Finite Group Databasebeta

← #14914128

Subgroups — #14914128

Order 2816.

3170 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623256C211yesmaximal, characteristic
2C2×#10623105C212yesmaximal, complemented
3#13071692C212yesmaximal, complemented
4#13071683C212yesmaximal, complemented
5#13071680C211yesmaximal, characteristic, complemented
6#13071680C211yesmaximal, characteristic, complemented
7#13071676C211yesmaximal, characteristic, complemented
8#13071561C212yesmaximal, complemented
9#13071540C214yesmaximal, complemented
10#13071517C212yesmaximal, complemented
11#13071315C214yesmaximal, complemented
12#13071207C212yesmaximal, complemented
13C4×#66948C212yesmaximal, complemented
14#13071124C212yesmaximal, complemented
15#13071020C211yesmaximal, characteristic, complemented
16C4×C4⋊C4×D11C211yesmaximal, characteristic, complemented
17C11×#2365C211yesmaximal, characteristic, complemented
18C22×#4343C2212yes—
19C2×C11×C4⋊Q8C2211yescharacteristic
20C2×C4×Q8×C11C2212yes—
21C2×#67000C2212yes—
22C2×Q8×Dic11C2212yes—
23#10623256C4116yescomplemented
24#10623105—216no—
25C2×#66948C2212yes—
26C2×#66948C2212yes—
27C2×#66946C2214yes—
28C2×#66946C2212yes—
29C2×#66946C2212yes—
30C2×#66946C2212yes—
31C2×#66946C2212yes—
32C2×C4⋊C4×D11C2211yescharacteristic
33C2×C4⋊C4×D11C2214yes—
34C2×C4⋊C4×D11C2211yescharacteristic
35C2×#66927C2211yescharacteristic
36C2×C4×D44C2214yes—
37C2×C4×D44C2212yes—
38C2×C4×D44C2212yes—
39C2×#66925C2212yes—
40C2×#66925C2214yes—
41C2×C42×D11C2212yes—
42C2×C42×D11C2211yescharacteristic
43C11×#391C2212yes—
44C11×#389C2212yes—
45C11×#387C2214yes—
46C4×C11×C4⋊C4C2212yes—
47C4×C11×C4⋊C4C2211yescharacteristic
48C4×C11×C4⋊C4C2211yescharacteristic
49#10622843C2212yes—
50#10622603C2214yes—
51#10622602C2214yes—
52#10622601C2212yes—
53#10622601C2212yes—
54#10622600C2211yescharacteristic
55#10622600C2211yescharacteristic
56#10622598C2212yes—
57#10622594C2214yes—
58#10622589C2211yescharacteristic
59#10622589C2211yescharacteristic
60C4⋊C4×Dic11C2212yes—
61C4⋊C4×Dic11C2211yescharacteristic
62C4⋊C4×Dic11C2211yescharacteristic
63#10622553C2214yes—
64#10622552C2212yes—
65#10622552C2212yes—
66C4×(C2×D11)⋊C4C2214yes—
67C4×C4⋊Dic11C2211yescharacteristic
68C4×C4⋊Dic11C2211yescharacteristic
69C4×Dic11⋊C4C2212yes—
70C4×Dic11⋊C4C2212yes—
71#10622283C2214yes—
72#10622282C2214yes—
73#10622281C2214yes—
74#10622280C2214yes—
75#10622280C2214yes—
76#10622280C2212yes—
77#10622279C2214yes—
78#10622278C2214yes—
79#10622278C2214yes—
80#10622278C2214yes—
81#10622278C2214yes—
82D11×#95C2212yes—
