Finite Group Databasebeta

← C2×#20288392 #28292492

Subgroups — C2×#20288392 #28292492

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
2C23×#11719949C211yesmaximal, characteristic, complemented
3#20288392C2132yesmaximal, direct product factor
4C2×Q8×C22⋊D53C211yesmaximal, characteristic, complemented
5C2×#16811285C211yesmaximal, characteristic, complemented
6C2×#16811284C211yesmaximal, characteristic, complemented
7C2×#16811276C213yesmaximal, complemented
8C2×#16811275C213yesmaximal, complemented
9C2×#16811269C213yesmaximal, complemented
10C2×#16811264C213yesmaximal, complemented
11C2×#16811203C213yesmaximal, complemented
12C2×#16811198C213yesmaximal, complemented
13C2×#16811132C213yesmaximal, complemented
14C2×C22⋊Q8×D53C213yesmaximal, complemented
15C2×#16811105C211yesmaximal, characteristic, complemented
16C2×D4×Q8×C53C211yesmaximal, characteristic, complemented
17C2×#13133265—216no—
18C2×#13133265C22116yescomplemented
19C22×#11719949—216no—
20C22×#11719949C2213yes—
21C22×#11719949C2213yes—
22C22×#11719949C2211yescharacteristic
23C22×#11719949C2211yescharacteristic
24C22×#11719949C22116yescomplemented
25C22×#11719949C2213yescomplemented
26C22×#11719945C2213yescomplemented
27C22×#11719945C2213yescomplemented
28C22×Q8×D53C2213yescomplemented
29C22×Q8×D53C2211yescharacteristic, complemented
30C23×D212C2213yes—
31C23×C4×D53C2213yes—
32Q8×C22⋊D53C22116yescomplemented
33#16811285C22116yescomplemented
34#16811284C22116yescomplemented
35#16811276C22148yescomplemented
36#16811275C22148yescomplemented
37#16811269C22148yescomplemented
38#16811264C22148yescomplemented
39#16811203C22148yescomplemented
40#16811198C22148yescomplemented
41C2×#13133215C2213yescomplemented
42C2×#13133206C2213yescomplemented
43C2×#13133205C2213yescomplemented
44#16811132C22148yescomplemented
45C2×#13133202C2216yescomplemented
46C2×#13133202C2216yescomplemented
47C2×#13133202C2213yescomplemented
48C2×#13133199C2213yescomplemented
49C2×#13133197C2213yescomplemented
50C2×#13133196C2213yes—
51C2×#13133195C2213yescomplemented
52C2×#13133195C2216yescomplemented
53C2×#13133194C2213yes—
54C2×#13133193C2213yescomplemented
55C2×#13133193C2213yescomplemented
56C22⋊Q8×D53C22148yescomplemented
57C2×#13133192C2216yescomplemented
58C2×#13133192C2213yescomplemented
59C2×#13133191C2213yescomplemented
60C2×#13133190C2213yescomplemented
61C2×#13133190C2216yescomplemented
62C2×#13133189C2211yescharacteristic
63C2×#13133187C2213yes—
64C2×#13133185C2213yes—
65#16811105C22116yescomplemented
66C2×Q8×Dic53C2211yescharacteristic, complemented
67C2×C4×D212C2213yescomplemented
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—
