Finite Group Databasebeta

← C2×#20288394 #28292497

Subgroups — C2×#20288394 #28292497

Order 13568.

11438 conjugacy classes of subgroups.

The subgroup lattice has 840 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#20288394C2132yesmaximal, direct product factor
4C2×Q8×D212C211yesmaximal, characteristic, complemented
5C2×Q8×C22⋊D53C211yesmaximal, characteristic, complemented
6C2×#16811280C211yesmaximal, characteristic, complemented
7C2×#16811278C213yesmaximal, complemented
8C2×#16811275C213yesmaximal, complemented
9C2×#16811270C213yesmaximal, complemented
10C2×#16811266C213yesmaximal, complemented
11C2×#16811202C213yesmaximal, complemented
12C2×#16811193C213yesmaximal, complemented
13C2×#16811132C213yesmaximal, complemented
14C2×C22⋊Q8×D53C213yesmaximal, complemented
15C2×#16811105C211yesmaximal, characteristic, complemented
16C2×C53×#548C211yesmaximal, characteristic, complemented
17C2×#13133265—216no—
18C2×#13133265C22116yescomplemented
19C22×#11719949C2211yescharacteristic
20C22×#11719949C2213yescomplemented
21C22×#11719945C2213yes—
22C22×#11719945C2213yescomplemented
23C22×#11719945C2213yescomplemented
24C22×#11719947C2213yes—
25C2×#41×D53—216no—
26C2×#41×D53C22116yescomplemented
27C22×Q8×D53C2211yescharacteristic
28C22×Q8×D53C2213yescomplemented
29C22×Q8×D53C2211yescharacteristic, complemented
30C22×D4×D53C2213yes—
31C23×C4×D53C2213yes—
32Q8×D212C22116yescomplemented
33Q8×C22⋊D53C22116yescomplemented
34#16811280C22116yescomplemented
35#16811278C22148yescomplemented
36#16811275C22148yescomplemented
37#16811270C22148yescomplemented
38#16811266C22148yescomplemented
39#16811202C22148yescomplemented
40#16811193C22148yescomplemented
41C2×#13133217C2213yescomplemented
42C2×#13133215C2213yescomplemented
43C2×#13133204C2213yescomplemented
44#16811132C22148yescomplemented
45C2×#13133202C2213yescomplemented
46C2×#13133199C2216yescomplemented
47C2×#13133199C2216yescomplemented
48C2×#13133199C2213yescomplemented
49C2×#13133197C2213yes—
50C2×#13133197C2213yescomplemented
51C2×#13133196C2213yescomplemented
52C2×#13133196C2213yescomplemented
53C2×#13133195C2213yes—
54C2×#13133194C2213yescomplemented
55C2×#13133194C2216yescomplemented
56C2×#13133193C2213yes—
57C22⋊Q8×D53C22148yescomplemented
58C2×#13133190C2211yescharacteristic
59C2×#13133190C2216yescomplemented
60C2×#13133189C2213yescomplemented
61C2×#13133188C2213yescomplemented
62C2×#13133188C2216yescomplemented
63C2×#13133187C2213yes—
64C2×#13133185C2213yes—
65#16811105C22116yescomplemented
66C2×Q8×Dic53C2211yescharacteristic, complemented
67C2×C4×D212C2213yes—
68C2×C4×D212C2213yescomplemented
69C2×#13133179C2213yescomplemented
70C2×C4×C22⋊D53C2213yes—
