Finite Group Databasebeta

← #14786420

Subgroups — #14786420

Order 2816.

1520 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623359C211yesmaximal, characteristic
2C2×#10622418C211yesmaximal, characteristic, complemented
3C2×#10622387C211yesmaximal, characteristic, complemented
4D11×#380C211yesmaximal, characteristic, complemented
5#13069818C211yesmaximal, characteristic, complemented
6#13069817C211yesmaximal, characteristic, complemented
7#13069804C211yesmaximal, characteristic, complemented
8#13069803C211yesmaximal, characteristic, complemented
9#13068930C211yesmaximal, characteristic, complemented
10#13068920C211yesmaximal, characteristic, complemented
11#13068817C211yesmaximal, characteristic, complemented
12#13068813C211yesmaximal, characteristic, complemented
13#13068556C211yesmaximal, characteristic, complemented
14#13068525C211yesmaximal, characteristic, complemented
15C11×#1788C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18#10623359—24no—
19#10623359—24no—
20C2×#66999C2211yescharacteristic
21C2×#66999C2211yescharacteristic
22C2×#66991C2211yescharacteristic
23C2×#66991C2211yescharacteristic
24C2×#66990—21no—
25C2×#66988—21no—
26C2×C4×C22⋊D11—21no—
27C2×C4×C22⋊D11—21no—
28C2×#66979C2211yescharacteristic
29C2×C4⋊C4×D11C2211yescharacteristic
30C2×C4⋊C4×D11C2211yescharacteristic
31C2×C22⋊C4×D11—21no—
32C2×C11×#103C2211yescharacteristic, complemented
33C2×C11×#103C2211yescharacteristic, complemented
34C2×C11×#102C2211yescharacteristic, complemented
35C2×C11×#102C2211yescharacteristic, complemented
36C2×C11×C22⋊C8C2211yescharacteristic
37C11×#380C2211yescharacteristic
38C2×#66899C2211yescharacteristic, complemented
39C2×#66899C2211yescharacteristic, complemented
40C2×#66896C2211yescharacteristic, complemented
41C2×#66896C2211yescharacteristic, complemented
42#10622825C2211yescharacteristic
43C2×C22⋊(C11⋊C8)C2211yescharacteristic
44C2×(C2×D11)⋊C8C2211yescharacteristic
45C2×(C2×D11)⋊C8C2211yescharacteristic
46C2×(C2×D11)⋊C8C2211yescharacteristic
47C2×(C2×D11)⋊C8C2211yescharacteristic
48C2×#66882C2211yescharacteristic, complemented
49C2×#66881C2211yescharacteristic, complemented
50#10622600C2211yescharacteristic
51#10622600C2211yescharacteristic
52C2×#66872C2211yescharacteristic, complemented
53C2×#66871C2211yescharacteristic, complemented
54#10622555—21no—
55#10622418—24no—
56#10622387—24no—
57#10622280—21no—
58D11×#95—21no—
59#10622189C2211yescharacteristic, complemented
60#10622189C2211yescharacteristic, complemented
61#10622167C2211yescharacteristic, complemented
62#10622167C2211yescharacteristic, complemented
63C24×D11D411yescharacteristic
64C2×C11×#41—22no—
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—22no—
68C2×C11×#41—41no—
69C2×C11×#41—41no—
