Finite Group Databasebeta

← C2×#20288361 #28292254

Subgroups — C2×#20288361 #28292254

Order 13568.

11254 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×#13133264C211yesmaximal, characteristic, complemented
2C23×Q8×D53C211yesmaximal, characteristic, complemented
3#20288361C2132yesmaximal, direct product factor
4C2×Q8×D212C211yesmaximal, characteristic, complemented
5C2×D4×Dic106C213yesmaximal, complemented
6C2×Q8×C22⋊D53C211yesmaximal, characteristic, complemented
7C2×#16811286C213yesmaximal, complemented
8C2×#16811281C213yesmaximal, complemented
9C2×#16811280C211yesmaximal, characteristic, complemented
10C2×#16811279C213yesmaximal, complemented
11C2×#16811196C213yesmaximal, complemented
12C2×#16811193C213yesmaximal, complemented
13C2×#16811133C213yesmaximal, complemented
14C2×#16811132C213yesmaximal, complemented
15C2×#16811099C211yesmaximal, characteristic, complemented
16C2×C53×#548C211yesmaximal, characteristic, complemented
17C2×#13133264—216no—
18C2×#13133264C22116yescomplemented
19C22×#11719945C2213yes—
20C22×#11719947C2213yes—
21C22×#11719947C2213yescomplemented
22C23×Dic106C2213yes—
23C23×Dic106C2213yescomplemented
24C22×Q8×D53—216no—
25C22×Q8×D53C2213yes—
26C22×Q8×D53C2211yescharacteristic
27C22×Q8×D53C2213yes—
28C22×Q8×D53C2211yescharacteristic
29C22×Q8×D53C22116yescomplemented
30C22×Q8×D53C2211yescharacteristic, complemented
31C23×C4×D53C2213yes—
32Q8×D212C22116yescomplemented
33D4×Dic106C22148yescomplemented
34Q8×C22⋊D53C22116yescomplemented
35#16811286C22148yescomplemented
36#16811281C22148yescomplemented
37#16811280C22116yescomplemented
38#16811279C22148yescomplemented
39#16811196C22148yescomplemented
40#16811193C22148yescomplemented
41C2×#13133217C2213yescomplemented
42C2×#13133216C2216yescomplemented
43C2×#13133215C2213yescomplemented
44C2×#13133204C2213yescomplemented
45C2×#13133203C2216yescomplemented
46#16811133C22148yescomplemented
47#16811132C22148yescomplemented
48C2×#13133202C2213yes—
49C2×#13133199C2213yes—
50C2×#13133199C2216yes—
51C2×#13133197C2213yes—
52C2×#13133197C2213yescomplemented
53C2×#13133196C2213yes—
54C2×#13133196C2213yescomplemented
55C2×#13133195C2213yes—
56C2×#13133194C2213yes—
57C2×#13133194C2216yescomplemented
58C2×#13133194C2216yescomplemented
59C2×#13133193C2213yescomplemented
60C2×#13133190C2213yes—
61C2×#13133189C2213yes—
62C2×#13133188C2213yes—
63C2×#13133187C2211yescharacteristic
64C2×#13133185C2213yes—
65#16811099C22116yescomplemented
66C2×Q8×Dic53C2211yescharacteristic, complemented
67C2×C4×Dic106C2213yescomplemented
68C2×#13133182C2213yescomplemented
69C2×C4×D212C2213yes—
70C2×D4×Dic53C2216yes—
