Finite Group Databasebeta

← #14916543

Subgroups — #14916543

Order 2816.

2714 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623322C211yesmaximal, characteristic
2#13071760C214yesmaximal, complemented
3#13071595C214yesmaximal, complemented
4#13071547C212yesmaximal, complemented
5#13071541C212yesmaximal, complemented
6C4⋊C4×C22⋊D11C212yesmaximal, complemented
7#13071512C212yesmaximal, complemented
8#13071349C212yesmaximal, complemented
9#13071346C212yesmaximal, complemented
10#13071319C212yesmaximal, complemented
11#13071316C212yesmaximal, complemented
12#13071223C212yesmaximal, complemented
13#13071205C212yesmaximal, complemented
14C2×#10622825C211yesmaximal, characteristic, complemented
15C2×C11×#380C211yesmaximal, characteristic, complemented
16C24×C4×C11C2211yescharacteristic
17C22×#4339C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2212yes—
21C2×#67006C2212yes—
22C22×C22⋊Dic11C2212yes—
23#10623322C4116yescomplemented
24C2×#66983C2211yescharacteristic
25C2×#66983C2211yescharacteristic
26C2×#66982C2212yes—
27C2×C4×C22⋊D11C2214yes—
28C2×C4×C22⋊D11C2212yes—
29C2×C4×C22⋊D11C2212yes—
30C2×#66979C2211yescharacteristic
31C22×C4⋊Dic11C2211yescharacteristic
32C22×C4⋊Dic11C2211yescharacteristic
33C2×#66977C2211yescharacteristic
34C2×#66977C2211yescharacteristic
35C2×#66945C2212yescomplemented
36C2×C4⋊C4×D11C2212yescomplemented
37C2×(C22⋊D11)⋊C4C2214yes—
38C11×#380C2212yes—
39C11×#380C2212yes—
40C11×#380C2212yes—
41C11×#380C2212yes—
42C2×C11×#95C2212yes—
43#10622826C2214yes—
44#10622825C2212yes—
45#10622825C2212yes—
46#10622825C2212yes—
47#10622825C2212yes—
48#10622823C2214yes—
49C4×C22⋊Dic11C2214yes—
50C2×C11⋊#95C2212yes—
51#10622603C2214yescomplemented
52#10622602C2214yescomplemented
53#10622600C2212yescomplemented
54#10622600C2212yescomplemented
55#10622591C2214yescomplemented
56#10622590C2212yescomplemented
57#10622589C2212yescomplemented
58C4⋊C4×Dic11C2212yescomplemented
59C4⋊C4×Dic11C2212yescomplemented
60#10622585C2214yescomplemented
61#10622571C2214yes—
62#10622570C2214yes—
63#10622569C2214yes—
64#10622559C2214yes—
65#10622558C2214yes—
66#10622557C2214yes—
67C22⋊C4×Dic11C2214yes—
68#10622283C2214yescomplemented
69#10622281C2214yescomplemented
70#10622278C2214yescomplemented
71#10622268C2214yescomplemented
72#10622267C2214yescomplemented
73#10622266C2214yescomplemented
74#10622260C2214yescomplemented
75#10622259C2214yescomplemented
76C25×C11C2311yescharacteristic
77C23×C4×C11—42no—
78C23×C4×C11—42no—
79C23×C4×C11C2×C418yescomplemented
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2312yes—
84C23×C4×C11C2312yes—
