Finite Group Databasebeta

← #14648917

Subgroups — #14648917

Order 2816.

966 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622659C211yesmaximal, characteristic
2#13068546C211yesmaximal, characteristic
3C2×#10622176C211yesmaximal, characteristic, complemented
4#13066856C211yesmaximal, characteristic
5#13066494C211yesmaximal, characteristic, complemented
6#13066459C211yesmaximal, characteristic, complemented
7C11×#2329C211yesmaximal, characteristic, complemented
8C23×D44C2211yescharacteristic
9C2×C11×C22⋊Q8C2211yescharacteristic
10C22×#4325—21no—
11C22×(C2×D11)⋊C4—21no—
12C22×(C2×D11)⋊C4—21no—
13C11×#391—21no—
14C11×#389—21no—
15C11×#387—21no—
16C11×#387—21no—
17C11×#385—21no—
18C11×#380C2211yescharacteristic
19C4×C11×C22⋊C4—21no—
20C2×C11×#95C2211yescharacteristic
21C2×C11⋊#95C2211yescharacteristic
22C2×C22⋊(C11⋊C8)C2211yescharacteristic
23C2×C22⋊(C11⋊C8)C2211yescharacteristic
24#10622659—22no—
25#10622659C414yescomplemented
26C2×#66873—21no—
27C2×#66873—21no—
28C2×#66873—21no—
29#10622176—22no—
30C24×D11—21no—
31C22×Q8×C11D411yescharacteristic
32C23×C4×C11D411yescharacteristic
33C23×C4×C11D411yescharacteristic
34C23×C4×C11C2311yescharacteristic
35C23×Dic11—21no—
36C22×D44—21no—
37C22×D44—21no—
38C22×D44—21no—
39C22×D44—21no—
40C22×D44—21no—
41C22×D44—42no—
42C22×D44—42no—
43C22×D44C2×C412yes—
44C11×C22⋊Q8—21no—
45C11×C22⋊Q8—21no—
46C11×C22⋊Q8C2×C412yes—
47C11×C22⋊Q8D412yes—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4D411yescharacteristic
52C2×C11×C4⋊C4D411yescharacteristic
53C2×C11×C4⋊C4D411yescharacteristic
54C2×C11×C22⋊C4—21no—
55C2×C11×C22⋊C4—21no—
56C2×C42×C11—21no—
57C2×C42×C11—21no—
58C2×#4325—24no—
59C2×#4325—42no—
60C2×#4325—42no—
61C2×(C2×D11)⋊C4—42no—
62C2×(C2×D11)⋊C4—42no—
63C2×(C2×D11)⋊C4—42no—
64C2×(C2×D11)⋊C4—42no—
65C2×(C2×D11)⋊C4—42no—
66C2×(C2×D11)⋊C4—42no—
67C22×C11⋊C8—21no—
68C22×C11⋊C8—21no—
69C11×#95—21no—
70C11×#95—21no—
71C11×#95—21no—
72C11×#95—21no—
73C11×#95—21no—
74C11×#95—21no—
75C11×#95—21no—
76C11⋊#95—21no—
77C11⋊#95—21no—
78C22⋊(C11⋊C8)—21no—
79C22⋊(C11⋊C8)—21no—
80C22⋊(C11⋊C8)—21no—
81C22⋊(C11⋊C8)C2×C412yes—
82#66873—24no—
83#66873—42no—
84#66873—42no—
85#9042—111nomaximal, Sylow
86C24×C11C2×D411yescharacteristic
87C23×D11—22no—
88C23×D11—22no—
89C23×D11—22no—
90C23×D11—41no—
91C23×D11—41no—
92C23×D11—41no—
93C23×D11—41no—
94C23×D11—41no—
95C23×D11—41no—
96C23×D11—41no—
97C23×D11—41no—
98C23×D11—41no—
99C23×D11—41no—
100C23×D11—41no—
101C23×D11—41no—
102C2×Q8×C11—21no—
103C2×Q8×C11—41no—
104C2×Q8×C11—41no—
105C2×Q8×C11C22⋊C412yescomplemented
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—41no—
116C22×C4×C11—41no—
117C22×C4×C11—41no—
118C22×C4×C11—41no—
119C22×C4×C11—41no—
120C22×C4×C11—41no—
121C22×C4×C11SD1612yescomplemented
122C22×C4×C11C22×C411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11#4111yescharacteristic
127C22×C4×C11#4111yescharacteristic
128C22×Dic11—22no—
129C22×Dic11—41no—
130C22×Dic11—41no—
131C22×Dic11—41no—
132C22×Dic11—41no—
133C22×Dic11—41no—
134C22×Dic11—41no—
135C2×D44—22no—
136C2×D44—22no—
137C2×D44—22no—
138C2×D44—22no—
139C2×D44—22no—
140C2×D44—22no—
141C2×D44—41no—
142C2×D44—41no—
143C2×D44—41no—
144C2×D44—41no—
145C2×D44—44no—
146C2×D44—44no—
