Finite Group Databasebeta

← #14920727

Subgroups — #14920727

Order 2816.

2294 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623237C211yesmaximal, characteristic
2C2×C4×Q8×D11C211yesmaximal, characteristic, complemented
3#13074526C211yesmaximal, characteristic, complemented
4#13074524C211yesmaximal, characteristic, complemented
5#13074522C211yesmaximal, characteristic, complemented
6#13074496C212yesmaximal, complemented
7#13074480C212yesmaximal, complemented
8#13074434C212yesmaximal, complemented
9#13074397C211yesmaximal, characteristic, complemented
10#13074395C211yesmaximal, characteristic, complemented
11#13074363C212yesmaximal
12#13074336C211yesmaximal, characteristic, complemented
13#13074334C211yesmaximal, characteristic, complemented
14#13071908C211yesmaximal, characteristic, complemented
15#13071906C211yesmaximal, characteristic, complemented
16#13071901C211yesmaximal, characteristic, complemented
17#13071898C211yesmaximal, characteristic, complemented
18#13071893C212yesmaximal, complemented
19#13071891C212yesmaximal, complemented
20#13071143C212yesmaximal, complemented
21#13071137C212yesmaximal, complemented
22#13071009C211yesmaximal, characteristic, complemented
23C11×#2637C211yesmaximal, characteristic, complemented
24C22×Q8×D11C2211yescharacteristic
25C2×C11×#126C2211yescharacteristic
26C2×C4×Q8×C11C2211yescharacteristic
27C2×Q8×Dic11C2211yescharacteristic
28#10623237—28no—
29C4×Q8×D11—28no—
30C2×#66949C2211yescharacteristic
31C2×#66947C2211yescharacteristic
32C2×#66947C2212yes—
33C2×#66946C2211yescharacteristic
34C2×#66945C2211yescharacteristic
35C2×C4⋊C4×D11C2212yes—
36C2×C4⋊C4×D11C2211yescharacteristic
37C2×#66942C2211yescharacteristic
38C2×#66940C2212yes—
39C2×#66940C2211yescharacteristic
40C2×#66940C2211yescharacteristic
41C2×#66938C2211yescharacteristic
42C2×#66937C2211yescharacteristic
43C2×#66936C2211yescharacteristic
44C2×#66936C2212yes—
45C2×(C22⋊D11)⋊C4C2211yescharacteristic
46C2×(C22⋊D11)⋊C4C2211yescharacteristic
47C2×#66930C2211yescharacteristic
48C2×#66929C2211yescharacteristic
49C2×C42×D11C2212yes—
50C2×C42×D11C2211yescharacteristic
51C2×C4×Dic22C2212yes—
52C2×C4×Dic22C2211yescharacteristic
53C11×#398C2212yes—
54C11×#398C2211yescharacteristic
55C11×#397C2211yescharacteristic
56C11×#396C2212yes—
57C11×#395C2211yescharacteristic
58C11×#393C2211yescharacteristic
59C11×#388C2212yes—
60C11×#387C2212yes—
61C11×#382C2211yescharacteristic
62#10622844C2211yescharacteristic
63#10622842C2211yescharacteristic
64#10622607C2212yes—
65#10622607C2212yes—
66#10622606C2211yescharacteristic
67#10622605C2212yes—
68#10622602C2212yes—
69#10622600C2212yes—
70#10622597C2212yes—
71#10622597C2212yes—
72#10622597C2212yes—
73#10622596C2212yes—
74#10622596C2211yescharacteristic
75#10622593C2211yescharacteristic
76#10622592C2212yes—