76C23×Q8×C53C2211yescharacteristic
77C23×Q8×C53C2211yescharacteristic, complemented
78D4×Q8×C53C22116yescomplemented
79C2×C4⋊Q8×C53C2213yescomplemented
80C2×C22⋊Q8×C53C2213yes—
81C2×C22⋊Q8×C53C2213yescomplemented
82C2×C4×Q8×C53C2211yescharacteristic, complemented
83C2×C4×D4×C53C2213yes—
84C24×D53C2313yes—
85#13133265—2128no—
86C2×#11719949—28no—
87C2×#11719949—2128no—
88C2×#11719949—224no—
89C2×#11719949—224no—
90C2×#11719949—224no—
91C2×#11719949D4116yescomplemented
92C2×#11719949C23124yes—
93C2×#11719949C2318yes—
94C2×#11719949C23124yes—
95C2×#11719949C2318yes—
96C2×#11719949C23124yescomplemented
97C2×#11719945—224no—
98C2×#11719945—224no—
99C2×#11719945C23124yescomplemented
100C2×#11719945C23124yescomplemented
101C22×Dic106C2313yes—
102C22×Dic106C2313yes—
103C2×Q8×D53—28no—
104C2×Q8×D53—224no—
105C2×Q8×D53C2318yescomplemented
106C2×Q8×D53C23124yescomplemented
107C22×D212—224no—
108C22×D212C23124yes—
109C22×D212C2313yes—
110C22×D212C2316yes—
111C22×D212C2313yes—
112C22×D212C2313yes—
113C22×D212C2313yes—
114C22×C22⋊D53C2311yescharacteristic
115C22×C22⋊D53C2313yes—
116C22×C22⋊D53C2311yescharacteristic
117C22×C22⋊D53C2313yes—
118C23×Dic53C2311yescharacteristic
119C22×C4×D53—224no—
120C22×C4×D53C2316yes—
121C22×C4×D53C2313yes—
122C22×C4×D53C2313yes—
123C22×C4×D53C2313yes—
124C22×C4×D53C2313yes—
125C22×C4×D53C23124yes—
126C22×C4×D53C2316yes—
127C22×C4×D53C2313yes—
128#13133215C23124yescomplemented
129#13133206C23124yescomplemented
130#13133205C23124yescomplemented
131#13133202C23148yescomplemented
132#13133202C23148yescomplemented
133#13133202C23124yescomplemented
134#13133199C23124yescomplemented
135#13133197C23124yescomplemented
136#13133196C23124yes—
137#13133195C23148yescomplemented
138#13133195C23124yescomplemented
139#13133194C23124yes—
140#13133193C23124yescomplemented
141#13133193C23124yescomplemented
142#13133192C23148yescomplemented
143#13133192C23124yescomplemented
144#13133191C23124yescomplemented
145#13133190C23148yescomplemented
146#13133190C23124yescomplemented
147#13133189C2318yes—
148#13133187C23124yes—
149#13133185C23124yes—
150Q8×Dic53C2318yescomplemented
151C4×D212C23124yescomplemented
152C4×D212C23124yescomplemented
153#13133179C23124yescomplemented
154C4×C22⋊D53C23124yes—
155C4×C22⋊D53C23124yescomplemented
156#13133174C23124yescomplemented
157C2×C4⋊Dic53C2313yes—
158C2×C4⋊Dic53C2313yes—
159C2×#11719919C2313yes—
160C2×#11719919C2313yes—
161C2×#11719919C2316yes—
162C2×#11719919C2311yescharacteristic
163C2×#11719919C2313yes—
164C4⋊C4×D53C23148yescomplemented
165C4⋊C4×D53C23124yescomplemented
166C2×C22⋊Dic53C2313yes—
167C2×C22⋊Dic53C2311yescharacteristic
168C2×#11719921C2316yes—