147C2×D44—44no—
148C2×D44—44no—
149C2×D44—41no—
150C2×D44—41no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—41no—
155C11×C4⋊C4—41no—
156C11×C4⋊C4—81no—
157C11×C4⋊C4—81no—
158C11×C4⋊C4C22⋊C412yescomplemented
159C11×C22⋊C4—22no—
160C11×C22⋊C4—22no—
161C11×C22⋊C4—41no—
162C11×C22⋊C4—41no—
163C42×C11—81no—
164C42×C11—81no—
165#4325—48no—
166(C2×D11)⋊C4—48no—
167(C2×D11)⋊C4—48no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—41no—
170C2×C11⋊C8—41no—
171C2×C11⋊C8—41no—
172C2×C11⋊C8—41no—
173C2×C11⋊C8—41no—
174C2×#450—111no—
175#2329D1111yescharacteristic, complemented
176#1786—111no—
177C2×#328—111no—
178#1438—111no—
179#1294—111no—
180#1280—111no—
181C23×C11—21no—
182C23×C11—21no—
183C23×C11—21no—
184C23×C11—21no—
185C23×C11C4×D411yescharacteristic
186C23×C11#12011yescharacteristic
187C23×C11#12111yescharacteristic
188C23×C11C2×SD1611yescharacteristic
189C23×C11#13511yescharacteristic
190C23×C11AGL(1,ℤ/8)11yescharacteristic
191C23×C11#13711yescharacteristic
192C22×D11—24no—
193C22×D11—42no—
194C22×D11—42no—
195C22×D11—42no—
196C22×D11—42no—
197C22×D11—42no—
198C22×D11—42no—
199C22×D11—42no—
200C22×D11—42no—
201C22×D11—42no—
202C22×D11—42no—
203C22×D11—42no—
204C22×D11—42no—
205C22×D11—42no—
206C22×D11—42no—
207C22×D11—42no—
208C22×D11—42no—
209C22×D11—42no—
210C22×D11—42no—
211C22×D11—81no—
212C22×D11—81no—
213C22×D11—81no—
214C22×D11—81no—
215C22×D11—81no—
216C22×D11—81no—
217C22×D11—81no—
218C22×D11—81no—
219C22×D11—81no—
220C22×D11—81no—
221C22×D11—81no—
222C22×D11—81no—
223C22×D11—81no—
224C22×D11—81no—
225C22×D11—81no—
226C22×D11—81no—
227Q8×C11—42no—
228Q8×C11—81no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—81no—
258C2×C4×C11—81no—
259C2×C4×C11C2×C22⋊C411yescharacteristic
260C2×C4×C11C4×D411yescharacteristic
261C2×C4×C11#12111yescharacteristic
262C2×C4×C11#12311yescharacteristic
263C2×Dic11—42no—
264C2×Dic11—42no—
265C2×Dic11—42no—
266C2×Dic11—81no—
267C2×Dic11—81no—
268C2×Dic11—81no—
269C2×Dic11—81no—
270D44—24no—
271D44—24no—
272D44—42no—
273D44—42no—
274D44—42no—
275D44—42no—
276D44—42no—
277D44—42no—
278C11⋊C8—42no—
279C11⋊C8—81no—
280C23×D4—111no—
281C22×SD16—221no—
282C2×C22⋊Q8C2×D1111yescharacteristic
283C22×C22⋊C4—221no—
284C22×C22⋊C4—221no—
285#450—114no—
286#450—222no—
287C2×#102—221no—
288C2×#102—221no—
289C2×#102—221no—
290C2×C22⋊C8—111no—
291C2×C22⋊C8—111no—
292#391—21no—
293#389—21no—
294#387—21no—
295#387—21no—
296#385—21no—
297#380C2×D1111yescharacteristic
298C4×C22⋊C4—21no—
299C2×#95—111no—
300C2×#95C2×D1111yescharacteristic
301#328—222no—
302C22×C11—21no—
303C22×C11—21no—
304C22×C11—21no—
305C22×C11—21no—
306C22×C11—21no—
307C22×C11—21no—
308C22×C11—21no—
309C22×C11—21no—
310C22×C11—21no—
311C22×C11—21no—
312C22×C11—21no—
313C22×C11—21no—
314C22×C11#38611yescharacteristic
315C22×C11C4×SD1611yescharacteristic
316C22×C11#44011yescharacteristic
317C22×C11#44811yescharacteristic
318C22×C11#44911yescharacteristic
319C22×C11#45311yescharacteristic
320C22×C11#45411yescharacteristic
321C22×C11B(4,𝔽2)11yescharacteristic
322C22×C11B(4,𝔽2)11yescharacteristic
323C22×C11#46011yescharacteristic
324C22×C11#46411yescharacteristic
325C2×D11—44no—
326C2×D11—44no—
327C2×D11—44no—
328C2×D11—82no—
329C2×D11—82no—
330C2×D11—82no—
