168111722
C2×#168111362
C2×#168111332
C2×C4×#117199492
C2×C4×D4×D532
C2×C53×#5482
C2×D4×#4153