169C2×#11719921C2316yes—
170C2×#11719921C2313yes—
171C2×#11719921C2313yes—
172C2×#11719921C2313yes—
173C2×#11719921C2313yes—
174C2×#11719921C2311yescharacteristic
175C2×#11719921C2313yes—
176C22⋊C4×D53C23148yes—
177C2×C4×Dic53C2313yes—
178C22×Q8×C53—28no—
179C22×Q8×C53—28no—
180C22×Q8×C53C2318yes—
181C22×Q8×C53C2313yes—
182C22×Q8×C53C2313yes—
183C22×Q8×C53C2311yescharacteristic
184C22×Q8×C53C2318yescomplemented
185C22×D4×C53C2311yescharacteristic
186C23×C4×C53C2313yes—
187C23×C4×C53C2313yes—
188C4⋊Q8×C53C23124yescomplemented
189C22⋊Q8×C53C23124yes—
190C22⋊Q8×C53C23124yescomplemented
191C4×Q8×C53C2318yescomplemented
192C4×D4×C53C23124yes—
193C2×C4⋊C4×C53C2313yes—
194C2×C4⋊C4×C53C2313yes—
195C2×C4⋊C4×C53C2316yes—
196C2×C22⋊C4×C53C2313yes—
197C2×C22⋊C4×C53C2313yes—
198C2×C42×C53C2313yes—
199C24×C53C2411yescharacteristic
200C24×C53C2411yescharacteristic
201C23×D53—212no—
202C23×D53—212no—
203C23×D53—46no—
204C23×D53C2413yes—
205C23×D53C2411yescharacteristic
206C23×D53C24112yes—
207C23×D53C2413yes—
208C2×Q8×C53—232no—
209C2×Q8×C53—232no—
210C2×Q8×C53—212no—
211C2×Q8×C53—212no—
212C2×Q8×C53C2×D418yes—
213C2×Q8×C53C24112yes—
214C2×Q8×C53C24112yes—
215C2×Q8×C53C2414yes—
216C2×D4×C53—24no—
217C2×D4×C53C2414yes—
218C22×C4×C53—212no—
219C22×C4×C53—212no—
220C22×C4×C53C2411yescharacteristic
221C22×C4×C53C2413yes—
222C22×C4×C53C2413yes—
223C22×C4×C53C2413yes—
224C22×C4×C53C24112yes—
225C22×C4×C53C24112yes—
226C22×C4×C53C2413yes—
227C2×C22⋊D53—24no—
228C2×C22⋊D53—212no—
229C2×C22⋊D53—24no—
230C2×C22⋊D53—46no—
231C2×C22⋊D53C2414yes—
232C2×C22⋊D53C24112yes—
233C2×C22⋊D53C2414yes—
234C2×C22⋊D53C24112yes—
235C22×Dic53—24no—
236C22×Dic53C2411yescharacteristic
237C22×Dic53C2413yes—
238C22×Dic53C2413yes—
239C22×Dic53C2411yescharacteristic
240C22×Dic53C2414yes—
241C22×Dic53C2411yescharacteristic
242#11719949—232no—
243#11719949—296no—
244#11719949—296no—
245#11719949—296no—
246#11719949C2×D4164yescomplemented
247Q8×D53—232no—
248Q8×D53—296no—
249#11719945—296no—
250#11719945—296no—
251C2×D212—224no—
252C2×D212—212no—
253C2×D212—212no—
254C2×D212—296no—
255C2×D212—46no—
256C2×D212C2×D4124yes—
257C2×D212C24112yes—
258C2×D212C24124yes—
259C2×D212C24112yes—
260C2×D212C24112yes—
261C2×D212C24112yes—
262C2×C4×D53—212no—
263C2×C4×D53—224no—
264C2×C4×D53—212no—
265C2×C4×D53—212no—
266C2×C4×D53—212no—
267C2×C4×D53—296no—
268C2×C4×D53—412no—
269C2×C4×D53C2×D4124yes—
270C2×C4×D53C24124yes—
271C2×C4×D53C24112yes—
272C2×C4×D53C24112yes—
273C2×C4×D53C24112yes—
274C2×C4×D53C24112yes—
275C2×C4×D53C24124yes—
276C2×C4×D53C24112yes—
277C2×Dic106—212no—
278C2×Dic106—212no—
279C2×Dic106C24112yes—
280C2×Dic106C24112yes—
