Finite Group Databasebeta

← #14660288

Subgroups — #14660288

Order 2816.

1630 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623359C211yesmaximal, characteristic
2C22×#66901C211yesmaximal, characteristic, complemented
3C2×#10622739C211yesmaximal, characteristic, complemented
4C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
5C2×#10622193C211yesmaximal, characteristic, complemented
6C2×#10622161C211yesmaximal, characteristic, complemented
7C22×C11×#104C211yesmaximal, characteristic, complemented
8C22×C11×#41C2211yescharacteristic
9C23×C4×D11C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C22×C42×C11C2211yescharacteristic
12#10623359—22no—
13#10623359—22no—
14#10623359—22no—
15#10623359—22no—
16C2×#66999C412yescomplemented
17C2×#66991C412yescomplemented
18C2×#66990—21no—
19C2×#66988—21no—
20C2×C4×C22⋊D11—22no—
21C22×(C2×D11)⋊C4—21no—
22C2×#66979C2211yescharacteristic
23C22×C4×Dic11C2211yescharacteristic
24C22×#4318C2211yescharacteristic
25C2×C11×#104—22no—
26C2×C11×#104—22no—
27C2×C11×#104—22no—
28C2×#66901—22no—
29C2×#66901—22no—
30C2×#66901—22no—
31C2×C11⋊#95—21no—
32#10622739—22no—
33#10622739—22no—
34C2×(C2×D11)⋊C8—22no—
35C4×(C2×D11)⋊C4—22no—
36C4×(C2×D11)⋊C4—22no—
37#10622193—22no—
38#10622161—22no—
39C24×D11D411yescharacteristic
40C2×C11×#41—21no—
41C2×C11×#41—21no—
42C2×C11×#41—21no—
43C2×C11×#41—21no—
44C2×C11×#41—21no—
45C2×C11×#41—21no—
46C2×C11×#41—21no—
47C2×C11×#41—21no—
48C2×C11×#41—21no—
49C2×C11×#41—21no—
50C2×C11×#41D412yes—
51C2×C11×#41D412yes—
52C22×Q8×C11C2×C411yescharacteristic
53C22×D4×C11—21no—
54C22×D4×C11C2×C411yescharacteristic
55C23×C4×C11—21no—
56C23×C4×C11—21no—
57C23×C4×C11C2311yescharacteristic
58C22×C22⋊D11—22no—
59C23×Dic11—21no—
60C23×Dic11D411yescharacteristic
61C22×C4×D11—21no—
62C22×C4×D11—21no—
63C22×C4×D11—21no—
64C22×C4×D11—21no—
65C22×C4×D11—21no—
66C22×C4×D11—21no—
67C22×C4×D11—21no—
68C22×C4×D11—21no—
69C22×C4×D11—21no—
70C22×C4×D11—21no—
71C22×C4×D11—21no—
72C22×C4×D11—21no—
73C22×C4×D11C2×C412yes—
74C22×C4×D11D412yes—
75C2×C11×M16—21no—
76C2×C11×M16—21no—
77C2×C11×M16—21no—
78C2×C11×M16—21no—
79C2×C11×M16—21no—
80C2×C11×M16D412yescomplemented
81C22×C8×C11—21no—
82C2×C42×C11—21no—
83C2×C42×C11—21no—
84C2×C42×C11—21no—
85C2×C42×C11—21no—
86C2×C42×C11—21no—
87C2×C42×C11D412yescomplemented
88C2×C22⋊Dic11—21no—
89C2×C22⋊Dic11—22no—
90#66999—24no—
91#66999—24no—
92#66991—24no—
93#66991—24no—
94#66990—24no—
95#66990—24no—
96#66988—24no—
97#66988—24no—
98C4×C22⋊D11—28no—
99C4×C22⋊D11—28no—
100C2×(C2×D11)⋊C4—28no—
101C2×(C2×D11)⋊C4—24no—
102C2×(C2×D11)⋊C4—22no—
103#66979—21no—
104#66979—21no—
105#66979D412yes—
106#66979D412yes—
107C2×C4⋊Dic11C2×C412yes—
108C2×Dic11⋊C4—22no—
109C2×C4×Dic11—21no—
110C2×C4×Dic11—21no—
111C2×C4×Dic11—21no—
