Finite Group Databasebeta

← #14786767

Subgroups — #14786767

Order 2816.

1462 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622648C211yesmaximal, characteristic, complemented
2C2×#10622846C211yesmaximal, characteristic, complemented
3#13072913C211yesmaximal, characteristic, complemented
4#13069852C211yesmaximal, characteristic, complemented
5#13069852C211yesmaximal, characteristic, complemented
6#13069816C211yesmaximal, characteristic, complemented
7#13069809C211yesmaximal, characteristic, complemented
8#13069045C211yesmaximal, characteristic, complemented
9#13068909C211yesmaximal, characteristic, complemented
10#13068877C211yesmaximal, characteristic, complemented
11#13068863C211yesmaximal, characteristic, complemented
12#13068556C211yesmaximal, characteristic, complemented
13#13068547C211yesmaximal, characteristic, complemented
14#13068547C211yesmaximal, characteristic, complemented
15C2×C11×#546C211yesmaximal, characteristic
16C22×C11×#41C2211yescharacteristic
17C23×D4×C11C2211yescharacteristic
18C11×#546—24no—
19C11×#546—24no—
20C2×C11×#124C2211yescharacteristic
21C2×C11×#123—21no—
22C2×C11×C22⋊Q8C2211yescharacteristic
23C2×C11×#121—21no—
24C2×C11×#121C2211yescharacteristic
25C2×C11×#120—21no—
26C2×C4×D4×C11C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C22×C11×C22⋊C4—21no—
29C2×#66979C2211yescharacteristic, complemented
30C23×C11⋊C8C2211yescharacteristic, complemented
31#10622846—24no—
32C2×#66899C2211yescharacteristic, complemented
33C2×#66899C2211yescharacteristic, complemented
34C2×#66899C2211yescharacteristic, complemented
35C2×#66899C2211yescharacteristic, complemented
36#10622835—21no—
37C2×#66896C2211yescharacteristic
38C2×#66896C2211yescharacteristic
39C2×#66896C2211yescharacteristic
40C2×#66896C2211yescharacteristic
41C2×#66896C2211yescharacteristic
42C2×#66896C2211yescharacteristic
43C2×#66896C2211yescharacteristic
44C2×#66896C2211yescharacteristic
45#10622825C2211yescharacteristic
46#10622825C2211yescharacteristic
47#10622825C2211yescharacteristic, complemented
48C2×C22⋊(C11⋊C8)C2211yescharacteristic
49C2×C22⋊(C11⋊C8)C2211yescharacteristic
50C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
51#10622648—24no—
52#10622591—21no—
53C2×#66872C2211yescharacteristic, complemented
54C2×#66871C2211yescharacteristic, complemented
55#10622565—21no—
56#10622557—21no—
57#10622541C2211yescharacteristic, complemented
58#10622541C2211yescharacteristic, complemented
59#10622167C2211yescharacteristic, complemented
60#10622167C2211yescharacteristic, complemented
61#10622162C2211yescharacteristic, complemented
62#10622162C2211yescharacteristic, complemented
63C25×C11—21no—
64C2×C11×#41—22no—
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—41no—
68C2×C11×#41—41no—
69C2×C11×#41D414yes—
70C22×Q8×C11C2311yescharacteristic
71C22×D4×C11—21no—
72C22×D4×C11—21no—
73C22×D4×C11—22no—
74C22×D4×C11—22no—
75C22×D4×C11—22no—
76C22×D4×C11—22no—
77C22×D4×C11—21no—
78C22×D4×C11—41no—
79C22×D4×C11—41no—
80C22×D4×C11D411yescharacteristic
81C22×D4×C11C2311yescharacteristic
82C22×D4×C11C2311yescharacteristic
83C23×C4×C11—21no—
