Finite Group Databasebeta

← #14961161

Subgroups — #14961161

Order 2816.

2522 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623188C212yesmaximal, complemented
2#13076897C212yesmaximal, complemented
3#13075519C211yesmaximal, characteristic, complemented
4#13075433C212yesmaximal, complemented
5#13075384C211yesmaximal, characteristic, complemented
6#13075156C212yesmaximal, complemented
7#13075092C212yesmaximal, complemented
8#13074921C212yesmaximal, complemented
9#13074908C211yesmaximal, characteristic, complemented
10#13074867C212yesmaximal, complemented
11#13074849C212yesmaximal, complemented
12#13074351C211yesmaximal, characteristic, complemented
13#13074349C211yesmaximal, characteristic, complemented
14#13073799C212yesmaximal, complemented
15#13073575C212yesmaximal, complemented
16#13072069C212yesmaximal, complemented
17#13072051C212yesmaximal, complemented
18D11×#385C211yesmaximal, characteristic, complemented
19C11×#2693C211yesmaximal, characteristic, complemented
20C23×C4×D11C2211yescharacteristic
21C2×C11×#123C2212yes—
22C2×#66992C2212yes—
23C2×#66991C2212yes—
24C2×#66991C2211yescharacteristic
25C2×#66990C2212yes—
26C2×#66983C2212yes—
27C2×C4×C22⋊D11C2212yes—
28C2×#66977C2212yescomplemented
29#10623188—216no—
30C2×#66951C2212yes—
31C2×#66950C2212yes—
32C2×#66948C2211yescharacteristic
33C2×#66947C2212yes—
34C2×#66946C2212yes—
35C2×C4⋊C4×D11C2212yes—
36C2×#66938C2212yes—
37C2×#66938C2212yes—
38C2×#66937C2212yes—
39C2×#66937C2212yes—
40C2×#66937C2212yes—
41C2×#66937C2212yescomplemented
42C2×#66935C2212yes—
43C2×C22⋊C4×D11C2211yescharacteristic
44C2×C22⋊C4×D11C2211yescharacteristic
45C2×#66932C2212yes—
46C11×#400C2212yescomplemented
47C11×#397C2211yescharacteristic
48C11×#396C2212yescomplemented
49C11×#392C2211yescharacteristic
50C11×#386C2212yes—
51C11×#386C2212yescomplemented
52C11×#385C2211yescharacteristic
53C11×#380C2212yescomplemented
54#10622836C2211yescharacteristic
55#10622836C2212yescomplemented
56#10622835C2212yes—
57#10622826C2212yes—
58#10622826C2212yescomplemented
59#10622823C2211yescharacteristic
60#10622607C2212yescomplemented
61#10622606C2211yescharacteristic
62#10622605C2212yescomplemented
63#10622604C2212yescomplemented
64#10622602C2212yes—
65#10622592C2212yescomplemented
66#10622587C2212yescomplemented
67#10622586C2212yescomplemented
68#10622585C2212yescomplemented
69#10622574C2212yescomplemented
70#10622573C2211yescharacteristic
71#10622572C2212yes—
72#10622572C2212yes—
73#10622572C2212yescomplemented
74#10622570C2212yescomplemented
75#10622569C2212yes—
76#10622569C2212yes—
77#10622569C2212yes—
78#10622566C2211yescharacteristic
79#10622565C2212yescomplemented
80#10622563C2211yescharacteristic
81#10622561C2212yescomplemented
82#10622561C2212yescomplemented
