Finite Group Databasebeta

← #14781722

Subgroups — #14781722

Order 2816.

1494 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67003C211yesmaximal, characteristic
2C22×C4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
3C2×#10622846C211yesmaximal, characteristic, complemented
4C2×#10622615C211yesmaximal, characteristic, complemented
5#13071106C211yesmaximal, characteristic, complemented
6#13069938C212yesmaximal, complemented
7#13069933C212yesmaximal, complemented
8#13069931C212yesmaximal, complemented
9#13069926C212yesmaximal, complemented
10#13068332C211yesmaximal, characteristic, complemented
11C11×#2297C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C22×#4339C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C22×C42×C11C2211yescharacteristic
16C2×#67003—24no—
17C2×#67003—24no—
18C2×#67003—24no—
19C22×#4326C2211yescharacteristic
20C22×#4325C2211yescharacteristic
21C22×#4324C2211yescharacteristic
22C22×#4323C2211yescharacteristic
23C2×#66979C2211yescharacteristic
24C23×C11⋊C8C2211yescharacteristic
25C23×C11⋊C8C2211yescharacteristic
26C11×#391C2212yes—
27C11×#390C2212yes—
28C11×#386—21no—
29C11×#386—21no—
30C4×C11×C22⋊C4—22no—
31#10622846—24no—
32C2×#66899C2212yes—
33C2×#66896C2212yes—
34#10622826—21no—
35#10622826—21no—
36#10622615—24no—
37C2×#66874C2212yes—
38C2×#66873C2212yes—
39#10622552C2212yes—
40C4×(C2×D11)⋊C4—22no—
41#10622542C2212yes—
42C2×C4⋊(C11⋊C8)—24no—
43C2×C4⋊(C11⋊C8)C2212yes—
44C2×C4⋊(C11⋊C8)C2212yes—
45#10622167C2212yes—
46#10622167C2212yes—
47C2×C11×#41—22no—
48C2×C11×#41—22no—
49C2×C11×#41—22no—
50C2×C11×#41—22no—
51C2×C11×#41—22no—
52C2×C11×#41D414yes—
53C22×Q8×C11C2311yescharacteristic
54C22×D4×C11—21no—
55C22×D4×C11C2311yescharacteristic
56C23×C4×C11—21no—
57C23×C4×C11D411yescharacteristic
58C23×C4×C11D411yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C22×C22⋊D11—21no—
61C2×#4339—22no—
62C2×#4339—22no—
63C2×#4339—22no—
64C2×#4339—22no—
65C2×#4339—22no—
66C2×#4339D414yes—
67C22×D44C2311yescharacteristic
68C22×C4×D11—21no—
69C22×Dic22C2311yescharacteristic
70C11×#117—22no—
71C11×#117—22no—
72C2×C11×C4⋊C4C2312yes—
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4—22no—
76C2×C42×C11—22no—
77C2×C42×C11—22no—
78C2×C42×C11—21no—
79C2×C42×C11D412yes—
80C2×C42×C11C2312yes—
81C2×C22⋊Dic11—21no—
82#67003—232no—
83C2×#4326—22no—
84C2×#4326—22no—
85C2×#4326—22no—
86C2×#4325—22no—
87C2×#4325—22no—
88C2×#4325—22no—
89C2×#4324—22no—
90C2×#4324—22no—
91C2×#4324—22no—
92C2×#4323—22no—
93C2×#4323—22no—
94C2×#4323—22no—
95C2×(C2×D11)⋊C4—22no—
96C2×(C2×D11)⋊C4—22no—
97#66979—22no—
98#66979—22no—
99C2×C4⋊Dic11C2312yes—
100C2×C4×Dic11—21no—
101C22×C11⋊C8—22no—
102C22×C11⋊C8—22no—
103C22×C11⋊C8—22no—
104C22×C11⋊C8—22no—
105C22×C11⋊C8—22no—