71C2×C4×C22⋊D53C2213yes—
72C2×C4×C22⋊D53C2213yes—
73C2×#13133177C2216yes—
74C2×#13133175C2213yes—
75C2×#13133174C2213yes—
76C22×#41×C53C2211yescharacteristic, complemented
77C23×Q8×C53C2211yescharacteristic
78C53×#548C22116yescomplemented
79C2×#124×C53C2213yescomplemented
80C2×C22⋊Q8×C53C2213yescomplemented
81C2×#121×C53C2213yes—
82C2×C4×Q8×C53C2211yescharacteristic, complemented
83C2×C4×D4×C53C2213yes—
84C24×D53C2311yescharacteristic
85#13133264—2128no—
86C2×#11719945—224no—
87C2×#11719945C23124yes—
88C2×#11719947—224no—
89C2×#11719947—224no—
90C2×#11719947C23124yes—
91C2×#11719947C23124yescomplemented
92C22×Dic106—224no—
93C22×Dic106—224no—
94C22×Dic106C23124yes—
95C22×Dic106C2313yes—
96C22×Dic106C2316yes—
97C22×Dic106C2313yes—
98C22×Dic106C2313yes—
99C22×Dic106C2313yes—
100C22×Dic106C23124yescomplemented
101C2×Q8×D53—28no—
102C2×Q8×D53—28no—
103C2×Q8×D53—2128no—
104C2×Q8×D53—224no—
105C2×Q8×D53—224no—
106C2×Q8×D53D4116yescomplemented
107C2×Q8×D53C2318yes—
108C2×Q8×D53C23124yes—
109C2×Q8×D53C23124yes—
110C2×Q8×D53C2318yes—
111C2×Q8×D53C2318yescomplemented
112C22×D212C2311yescharacteristic
113C22×D212C2311yescharacteristic
114C22×C22⋊D53C2313yes—
115C22×C22⋊D53C2311yescharacteristic
116C22×C22⋊D53C2313yes—
117C22×C22⋊D53C2313yes—
118C23×Dic53C2316yes—
119C23×Dic53C2313yes—
120C22×C4×D53—224no—
121C22×C4×D53C2313yes—
122C22×C4×D53C2313yes—
123C22×C4×D53C2313yes—
124C22×C4×D53C2313yes—
125C22×C4×D53C23124yes—
126C22×C4×D53C2313yes—
127#13133217C23124yescomplemented
128#13133216C23148yescomplemented
129#13133215C23124yescomplemented
130#13133204C23124yescomplemented
131#13133203C23148yescomplemented
132#13133202C23124yes—
133#13133199C23124yes—
134#13133199C23148yes—
135#13133197C23124yes—
136#13133197C23124yescomplemented
137#13133196C23124yes—
138#13133196C23124yescomplemented
139#13133195C23124yes—
140#13133194C23124yes—
141#13133194C23148yescomplemented
142#13133194C23148yescomplemented
143#13133193C23124yescomplemented
144#13133190C23124yes—
145#13133189C23124yes—
146#13133188C23124yes—
147#13133187C2318yes—
148#13133185C23124yes—
149Q8×Dic53C2318yescomplemented
150C4×Dic106C23124yescomplemented
151#13133182C23124yescomplemented
152C4×D212C23124yes—
153D4×Dic53C23148yes—
154C4×C22⋊D53C23124yes—
155C4×C22⋊D53C23124yes—
156#13133177C23148yes—
157#13133175C23124yes—
158#13133174C23124yes—
159C2×C4⋊Dic53C2313yes—
160C2×C4⋊Dic53C2316yes—
161C2×C4⋊Dic53C2313yes—
162C2×#11719919C2313yes—
163C2×#11719919C2313yes—
164C2×#11719919C2316yes—
165C2×#11719919C2313yes—
166C2×#11719919C2313yes—
167C2×C22⋊Dic53C2313yes—
168C2×C22⋊Dic53C2313yes—
169C2×C22⋊Dic53C2316yes—