83#10622559C2211yescharacteristic
84#10622557C2212yescomplemented
85#10622555C2212yes—
86#10622287C2211yescharacteristic
87#10622286C2212yescomplemented
88#10622285C2212yes—
89#10622284C2211yescharacteristic
90#10622283C2212yescomplemented
91#10622281C2212yes—
92#10622281C2212yescomplemented
93#10622281C2212yescomplemented
94#10622280C2211yescharacteristic
95#10622280C2212yes—
96#10622280C2212yes—
97#10622280C2211yescharacteristic
98#10622280C2212yescomplemented
99#10622278C2212yes—
100#10622278C2212yes—
101#10622278C2212yes—
102D11×#95C2212yes—
103#10622270C2212yescomplemented
104#10622270C2212yescomplemented
105#10622270C2212yescomplemented
106#10622268C2212yescomplemented
107#10622268C2212yescomplemented
108C24×D11C2311yescharacteristic
109C22×D4×C11C2312yes—
110C22×D4×C11C2311yescharacteristic
111C23×C4×C11C2312yes—
112C23×C4×C11C2311yescharacteristic
113C22×C22⋊D11C2312yes—
114C22×C22⋊D11C2312yes—
115C22×C22⋊D11C2312yes—
116C22×C22⋊D11C2312yes—
117C22×C22⋊D11C2312yes—
118C23×Dic11C2311yescharacteristic
119C22×D44C2312yes—
120C22×D44C2312yes—
121C22×D44C2311yescharacteristic
122C22×C4×D11—44no—
123C22×C4×D11—42no—
124C22×C4×D11C2312yes—
125C22×C4×D11C2311yescharacteristic
126C22×C4×D11C2311yescharacteristic
127C22×C4×D11C2312yes—
128C22×C4×D11C2312yes—
129C22×C4×D11C2312yes—
130C22×Dic22C2312yes—
131C11×#123—28no—
132C2×C11×C4⋊C4C2312yes—
133C2×C11×C4⋊C4C2312yes—
134C2×C11×C4⋊C4C2312yes—
135C2×C11×C4⋊C4C2311yescharacteristic
136C2×C11×C22⋊C4C2312yes—
137C2×C11×C22⋊C4C2312yes—
138C2×C11×C22⋊C4C2311yescharacteristic
139C2×C11×C22⋊C4C2312yes—
140C2×C11×C22⋊C4C2312yes—
141C2×C11×C22⋊C4C2312yes—
142C2×C11×C22⋊C4C2311yescharacteristic
143C2×C22⋊Dic11C2312yes—
144C2×C22⋊Dic11C2312yes—
145C2×C22⋊Dic11C2312yes—
146C2×C22⋊Dic11C2311yescharacteristic
147C2×C22⋊Dic11C2312yes—
148C2×C22⋊Dic11C2312yes—
149C2×C22⋊Dic11C2311yescharacteristic
150#66992—44no—
151#66991—28no—
152#66991—42no—
153#66990—28no—
154#66983—28no—
155C4×C22⋊D11—28no—
156C2×(C2×D11)⋊C4C2312yes—
157C2×(C2×D11)⋊C4C2312yes—
158C2×(C2×D11)⋊C4C2312yes—
159C2×(C2×D11)⋊C4C2312yes—
160C2×(C2×D11)⋊C4C2312yes—
161C2×(C2×D11)⋊C4C2312yes—
162C2×(C2×D11)⋊C4C2312yes—
163C2×(C2×D11)⋊C4C2311yescharacteristic
164C2×(C2×D11)⋊C4C2311yescharacteristic
165C2×(C2×D11)⋊C4C2312yes—
166C2×(C2×D11)⋊C4C2312yes—
167C2×(C2×D11)⋊C4C2312yes—
168C2×(C2×D11)⋊C4C2312yes—
169C2×(C2×D11)⋊C4C2312yes—
170C2×(C2×D11)⋊C4C2312yes—
171C2×C4⋊Dic11C2312yes—
172C2×C4⋊Dic11C2312yes—
173C2×C4⋊Dic11C2312yes—
174C2×C4⋊Dic11C2311yescharacteristic
175#66977—44no—
176C2×Dic11⋊C4C2312yes—
177C2×Dic11⋊C4C2312yes—
178C2×Dic11⋊C4C2312yes—
179C2×Dic11⋊C4C2312yes—
180C2×Dic11⋊C4C2312yes—
181C2×Dic11⋊C4C2312yes—
182C2×Dic11⋊C4C2312yes—
183C2×Dic11⋊C4C2312yes—
184C2×Dic11⋊C4C2312yes—
185C2×C4×Dic11C2312yes—