77#10622592C2212yes—
78#10622592C2211yescharacteristic
79#10622591C2212yes—
80C4⋊C4×Dic11C2212yes—
81C4⋊C4×Dic11C2212yes—
82C4⋊C4×Dic11C2212yes—
83#10622574C2212yes—
84#10622572C2212yes—
85#10622569C2212yes—
86#10622566C2211yescharacteristic
87#10622562C2212yes—
88#10622561C2212yes—
89#10622560C2212yes—
90#10622560C2211yescharacteristic
91#10622557C2212yes—
92C22⋊C4×Dic11C2212yes—
93C22⋊C4×Dic11C2212yes—
94#10622553C2212yes—
95#10622549C2211yescharacteristic
96#10622546C2212yes—
97#10622287C2211yescharacteristic
98#10622286C2212yes—
99#10622286C2211yescharacteristic
100#10622283C2212yes—
101#10622281C2212yes—
102#10622279C2212yes—
103#10622279C2212yes—
104#10622279C2212yes—
105#10622278C2212yes—
106#10622277C2212yes—
107#10622277C2212yes—
108#10622277C2211yescharacteristic
109#10622277C2211yescharacteristic
110#10622274C2211yescharacteristic
111#10622273C2212yes—
112#10622273C2212yes—
113#10622271C2212yes—
114#10622271C2212yes—
115#10622270C2212yes—
116#10622269C2212yes—
117#10622269C2212yes—
118#10622269C2211yescharacteristic
119#10622266C2212yes—
120#10622264C2212yes—
121#10622262C2212yes—
122#10622262C2212yes—
123#10622261C2211yescharacteristic
124#10622261C2211yescharacteristic
125C22×Q8×C11C2311yescharacteristic
126C22×C22⋊D11C2311yescharacteristic
127C22×C22⋊D11C2311yescharacteristic
128C23×Dic11C2311yescharacteristic
129C2×Q8×D11—24no—
130C2×Q8×D11—28no—
131C22×D44C2311yescharacteristic
132C22×C4×D11C2311yescharacteristic
133C22×C4×D11C2311yescharacteristic
134C22×C4×D11C2311yescharacteristic
135C22×C4×D11C2312yes—
136C22×C4×D11C2312yes—
137C22×C4×D11C2311yescharacteristic
138C22×Dic22C2312yes—
139C22×Dic22C2311yescharacteristic
140C22×Dic22C2311yescharacteristic
141C11×#126—24no—
142C4×Q8×C11—24no—
143C2×C11×C4⋊C4C2311yescharacteristic
144C2×C11×C4⋊C4C2312yes—
145C2×C11×C4⋊C4C2311yescharacteristic
146C2×C11×C4⋊C4C2311yescharacteristic
147C2×C11×C4⋊C4C2311yescharacteristic
148C2×C11×C4⋊C4C2312yes—
149C2×C11×C4⋊C4C2312yes—
150C2×C11×C4⋊C4C2312yes—
151C2×C11×C22⋊C4C2311yescharacteristic
152C2×C11×C22⋊C4C2311yescharacteristic
153C2×C11×C22⋊C4C2311yescharacteristic
154C2×C11×C22⋊C4C2312yes—
155C2×C11×C22⋊C4C2312yes—
156C2×C42×C11C2312yes—
157C2×C42×C11C2311yescharacteristic
158C2×C22⋊Dic11C2311yescharacteristic
159C2×C22⋊Dic11C2312yes—
160C2×C22⋊Dic11C2312yes—
161Q8×Dic11—24no—
162C2×(C2×D11)⋊C4C2311yescharacteristic
163C2×(C2×D11)⋊C4C2311yescharacteristic
164C2×(C2×D11)⋊C4C2311yescharacteristic
165C2×(C2×D11)⋊C4C2311yescharacteristic
166C2×(C2×D11)⋊C4C2311yescharacteristic
167C2×(C2×D11)⋊C4C2312yes—
168C2×(C2×D11)⋊C4C2311yescharacteristic
169C2×(C2×D11)⋊C4C2312yes—
170C2×(C2×D11)⋊C4C2312yes—
171C2×(C2×D11)⋊C4C2312yes—
172C2×(C2×D11)⋊C4C2312yes—
173C2×(C2×D11)⋊C4C2312yes—
174C2×C4⋊Dic11C2312yes—
175C2×C4⋊Dic11C2311yescharacteristic
