Finite Group Databasebeta

← #14925773

Subgroups — #14925773

Order 2816.

2834 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623048C211yesmaximal, characteristic, complemented
2C22×C4×C22⋊D11C211yesmaximal, characteristic
3#13073786C212yesmaximal, complemented
4#13073781C212yesmaximal, complemented
5#13073779C212yesmaximal, complemented
6#13073773C212yesmaximal, complemented
7#13073771C212yesmaximal, complemented
8#13073610C212yesmaximal, complemented
9#13073099C212yesmaximal, complemented
10#13072265C212yesmaximal
11#13071903C214yesmaximal, complemented
12C4×#66938C214yesmaximal, complemented
13#13070999C211yesmaximal, characteristic, complemented
14#13070995C211yesmaximal, characteristic, complemented
15#13070995C211yesmaximal, characteristic, complemented
16#117×Dic11C211yesmaximal, characteristic, complemented
17C11×#2280C211yesmaximal, characteristic, complemented
18C24×C4×C11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic
21C2×C11×#117C2211yescharacteristic
22C2×C11×#117C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C2×C4×C22⋊D11—28no—
25C2×C4×C22⋊D11C2212yes—
26C2×C4×C22⋊D11C2212yes—
27C2×C4×C22⋊D11C2212yes—
28C2×C4×C22⋊D11C2212yes—
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C2×#66979C2211yescharacteristic
31C2×#66979C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33C22×C4×Dic11C2211yescharacteristic
34#10623048—28no—
35C2×#66943C2211yescharacteristic, complemented
36C2×#66943C2211yescharacteristic, complemented
37C2×#66941C2211yescharacteristic, complemented
38C2×#66941C2211yescharacteristic, complemented
39C2×#66938C2214yes—
40C2×#66931C2212yes—
41C2×#66931C2212yes—
42C2×C4×Dic22C2212yescomplemented
43C2×C4×Dic22C2212yescomplemented
44C11×#381C2212yes—
45C11×#380C2212yescomplemented
46C11×#380C2212yescomplemented
47C11×#379C2212yes—
48C4×C11×C22⋊C4C2214yescomplemented
49#10622860C2212yes—
50#10622825C2212yescomplemented
51#10622825C2212yescomplemented
52#10622824C2212yes—
53C4×C22⋊Dic11C2214yescomplemented
54#10622600C2212yescomplemented
55#10622600C2212yescomplemented
56#10622600C2212yescomplemented
57#10622600C2212yescomplemented
58C4⋊C4×Dic11C2212yescomplemented
59C4⋊C4×Dic11C2212yescomplemented
60#10622574C2214yes—
61#10622572C2214yes—
62#10622570C2214yes—
63#10622568C2212yes—
64#10622568C2212yes—
65#10622565C2214yescomplemented
66#10622564C2214yescomplemented
67#10622560C2214yescomplemented
68#10622557C2214yescomplemented
69#10622556C2212yes—
70#10622556C2212yes—
71C22⋊C4×Dic11C2212yes—
72C22⋊C4×Dic11C2212yes—
73C4×(C2×D11)⋊C4C2214yescomplemented
74C4×(C2×D11)⋊C4C2214yescomplemented
75#10622545C2212yescomplemented
76C42×Dic11C2212yescomplemented
77#10622288C2214yescomplemented
78#10622286C2214yescomplemented