186C2×C4×Dic11C2312yes—
187#66951—28no—
188#66950—28no—
189#66948—42no—
190#66947—28no—
191#66946—28no—
192C4⋊C4×D11—44no—
193#66938—28no—
194#66938—28no—
195#66937—28no—
196#66937—44no—
197#66937—44no—
198#66937—44no—
199#66935—28no—
200C22⋊C4×D11—42no—
201C22⋊C4×D11D418yescomplemented
202#66932—28no—
203C11×#95C2312yes—
204C11×#95C2312yes—
205C11×#95C2311yescharacteristic
206C11×#95C2312yes—
207C11×#95C2312yes—
208C11×#95C2311yescharacteristic
209C11⋊#95C2311yescharacteristic
210C11⋊#95C2312yes—
211C11⋊#95C2312yes—
212C11⋊#95C2312yes—
213C11⋊#95C2312yes—
214C11⋊#95C2312yes—
215C11⋊#95C2312yes—
216C11⋊#95C2312yes—
217C11⋊#95C2312yes—
218C11⋊#95C2312yes—
219C11⋊#95C2312yes—
220C11⋊#95C2311yescharacteristic
221#36738—111nomaximal, Sylow
222C24×C11C2412yes—
223C24×C11C2411yescharacteristic
224C23×D11—22no—
225C23×D11—22no—
226C23×D11—42no—
227C23×D11—42no—
228C23×D11C2×D414yes—
229C23×D11C2412yes—
230C23×D11C2411yescharacteristic
231C23×D11C2411yescharacteristic
232C2×D4×C11—24no—
233C2×D4×C11—41no—
234C2×D4×C11—42no—
235C2×D4×C11—42no—
236C2×D4×C11—42no—
237C22×C4×C11—24no—
238C22×C4×C11—42no—
239C22×C4×C11—41no—
240C22×C4×C11—42no—
241C22×C4×C11—42no—
242C22×C4×C11C2411yescharacteristic
243C22×C4×C11C2412yes—
244C22×C4×C11C2411yescharacteristic
245C22×C4×C11C2412yes—
246C22×C4×C11C2412yes—
247C22×C4×C11C2412yes—
248C22×C4×C11C2412yes—
249C2×C22⋊D11—24no—
250C2×C22⋊D11—24no—
251C2×C22⋊D11—24no—
252C2×C22⋊D11—24no—
253C2×C22⋊D11—24no—
254C2×C22⋊D11—24no—
255C2×C22⋊D11—24no—
256C2×C22⋊D11—42no—
257C2×C22⋊D11—42no—
258C2×C22⋊D11—42no—
259C2×C22⋊D11—42no—
260C2×C22⋊D11—42no—
261C2×C22⋊D11—42no—
262C2×C22⋊D11—42no—
263C2×C22⋊D11—42no—
264C22×Dic11—24no—
265C22×Dic11—41no—
266C22×Dic11C2411yescharacteristic
267C22×Dic11C2412yes—
268C22×Dic11C2412yes—
269C22×Dic11C2412yes—
270C22×Dic11C2411yescharacteristic
271C22×Dic11C2412yes—
272C22×Dic11C2412yes—
273C2×D44—24no—
274C2×D44—24no—
275C2×D44—24no—
276C2×D44—24no—
277C2×D44—42no—
278C2×D44—42no—
279C2×D44—41no—
280C2×D44—42no—
281C2×C4×D11—24no—
282C2×C4×D11—24no—
283C2×C4×D11—24no—
284C2×C4×D11—24no—
285C2×C4×D11—22no—
286C2×C4×D11—22no—
287C2×C4×D11—42no—
288C2×C4×D11—42no—
289C2×C4×D11—42no—
290C2×C4×D11—42no—
291C2×C4×D11—42no—
292C2×C4×D11—42no—
293C2×C4×D11—42no—
294C2×C4×D11—42no—
295C2×C4×D11—42no—
296C2×C4×D11—416no—
297C2×C4×D11C2×D418yes—
298C2×Dic22—24no—
299C2×Dic22—42no—
300C2×Dic22—42no—
301C11×C4⋊C4—24no—
302C11×C4⋊C4—24no—
303C11×C4⋊C4—42no—
304C11×C4⋊C4—41no—
305C11×C22⋊C4—24no—
306C11×C22⋊C4—24no—
307C11×C22⋊C4—41no—
308C11×C22⋊C4—42no—
309C11×C22⋊C4—42no—
310C11×C22⋊C4—42no—
311C11×C22⋊C4C2×D414yes—
312C22⋊Dic11—24no—
313C22⋊Dic11—24no—
314C22⋊Dic11—24no—
315C22⋊Dic11—41no—
316C22⋊Dic11—42no—
317C22⋊Dic11—42no—
318C22⋊Dic11C2×D414yes—