71C2×C4×C22⋊D53C2213yescomplemented
72C2×#13133174C2213yescomplemented
73C2×C4⋊C4×D53C2213yescomplemented
74C2×C4⋊C4×D53C2216yescomplemented
75C2×C22⋊C4×D53C2216yes—
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—224no—
87C2×#11719949D4116yescomplemented
88C2×#11719949C2318yes—
89C2×#11719949C23124yescomplemented
90C2×#11719945—224no—
91C2×#11719945—224no—
92C2×#11719945—224no—
93C2×#11719945C23124yes—
94C2×#11719945C23124yescomplemented
95C2×#11719945C23124yescomplemented
96C2×#11719947—224no—
97C2×#11719947C23124yes—
98#41×D53—2128no—
99C22×Dic106C2313yes—
100C22×Dic106C2313yes—
101C22×Dic106C2313yes—
102C2×Q8×D53—28no—
103C2×Q8×D53—28no—
104C2×Q8×D53—224no—
105C2×Q8×D53C2318yes—
106C2×Q8×D53C2318yescomplemented
107C2×Q8×D53C23124yescomplemented
108C22×D212C2311yescharacteristic
109C22×D212C2313yes—
110C22×D212C2313yes—
111C22×C22⋊D53C2311yescharacteristic
112C22×C22⋊D53C2313yes—
113C22×C22⋊D53C2316yes—
114C22×C22⋊D53C2311yescharacteristic
115C22×C22⋊D53C2313yes—
116C2×D4×D53—224no—
117C2×D4×D53C23124yes—
118C23×Dic53C2313yes—
119C22×C4×D53—224no—
120C22×C4×D53C2316yes—
121C22×C4×D53C2313yes—
122C22×C4×D53C2313yes—
123C22×C4×D53C2313yes—
124C22×C4×D53C2311yescharacteristic
125C22×C4×D53C23124yes—
126C22×C4×D53C2316yes—
127C22×C4×D53C2313yes—
128#13133217C23124yescomplemented
129#13133215C23124yescomplemented
130#13133204C23124yescomplemented
131#13133202C23124yescomplemented
132#13133199C23148yescomplemented
133#13133199C23148yescomplemented
134#13133199C23124yescomplemented
135#13133197C23124yes—
136#13133197C23124yescomplemented
137#13133196C23124yescomplemented
138#13133196C23124yescomplemented
139#13133195C23124yes—
140#13133194C23148yescomplemented
141#13133194C23124yescomplemented
142#13133193C23124yes—
143#13133190C2318yes—
144#13133190C23148yescomplemented
145#13133189C23124yescomplemented
146#13133188C23124yescomplemented
147#13133188C23148yescomplemented
148#13133187C23124yes—
149#13133185C23124yes—
150Q8×Dic53C2318yescomplemented
151C4×D212C23124yes—
152C4×D212C23124yescomplemented
153#13133179C23124yescomplemented
154C4×C22⋊D53C23124yes—
155C4×C22⋊D53C23124yescomplemented
156#13133174C23124yescomplemented
157C2×C4⋊Dic53C2313yes—
158C2×C4⋊Dic53C2316yes—
159C2×C4⋊Dic53C2313yes—
160C2×#11719919C2313yes—
161C2×#11719919C2313yes—
162C2×#11719919C2316yes—
163C2×#11719919C2311yescharacteristic
164C2×#11719919C2313yes—
165C4⋊C4×D53C23148yescomplemented
166C4⋊C4×D53C23124yescomplemented
167C2×C22⋊Dic53C2316yes—
168C2×C22⋊Dic53C2313yes—
169C2×C22⋊Dic53C2313yes—
170C2×#11719921C2313yes—
171C2×#11719921C2313yes—
172C2×#11719921C2313yes—
173C2×#11719921C2313yes—