83#10622263C2212yes—
84#10622262C2212yes—
85C22×Q8×C11C2312yes—
86C2×#4343—28no—
87C2×#4343—28no—
88C2×#4343C2×C4116yescomplemented
89C22×D44C2312yes—
90C22×D44C2312yes—
91C22×D44C2314yes—
92C22×D44C2312yes—
93C22×C4×D11C2311yescharacteristic
94C22×C4×D11C2314yes—
95C22×C4×D11C2312yes—
96C22×C4×D11C2314yes—
97C22×C4×D11C2314yes—
98C22×C4×D11C2311yescharacteristic
99C22×C4×D11C2312yes—
100C22×C4×D11C2311yescharacteristic
101C11×C4⋊Q8C2×C418yescomplemented
102C4×Q8×C11—28no—
103C2×C11×C4⋊C4C2314yes—
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C4⋊C4C2311yescharacteristic
106C2×C11×C4⋊C4C2311yescharacteristic
107C2×C11×C4⋊C4C2312yes—
108C2×C11×C4⋊C4C2312yes—
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C42×C11C2312yes—
111C2×C42×C11C2312yes—
112C2×C42×C11C2314yes—
113C2×C42×C11C2311yescharacteristic
114#67000C2×C4116yescomplemented
115Q8×Dic11—28no—
116C2×(C2×D11)⋊C4C2312yes—
117C2×(C2×D11)⋊C4C2314yes—
118C2×(C2×D11)⋊C4C2312yes—
119C2×(C2×D11)⋊C4C2314yes—
120C2×(C2×D11)⋊C4C2314yes—
121C2×(C2×D11)⋊C4C2314yes—
122C2×(C2×D11)⋊C4C2314yes—
123C2×(C2×D11)⋊C4C2314yes—
124C2×(C2×D11)⋊C4C2314yes—
125C2×(C2×D11)⋊C4C2314yes—
126C2×C4⋊Dic11C2311yescharacteristic
127C2×C4⋊Dic11C2314yes—
128C2×C4⋊Dic11C2311yescharacteristic
129C2×C4⋊Dic11C2311yescharacteristic
130C2×C4⋊Dic11C2311yescharacteristic
131C2×Dic11⋊C4C2312yes—
132C2×Dic11⋊C4C2312yes—
133C2×Dic11⋊C4C2312yes—
134C2×Dic11⋊C4C2312yes—
135C2×Dic11⋊C4C2312yes—
136C2×Dic11⋊C4C2312yes—
137C2×C4×Dic11C2312yes—
138C2×C4×Dic11C2314yes—
139C2×C4×Dic11C2312yes—
140C2×C4×Dic11C2312yes—
141C2×C4×Dic11C2312yes—
142C2×C4×Dic11C2311yescharacteristic
143C2×C4×Dic11C2311yescharacteristic
144C2×C4×Dic11C2311yescharacteristic
145#66948C2×C4116yescomplemented
146#66948C2×C4116yescomplemented
147#66946—216no—
148#66946—28no—
149#66946—44no—
150#66946C2×C4116yescomplemented
151#66946C2×C4116yescomplemented
152C4⋊C4×D11—24no—
153C4⋊C4×D11—216no—
154C4⋊C4×D11D418yescomplemented
155#66927C2×C418yescomplemented
156C4×D44—216no—
157C4×D44—28no—
158C4×D44—44no—
159#66925—28no—
160#66925—216no—
161C42×D11—44no—
162C42×D11C2×C418yescomplemented
163C11×#95C2312yes—
164C11×#95C2312yes—
165C11×#95C2314yes—
166C11×#95C2314yes—
167C11⋊#95C2312yes—
168C11⋊#95C2312yes—
169C11⋊#95C2312yes—
170C11⋊#95C2312yes—
171C11⋊#95C2312yes—
172C11⋊#95C2312yes—
173C11⋊#95C2314yes—
174C11⋊#95C2314yes—
175#34206—111nomaximal, Sylow
176C23×D11C2414yes—
177C23×D11C2411yescharacteristic
178C2×Q8×C11—24no—
179C2×Q8×C11—24no—
180C2×Q8×C11C22×C418yes—
181C22×C4×C11C2412yes—