79#10622283C2214yescomplemented
80#10622282C2214yescomplemented
81#10622273C2214yescomplemented
82#10622271C2214yescomplemented
83#10622263C2214yescomplemented
84#10622259C2214yescomplemented
85C25×C11C2311yescharacteristic
86C24×D11C2311yescharacteristic
87C23×C4×C11—24no—
88C23×C4×C11—24no—
89C23×C4×C11—24no—
90C23×C4×C11C2311yescharacteristic
91C23×C4×C11C2312yes—
92C23×C4×C11C2312yes—
93C23×C4×C11C2311yescharacteristic
94C22×C22⋊D11—28no—
95C22×C22⋊D11—24no—
96C22×C22⋊D11C2312yes—
97C22×C22⋊D11C2312yes—
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2311yescharacteristic
101C22×C4×D11—24no—
102C22×C4×D11—24no—
103C22×C4×D11—24no—
104C22×C4×D11C2312yes—
105C22×C4×D11C2312yes—
106C22×Dic22C2312yes—
107C22×Dic22C2312yes—
108C11×#117—24no—
109C11×#117—24no—
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C11×C4⋊C4C2312yes—
113C2×C11×C22⋊C4C2312yes—
114C2×C11×C22⋊C4C2314yes—
115C2×C11×C22⋊C4C2312yes—
116C2×C11×C22⋊C4C2314yes—
117C2×C42×C11C2312yes—
118C2×C42×C11C2312yes—
119C2×C22⋊Dic11—24no—
120C2×C22⋊Dic11C2312yes—
121C2×C22⋊Dic11C2314yes—
122C2×C22⋊Dic11C2312yes—
123C2×C22⋊Dic11C2312yes—
124C2×C22⋊Dic11C2312yes—
125C2×C22⋊Dic11C2314yes—
126C4×C22⋊D11—28no—
127C4×C22⋊D11—28no—
128C4×C22⋊D11—28no—
129C4×C22⋊D11—28no—
130C2×(C2×D11)⋊C4—24no—
131C2×(C2×D11)⋊C4C2314yes—
132C2×(C2×D11)⋊C4C2314yes—
133C2×(C2×D11)⋊C4C2312yes—
134C2×(C2×D11)⋊C4C2312yes—
135C2×(C2×D11)⋊C4C2314yes—
136C2×(C2×D11)⋊C4C2314yes—
137#66979—24no—
138#66979—24no—
139C2×C4⋊Dic11C2312yes—
140C2×C4⋊Dic11C2312yes—
141C2×C4⋊Dic11C2311yescharacteristic
142C2×C4⋊Dic11C2311yescharacteristic
143C2×C4⋊Dic11C2312yes—
144C2×Dic11⋊C4—24no—
145C2×Dic11⋊C4C2312yes—
146C2×Dic11⋊C4C2312yes—
147C2×Dic11⋊C4C2312yes—
148C2×Dic11⋊C4C2312yes—
149C2×Dic11⋊C4C2312yes—
150C2×Dic11⋊C4C2312yes—
151C2×C4×Dic11D418yes—
152C2×C4×Dic11C2312yes—
153C2×C4×Dic11C2314yes—
154C2×C4×Dic11C2312yes—
155C2×C4×Dic11C2314yes—
156C2×C4×Dic11C2311yescharacteristic
157C2×C4×Dic11C2311yescharacteristic
158C2×C4×Dic11C2311yescharacteristic
159C2×C4×Dic11C2311yescharacteristic
160#66943—24no—
161#66943—24no—
162#66941—24no—
163#66941—24no—
164#66938—216no—
165#66931—28no—
166#66931—28no—
167C4×Dic22—28no—
168C4×Dic22—28no—
169C11×#95C2314yes—
170C11×#95C2314yes—
171C11⋊#95C2314yes—
172C11⋊#95C2314yes—
173C11⋊#95C2314yes—
174C11⋊#95C2314yes—
175C11⋊#95C2314yes—
176C11⋊#95C2314yes—
177C11⋊#95C2314yes—
178C11⋊#95C2314yes—
179#34946—111nomaximal, Sylow
180C24×C11—22no—
181C24×C11—24no—
182C24×C11—22no—
183C24×C11—22no—
184C24×C11—42no—
185C24×C11C2412yes—
186C24×C11C2411yescharacteristic
187C23×D11—22no—
188C23×D11—24no—
189C23×D11—22no—
190C23×D11—22no—
191C23×D11—42no—
192C23×D11C2412yes—
193C22×C4×C11—22no—
194C22×C4×C11—22no—