84C23×C4×C11—21no—
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C11×#124—22no—
88C11×#124—22no—
89C11×#123—28no—
90C11×C22⋊Q8—22no—
91C11×C22⋊Q8—22no—
92C11×#121—28no—
93C11×#121—22no—
94C11×#121D414yes—
95C11×#120—28no—
96C4×D4×C11—22no—
97C4×D4×C11—22no—
98C4×D4×C11—22no—
99C4×D4×C11—22no—
100C2×C11×C4⋊C4—21no—
101C2×C11×C4⋊C4D411yescharacteristic
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C11×C22⋊C4—28no—
104C2×C11×C22⋊C4—21no—
105C2×C11×C22⋊C4—21no—
106C2×C11×C22⋊C4—21no—
107C2×C11×C22⋊C4—21no—
108C2×C11×C22⋊C4—21no—
109C2×C11×C22⋊C4D411yescharacteristic
110C2×C11×C22⋊C4D411yescharacteristic
111C2×C42×C11C2311yescharacteristic
112C2×C22⋊Dic11—21no—
113C2×C22⋊Dic11—21no—
114C2×C22⋊Dic11—21no—
115C2×C22⋊Dic11—21no—
116#66979—22no—
117#66979—22no—
118C2×C4⋊Dic11C2311yescharacteristic
119C2×C4⋊Dic11C2311yescharacteristic
120C2×C4⋊Dic11C2311yescharacteristic
121C2×C4⋊Dic11C2311yescharacteristic
122C2×Dic11⋊C4—21no—
123C2×Dic11⋊C4—21no—
124C2×C4×Dic11—21no—
125C22×C11⋊C8—22no—
126C22×C11⋊C8—41no—
127C22×C11⋊C8—41no—
128C22×C11⋊C8C2311yescharacteristic
129C22×C11⋊C8C2311yescharacteristic
130C22×C11⋊C8C2311yescharacteristic
131C22×C11⋊C8C2311yescharacteristic
132#66899—22no—
133#66899—22no—
134#66899—41no—
135#66899—41no—
136#66896—22no—
137#66896—22no—
138#66896—22no—
139#66896—22no—
140#66896—22no—
141#66896—22no—
142#66896—41no—
143#66896—41no—
144C11⋊#95—21no—
145C11⋊#95—21no—
146C11⋊#95—21no—
147C11⋊#95—21no—
148C11⋊#95—21no—
149C22⋊(C11⋊C8)—22no—
150C22⋊(C11⋊C8)—41no—
151C22⋊(C11⋊C8)—41no—
152#66872—22no—
153#66871—22no—
154#24037—111nomaximal, Sylow
155C24×C11—21no—
156C24×C11—24no—
157C24×C11—21no—
158C24×C11—42no—
159C24×C11—42no—
160C24×C11—42no—
161C24×C11—42no—
162C24×C11—81no—
163C24×C11—81no—
164C24×C11C2×D411yescharacteristic
165C24×C11C2×D411yescharacteristic
166C11×#41—28no—
167C11×#41—44no—
168C11×#41—44no—
169C11×#41—44no—
170C2×Q8×C11—21no—
171C2×Q8×C11—21no—
172C2×Q8×C11—21no—
173C2×Q8×C11—21no—
174C2×Q8×C11—21no—
175C2×Q8×C11C2×D412yes—
176C2×D4×C11—24no—
177C2×D4×C11—22no—
178C2×D4×C11—24no—
179C2×D4×C11—22no—
180C2×D4×C11—24no—
181C2×D4×C11—21no—
182C2×D4×C11—21no—
183C2×D4×C11—21no—
184C2×D4×C11—21no—
185C2×D4×C11—21no—
186C2×D4×C11—21no—
187C2×D4×C11—21no—
188C2×D4×C11—21no—
189C2×D4×C11—41no—
190C2×D4×C11—42no—
191C2×D4×C11—42no—
192C2×D4×C11—44no—
193C2×D4×C11—44no—
194C2×D4×C11—44no—
195C2×D4×C11—42no—
196C2×D4×C11—42no—
197C2×D4×C11—44no—
198C2×D4×C11—81no—
199C2×D4×C11—81no—
200C2×D4×C11C2×D412yes—
201C2×D4×C11C2×D412yes—
202C2×D4×C11#4112yes—
203C2×D4×C11#4112yes—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—24no—
211C22×C4×C11—24no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—21no—
217C22×C4×C11—21no—
218C22×C4×C11—42no—
219C22×C4×C11—42no—
220C22×C4×C11—81no—
221C22×C4×C11—81no—
222C22×C4×C11C2×D411yescharacteristic
223C22×C4×C11C2×D411yescharacteristic
224C22×C4×C11C2×D411yescharacteristic
225C22×C4×C11C2×D411yescharacteristic
226C22×C4×C11C2×D412yes—
227C22×C4×C11C2×D412yes—
228C22×C4×C11C2411yescharacteristic
229C22×Dic11—21no—
230C22×Dic11—21no—
231C22×Dic11—21no—
232C22×Dic11—21no—