176C2×C4⋊Dic11C2311yescharacteristic
177C2×C4⋊Dic11C2312yes—
178C2×C4⋊Dic11C2312yes—
179C2×C4⋊Dic11C2312yes—
180C2×Dic11⋊C4C2312yes—
181C2×Dic11⋊C4C2312yes—
182C2×Dic11⋊C4C2312yes—
183C2×Dic11⋊C4C2311yescharacteristic
184C2×Dic11⋊C4C2311yescharacteristic
185C2×Dic11⋊C4C2311yescharacteristic
186C2×Dic11⋊C4C2311yescharacteristic
187C2×Dic11⋊C4C2311yescharacteristic
188C2×Dic11⋊C4C2312yes—
189C2×Dic11⋊C4C2311yescharacteristic
190C2×Dic11⋊C4C2312yes—
191C2×Dic11⋊C4C2312yes—
192C2×Dic11⋊C4C2312yes—
193C2×C4×Dic11C2312yes—
194C2×C4×Dic11C2312yes—
195C2×C4×Dic11C2312yes—
196C2×C4×Dic11C2311yescharacteristic
197C2×C4×Dic11C2311yescharacteristic
198C2×C4×Dic11C2312yes—
199C2×C4×Dic11C2312yes—
200C2×C4×Dic11C2311yescharacteristic
201C2×C4×Dic11C2311yescharacteristic
202C2×C4×Dic11C2311yescharacteristic
203#66949—24no—
204#66947—24no—
205#66947—28no—
206#66946—24no—
207#66945—24no—
208C4⋊C4×D11—24no—
209C4⋊C4×D11—28no—
210#66942—24no—
211#66940—24no—
212#66940—24no—
213#66940—28no—
214#66938—24no—
215#66937—24no—
216#66936—24no—
217#66936—28no—
218(C22⋊D11)⋊C4—24no—
219(C22⋊D11)⋊C4—24no—
220#66930—24no—
221#66929—24no—
222C42×D11—28no—
223C42×D11D418yes—
224C4×Dic22—24no—
225C4×Dic22—28no—
226C11×#95C2311yescharacteristic
227C11×#95C2311yescharacteristic
228C11×#95C2312yes—
229C11×#95C2312yes—
230C11×#95C2312yes—
231C11×#95C2312yes—
232C11×#95C2312yes—
233C11⋊#95C2312yes—
234C11⋊#95C2312yes—
235C11⋊#95C2311yescharacteristic
236C11⋊#95C2311yescharacteristic
237C11⋊#95C2312yes—
238C11⋊#95C2312yes—
239C11⋊#95C2312yes—
240C11⋊#95C2312yes—
241C11⋊#95C2312yes—
242C11⋊#95C2312yes—
243C11⋊#95C2312yes—
244C11⋊#95C2312yes—
245C11⋊#95C2312yes—
246C11⋊#95C2312yes—
247C11⋊#95C2312yes—
248C11⋊#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252#34602—111nomaximal, Sylow
253C24×C11C2411yescharacteristic
254C23×D11C2411yescharacteristic
255C23×D11C2411yescharacteristic
256C2×Q8×C11—22no—
257C2×Q8×C11—24no—
258C22×C4×C11C2412yes—
259C22×C4×C11C2412yes—
260C22×C4×C11C2411yescharacteristic
261C22×C4×C11C2411yescharacteristic
262C22×C4×C11C2412yes—
263C22×C4×C11C2411yescharacteristic
264C22×C4×C11C2411yescharacteristic
265C22×C4×C11C2411yescharacteristic
266C22×C4×C11C2411yescharacteristic
267C22×C4×C11C2412yes—
268C2×C22⋊D11—22no—
269C2×C22⋊D11—22no—
270C2×C22⋊D11—24no—
271C2×C22⋊D11—41no—
272C2×C22⋊D11—41no—
273C22×Dic11—22no—
274C22×Dic11—24no—
275C22×Dic11C2412yes—
276C22×Dic11C2412yes—
277C22×Dic11C2411yescharacteristic
278C22×Dic11C2412yes—
279C22×Dic11C2411yescharacteristic
280C22×Dic11C2411yescharacteristic
281C22×Dic11C2411yescharacteristic
282C22×Dic11C2411yescharacteristic
283C22×Dic11C2412yes—
284C22×Dic11C2411yescharacteristic
285Q8×D11—232no—
286C2×D44—22no—
287C2×D44—24no—
288C2×C4×D11—24no—
289C2×C4×D11—22no—
290C2×C4×D11—24no—