174C2×#11719921C2311yescharacteristic
175C2×#11719921C2313yes—
176C22⋊C4×D53C23148yes—
177C2×C4×Dic53C2313yes—
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—212no—
203C23×D53—46no—
204C23×D53C2411yescharacteristic
205C23×D53C24112yes—
206C23×D53C2413yes—
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—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—224no—
228C2×C22⋊D53—212no—
229C2×C22⋊D53—24no—
230C2×C22⋊D53—24no—
231C2×C22⋊D53—46no—
232C2×C22⋊D53C2414yes—
233C2×C22⋊D53C24112yes—
234C2×C22⋊D53C24124yes—
235C2×C22⋊D53C2414yes—
236C2×C22⋊D53C24112yes—
237C22×Dic53—212no—
238C22×Dic53C2411yescharacteristic
239C22×Dic53C2413yes—
240C22×Dic53C2413yes—
241C22×Dic53C2413yes—
242C22×Dic53C24112yes—
243C22×Dic53C2411yescharacteristic
244#11719949—296no—
245#11719949C2×D4164yescomplemented
246Q8×D53—232no—
247Q8×D53—232no—
248Q8×D53—296no—
249#11719947—296no—
250D4×D53—296no—
251#11719945—296no—
252#11719945—296no—
253#11719945—296no—
254C2×D212—212no—
255C2×D212—24no—
256C2×D212C2×D4124yes—
257C2×D212C2414yes—
258C2×D212C24112yes—
259C2×D212C24112yes—
260C2×C4×D53—212no—
261C2×C4×D53—224no—
262C2×C4×D53—212no—
263C2×C4×D53—212no—
264C2×C4×D53—24no—
265C2×C4×D53—296no—
266C2×C4×D53—412no—
267C2×C4×D53C2×D4124yes—
268C2×C4×D53C24124yes—
269C2×C4×D53C24112yes—
270C2×C4×D53C24112yes—
271C2×C4×D53C24112yes—
272C2×C4×D53C2414yes—
273C2×C4×D53C24124yes—
274C2×C4×D53C24112yes—
275C2×Dic106—212no—
276C2×Dic106—212no—
277C2×Dic106—212no—
278C2×Dic106C24112yes—
279C2×Dic106C24112yes—
280C2×Dic106C24112yes—
281C4⋊C4×C53C24112yes—
282C4⋊C4×C53C24112yes—
283C22⋊C4×C53C2414yes—
284C22⋊C4×C53C24112yes—
285C22⋊C4×C53C24124yes—
286C42×C53C24112yes—
287C22⋊Dic53C24124yes—
288C22⋊Dic53C24112yes—
289C22⋊Dic53C24112yes—
290#11719921C24112yes—
291#11719921C24112yes—
292#11719921C24112yes—
293#11719921C24112yes—
294#11719921C2414yes—
295#11719921C24112yes—
296C4⋊Dic53C24112yes—
297C4⋊Dic53C24124yes—
298C4⋊Dic53C24112yes—
299#11719919C24112yes—
300#11719919C24112yes—
301#11719919C24124yes—
302#11719919C2414yes—
303#11719919C24112yes—
304C4×Dic53C24112yes—
305C23×C53—26no—
306C23×C53—22no—
307C23×C53—22no—
308C23×C53—26no—
309C23×C53—26no—
310C23×C53—22no—
311C23×C53C2516yes—
312C23×C53C2512yes—
313C23×C53C2511yescharacteristic
314C22×D53—22no—
315C22×D53—26no—
316C22×D53—26no—
317C22×D53—22no—
318C22×D53—22no—
319C22×D53—22no—
320C22×D53—22no—
321C22×D53—224no—
322C22×D53—224no—
323C22×D53—412no—
324C22×D53—448no—
325C22×D53C22×D4112yes—
326C22×D532−1+414yescomplemented
327C22×D53C2512yes—
328C22×D53C2516yes—
329C22×D53C2512yes—
330Q8×C53—224no—
331Q8×C53C22×D4116yes—
332D4×C53—224no—
333D4×C53—412no—
334C2×C4×C53—26no—