233C11×C4⋊C4—24no—
234C11×C4⋊C4—22no—
235C11×C4⋊C4—21no—
236C11×C4⋊C4C2×D412yes—
237C11×C22⋊C4—24no—
238C11×C22⋊C4—24no—
239C11×C22⋊C4—24no—
240C11×C22⋊C4—24no—
241C11×C22⋊C4—22no—
242C11×C22⋊C4—22no—
243C11×C22⋊C4—24no—
244C42×C11—21no—
245C42×C11—21no—
246C22⋊Dic11—42no—
247C22⋊Dic11—42no—
248C22⋊Dic11—81no—
249C22⋊Dic11—81no—
250C4⋊Dic11—21no—
251C4⋊Dic11—21no—
252C4⋊Dic11—21no—
253C4⋊Dic11—21no—
254C4⋊Dic11—21no—
255C4⋊Dic11—21no—
256C4⋊Dic11—21no—
257C4⋊Dic11—21no—
258Dic11⋊C4—42no—
259Dic11⋊C4—81no—
260C4×Dic11—42no—
261C2×C11⋊C8—21no—
262C2×C11⋊C8—21no—
263C2×C11⋊C8—21no—
264C2×C11⋊C8—21no—
265C2×C11⋊C8—21no—
266C2×C11⋊C8—21no—
267C2×C11⋊C8—21no—
268C2×C11⋊C8—21no—
269C2×C11⋊C8—21no—
270C2×C11⋊C8—21no—
271C2×C11⋊C8—21no—
272C2×C11⋊C8—21no—
273C2×C11⋊C8—44no—
274C2×#546D1111yescharacteristic
275C2×#482—111no—
276C2×#416—111no—
277#2485—111no—
278#2042—111no—
279#2042—111no—
280#2036—111no—
281#2035—111no—
282#1893—111no—
283#1869—111no—
284#1864—111no—
285#1862—111no—
286#1788—111no—
287#1786—111no—
288#1786—111no—
289C23×C11—21no—
290C23×C11—22no—
291C23×C11—21no—
292C23×C11—21no—
293C23×C11—21no—
294C23×C11—21no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11—21no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11—21no—
301C23×C11—21no—
302C23×C11—21no—
303C23×C11—21no—
304C23×C11—22no—
305C23×C11—48no—
306C23×C11—48no—
307C23×C11—41no—
308C23×C11—41no—
309C23×C11—41no—
310C23×C11—41no—
311C23×C11—41no—
312C23×C11—41no—
313C23×C11—41no—
314C23×C11—41no—
315C23×C11—41no—
316C23×C11—41no—
317C23×C11—84no—
318C23×C11—84no—
319C23×C11—84no—
320C23×C11—84no—
321C23×C11—84no—
322C23×C11#12012yes—
323C23×C11#13512yes—
324C23×C11C22×D411yescharacteristic
325Q8×C11—22no—
326Q8×C11—22no—
327Q8×C11—41no—
328Q8×C11—41no—
329D4×C11—22no—
330D4×C11—22no—
331D4×C11—22no—
332D4×C11—22no—
333D4×C11—22no—
334D4×C11—44no—
335D4×C11—48no—
336D4×C11—48no—
337D4×C11—41no—
338D4×C11—41no—
339D4×C11—84no—
340D4×C11#12314yes—
341C2×C4×C11—21no—
342C2×C4×C11—21no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—21no—
348C2×C4×C11—21no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—21no—
352C2×C4×C11—21no—
353C2×C4×C11—21no—
354C2×C4×C11—21no—
355C2×C4×C11—21no—
356C2×C4×C11—21no—
357C2×C4×C11—21no—
358C2×C4×C11—48no—
359C2×C4×C11—41no—
360C2×C4×C11—41no—
361C2×C4×C11—41no—
362C2×C4×C11—41no—
363C2×C4×C11—41no—
364C2×C4×C11—41no—
365C2×C4×C11—41no—
366C2×C4×C11—41no—
367C2×C4×C11—84no—
368C2×C4×C11#12012yes—
369C2×C4×C11C22×D411yescharacteristic
370C2×C4×C11C22×D411yescharacteristic
371C2×C4×C11C2×#4111yescharacteristic
372C2×C4×C11C2×#4111yescharacteristic
373C2×C4×C11H(5,𝔽2)11yescharacteristic
374C2×C4×C11H(5,𝔽2)11yescharacteristic
375C2×Dic11—41no—
376C2×Dic11—41no—
377C2×Dic11—41no—
378C2×Dic11—41no—
379C2×Dic11—41no—
380C2×Dic11—41no—
381C2×Dic11—41no—
382C2×Dic11—41no—
383C2×Dic11—41no—
384C2×Dic11—41no—
385C2×Dic11—41no—
386C2×Dic11—41no—
387C11⋊C8—41no—
388C11⋊C8—41no—
389C11⋊C8—41no—
390C11⋊C8—41no—
391C22×#41C2×D1111yescharacteristic
392C23×D4C2×D1111yescharacteristic
393C23×C8—111no—
394#546—24no—
395#546—24no—