182C22×C4×C11C2412yes—
183C22×C4×C11C2412yes—
184C22×C4×C11C2411yescharacteristic
185C22×C4×C11C2414yes—
186C22×C4×C11C2412yes—
187C22×C4×C11C2411yescharacteristic
188C22×C4×C11C2411yescharacteristic
189C22×Dic11C2412yes—
190C22×Dic11C2412yes—
191C22×Dic11C2412yes—
192C22×Dic11C2411yescharacteristic
193C22×Dic11C2411yescharacteristic
194C22×Dic11C2412yes—
195C22×Dic11C2411yescharacteristic
196#4343—264no—
197C2×D44—28no—
198C2×D44—28no—
199C2×D44—24no—
200C2×D44—24no—
201C2×D44—24no—
202C2×D44—24no—
203C2×D44—42no—
204C2×D44—42no—
205C2×D44C22×C418yes—
206C2×D44C22×C418yes—
207C2×D44C22×C4116yes—
208C2×D44C22×C418yes—
209C2×C4×D11—28no—
210C2×C4×D11—28no—
211C2×C4×D11—28no—
212C2×C4×D11—24no—
213C2×C4×D11—28no—
214C2×C4×D11—22no—
215C2×C4×D11—22no—
216C2×C4×D11—42no—
217C2×C4×D11—42no—
218C2×C4×D11—42no—
219C2×C4×D11—41no—
220C2×C4×D11—41no—
221C2×C4×D11—42no—
222C2×C4×D11—44no—
223C2×C4×D11—44no—
224C2×C4×D11—44no—
225C2×C4×D11—44no—
226C2×C4×D11C22×C414yes—
227C2×C4×D11C22×C4116yes—
228C2×C4×D11C22×C414yes—
229C2×C4×D11C22×C414yes—
230C2×C4×D11C2×D418yes—
231C2×C4×D11C2×D414yes—
232C2×C4×D11#4114yes—
233C11×C4⋊C4—28no—
234C11×C4⋊C4—22no—
235C11×C4⋊C4—22no—
236C11×C4⋊C4—22no—
237C11×C4⋊C4C22×C418yes—
238C11×C4⋊C4C22×C418yes—
239C11×C4⋊C4C2×D414yes—
240C42×C11—28no—
241C42×C11—24no—
242C42×C11—24no—
243C42×C11C22×C414yes—
244(C2×D11)⋊C4—28no—
245(C2×D11)⋊C4—24no—
246(C2×D11)⋊C4—24no—
247(C2×D11)⋊C4—28no—
248(C2×D11)⋊C4—44no—
249(C2×D11)⋊C4—44no—
250(C2×D11)⋊C4—44no—
251(C2×D11)⋊C4—44no—
252(C2×D11)⋊C4C22×C4116yes—
253(C2×D11)⋊C4C22×C4116yes—
254C4⋊Dic11—28no—
255C4⋊Dic11—22no—
256C4⋊Dic11—22no—
257C4⋊Dic11—22no—
258C4⋊Dic11C2×D414yes—
259Dic11⋊C4—24no—
260Dic11⋊C4—24no—
261Dic11⋊C4—24no—
262Dic11⋊C4—42no—
263Dic11⋊C4—42no—
264Dic11⋊C4C2×D418yes—
265C4×Dic11—28no—
266C4×Dic11—24no—
267C4×Dic11—24no—
268C4×Dic11—42no—
269C4×Dic11—42no—
270C4×Dic11C22×C414yes—
271C4×Dic11C22×C414yes—
272C4×Dic11C22×C414yes—
273C2×#532—111no—
274C2×#520—112no—
275#2367—112no—
276#2367—112no—
277#2366—111no—
278#2366—111no—
279#2365—111no—
280#2365D1111yescharacteristic, complemented
281#2354—112no—
282#2352—114no—
283D4×C4⋊C4—112no—
284#2325—114no—
285#2311—112no—
286C4×#121—112no—
287C4×#121—112no—
288#2285—111no—
289C2×C4×C4⋊C4—111no—
290C23×C11C2511yescharacteristic
291C22×D11—21no—
292C22×D11—21no—
293C22×D11—21no—
294C22×D11—21no—
295C22×D11—24no—
296C22×D11—24no—
297C22×D11—24no—
298C22×D11—24no—
299C22×D11—24no—
300C22×D11—24no—
301C22×D11C23×C418yes—
302C22×D11C23×C412yes—