106C22×C11⋊C8D414yes—
107C22×C11⋊C8C2312yes—
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C11×#95—22no—
111C11×#95—22no—
112#66899—24no—
113#66896—24no—
114C11⋊#95—22no—
115C11⋊#95—22no—
116#66874—24no—
117#66873—24no—
118C4⋊(C11⋊C8)—24no—
119C4⋊(C11⋊C8)—24no—
120#23539—111nomaximal, Sylow
121C24×C11—21no—
122C24×C11C2×D411yescharacteristic
123C23×D11—21no—
124C11×#41—28no—
125C11×#41—28no—
126C11×#41—44no—
127C11×#41—44no—
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11C2×D412yes—
134C2×D4×C11—24no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—42no—
141C2×D4×C11—42no—
142C2×D4×C11C2×D412yes—
143C22×C4×C11—22no—
144C22×C4×C11—24no—
145C22×C4×C11—22no—
146C22×C4×C11—21no—
147C22×C4×C11—24no—
148C22×C4×C11—22no—
149C22×C4×C11—42no—
150C22×C4×C11—42no—
151C22×C4×C11—42no—
152C22×C4×C11C2×D412yes—
153C22×C4×C11C2×D412yes—
154C22×C4×C11C2×D412yes—
155C22×C4×C11C2×D412yes—
156C22×C4×C11C2×D412yes—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11#4112yes—
159C22×C4×C11#4112yes—
160C22×C4×C11#4112yes—
161C22×C4×C11C2411yescharacteristic
162C2×C22⋊D11—24no—
163C2×C22⋊D11—42no—
164C2×C22⋊D11—42no—
165C22×Dic11—21no—
166C22×Dic11—22no—
167#4339—28no—
168#4339—28no—
169#4339—44no—
170#4339—44no—
171C2×D44—21no—
172C2×D44—21no—
173C2×D44—21no—
174C2×D44—21no—
175C2×D44—21no—
176C2×D44C2×D412yes—
177C2×C4×D11—24no—
178C2×C4×D11—42no—
179C2×C4×D11—42no—
180C2×Dic22—21no—
181C2×Dic22—21no—
182C2×Dic22—21no—
183C2×Dic22—21no—
184C2×Dic22—21no—
185C2×Dic22C2×D412yes—
186C11×C4⋊C4—22no—
187C11×C4⋊C4—22no—
188C11×C22⋊C4—44no—
189C11×C22⋊C4—42no—
190C11×C22⋊C4—44no—
191C42×C11—24no—
192C42×C11—22no—
193C42×C11—22no—
194C42×C11—42no—
195C22⋊Dic11—42no—
196#4326—28no—
197#4325—28no—
198#4324—28no—
199#4323—28no—
200(C2×D11)⋊C4—44no—
201(C2×D11)⋊C4—44no—
202C4⋊Dic11—22no—
203C4⋊Dic11—22no—
204C4×Dic11—42no—
205C2×C11⋊C8—28no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—22no—
211C2×C11⋊C8—22no—
212C2×C11⋊C8—22no—
213C2×C11⋊C8—44no—
214C2×C11⋊C8C2×D412yes—
215C2×C11⋊C8C2×D412yes—
216C22×#135—111no—
217C22×C4⋊C8—111no—
218C2×#416—111no—
219C2×#416—111no—
220#2297—111no—
221#2297D1111yescharacteristic, complemented
222#2056—112no—
223#2055—112no—
224#2055—112no—
225#2054—112no—
226#1735—111no—
227C23×C11—22no—
228C23×C11—22no—
229C23×C11—22no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11—42no—
233C23×C11—42no—
234C23×C11#12112yes—
235C23×C11#12112yes—
236C23×C11#12112yes—
237C23×C11C22×D411yescharacteristic
238C22×D11—22no—
239C22×D11—41no—
240C22×D11—41no—
241C22×D11—42no—
242C22×D11—42no—
243Q8×C11—22no—
244Q8×C11—22no—
245Q8×C11—41no—
246Q8×C11—41no—
247D4×C11—22no—
248D4×C11—22no—
249D4×C11—48no—
250D4×C11—41no—
251D4×C11—41no—