319(C2×D11)⋊C4—24no—
320(C2×D11)⋊C4—24no—
321(C2×D11)⋊C4—24no—
322(C2×D11)⋊C4—24no—
323(C2×D11)⋊C4—24no—
324(C2×D11)⋊C4—24no—
325(C2×D11)⋊C4—24no—
326(C2×D11)⋊C4—41no—
327(C2×D11)⋊C4—41no—
328(C2×D11)⋊C4—42no—
329(C2×D11)⋊C4—42no—
330(C2×D11)⋊C4—42no—
331(C2×D11)⋊C4—42no—
332(C2×D11)⋊C4—42no—
333(C2×D11)⋊C4C2×D418yes—
334C4⋊Dic11—24no—
335C4⋊Dic11—24no—
336C4⋊Dic11—24no—
337C4⋊Dic11—41no—
338Dic11⋊C4—24no—
339Dic11⋊C4—24no—
340Dic11⋊C4—24no—
341Dic11⋊C4—24no—
342Dic11⋊C4—42no—
343Dic11⋊C4—42no—
344Dic11⋊C4—42no—
345Dic11⋊C4—42no—
346Dic11⋊C4—42no—
347C4×Dic11—24no—
348C4×Dic11—24no—
349C2×#538—112no—
350#2847—112no—
351#2722—111no—
352#2715—112no—
353#2712—111no—
354#2695—112no—
355#2693D1111yescharacteristic, complemented
356#2691—112no—
357#2676—112no—
358#2675—111no—
359#2672—112no—
360#2671—112no—
361#2617—111no—
362#2617—111no—
363#2564—112no—
364#2543—112no—
365#2417—112no—
366#2416—112no—
367C2×#385—111no—
368C23×C11—21no—
369C23×C11—22no—
370C23×C11—21no—
371C23×C11—22no—
372C23×C11—22no—
373C23×C11—22no—
374C23×C11—22no—
375C23×C11—22no—
376C23×C11—22no—
377C23×C11—22no—
378C23×C11—22no—
379C23×C11C22×D412yes—
380C23×C11C2511yescharacteristic
381C22×D11—22no—
382C22×D11—22no—
383C22×D11—21no—
384C22×D11—22no—
385C22×D11—21no—
386C22×D11—22no—
387C22×D11—28no—
388C22×D11—22no—
389C22×D11—22no—
390C22×D11—22no—
391C22×D11—22no—
392C22×D11—22no—
393C22×D11—22no—
394C22×D11—22no—
395C22×D11—48no—
396C22×D11—44no—
397C22×D11—44no—
398C22×D11—48no—
399C22×D11C22×D412yes—
400C22×D11C22×D412yes—
401C22×D11H(5,𝔽2)12yes—
402C22×D112−1+412yes—
403D4×C11—84no—
404D4×C11—82no—
405C2×C4×C11—22no—
406C2×C4×C11—22no—
407C2×C4×C11—22no—
408C2×C4×C11—22no—
409C2×C4×C11—22no—
410C2×C4×C11—22no—
411C2×C4×C11—22no—
412C2×C4×C11—22no—
413C2×C4×C11—22no—
414C2×C4×C11—22no—
415C2×C4×C11—21no—
416C2×C4×C11—21no—
417C2×C4×C11—22no—
418C2×C4×C11—22no—
419C2×C4×C11—22no—
420C2×C4×C11—22no—
421C2×C4×C11—22no—
422C2×C4×C11—22no—
423C2×C4×C11—44no—
424C2×C4×C11—84no—
425C2×C4×C11C22×D414yes—
426C22⋊D11—48no—
427C22⋊D11—84no—
428C22⋊D11—84no—
429C22⋊D11—84no—
430C22⋊D11—84no—
431C2×Dic11—22no—
432C2×Dic11—22no—
433C2×Dic11—22no—
434C2×Dic11—22no—
435C2×Dic11—22no—
436C2×Dic11—22no—
437C2×Dic11—22no—
438C2×Dic11—22no—
439C2×Dic11—22no—
440C2×Dic11—22no—
441C2×Dic11—22no—
442C2×Dic11—21no—
443C2×Dic11—21no—
444C2×Dic11—22no—
445C2×Dic11—22no—
446C2×Dic11—22no—
447C2×Dic11—22no—
448C2×Dic11—44no—
449C2×Dic11C22×D414yes—
450C2×Dic11H(5,𝔽2)14yes—
451D44—48no—
452D44—84no—
453D44—82no—
454C4×D11—48no—
455C4×D11—48no—
456C4×D11—48no—
457C4×D11—84no—
458C4×D11—82no—
459C4×D11—82no—
460Dic22—84no—
461C24×C4—111no—
462#538—2216no—
463C2×#126—112no—
464C2×#126—112no—
465C2×#124—112no—
466C2×#124—112no—
467C2×#123—112no—