281C4⋊C4×C53C24112yes—
282C4⋊C4×C53C24112yes—
283C4⋊C4×C53C24124yes—
284C22⋊C4×C53C24112yes—
285C22⋊C4×C53C24112yes—
286C42×C53C24112yes—
287C22⋊Dic53C24112yes—
288C22⋊Dic53C2414yes—
289#11719921C24124yes—
290#11719921C24124yes—
291#11719921C24112yes—
292#11719921C24112yes—
293#11719921C24112yes—
294#11719921C24112yes—
295#11719921C2414yes—
296#11719921C24112yes—
297C4⋊Dic53C24112yes—
298C4⋊Dic53C24112yes—
299#11719919C24112yes—
300#11719919C24112yes—
301#11719919C24124yes—
302#11719919C2414yes—
303#11719919C24112yes—
304C4×Dic53C24112yes—
305C23×C53—22no—
306C23×C53—22no—
307C23×C53—22no—
308C23×C53—22no—
309C23×C53—22no—
310C23×C532−1+414yescomplemented
311C23×C53C2512yes—
312C23×C53C2512yes—
313C23×C53C2511yescharacteristic
314C22×D53—26no—
315C22×D53—26no—
316C22×D53—22no—
317C22×D53—26no—
318C22×D53—22no—
319C22×D53—26no—
320C22×D53—224no—
321C22×D53—22no—
322C22×D53—26no—
323C22×D53—224no—
324C22×D53—412no—
325C22×D53—448no—
326C22×D53C22×D4112yes—
327C22×D53C2512yes—
328C22×D53C2516yes—
329C22×D53C2516yes—
330Q8×C53—224no—
331Q8×C53—224no—
332Q8×C53C22×D4116yes—
333D4×C53—28no—
334C2×C4×C53—26no—
335C2×C4×C53—26no—
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×C53C2516yes—
343C2×C4×C53C2516yes—
344C2×C4×C53C2512yes—
345C2×C4×C53C2516yes—
346C22⋊D53—28no—
347C22⋊D53—224no—
348C22⋊D53—28no—
349C22⋊D53—412no—
350C2×Dic53—26no—
351C2×Dic53—22no—
352C2×Dic53—22no—
353C2×Dic53—26no—
354C2×Dic53—28no—
355C2×Dic53C22×D414yes—
356C2×Dic53C2516yes—
357C2×Dic53C2512yes—
358C2×Dic53C2516yes—
359C2×Dic53C2512yes—
360C2×Dic53C2512yes—
361D212—248no—
362D212—224no—
363D212—224no—
364D212—412no—
365D212C22×D4148yes—
366C4×D53—224no—
367C4×D53—248no—
368C4×D53—224no—
369C4×D53—224no—
370C4×D53—224no—
371C4×D53—424no—
372C4×D53C22×D4148yes—
373Dic106—224no—
374Dic106—224no—
375C2×#3489—531nomaximal, Sylow
376C22×C53—22no—
377C22×C53—22no—
378C22×C53—28no—
379C22×C53—22no—
380C22×C53—22no—
381C22×C53—22no—
382C22×C53—44no—
383C22×C53C23×D412yes—
384C22×C53C2×2−1+412yes—
385C22×C53C2×2−1+414yescomplemented
386C22×C53#58512yes—
387C22×C53C2611yescharacteristic
388C2×D53—26no—
389C2×D53—26no—
390C2×D53—224no—
391C2×D53—22no—
392C2×D53—26no—
393C2×D53—22no—
394C2×D53—26no—
395C2×D53—22no—
396C2×D53—26no—
397C2×D53—448no—
398C2×D53—44no—
399C2×D53—412no—
400C2×D53C23×D4112yes—
401C4×C53—26no—
402C4×C53—26no—
403C4×C53—22no—
404C4×C53—26no—
405C4×C53C23×D4112yes—
406Dic53—26no—
407Dic53—22no—
408Dic53—22no—
409Dic53—26no—
410Dic53C23×D414yes—
411C22×2−1+4—531no—
412C23×#41—531no—
413#3489—5332no—
414C2×D4×Q8—531no—
415C2×D4×Q8D5311yescharacteristic, complemented
416C2×#548—531no—
417C2×#548—531no—