170C2×#11719921C2311yescharacteristic
171C2×#11719921C2313yes—
172C2×#11719921C2313yes—
173C2×#11719921C2311yescharacteristic
174C2×#11719921C2313yes—
175C2×#11719921C2313yes—
176C2×C4×Dic53C2313yes—
177C2×C4×Dic53C2316yes—
178C2×#41×C53—28no—
179C2×#41×C53C2318yescomplemented
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×C53C23124yescomplemented
189C22⋊Q8×C53C23124yescomplemented
190#121×C53C23124yes—
191C4×Q8×C53C2318yescomplemented
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×D53—24no—
202C23×D53—24no—
203C23×D53—24no—
204C23×D53C2411yescharacteristic
205C23×D53C2414yes—
206C23×D53C2411yescharacteristic
207C23×D53C2411yescharacteristic
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—212no—
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—212no—
229C2×C22⋊D53—212no—
230C2×C22⋊D53—212no—
231C2×C22⋊D53C24112yes—
232C2×C22⋊D53C2414yes—
233C2×C22⋊D53C24112yes—
234C2×C22⋊D53C24112yes—
235C22×Dic53—212no—
236C22×Dic53—224no—
237C22×Dic53C2411yescharacteristic
238C22×Dic53C2413yes—
239C22×Dic53C2413yes—
240C22×Dic53C2413yes—
241C22×Dic53C24124yes—
242C22×Dic53C24112yes—
243C22×Dic53C2413yes—
244Q8×D53—232no—
245Q8×D53—232no—
246Q8×D53—296no—
247Q8×D53—296no—
248Q8×D53C2×D4164yescomplemented
249#11719947—296no—
250#11719947—296no—
251#11719945—296no—
252C2×D212—24no—
253C2×D212—24no—
254C2×D212C2414yes—
255C2×D212C2414yes—
256C2×C4×D53—212no—
257C2×C4×D53—212no—
258C2×C4×D53—212no—
259C2×C4×D53—212no—
260C2×C4×D53—296no—
261C2×C4×D53C2×D4124yes—
262C2×C4×D53C24112yes—
263C2×C4×D53C24112yes—
264C2×C4×D53C24112yes—
265C2×C4×D53C24112yes—
266C2×C4×D53C24112yes—
267C2×Dic106—212no—
268C2×Dic106—212no—
269C2×Dic106—224no—
270C2×Dic106—212no—
271C2×Dic106—296no—
272C2×Dic106—296no—
273C2×Dic106C2×D4124yes—
274C2×Dic106C24112yes—
275C2×Dic106C24124yes—
276C2×Dic106C24112yes—
277C2×Dic106C24112yes—
278C2×Dic106C24112yes—
279C4⋊C4×C53C24112yes—
280C4⋊C4×C53C24112yes—
281C22⋊C4×C53C2414yes—
282C22⋊C4×C53C24112yes—
283C22⋊C4×C53C24124yes—
284C42×C53C24112yes—
285C22⋊Dic53C24112yes—
286C22⋊Dic53C24112yes—
287C22⋊Dic53C24124yes—
288#11719921C2414yes—
289#11719921C24112yes—
290#11719921C24112yes—
291#11719921C2414yes—
292#11719921C24112yes—
293#11719921C24112yes—
294C4⋊Dic53C24112yes—
295C4⋊Dic53C24124yes—
296C4⋊Dic53C24112yes—
297#11719919C24112yes—
298#11719919C24112yes—
299#11719919C24124yes—
300#11719919C24112yes—
301#11719919C24112yes—
302C4×Dic53C24112yes—
303C4×Dic53C24124yes—
304C23×C53—22no—
305C23×C53—22no—
306C23×C53—26no—
307C23×C53—26no—
308C23×C53—26no—
309C23×C532−1+414yescomplemented
310C23×C53C2516yes—
311C23×C53C2512yes—