112C2×C4×Dic11—21no—
113C2×C4×Dic11—21no—
114C2×C4×Dic11—21no—
115C2×C4×Dic11D412yescomplemented
116C2×#4318—21no—
117C2×#4318—21no—
118C2×#4318—21no—
119C2×#4318—21no—
120C2×#4318—21no—
121C2×#4318D412yescomplemented
122C22×C11⋊C8—21no—
123C11×#104—28no—
124#66901—28no—
125C11⋊#95—24no—
126(C2×D11)⋊C8—28no—
127#10971—111nomaximal, Sylow
128C24×C11—21no—
129C24×C11C2×D411yescharacteristic
130C23×D11—21no—
131C23×D11—21no—
132C23×D11—24no—
133C23×D11—21no—
134C23×D11—21no—
135C23×D11—21no—
136C23×D11—21no—
137C23×D11—42no—
138C23×D11C22⋊C412yes—
139C11×#41—22no—
140C11×#41—22no—
141C11×#41—22no—
142C11×#41—22no—
143C11×#41—22no—
144C11×#41—22no—
145C11×#41—22no—
146C11×#41—22no—
147C11×#41—41no—
148C11×#41—41no—
149C11×#41—41no—
150C11×#41—41no—
151C11×#41—41no—
152C11×#41—41no—
153C11×#41—41no—
154C11×#41—41no—
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×Q8×C11—21no—
158C2×Q8×C11—21no—
159C2×Q8×C11—21no—
160C2×Q8×C11C22⋊C412yescomplemented
161C2×D4×C11—22no—
162C2×D4×C11—22no—
163C2×D4×C11—21no—
164C2×D4×C11—21no—
165C2×D4×C11—21no—
166C2×D4×C11—21no—
167C2×D4×C11—21no—
168C2×D4×C11—41no—
169C2×D4×C11—41no—
170C2×D4×C11—41no—
171C2×D4×C11—41no—
172C2×D4×C11C22⋊C412yescomplemented
173C22×C4×C11—24no—
174C22×C4×C11—21no—
175C22×C4×C11—22no—
176C22×C4×C11—22no—
177C22×C4×C11—22no—
178C22×C4×C11—42no—
179C22×C4×C11—41no—
180C22×C4×C11—41no—
181C22×C4×C11—41no—
182C22×C4×C11—41no—
183C22×C4×C11—41no—
184C22×C4×C11—41no—
185C22×C4×C11C22×C411yescharacteristic
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11C2×D411yescharacteristic
195C22×C4×C11#4111yescharacteristic
196C22×C4×C11#4111yescharacteristic
197C22×C4×C11#4111yescharacteristic
198C22×C4×C11#4111yescharacteristic
199C2×C22⋊D11—28no—
200C2×C22⋊D11—44no—
201C2×C22⋊D11—44no—
202C22×Dic11—24no—
203C22×Dic11—22no—
204C22×Dic11—21no—
205C22×Dic11—22no—
206C22×Dic11—21no—
207C22×Dic11—21no—
208C22×Dic11—21no—
209C22×Dic11—21no—
210C22×Dic11—21no—
211C22×Dic11—42no—
212C22×Dic11—41no—
213C22×Dic11—41no—
214C22×Dic11C22⋊C412yes—
215C2×C4×D11—22no—
216C2×C4×D11—22no—
217C2×C4×D11—22no—
218C2×C4×D11—22no—
219C2×C4×D11—22no—
220C2×C4×D11—22no—
221C2×C4×D11—22no—
222C2×C4×D11—22no—
223C2×C4×D11—22no—
224C2×C4×D11—22no—
225C2×C4×D11—22no—
226C2×C4×D11—22no—
227C2×C4×D11—41no—
228C2×C4×D11—41no—
229C2×C4×D11—41no—
230C2×C4×D11—41no—
231C2×C4×D11—41no—
232C2×C4×D11—41no—
233C2×C4×D11—41no—
234C2×C4×D11—41no—
235C2×C4×D11—41no—
236C2×C4×D11—41no—
237C2×C4×D11—41no—
238C2×C4×D11—41no—
239C2×C4×D11—41no—
240C2×C4×D11—41no—
241C2×C4×D11—41no—
242C2×C4×D11—41no—
243C11×M16—22no—
244C11×M16—22no—
245C11×M16—41no—
246C11×M16—41no—
247C2×C8×C11—22no—
248C2×C8×C11—41no—
249C2×C8×C11—41no—
250C42×C11—22no—
251C42×C11—22no—
252C42×C11—41no—
253C42×C11—41no—