291C2×C4×D11—24no—
292C2×C4×D11—24no—
293C2×C4×D11—24no—
294C2×C4×D11—24no—
295C2×C4×D11—41no—
296C2×C4×D11—41no—
297C2×C4×D11—42no—
298C2×C4×D11—42no—
299C2×C4×D11C2×D414yes—
300C2×C4×D11C2×D414yes—
301C2×C4×D11C2×D414yes—
302C2×C4×D11#4118yes—
303C2×Dic22—24no—
304C2×Dic22—24no—
305C2×Dic22—24no—
306C2×Dic22—22no—
307C2×Dic22—22no—
308C2×Dic22—24no—
309C2×Dic22—41no—
310C2×Dic22—41no—
311C11×C4⋊C4—24no—
312C11×C4⋊C4—22no—
313C11×C4⋊C4—22no—
314C11×C4⋊C4—22no—
315C11×C4⋊C4—22no—
316C11×C4⋊C4—24no—
317C11×C4⋊C4—42no—
318C11×C4⋊C4—42no—
319C11×C22⋊C4—22no—
320C11×C22⋊C4—22no—
321C11×C22⋊C4—22no—
322C11×C22⋊C4—24no—
323C11×C22⋊C4—42no—
324C42×C11—24no—
325C42×C11C2×D414yes—
326C22⋊Dic11—22no—
327C22⋊Dic11—24no—
328C22⋊Dic11—42no—
329(C2×D11)⋊C4—22no—
330(C2×D11)⋊C4—24no—
331(C2×D11)⋊C4—22no—
332(C2×D11)⋊C4—22no—
333(C2×D11)⋊C4—24no—
334(C2×D11)⋊C4—24no—
335(C2×D11)⋊C4—22no—
336(C2×D11)⋊C4—22no—
337(C2×D11)⋊C4—22no—
338(C2×D11)⋊C4—24no—
339(C2×D11)⋊C4—42no—
340(C2×D11)⋊C4—42no—
341C4⋊Dic11—24no—
342C4⋊Dic11—22no—
343C4⋊Dic11—24no—
344C4⋊Dic11—22no—
345C4⋊Dic11—42no—
346C4⋊Dic11—42no—
347Dic11⋊C4—24no—
348Dic11⋊C4—24no—
349Dic11⋊C4—22no—
350Dic11⋊C4—22no—
351Dic11⋊C4—22no—
352Dic11⋊C4—24no—
353Dic11⋊C4—24no—
354Dic11⋊C4—22no—
355Dic11⋊C4—22no—
356Dic11⋊C4—22no—
357Dic11⋊C4—24no—
358Dic11⋊C4—42no—
359Dic11⋊C4—42no—
360C4×Dic11—24no—
361C4×Dic11—24no—
362C4×Dic11—22no—
363C4×Dic11—22no—
364C4×Dic11—24no—
365C4×Dic11—24no—
366C4×Dic11—24no—
367C4×Dic11C2×D414yes—
368C4×Dic11C2×D414yes—
369C4×Dic11C2×D414yes—
370C2×#529—111no—
371C22×C4×Q8—111no—
372#2637—111no—
373#2637—111no—
374#2637—111no—
375#2637D1111yescharacteristic, complemented
376#2634—112no—
377#2632—112no—
378#2627—112no—
379#2623—111no—
380#2623—111no—
381#2618—112no—
382#2614—111no—
383#2614—111no—
384#2399—111no—
385#2399—111no—
386#2398—111no—
387#2398—111no—
388#2396—112no—
389#2396—112no—
390C4×#123—112no—
391C4×#123—112no—
392#2283—111no—
393C23×C11—21no—
394C23×C11—22no—
395C23×C11—22no—
396C23×C11—21no—
397C23×C11—21no—
398C23×C11C2511yescharacteristic
399C22×D11—22no—
400C22×D11—21no—
401C22×D11—21no—
402C22×D11—21no—
403C22×D11—22no—
404C22×D11—22no—
405C22×D11—21no—
406C22×D11—21no—
407C22×D11C22×D412yes—
408C22×D11C2×#4114yes—
409Q8×C11—28no—
410C2×C4×C11—22no—
411C2×C4×C11—22no—
412C2×C4×C11—22no—
413C2×C4×C11—22no—
414C2×C4×C11—21no—
415C2×C4×C11—21no—
416C2×C4×C11—22no—
417C2×C4×C11—21no—
418C2×C4×C11—21no—
419C2×C4×C11—21no—
420C2×C4×C11—22no—
421C2×C4×C11—22no—
422C2×C4×C11—22no—
423C2×C4×C11—22no—
424C2×C4×C11—22no—
425C2×C4×C11—22no—
426C2×C4×C11—21no—
427C2×C4×C11—22no—
428C2×C4×C11—22no—
429C2×C4×C11—22no—
430C2×C4×C11—22no—
431C2×C4×C11—21no—
432C2×C4×C11C22×D412yes—
433C2×C4×C11C22×D412yes—
434C2×C4×C11C22×D412yes—
435C2×C4×C11C2×#4114yes—