312C23×C53C2511yescharacteristic
313C22×D53—232no—
314C22×D53—22no—
315C22×D53—22no—
316C22×D53—22no—
317C22×D53—22no—
318C22×D53—28no—
319C22×D53—28no—
320C22×D53—28no—
321C22×D53—22no—
322C22×D53—22no—
323C22×D53—22no—
324C22×D53C22×D414yes—
325C22×D532−1+414yescomplemented
326C22×D53C2512yes—
327C22×D53C2512yes—
328C22×D53C2512yes—
329Q8×C53—224no—
330Q8×C53C22×D4116yes—
331D4×C53—224no—
332D4×C53—224no—
333C2×C4×C53—22no—
334C2×C4×C53—26no—
335C2×C4×C53—22no—
336C2×C4×C53—26no—
337C2×C4×C53—224no—
338C2×C4×C53—224no—
339C2×C4×C53C22×D4112yes—
340C2×C4×C53C2512yes—
341C2×C4×C53C2516yes—
342C2×C4×C53C2512yes—
343C2×C4×C53C2516yes—
344C2×C4×C53C2516yes—
345C22⋊D53—28no—
346C22⋊D53—224no—
347C22⋊D53—224no—
348C22⋊D53—224no—
349C2×Dic53—26no—
350C2×Dic53—26no—
351C2×Dic53—26no—
352C2×Dic53—22no—
353C2×Dic53—224no—
354C2×Dic53—248no—
355C2×Dic53C22×D4112yes—
356C2×Dic53C2516yes—
357C2×Dic53C2516yes—
358C2×Dic53C2512yes—
359C2×Dic53C2516yes—
360C2×Dic53C2516yes—
361D212—28no—
362D212—28no—
363C4×D53—224no—
364C4×D53—224no—
365C4×D53—224no—
366C4×D53—224no—
367C4×D53C22×D4148yes—
368Dic106—224no—
369Dic106—224no—
370Dic106—224no—
371Dic106—248no—
372Dic106C22×D4148yes—
373C2×#3486—531nomaximal, Sylow
374C22×C53—22no—
375C22×C53—22no—
376C22×C53—28no—
377C22×C53—26no—
378C22×C53—26no—
379C22×C53—26no—
380C22×C53—412no—
381C22×C53C23×D412yes—
382C22×C53C2×2−1+412yes—
383C22×C53C2×2−1+412yes—
384C22×C53C2×2−1+414yescomplemented
385C22×C53C2611yescharacteristic
386C2×D53—232no—
387C2×D53—22no—
388C2×D53—22no—
389C2×D53—22no—
390C2×D53—22no—
391C2×D53—28no—
392C2×D53—28no—
393C2×D53—22no—
394C2×D53—22no—
395C2×D53—22no—
396C2×D53—44no—
397C2×D53C23×D414yes—
398C2×D53C2×2−1+414yescomplemented
399C4×C53—22no—
400C4×C53—26no—
401C4×C53—22no—
402C4×C53—26no—
403C4×C53C23×D4112yes—
404Dic53—26no—
405Dic53—26no—
406Dic53—26no—
407Dic53—22no—
408Dic53C23×D4112yes—
409C22×2−1+4—531no—
410C24×Q8—531no—
411#3486—5332no—
412C2×D4×Q8—531no—
413C2×D4×Q8—533no—
414C2×D4×Q8—531no—
415C2×D4×Q8—533no—
416C2×#548—531no—
417C2×#548—533no—
418C2×#548—533no—
419C2×#548D5311yescharacteristic, complemented
420C2×#536—533no—
421C2×#536—533no—
422C2×#525—533no—
423C2×#525—533no—
424C2×#519—531no—
425C2×C53—24no—
426C2×C53—46no—
427C2×C53#348614yescomplemented
428C2×C53C24×D411yescharacteristic
429C2×C53C22×2−1+411yescharacteristic
430C2×C53C22×2−1+411yescharacteristic
431D53—24no—
432D53—24no—
433D53—42no—
434C2×2−1+4—5316no—
435C2×2−1+4—10616no—
436C22×#41—533no—
437C22×#41—533no—
438C22×#41—533no—
439C22×#41C2×D5311yescharacteristic, complemented
440C23×Q8—531no—
441C23×Q8—533no—