303C22×D11C22×D412yes—
304C22×D11C2×#4112yes—
305Q8×C11—216no—
306C2×C4×C11—24no—
307C2×C4×C11—24no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11C23×C412yes—
322C2×C4×C11C23×C418yes—
323C2×C4×C11C23×C412yes—
324C2×C4×C11C23×C412yes—
325C2×C4×C11C22×D414yes—
326C2×C4×C11C22×D412yes—
327C2×C4×C11C2×#4112yes—
328C2×C4×C11H(5,𝔽2)12yes—
329C2×C4×C112−1+412yes—
330C2×Dic11—22no—
331C2×Dic11—21no—
332C2×Dic11—21no—
333C2×Dic11—21no—
334C2×Dic11—21no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—22no—
338C2×Dic11—22no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—22no—
344C2×Dic11—22no—
345C2×Dic11C23×C412yes—
346C2×Dic11C23×C412yes—
347C2×Dic11C23×C412yes—
348C2×Dic11C22×D414yes—
349C2×Dic11C22×D412yes—
350C2×Dic11C2×#4112yes—
351D44—232no—
352D44—216no—
353D44—216no—
354D44—48no—
355C4×D11—28no—
356C4×D11—232no—
357C4×D11—44no—
358C4×D11—48no—
359C4×D11—48no—
360C4×D11—88no—
361C4×D11—88no—
362C4×D11C4×D4116yescomplemented
363C22×#41—112no—
364#532—1116no—
365C2×C4⋊Q8C2×D1111yescharacteristic
366C2×#127—111no—
367C2×#124—112no—
368C2×#121—112no—
369C2×#121—112no—
370#520—2216no—
371C2×C4×Q8—112no—
372C2×C4×Q8C2×D1112yes—
373C2×C4×D4—112no—
374C2×C4×D4—112no—
375C2×C4×D4—114no—
376C2×C4×D4—112no—
377C2×C4×D4—112no—
378C2×C4×D4—114no—
379C2×C4×D4—112no—
380C2×C4×D4—112no—
381C2×#117—112no—
382C2×#117—114no—
383C22×C4⋊C4—111no—
384C22×C4⋊C4—111no—
385C22×C4⋊C4—114no—
386C22×C42—111no—
387C22×C42—112no—
388#391—112no—
389#391C2×D1112yes—
390#390—112no—
391#390—112no—
392#390—112no—
393#390—112no—
394#389—112no—
395#389C2×D1112yes—
396#388—114no—
397#388—114no—
398#388—114no—
399#388—114no—
400#387—114no—
401#387C2×D1114yes—
402#386—114no—
403#386—114no—
404#386—114no—
405#386—114no—
406#385—114no—
407#385—114no—
408#384—111no—
409#384—111no—
410#382—112no—
411#380—111no—
412#380—111no—
413#380—114no—
414#380—114no—
415#380—112no—
416C4×C4⋊C4—112no—
417C4×C4⋊C4—111no—
418C4×C4⋊C4—111no—
419C4×C4⋊C4—112no—
420C4×C4⋊C4—111no—
421C4×C4⋊C4—111no—
422C4×C4⋊C4—112no—
423C4×C4⋊C4—112no—
424C4×C4⋊C4C2×D1112yes—
425C4×C4⋊C4C2×D1111yescharacteristic
426C4×C4⋊C4C2×D1111yescharacteristic
427C4×C22⋊C4—114no—
428C4×C22⋊C4—114no—
429C2×#95—112no—
430C22×C11C24×C411yescharacteristic
431C22×C11C23×D411yescharacteristic
432C22×C11C22×#4111yescharacteristic
433C22×C11C2×H(5,𝔽2)11yescharacteristic
434C22×C11C2×2−1+411yescharacteristic
435C22×C11#58511yescharacteristic
436C22×C11#58511yescharacteristic
437C2×D11—22no—
438C2×D11—22no—
439C2×D11—22no—
440C2×D11—22no—
441C2×D11—22no—