335C2×C4×C53—22no—
336C2×C4×C53—22no—
337C2×C4×C53—26no—
338C2×C4×C53—224no—
339C2×C4×C53—224no—
340C2×C4×C53C22×D4112yes—
341C2×C4×C53C2516yes—
342C2×C4×C53C2512yes—
343C2×C4×C53C2516yes—
344C2×C4×C53C2512yes—
345C2×C4×C53C2516yes—
346C22⋊D53—224no—
347C22⋊D53—248no—
348C22⋊D53—28no—
349C22⋊D53—28no—
350C22⋊D53—412no—
351C2×Dic53—26no—
352C2×Dic53—26no—
353C2×Dic53—22no—
354C2×Dic53—26no—
355C2×Dic53—224no—
356C2×Dic53C22×D414yes—
357C2×Dic53C2516yes—
358C2×Dic53C2516yes—
359C2×Dic53C2516yes—
360C2×Dic53C2512yes—
361C2×Dic53C2512yes—
362D212—224no—
363D212—28no—
364D212C22×D4148yes—
365C4×D53—224no—
366C4×D53—248no—
367C4×D53—224no—
368C4×D53—224no—
369C4×D53—28no—
370C4×D53—424no—
371C4×D53C22×D4148yes—
372Dic106—224no—
373Dic106—224no—
374Dic106—224no—
375C2×#3489—531nomaximal, Sylow
376C22×C53—26no—
377C22×C53—22no—
378C22×C53—22no—
379C22×C53—26no—
380C22×C53—26no—
381C22×C53—22no—
382C22×C53—412no—
383C22×C53—44no—
384C22×C53C23×D412yes—
385C22×C53C2×2−1+412yes—
386C22×C53#58512yes—
387C22×C53C2611yescharacteristic
388C2×D53—22no—
389C2×D53—26no—
390C2×D53—26no—
391C2×D53—22no—
392C2×D53—28no—
393C2×D53—224no—
394C2×D53—22no—
395C2×D53—22no—
396C2×D53—22no—
397C2×D53—448no—
398C2×D53—44no—
399C2×D53C23×D4112yes—
400C2×D53C2×2−1+414yescomplemented
401C4×C53—26no—
402C4×C53—22no—
403C4×C53—22no—
404C4×C53—26no—
405C4×C53C23×D4112yes—
406Dic53—26no—
407Dic53—26no—
408Dic53—22no—
409Dic53—26no—
410Dic53C23×D414yes—
411C22×2−1+4—531no—
412C23×#41—531no—
413#3489—5332no—
414C2×D4×Q8—531no—
415C2×D4×Q8—531no—
416C2×#548—531no—
417C2×#548D5311yescharacteristic, complemented
418C2×#547—533no—
419C2×#547—533no—
420C2×#546—533no—
421C2×#546—533no—
422C2×#537—533no—
423C2×#536—533no—
424C2×#525—533no—
425C22×C22⋊Q8—533no—
426C2×#520—531no—
427C2×C53—46no—
428C2×C53—42no—
429C2×C53#348914yescomplemented
430C2×C53C24×D411yescharacteristic
431C2×C53C22×2−1+411yescharacteristic
432C2×C53C2×#58511yescharacteristic
433D53—24no—
434D53—212no—
435D53—42no—
436C2×2−1+4—5316no—
437C2×2−1+4—10616no—
438C22×#41—5316no—
439C22×#41—531no—
440C22×#41—533no—
441C22×#41—533no—
442C22×#41—533no—
443C22×#41—533no—
444C22×#41—533no—
445C22×#41—10616no—
446C22×#41C2×D5311yescharacteristic
447C23×Q8—531no—
448C23×Q8—533no—
449C23×Q8—531no—
450C23×Q8C2×D5311yescharacteristic, complemented
451C23×D4—533no—
452C24×C4—533no—
453D4×Q8—5316no—
454D4×Q8—5316no—
455#548—5316no—
456#548C2×D53116yescomplemented
457#547—5348no—
458#547—5348no—
459#546—5348no—
460#546—5348no—
461#537—5348no—
462#536—5348no—
463C2×C4⋊Q8—533no—
464C2×C4⋊Q8—533no—
465C2×#124—533no—
466C2×#124C2×D5313yescomplemented
467#525—5348no—
468C2×#123—533no—