442C23×Q8—533no—
443C23×Q8—531no—
444C23×Q8—5316no—
445C23×Q8—531no—
446C23×Q8—533no—
447C23×Q8—533no—
448C23×Q8—10616no—
449C23×Q8C2×D5311yescharacteristic
450C24×C4—533no—
451D4×Q8—5316no—
452D4×Q8—5348no—
453D4×Q8—5316no—
454D4×Q8—5348no—
455#548—5316no—
456#548—5348no—
457#548—5348no—
458#548C2×D53116yescomplemented
459#536—5348no—
460#536—5348no—
461C2×C4⋊Q8—533no—
462C2×C4⋊Q8—536no—
463C2×C4⋊Q8—533no—
464C2×#124—533no—
465C2×#124—536no—
466C2×#124C2×D5313yescomplemented
467#525—5348no—
468#525—5348no—
469C2×#123—533no—
470C2×#123—536no—
471C2×#123—533no—
472C2×C22⋊Q8—533no—
473C2×C22⋊Q8—533no—
474C2×C22⋊Q8—533no—
475C2×C22⋊Q8—533no—
476C2×C22⋊Q8—533no—
477C2×C22⋊Q8—533no—
478C2×C22⋊Q8—533no—
479C2×C22⋊Q8—536no—
480C2×C22⋊Q8—536no—
481C2×C22⋊Q8C2×D5313yescomplemented
482C2×#121—533no—
483C2×#121—533no—
484C2×#121—533no—
485C2×#121C2×D5313yes—
486C2×#120—533no—
487C2×#120—531no—
488#519—5316no—
489C2×C4×Q8—531no—
490C2×C4×Q8—533no—
491C2×C4×Q8—533no—
492C2×C4×Q8C2×D5311yescharacteristic, complemented
493C2×C4×D4—536no—
494C2×C4×D4—533no—
495C2×C4×D4—533no—
496C2×C4×D4—536no—
497C2×C4×D4—533no—
498C2×C4×D4C2×D5313yes—
499C2×#117—533no—
500C2×#117—533no—
501C53C2×#348611yescharacteristic, complemented, Sylow
502C25—531no—
5032−1+4—106128no—
504C2×#41—28no—
505C2×#41—5324no—
506C2×#41—5324no—
507C2×#41—5324no—
508C2×#41—10624no—
509C2×#41—10624no—
510C2×#41—10624no—
511C2×#41C22×D5318yescomplemented
512C22×Q8—28no—
513C22×Q8—5316no—
514C22×Q8—538no—
515C22×Q8—5324no—
516C22×Q8—5324no—
517C22×Q8—538no—
518C22×Q8—538no—
519C22×Q8—533no—
520C22×Q8—536no—
521C22×Q8—533no—
522C22×Q8—533no—
523C22×Q8—533no—
524C22×Q8—5324no—
525C22×Q8—5324no—
526C22×Q8—10624no—
527C22×Q8—10624no—
528C22×Q8—10624no—
529C22×Q8—106128no—
530C22×Q8—10624no—
531C22×Q8—1068no—
532C22×Q8—1068no—
533C22×Q8C22×D5313yes—
534C22×Q8C22×D5318yes—
535C22×Q8C22×D5311yescharacteristic
536C22×D4—533no—
537C22×D4—531no—
538C22×D4—533no—
539C22×D4—533no—
540C22×D4—531no—
541C22×D4—531no—
542C22×D4C22×D5313yes—
543C22×D4C22×D5313yes—
544C23×C4—533no—
545C23×C4—533no—
546C23×C4—536no—
547C23×C4—533no—
548C23×C4—533no—
549C23×C4—533no—
550C23×C4—533no—
551C23×C4—5324no—
552C23×C4—10624no—
553C23×C4C22×D5313yes—
554C23×C4C22×D5313yes—
555C4⋊Q8—5324no—
556C4⋊Q8—5348no—
557C4⋊Q8—5324no—
558#124—5324no—
559#124—5348no—
560#124C22×D53124yescomplemented
561#123—5324no—
562#123—5348no—
563#123—5324no—
564C22⋊Q8—5324no—
565C22⋊Q8—5324no—
566C22⋊Q8—5324no—
567C22⋊Q8—5324no—
568C22⋊Q8—5324no—
569C22⋊Q8—5324no—
570C22⋊Q8—5324no—
571C22⋊Q8—5348no—
572C22⋊Q8—5348no—
573C22⋊Q8C22×D53124yescomplemented
574#121—5324no—