436C22⋊D11—44no—
437C22⋊D11—44no—
438C2×Dic11—22no—
439C2×Dic11—22no—
440C2×Dic11—22no—
441C2×Dic11—21no—
442C2×Dic11—21no—
443C2×Dic11—22no—
444C2×Dic11—21no—
445C2×Dic11—21no—
446C2×Dic11—21no—
447C2×Dic11—22no—
448C2×Dic11—22no—
449C2×Dic11—22no—
450C2×Dic11—22no—
451C2×Dic11—22no—
452C2×Dic11—22no—
453C2×Dic11—21no—
454C2×Dic11—22no—
455C2×Dic11—22no—
456C2×Dic11—22no—
457C2×Dic11—21no—
458C2×Dic11—22no—
459C2×Dic11—44no—
460C2×Dic11C22×D412yes—
461C2×Dic11C22×D412yes—
462C2×Dic11C22×D412yes—
463C2×Dic11C2×#4114yes—
464C2×Dic112−1+414yes—
465D44—44no—
466C4×D11—28no—
467C4×D11—216no—
468C4×D11—28no—
469C4×D11—44no—
470C4×D11—48no—
471C4×D11—44no—
472Dic22—216no—
473Dic22—28no—
474Dic22—44no—
475C23×Q8—111no—
476#529—228no—
477C2×#126—111no—
478C2×#126C2×D1111yescharacteristic
479C2×#125—111no—
480C2×#124—111no—
481C2×#123—112no—
482C2×#123—111no—
483C2×#123—112no—
484C2×#123—111no—
485C2×C22⋊Q8—111no—
486C2×#121—111no—
487C2×C4×Q8—111no—
488C2×C4×Q8—112no—
489C2×C4×Q8—111no—
490C2×C4×Q8—111no—
491C2×C4×Q8—112no—
492C2×C4×Q8—111no—
493C2×C4×Q8—228no—
494C2×C4×Q8C2×D1111yescharacteristic
495C2×C4×D4—111no—
496C2×C4×D4—111no—
497C2×C4×D4—111no—
498C2×#117—111no—
499C2×#117—111no—
500C22×C4⋊C4—112no—
501C22×C4⋊C4—111no—
502C22×C42—111no—
503C22×C42—112no—
504#400—112no—
505#400—112no—
506#400—112no—
507#400—112no—
508#399—112no—
509#399—112no—
510#398—112no—
511#398—111no—
512#398—111no—
513#398—112no—
514#398—112no—
515#398—112no—
516#398—112no—
517#398—111no—
518#398C2×D1111yescharacteristic
519#398C2×D1112yes—
520#397—111no—
521#397—111no—
522#397—111no—
523#397C2×D1111yescharacteristic
524#396—112no—
525#396—112no—
526#396—112no—
527#396C2×D1112yes—
528#395—111no—
529#395—112no—
530#395—111no—
531#395—112no—
532#395—112no—
533#395—111no—
534#395—112no—
535#395C2×D1111yescharacteristic
536#394—112no—
537#394—112no—
538#393—111no—
539#393—112no—
540#393—111no—
541#393—112no—
542#393—111no—
543#393C2×D1111yescharacteristic
544#388—112no—
545#388—112no—
546#388—112no—
547#388C2×D1112yes—
548#387—112no—
549#387—112no—
550#387—112no—
551#387C2×D1112yes—
552#386—112no—
553#386—112no—
554#385—112no—
555#385—112no—
556#383—112no—
557#382—111no—
558#382C2×D1111yescharacteristic
559#381—111no—
560#381—111no—
561#381—112no—
562#381—112no—
563#380—112no—
564C4×C4⋊C4—112no—
565C4×C4⋊C4—112no—
566C4×C4⋊C4—112no—
567C4×C4⋊C4—112no—
568C4×C4⋊C4—112no—
569C4×C22⋊C4—112no—
570C4×C22⋊C4—112no—
571C4×C22⋊C4—112no—
572C4×C22⋊C4—112no—
573C4×C22⋊C4—112no—
574#376—111no—
575#376—111no—
576C22×C11—41no—
577C22×C11—41no—
578C22×C11—41no—
579C22×C11—42no—
580C22×C11—42no—
581C22×C11C23×D411yescharacteristic
582C22×C11C22×#4112yes—
583C22×C11C2×2−1+412yes—
584C22×C11#58511yescharacteristic
585C22×C11#58511yescharacteristic
586C2×D11—22no—
587C2×D11—22no—