331C2×D11—82no—
332C2×D11—82no—
333C2×D11—82no—
334C2×D11—82no—
335C2×D11—82no—
336C2×D11—82no—
337C2×D11—82no—
338C2×D11—82no—
339C2×D11—82no—
340C4×C11—21no—
341C4×C11—21no—
342C4×C11—21no—
343C4×C11—21no—
344C4×C11—42no—
345C4×C11—42no—
346C4×C11—42no—
347C4×C11—81no—
348C4×C11—81no—
349C4×C11—81no—
350Dic11—82no—
351C25—221no—
352C22×Q8C22⋊D1111yescharacteristic
353C22×D4—112no—
354C22×D4—221no—
355C22×D4—221no—
356C22×D4—221no—
357C22×D4—221no—
358C22×D4—221no—
359C22×D4—442no—
360C22×D4—442no—
361C23×C4—221no—
362C23×C4C22⋊D1111yescharacteristic
363C23×C4C22⋊D1111yescharacteristic
364C23×C4C22×D1111yescharacteristic
365C2×SD16—224no—
366C2×SD16—442no—
367C2×SD16—442no—
368C22×C8—221no—
369C22×C8—221no—
370C22⋊Q8—21no—
371C22⋊Q8—21no—
372C22⋊Q8C4×D1112yes—
373C22⋊Q8D4412yes—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4C22⋊D1111yescharacteristic
378C2×C4⋊C4C22⋊D1111yescharacteristic
379C2×C4⋊C4C22⋊D1111yescharacteristic
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—442no—
383C2×C22⋊C4—442no—
384C2×C22⋊C4—442no—
385C2×C22⋊C4—442no—
386C2×C22⋊C4—442no—
387C2×C22⋊C4—442no—
388C2×C42—21no—
389C2×C42—21no—
390#102—224no—
391#102—442no—
392#102—442no—
393C22⋊C8—112no—
394C22⋊C8—221no—
395C22⋊C8—221no—
396C22⋊C8—221no—
397#95—21no—
398#95—21no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95—221no—
405#95—221no—
406C2×C11—21no—
407C2×C11—21no—
408C2×C11—21no—
409C2×C11—21no—
410C2×C11#159611yescharacteristic
411C2×C11#159711yescharacteristic
412C2×C11#159911yescharacteristic
413C2×C11#160011yescharacteristic
414C2×C11#188011yescharacteristic
415C2×C11#188311yescharacteristic
416C2×C11#188911yescharacteristic
417D11—84no—
418C24—222no—
419C24—222no—
420C24—222no—
421C24—441no—
422C24—441no—
423C24—441no—
424C24—441no—
425C24—441no—
426C24—441no—
427C24—441no—
428C24—441no—
429C24—441no—
430C24—441no—
431C24—441no—
432C24—441no—
433C24C2×C22⋊D1111yescharacteristic
434C2×Q8—21no—
435C2×Q8—41no—
436C2×Q8—41no—
437C2×Q8(C2×D11)⋊C412yescomplemented
438C2×D4—222no—
439C2×D4—222no—
440C2×D4—222no—
441C2×D4—222no—
442C2×D4—222no—
443C2×D4—222no—
444C2×D4—441no—
445C2×D4—441no—
446C2×D4—441no—
447C2×D4—441no—
448C2×D4—444no—
449C2×D4—444no—
450C2×D4—444no—
451C2×D4—444no—
452C2×D4—441no—
453C2×D4—441no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—222no—
470C22×C4—441no—
471C22×C4—441no—
472C22×C4—441no—
473C22×C4—441no—
474C22×C4—441no—
475C22×C4—441no—
476C22×C4#432512yescomplemented
477C22×C4C2×C4×D1111yescharacteristic
478C22×C4C2×D4411yescharacteristic
479C22×C4#433911yescharacteristic
480C22×C4#433911yescharacteristic
481C22×C4C2×C22⋊D1111yescharacteristic
482C22×C4C2×C22⋊D1111yescharacteristic
483SD16—448no—
484C2×C8—222no—
485C2×C8—441no—
486C2×C8—441no—
487C2×C8—441no—
488C2×C8—441no—
489C2×C8—441no—
490C4⋊C4—22no—
491C4⋊C4—21no—
492C4⋊C4—22no—
493C4⋊C4—41no—
494C4⋊C4—41no—
495C4⋊C4—81no—
496C4⋊C4—81no—
497C4⋊C4(C2×D11)⋊C412yescomplemented
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—448no—
503C22⋊C4—448no—
504C42—81no—
505C42—81no—
506C11#904211yescharacteristic, complemented, Sylow
507C23—21no—
508C23—21no—
509C23—21no—
510C23—21no—
511C23—224no—
512C23—442no—
513C23—442no—
514C23—442no—
515C23—442no—