575#121—5324no—
576#121—5324no—
577#121C22×D53124yes—
578#120—5324no—
579#120—538no—
580C4×Q8—538no—
581C4×Q8—5324no—
582C4×Q8—5324no—
583C4×Q8C22×D5318yescomplemented
584C4×D4—5348no—
585C4×D4—5324no—
586C4×D4—5324no—
587C4×D4—5348no—
588C4×D4—5324no—
589C4×D4C22×D53124yes—
590#117—5324no—
591#117—5324no—
592C2×C4⋊C4—533no—
593C2×C4⋊C4—533no—
594C2×C4⋊C4—533no—
595C2×C4⋊C4—533no—
596C2×C4⋊C4—533no—
597C2×C4⋊C4—536no—
598C2×C4⋊C4—536no—
599C2×C4⋊C4—533no—
600C2×C4⋊C4C22×D5313yes—
601C2×C4⋊C4C22×D5313yes—
602C2×C22⋊C4—533no—
603C2×C22⋊C4—536no—
604C2×C22⋊C4—533no—
605C2×C22⋊C4—533no—
606C2×C22⋊C4—531no—
607C2×C22⋊C4—531no—
608C2×C22⋊C4—533no—
609C2×C22⋊C4—533no—
610C2×C22⋊C4—533no—
611C2×C22⋊C4C22×D5316yes—
612C2×C22⋊C4C22×D5311yescharacteristic
613C2×C22⋊C4C22×D5313yes—
614C2×C42—536no—
615C2×C42—533no—
616C2×C42C22×D5313yes—
617C24—531no—
618C24—531no—
619C24—534no—
620C24—531no—
621C24—1064no—
622C24—1064no—
623C24—1064no—
624C24C23×D5313yes—
625C24C23×D5311yescharacteristic
626#41—232no—
627#41—10696no—
628#41—10696no—
629#41—10696no—
630C2×Q8—232no—
631C2×Q8—212no—
632C2×Q8—5364no—
633C2×Q8—5324no—
634C2×Q8—5312no—
635C2×Q8—5324no—
636C2×Q8—5312no—
637C2×Q8—5312no—
638C2×Q8—5312no—
639C2×Q8—10624no—
640C2×Q8—10612no—
641C2×Q8—10696no—
642C2×Q8—10696no—
643C2×Q8—10696no—
644C2×Q8—10696no—
645C2×Q8—10632no—
646C2×Q8—10632no—
647C2×Q8—10612no—
648C2×Q8—10612no—
649C2×Q8D4×D5318yes—
650C2×Q8C23×D53112yes—
651C2×Q8C23×D5314yes—
652C2×D4—212no—
653C2×D4—212no—
654C2×D4—5312no—
655C2×D4—534no—
656C2×D4—5312no—
657C2×D4—5312no—
658C2×D4—534no—
659C2×D4—534no—
660C2×D4—1064no—
661C2×D4—1064no—
662C2×D4—10612no—
663C2×D4—10612no—
664C2×D4—10612no—
665C2×D4—1064no—
666C2×D4C23×D53112yes—
667C2×D4C23×D53112yes—
668C22×C4—212no—
669C22×C4—212no—
670C22×C4—533no—
671C22×C4—5324no—
672C22×C4—5312no—
673C22×C4—5312no—
674C22×C4—5324no—
675C22×C4—533no—
676C22×C4—531no—
677C22×C4—533no—
678C22×C4—533no—
679C22×C4—5312no—
680C22×C4—5312no—
681C22×C4—5312no—
682C22×C4—5312no—
683C22×C4—10612no—
684C22×C4—10696no—
685C22×C4—10612no—
686C22×C4—10612no—
687C22×C4—10624no—
688C22×C4—10612no—
689C22×C4—10612no—
690C22×C4C23×D53112yes—
691C22×C4C23×D53112yes—
692C22×C4C23×D5313yes—
693C22×C4C23×D5311yescharacteristic
694C22×C4C23×D5313yes—
695C22×C4C23×D5311yescharacteristic
696C22×C4C23×D5313yes—
697C4⋊C4—5312no—
698C4⋊C4—5312no—
699C4⋊C4—5312no—
700C4⋊C4—5312no—
701C4⋊C4—5312no—
702C4⋊C4—5324no—
703C4⋊C4—5324no—
704C4⋊C4—5312no—
705C4⋊C4C23×D53112yes—
706C4⋊C4C23×D53112yes—
707C22⋊C4—5312no—
708C22⋊C4—5324no—
709C22⋊C4—5312no—
710C22⋊C4—5312no—
711C22⋊C4—534no—
712C22⋊C4—534no—