254C22⋊Dic11—28no—
255C22⋊Dic11—22no—
256C22⋊Dic11—22no—
257(C2×D11)⋊C4—216no—
258(C2×D11)⋊C4—28no—
259C4⋊Dic11—22no—
260C4⋊Dic11C22⋊C414yescomplemented
261Dic11⋊C4—28no—
262C4×Dic11—22no—
263C4×Dic11—22no—
264C4×Dic11—22no—
265C4×Dic11—22no—
266C4×Dic11—41no—
267C4×Dic11—41no—
268#4318—22no—
269#4318—22no—
270#4318—41no—
271#4318—41no—
272C2×C11⋊C8—22no—
273C2×C11⋊C8—41no—
274C2×C11⋊C8—41no—
275C2×#525—111no—
276C22×#104—111no—
277C22×#104D1111yescharacteristic, complemented
278C2×#407—111no—
279C2×C4×C22⋊C4—111no—
280C2×#339—111no—
281C2×#339—111no—
282C23×C11—22no—
283C23×C11—22no—
284C23×C11—22no—
285C23×C11—41no—
286C23×C11—41no—
287C23×C11—42no—
288C23×C11—42no—
289C23×C11C2×C22⋊C411yescharacteristic
290C23×C11#12011yescharacteristic
291C23×C11#12011yescharacteristic
292C23×C11#12011yescharacteristic
293C23×C11#12111yescharacteristic
294C23×C11#12111yescharacteristic
295C23×C11#12311yescharacteristic
296C22×D11—24no—
297C22×D11—24no—
298C22×D11—22no—
299C22×D11—22no—
300C22×D11—22no—
301C22×D11—22no—
302C22×D11—22no—
303C22×D11—22no—
304C22×D11—44no—
305C22×D11—44no—
306C22×D11—44no—
307C22×D11—44no—
308C22×D11—42no—
309C22×D11—42no—
310C22×D11—41no—
311C22×D11—41no—
312C22×D11—41no—
313C22×D11—41no—
314C22×D11#10414yescomplemented
315Q8×C11—22no—
316Q8×C11—22no—
317Q8×C11—41no—
318Q8×C11—41no—
319D4×C11—22no—
320D4×C11—22no—
321D4×C11—42no—
322D4×C11—42no—
323D4×C11—42no—
324D4×C11—42no—
325D4×C11—41no—
326D4×C11—41no—
327C2×C4×C11—24no—
328C2×C4×C11—22no—
329C2×C4×C11—44no—
330C2×C4×C11—42no—
331C2×C4×C11—44no—
332C2×C4×C11—41no—
333C2×C4×C11—41no—
334C2×C4×C11—42no—
335C2×C4×C11—42no—
336C2×C4×C11—42no—
337C2×C4×C11—42no—
338C2×C4×C11—42no—
339C2×C4×C11C2×C22⋊C411yescharacteristic
340C2×C4×C11C2×C22⋊C411yescharacteristic
341C2×C4×C11C4×D411yescharacteristic
342C2×C4×C11C4×D411yescharacteristic
343C2×C4×C11C4×D411yescharacteristic
344C2×C4×C11C4×D411yescharacteristic
345C2×C4×C11#12011yescharacteristic
346C2×C4×C11#12011yescharacteristic
347C2×C4×C11#12011yescharacteristic
348C2×C4×C11#12011yescharacteristic
349C2×C4×C11#12011yescharacteristic
350C2×C4×C11#12111yescharacteristic
351C2×C4×C11#12111yescharacteristic
352C2×C4×C11#12111yescharacteristic
353C2×C4×C11#12111yescharacteristic
354C2×C4×C11#12111yescharacteristic
355C2×C4×C11#12111yescharacteristic
356C2×C4×C11#12111yescharacteristic
357C2×C4×C11#12111yescharacteristic
358C2×C4×C11#12111yescharacteristic
359C2×C4×C11#12111yescharacteristic
360C2×C4×C11#12311yescharacteristic
361C2×C4×C11#12311yescharacteristic
362C2×C4×C11#12311yescharacteristic
363C2×C4×C11#12411yescharacteristic
364C2×C4×C11#12411yescharacteristic
365C2×C4×C11#12711yescharacteristic
366C2×C4×C11#12711yescharacteristic
367C22⋊D11—416no—
368C2×Dic11—24no—