469C2×#123—533no—
470C2×#123—536no—
471C2×#123—536no—
472C2×C22⋊Q8—533no—
473C2×C22⋊Q8—533no—
474C2×C22⋊Q8—533no—
475C2×C22⋊Q8—5348no—
476C2×C22⋊Q8—533no—
477C2×C22⋊Q8—533no—
478C2×C22⋊Q8—533no—
479C2×C22⋊Q8—536no—
480C2×C22⋊Q8—533no—
481C2×C22⋊Q8C2×D5313yescomplemented
482C2×#121—536no—
483C2×#121—533no—
484C2×#121—533no—
485C2×#121—531no—
486C2×#121—536no—
487C2×#121C2×D5313yescomplemented
488C2×#120—533no—
489C2×#120—533no—
490#520—5316no—
491C2×C4×Q8—531no—
492C2×C4×Q8C2×D5311yescharacteristic, complemented
493C2×C4×D4—533no—
494C2×C4×D4—533no—
495C2×C4×D4—533no—
496C2×C4×D4—533no—
497C2×C4×D4—533no—
498C2×C4×D4C2×D5313yescomplemented
499C2×#117—533no—
500C22×C4⋊C4—533no—
501C22×C4⋊C4—536no—
502C22×C22⋊C4—536no—
503C53C2×#348911yescharacteristic, complemented, Sylow
504C25—533no—
5052−1+4—106128no—
506C2×#41—28no—
507C2×#41—5316no—
508C2×#41—538no—
509C2×#41—5324no—
510C2×#41—5324no—
511C2×#41—5324no—
512C2×#41—5324no—
513C2×#41—5324no—
514C2×#41—10624no—
515C2×#41—10624no—
516C2×#41—10624no—
517C2×#41—10624no—
518C2×#41—10624no—
519C2×#41—106128no—
520C2×#41C22×D5318yes—
521C22×Q8—28no—
522C22×Q8—5324no—
523C22×Q8—538no—
524C22×Q8—538no—
525C22×Q8—533no—
526C22×Q8—533no—
527C22×Q8—533no—
528C22×Q8—10624no—
529C22×Q8—1068no—
530C22×Q8—1068no—
531C22×Q8C22×D5313yes—
532C22×Q8C22×D5311yescharacteristic
533C22×Q8C22×D5318yescomplemented
534C22×D4—531no—
535C22×D4—533no—
536C22×D4—531no—
537C22×D4—536no—
538C22×D4—533no—
539C22×D4—5324no—
540C22×D4—533no—
541C22×D4—531no—
542C22×D4—533no—
543C22×D4—10624no—
544C22×D4C22×D5313yes—
545C22×D4C22×D5313yes—
546C23×C4—533no—
547C23×C4—533no—
548C23×C4—536no—
549C23×C4—533no—
550C23×C4—533no—
551C23×C4—533no—
552C23×C4—531no—
553C23×C4—5324no—
554C23×C4—536no—
555C23×C4—10624no—
556C23×C4C22×D5313yes—
557C23×C4C22×D5313yes—
558C4⋊Q8—5324no—
559C4⋊Q8—5324no—
560#124—5324no—
561#124C22×D53124yescomplemented
562#123—5324no—
563#123—5324no—
564#123—5348no—
565#123—5348no—
566C22⋊Q8—5324no—
567C22⋊Q8—5324no—
568C22⋊Q8—5324no—
569C22⋊Q8—5324no—
570C22⋊Q8—5324no—
571C22⋊Q8—5324no—
572C22⋊Q8—5348no—
573C22⋊Q8—5324no—
574C22⋊Q8C22×D53124yescomplemented
575#121—5324no—
576#121—5348no—
577#121—5324no—
578#121—538no—
579#121—5348no—
580#121C22×D53124yescomplemented
581#120—5324no—
582#120—5324no—
583C4×Q8—538no—
584C4×Q8C22×D5318yescomplemented
585C4×D4—5324no—
586C4×D4—5324no—
587C4×D4—5324no—
588C4×D4—5324no—
589C4×D4—5324no—
590C4×D4C22×D53124yescomplemented
591#117—5324no—
592C2×C4⋊C4—533no—
593C2×C4⋊C4—533no—
594C2×C4⋊C4—533no—
595C2×C4⋊C4—536no—
596C2×C4⋊C4—536no—
597C2×C4⋊C4—531no—
598C2×C4⋊C4—533no—
599C2×C4⋊C4—533no—
600C2×C4⋊C4—5324no—
601C2×C4⋊C4—5348no—