70C22×Q8×C11C2311yescharacteristic
71C22×D4×C11—21no—
72C22×D4×C11C2311yescharacteristic
73C23×C4×C11—21no—
74C23×C4×C11C2311yescharacteristic
75C22×C22⋊D11—21no—
76C22×C22⋊D11—21no—
77C23×Dic11D411yescharacteristic
78C22×C4×D11—22no—
79C22×C4×D11—22no—
80C22×C4×D11—22no—
81C22×C4×D11—22no—
82C22×C4×D11—21no—
83C22×C4×D11—21no—
84C22×C4×D11—41no—
85C22×C4×D11—41no—
86C22×C4×D11D411yescharacteristic
87C22×C4×D11D411yescharacteristic
88C22×C4×D11C2311yescharacteristic
89C22×C4×D11C2311yescharacteristic
90C22×C8×C11C2311yescharacteristic
91C22×C8×C11C2311yescharacteristic
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C22⋊C4—21no—
95C2×C22⋊Dic11—21no—
96C2×C22⋊Dic11—21no—
97C2×C22⋊Dic11—21no—
98C2×C22⋊Dic11—21no—
99#66999—22no—
100#66999—22no—
101#66999—22no—
102#66999D414yes—
103#66991—22no—
104#66991—22no—
105#66991—22no—
106#66991D414yes—
107#66990—28no—
108#66988—28no—
109C4×C22⋊D11—28no—
110C4×C22⋊D11—28no—
111C2×(C2×D11)⋊C4—21no—
112C2×(C2×D11)⋊C4—21no—
113C2×(C2×D11)⋊C4—21no—
114C2×(C2×D11)⋊C4—21no—
115#66979—22no—
116#66979—22no—
117C2×C4⋊Dic11C2311yescharacteristic
118C2×C4⋊Dic11C2311yescharacteristic
119C2×C4⋊Dic11C2311yescharacteristic
120C2×C4⋊Dic11C2311yescharacteristic
121C2×Dic11⋊C4—21no—
122C2×Dic11⋊C4—21no—
123C2×Dic11⋊C4—21no—
124C2×Dic11⋊C4—21no—
125C2×C4×Dic11—21no—
126C22×C11⋊C8C2311yescharacteristic
127C22×C11⋊C8C2311yescharacteristic
128C4⋊C4×D11—22no—
129C4⋊C4×D11—22no—
130C4⋊C4×D11—41no—
131C4⋊C4×D11—41no—
132C22⋊C4×D11—44no—
133C11×#103—22no—
134C11×#103—41no—
135C11×#102—22no—
136C11×#102—41no—
137C11×C22⋊C8—22no—
138C11×#95—21no—
139#66899—22no—
140#66899—41no—
141#66896—22no—
142#66896—41no—
143C11⋊#95—21no—
144C11⋊#95—21no—
145C11⋊#95—21no—
146C22⋊(C11⋊C8)—22no—
147(C2×D11)⋊C8—22no—
148(C2×D11)⋊C8—22no—
149(C2×D11)⋊C8—41no—
150(C2×D11)⋊C8—41no—
151#66882—22no—
152#66881—22no—
153#66872—22no—
154#66871—22no—
155#24004—111nomaximal, Sylow
156C24×C11—21no—
157C24×C11C2×D411yescharacteristic
158C23×D11—22no—
159C23×D11—22no—
160C23×D11—22no—
161C23×D11—22no—
162C23×D11—22no—
163C23×D11—41no—
164C23×D11—41no—
165C23×D11C2×D411yescharacteristic
166C23×D11C2×D411yescharacteristic
167C11×#41—44no—
168C11×#41—44no—
169C11×#41—44no—
170C11×#41—44no—
171C2×Q8×C11—21no—
172C2×Q8×C11—21no—
173C2×Q8×C11—21no—
174C2×Q8×C11—21no—
175C2×Q8×C11—21no—
176C2×Q8×C11C2×D412yes—
177C2×D4×C11—24no—
178C2×D4×C11—21no—
179C2×D4×C11—21no—
180C2×D4×C11—21no—
181C2×D4×C11—21no—
182C2×D4×C11—21no—
183C2×D4×C11—42no—
184C2×D4×C11—42no—
185C2×D4×C11C2×D412yes—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—24no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—42no—
195C22×C4×C11—42no—
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11#4112yes—
198C22×C4×C11#4112yes—
199C22×C4×C11C2411yescharacteristic