369C2×Dic11—24no—
370C2×Dic11—22no—
371C2×Dic11—22no—
372C2×Dic11—22no—
373C2×Dic11—44no—
374C2×Dic11—42no—
375C2×Dic11—44no—
376C2×Dic11—42no—
377C2×Dic11—41no—
378C2×Dic11—41no—
379C2×Dic11—41no—
380C2×Dic11—41no—
381C2×Dic11—42no—
382C2×Dic11—42no—
383C4×D11—42no—
384C4×D11—42no—
385C4×D11—42no—
386C4×D11—42no—
387C4×D11—42no—
388C4×D11—42no—
389C4×D11—42no—
390C4×D11—42no—
391C8×C11—42no—
392C11⋊C8—42no—
393C22×#41C2×D1111yescharacteristic
394C24×C4—111no—
395C22×M16—111no—
396C22×M16C2×D1111yescharacteristic
397#525—222no—
398#525—222no—
399#525—222no—
400#525—222no—
401C2×#123—221no—
402C2×C22⋊Q8—112no—
403C2×#121—112no—
404C2×#120—221no—
405C2×C4×D4—222no—
406C2×#117—111no—
407C22×C22⋊C4—221no—
408C22×C42—111no—
409C22×C42C2×D1111yescharacteristic
410C2×#104—22no—
411C2×#104—22no—
412C2×#104—22no—
413C2×#104—222no—
414C2×#104—222no—
415C2×#104—222no—
416#407—222no—
417#407—222no—
418C2×C22⋊C8—222no—
419C4×C22⋊C4—222no—
420C4×C22⋊C4—222no—
421C2×#95—221no—
422#339—222no—
423#339—222no—
424C22×C11—22no—
425C22×C11—22no—
426C22×C11—21no—
427C22×C11—21no—
428C22×C11—21no—
429C22×C11—21no—
430C22×C11—22no—
431C22×C11—22no—
432C22×C11—42no—
433C22×C11—44no—
434C22×C11—82no—
435C22×C11—81no—
436C22×C11—81no—
437C22×C11#37911yescharacteristic
438C22×C11#38611yescharacteristic
439C22×C11#38611yescharacteristic
440C22×C11#39211yescharacteristic
441C22×C11#39211yescharacteristic
442C22×C11#39411yescharacteristic
443C22×C11#39411yescharacteristic
444C22×C11C2×#10412yes—
445C22×C11#42112yes—
446C2×D11—24no—
447C2×D11—24no—
448C2×D11—24no—
449C2×D11—44no—
450C2×D11—44no—
451C2×D11—44no—
452C2×D11—44no—
453C2×D11—42no—
454C2×D11—42no—
455C2×D11—42no—
456C2×D11—42no—
457C4×C11—44no—
458C4×C11—42no—
459C4×C11#38611yescharacteristic
460C4×C11#38611yescharacteristic
461C4×C11#39011yescharacteristic
462C4×C11#39011yescharacteristic
463C4×C11#39211yescharacteristic
464C4×C11#39211yescharacteristic
465C4×C11#39411yescharacteristic
466C4×C11#39411yescharacteristic
467Dic11—44no—
468Dic11—42no—
469Dic11—44no—
470C25—111no—
471C2×#41—21no—
472C2×#41—21no—
473C2×#41—21no—
474C2×#41—21no—
475C2×#41—21no—
476C2×#41—21no—
477C2×#41—21no—
478C2×#41—21no—
479C2×#41—21no—
480C2×#41—21no—
481C2×#41D4412yes—
482C2×#41C22⋊D1112yes—
483C22×Q8C4×D1111yescharacteristic
484C22×D4—21no—
485C22×D4—222no—
486C22×D4C4×D1111yescharacteristic
487C23×C4—21no—
488C23×C4—21no—
489C23×C4—111no—
490C23×C4—112no—
491C23×C4—112no—
492C23×C4—221no—
493C23×C4—221no—
494C23×C4—221no—
495C23×C4—221no—
496C23×C4—221no—
497C23×C4—221no—
498C23×C4—221no—
499C23×C4—221no—
500C23×C4—221no—
501C23×C4—221no—
502C23×C4—221no—
503C23×C4—221no—
504C23×C4—221no—
505C23×C4C22×D1111yescharacteristic
506C2×M16—21no—
507C2×M16—21no—
508C2×M16—21no—
509C2×M16—21no—