602C2×C4⋊C4C22×D5313yes—
603C2×C4⋊C4C22×D5313yes—
604C2×C22⋊C4—536no—
605C2×C22⋊C4—533no—
606C2×C22⋊C4—533no—
607C2×C22⋊C4—533no—
608C2×C22⋊C4—533no—
609C2×C22⋊C4—533no—
610C2×C22⋊C4—533no—
611C2×C22⋊C4—531no—
612C2×C22⋊C4—533no—
613C2×C22⋊C4—5348no—
614C2×C22⋊C4C22×D5316yes—
615C2×C22⋊C4C22×D5311yescharacteristic
616C2×C22⋊C4C22×D5313yes—
617C2×C42—533no—
618C2×C42C22×D5313yes—
619C24—531no—
620C24—533no—
621C24—531no—
622C24—5312no—
623C24—10612no—
624C24—10612no—
625C24—2126no—
626C24C23×D5313yes—
627C24C23×D5311yescharacteristic
628#41—232no—
629#41—5364no—
630#41—10696no—
631#41—10696no—
632#41—10696no—
633#41—10696no—
634#41—10696no—
635C2×Q8—232no—
636C2×Q8—212no—
637C2×Q8—5312no—
638C2×Q8—5312no—
639C2×Q8—5312no—
640C2×Q8—10612no—
641C2×Q8—10696no—
642C2×Q8—10632no—
643C2×Q8—10632no—
644C2×Q8—10612no—
645C2×Q8—10612no—
646C2×Q8D4×D5318yes—
647C2×Q8C23×D53112yes—
648C2×Q8C23×D5314yes—
649C2×D4—212no—
650C2×D4—46no—
651C2×D4—534no—
652C2×D4—5312no—
653C2×D4—534no—
654C2×D4—5324no—
655C2×D4—5312no—
656C2×D4—5324no—
657C2×D4—5312no—
658C2×D4—534no—
659C2×D4—5312no—
660C2×D4—1064no—
661C2×D4—10612no—
662C2×D4—1064no—
663C2×D4—10696no—
664C2×D4—1064no—
665C2×D4—10624no—
666C2×D4—10612no—
667C2×D4—2126no—
668C2×D4C23×D53112yes—
669C2×D4C23×D53112yes—
670C22×C4—212no—
671C22×C4—212no—
672C22×C4—531no—
673C22×C4—5324no—
674C22×C4—5312no—
675C22×C4—5312no—
676C22×C4—531no—
677C22×C4—533no—
678C22×C4—533no—
679C22×C4—533no—
680C22×C4—5324no—
681C22×C4—5312no—
682C22×C4—5312no—
683C22×C4—5312no—
684C22×C4—534no—
685C22×C4—5324no—
686C22×C4—1064no—
687C22×C4—10696no—
688C22×C4—10612no—
689C22×C4—10624no—
690C22×C4—10612no—
691C22×C4—10612no—
692C22×C4—10612no—
693C22×C4—21212no—
694C22×C4C23×D53112yes—
695C22×C4C23×D53112yes—
696C22×C4C23×D5311yescharacteristic
697C22×C4C23×D5313yes—
698C22×C4C23×D5313yes—
699C22×C4C23×D5311yescharacteristic
700C22×C4C23×D5313yes—
701C4⋊C4—5312no—
702C4⋊C4—5312no—
703C4⋊C4—5312no—
704C4⋊C4—5324no—
705C4⋊C4—5324no—
706C4⋊C4—534no—
707C4⋊C4—5312no—
708C4⋊C4—5312no—
709C4⋊C4C23×D53112yes—
710C4⋊C4C23×D53112yes—
711C22⋊C4—5324no—
712C22⋊C4—5312no—
713C22⋊C4—5312no—
714C22⋊C4—5312no—
715C22⋊C4—5312no—
716C22⋊C4—5312no—
717C22⋊C4—5312no—
718C22⋊C4—534no—
719C22⋊C4—5312no—
720C22⋊C4C23×D53124yes—
721C22⋊C4C23×D5314yes—
722C22⋊C4C23×D53112yes—
723C42—5312no—
724C42C23×D53112yes—
725C23—22no—
726C23—26no—
727C23—22no—
728C23—26no—
729C23—22no—
730C23—26no—
731C23—5312no—
732C23—534no—
733C23—532no—
734C23—536no—
735C23—532no—
736C23—10624no—
737C23—10624no—
738C23—1062no—
739C23—1066no—
740C23—1066no—
741C23—1062no—
742C23—1062no—
743C23—1062no—
744C23—1062no—
745C23—21212no—