200C2×C22⋊D11—24no—
201C2×C22⋊D11—24no—
202C2×C22⋊D11—42no—
203C2×C22⋊D11—42no—
204C2×C22⋊D11—42no—
205C2×C22⋊D11—42no—
206C22×Dic11—22no—
207C22×Dic11—22no—
208C22×Dic11—21no—
209C22×Dic11—21no—
210C22×Dic11—21no—
211C22×Dic11—21no—
212C22×Dic11—41no—
213C22×Dic11C2×D411yescharacteristic
214C22×Dic11C2×D411yescharacteristic
215C2×C4×D11—22no—
216C2×C4×D11—22no—
217C2×C4×D11—22no—
218C2×C4×D11—22no—
219C2×C4×D11—21no—
220C2×C4×D11—21no—
221C2×C4×D11—21no—
222C2×C4×D11—21no—
223C2×C4×D11—21no—
224C2×C4×D11—21no—
225C2×C4×D11—21no—
226C2×C4×D11—21no—
227C2×C4×D11—21no—
228C2×C4×D11—21no—
229C2×C4×D11—41no—
230C2×C4×D11—41no—
231C2×C4×D11—44no—
232C2×C4×D11—44no—
233C2×C4×D11—44no—
234C2×C4×D11—44no—
235C2×C4×D11—42no—
236C2×C4×D11—42no—
237C2×C4×D11—42no—
238C2×C4×D11—42no—
239C2×C4×D11—42no—
240C2×C4×D11—42no—
241C2×C4×D11C2×D412yes—
242C2×C4×D11C2×D412yes—
243C2×C8×C11—21no—
244C2×C8×C11—21no—
245C2×C8×C11—21no—
246C2×C8×C11—21no—
247C2×C8×C11—21no—
248C2×C8×C11—21no—
249C11×C4⋊C4—21no—
250C11×C4⋊C4—21no—
251C11×C4⋊C4—21no—
252C11×C4⋊C4—21no—
253C11×C22⋊C4—42no—
254C22⋊Dic11—24no—
255C22⋊Dic11—24no—
256C22⋊Dic11—24no—
257C22⋊Dic11—42no—
258(C2×D11)⋊C4—24no—
259(C2×D11)⋊C4—24no—
260(C2×D11)⋊C4—42no—
261(C2×D11)⋊C4—42no—
262C4⋊Dic11—21no—
263C4⋊Dic11—21no—
264C4⋊Dic11—21no—
265C4⋊Dic11—21no—
266C4⋊Dic11—21no—
267C4⋊Dic11—21no—
268C4⋊Dic11C2×D412yes—
269C4⋊Dic11C2×D412yes—
270Dic11⋊C4—24no—
271Dic11⋊C4—24no—
272Dic11⋊C4—42no—
273Dic11⋊C4—42no—
274C4×Dic11—24no—
275C2×C11⋊C8—21no—
276C2×C11⋊C8—21no—
277C2×C11⋊C8—21no—
278C2×C11⋊C8—21no—
279C2×C11⋊C8—21no—
280C2×C11⋊C8—21no—
281C2×#525—111no—
282C2×#483—111no—
283C2×#480—111no—
284C2×#380—111no—
285#2036—111no—
286#2036—111no—
287#2034—111no—
288#2034—111no—
289#1874—111no—
290#1872—111no—
291#1854—111no—
292#1854—111no—
293#1788—111no—
294#1788D1111yescharacteristic, complemented
295#1779—111no—
296C23×C11—21no—
297C23×C11—21no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11—21no—
301C23×C11—21no—
302C23×C11—22no—
303C23×C11—41no—
304C23×C11—41no—
305C23×C11—41no—
306C23×C11—41no—
307C23×C11—41no—
308C23×C11—41no—
309C23×C11#12312yes—
310C23×C11C22×D411yescharacteristic
311C22×D11—21no—
312C22×D11—21no—
313C22×D11—21no—
314C22×D11—21no—
315C22×D11—28no—
316C22×D11—21no—
317C22×D11—21no—
318C22×D11—21no—
319C22×D11—21no—
320C22×D11—21no—
321C22×D11—21no—
322C22×D11—44no—
323C22×D11—44no—
324C22×D11—44no—
325C22×D11—44no—
326C22×D11—44no—
327C22×D11—44no—
328C22×D11#12012yes—
329C22×D11#13512yes—
330C22×D11AGL(1,ℤ/8)12yes—
331C22×D11#13712yes—
332Q8×C11—22no—
333Q8×C11—22no—
334Q8×C11—41no—
335Q8×C11—41no—
336D4×C11—22no—
337D4×C11—22no—
338D4×C11—48no—
339D4×C11—41no—
340D4×C11—41no—
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—22no—