510C2×M16—21no—
511C2×M16—112no—
512C2×M16—221no—
513C2×M16—221no—
514C2×M16—221no—
515C2×M16—221no—
516C2×M16—221no—
517C2×M16C22⋊D1112yescomplemented
518C22×C8—21no—
519C22×C8—221no—
520#123—224no—
521#123—224no—
522C22⋊Q8—224no—
523C22⋊Q8—224no—
524#121—224no—
525#121—224no—
526#120—224no—
527#120—224no—
528C4×D4—228no—
529C4×D4—228no—
530#117—112no—
531#117—112no—
532#117—221no—
533#117—221no—
534C2×C4⋊C4—112no—
535C2×C4⋊C4—222no—
536C2×C22⋊C4—222no—
537C2×C22⋊C4—224no—
538C2×C22⋊C4—228no—
539C2×C22⋊C4—222no—
540C2×C22⋊C4—221no—
541C2×C42—21no—
542C2×C42—21no—
543C2×C42—21no—
544C2×C42—21no—
545C2×C42—21no—
546C2×C42—112no—
547C2×C42—221no—
548C2×C42—221no—
549C2×C42—221no—
550C2×C42—221no—
551C2×C42—221no—
552C2×C42—221no—
553C2×C42C22⋊D1112yescomplemented
554#104—28no—
555#104—228no—
556C22⋊C8—228no—
557#95—224no—
558C2×C11—21no—
559C2×C11—21no—
560C2×C11—21no—
561C2×C11—21no—
562C2×C11—82no—
563C2×C11#143811yescharacteristic
564C2×C11#178912yes—
565C2×C11#187112yes—
566C2×C11#189611yescharacteristic
567C2×C11#189711yescharacteristic
568D11—44no—
569C24—21no—
570C24—112no—
571C24—224no—
572C24—221no—
573C24—221no—
574C24—221no—
575C24—221no—
576C24—221no—
577C24—221no—
578C24—442no—
579C24D4×D1111yescharacteristic
580#41—22no—
581#41—22no—
582#41—22no—
583#41—22no—
584#41—22no—
585#41—22no—
586#41—22no—
587#41—22no—
588#41—41no—
589#41—41no—
590#41—41no—
591#41—41no—
592#41—41no—
593#41—41no—
594#41—41no—
595#41—41no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8(C2×D11)⋊C412yescomplemented
602C2×D4—22no—
603C2×D4—22no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—41no—
610C2×D4—41no—
611C2×D4—41no—
612C2×D4—41no—
613C2×D4—228no—
614C2×D4—444no—
615C2×D4—444no—
616C2×D4(C2×D11)⋊C412yescomplemented
617C22×C4—24no—
618C22×C4—21no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—42no—
623C22×C4—41no—
624C22×C4—41no—
625C22×C4—41no—
626C22×C4—41no—
627C22×C4—41no—
628C22×C4—41no—
629C22×C4—112no—
630C22×C4—224no—
631C22×C4—222no—
632C22×C4—221no—
633C22×C4—221no—
634C22×C4—221no—
635C22×C4—221no—
636C22×C4—222no—
637C22×C4—221no—
638C22×C4—221no—
639C22×C4—222no—
640C22×C4—222no—
641C22×C4—222no—
642C22×C4—222no—
643C22×C4—222no—
644C22×C4—222no—
645C22×C4—222no—
646C22×C4—222no—
647C22×C4—222no—
648C22×C4—222no—
649C22×C4—222no—
650C22×C4—222no—
651C22×C4—442no—
652C22×C4—441no—
653C22×C4—441no—
654C22×C4—441no—
655C22×C4—441no—
656C22×C4—441no—
657C22×C4—441no—
658C22×C4—441no—
659C22×C4—441no—
660C22×C4—441no—
661C22×C4—441no—
662C22×C4—441no—
663C22×C4—441no—
664C22×C4—441no—
665C22×C4—441no—
666C22×C4—441no—
667C22×C4—441no—
668C22×C4—441no—
669C22×C4—441no—
670C22×C4C2×C4×D1111yescharacteristic
671C22×C4C2×D4411yescharacteristic
672C22×C4#433911yescharacteristic