252C2×C4×C11—28no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—44no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—48no—
263C2×C4×C11—42no—
264C2×C4×C11—42no—
265C2×C4×C11—42no—
266C2×C4×C11#12014yes—
267C2×C4×C11#12112yes—
268C2×C4×C11#12112yes—
269C2×C4×C11#12112yes—
270C2×C4×C11#12314yes—
271C2×C4×C11#12314yes—
272C2×C4×C11#12414yes—
273C2×C4×C11#13514yescomplemented
274C2×C4×C11C22×D411yescharacteristic
275C2×C4×C11C22×D411yescharacteristic
276C2×C4×C11C22×D411yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11C2×#4111yescharacteristic
279C2×C4×C11C2×#4111yescharacteristic
280C22⋊D11—48no—
281C2×Dic11—22no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—42no—
285C2×Dic11—42no—
286C2×Dic11—42no—
287D44—22no—
288D44—22no—
289D44—41no—
290D44—41no—
291C4×D11—48no—
292Dic22—22no—
293Dic22—22no—
294Dic22—41no—
295Dic22—41no—
296C11⋊C8—22no—
297C11⋊C8—22no—
298C11⋊C8—42no—
299C22×#41—111no—
300C22×#41C2×D1111yescharacteristic
301C2×#135—224no—
302C2×#135—224no—
303C2×#135—224no—
304C22×Q16—111no—
305C22×SD16—111no—
306C22×SD16—111no—
307C22×D8—111no—
308C23×C8—111no—
309C23×C8—111no—
310C2×#117—111no—
311C2×#117C2×D1111yescharacteristic
312C22×C42C2×D1111yescharacteristic
313C2×C4⋊C8—112no—
314C2×C4⋊C8—112no—
315C2×C4⋊C8—224no—
316#416—224no—
317#416—224no—
318C2×#103—112no—
319C2×#103—112no—
320C2×#102—112no—
321C2×#102—112no—
322#391—112no—
323#391C2×D1112yes—
324#390—112no—
325#390C2×D1112yes—
326#386—21no—
327#386—21no—
328#386—221no—
329#386—221no—
330C4×C22⋊C4—22no—
331C4×C22⋊C4—222no—
332#340—112no—
333#340—112no—
334C22×C11—24no—
335C22×C11—24no—
336C22×C11—22no—
337C22×C11—22no—
338C22×C11—42no—
339C22×C11—44no—
340C22×C11—82no—
341C22×C11—81no—
342C22×C11—81no—
343C22×C11#39414yes—
344C22×C11C2×#12111yescharacteristic
345C22×C11C2×#12111yescharacteristic
346C22×C11C2×#12111yescharacteristic
347C22×C11C2×#13512yes—
348C22×C11#57512yes—
349C2×D11—42no—
350C2×D11—44no—
351C2×D11—82no—
352C2×D11—81no—
353C2×D11—81no—
354C4×C11—24no—
355C4×C11—42no—
356C4×C11—42no—
357C4×C11—82no—
358C4×C11#39414yes—
359C4×C11C2×#12011yescharacteristic
360C4×C11C2×#12311yescharacteristic
361C4×C11C2×#12311yescharacteristic
362C4×C11C2×#12411yescharacteristic
363Dic11—42no—
364Dic11—82no—
365C2×#41—22no—
366C2×#41—22no—
367C2×#41—22no—
368C2×#41—22no—
369C2×#41—22no—
370C2×#41—114no—
371C2×#41—222no—
372C2×#41—222no—
373C2×#41—222no—
374C2×#41—222no—
375C2×#41—222no—
376C2×#41D4414yes—
377C22×Q8—111no—
378C22×Q8C22×D1111yescharacteristic
379C22×D4—21no—
380C22×D4—111no—
381C22×D4—221no—
382C22×D4C22×D1111yescharacteristic
383C23×C4—21no—
384C23×C4—221no—
385C23×C4C22⋊D1111yescharacteristic
386C23×C4C22⋊D1111yescharacteristic
387C23×C4C22×D1111yescharacteristic
388#135—2232no—