713C22⋊C4—5312no—
714C22⋊C4—5312no—
715C22⋊C4—5312no—
716C22⋊C4C23×D53124yes—
717C22⋊C4C23×D5314yes—
718C22⋊C4C23×D53112yes—
719C42—5324no—
720C42—5312no—
721C42C23×D53112yes—
722C23—22no—
723C23—22no—
724C23—26no—
725C23—26no—
726C23—26no—
727C23—534no—
728C23—534no—
729C23—532no—
730C23—532no—
731C23—532no—
732C23—1068no—
733C23—1068no—
734C23—10632no—
735C23—1062no—
736C23—1062no—
737C23—1062no—
738C23—1062no—
739C23—1068no—
740C23—1062no—
741C23—1062no—
742C23—1062no—
743C23#1313326414yescomplemented
744C23C24×D5316yes—
745C23C24×D5312yes—
746C23C24×D5311yescharacteristic
747Q8—224no—
748Q8—5348no—
749Q8—10648no—
750Q8—10624no—
751Q8—10624no—
752Q8—10624no—
753Q8C2×D4×D53116yes—
754D4—224no—
755D4—224no—
756D4—1068no—
757D4—1068no—
758D4—10624no—
759D4—10624no—
760D4—10624no—
761D4—1068no—
762C2×C4—22no—
763C2×C4—26no—
764C2×C4—22no—
765C2×C4—26no—
766C2×C4—224no—
767C2×C4—224no—
768C2×C4—5312no—
769C2×C4—536no—
770C2×C4—5348no—
771C2×C4—536no—
772C2×C4—532no—
773C2×C4—536no—
774C2×C4—536no—
775C2×C4—10624no—
776C2×C4—10624no—
777C2×C4—10624no—
778C2×C4—10648no—
779C2×C4—1066no—
780C2×C4—1066no—
781C2×C4—1066no—
782C2×C4—1062no—
783C2×C4—10624no—
784C2×C4—10624no—
785C2×C4C2×D4×D53112yes—
786C2×C4C24×D5316yes—
787C2×C4C24×D5312yes—
788C2×C4C24×D5316yes—
789C2×C4C24×D5312yes—
790C2×C4C24×D5316yes—
791C22—28no—
792C22—22no—
793C22—22no—
794C22—26no—
795C22—26no—
796C22—26no—
797C22—412no—
798C22—534no—
799C22—534no—
800C22—10632no—
801C22—1068no—
802C22—1068no—
803C22—1062no—
804C22—1062no—
805C22—1062no—
806C22—1062no—
807C22—1062no—
808C22—1062no—
809C22—1062no—
810C22—2124no—
811C22C22×D4×D5312yes—
812C222−1+4×D5312yes—
813C22C2×#1313326412yes—
814C22C2×#1313326414yescomplemented
815C22C25×D5311yescharacteristic
816C4—22no—
817C4—26no—
818C4—22no—
819C4—26no—
820C4—5312no—
821C4—1066no—
822C4—1066no—
823C4—1066no—
824C4—1062no—
825C4C22×D4×D53112yes—
826C2—24no—
827C2—46no—
828C2—1064no—
829C2—1064no—
830C2—2122no—
831C2#2028836114yesdirect product factor
832C2C23×D4×D5311yescharacteristic
833C2C2×2−1+4×D5311yescharacteristic
834C2C22×#1313326411yescharacteristic
subgroupG/H
centerC23C24×D53
commutator, cosocleC22×C53C26
FrattiniC22C25×D53
FittingC2×C53×#548C2
socleC23×C53C25
hypercenterC2×#548D53
hypocenterC53C2×#3486
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×#13133264C2semidirect
2. C23×Q8×D53C2semidirect
3. #20288361C2direct (N × H)
4. C2×Q8×D212C2semidirect
5. C2×D4×Dic106C2semidirect
6. C2×Q8×C22⋊D53C2semidirect
7. C2×#16811286C2semidirect
8. C2×#16811281C2semidirect
9. C2×#16811280C2semidirect
10. C2×#16811279C2semidirect