468C2×#123C2×D1112yes—
469C2×C22⋊Q8—112no—
470C2×C22⋊Q8—112no—
471C2×#121—112no—
472C2×#121—112no—
473C2×#121—112no—
474C2×#121—111no—
475C2×#121—111no—
476C2×#121—112no—
477C2×#121—112no—
478C2×#121—112no—
479C2×#121—112no—
480C2×#120—112no—
481C2×#120—112no—
482C2×C4×D4—112no—
483C2×C4×D4—112no—
484C22×C4⋊C4—112no—
485C22×C22⋊C4—111no—
486C22×C22⋊C4—111no—
487#400C2×D1112yescomplemented
488#399—112no—
489#398—112no—
490#398—112no—
491#398—112no—
492#397—111no—
493#397—111no—
494#397—112no—
495#397—111no—
496#397C2×D1111yescharacteristic
497#396—112no—
498#396—112no—
499#396—112no—
500#396C2×D1112yescomplemented
501#395—112no—
502#394—112no—
503#394—112no—
504#394—112no—
505#394—112no—
506#394—112no—
507#394—112no—
508#394—112no—
509#393—112no—
510#392—111no—
511#392—112no—
512#392—111no—
513#392—111no—
514#392C2×D1111yescharacteristic
515#391—112no—
516#390—112no—
517#389—112no—
518#389—112no—
519#388—112no—
520#388—112no—
521#387—112no—
522#387—112no—
523#386—112no—
524#386—112no—
525#386—112no—
526#386—112no—
527#386—112no—
528#386—112no—
529#386—112no—
530#386—112no—
531#386C2×D1112yes—
532#386C2×D1112yescomplemented
533#385—111no—
534#385—112no—
535#385—111no—
536#385—111no—
537#385—112no—
538#385—112no—
539#385—112no—
540#385C2×D1111yescharacteristic
541#380—112no—
542#380—111no—
543#380—112no—
544#380—112no—
545#380—111no—
546#380—112no—
547#380C2×D1112yescomplemented
548C2×#95—112no—
549C22×C11—22no—
550C22×C11—24no—
551C22×C11—41no—
552C22×C11—41no—
553C22×C11—42no—
554C22×C11—42no—
555C22×C11—42no—
556C22×C11—42no—
557C22×C11—42no—
558C22×C11—42no—
559C22×C11—42no—
560C22×C11—42no—
561C22×C11C23×D411yescharacteristic
562C22×C11C2×H(5,𝔽2)11yescharacteristic
563C22×C11C2×H(5,𝔽2)12yes—
564C22×C11C2×2−1+411yescharacteristic
565C22×C11#58512yes—
566C2×D11—24no—
567C2×D11—22no—
568C2×D11—22no—
569C2×D11—24no—
570C2×D11—22no—
571C2×D11—24no—
572C2×D11—416no—
573C2×D11—41no—
574C2×D11—41no—
575C2×D11—42no—
576C2×D11—42no—
577C2×D11—42no—
578C2×D11—42no—
579C2×D11—42no—
580C2×D11—42no—
581C2×D11—42no—
582C2×D11—42no—
583C2×D11#53714yes—
584C4×C11—24no—
585C4×C11—42no—
586C4×C11—42no—
587C4×C11—42no—
588C4×C11—42no—
589C4×C11—41no—
590C4×C11—41no—
591Dic11—24no—
592Dic11—24no—
593Dic11—42no—
594Dic11—42no—
595Dic11—42no—
596Dic11—41no—
597Dic11—41no—
598C25—111no—
599C22×Q8—112no—
600C22×D4—112no—
601C22×D4—112no—
602C22×D4—112no—
603C22×D4—112no—
604C22×D4—112no—
605C22×D4—112no—
606C22×D4—112no—
607C22×D4—111no—
608C22×D4C22×D1112yes—
609C22×D4C22×D1111yescharacteristic
610C23×C4—112no—
611C23×C4—111no—
612C23×C4—112no—
613C23×C4—111no—
614C23×C4—111no—
615C23×C4—112no—
616C23×C4—112no—
617C23×C4—444no—
618C23×C4—442no—
619C23×C4C22×D1112yes—
620C23×C4C22×D1111yescharacteristic
621#126—228no—