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—24no—
428C2×C53—42no—
429C2×C53#348914yescomplemented
430C2×C53C24×D411yescharacteristic
431C2×C53C22×2−1+411yescharacteristic
432C2×C53C2×#58511yescharacteristic
433D53—212no—
434D53—42no—
435D53—46no—
436C2×2−1+4—5316no—
437C2×2−1+4—10616no—
438C22×#41—531no—
439C22×#41—533no—
440C22×#41—533no—
441C22×#41—531no—
442C22×#41—5316no—
443C22×#41—533no—
444C22×#41—533no—
445C22×#41—533no—
446C22×#41—10616no—
447C23×Q8—533no—
448C23×Q8—531no—
449C23×Q8C2×D5311yescharacteristic
450C23×Q8C2×D5311yescharacteristic, complemented
451C23×D4—533no—
452C24×C4—533no—
453D4×Q8—5316no—
454D4×Q8C2×D53116yescomplemented
455#548—5316no—
456#548—5316no—
457#547—5348no—
458#547—5348no—
459#546—5348no—
460#546—5348no—
461#537—5348no—
462#536—5348no—
463C2×C4⋊Q8—533no—
464C2×C4⋊Q8C2×D5313yescomplemented
465C2×#124—533no—
466C2×#124—533no—
467#525—5348no—
468C2×#123—533no—
469C2×#123—536no—
470C2×#123—536no—
471C2×#123—533no—
472C2×C22⋊Q8—533no—
473C2×C22⋊Q8—533no—
474C2×C22⋊Q8—533no—
475C2×C22⋊Q8—5348no—
476C2×C22⋊Q8—536no—
477C2×C22⋊Q8—533no—
478C2×C22⋊Q8—533no—
479C2×C22⋊Q8—533no—
480C2×C22⋊Q8C2×D5313yes—
481C2×C22⋊Q8C2×D5313yescomplemented
482C2×#121—531no—
483C2×#121—533no—
484C2×#121—536no—
485C2×#121—533no—
486C2×#121—533no—
487C2×#121—536no—
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×D5313yes—
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—5316no—
507C2×#41—538no—
508C2×#41—5324no—
509C2×#41—5324no—
510C2×#41—5324no—
511C2×#41—538no—
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×#41—1068no—
521C22×Q8—28no—
522C22×Q8—28no—
523C22×Q8—5324no—
524C22×Q8—538no—
525C22×Q8—533no—
526C22×Q8—533no—
527C22×Q8—10624no—
528C22×Q8—1068no—
529C22×Q8C22×D5313yes—
530C22×Q8C22×D5313yes—
531C22×Q8C22×D5318yes—
532C22×Q8C22×D5311yescharacteristic
533C22×Q8C22×D5318yescomplemented
534C22×D4—531no—
535C22×D4—533no—
536C22×D4—531no—
537C22×D4—533no—
538C22×D4—533no—
539C22×D4—533no—
540C22×D4—536no—
541C22×D4—533no—
542C22×D4—5324no—
543C22×D4—533no—
544C22×D4—10624no—
545C22×D4C22×D5311yescharacteristic
546C23×C4—533no—
547C23×C4—531no—
548C23×C4—536no—
549C23×C4—533no—
550C23×C4—533no—
551C23×C4—533no—
552C23×C4—533no—
553C23×C4—5324no—
554C23×C4—536no—
555C23×C4—10624no—
556C23×C4C22×D5313yes—
557C23×C4C22×D5313yes—
558C4⋊Q8—5324no—
559C4⋊Q8C22×D53124yescomplemented
560#124—5324no—
561#124—5324no—
562#123—5324no—
563#123—5348no—
564#123—5348no—
565#123—5324no—
566C22⋊Q8—5324no—
567C22⋊Q8—5324no—
568C22⋊Q8—5324no—
569C22⋊Q8—5348no—
570C22⋊Q8—5324no—
571C22⋊Q8—5324no—
572C22⋊Q8—5324no—
573C22⋊Q8C22×D53124yes—
574C22⋊Q8C22×D53124yescomplemented