588C2×D11—24no—
589C2×D11—24no—
590C2×D11—41no—
591C2×D11—41no—
592C2×D11—41no—
593C2×D11—42no—
594C2×D11—42no—
595C2×D11#52514yes—
596C4×C11—22no—
597C4×C11—24no—
598C4×C11—22no—
599C4×C11—22no—
600C4×C11—41no—
601C4×C11—41no—
602C4×C11—41no—
603C4×C11—42no—
604C4×C11—42no—
605C4×C11—42no—
606Dic11—22no—
607Dic11—24no—
608Dic11—22no—
609Dic11—41no—
610Dic11—41no—
611Dic11—41no—
612Dic11—42no—
613Dic11—42no—
614Dic11—42no—
615Dic11#53614yes—
616C22×Q8—111no—
617C22×Q8—112no—
618C22×Q8—111no—
619C22×Q8—224no—
620C22×Q8—228no—
621C22×Q8C22×D1111yescharacteristic
622C22×D4—111no—
623C22×D4—111no—
624C22×D4—111no—
625C23×C4—111no—
626C23×C4—112no—
627C23×C4—111no—
628C23×C4—111no—
629C23×C4—111no—
630C23×C4—111no—
631C23×C4—112no—
632#126—24no—
633#126—224no—
634#125—224no—
635#124—224no—
636#123—224no—
637#123—228no—
638#123—224no—
639#123—228no—
640C22⋊Q8—224no—
641#121—224no—
642C4×Q8—24no—
643C4×Q8—228no—
644C4×Q8—228no—
645C4×Q8—224no—
646C4×Q8—224no—
647C4×Q8—224no—
648C4×Q8—224no—
649C4×D4—224no—
650C4×D4—224no—
651C4×D4—224no—
652#117—224no—
653#117—224no—
654C2×C4⋊C4—112no—
655C2×C4⋊C4—112no—
656C2×C4⋊C4—112no—
657C2×C4⋊C4—111no—
658C2×C4⋊C4—112no—
659C2×C4⋊C4—111no—
660C2×C4⋊C4—111no—
661C2×C4⋊C4—111no—
662C2×C4⋊C4—111no—
663C2×C4⋊C4—111no—
664C2×C4⋊C4—111no—
665C2×C4⋊C4—111no—
666C2×C4⋊C4—112no—
667C2×C4⋊C4—112no—
668C2×C4⋊C4—112no—
669C2×C4⋊C4—112no—
670C2×C4⋊C4—112no—
671C2×C4⋊C4—112no—
672C2×C4⋊C4—112no—
673C2×C4⋊C4—224no—
674C2×C4⋊C4—228no—
675C2×C4⋊C4C22×D1112yes—
676C2×C4⋊C4C22×D1111yescharacteristic
677C2×C4⋊C4C22×D1111yescharacteristic
678C2×C4⋊C4C22×D1111yescharacteristic
679C2×C4⋊C4C22×D1111yescharacteristic
680C2×C4⋊C4C22×D1112yes—
681C2×C4⋊C4C22×D1112yes—
682C2×C4⋊C4C22×D1112yes—
683C2×C22⋊C4—111no—
684C2×C22⋊C4—112no—
685C2×C22⋊C4—111no—
686C2×C22⋊C4—111no—
687C2×C22⋊C4—111no—
688C2×C22⋊C4—111no—
689C2×C22⋊C4—111no—
690C2×C22⋊C4—111no—
691C2×C22⋊C4—112no—
692C2×C22⋊C4—112no—
693C2×C22⋊C4—112no—
694C2×C22⋊C4—112no—
695C2×C22⋊C4—112no—
696C2×C22⋊C4—112no—
697C2×C22⋊C4—112no—
698C2×C22⋊C4C22×D1111yescharacteristic
699C2×C22⋊C4C22×D1111yescharacteristic
700C2×C22⋊C4C22×D1111yescharacteristic
701C2×C22⋊C4C22×D1112yes—
702C2×C22⋊C4C22×D1112yes—
703C2×C42—111no—
704C2×C42—111no—
705C2×C42—111no—
706C2×C42—118no—
707C2×C42—111no—
708C2×C42—111no—
709C2×C42—112no—
710C2×C42—112no—
711C2×C42—112no—
712C2×C42—112no—
713C2×C42—112no—
714C2×C42—228no—
715C2×C42C22×D1112yes—
716C2×C42C22×D1111yescharacteristic
717#95—112no—
718#95—112no—
719#95—111no—
720#95—111no—
721#95—112no—
722#95—112no—
723#95—112no—
724#95—112no—
725#95—112no—
726#95—112no—
727#95—112no—
728#95—112no—
729#95—112no—
730#95—112no—
731#95—112no—
732#95—112no—
733#95—112no—
734#95—112no—
735#95—112no—
736#95C22×D1111yescharacteristic
737#95C22×D1111yescharacteristic