195C22×C4×C11—22no—
196C22×C4×C11—24no—
197C22×C4×C11—24no—
198C22×C4×C11—24no—
199C22×C4×C11—24no—
200C22×C4×C11—24no—
201C22×C4×C11—24no—
202C22×C4×C11—416no—
203C22×C4×C11C2×D414yes—
204C22×C4×C11#4114yes—
205C22×C4×C11#4114yes—
206C22×C4×C11C2412yes—
207C22×C4×C11C2414yes—
208C22×C4×C11C2412yes—
209C22×C4×C11C2412yes—
210C22×C4×C11C2411yescharacteristic
211C22×C4×C11C2411yescharacteristic
212C2×C22⋊D11—232no—
213C2×C22⋊D11—24no—
214C2×C22⋊D11—24no—
215C2×C22⋊D11—24no—
216C2×C22⋊D11—24no—
217C2×C22⋊D11—24no—
218C2×C22⋊D11#4118yes—
219C22×Dic11—24no—
220C22×Dic11—22no—
221C22×Dic11—22no—
222C22×Dic11—22no—
223C22×Dic11—42no—
224C22×Dic11C2×D414yes—
225C22×Dic11C2×D414yes—
226C22×Dic11C2412yes—
227C22×Dic11C2414yes—
228C22×Dic11C2412yes—
229C22×Dic11C2412yes—
230C22×Dic11C2411yescharacteristic
231C22×Dic11C2411yescharacteristic
232C22×Dic11C2411yescharacteristic
233C22×Dic11C2411yescharacteristic
234C2×C4×D11—24no—
235C2×C4×D11—24no—
236C2×C4×D11—24no—
237C2×C4×D11—24no—
238C2×C4×D11—24no—
239C2×C4×D11—24no—
240C2×C4×D11—416no—
241C2×Dic22—24no—
242C2×Dic22—24no—
243C2×Dic22—28no—
244C2×Dic22—44no—
245C11×C4⋊C4—22no—
246C11×C4⋊C4—22no—
247C11×C4⋊C4—24no—
248C11×C22⋊C4—24no—
249C11×C22⋊C4—28no—
250C11×C22⋊C4—24no—
251C11×C22⋊C4—44no—
252C42×C11—24no—
253C42×C11—24no—
254C22⋊Dic11—24no—
255C22⋊Dic11—24no—
256C22⋊Dic11—24no—
257C22⋊Dic11—28no—
258C22⋊Dic11—24no—
259C22⋊Dic11—44no—
260(C2×D11)⋊C4—24no—
261(C2×D11)⋊C4—24no—
262(C2×D11)⋊C4—28no—
263(C2×D11)⋊C4—28no—
264(C2×D11)⋊C4—44no—
265(C2×D11)⋊C4—44no—
266C4⋊Dic11—24no—
267C4⋊Dic11—24no—
268C4⋊Dic11—22no—
269C4⋊Dic11—22no—
270C4⋊Dic11—24no—
271Dic11⋊C4—24no—
272Dic11⋊C4—24no—
273Dic11⋊C4—24no—
274Dic11⋊C4—24no—
275Dic11⋊C4—24no—
276Dic11⋊C4—24no—
277C4×Dic11—28no—
278C4×Dic11—24no—
279C4×Dic11—24no—
280C4×Dic11—44no—
281C4×Dic11C2×D414yes—
282C4×Dic11C2×D414yes—
283C4×Dic11C2×D414yes—
284C4×Dic11C2×D414yes—
285C2×#533—111no—
286C22×C4×D4—111no—
287#2563—112no—
288#2562—112no—
289#2562—112no—
290#2561—112no—
291#2561—112no—
292#2547—112no—
293#2503—112no—
294#2435—112no—
295#2398—114no—
296C4×#124—114no—
297#2280—111no—
298#2280—111no—
299#2280—111no—
300#2280D1111yescharacteristic, complemented
301C4×#117—111no—
302C23×C11—22no—
303C23×C11—22no—
304C23×C11—28no—
305C23×C11—22no—
306C23×C11—22no—
307C23×C11—22no—
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—48no—
312C23×C11—48no—
313C23×C11—44no—
314C23×C11—44no—
315C23×C11C22×D412yes—
316C23×C11C2×#4112yes—
317C23×C11C2×#4112yes—
318C23×C11C2×#4114yes—
319C23×C11C2511yescharacteristic
320C22×D11—28no—
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—22no—
325C22×D11—22no—
326C22×D11—22no—
327C22×D11—48no—
328C22×D11—48no—
329C22×D11—44no—