575#121—538no—
576#121—5324no—
577#121—5348no—
578#121—5324no—
579#121—5324no—
580#121—5348no—
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×D53124yes—
591#117—5324no—
592C2×C4⋊C4—533no—
593C2×C4⋊C4—533no—
594C2×C4⋊C4—533no—
595C2×C4⋊C4—533no—
596C2×C4⋊C4—536no—
597C2×C4⋊C4—531no—
598C2×C4⋊C4—533no—
599C2×C4⋊C4—5324no—
600C2×C4⋊C4—5348no—
601C2×C4⋊C4C22×D5313yes—
602C2×C4⋊C4C22×D5316yes—
603C2×C4⋊C4C22×D5313yes—
604C2×C22⋊C4—533no—
605C2×C22⋊C4—531no—
606C2×C22⋊C4—536no—
607C2×C22⋊C4—536no—
608C2×C22⋊C4—533no—
609C2×C22⋊C4—533no—
610C2×C22⋊C4—531no—
611C2×C22⋊C4—533no—
612C2×C22⋊C4—533no—
613C2×C22⋊C4—533no—
614C2×C22⋊C4—5348no—
615C2×C22⋊C4C22×D5313yes—
616C2×C22⋊C4C22×D5313yes—
617C2×C42—533no—
618C2×C42C22×D5313yes—
619C24—533no—
620C24—533no—
621C24—531no—
622C24—5312no—
623C24—10612no—
624C24—10612no—
625C24—2126no—
626C24C23×D5311yescharacteristic
627C24C23×D5311yescharacteristic
628#41—5364no—
629#41—10696no—
630#41—10696no—
631#41—10696no—
632#41—10696no—
633#41—10696no—
634#41—10632no—
635C2×Q8—232no—
636C2×Q8—232no—
637C2×Q8—212no—
638C2×Q8—212no—
639C2×Q8—5312no—
640C2×Q8—5312no—
641C2×Q8—10612no—
642C2×Q8—10696no—
643C2×Q8—10632no—
644C2×Q8—10612no—
645C2×Q8D4×D5318yes—
646C2×Q8C23×D53112yes—
647C2×Q8C23×D53112yes—
648C2×Q8C23×D5314yes—
649C2×D4—24no—
650C2×D4—534no—
651C2×D4—5312no—
652C2×D4—534no—
653C2×D4—5312no—
654C2×D4—5324no—
655C2×D4—5312no—
656C2×D4—5312no—
657C2×D4—5324no—
658C2×D4—5312no—
659C2×D4—5312no—
660C2×D4—10696no—
661C2×D4—10624no—
662C2×D4—10612no—
663C2×D4—1064no—
664C2×D4—10612no—
665C2×D4—1064no—
666C2×D4—10612no—
667C2×D4—2126no—
668C2×D4—2126no—
669C2×D4C23×D5314yes—
670C22×C4—212no—
671C22×C4—212no—
672C22×C4—531no—
673C22×C4—5324no—
674C22×C4—5312no—
675C22×C4—534no—
676C22×C4—531no—
677C22×C4—533no—
678C22×C4—533no—
679C22×C4—531no—
680C22×C4—5324no—
681C22×C4—5312no—
682C22×C4—5312no—
683C22×C4—5312no—
684C22×C4—5312no—
685C22×C4—5324no—
686C22×C4—10612no—
687C22×C4—10696no—
688C22×C4—10612no—
689C22×C4—10624no—
690C22×C4—1064no—
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×D5313yes—
700C22×C4C23×D5313yes—
701C4⋊C4—5312no—
702C4⋊C4—5312no—
703C4⋊C4—5312no—
704C4⋊C4—5312no—
705C4⋊C4—5324no—
706C4⋊C4—534no—
707C4⋊C4—5312no—
708C4⋊C4C23×D53112yes—
709C4⋊C4C23×D53124yes—
710C4⋊C4C23×D53112yes—
711C22⋊C4—5312no—
712C22⋊C4—534no—
713C22⋊C4—5324no—
714C22⋊C4—5324no—
715C22⋊C4—5312no—
716C22⋊C4—5312no—
717C22⋊C4—534no—
718C22⋊C4—5312no—
719C22⋊C4—5312no—
720C22⋊C4—5312no—
721C22⋊C4C23×D53112yes—
722C22⋊C4C23×D53112yes—
723C42—5312no—
724C42C23×D53112yes—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—5312no—
731C23—536no—
732C23—536no—