389C2×Q16—222no—
390C2×Q16—222no—
391C2×Q16—222no—
392C2×SD16—222no—
393C2×SD16—222no—
394C2×SD16—222no—
395C2×SD16—222no—
396C2×SD16—222no—
397C2×SD16—222no—
398C2×D8—222no—
399C2×D8—222no—
400C2×D8—222no—
401C22×C8—114no—
402C22×C8—111no—
403C22×C8—111no—
404C22×C8—112no—
405C22×C8—222no—
406C22×C8—222no—
407C22×C8—222no—
408C22×C8—222no—
409C22×C8—222no—
410#117—22no—
411#117—22no—
412#117—222no—
413#117—222no—
414C2×C4⋊C4—112no—
415C2×C4⋊C4C22×D1112yes—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—221no—
420C2×C22⋊C4—222no—
421C2×C22⋊C4—222no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—21no—
425C2×C42—221no—
426C2×C42C22⋊D1112yes—
427C2×C42C22×D1112yes—
428C4⋊C8—224no—
429C4⋊C8—224no—
430#103—224no—
431#103—224no—
432#102—224no—
433#102—224no—
434#95—22no—
435#95—22no—
436#95—222no—
437#95—222no—
438C2×C11—24no—
439C2×C11—82no—
440C2×C11C2×#39411yescharacteristic
441C2×C11#303512yes—
442C2×C11#303512yes—
443C2×C11#305011yescharacteristic
444C2×C11#305411yescharacteristic
445D11—82no—
446C24—21no—
447C24—221no—
448C24C2×C22⋊D1111yescharacteristic
449#41—28no—
450#41—28no—
451#41—44no—
452#41—44no—
453#41—228no—
454#41—228no—
455#41—444no—
456#41—444no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—112no—
463C2×Q8—221no—
464C2×Q8—221no—
465C2×Q8—221no—
466C2×Q8—221no—
467C2×Q8—221no—
468C2×Q8C2×D4412yes—
469C2×D4—24no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—42no—
476C2×D4—42no—
477C2×D4—112no—
478C2×D4—224no—
479C2×D4—221no—
480C2×D4—221no—
481C2×D4—221no—
482C2×D4—221no—
483C2×D4—221no—
484C2×D4—442no—
485C2×D4—442no—
486C2×D4C2×D4412yes—
487C22×C4—22no—
488C22×C4—24no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—24no—
492C22×C4—22no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—221no—
497C22×C4—224no—
498C22×C4—222no—
499C22×C4—442no—
500C22×C4—442no—
501C22×C4C2×D4412yes—
502C22×C4#433912yes—
503C22×C4D4×D1112yes—
504C22×C4D4×D1112yes—
505C22×C4#434112yes—
506C22×C4#434112yes—
507C22×C4C2×C22⋊D1112yes—
508C22×C4C2×C22⋊D1112yes—
509C22×C4C2×C22⋊D1111yescharacteristic
510C22×C4C23×D1111yescharacteristic
511Q16—228no—
512SD16—228no—
513SD16—228no—
514D8—228no—
515C2×C8—112no—
516C2×C8—112no—
517C2×C8—228no—
518C2×C8—221no—
519C2×C8—221no—
520C2×C8—221no—
521C2×C8—221no—
522C2×C8—222no—
523C2×C8—222no—
524C2×C8—222no—
525C2×C8—444no—
526C4⋊C4—22no—
527C4⋊C4—22no—
528C4⋊C4—222no—
529C4⋊C4—222no—
530C22⋊C4—44no—
531C22⋊C4—42no—
532C22⋊C4—44no—
533C22⋊C4—444no—
534C22⋊C4—442no—
535C22⋊C4—444no—
536C42—24no—
537C42—22no—
538C42—22no—
539C42—42no—
540C42—442no—
541C11#2353911yescharacteristic, complemented, Sylow
542C23—22no—
543C23—22no—
544C23—22no—
545C23—41no—
546C23—41no—
547C23—42no—
548C23—42no—
549C23—222no—