330C22×D11—44no—
331C22×D11C2×#4114yes—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—24no—
336C2×C4×C11—24no—
337C2×C4×C11—24no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—24no—
341C2×C4×C11—24no—
342C2×C4×C11—44no—
343C2×C4×C11—48no—
344C2×C4×C11—48no—
345C2×C4×C11#124116yescomplemented
346C2×C4×C11C22×D412yes—
347C2×C4×C11C22×D412yes—
348C2×C4×C11C2×#4112yes—
349C2×C4×C11C2×#4112yes—
350C2×C4×C11C2×#4112yes—
351C2×C4×C11C2×#4112yes—
352C22⋊D11—216no—
353C22⋊D11—216no—
354C2×Dic11—22no—
355C2×Dic11—22no—
356C2×Dic11—22no—
357C2×Dic11—28no—
358C2×Dic11—22no—
359C2×Dic11—22no—
360C2×Dic11—22no—
361C2×Dic11—24no—
362C2×Dic11—24no—
363C2×Dic11—24no—
364C2×Dic11—22no—
365C2×Dic11—22no—
366C2×Dic11—24no—
367C2×Dic11—24no—
368C2×Dic11—44no—
369C2×Dic11—44no—
370C2×Dic11C22×D412yes—
371C2×Dic11C22×D412yes—
372C2×Dic11C22×D412yes—
373C2×Dic11C22×D412yes—
374C2×Dic11C2×#4114yes—
375C4×D11—48no—
376C4×D11—48no—
377Dic22—48no—
378Dic22—48no—
379C23×D4—111no—
380C24×C4—111no—
381C24×C4C2×D1111yescharacteristic
382#533—228no—
383C2×C4⋊Q8—111no—
384C2×C4⋊Q8—111no—
385C2×#125—111no—
386C2×#125—111no—
387C2×#124—114no—
388C2×C22⋊Q8—112no—
389C2×C22⋊Q8—112no—
390C2×C4×Q8—112no—
391C2×C4×Q8—112no—
392C2×C4×D4—112no—
393C2×C4×D4—112no—
394C2×C4×D4—112no—
395C2×C4×D4—112no—
396C2×C4×D4—228no—
397C2×#117—111no—
398C2×#117—111no—
399C2×#117C2×D1111yescharacteristic
400C2×#117C2×D1111yescharacteristic
401C22×C4⋊C4—111no—
402C22×C22⋊C4—111no—
403C22×C22⋊C4—111no—
404C22×C42—111no—
405#400—114no—
406#400—114no—
407#397—114no—
408#397—114no—
409#394—114no—
410#394—114no—
411#393—114no—
412#393—114no—
413#391—114no—
414#390—114no—
415#388—114no—
416#388—114no—
417#388—114no—
418#388—114no—
419#382—114no—
420#381—112no—
421#381—112no—
422#381—112no—
423#381C2×D1112yes—
424#380—112no—
425#380—112no—
426#380—112no—
427#380—112no—
428#380—112no—
429#380—112no—
430#380C2×D1112yescomplemented
431#380C2×D1112yescomplemented
432#379—112no—
433#379—112no—
434#379—112no—
435#379C2×D1112yes—
436C4×C4⋊C4—112no—
437C4×C4⋊C4—112no—
438C4×C22⋊C4—114no—
439C4×C22⋊C4—112no—
440C4×C22⋊C4—112no—
441C4×C22⋊C4—114no—
442C4×C22⋊C4—114no—
443C4×C22⋊C4C2×D1114yescomplemented
444#376—112no—
445C43—112no—
446C22×C11—22no—
447C22×C11—22no—
448C22×C11—24no—
449C22×C11—24no—
450C22×C11—24no—
451C22×C11—24no—
452C22×C11—24no—
453C22×C11—416no—
454C22×C11—42no—
455C22×C11—42no—
456C22×C11—42no—
457C22×C11—42no—
458C22×C11C2×#12414yes—
459C22×C11C23×D411yescharacteristic
460C22×C11C22×#4111yescharacteristic
461C22×C11C22×#4111yescharacteristic
462C22×C11C22×#4112yes—
463C22×C11#58512yes—
464C2×D11—24no—
465C2×D11—24no—
466C2×D11—24no—
467C2×D11—416no—
468C2×D11—42no—
469C2×D11—42no—
470C2×D11—42no—