396C2×#124C2×D1111yescharacteristic
397C2×#123—21no—
398C2×C22⋊Q8C2×D1111yescharacteristic
399C2×#121—21no—
400C2×#121C2×D1111yescharacteristic
401C2×#120—21no—
402C2×C4×D4C2×D1111yescharacteristic
403C2×C4×D4C2×D1111yescharacteristic
404C2×#117—111no—
405C22×C22⋊C4—21no—
406#482—224no—
407C2×#107—111no—
408C2×#106—111no—
409#416—224no—
410C2×#103—111no—
411C2×#103—111no—
412C2×#103—111no—
413C2×#103—111no—
414C2×#102—111no—
415C2×#102—111no—
416C2×#102—111no—
417C2×#102—111no—
418C2×#102—111no—
419C2×#102—111no—
420C2×#102—111no—
421C2×#102—111no—
422C2×C22⋊C8—111no—
423C2×C22⋊C8—111no—
424C2×C22⋊C8—111no—
425#397—221no—
426#394—221no—
427#389—111no—
428#389—111no—
429#388—221no—
430#387—221no—
431#380—111no—
432#380—111no—
433#380—111no—
434#340—111no—
435#340—111no—
436#336—111no—
437#336—111no—
438C22×C11—22no—
439C22×C11—24no—
440C22×C11—22no—
441C22×C11—22no—
442C22×C11—22no—
443C22×C11—22no—
444C22×C11—22no—
445C22×C11—41no—
446C22×C11—42no—
447C22×C11—42no—
448C22×C11—41no—
449C22×C11—41no—
450C22×C11—42no—
451C22×C11—41no—
452C22×C11—42no—
453C22×C11—41no—
454C22×C11—41no—
455C22×C11—42no—
456C22×C11—41no—
457C22×C11—41no—
458C22×C11—42no—
459C22×C11—42no—
460C22×C11—42no—
461C22×C11—42no—
462C22×C11—816no—
463C22×C11—81no—
464C22×C11—81no—
465C22×C11—81no—
466C22×C11—81no—
467C22×C11C2×#12011yescharacteristic
468C22×C11#54611yescharacteristic
469C22×C11#54611yescharacteristic
470C22×C11C2×#13511yescharacteristic
471C22×C11#57511yescharacteristic
472C22×C11#57611yescharacteristic
473C22×C11#57711yescharacteristic
474C4×C11—22no—
475C4×C11—41no—
476C4×C11—42no—
477C4×C11—41no—
478C4×C11—41no—
479C4×C11—42no—
480C4×C11C2×#12311yescharacteristic
481C4×C11#53411yescharacteristic
482C4×C11#54611yescharacteristic
483C4×C11#54611yescharacteristic
484Dic11—81no—
485Dic11—81no—
486Dic11—81no—
487Dic11—81no—
488C25—21no—
489C2×#41—22no—
490C2×#41—22no—
491C2×#41—22no—
492C2×#41—41no—
493C2×#41—41no—
494C2×#41C22⋊D1114yes—
495C22×Q8C22×D1111yescharacteristic
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—22no—
499C22×D4—22no—
500C22×D4—22no—
501C22×D4—22no—
502C22×D4—21no—
503C22×D4—41no—
504C22×D4—41no—
505C22×D4C22⋊D1111yescharacteristic
506C22×D4C22×D1111yescharacteristic
507C22×D4C22×D1111yescharacteristic
508C23×C4—21no—
509C23×C4—21no—
510C23×C4C22×D1111yescharacteristic
511C23×C4C22×D1111yescharacteristic
512C22×C8—111no—
513C22×C8—111no—
514C22×C8—111no—
515C22×C8—111no—
516C22×C8—222no—
517C22×C8—441no—
518C22×C8—441no—
519#124—22no—
520#124—22no—
521#123—28no—
522C22⋊Q8—22no—
523C22⋊Q8—22no—
524#121—28no—
525#121—22no—
526#121C22⋊D1114yes—
527#120—28no—
528C4×D4—22no—
529C4×D4—22no—
530C4×D4—22no—
531C4×D4—22no—
532#117—222no—
533#117—222no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—111no—
536C2×C4⋊C4—111no—
537C2×C4⋊C4—111no—
538C2×C4⋊C4—111no—
539C2×C4⋊C4—221no—
540C2×C4⋊C4—221no—
541C2×C4⋊C4C22⋊D1111yescharacteristic
542C2×C4⋊C4C22×D1111yescharacteristic
543C2×C22⋊C4—28no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—221no—
550C2×C22⋊C4—221no—
551C2×C22⋊C4—221no—
552C2×C22⋊C4—221no—
553C2×C22⋊C4C22⋊D1111yescharacteristic