348C2×C4×C11—48no—
349C2×C4×C11—41no—
350C2×C4×C11—41no—
351C2×C4×C11—41no—
352C2×C4×C11—41no—
353C2×C4×C11—41no—
354C2×C4×C11—41no—
355C2×C4×C11—41no—
356C2×C4×C11—41no—
357C2×C4×C11#12312yes—
358C2×C4×C11C22×D411yescharacteristic
359C2×C4×C11C22×D411yescharacteristic
360C2×C4×C11C2×#4111yescharacteristic
361C2×C4×C11C2×#4111yescharacteristic
362C2×C4×C11H(5,𝔽2)11yescharacteristic
363C2×C4×C11H(5,𝔽2)11yescharacteristic
364C22⋊D11—48no—
365C22⋊D11—48no—
366C2×Dic11—21no—
367C2×Dic11—21no—
368C2×Dic11—22no—
369C2×Dic11—22no—
370C2×Dic11—21no—
371C2×Dic11—21no—
372C2×Dic11—21no—
373C2×Dic11—44no—
374C2×Dic11—41no—
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#12012yes—
385C4×D11—22no—
386C4×D11—22no—
387C4×D11—22no—
388C4×D11—22no—
389C4×D11—44no—
390C4×D11—44no—
391C4×D11—41no—
392C4×D11—41no—
393C4×D11—41no—
394C4×D11—41no—
395C4×D11—84no—
396C4×D11—84no—
397C8×C11—41no—
398C8×C11—41no—
399C11⋊C8—41no—
400C11⋊C8—41no—
401C22×#41C2×D1111yescharacteristic
402C24×C4—111no—
403#525—224no—
404#525—224no—
405C2×#123—221no—
406C2×C22⋊Q8—111no—
407C2×C22⋊Q8—111no—
408C2×#121—111no—
409C2×#121—111no—
410C2×#120—221no—
411C2×C4×D4—221no—
412C2×C4×D4—221no—
413C2×#117—111no—
414C22×C4⋊C4—111no—
415C22×C4⋊C4—111no—
416C22×C22⋊C4—221no—
417#483—224no—
418#480—224no—
419C2×#107—111no—
420C2×#107—111no—
421C2×#106—111no—
422C2×#106—111no—
423C2×#103—111no—
424C2×#103—111no—
425C2×#103C2×D1111yescharacteristic, complemented
426C2×#103C2×D1111yescharacteristic, complemented
427C2×#102—111no—
428C2×#102—111no—
429C2×#102C2×D1111yescharacteristic, complemented
430C2×#102C2×D1111yescharacteristic, complemented
431C2×C22⋊C8—111no—
432C2×C22⋊C8—111no—
433C2×C22⋊C8—111no—
434C2×C22⋊C8—111no—
435C2×C22⋊C8—111no—
436C2×C22⋊C8C2×D1111yescharacteristic
437#380—111no—
438#380—111no—
439#380—111no—
440#380—221no—
441#380—221no—
442#380C2×D1111yescharacteristic
443C2×#95—221no—
444#340—111no—
445#340—111no—
446#340—111no—
447#340—111no—
448C22×C11—22no—
449C22×C11—22no—
450C22×C11—22no—
451C22×C11—41no—
452C22×C11—41no—
453C22×C11—41no—
454C22×C11—41no—
455C22×C11—42no—
456C22×C11—42no—
457C22×C11—42no—
458C22×C11—81no—
459C22×C11—81no—
460C22×C11—81no—
461C22×C11—81no—
462C22×C11C2×#12011yescharacteristic
463C22×C11C2×#12311yescharacteristic
464C22×C11#53411yescharacteristic
465C22×C11C2×#13511yescharacteristic
466C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
467C22×C11C2×#13711yescharacteristic
468C22×C11#57511yescharacteristic
469C2×D11—22no—
470C2×D11—22no—
471C2×D11—22no—
472C2×D11—22no—
473C2×D11—22no—
474C2×D11—22no—
475C2×D11—22no—
476C2×D11—22no—
477C2×D11—22no—
478C2×D11—416no—
479C2×D11—41no—
480C2×D11—41no—
481C2×D11—41no—
482C2×D11—41no—
483C2×D11#44914yes—
484C4×C11—22no—