746C23—21248no—
747C23C24×D5316yes—
748C23C24×D5312yes—
749C23C24×D5311yescharacteristic
750Q8—224no—
751Q8—10624no—
752Q8—10624no—
753Q8—10624no—
754Q8C2×D4×D53116yes—
755D4—224no—
756D4—412no—
757D4—5348no—
758D4—1068no—
759D4—10624no—
760D4—1068no—
761D4—1068no—
762D4—10648no—
763D4—10624no—
764D4—21212no—
765C2×C4—22no—
766C2×C4—26no—
767C2×C4—22no—
768C2×C4—26no—
769C2×C4—224no—
770C2×C4—224no—
771C2×C4—534no—
772C2×C4—532no—
773C2×C4—5348no—
774C2×C4—532no—
775C2×C4—536no—
776C2×C4—536no—
777C2×C4—536no—
778C2×C4—1068no—
779C2×C4—10624no—
780C2×C4—10648no—
781C2×C4—10624no—
782C2×C4—1066no—
783C2×C4—1066no—
784C2×C4—1062no—
785C2×C4—1066no—
786C2×C4—10624no—
787C2×C4—10624no—
788C2×C4—21224no—
789C2×C4C2×D4×D53112yes—
790C2×C4C24×D5312yes—
791C2×C4C24×D5316yes—
792C2×C4C24×D5316yes—
793C2×C4C24×D5312yes—
794C2×C4C24×D5316yes—
795C22—22no—
796C22—26no—
797C22—22no—
798C22—26no—
799C22—22no—
800C22—26no—
801C22—412no—
802C22—44no—
803C22—5312no—
804C22—534no—
805C22—1068no—
806C22—10624no—
807C22—1062no—
808C22—1066no—
809C22—1066no—
810C22—1062no—
811C22—1062no—
812C22—1062no—
813C22—1062no—
814C22—21248no—
815C22—2124no—
816C22C22×D4×D5312yes—
817C222−1+4×D5312yes—
818C22#1681145912yes—
819C22C25×D5311yescharacteristic
820C4—22no—
821C4—26no—
822C4—22no—
823C4—26no—
824C4—534no—
825C4—1066no—
826C4—1066no—
827C4—1062no—
828C4—1066no—
829C4C22×D4×D53112yes—
830C2—46no—
831C2—42no—
832C2—1064no—
833C2—10612no—
834C2—2122no—
835C2#2028839414yesdirect product factor
836C2C23×D4×D5311yescharacteristic
837C2C2×2−1+4×D5311yescharacteristic
838C2C2×#1681145911yescharacteristic
subgroupG/H
centerC23C24×D53
commutator, cosocleC22×C53C26
FrattiniC22C25×D53
FittingC2×C53×#548C2
socleC23×C53C25
hypercenterC2×#548D53
hypocenterC53C2×#3489
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. #20288394C2direct (N × H)
4. C2×Q8×D212C2semidirect
5. C2×Q8×C22⋊D53C2semidirect
6. C2×#16811280C2semidirect
7. C2×#16811278C2semidirect
8. C2×#16811275C2semidirect
9. C2×#16811270C2semidirect
10. C2×#16811266C2semidirect
11. C2×#16811202C2semidirect
12. C2×#16811193C2semidirect
13. C2×#16811132C2semidirect
14. C2×C22⋊Q8×D53C2semidirect
15. C2×#16811105C2semidirect
16. C2×C53×#548C2semidirect
18. C2×#13133265C22semidirect
20. C22×#11719949C22semidirect
22. C22×#11719945C22semidirect
23. C22×#11719945C22semidirect
26. C2×#41×D53C22semidirect
28. C22×Q8×D53C22semidirect
29. C22×Q8×D53C22semidirect
32. Q8×D212C22semidirect
33. Q8×C22⋊D53C22semidirect
34. #16811280C22semidirect
35. #16811278C22semidirect
36. #16811275C22semidirect
37. #16811270C22semidirect
38. #16811266C22semidirect
39. #16811202C22semidirect