673C22×C4#433911yescharacteristic
674C22×C4D4×D1111yescharacteristic
675C22×C4D4×D1111yescharacteristic
676C22×C4D4×D1111yescharacteristic
677C22×C4D4×D1111yescharacteristic
678C22×C4D4×D1111yescharacteristic
679C22×C4#434111yescharacteristic
680C22×C4#434111yescharacteristic
681C22×C4C2×C22⋊D1111yescharacteristic
682C22×C4C2×C22⋊D1111yescharacteristic
683C22×C4C2×C22⋊D1111yescharacteristic
684M16—22no—
685M16—22no—
686M16—41no—
687M16—41no—
688M16—222no—
689M16—222no—
690M16—441no—
691M16—441no—
692C2×C8—22no—
693C2×C8—41no—
694C2×C8—41no—
695C2×C8—222no—
696C2×C8—441no—
697C2×C8—441no—
698C4⋊C4—114no—
699C4⋊C4—228no—
700C4⋊C4—222no—
701C22⋊C4—2216no—
702C22⋊C4—228no—
703C22⋊C4—228no—
704C22⋊C4—222no—
705C22⋊C4—222no—
706C42—22no—
707C42—22no—
708C42—41no—
709C42—41no—
710C42—222no—
711C42—222no—
712C42—222no—
713C42—222no—
714C42—441no—
715C42—441no—
716C11#1097111yescharacteristic, complemented, Sylow
717C23—22no—
718C23—22no—
719C23—22no—
720C23—41no—
721C23—41no—
722C23—42no—
723C23—42no—
724C23—114no—
725C23—224no—
726C23—224no—
727C23—222no—
728C23—222no—
729C23—222no—
730C23—222no—
731C23—222no—
732C23—222no—
733C23—444no—
734C23—444no—
735C23—444no—
736C23—444no—
737C23—442no—
738C23—442no—
739C23—441no—
740C23—441no—
741C23—441no—
742C23—441no—
743C23C22⋊C4×D1111yescharacteristic
744C23#6693511yescharacteristic
745C23#6693611yescharacteristic
746C23#6693711yescharacteristic
747C23#6699011yescharacteristic
748C23#6699011yescharacteristic
749C23#6699111yescharacteristic
750Q8—22no—
751Q8—22no—
752Q8—41no—
753Q8—41no—
754D4—22no—
755D4—22no—
756D4—42no—
757D4—42no—
758D4—42no—
759D4—42no—
760D4—41no—
761D4—41no—
762D4—4416no—
763C2×C4—24no—
764C2×C4—22no—
765C2×C4—42no—
766C2×C4—44no—
767C2×C4—44no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—224no—
776C2×C4—224no—
777C2×C4—222no—
778C2×C4—222no—
779C2×C4—222no—
780C2×C4—442no—
781C2×C4—444no—
782C2×C4—444no—
783C2×C4—441no—
784C2×C4—442no—
785C2×C4—441no—
786C2×C4—441no—
787C2×C4—441no—
788C2×C4—442no—
789C2×C4—442no—
790C2×C4—442no—
791C2×C4—442no—
792C2×C4—442no—
793C2×C4—442no—
794C2×C4—442no—
795C2×C4—442no—
796C2×C4—442no—
797C2×C4—442no—
798C2×C4C22⋊C4×D1111yescharacteristic
799C2×C4(C22⋊D11)⋊C411yescharacteristic
800C2×C4(C22⋊D11)⋊C411yescharacteristic
801C2×C4#6693511yescharacteristic
802C2×C4#6693511yescharacteristic
803C2×C4#6693611yescharacteristic
804C2×C4#6693711yescharacteristic
805C2×C4#6693711yescharacteristic
806C2×C4#6693711yescharacteristic
807C2×C4#6693811yescharacteristic
808C2×C4#6693811yescharacteristic
809C2×C4#6693911yescharacteristic
810C2×C4C2×(C2×D11)⋊C411yescharacteristic
811C2×C4C4×C22⋊D1111yescharacteristic
812C2×C4C4×C22⋊D1111yescharacteristic
813C2×C4#6698211yescharacteristic
814C2×C4#6698311yescharacteristic