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C22×C22⋊D11C2312yes—
89C22×C22⋊D11C2312yes—
90C22×C22⋊D11C2312yes—
91C23×Dic11C2312yes—
92C23×Dic11C2312yes—
93C2×#4339—42no—
94C2×#4339—42no—
95C2×#4339C2×C418yescomplemented
96C22×D44C2311yescharacteristic
97C22×C4×D11C2312yes—
98C22×C4×D11C2314yes—
99C22×Dic22C2311yescharacteristic
100C2×C11×C4⋊C4—42no—
101C2×C11×C4⋊C4—42no—
102C2×C11×C4⋊C4C2312yes—
103C2×C11×C4⋊C4C2312yes—
104C2×C11×C4⋊C4C2312yes—
105C2×C11×C4⋊C4C2312yes—
106C2×C11×C22⋊C4—44no—
107C2×C11×C22⋊C4C2314yes—
108C2×C11×C22⋊C4C2314yes—
109#67006C2×C4116yescomplemented
110C2×C22⋊Dic11—44no—
111C2×C22⋊Dic11C2314yes—
112C2×C22⋊Dic11C2314yes—
113C2×C22⋊Dic11C2312yes—
114C2×C22⋊Dic11C2312yes—
115C2×C22⋊Dic11C2312yes—
116#66983C2×C418yescomplemented
117#66983C2×C418yescomplemented
118#66982C2×C4116yescomplemented
119C4×C22⋊D11—48no—
120C4×C22⋊D11C2×C4116yescomplemented
121C4×C22⋊D11C2×C4116yescomplemented
122C2×(C2×D11)⋊C4C2314yes—
123C2×(C2×D11)⋊C4C2314yes—
124C2×(C2×D11)⋊C4C2314yes—
125C2×(C2×D11)⋊C4C2312yes—
126C2×(C2×D11)⋊C4C2312yes—
127#66979C2×C418yescomplemented
128C2×C4⋊Dic11—42no—
129C2×C4⋊Dic11—42no—
130C2×C4⋊Dic11C2312yes—
131C2×C4⋊Dic11C2312yes—
132C2×C4⋊Dic11C2312yes—
133C2×C4⋊Dic11C2312yes—
134C2×C4⋊Dic11C2311yescharacteristic
135C2×C4⋊Dic11C2311yescharacteristic
136#66977C2×C418yescomplemented
137#66977C2×C418yescomplemented
138C2×Dic11⋊C4C2314yes—
139C2×Dic11⋊C4C2314yes—
140C2×Dic11⋊C4C2314yes—
141C2×Dic11⋊C4C2312yes—
142C2×Dic11⋊C4C2312yes—
143C2×C4×Dic11C2314yes—
144C2×C4×Dic11C2314yes—
145C2×C4×Dic11C2314yes—
146C2×C4×Dic11C2312yes—
147#66945—44no—
148C4⋊C4×D11—44no—
149(C22⋊D11)⋊C4—48no—
150C11×#95C2314yes—
151C11×#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C11⋊#95C2314yes—
159C11⋊#95C2314yes—
160#34360—111nomaximal, Sylow
161C24×C11—22no—
162C24×C11—22no—
163C24×C11—22no—
164C24×C11—22no—
165C24×C11—41no—
166C24×C11—41no—
167C24×C11C22×C414yes—
168C24×C11C2411yescharacteristic
169C24×C11C2411yescharacteristic
170C24×C11C2411yescharacteristic
171C23×D11C2412yes—
172C22×C4×C11—22no—
173C22×C4×C11—22no—
174C22×C4×C11—22no—
175C22×C4×C11—22no—
176C22×C4×C11—22no—
177C22×C4×C11—22no—
178C22×C4×C11—24no—
179C22×C4×C11—24no—
180C22×C4×C11—416no—
181C22×C4×C11—41no—
182C22×C4×C11—41no—
183C22×C4×C11—41no—
184C22×C4×C11—41no—
185C22×C4×C11—41no—
186C22×C4×C11—41no—
187C22×C4×C11—42no—
188C22×C4×C11—42no—
189C22×C4×C11—42no—
190C22×C4×C11—42no—
191C22×C4×C11C22×C414yes—
192C22×C4×C11C22×C414yes—
193C22×C4×C11C22×C414yes—
194C22×C4×C11C22×C414yes—
195C22×C4×C11C22×C414yes—
196C22×C4×C11C22×C414yes—
197C22×C4×C11C2414yes—
198C22×C4×C11C2414yes—