733C23—532no—
734C23—10624no—
735C23—1066no—
736C23—1066no—
737C23—1062no—
738C23—1066no—
739C23—1062no—
740C23—1066no—
741C23—10624no—
742C23—1062no—
743C23—1066no—
744C23—21212no—
745C23—21248no—
746C23#1313326514yescomplemented
747C23C24×D5312yes—
748C23C24×D5312yes—
749C23C24×D5311yescharacteristic
750Q8—224no—
751Q8—224no—
752Q8—10624no—
753Q8—10624no—
754Q8C2×D4×D53116yes—
755D4—28no—
756D4—5348no—
757D4—10648no—
758D4—10624no—
759D4—1068no—
760D4—10624no—
761D4—1068no—
762D4—10624no—
763D4—21212no—
764D4—21212no—
765C2×C4—26no—
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—532no—
778C2×C4—10624no—
779C2×C4—10624no—
780C2×C4—10648no—
781C2×C4—1068no—
782C2×C4—1062no—
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×D5316yes—
794C2×C4C24×D5316yes—
795C22—28no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—44no—
802C22—5312no—
803C22—10624no—
804C22—1066no—
805C22—1066no—
806C22—1062no—
807C22—1066no—
808C22—1062no—
809C22—1066no—
810C22—1062no—
811C22—1066no—
812C22—21248no—
813C22—21212no—
814C22—2124no—
815C22C22×D4×D5312yes—
816C22C2×#1313326512yes—
817C22C2×#1313326514yescomplemented
818C22#1681146012yes—
819C22C25×D5311yescharacteristic
820C4—26no—
821C4—26no—
822C4—22no—
823C4—26no—
824C4—534no—
825C4—1062no—
826C4—1066no—
827C4—1062no—
828C4—1066no—
829C4C22×D4×D53112yes—
830C2—24no—
831C2—42no—
832C2—10612no—
833C2—2126no—
834C2—2122no—
835C2#2028839214yesdirect product factor
836C2C23×D4×D5311yescharacteristic
837C2C22×#1313326511yescharacteristic
838C2C2×#1681146011yescharacteristic
subgroupG/H
centerC23C24×D53
commutator, cosocleC22×C53C26
FrattiniC22C25×D53
FittingC2×D4×Q8×C53C2
socleC23×C53C25
hypercenterC2×D4×Q8D53
hypocenterC53C2×#3489
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. C22×#13133265C2semidirect
2. C23×#11719949C2semidirect
3. #20288392C2direct (N × H)
4. C2×Q8×C22⋊D53C2semidirect
5. C2×#16811285C2semidirect
6. C2×#16811284C2semidirect
7. C2×#16811276C2semidirect
8. C2×#16811275C2semidirect
9. C2×#16811269C2semidirect
10. C2×#16811264C2semidirect
11. C2×#16811203C2semidirect
12. C2×#16811198C2semidirect
13. C2×#16811132C2semidirect
14. C2×C22⋊Q8×D53C2semidirect
15. C2×#16811105C2semidirect
16. C2×D4×Q8×C53C2semidirect
18. C2×#13133265C22semidirect
24. C22×#11719949C22semidirect
25. C22×#11719949C22semidirect
26. C22×#11719945C22semidirect
27. C22×#11719945C22semidirect
28. C22×Q8×D53C22semidirect
29. C22×Q8×D53C22semidirect
32. Q8×C22⋊D53C22semidirect
33. #16811285C22semidirect
34. #16811284C22semidirect
35. #16811276C22semidirect
36. #16811275C22semidirect
37. #16811269C22semidirect
38. #16811264C22semidirect
39. #16811203C22semidirect