554C2×C22⋊C4C22⋊D1111yescharacteristic
555C2×C42—221no—
556C2×C42C22×D1111yescharacteristic
557#107—222no—
558#106—222no—
559#103—222no—
560#103—222no—
561#103—441no—
562#103—441no—
563#102—222no—
564#102—222no—
565#102—222no—
566#102—222no—
567#102—222no—
568#102—222no—
569#102—441no—
570#102—441no—
571C22⋊C8—222no—
572C22⋊C8—441no—
573C22⋊C8—441no—
574#95—221no—
575#95—221no—
576#95—221no—
577#95—221no—
578#95—221no—
579C2×C11—42no—
580C2×C11—42no—
581C2×C11—44no—
582C2×C11—82no—
583C2×C11#240511yescharacteristic
584C2×C11#300211yescharacteristic
585C2×C11#301211yescharacteristic
586C2×C11#329611yescharacteristic
587C2×C11#329711yescharacteristic
588C2×C11#331111yescharacteristic
589C2×C11#331911yescharacteristic
590C24—21no—
591C24—24no—
592C24—21no—
593C24—42no—
594C24—42no—
595C24—42no—
596C24—42no—
597C24—81no—
598C24—81no—
599C24C2×C22⋊D1111yescharacteristic
600C24C2×C22⋊D1111yescharacteristic
601#41—28no—
602#41—44no—
603#41—44no—
604#41—44no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8C2×C22⋊D1112yes—
611C2×D4—24no—
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—24no—
615C2×D4—24no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—41no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—44no—
628C2×D4—44no—
629C2×D4—44no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—44no—
633C2×D4—81no—
634C2×D4—81no—
635C2×D4#434112yes—
636C2×D4#434112yes—
637C2×D4C2×C22⋊D1112yes—
638C2×D4C2×C22⋊D1112yes—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—24no—
646C22×C4—24no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—42no—
654C22×C4—42no—
655C22×C4—81no—
656C22×C4—81no—
657C22×C4—221no—
658C22×C4—221no—
659C22×C4—221no—
660C22×C4—221no—
661C22×C4C2×C22⋊D1111yescharacteristic
662C22×C4C2×C22⋊D1111yescharacteristic
663C22×C4C2×C22⋊D1111yescharacteristic
664C22×C4C2×C22⋊D1111yescharacteristic
665C22×C4C2×C22⋊D1112yes—
666C22×C4C2×C22⋊D1112yes—
667C22×C4C23×D1111yescharacteristic
668C2×C8—221no—
669C2×C8—221no—
670C2×C8—221no—
671C2×C8—221no—
672C2×C8—221no—
673C2×C8—221no—
674C2×C8—221no—
675C2×C8—221no—
676C2×C8—221no—
677C2×C8—221no—
678C2×C8—221no—
679C2×C8—221no—
680C2×C8—444no—
681C4⋊C4—24no—
682C4⋊C4—22no—
683C4⋊C4—21no—
684C4⋊C4—221no—
685C4⋊C4—221no—
686C4⋊C4—221no—
687C4⋊C4—221no—
688C4⋊C4—221no—
689C4⋊C4—221no—
690C4⋊C4—221no—
691C4⋊C4—221no—
692C4⋊C4—442no—
693C4⋊C4—881no—
694C4⋊C4C2×C22⋊D1112yes—
695C22⋊C4—24no—
696C22⋊C4—24no—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—22no—
700C22⋊C4—22no—
701C22⋊C4—24no—
702C22⋊C4—442no—
703C22⋊C4—442no—
704C22⋊C4—881no—
705C22⋊C4—881no—
706C42—21no—
707C42—21no—
708C42—442no—
709C11#2403711yescharacteristic, complemented, Sylow
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—22no—
715C23—22no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—22no—
725C23—22no—
726C23—48no—
727C23—48no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—84no—
739C23—84no—
740C23—84no—
741C23—84no—
742C23—84no—
743C23#6700312yes—
744C23#6700612yes—
745C23C22×C22⋊D1111yescharacteristic
746Q8—22no—
747Q8—22no—
748Q8—41no—
749Q8—41no—
750D4—22no—