199C22×C4×C11C2411yescharacteristic
200C22×C4×C11C2411yescharacteristic
201C22×C4×C11C2411yescharacteristic
202C22×C4×C11C2411yescharacteristic
203C2×C22⋊D11—24no—
204C2×C22⋊D11—24no—
205C2×C22⋊D11—24no—
206C2×C22⋊D11—24no—
207C2×C22⋊D11—42no—
208C2×C22⋊D11—42no—
209C2×C22⋊D11C22×C418yes—
210C2×C22⋊D11C22×C418yes—
211C2×C22⋊D11C22×C418yes—
212C22×Dic11—24no—
213C22×Dic11—24no—
214C22×Dic11—42no—
215C22×Dic11—42no—
216C22×Dic11—42no—
217C22×Dic11—42no—
218C22×Dic11C2414yes—
219C22×Dic11C2414yes—
220C22×Dic11C2412yes—
221C22×Dic11C2412yes—
222C22×Dic11C2412yes—
223#4339—416no—
224C2×D44—41no—
225C2×D44—41no—
226C2×D44C22×C414yes—
227C2×C4×D11—24no—
228C2×C4×D11—24no—
229C2×C4×D11—44no—
230C2×C4×D11—44no—
231C2×C4×D11—44no—
232C2×C4×D11C22×C418yes—
233C2×Dic22—41no—
234C2×Dic22—41no—
235C2×Dic22C22×C414yes—
236C11×C4⋊C4—24no—
237C11×C4⋊C4—24no—
238C11×C4⋊C4—42no—
239C11×C4⋊C4—42no—
240C11×C22⋊C4—28no—
241C11×C22⋊C4—44no—
242C22⋊Dic11—28no—
243C22⋊Dic11—44no—
244C22⋊Dic11C22×C418yes—
245C22⋊Dic11C22×C418yes—
246C22⋊Dic11C22×C418yes—
247(C2×D11)⋊C4—44no—
248(C2×D11)⋊C4—44no—
249(C2×D11)⋊C4—44no—
250(C2×D11)⋊C4C22×C418yes—
251(C2×D11)⋊C4C22×C418yes—
252C4⋊Dic11—24no—
253C4⋊Dic11—24no—
254C4⋊Dic11—42no—
255C4⋊Dic11—42no—
256C4⋊Dic11C22×C414yes—
257C4⋊Dic11C22×C414yes—
258Dic11⋊C4—44no—
259Dic11⋊C4—44no—
260Dic11⋊C4—44no—
261Dic11⋊C4C22×C418yes—
262Dic11⋊C4C22×C418yes—
263C4×Dic11—44no—
264C4×Dic11—44no—
265C4×Dic11—44no—
266C4×Dic11C22×C418yes—
267C2×#525—111no—
268#2376—114no—
269#2358—114no—
270#2352—112no—
271#2352—112no—
272D4×C4⋊C4—112no—
273D4×C4⋊C4—112no—
274#2329—112no—
275#2329—112no—
276#2325—112no—
277#2325—112no—
278#2314—112no—
279#2311—112no—
280C2×#380—111no—
281C2×#380D1111yescharacteristic, complemented
282C23×C11—21no—
283C23×C11—21no—
284C23×C11—21no—
285C23×C11—21no—
286C23×C11—21no—
287C23×C11—21no—
288C23×C11—21no—
289C23×C11—21no—
290C23×C11—28no—
291C23×C11—28no—
292C23×C11—21no—
293C23×C11—21no—
294C23×C11—21no—
295C23×C11—21no—
296C23×C11—21no—
297C23×C11—21no—
298C23×C11—44no—
299C23×C11—44no—
300C23×C11—44no—
301C23×C11—44no—
302C23×C11—44no—
303C23×C11C23×C412yes—
304C23×C11C23×C412yes—
305C23×C11C23×C412yes—
306C23×C11H(5,𝔽2)12yes—
307C23×C11H(5,𝔽2)12yes—
308C23×C112−1+412yes—
309C23×C112−1+412yes—
310C23×C11C2511yescharacteristic
311C22×D11—22no—
312C22×D11—22no—
313C22×D11—22no—
314C22×D11—22no—
315C22×D11—22no—
316C22×D11—22no—
317C22×D11C23×C414yes—
318C2×C4×C11—21no—
319C2×C4×C11—21no—
320C2×C4×C11—21no—
321C2×C4×C11—21no—
322C2×C4×C11—21no—
323C2×C4×C11—21no—
324C2×C4×C11—28no—
325C2×C4×C11—28no—
326C2×C4×C11—28no—
327C2×C4×C11—24no—