40. #16811193C22semidirect
41. C2×#13133217C22semidirect
42. C2×#13133215C22semidirect
43. C2×#13133204C22semidirect
44. #16811132C22semidirect
45. C2×#13133202C22semidirect
46. C2×#13133199C22semidirect
47. C2×#13133199C22semidirect
48. C2×#13133199C22semidirect
50. C2×#13133197C22semidirect
51. C2×#13133196C22semidirect
52. C2×#13133196C22semidirect
54. C2×#13133194C22semidirect
55. C2×#13133194C22semidirect
57. C22⋊Q8×D53C22semidirect
59. C2×#13133190C22semidirect
60. C2×#13133189C22semidirect
61. C2×#13133188C22semidirect
62. C2×#13133188C22semidirect
65. #16811105C22semidirect
66. C2×Q8×Dic53C22semidirect
68. C2×C4×D212C22semidirect
69. C2×#13133179C22semidirect
71. C2×C4×C22⋊D53C22semidirect
72. C2×#13133174C22semidirect
73. C2×C4⋊C4×D53C22semidirect
74. C2×C4⋊C4×D53C22semidirect
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
87. C2×#11719949D4semidirect
89. C2×#11719949C23semidirect
94. C2×#11719945C23semidirect
95. C2×#11719945C23semidirect
106. C2×Q8×D53C23semidirect
107. C2×Q8×D53C23semidirect
128. #13133217C23semidirect
129. #13133215C23semidirect
130. #13133204C23semidirect
131. #13133202C23semidirect
132. #13133199C23semidirect
133. #13133199C23semidirect
134. #13133199C23semidirect
136. #13133197C23semidirect
137. #13133196C23semidirect
138. #13133196C23semidirect
140. #13133194C23semidirect
141. #13133194C23semidirect
144. #13133190C23semidirect
145. #13133189C23semidirect
146. #13133188C23semidirect
147. #13133188C23semidirect
150. Q8×Dic53C23semidirect
152. C4×D212C23semidirect
153. #13133179C23semidirect
155. C4×C22⋊D53C23semidirect
156. #13133174C23semidirect
165. C4⋊C4×D53C23semidirect
166. C4⋊C4×D53C23semidirect
183. C22×Q8×C53C23semidirect
188. #124×C53C23semidirect
189. C22⋊Q8×C53C23semidirect
190. #121×C53C23semidirect
191. C4×Q8×C53C23semidirect
192. C4×D4×C53C23semidirect
245. #11719949C2×D4semidirect
326. C22×D532−1+4semidirect
400. C2×D53C2×2−1+4semidirect
417. C2×#548D53semidirect
429. C2×C53#3489semidirect
450. C23×Q8C2×D53semidirect
456. #548C2×D53semidirect
466. C2×#124C2×D53semidirect
481. C2×C22⋊Q8C2×D53semidirect
487. C2×#121C2×D53semidirect
492. C2×C4×Q8C2×D53semidirect
498. C2×C4×D4C2×D53semidirect
503. C53C2×#3489semidirect
533. C22×Q8C22×D53semidirect
561. #124C22×D53semidirect
574. C22⋊Q8C22×D53semidirect
580. #121C22×D53semidirect
584. C4×Q8C22×D53semidirect
590. C4×D4C22×D53semidirect
835. C2#20288394direct (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
#202883942
C2×Q8×D2122
C2×Q8×C22⋊D532
C2×#168112802
C2×#168112782
C2×#168112752
C2×#168112702
C2×#168112662
C2×#168112022
C2×#168111932
C2×#168111322
C2×C22⋊Q8×D532
C2×#168111052
C2×C53×#5482
C2×#348953