815C2×C4#6698311yescharacteristic
816C2×C4#6699011yescharacteristic
817C2×C4#6699011yescharacteristic
818C2×C4#6699111yescharacteristic
819C2×C4#6699211yescharacteristic
820C2×C4#6699211yescharacteristic
821C2×C4#6699211yescharacteristic
822C2×C4#6699211yescharacteristic
823C2×C4#6699311yescharacteristic
824C2×C4#6699311yescharacteristic
825C2×C4#6700611yescharacteristic
826C8—42no—
827C8—442no—
828C22—21no—
829C22—21no—
830C22—21no—
831C22—21no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—44no—
837C22—42no—
838C22—81no—
839C22—81no—
840C22—82no—
841C22—224no—
842C22—224no—
843C22—224no—
844C22—444no—
845C22—444no—
846C22—444no—
847C22—444no—
848C22—442no—
849C22—442no—
850C22—442no—
851C22—442no—
852C22D11×#10412yes—
853C22#1062243412yes—
854C22#1062256811yescharacteristic
855C22#1062256911yescharacteristic
856C22#1062256911yescharacteristic
857C22#1062257211yescharacteristic
858C22#1062257311yescharacteristic
859C22#1062257411yescharacteristic
860C22#1062283611yescharacteristic
861C4—44no—
862C4—42no—
863C4—444no—
864C4—444no—
865C4—442no—
866C4#1062257011yescharacteristic
867C4#1062257011yescharacteristic
868C4#1062257111yescharacteristic
869C4#1062257211yescharacteristic
870C4#1062257311yescharacteristic
871C4#1062257411yescharacteristic
872C4#1062282611yescharacteristic
873C4#1062283611yescharacteristic
874C2—21no—
875C2—21no—
876C2—21no—
877C2—21no—
878C2—82no—
879C2—444no—
880C2#1306685511yescharacteristic
881C2#1306855812yes—
882C2#1306891512yes—
883C2#1306905611yescharacteristic
884C2#1306906111yescharacteristic
subgroupG/H
centerC22×C4D4×D11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC22×C11×#104C2
socleC23×C11C2×C22⋊C4
prime radicalC2×#10623359C2
cosocleC23×C4×C11C23
hypercenterC22×#104D11
hypocenterC11#10971
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×#104

Complements

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

NH ≅ G/Ntype
2. C22×#66901C2semidirect
3. C2×#10622739C2semidirect
4. C2×C4×(C2×D11)⋊C4C2semidirect
5. C2×#10622193C2semidirect
6. C2×#10622161C2semidirect
7. C22×C11×#104C2semidirect
16. C2×#66999C4semidirect
17. C2×#66991C4semidirect
80. C2×C11×M16D4semidirect
87. C2×C42×C11D4semidirect
115. C2×C4×Dic11D4semidirect
121. C2×#4318D4semidirect
160. C2×Q8×C11C22⋊C4semidirect
172. C2×D4×C11C22⋊C4semidirect
260. C4⋊Dic11C22⋊C4semidirect
277. C22×#104D11semidirect
314. C22×D11#104semidirect
517. C2×M16C22⋊D11semidirect
553. C2×C42C22⋊D11semidirect
601. C2×Q8(C2×D11)⋊C4semidirect
616. C2×D4(C2×D11)⋊C4semidirect
716. C11#10971semidirect

Maximal subgroups

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

subgroupindex
C2×#106233592
C22×#669012
C2×#106227392
C2×C4×(C2×D11)⋊C42
C2×#106221932
C2×#106221612
C22×C11×#1042
#1097111