471C2×D11—42no—
472C4×C11—42no—
473C4×C11—42no—
474C4×C11—42no—
475C4×C11—44no—
476C4×C11C2×#12414yes—
477C4×C11C2×#12414yes—
478Dic11—22no—
479Dic11—22no—
480Dic11—22no—
481Dic11—42no—
482Dic11—42no—
483Dic11—42no—
484Dic11—44no—
485Dic11#52514yes—
486C25—111no—
487C25C22×D1111yescharacteristic
488C22×Q8—112no—
489C22×Q8—112no—
490C22×D4—112no—
491C22×D4—112no—
492C22×D4—224no—
493C22×D4—228no—
494C23×C4—24no—
495C23×C4—24no—
496C23×C4—24no—
497C23×C4—111no—
498C23×C4—111no—
499C23×C4—111no—
500C23×C4—112no—
501C23×C4—112no—
502C23×C4—224no—
503C23×C4—224no—
504C23×C4—224no—
505C23×C4C22×D1111yescharacteristic
506C23×C4C22×D1112yes—
507C23×C4C22×D1112yes—
508C23×C4C22×D1111yescharacteristic
509C4⋊Q8—224no—
510C4⋊Q8—224no—
511#125—224no—
512#125—224no—
513#124—2216no—
514C22⋊Q8—228no—
515C22⋊Q8—228no—
516C4×Q8—228no—
517C4×Q8—228no—
518C4×D4—228no—
519C4×D4—228no—
520C4×D4—228no—
521C4×D4—228no—
522#117—24no—
523#117—24no—
524#117—224no—
525#117—224no—
526C2×C4⋊C4—112no—
527C2×C4⋊C4—112no—
528C2×C4⋊C4—111no—
529C2×C4⋊C4—111no—
530C2×C4⋊C4—112no—
531C2×C4⋊C4—112no—
532C2×C4⋊C4—112no—
533C2×C4⋊C4—112no—
534C2×C4⋊C4—112no—
535C2×C4⋊C4—112no—
536C2×C4⋊C4—112no—
537C2×C4⋊C4—224no—
538C2×C4⋊C4C22×D1111yescharacteristic
539C2×C4⋊C4C22×D1111yescharacteristic
540C2×C4⋊C4C22×D1112yes—
541C2×C22⋊C4—112no—
542C2×C22⋊C4—112no—
543C2×C22⋊C4—112no—
544C2×C22⋊C4—112no—
545C2×C22⋊C4—114no—
546C2×C22⋊C4—112no—
547C2×C22⋊C4—112no—
548C2×C22⋊C4—114no—
549C2×C22⋊C4—114no—
550C2×C22⋊C4—114no—
551C2×C22⋊C4—114no—
552C2×C22⋊C4—114no—
553C2×C22⋊C4—224no—
554C2×C22⋊C4—224no—
555C2×C22⋊C4C22×D1112yes—
556C2×C22⋊C4C22×D1112yes—
557C2×C22⋊C4C22×D1114yes—
558C2×C22⋊C4C22×D1114yes—
559C2×C42—118no—
560C2×C42—111no—
561C2×C42—111no—
562C2×C42—111no—
563C2×C42—111no—
564C2×C42—114no—
565C2×C42—112no—
566C2×C42—112no—
567C2×C42—114no—
568C2×C42C22×D1112yes—
569C2×C42C22×D1112yes—
570#95—114no—
571#95—114no—
572#95—114no—
573#95—114no—
574#95—114no—
575#95—114no—
576#95—114no—
577#95—114no—
578#95C22×D1114yes—
579#95C22×D1114yes—
580C2×C11—24no—
581C2×C11—44no—
582C2×C11C2×#52511yescharacteristic
583C2×C11C22×#12411yescharacteristic
584C2×C11#344911yescharacteristic
585C2×C11#347512yes—
586C2×C11#347512yes—
587D11—44no—
588C24—22no—
589C24—24no—
590C24—22no—
591C24—22no—
592C24—42no—
593C24—112no—
594C24—224no—
595C24—222no—
596C24—222no—
597C24—222no—
598C24—442no—
599C24C23×D1112yes—
600C24C23×D1111yescharacteristic
601C2×Q8—224no—
602C2×Q8—224no—
603C2×Q8—228no—
604C2×Q8—444no—
605C2×D4—118no—
606C2×D4—224no—
607C2×D4—224no—
608C2×D4—224no—
609C2×D4—224no—
610C2×D4—2232no—
611C2×D4—224no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—24no—
616C22×C4—24no—
617C22×C4—24no—