738#95C22×D1112yes—
739#95C22×D1112yes—
740#95C22×D1112yes—
741#95C22×D1112yes—
742#95C22×D1112yes—
743C2×C11—81no—
744C2×C11C2×#52511yescharacteristic
745C2×C11C2×#53611yescharacteristic
746C2×C11#344911yescharacteristic
747C2×C11#346112yes—
748C2×C11#346112yes—
749D11—24no—
750D11—81no—
751C24—111no—
752C24—111no—
753C24C23×D1111yescharacteristic
754C2×Q8—22no—
755C2×Q8—24no—
756C2×Q8—224no—
757C2×Q8—224no—
758C2×Q8—224no—
759C2×Q8—222no—
760C2×Q8—2232no—
761C2×Q8—222no—
762C2×Q8—224no—
763C2×Q8—441no—
764C2×Q8—441no—
765C2×D4—222no—
766C2×D4—224no—
767C2×D4—222no—
768C2×D4—222no—
769C2×D4—224no—
770C2×D4—441no—
771C2×D4—441no—
772C22×C4—111no—
773C22×C4—111no—
774C22×C4—112no—
775C22×C4—111no—
776C22×C4—114no—
777C22×C4—114no—
778C22×C4—118no—
779C22×C4—114no—
780C22×C4—112no—
781C22×C4—112no—
782C22×C4—111no—
783C22×C4—112no—
784C22×C4—111no—
785C22×C4—111no—
786C22×C4—224no—
787C22×C4—222no—
788C22×C4—224no—
789C22×C4—224no—
790C22×C4—224no—
791C22×C4—224no—
792C22×C4—224no—
793C22×C4—222no—
794C22×C4—224no—
795C22×C4—441no—
796C22×C4—441no—
797C22×C4—442no—
798C22×C4—442no—
799C22×C4C23×D1112yes—
800C22×C4C23×D1112yes—
801C22×C4C23×D1111yescharacteristic
802C22×C4C23×D1112yes—
803C22×C4C23×D1111yescharacteristic
804C22×C4C23×D1111yescharacteristic
805C22×C4C23×D1111yescharacteristic
806C22×C4C23×D1111yescharacteristic
807C22×C4C23×D1111yescharacteristic
808C22×C4C23×D1112yes—
809C4⋊C4—24no—
810C4⋊C4—22no—
811C4⋊C4—22no—
812C4⋊C4—22no—
813C4⋊C4—22no—
814C4⋊C4—24no—
815C4⋊C4—42no—
816C4⋊C4—42no—
817C4⋊C4—224no—
818C4⋊C4—224no—
819C4⋊C4—224no—
820C4⋊C4—222no—
821C4⋊C4—222no—
822C4⋊C4—222no—
823C4⋊C4—222no—
824C4⋊C4—224no—
825C4⋊C4—224no—
826C4⋊C4—224no—
827C4⋊C4—222no—
828C4⋊C4—222no—
829C4⋊C4—222no—
830C4⋊C4—222no—
831C4⋊C4—224no—
832C4⋊C4—442no—
833C4⋊C4—442no—
834C4⋊C4—442no—
835C4⋊C4—442no—
836C22⋊C4—22no—
837C22⋊C4—22no—
838C22⋊C4—22no—
839C22⋊C4—24no—
840C22⋊C4—42no—
841C22⋊C4—222no—
842C22⋊C4—224no—
843C22⋊C4—222no—
844C22⋊C4—222no—
845C22⋊C4—224no—
846C22⋊C4—224no—
847C22⋊C4—222no—
848C22⋊C4—224no—
849C22⋊C4—222no—
850C22⋊C4—222no—
851C22⋊C4—222no—
852C22⋊C4—224no—
853C22⋊C4—442no—
854C22⋊C4—442no—
855C22⋊C4—442no—
856C42—24no—
857C42—114no—
858C42—114no—
859C42—114no—
860C42—224no—
861C42—224no—
862C42—222no—
863C42—222no—
864C42—224no—
865C42—224no—
866C42—224no—
867C42D4×D1114yes—
868C11#3460211yescharacteristic, complemented, Sylow
869C23—21no—
870C23—22no—
871C23—21no—
872C23—22no—
873C23—21no—
874C23—112no—
875C23—114no—
876C23—221no—
877C23—222no—
878C23—221no—
879C23—221no—
880C23—222no—
881C23—221no—
882C23—222no—
883C23—221no—
884C23C24×D1111yescharacteristic
885Q8—28no—
886Q8—228no—
887Q8—2216no—
888Q8—444no—
889D4—444no—
890D4—444no—
891D4—444no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—21no—