485C4×C11—42no—
486C4×C11—81no—
487C4×C11—81no—
488C4×C11#54611yescharacteristic
489C4×C11#54611yescharacteristic
490C4×C11#54611yescharacteristic
491C4×C11#54611yescharacteristic
492Dic11—22no—
493Dic11—41no—
494Dic11—42no—
495Dic11—42no—
496Dic11—81no—
497Dic11—81no—
498C25—111no—
499C2×#41—22no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—41no—
504C2×#41—41no—
505C22×Q8C22×D1111yescharacteristic
506C22×D4—21no—
507C22×D4—221no—
508C22×D4—221no—
509C22×D4C22×D1111yescharacteristic
510C23×C4—21no—
511C23×C4—111no—
512C23×C4—111no—
513C23×C4—111no—
514C23×C4—111no—
515C23×C4—111no—
516C23×C4—222no—
517C23×C4—222no—
518C23×C4—221no—
519C23×C4—221no—
520C23×C4—222no—
521C23×C4—222no—
522C23×C4—441no—
523C23×C4—441no—
524C23×C4C22×D1111yescharacteristic
525C22×C8—111no—
526C22×C8—111no—
527C22×C8C22×D1111yescharacteristic
528C22×C8C22×D1111yescharacteristic
529#123—228no—
530C22⋊Q8—114no—
531C22⋊Q8—222no—
532C22⋊Q8—222no—
533C22⋊Q8—222no—
534#121—114no—
535#121—222no—
536#121—222no—
537#121—222no—
538#120—228no—
539C4×D4—228no—
540C4×D4—228no—
541#117—222no—
542#117—222no—
543C2×C4⋊C4—111no—
544C2×C4⋊C4—111no—
545C2×C4⋊C4—111no—
546C2×C4⋊C4—111no—
547C2×C4⋊C4—222no—
548C2×C4⋊C4—222no—
549C2×C4⋊C4—221no—
550C2×C4⋊C4—221no—
551C2×C4⋊C4—221no—
552C2×C4⋊C4—221no—
553C2×C4⋊C4—441no—
554C2×C4⋊C4—441no—
555C2×C4⋊C4C22×D1111yescharacteristic
556C2×C4⋊C4C22×D1111yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—221no—
559C2×C22⋊C4—221no—
560C2×C22⋊C4—221no—
561C2×C22⋊C4—221no—
562C2×C22⋊C4—221no—
563C2×C22⋊C4—221no—
564C2×C22⋊C4—221no—
565C2×C22⋊C4—221no—
566C2×C22⋊C4—444no—
567C2×C42—221no—
568#107—222no—
569#107—222no—
570#106—222no—
571#106—222no—
572#103—22no—
573#103—41no—
574#103—222no—
575#103—441no—
576#102—22no—
577#102—41no—
578#102—222no—
579#102—441no—
580C22⋊C8—22no—
581C22⋊C8—222no—
582C22⋊C8—222no—
583C22⋊C8—222no—
584C22⋊C8—441no—
585C22⋊C8—441no—
586#95—21no—
587#95—221no—
588#95—221no—
589#95—221no—
590C2×C11—42no—
591C2×C11—82no—
592C2×C11#240511yescharacteristic
593C2×C11C2×#44911yescharacteristic
594C2×C11#300711yescharacteristic
595C2×C11#309111yescharacteristic
596C2×C11#309211yescharacteristic
597C2×C11#319011yescharacteristic
598C2×C11#319411yescharacteristic
599D11—24no—
600D11—42no—
601C24—21no—
602C24—111no—
603C24—111no—
604C24—222no—
605C24—222no—
606C24—222no—
607C24—222no—
608C24—222no—
609C24—441no—
610C24—441no—
611C24D4×D1111yescharacteristic
612#41—44no—
613#41—44no—
614#41—44no—
615#41—44no—
616C2×Q8—21no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8D4×D1112yes—
622C2×D4—24no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—42no—
629C2×D4—42no—
630C2×D4—224no—
631C2×D4—224no—
632C2×D4—442no—
633C2×D4—442no—
634C2×D4—442no—
635C2×D4—442no—