11. C2×#16811196C2semidirect
12. C2×#16811193C2semidirect
13. C2×#16811133C2semidirect
14. C2×#16811132C2semidirect
15. C2×#16811099C2semidirect
16. C2×C53×#548C2semidirect
18. C2×#13133264C22semidirect
21. C22×#11719947C22semidirect
23. C23×Dic106C22semidirect
29. C22×Q8×D53C22semidirect
30. C22×Q8×D53C22semidirect
32. Q8×D212C22semidirect
33. D4×Dic106C22semidirect
34. Q8×C22⋊D53C22semidirect
35. #16811286C22semidirect
36. #16811281C22semidirect
37. #16811280C22semidirect
38. #16811279C22semidirect
39. #16811196C22semidirect
40. #16811193C22semidirect
41. C2×#13133217C22semidirect
42. C2×#13133216C22semidirect
43. C2×#13133215C22semidirect
44. C2×#13133204C22semidirect
45. C2×#13133203C22semidirect
46. #16811133C22semidirect
47. #16811132C22semidirect
52. C2×#13133197C22semidirect
54. C2×#13133196C22semidirect
57. C2×#13133194C22semidirect
58. C2×#13133194C22semidirect
59. C2×#13133193C22semidirect
65. #16811099C22semidirect
66. C2×Q8×Dic53C22semidirect
67. C2×C4×Dic106C22semidirect
68. C2×#13133182C22semidirect
76. C22×#41×C53C22semidirect
78. C53×#548C22semidirect
79. C2×#124×C53C22semidirect
80. C2×C22⋊Q8×C53C22semidirect
82. C2×C4×Q8×C53C22semidirect
91. C2×#11719947C23semidirect
100. C22×Dic106C23semidirect
106. C2×Q8×D53D4semidirect
111. C2×Q8×D53C23semidirect
127. #13133217C23semidirect
128. #13133216C23semidirect
129. #13133215C23semidirect
130. #13133204C23semidirect
131. #13133203C23semidirect
136. #13133197C23semidirect
138. #13133196C23semidirect
141. #13133194C23semidirect
142. #13133194C23semidirect
143. #13133193C23semidirect
149. Q8×Dic53C23semidirect
150. C4×Dic106C23semidirect
151. #13133182C23semidirect
179. C2×#41×C53C23semidirect
188. #124×C53C23semidirect
189. C22⋊Q8×C53C23semidirect
191. C4×Q8×C53C23semidirect
248. Q8×D53C2×D4semidirect
309. C23×C532−1+4semidirect
325. C22×D532−1+4semidirect
384. C22×C53C2×2−1+4semidirect
398. C2×D53C2×2−1+4semidirect
419. C2×#548D53semidirect
427. C2×C53#3486semidirect
439. C22×#41C2×D53semidirect
458. #548C2×D53semidirect
466. C2×#124C2×D53semidirect
481. C2×C22⋊Q8C2×D53semidirect
492. C2×C4×Q8C2×D53semidirect
501. C53C2×#3486semidirect
511. C2×#41C22×D53semidirect
560. #124C22×D53semidirect
573. C22⋊Q8C22×D53semidirect
583. C4×Q8C22×D53semidirect
743. C23#13133264semidirect
814. C22C2×#13133264semidirect
831. C2#20288361direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131332642
C23×Q8×D532
#202883612
C2×Q8×D2122
C2×D4×Dic1062
C2×Q8×C22⋊D532
C2×#168112862
C2×#168112812
C2×#168112802
C2×#168112792
C2×#168111962
C2×#168111932
C2×#168111332
C2×#168111322
C2×#168110992
C2×C53×#5482
C2×#348653