896C2×C4—22no—
897C2×C4—21no—
898C2×C4—22no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—21no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—21no—
914C2×C4—112no—
915C2×C4—114no—
916C2×C4—112no—
917C2×C4—112no—
918C2×C4—114no—
919C2×C4—228no—
920C2×C4—228no—
921C2×C4—2216no—
922C2×C4—222no—
923C2×C4—222no—
924C2×C4—222no—
925C2×C4—221no—
926C2×C4—221no—
927C2×C4—222no—
928C2×C4—221no—
929C2×C4—221no—
930C2×C4—221no—
931C2×C4—222no—
932C2×C4—222no—
933C2×C4—222no—
934C2×C4—222no—
935C2×C4—221no—
936C2×C4—222no—
937C2×C4—222no—
938C2×C4—222no—
939C2×C4—222no—
940C2×C4—222no—
941C2×C4—222no—
942C2×C4—221no—
943C2×C4—444no—
944C2×C4—444no—
945C2×C4—448no—
946C2×C4—444no—
947C2×C4C2×D4×D1112yes—
948C2×C4C2×D4×D1112yes—
949C2×C4C2×D4×D1112yes—
950C2×C4#41×D1114yes—
951C22—41no—
952C22—41no—
953C22—42no—
954C22—42no—
955C22—41no—
956C22—114no—
957C22—222no—
958C22—222no—
959C22—224no—
960C22—224no—
961C22—441no—
962C22—441no—
963C22—442no—
964C22—442no—
965C22—441no—
966C22C22×D4×D1111yescharacteristic
967C22C2×#41×D1112yes—
968C22#1062345511yescharacteristic
969C22D11×2−1+412yes—
970C22#1062345711yescharacteristic
971C4—22no—
972C4—22no—
973C4—22no—
974C4—24no—
975C4—41no—
976C4—42no—
977C4—41no—
978C4—42no—
979C4—42no—
980C4—41no—
981C4—114no—
982C4—222no—
983C4—222no—
984C4—224no—
985C4—441no—
986C4—442no—
987C4—441no—
988C4—442no—
989C4—442no—
990C4—441no—
991C2—81no—
992C2—224no—
993C2—881no—
994C2D11×#52511yescharacteristic
995C2D11×#53611yescharacteristic
996C2#1308194411yescharacteristic
997C2#1308204212yes—
998C2#1308204812yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2637C2
prime radicalC2×#66937C22
hypercenter#2637D11
hypocenterC11#34602
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2637

Complements

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

NH ≅ G/Ntype
2. C2×C4×Q8×D11C2semidirect
3. #13074526C2semidirect
4. #13074524C2semidirect
5. #13074522C2semidirect
6. #13074496C2semidirect
7. #13074480C2semidirect
8. #13074434C2semidirect
9. #13074397C2semidirect
10. #13074395C2semidirect
12. #13074336C2semidirect
13. #13074334C2semidirect
14. #13071908C2semidirect
15. #13071906C2semidirect
16. #13071901C2semidirect
17. #13071898C2semidirect
18. #13071893C2semidirect
19. #13071891C2semidirect
20. #13071143C2semidirect
21. #13071137C2semidirect
22. #13071009C2semidirect
23. C11×#2637C2semidirect
375. #2637D11semidirect
868. C11#34602semidirect

Maximal subgroups

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

subgroupindex
C2×#106232372
C2×C4×Q8×D112
#130745262
#130745242
#130745222
#130744962
#130744802
#130744342
#130743972
#130743952
#130743632
#130743362
#130743342
#130719082
#130719062
#130719012
#130718982
#130718932
#130718912
#130711432
#130711372
#130710092
C11×#26372
#3460211