328C2×C4×C11—24no—
329C2×C4×C11—24no—
330C2×C4×C11—24no—
331C2×C4×C11—24no—
332C2×C4×C11—24no—
333C2×C4×C11—44no—
334C2×C4×C11—44no—
335C2×C4×C11—44no—
336C2×C4×C11—84no—
337C2×C4×C11—84no—
338C2×C4×C11C23×C412yes—
339C2×C4×C11C23×C412yes—
340C2×C4×C11C23×C412yes—
341C2×C4×C11C23×C412yes—
342C2×C4×C11H(5,𝔽2)12yes—
343C2×C4×C11H(5,𝔽2)12yes—
344C22⋊D11—216no—
345C22⋊D11—216no—
346C22⋊D11—48no—
347C2×Dic11—22no—
348C2×Dic11—22no—
349C2×Dic11—22no—
350C2×Dic11—22no—
351C2×Dic11—22no—
352C2×Dic11—22no—
353C2×Dic11—24no—
354C2×Dic11—24no—
355C2×Dic11—24no—
356C2×Dic11—24no—
357C2×Dic11—24no—
358C2×Dic11—24no—
359C2×Dic11—84no—
360C2×Dic11—84no—
361C2×Dic11C23×C414yes—
362C2×Dic11C23×C414yes—
363C2×Dic11C23×C414yes—
364D44—44no—
365C4×D11—216no—
366C4×D11—88no—
367Dic22—44no—
368C22×#41—111no—
369C24×C4C2×D1111yescharacteristic
370#525—1116no—
371C2×#123—112no—
372C2×C22⋊Q8—111no—
373C2×C22⋊Q8—111no—
374C2×#121—111no—
375C2×#121—111no—
376C2×#120—112no—
377C2×C4×D4—112no—
378C2×C4×D4—112no—
379C2×C4×D4—114no—
380C2×C4×D4—114no—
381C2×#117—111no—
382C2×#117—112no—
383C22×C4⋊C4—111no—
384C22×C4⋊C4—111no—
385C22×C4⋊C4—112no—
386C22×C4⋊C4C2×D1111yescharacteristic
387C22×C4⋊C4C2×D1111yescharacteristic
388C22×C22⋊C4—112no—
389C22×C22⋊C4C2×D1112yes—
390#391—114no—
391#390—114no—
392#389—114no—
393#389—114no—
394#388—114no—
395#388—114no—
396#388—114no—
397#388—114no—
398#387—114no—
399#387—114no—
400#387—114no—
401#387—114no—
402#386—114no—
403#386—114no—
404#386—114no—
405#386—114no—
406#385—114no—
407#385—114no—
408#385—114no—
409#385—114no—
410#384—112no—
411#382—112no—
412#380—112no—
413#380—112no—
414#380—112no—
415#380—112no—
416#380—112no—
417#380—112no—
418#380C2×D1112yes—
419#380C2×D1112yes—
420#380C2×D1112yes—
421#380C2×D1112yes—
422C4×C4⋊C4—112no—
423C4×C4⋊C4—112no—
424C4×C22⋊C4—114no—
425C4×C22⋊C4—114no—
426C2×#95—112no—
427C2×#95C2×D1112yes—
428C22×C11—22no—
429C22×C11—22no—
430C22×C11—22no—
431C22×C11—22no—
432C22×C11—22no—
433C22×C11—22no—
434C22×C11—22no—
435C22×C11—22no—
436C22×C11—22no—
437C22×C11—22no—
438C22×C11—22no—
439C22×C11—22no—
440C22×C11—22no—
441C22×C11—22no—
442C22×C11—22no—
443C22×C11—416no—
444C22×C11—41no—
445C22×C11—41no—
446C22×C11—41no—
447C22×C11—41no—
448C22×C11#52014yes—
449C22×C11#52014yes—
450C22×C11C24×C411yescharacteristic
451C22×C11C2×H(5,𝔽2)11yescharacteristic
452C22×C11C2×H(5,𝔽2)11yescharacteristic
453C22×C11C2×H(5,𝔽2)11yescharacteristic
454C22×C11C2×H(5,𝔽2)11yescharacteristic
455C22×C11C2×2−1+411yescharacteristic
456C22×C11C2×2−1+411yescharacteristic
457C2×D11—24no—
458C2×D11—24no—
459C2×D11—24no—
460C2×D11—42no—
461C2×D11—42no—