622#126—228no—
623#124—228no—
624#124—228no—
625#123—28no—
626#123—228no—
627C22⋊Q8—228no—
628C22⋊Q8—444no—
629#121—228no—
630#121—228no—
631#121—228no—
632#121—444no—
633#121—444no—
634#121—444no—
635#121—444no—
636#121—442no—
637#121—442no—
638#120—228no—
639#120—228no—
640C4×D4—228no—
641C4×D4—228no—
642C2×C4⋊C4—112no—
643C2×C4⋊C4—112no—
644C2×C4⋊C4—112no—
645C2×C4⋊C4—112no—
646C2×C4⋊C4—112no—
647C2×C4⋊C4—112no—
648C2×C4⋊C4—112no—
649C2×C4⋊C4—112no—
650C2×C4⋊C4—112no—
651C2×C4⋊C4—112no—
652C2×C4⋊C4—111no—
653C2×C4⋊C4—112no—
654C2×C4⋊C4—112no—
655C2×C4⋊C4—444no—
656C2×C4⋊C4C22×D1112yes—
657C2×C4⋊C4C22×D1112yes—
658C2×C4⋊C4C22×D1112yes—
659C2×C4⋊C4C22×D1111yescharacteristic
660C2×C22⋊C4—111no—
661C2×C22⋊C4—112no—
662C2×C22⋊C4—118no—
663C2×C22⋊C4—112no—
664C2×C22⋊C4—112no—
665C2×C22⋊C4—112no—
666C2×C22⋊C4—112no—
667C2×C22⋊C4—112no—
668C2×C22⋊C4—112no—
669C2×C22⋊C4—112no—
670C2×C22⋊C4—112no—
671C2×C22⋊C4—112no—
672C2×C22⋊C4—112no—
673C2×C22⋊C4—111no—
674C2×C22⋊C4—112no—
675C2×C22⋊C4—112no—
676C2×C22⋊C4—111no—
677C2×C22⋊C4—111no—
678C2×C22⋊C4—112no—
679C2×C22⋊C4—112no—
680C2×C22⋊C4—112no—
681C2×C22⋊C4—112no—
682C2×C22⋊C4—112no—
683C2×C22⋊C4—442no—
684C2×C22⋊C4C22×D1112yes—
685C2×C22⋊C4C22×D1112yes—
686C2×C22⋊C4C22×D1111yescharacteristic
687C2×C22⋊C4C22×D1112yes—
688C2×C22⋊C4C22×D1112yes—
689C2×C22⋊C4C22×D1112yes—
690C2×C22⋊C4C22×D1111yescharacteristic
691C2×C42—112no—
692C2×C42—112no—
693#95—112no—
694#95—112no—
695#95—112no—
696#95—112no—
697#95—112no—
698#95—112no—
699#95—112no—
700#95—112no—
701#95—111no—
702#95—111no—
703#95—112no—
704#95—112no—
705#95C22×D1112yes—
706#95C22×D1112yes—
707#95C22×D1111yescharacteristic
708#95C22×D1112yes—
709#95C22×D1111yescharacteristic
710#95C22×D1112yes—
711C2×C11—42no—
712C2×C11—82no—
713C2×C11C2×#53711yescharacteristic
714C2×C11#349612yes—
715C2×C11#353211yescharacteristic
716C2×C11#353311yescharacteristic
717C2×C11#354112yes—
718D11—24no—
719D11—42no—
720D11—82no—
721C24—111no—
722C24—111no—
723C24—114no—
724C24—112no—
725C24—222no—
726C24—222no—
727C24—442no—
728C24—442no—
729C24C23×D1112yes—
730C24C23×D1111yescharacteristic
731C2×Q8—224no—
732C2×Q8—442no—
733C2×Q8—442no—
734C2×D4—24no—
735C2×D4—42no—
736C2×D4—41no—
737C2×D4—42no—
738C2×D4—42no—
739C2×D4—224no—
740C2×D4—224no—
741C2×D4—224no—
742C2×D4—224no—
743C2×D4—224no—
744C2×D4—224no—
745C2×D4—224no—
746C2×D4—224no—
747C2×D4—224no—
748C2×D4—224no—
749C2×D4—224no—
750C2×D4—441no—
751C2×D4—442no—
752C2×D4—442no—
753C2×D4—442no—
754C2×D4—442no—
755C2×D4—442no—
756C2×D4—442no—
757C2×D4—442no—
758C2×D4—442no—
759C2×D4—442no—
760C2×D4—442no—
761C2×D4—442no—
762C22×C4—24no—
763C22×C4—41no—
764C22×C4—42no—
765C22×C4—42no—
766C22×C4—42no—
767C22×C4—112no—
768C22×C4—112no—
769C22×C4—118no—
770C22×C4—111no—