618C22×C4—24no—
619C22×C4—24no—
620C22×C4—24no—
621C22×C4—416no—
622C22×C4—111no—
623C22×C4—114no—
624C22×C4—111no—
625C22×C4—111no—
626C22×C4—111no—
627C22×C4—114no—
628C22×C4—112no—
629C22×C4—114no—
630C22×C4—112no—
631C22×C4—112no—
632C22×C4—224no—
633C22×C4—222no—
634C22×C4—222no—
635C22×C4—222no—
636C22×C4—224no—
637C22×C4—224no—
638C22×C4—224no—
639C22×C4—224no—
640C22×C4—224no—
641C22×C4—224no—
642C22×C4—442no—
643C22×C4—4416no—
644C22×C4#433914yes—
645C22×C4D4×D1114yes—
646C22×C4#434114yes—
647C22×C4C23×D1112yes—
648C22×C4C23×D1114yes—
649C22×C4C23×D1112yes—
650C22×C4C23×D1112yes—
651C22×C4C23×D1111yescharacteristic
652C22×C4C23×D1111yescharacteristic
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—24no—
656C4⋊C4—224no—
657C4⋊C4—224no—
658C4⋊C4—224no—
659C4⋊C4—224no—
660C4⋊C4—224no—
661C4⋊C4—224no—
662C4⋊C4—224no—
663C4⋊C4—224no—
664C4⋊C4—224no—
665C4⋊C4—222no—
666C4⋊C4—222no—
667C22⋊C4—24no—
668C22⋊C4—24no—
669C22⋊C4—28no—
670C22⋊C4—44no—
671C22⋊C4—224no—
672C22⋊C4—224no—
673C22⋊C4—228no—
674C22⋊C4—228no—
675C22⋊C4—224no—
676C22⋊C4—224no—
677C22⋊C4—224no—
678C22⋊C4—224no—
679C22⋊C4—228no—
680C22⋊C4—444no—
681C22⋊C4—444no—
682C22⋊C4—444no—
683C42—24no—
684C42—24no—
685C42—114no—
686C42—114no—
687C42—114no—
688C42—114no—
689C42—228no—
690C42—224no—
691C42—224no—
692C42—444no—
693C11#3494611yescharacteristic, complemented, Sylow
694C23—22no—
695C23—22no—
696C23—28no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—48no—
704C23—48no—
705C23—44no—
706C23—44no—
707C23—114no—
708C23—228no—
709C23—222no—
710C23—222no—
711C23—222no—
712C23—222no—
713C23—222no—
714C23—222no—
715C23—448no—
716C23—448no—
717C23—444no—
718C23—444no—
719C23C2×#433912yes—
720C23C2×D4×D1112yes—
721C23C2×#434112yes—
722C23#41×D1114yes—
723C23C24×D1111yescharacteristic
724Q8—448no—
725Q8—448no—
726D4—2216no—
727D4—2216no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—24no—
733C2×C4—22no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—44no—
739C2×C4—48no—
740C2×C4—48no—
741C2×C4—112no—
742C2×C4—114no—
743C2×C4—112no—
744C2×C4—112no—
745C2×C4—112no—
746C2×C4—228no—
747C2×C4—222no—
748C2×C4—222no—
749C2×C4—222no—
750C2×C4—224no—
751C2×C4—222no—
752C2×C4—222no—
753C2×C4—222no—
754C2×C4—222no—
755C2×C4—222no—
756C2×C4—224no—
757C2×C4—224no—
758C2×C4—224no—
759C2×C4—224no—
760C2×C4—444no—
761C2×C4—444no—
762C2×C4—448no—
763C2×C4—448no—
764C2×C4#66938116yescomplemented
765C2×C4C2×#433912yes—
766C2×C4C2×#433912yes—
767C2×C4C2×D4×D1112yes—
768C2×C4C2×D4×D1112yes—
769C2×C4C2×#434112yes—
770C2×C4C2×#434112yes—
771C22—24no—
772C22—24no—
773C22—22no—
774C22—22no—
775C22—24no—
776C22—24no—
777C22—24no—
778C22—416no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—224no—
784C22—224no—