462C2×D11—42no—
463C2×D11—42no—
464C4×C11—22no—
465C4×C11—22no—
466C4×C11—22no—
467C4×C11—44no—
468C4×C11—44no—
469C4×C11#51814yes—
470Dic11—24no—
471Dic11—24no—
472Dic11—24no—
473Dic11—44no—
474Dic11—44no—
475C25C22×D1111yescharacteristic
476C2×#41—118no—
477C2×#41—442no—
478C2×#41—442no—
479C22×Q8—111no—
480C22×D4—112no—
481C22×D4—112no—
482C22×D4—112no—
483C22×D4—111no—
484C23×C4—42no—
485C23×C4—42no—
486C23×C4—112no—
487C23×C4—112no—
488C23×C4—112no—
489C23×C4—114no—
490C23×C4C4×D1118yescomplemented
491C23×C4C22×D1111yescharacteristic
492C23×C4C22×D1111yescharacteristic
493C23×C4C22×D1111yescharacteristic
494C23×C4C22×D1112yes—
495C23×C4C22×D1112yes—
496C23×C4C22×D1111yescharacteristic
497C23×C4C22×D1111yescharacteristic
498C23×C4C22×D1111yescharacteristic
499#123—1116no—
500C22⋊Q8—118no—
501C22⋊Q8—118no—
502#121—118no—
503#121—118no—
504#120—1116no—
505C4×D4—1116no—
506C4×D4—1116no—
507C4×D4—448no—
508C4×D4—448no—
509#117—118no—
510#117—444no—
511C2×C4⋊C4—42no—
512C2×C4⋊C4—42no—
513C2×C4⋊C4—111no—
514C2×C4⋊C4—111no—
515C2×C4⋊C4—112no—
516C2×C4⋊C4—112no—
517C2×C4⋊C4—112no—
518C2×C4⋊C4—112no—
519C2×C4⋊C4—112no—
520C2×C4⋊C4—112no—
521C2×C4⋊C4—114no—
522C2×C4⋊C4—114no—
523C2×C4⋊C4—114no—
524C2×C4⋊C4—444no—
525C2×C4⋊C4—442no—
526C2×C4⋊C4—442no—
527C2×C4⋊C4C22×D1112yes—
528C2×C4⋊C4C22×D1112yes—
529C2×C4⋊C4C22×D1112yes—
530C2×C4⋊C4C22×D1112yes—
531C2×C22⋊C4—44no—
532C2×C22⋊C4—112no—
533C2×C22⋊C4—112no—
534C2×C22⋊C4—112no—
535C2×C22⋊C4—112no—
536C2×C22⋊C4—112no—
537C2×C22⋊C4—114no—
538C2×C22⋊C4—114no—
539C2×C22⋊C4—114no—
540C2×C22⋊C4—114no—
541C2×C22⋊C4—114no—
542C2×C22⋊C4—444no—
543C2×C22⋊C4C22×D1114yes—
544C2×C22⋊C4C22×D1114yes—
545C2×C42—112no—
546C2×C42—114no—
547C2×C42—114no—
548C2×C42—114no—
549#95—114no—
550#95—114no—
551#95—114no—
552#95—114no—
553#95—114no—
554#95—114no—
555#95—114no—
556#95—114no—
557#95C22×D1114yes—
558#95C22×D1114yes—
559C2×C11—24no—
560C2×C11—24no—
561C2×C11—42no—
562C2×C11C2×#51811yescharacteristic
563C2×C11C2×#52011yescharacteristic
564C2×C11C2×#52011yescharacteristic
565C2×C11#353611yescharacteristic
566C2×C11#353611yescharacteristic
567C2×C11#353711yescharacteristic
568C2×C11#353811yescharacteristic
569D11—44no—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—41no—
575C24—41no—
576C24—112no—
577C24C2×C4×D1114yes—
578C24C23×D1111yescharacteristic
579C24C23×D1111yescharacteristic
580C24C23×D1111yescharacteristic
581#41—4416no—
582C2×Q8—114no—
583C2×Q8—441no—
584C2×Q8—441no—
585C2×D4—118no—
586C2×D4—118no—
587C2×D4—118no—
588C2×D4—114no—
589C2×D4—224no—
590C2×D4—224no—
591C2×D4—224no—
592C2×D4—224no—
593C2×D4—441no—
594C2×D4—441no—