516C23—442no—
517C23—442no—
518C23—442no—
519C23—442no—
520C23—442no—
521C23—442no—
522C23—442no—
523C23—442no—
524C23—442no—
525C23—442no—
526C23—442no—
527C23—442no—
528C23—442no—
529C23—442no—
530C23—881no—
531C23—881no—
532C23—881no—
533C23—881no—
534C23—881no—
535C23—881no—
536C23—881no—
537C23—881no—
538C23—881no—
539C23—881no—
540C23—881no—
541C23—881no—
542C23—881no—
543C23—881no—
544C23—881no—
545C23—881no—
546C23C4×C22⋊D1111yescharacteristic
547C23#6698311yescharacteristic
548C23C2×#432511yescharacteristic
549C23#6699511yescharacteristic
550C23#6700211yescharacteristic
551C23#6700311yescharacteristic
552C23#6700611yescharacteristic
553Q8—42no—
554Q8—81no—
555D4—224no—
556D4—224no—
557D4—442no—
558D4—442no—
559D4—442no—
560D4—442no—
561D4—442no—
562D4—442no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—81no—
592C2×C4—81no—
593C2×C4—442no—
594C2×C4—442no—
595C2×C4—442no—
596C2×C4—881no—
597C2×C4—881no—
598C2×C4—881no—
599C2×C4—881no—
600C2×C4C2×(C2×D11)⋊C411yescharacteristic
601C2×C4C4×C22⋊D1111yescharacteristic
602C2×C4#6698211yescharacteristic
603C2×C4#6698311yescharacteristic
604C8—442no—
605C8—881no—
606C22—21no—
607C22—21no—
608C22—21no—
609C22—21no—
610C22—21no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—21no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—444no—
619C22—444no—
620C22—444no—
621C22—882no—
622C22—882no—
623C22—882no—
624C22—882no—
625C22—882no—
626C22—882no—
627C22—882no—
628C22—882no—
629C22—882no—
630C22—882no—
631C22—882no—
632C22—882no—
633C22C4×#432511yescharacteristic
634C22#1062263911yescharacteristic
635C22#1062264011yescharacteristic
636C22#1062264111yescharacteristic
637C22#1062282611yescharacteristic
638C22#1062284011yescharacteristic
639C22#1062285111yescharacteristic
640C22#1062285411yescharacteristic
641C22#1062285711yescharacteristic
642C22#1062285711yescharacteristic
643C22#1062285811yescharacteristic
644C4—21no—
645C4—21no—
646C4—21no—
647C4—21no—
648C4—42no—
649C4—42no—
650C4—42no—
651C4—81no—
652C4—81no—
653C4—81no—
654C4—882no—
655C2—21no—
656C2—21no—
657C2—21no—
658C2—21no—
659C2—884no—
660C2#1306753911yescharacteristic
661C2#1306754511yescharacteristic
662C2#1306755611yescharacteristic
663C2#1306756211yescharacteristic
664C2#1306897111yescharacteristic
665C2#1306899211yescharacteristic
666C2#1306902411yescharacteristic
subgroupG/H
centerC23#67006
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#2329C2
socleC23×C11#120
prime radicalC23×D44C22
cosocleC23×C4×C11C23
hypercenter#2329D11
hypocenterC11#9042
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2329

Complements

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

NH ≅ G/Ntype
3. C2×#10622176C2semidirect
5. #13066494C2semidirect
6. #13066459C2semidirect
7. C11×#2329C2semidirect
25. #10622659C4semidirect
105. C2×Q8×C11C22⋊C4semidirect
121. C22×C4×C11SD16semidirect
158. C11×C4⋊C4C22⋊C4semidirect
175. #2329D11semidirect
437. C2×Q8(C2×D11)⋊C4semidirect
476. C22×C4#4325semidirect
497. C4⋊C4(C2×D11)⋊C4semidirect
506. C11#9042semidirect

Maximal subgroups

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

subgroupindex
C2×#106226592
#130685462
C2×#106221762
#130668562
#130664942
#130664592
C11×#23292
#904211