785C22—224no—
786C22—4416no—
787C22—442no—
788C22—442no—
789C22—442no—
790C22—442no—
791C22C2×#6693814yes—
792C22C22×#433911yescharacteristic
793C22C22×D4×D1111yescharacteristic
794C22C22×#434111yescharacteristic
795C22C2×#41×D1112yes—
796C22#1062345312yes—
797C4—42no—
798C4—44no—
799C4—42no—
800C4—42no—
801C4—114no—
802C4—222no—
803C4—222no—
804C4—222no—
805C4—442no—
806C4—444no—
807C4—442no—
808C4—442no—
809C4C2×#6693814yes—
810C4C2×#6693814yes—
811C2—24no—
812C2—44no—
813C2—444no—
814C2D11×#52511yescharacteristic
815C2C22×#6693811yescharacteristic
816C2#1308194611yescharacteristic
817C2#1308217012yes—
818C2#1308217612yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC11×#2280C2
prime radicalC23×C22⋊D11C22
hypercenter#2280D11
hypocenterC11#34946
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2280

Complements

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

NH ≅ G/Ntype
1. C2×#10623048C2semidirect
3. #13073786C2semidirect
4. #13073781C2semidirect
5. #13073779C2semidirect
6. #13073773C2semidirect
7. #13073771C2semidirect
8. #13073610C2semidirect
9. #13073099C2semidirect
11. #13071903C2semidirect
12. C4×#66938C2semidirect
13. #13070999C2semidirect
14. #13070995C2semidirect
15. #13070995C2semidirect
16. #117×Dic11C2semidirect
17. C11×#2280C2semidirect
35. C2×#66943C22semidirect
36. C2×#66943C22semidirect
37. C2×#66941C22semidirect
38. C2×#66941C22semidirect
42. C2×C4×Dic22C22semidirect
43. C2×C4×Dic22C22semidirect
45. C11×#380C22semidirect
46. C11×#380C22semidirect
48. C4×C11×C22⋊C4C22semidirect
50. #10622825C22semidirect
51. #10622825C22semidirect
53. C4×C22⋊Dic11C22semidirect
54. #10622600C22semidirect
55. #10622600C22semidirect
56. #10622600C22semidirect
57. #10622600C22semidirect
58. C4⋊C4×Dic11C22semidirect
59. C4⋊C4×Dic11C22semidirect
65. #10622565C22semidirect
66. #10622564C22semidirect
67. #10622560C22semidirect
68. #10622557C22semidirect
73. C4×(C2×D11)⋊C4C22semidirect
74. C4×(C2×D11)⋊C4C22semidirect
75. #10622545C22semidirect
76. C42×Dic11C22semidirect
77. #10622288C22semidirect
78. #10622286C22semidirect
79. #10622283C22semidirect
80. #10622282C22semidirect
81. #10622273C22semidirect
82. #10622271C22semidirect
83. #10622263C22semidirect
84. #10622259C22semidirect
300. #2280D11semidirect
345. C2×C4×C11#124semidirect
430. #380C2×D11semidirect
431. #380C2×D11semidirect
443. C4×C22⋊C4C2×D11semidirect
693. C11#34946semidirect
764. C2×C4#66938semidirect

Maximal subgroups

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

subgroupindex
C2×#106230482
C22×C4×C22⋊D112
#130737862
#130737812
#130737792
#130737732
#130737712
#130736102
#130730992
#130722652
#130719032
C4×#669382
#130709992
#130709952
#117×Dic112
C11×#22802
#3494611