595C2×D4—442no—
596C2×D4—442no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—24no—
604C22×C4—24no—
605C22×C4—416no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—112no—
617C22×C4—112no—
618C22×C4—112no—
619C22×C4—118no—
620C22×C4—114no—
621C22×C4—114no—
622C22×C4—224no—
623C22×C4—224no—
624C22×C4—224no—
625C22×C4—224no—
626C22×C4—444no—
627C22×C4—444no—
628C22×C4—444no—
629C22×C4—442no—
630C22×C4—442no—
631C22×C4—442no—
632C22×C4—442no—
633C22×C4C2×C4×D1114yes—
634C22×C4C2×C4×D1114yes—
635C22×C4C2×C4×D1114yes—
636C22×C4C2×C4×D1114yes—
637C22×C4C2×C4×D1114yes—
638C22×C4C2×C4×D1114yes—
639C22×C4C23×D1114yes—
640C22×C4C23×D1114yes—
641C22×C4C23×D1111yescharacteristic
642C22×C4C23×D1111yescharacteristic
643C22×C4C23×D1111yescharacteristic
644C22×C4C23×D1111yescharacteristic
645C4⋊C4—24no—
646C4⋊C4—24no—
647C4⋊C4—42no—
648C4⋊C4—42no—
649C4⋊C4—114no—
650C4⋊C4—114no—
651C4⋊C4—118no—
652C4⋊C4—118no—
653C4⋊C4—224no—
654C4⋊C4—224no—
655C4⋊C4—444no—
656C4⋊C4—442no—
657C4⋊C4—442no—
658C4⋊C4—444no—
659C4⋊C4—444no—
660C22⋊C4—28no—
661C22⋊C4—44no—
662C22⋊C4—118no—
663C22⋊C4—118no—
664C22⋊C4—118no—
665C22⋊C4—118no—
666C22⋊C4—118no—
667C22⋊C4—228no—
668C22⋊C4—444no—
669C22⋊C4—444no—
670C22⋊C4—444no—
671C22⋊C4—444no—
672C42—118no—
673C42—444no—
674C42—444no—
675C42—444no—
676C11#3436011yescharacteristic, complemented, Sylow
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—28no—
686C23—28no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—44no—
694C23—44no—
695C23—44no—
696C23—44no—
697C23—44no—
698C23—114no—
699C23—222no—
700C23—222no—
701C23—222no—
702C23—222no—
703C23—222no—
704C23—222no—
705C23C22×C4×D1112yes—
706C23C22×C4×D1112yes—
707C23C22×C4×D1112yes—
708C23#6703712yes—
709C23#6704012yes—
710C23#6704212yes—
711C23#6704312yes—
712C23C24×D1111yescharacteristic
713Q8—444no—
714D4—2216no—
715D4—2216no—
716D4—444no—
717D4—448no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—28no—
725C2×C4—28no—
726C2×C4—28no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—84no—
737C2×C4—84no—
738C2×C4—114no—
739C2×C4—114no—
740C2×C4—114no—
741C2×C4—222no—
742C2×C4—222no—
743C2×C4—222no—
744C2×C4—222no—
745C2×C4—222no—
746C2×C4—222no—
747C2×C4—2216no—
748C2×C4—224no—
749C2×C4—224no—
750C2×C4—224no—
751C2×C4—224no—
752C2×C4—224no—
753C2×C4—224no—
754C2×C4—888no—
755C2×C4—884no—
756C2×C4—884no—
757C2×C4C22×C4×D1112yes—
758C2×C4C22×C4×D1112yes—
759C2×C4C22×C4×D1112yes—
760C2×C4C22×C4×D1112yes—
761C2×C4#6703712yes—
762C2×C4#6703712yes—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—416no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—224no—
784C22—224no—