771C22×C4—112no—
772C22×C4—112no—
773C22×C4—112no—
774C22×C4—111no—
775C22×C4—224no—
776C22×C4—224no—
777C22×C4—224no—
778C22×C4—224no—
779C22×C4—222no—
780C22×C4—222no—
781C22×C4—224no—
782C22×C4—442no—
783C22×C4—442no—
784C22×C4—442no—
785C22×C4—442no—
786C22×C4—442no—
787C22×C4—442no—
788C22×C4—442no—
789C22×C4—442no—
790C22×C4—442no—
791C22×C4—4416no—
792C22×C4—441no—
793C22×C4C23×D1111yescharacteristic
794C22×C4C23×D1112yes—
795C22×C4C23×D1111yescharacteristic
796C22×C4C23×D1112yes—
797C22×C4C23×D1112yes—
798C22×C4C23×D1112yes—
799C22×C4C23×D1112yes—
800C4⋊C4—24no—
801C4⋊C4—24no—
802C4⋊C4—42no—
803C4⋊C4—41no—
804C4⋊C4—224no—
805C4⋊C4—224no—
806C4⋊C4—224no—
807C4⋊C4—224no—
808C4⋊C4—224no—
809C4⋊C4—224no—
810C4⋊C4—224no—
811C4⋊C4—442no—
812C4⋊C4—442no—
813C4⋊C4—442no—
814C4⋊C4—441no—
815C4⋊C4—442no—
816C4⋊C4—442no—
817C22⋊C4—24no—
818C22⋊C4—24no—
819C22⋊C4—41no—
820C22⋊C4—42no—
821C22⋊C4—42no—
822C22⋊C4—42no—
823C22⋊C4—114no—
824C22⋊C4—118no—
825C22⋊C4—224no—
826C22⋊C4—224no—
827C22⋊C4—224no—
828C22⋊C4—224no—
829C22⋊C4—224no—
830C22⋊C4—224no—
831C22⋊C4—224no—
832C22⋊C4—224no—
833C22⋊C4—224no—
834C22⋊C4—224no—
835C22⋊C4—441no—
836C22⋊C4—441no—
837C22⋊C4—442no—
838C22⋊C4—442no—
839C22⋊C4—442no—
840C22⋊C4—442no—
841C22⋊C4—442no—
842C22⋊C4—441no—
843C22⋊C4—442no—
844C22⋊C4—442no—
845C22⋊C4D4×D1114yes—
846C42—224no—
847C42—224no—
848C11#3673811yescharacteristic, complemented, Sylow
849C23—22no—
850C23—21no—
851C23—22no—
852C23—21no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—112no—
861C23—112no—
862C23—112no—
863C23—112no—
864C23—228no—
865C23—222no—
866C23—222no—
867C23—222no—
868C23—221no—
869C23—222no—
870C23—221no—
871C23—222no—
872C23—222no—
873C23—222no—
874C23—222no—
875C23—222no—
876C23—222no—
877C23—222no—
878C23—448no—
879C23—444no—
880C23—448no—
881C23—444no—
882C23C2×D4×D1112yes—
883C23C24×D1111yescharacteristic
884Q8—884no—
885D4—84no—
886D4—82no—
887D4—448no—
888D4—448no—
889D4—884no—
890D4—882no—
891D4—884no—
892D4—884no—
893D4—884no—
894D4—884no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—44no—
914C2×C4—84no—
915C2×C4—114no—
916C2×C4—114no—
917C2×C4—222no—
918C2×C4—222no—
919C2×C4—222no—
920C2×C4—222no—
921C2×C4—222no—
922C2×C4—222no—
923C2×C4—222no—
924C2×C4—222no—
925C2×C4—222no—
926C2×C4—222no—
927C2×C4—222no—
928C2×C4—221no—
929C2×C4—221no—
930C2×C4—222no—
931C2×C4—222no—
932C2×C4—222no—
933C2×C4—222no—
934C2×C4—448no—
935C2×C4—448no—
936C2×C4—448no—
937C2×C4—444no—
938C2×C4—884no—
939C2×C4—882no—
940C2×C4—882no—
941C2×C4C2×D4×D1114yes—
942C22—24no—
943C22—22no—
944C22—42no—
945C22—41no—
946C22—41no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—114no—
955C22—224no—
956C22—224no—
957C22—222no—
958C22—222no—
959C22—224no—
960C22—222no—
961C22—4416no—
962C22—442no—