550C23—441no—
551C23—441no—
552C23—442no—
553C23—442no—
554C23#6698312yes—
555C23#6699112yes—
556C23#6699212yes—
557C23C22×C22⋊D1111yescharacteristic
558Q8—22no—
559Q8—22no—
560Q8—41no—
561Q8—41no—
562Q8—222no—
563Q8—222no—
564Q8—441no—
565Q8—441no—
566D4—22no—
567D4—22no—
568D4—48no—
569D4—41no—
570D4—41no—
571D4—222no—
572D4—222no—
573D4—448no—
574D4—441no—
575D4—441no—
576C2×C4—28no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—44no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—48no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—222no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4—448no—
594C2×C4—442no—
595C2×C4—442no—
596C2×C4—442no—
597C2×C4#6693514yes—
598C2×C4#6693614yes—
599C2×C4#6693814yes—
600C2×C4#6693914yes—
601C2×C4#6698312yes—
602C2×C4#6699112yes—
603C2×C4#6699212yes—
604C2×C4#6700314yescomplemented
605C2×C4C22×D4411yescharacteristic
606C2×C4C2×#433911yescharacteristic
607C2×C4C2×D4×D1111yescharacteristic
608C2×C4C2×D4×D1111yescharacteristic
609C2×C4C2×#434111yescharacteristic
610C2×C4C2×#434111yescharacteristic
611C8—222no—
612C8—222no—
613C8—442no—
614C22—24no—
615C22—24no—
616C22—22no—
617C22—22no—
618C22—44no—
619C22—42no—
620C22—82no—
621C22—81no—
622C22—81no—
623C22—444no—
624C22—442no—
625C22—882no—
626C22—881no—
627C22—881no—
628C22#1062257414yes—
629C22C2×#6698311yescharacteristic
630C22C2×#6699111yescharacteristic
631C22C2×#6699211yescharacteristic
632C22C2×#6700312yes—
633C22#1062335312yes—
634C4—24no—
635C4—42no—
636C4—42no—
637C4—82no—
638C4—442no—
639C4—882no—
640C4#1062257414yes—
641C4C2×#6693511yescharacteristic
642C4C2×#6693611yescharacteristic
643C4C2×#6693811yescharacteristic
644C4C2×#6693911yescharacteristic
645C2—24no—
646C2—82no—
647C2—882no—
648C2C2×#1062257411yescharacteristic
649C2#1307806512yes—
650C2#1307807112yes—
651C2#1307819411yescharacteristic
652C2#1307822211yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2297C2
socleC23×C11C22×D4
prime radicalC22×#67003C2
hypercenter#2297D11
hypocenterC11#23539
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ #2297

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊(C11⋊C8)C2semidirect
3. C2×#10622846C2semidirect
4. C2×#10622615C2semidirect
5. #13071106C2semidirect
6. #13069938C2semidirect
7. #13069933C2semidirect
8. #13069931C2semidirect
9. #13069926C2semidirect
10. #13068332C2semidirect
11. C11×#2297C2semidirect
221. #2297D11semidirect
273. C2×C4×C11#135semidirect
541. C11#23539semidirect
604. C2×C4#67003semidirect

Maximal subgroups

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

subgroupindex
C22×#670032
C22×C4⋊(C11⋊C8)2
C2×#106228462
C2×#106226152
#130711062
#130699382
#130699332
#130699312
#130699262
#130683322
C11×#22972
#2353911