442C2×D11—22no—
443C2×D11—28no—
444C2×D11—28no—
445C2×D11—28no—
446C2×D11—44no—
447C2×D11—44no—
448C2×D11—44no—
449C2×D11—44no—
450C2×D11C2×C4×D414yes—
451C4×C11—28no—
452C4×C11—22no—
453C4×C11—24no—
454C4×C11—42no—
455C4×C11—42no—
456C4×C11—42no—
457C4×C11C2×C4×D414yes—
458C4×C11#52014yescomplemented
459Dic11—22no—
460Dic11—22no—
461Dic11—24no—
462Dic11—42no—
463Dic11—42no—
464Dic11—42no—
465Dic11C2×C4×D414yes—
466C2×#41—1116no—
467C2×#41—228no—
468C2×#41—228no—
469C22×Q8C22×D1112yes—
470C22×D4—112no—
471C22×D4—114no—
472C22×D4—112no—
473C22×D4—112no—
474C23×C4—111no—
475C23×C4—114no—
476C23×C4—111no—
477C23×C4—112no—
478C23×C4—111no—
479C23×C4—114no—
480C23×C4—114no—
481C23×C4—112no—
482C4⋊Q8C4×D1118yescomplemented
483#127—118no—
484#124—1116no—
485#121—1116no—
486#121—1116no—
487C4×Q8—28no—
488C4×Q8—228no—
489C4×D4—1116no—
490C4×D4—1116no—
491C4×D4—228no—
492C4×D4—2216no—
493C4×D4—2216no—
494C4×D4—228no—
495C4×D4—444no—
496C4×D4—444no—
497#117—2216no—
498#117—228no—
499C2×C4⋊C4—112no—
500C2×C4⋊C4—111no—
501C2×C4⋊C4—118no—
502C2×C4⋊C4—112no—
503C2×C4⋊C4—114no—
504C2×C4⋊C4—112no—
505C2×C4⋊C4—111no—
506C2×C4⋊C4—112no—
507C2×C4⋊C4—111no—
508C2×C4⋊C4—111no—
509C2×C4⋊C4—112no—
510C2×C4⋊C4—112no—
511C2×C4⋊C4—2216no—
512C2×C4⋊C4—224no—
513C2×C4⋊C4C22×D1114yes—
514C2×C4⋊C4C22×D1111yescharacteristic
515C2×C4⋊C4C22×D1111yescharacteristic
516C2×C4⋊C4C22×D1111yescharacteristic
517C2×C4⋊C4C22×D1112yes—
518C2×C4⋊C4C22×D1112yes—
519C2×C4⋊C4C22×D1111yescharacteristic
520C2×C22⋊C4—114no—
521C2×C22⋊C4—114no—
522C2×C22⋊C4—112no—
523C2×C22⋊C4—112no—
524C2×C22⋊C4—114no—
525C2×C22⋊C4—114no—
526C2×C22⋊C4—114no—
527C2×C22⋊C4—114no—
528C2×C22⋊C4—114no—
529C2×C22⋊C4—114no—
530C2×C42—111no—
531C2×C42—111no—
532C2×C42—111no—
533C2×C42—118no—
534C2×C42—114no—
535C2×C42—112no—
536C2×C42—112no—
537C2×C42—112no—
538C2×C42—112no—
539C2×C42—444no—
540C2×C42C22×D1114yes—
541C2×C42C22×D1112yes—
542C2×C42C22×D1112yes—
543C2×C42C22×D1111yescharacteristic
544#95—112no—
545#95—112no—
546#95—112no—
547#95—112no—
548#95—112no—
549#95—114no—
550#95—112no—
551#95—114no—
552#95C22×D1112yes—
553#95C22×D1114yes—
554#95C22×D1112yes—
555#95C22×D1114yes—
556C2×C11C22×C4×D411yescharacteristic
557C2×C11C2×#52011yescharacteristic
558C2×C11#342811yescharacteristic
559C2×C11#349611yescharacteristic
560C2×C11#349711yescharacteristic
561C2×C11#350611yescharacteristic
562C2×C11#350711yescharacteristic
563D11—24no—
564D11—48no—
565C24—111no—
566C24—114no—
567#41—2264no—
568C2×Q8—24no—
569C2×Q8—24no—
570C2×Q8C2×C4×D1118yes—