636C2×D4D4×D1112yes—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—24no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—42no—
646C22×C4—42no—
647C22×C4—111no—
648C22×C4—112no—
649C22×C4—112no—
650C22×C4—111no—
651C22×C4—222no—
652C22×C4—222no—
653C22×C4—222no—
654C22×C4—221no—
655C22×C4—221no—
656C22×C4—221no—
657C22×C4—221no—
658C22×C4—222no—
659C22×C4—221no—
660C22×C4—221no—
661C22×C4—222no—
662C22×C4—222no—
663C22×C4—221no—
664C22×C4—221no—
665C22×C4—221no—
666C22×C4—221no—
667C22×C4—221no—
668C22×C4—221no—
669C22×C4—221no—
670C22×C4—221no—
671C22×C4—441no—
672C22×C4—441no—
673C22×C4—444no—
674C22×C4—444no—
675C22×C4—444no—
676C22×C4—444no—
677C22×C4—442no—
678C22×C4—442no—
679C22×C4—442no—
680C22×C4—442no—
681C22×C4—442no—
682C22×C4—442no—
683C22×C4—441no—
684C22×C4#433912yes—
685C22×C4D4×D1111yescharacteristic
686C22×C4#434112yes—
687C22×C4C23×D1111yescharacteristic
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—221no—
695C2×C8—221no—
696C2×C8—221no—
697C2×C8—221no—
698C2×C8—221no—
699C2×C8—221no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—112no—
705C4⋊C4—112no—
706C4⋊C4—224no—
707C4⋊C4—224no—
708C4⋊C4—221no—
709C4⋊C4—221no—
710C4⋊C4—221no—
711C4⋊C4—221no—
712C4⋊C4—221no—
713C4⋊C4—221no—
714C4⋊C4—442no—
715C4⋊C4—442no—
716C22⋊C4—42no—
717C22⋊C4—224no—
718C22⋊C4—224no—
719C22⋊C4—224no—
720C22⋊C4—224no—
721C22⋊C4—224no—
722C22⋊C4—442no—
723C22⋊C4—442no—
724C22⋊C4—442no—
725C42—224no—
726C11#2400411yescharacteristic, complemented, Sylow
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—22no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—112no—
741C23—112no—
742C23—112no—
743C23—112no—
744C23—228no—
745C23—221no—
746C23—221no—
747C23—221no—
748C23—221no—
749C23—221no—
750C23—221no—
751C23—221no—
752C23—221no—
753C23—221no—
754C23—221no—
755C23—444no—
756C23—444no—
757C23—444no—
758C23—444no—
759C23—444no—
760C23—444no—
761C23#6693612yes—
762C23C2×D4×D1111yescharacteristic
763Q8—22no—
764Q8—22no—
765Q8—41no—
766Q8—41no—
767D4—22no—
768D4—22no—
769D4—48no—
770D4—41no—
771D4—41no—
772D4—448no—
773D4—448no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—48no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—112no—
791C2×C4—221no—
792C2×C4—221no—
793C2×C4—222no—
794C2×C4—222no—
795C2×C4—222no—
796C2×C4—222no—
797C2×C4—221no—
798C2×C4—222no—
799C2×C4—222no—
800C2×C4—221no—
801C2×C4—221no—
802C2×C4—444no—
803C2×C4—444no—
804C2×C4—444no—
805C2×C4—441no—
806C2×C4—441no—
807C2×C4—441no—
808C2×C4—441no—
809C2×C4—441no—
810C2×C4—441no—
811C2×C4—441no—
812C2×C4—441no—
813C2×C4—441no—
814C2×C4—441no—
815C2×C4—441no—
816C2×C4—441no—
817C2×C4—441no—
818C2×C4—441no—
819C2×C4—884no—
820C2×C4—884no—
821C2×C4#6693612yes—
822C2×C4C2×#433911yescharacteristic