963C22—441no—
964C22—441no—
965C22—442no—
966C22—442no—
967C22—442no—
968C22—442no—
969C22—442no—
970C22—442no—
971C22—442no—
972C22C22×D4×D1111yescharacteristic
973C22#1062345312yes—
974C22D11×H(5,𝔽2)12yes—
975C22D11×H(5,𝔽2)11yescharacteristic
976C22D11×2−1+411yescharacteristic
977C4—24no—
978C4—42no—
979C4—42no—
980C4—42no—
981C4—42no—
982C4—41no—
983C4—41no—
984C4—224no—
985C4—224no—
986C4—442no—
987C4—442no—
988C4—442no—
989C4—441no—
990C4—441no—
991C2—42no—
992C2—82no—
993C2—224no—
994C2—442no—
995C2—882no—
996C2D11×#53711yescharacteristic
997C2#1308237612yes—
998C2#1308276911yescharacteristic
999C2#1308278111yescharacteristic
1000C2#1308290812yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2693C2
hypercenter#2693D11
hypocenterC11#36738
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2693

Complements

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

NH ≅ G/Ntype
1. C2×#10623188C2semidirect
2. #13076897C2semidirect
3. #13075519C2semidirect
4. #13075433C2semidirect
5. #13075384C2semidirect
6. #13075156C2semidirect
7. #13075092C2semidirect
8. #13074921C2semidirect
9. #13074908C2semidirect
10. #13074867C2semidirect
11. #13074849C2semidirect
12. #13074351C2semidirect
13. #13074349C2semidirect
14. #13073799C2semidirect
15. #13073575C2semidirect
16. #13072069C2semidirect
17. #13072051C2semidirect
18. D11×#385C2semidirect
19. C11×#2693C2semidirect
28. C2×#66977C22semidirect
41. C2×#66937C22semidirect
46. C11×#400C22semidirect
48. C11×#396C22semidirect
51. C11×#386C22semidirect
53. C11×#380C22semidirect
55. #10622836C22semidirect
58. #10622826C22semidirect
60. #10622607C22semidirect
62. #10622605C22semidirect
63. #10622604C22semidirect
65. #10622592C22semidirect
66. #10622587C22semidirect
67. #10622586C22semidirect
68. #10622585C22semidirect
69. #10622574C22semidirect
73. #10622572C22semidirect
74. #10622570C22semidirect
79. #10622565C22semidirect
81. #10622561C22semidirect
82. #10622561C22semidirect
84. #10622557C22semidirect
87. #10622286C22semidirect
90. #10622283C22semidirect
92. #10622281C22semidirect
93. #10622281C22semidirect
98. #10622280C22semidirect
103. #10622270C22semidirect
104. #10622270C22semidirect
105. #10622270C22semidirect
106. #10622268C22semidirect
107. #10622268C22semidirect
201. C22⋊C4×D11D4semidirect
355. #2693D11semidirect
487. #400C2×D11semidirect
500. #396C2×D11semidirect
532. #386C2×D11semidirect
547. #380C2×D11semidirect
848. C11#36738semidirect

Maximal subgroups

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

subgroupindex
C2×#106231882
#130768972
#130755192
#130754332
#130753842
#130751562
#130750922
#130749212
#130749082
#130748672
#130748492
#130743512
#130743492
#130737992
#130735752
#130720692
#130720512
D11×#3852
C11×#26932
#3673811