751D4—22no—
752D4—22no—
753D4—22no—
754D4—22no—
755D4—44no—
756D4—48no—
757D4—48no—
758D4—41no—
759D4—41no—
760D4—84no—
761D4#6698814yes—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—48no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—84no—
789C2×C4—441no—
790C2×C4—441no—
791C2×C4—441no—
792C2×C4—441no—
793C2×C4—441no—
794C2×C4—441no—
795C2×C4—441no—
796C2×C4—441no—
797C2×C4—441no—
798C2×C4—441no—
799C2×C4—441no—
800C2×C4—441no—
801C2×C4#6700612yes—
802C2×C4C2×#434111yescharacteristic
803C2×C4C2×#434111yescharacteristic
804C2×C4#6703711yescharacteristic
805C2×C4#6703711yescharacteristic
806C2×C4C22×C22⋊D1111yescharacteristic
807C2×C4C22×C22⋊D1111yescharacteristic
808C8—441no—
809C8—441no—
810C8—441no—
811C8—441no—
812C22—22no—
813C22—24no—
814C22—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—41no—
820C22—42no—
821C22—41no—
822C22—41no—
823C22—42no—
824C22—41no—
825C22—42no—
826C22—41no—
827C22—42no—
828C22—42no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—816no—
837C22—81no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22#1062333711yescharacteristic
842C22#1062333711yescharacteristic
843C22C2×#6700311yescharacteristic
844C22#1062335311yescharacteristic
845C22#1062336611yescharacteristic
846C22#1062336711yescharacteristic
847C22C2×#6700611yescharacteristic
848C4—22no—
849C4—41no—
850C4—42no—
851C4—41no—
852C4—41no—
853C4—42no—
854C4—881no—
855C4—881no—
856C4—881no—
857C4—881no—
858C4C2×#6698811yescharacteristic
859C4#1062333511yescharacteristic
860C4#1062333711yescharacteristic
861C4#1062333711yescharacteristic
862C2—42no—
863C2—42no—
864C2—44no—
865C2—82no—
866C2#1307193911yescharacteristic
867C2#1307783411yescharacteristic
868C2#1307792011yescharacteristic
869C2#1308045111yescharacteristic
870C2#1308046611yescharacteristic
871C2#1308065211yescharacteristic
872C2#1308077211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#546C2
socleC23×C11C22×D4
hypercenterC2×#546D11
hypocenterC11#24037
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. C2×#10622648C2semidirect
2. C2×#10622846C2semidirect
3. #13072913C2semidirect
4. #13069852C2semidirect
5. #13069852C2semidirect
6. #13069816C2semidirect
7. #13069809C2semidirect
8. #13069045C2semidirect
9. #13068909C2semidirect
10. #13068877C2semidirect
11. #13068863C2semidirect
12. #13068556C2semidirect
13. #13068547C2semidirect
14. #13068547C2semidirect
29. C2×#66979C22semidirect
30. C23×C11⋊C8C22semidirect
32. C2×#66899C22semidirect
33. C2×#66899C22semidirect
34. C2×#66899C22semidirect
35. C2×#66899C22semidirect
47. #10622825C22semidirect
50. C2×C22⋊(C11⋊C8)C22semidirect
53. C2×#66872C22semidirect
54. C2×#66871C22semidirect
57. #10622541C22semidirect
58. #10622541C22semidirect
59. #10622167C22semidirect
60. #10622167C22semidirect
61. #10622162C22semidirect
62. #10622162C22semidirect
709. C11#24037semidirect

Maximal subgroups

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

subgroupindex
C2×#106226482
C2×#106228462
#130729132
#130698522
#130698162
#130698092
#130690452
#130689092
#130688772
#130688632
#130685562
#130685472
C2×C11×#5462
#2403711