571C2×D4—118no—
572C2×D4—1116no—
573C2×D4—118no—
574C2×D4—118no—
575C2×D4—228no—
576C2×D4—228no—
577C2×D4—224no—
578C2×D4—224no—
579C2×D4—224no—
580C2×D4—224no—
581C2×D4—442no—
582C2×D4—442no—
583C22×C4—111no—
584C22×C4—114no—
585C22×C4—114no—
586C22×C4—114no—
587C22×C4—111no—
588C22×C4—111no—
589C22×C4—112no—
590C22×C4—114no—
591C22×C4—1116no—
592C22×C4—114no—
593C22×C4—118no—
594C22×C4—112no—
595C22×C4—112no—
596C22×C4—112no—
597C22×C4—228no—
598C22×C4—228no—
599C22×C4—228no—
600C22×C4—224no—
601C22×C4—222no—
602C22×C4—222no—
603C22×C4—228no—
604C22×C4—442no—
605C22×C4—442no—
606C22×C4—442no—
607C22×C4—441no—
608C22×C4—441no—
609C22×C4—442no—
610C22×C4—444no—
611C22×C4—444no—
612C22×C4—444no—
613C22×C4—444no—
614C22×C4C23×D1112yes—
615C22×C4C23×D1112yes—
616C22×C4C23×D1112yes—
617C22×C4C23×D1111yescharacteristic
618C22×C4C23×D1114yes—
619C22×C4C23×D1112yes—
620C22×C4C23×D1111yescharacteristic
621C22×C4C23×D1111yescharacteristic
622C4⋊C4—28no—
623C4⋊C4—22no—
624C4⋊C4—22no—
625C4⋊C4—22no—
626C4⋊C4—118no—
627C4⋊C4—114no—
628C4⋊C4—224no—
629C4⋊C4—228no—
630C4⋊C4—224no—
631C4⋊C4—224no—
632C4⋊C4—222no—
633C4⋊C4—222no—
634C4⋊C4—222no—
635C4⋊C4—442no—
636C4⋊C4—442no—
637C4⋊C4C2×C4×D1118yes—
638C4⋊C4C2×C4×D1118yes—
639C4⋊C4D4×D1114yes—
640C22⋊C4—1116no—
641C22⋊C4—1116no—
642C22⋊C4—228no—
643C22⋊C4—224no—
644C22⋊C4—224no—
645C22⋊C4—228no—
646C22⋊C4—444no—
647C22⋊C4—444no—
648C22⋊C4—444no—
649C22⋊C4—444no—
650C42—28no—
651C42—24no—
652C42—24no—
653C42—114no—
654C42—114no—
655C42—114no—
656C42—228no—
657C42—224no—
658C42—224no—
659C42—442no—
660C42—442no—
661C42C2×C4×D1114yes—
662C11#3420611yescharacteristic, complemented, Sylow
663C23—112no—
664C23—112no—
665C23—112no—
666C23—118no—
667C23—221no—
668C23—221no—
669C23—221no—
670C23—221no—
671C23—224no—
672C23—224no—
673C23—224no—
674C23—224no—
675C23—224no—
676C23—224no—
677C23C24×D1111yescharacteristic
678Q8—216no—
679D4—2232no—
680D4—2216no—
681D4—2216no—
682D4—448no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—112no—
699C2×C4—112no—
700C2×C4—112no—
701C2×C4—1116no—
702C2×C4—112no—
703C2×C4—112no—
704C2×C4—114no—
705C2×C4—2232no—
706C2×C4—221no—
707C2×C4—222no—
708C2×C4—221no—
709C2×C4—221no—
710C2×C4—221no—
711C2×C4—222no—
712C2×C4—228no—
713C2×C4—222no—
714C2×C4—222no—
715C2×C4—222no—
716C2×C4—222no—
717C2×C4—222no—
718C2×C4—222no—
719C2×C4—222no—
720C2×C4—222no—
721C2×C4—222no—
722C2×C4—448no—
723C2×C4—444no—
724C2×C4—448no—
725C2×C4—888no—
726C2×C4—888no—
727C2×C4C22×C4×D1112yes—
728C2×C4C22×C4×D1118yes—