40. #16811198C22semidirect
41. C2×#13133215C22semidirect
42. C2×#13133206C22semidirect
43. C2×#13133205C22semidirect
44. #16811132C22semidirect
45. C2×#13133202C22semidirect
46. C2×#13133202C22semidirect
47. C2×#13133202C22semidirect
48. C2×#13133199C22semidirect
49. C2×#13133197C22semidirect
51. C2×#13133195C22semidirect
52. C2×#13133195C22semidirect
54. C2×#13133193C22semidirect
55. C2×#13133193C22semidirect
56. C22⋊Q8×D53C22semidirect
57. C2×#13133192C22semidirect
58. C2×#13133192C22semidirect
59. C2×#13133191C22semidirect
60. C2×#13133190C22semidirect
61. C2×#13133190C22semidirect
65. #16811105C22semidirect
66. C2×Q8×Dic53C22semidirect
67. C2×C4×D212C22semidirect
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. D4×Q8×C53C22semidirect
79. C2×C4⋊Q8×C53C22semidirect
81. C2×C22⋊Q8×C53C22semidirect
82. C2×C4×Q8×C53C22semidirect
91. C2×#11719949D4semidirect
96. C2×#11719949C23semidirect
99. C2×#11719945C23semidirect
100. C2×#11719945C23semidirect
105. C2×Q8×D53C23semidirect
106. C2×Q8×D53C23semidirect
128. #13133215C23semidirect
129. #13133206C23semidirect
130. #13133205C23semidirect
131. #13133202C23semidirect
132. #13133202C23semidirect
133. #13133202C23semidirect
134. #13133199C23semidirect
135. #13133197C23semidirect
137. #13133195C23semidirect
138. #13133195C23semidirect
140. #13133193C23semidirect
141. #13133193C23semidirect
142. #13133192C23semidirect
143. #13133192C23semidirect
144. #13133191C23semidirect
145. #13133190C23semidirect
146. #13133190C23semidirect
150. Q8×Dic53C23semidirect
151. C4×D212C23semidirect
152. C4×D212C23semidirect
153. #13133179C23semidirect
155. C4×C22⋊D53C23semidirect
156. #13133174C23semidirect
164. C4⋊C4×D53C23semidirect
165. C4⋊C4×D53C23semidirect
184. C22×Q8×C53C23semidirect
188. C4⋊Q8×C53C23semidirect
190. C22⋊Q8×C53C23semidirect
191. C4×Q8×C53C23semidirect
246. #11719949C2×D4semidirect
310. C23×C532−1+4semidirect
385. C22×C53C2×2−1+4semidirect
415. C2×D4×Q8D53semidirect
429. C2×C53#3489semidirect
450. C23×Q8C2×D53semidirect
454. D4×Q8C2×D53semidirect
464. C2×C4⋊Q8C2×D53semidirect
481. C2×C22⋊Q8C2×D53semidirect
492. C2×C4×Q8C2×D53semidirect
503. C53C2×#3489semidirect
533. C22×Q8C22×D53semidirect
559. C4⋊Q8C22×D53semidirect
574. C22⋊Q8C22×D53semidirect
584. C4×Q8C22×D53semidirect
746. C23#13133265semidirect
817. C22C2×#13133265semidirect
835. C2#20288392direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131332652
C23×#117199492
#202883922
C2×Q8×C22⋊D532
C2×#168112852
C2×#168112842
C2×#168112762
C2×#168112752
C2×#168112692
C2×#168112642
C2×#168112032
C2×#168111982
C2×#168111322
C2×C22⋊Q8×D532
C2×#168111052
C2×D4×Q8×C532
C2×#348953