785C22—224no—
786C22—442no—
787C22—442no—
788C22—442no—
789C22—442no—
790C22#1062303514yes—
791C22#1062305414yes—
792C22C23×C4×D1111yescharacteristic
793C22C2×#6703711yescharacteristic
794C22C2×#6703711yescharacteristic
795C22C2×#6703711yescharacteristic
796C22C2×#6704011yescharacteristic
797C22C2×#6704211yescharacteristic
798C22C2×#6704311yescharacteristic
799C4—22no—
800C4—22no—
801C4—22no—
802C4—44no—
803C4—44no—
804C4—224no—
805C4—224no—
806C4—224no—
807C4—444no—
808C4—444no—
809C4#1062301714yes—
810C2—24no—
811C2—24no—
812C2—42no—
813C2—444no—
814C2C2×#1062301711yescharacteristic
815C2C2×#1062305411yescharacteristic
816C2C2×#1062303511yescharacteristic
817C2#1308283811yescharacteristic
818C2#1308284511yescharacteristic
819C2#1308285111yescharacteristic
820C2#1308286111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC2×C11×#380C2
socle, cosocleC23×C11C25
prime radicalC2×#10623322C2
hypercenterC2×#380D11
hypocenterC11#34360
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. #13071760C2semidirect
3. #13071595C2semidirect
4. #13071547C2semidirect
5. #13071541C2semidirect
6. C4⋊C4×C22⋊D11C2semidirect
7. #13071512C2semidirect
8. #13071349C2semidirect
9. #13071346C2semidirect
10. #13071319C2semidirect
11. #13071316C2semidirect
12. #13071223C2semidirect
13. #13071205C2semidirect
14. C2×#10622825C2semidirect
15. C2×C11×#380C2semidirect
23. #10623322C4semidirect
35. C2×#66945C22semidirect
36. C2×C4⋊C4×D11C22semidirect
51. #10622603C22semidirect
52. #10622602C22semidirect
53. #10622600C22semidirect
54. #10622600C22semidirect
55. #10622591C22semidirect
56. #10622590C22semidirect
57. #10622589C22semidirect
58. C4⋊C4×Dic11C22semidirect
59. C4⋊C4×Dic11C22semidirect
60. #10622585C22semidirect
68. #10622283C22semidirect
69. #10622281C22semidirect
70. #10622278C22semidirect
71. #10622268C22semidirect
72. #10622267C22semidirect
73. #10622266C22semidirect
74. #10622260C22semidirect
75. #10622259C22semidirect
79. C23×C4×C11C2×C4semidirect
95. C2×#4339C2×C4semidirect
109. #67006C2×C4semidirect
116. #66983C2×C4semidirect
117. #66983C2×C4semidirect
118. #66982C2×C4semidirect
120. C4×C22⋊D11C2×C4semidirect
121. C4×C22⋊D11C2×C4semidirect
127. #66979C2×C4semidirect
136. #66977C2×C4semidirect
137. #66977C2×C4semidirect
281. C2×#380D11semidirect
490. C23×C4C4×D11semidirect
676. C11#34360semidirect

Maximal subgroups

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

subgroupindex
C2×#106233222
#130717602
#130715952
#130715472
#130715412
C4⋊C4×C22⋊D112
#130715122
#130713492
#130713462
#130713192
#130713162
#130712232
#130712052
C2×#106228252
C2×C11×#3802
#3436011