729C2×C4C22×C4×D1112yes—
730C2×C4C22×C4×D1112yes—
731C2×C4C2×D4×D1114yes—
732C2×C4C2×D4×D1112yes—
733C2×C4#6704012yes—
734C2×C4#41×D1112yes—
735C2×C4#6704212yes—
736C22—114no—
737C22—222no—
738C22—222no—
739C22—222no—
740C22—222no—
741C22—222no—
742C22—222no—
743C22—228no—
744C22—228no—
745C22—228no—
746C22—444no—
747C22—444no—
748C22—444no—
749C22—444no—
750C22C23×C4×D1111yescharacteristic
751C22C22×D4×D1111yescharacteristic
752C22C2×#6704011yescharacteristic
753C22C2×#41×D1111yescharacteristic
754C22C2×#6704211yescharacteristic
755C22#1062345711yescharacteristic
756C22#1062345711yescharacteristic
757C4—24no—
758C4—28no—
759C4—22no—
760C4—42no—
761C4—42no—
762C4—42no—
763C4—114no—
764C4—224no—
765C4—222no—
766C4—222no—
767C4—442no—
768C4—442no—
769C4—442no—
770C4C4×D4×D1114yes—
771C4#1062310514yescomplemented
772C2—224no—
773C2—448no—
774C2C2×C4×D4×D1111yescharacteristic
775C2C2×#1062310511yescharacteristic
776C2#1308181811yescharacteristic
777C2#1308237411yescharacteristic
778C2#1308238611yescharacteristic
779C2#1308246911yescharacteristic
780C2#1308248211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2365C2
socle, cosocleC23×C11C25
prime radicalC2×#10623256C2
hypercenter#2365D11
hypocenterC11#34206
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2365

Complements

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

NH ≅ G/Ntype
2. C2×#10623105C2semidirect
3. #13071692C2semidirect
4. #13071683C2semidirect
5. #13071680C2semidirect
6. #13071680C2semidirect
7. #13071676C2semidirect
8. #13071561C2semidirect
9. #13071540C2semidirect
10. #13071517C2semidirect
11. #13071315C2semidirect
12. #13071207C2semidirect
13. C4×#66948C2semidirect
14. #13071124C2semidirect
15. #13071020C2semidirect
16. C4×C4⋊C4×D11C2semidirect
17. C11×#2365C2semidirect
23. #10623256C4semidirect
88. C2×#4343C2×C4semidirect
101. C11×C4⋊Q8C2×C4semidirect
114. #67000C2×C4semidirect
145. #66948C2×C4semidirect
146. #66948C2×C4semidirect
150. #66946C2×C4semidirect
151. #66946C2×C4semidirect
154. C4⋊C4×D11D4semidirect
155. #66927C2×C4semidirect
162. C42×D11C2×C4semidirect
280. #2365D11semidirect
362. C4×D11C4×D4semidirect
458. C4×C11#520semidirect
482. C4⋊Q8C4×D11semidirect
662. C11#34206semidirect
771. C4#10623105semidirect

Maximal subgroups

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

subgroupindex
C2×#106232562
C2×#106231052
#130716922
#130716832
#130716802
#130716762
#130715612
#130715402
#130715172
#130713152
#130712072
C4×#669482
#130711242
#130710202
C4×C4⋊C4×D112
C11×#23652
#3420611