823C2×C4C2×D4×D1111yescharacteristic
824C2×C4C2×D4×D1111yescharacteristic
825C2×C4C2×#434111yescharacteristic
826C2×C4#6703711yescharacteristic
827C2×C4#6703711yescharacteristic
828C8—41no—
829C8—41no—
830C8—441no—
831C8—441no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—81no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—114no—
847C22—222no—
848C22—222no—
849C22—222no—
850C22—222no—
851C22—222no—
852C22—222no—
853C22—222no—
854C22—222no—
855C22—222no—
856C22—4416no—
857C22—441no—
858C22—441no—
859C22—441no—
860C22—441no—
861C22C2×#6693611yescharacteristic
862C22D11×#12011yescharacteristic
863C22#1062312011yescharacteristic
864C22D11×#13511yescharacteristic
865C22#1062329911yescharacteristic
866C22D11×AGL(1,ℤ/8)11yescharacteristic
867C22D11×#13711yescharacteristic
868C4—22no—
869C4—42no—
870C4—81no—
871C4—81no—
872C4—222no—
873C4—442no—
874C4—441no—
875C4—442no—
876C4—881no—
877C4—881no—
878C4#1062302111yescharacteristic
879C4#1062302111yescharacteristic
880C4#1062312211yescharacteristic
881C4#1062312211yescharacteristic
882C2—42no—
883C2—82no—
884C2—224no—
885C2—442no—
886C2#1307194111yescharacteristic
887C2D11×#44911yescharacteristic
888C2#1307787311yescharacteristic
889C2#1307852711yescharacteristic
890C2#1307853711yescharacteristic
891C2#1307939511yescharacteristic
892C2#1307942811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1788C2
socleC23×C11C22×D4
prime radicalC2×#10623359C2
hypercenter#1788D11
hypocenterC11#24004
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
2. C2×#10622418C2semidirect
3. C2×#10622387C2semidirect
4. D11×#380C2semidirect
5. #13069818C2semidirect
6. #13069817C2semidirect
7. #13069804C2semidirect
8. #13069803C2semidirect
9. #13068930C2semidirect
10. #13068920C2semidirect
11. #13068817C2semidirect
12. #13068813C2semidirect
13. #13068556C2semidirect
14. #13068525C2semidirect
15. C11×#1788C2semidirect
32. C2×C11×#103C22semidirect
33. C2×C11×#103C22semidirect
34. C2×C11×#102C22semidirect
35. C2×C11×#102C22semidirect
38. C2×#66899C22semidirect
39. C2×#66899C22semidirect
40. C2×#66896C22semidirect
41. C2×#66896C22semidirect
48. C2×#66882C22semidirect
49. C2×#66881C22semidirect
52. C2×#66872C22semidirect
53. C2×#66871C22semidirect
59. #10622189C22semidirect
60. #10622189C22semidirect
61. #10622167C22semidirect
62. #10622167C22semidirect
294. #1788D11semidirect
425. C2×#103C2×D11semidirect
426. C2×#103C2×D11semidirect
429. C2×#102C2×D11semidirect
430. C2×#102C2×D11semidirect
726. C11#24004semidirect

Maximal subgroups

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

subgroupindex
C2×#106233592
C2×#106224182
C2×#106223872
D11×#3802
#130698182
#130698172
#130698042
#130698032
#130689302
#130689202
#130688172
#130688132
#130685562
#130685252
C11×#17882
#2400411