Finite Group Databasebeta

← #14721539

Subgroups — #14721539

Order 2816.

990 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082417C211yesmaximal, characteristic
2#13077644C211yesmaximal, characteristic
3#13071557C211yesmaximal, characteristic
4#13067186C212yesmaximal, complemented
5#13067168C211yesmaximal, characteristic, complemented
6#13067167C211yesmaximal, characteristic, complemented
7#13067147C212yesmaximal, complemented
8#13067134C212yesmaximal, complemented
9#13067127C211yesmaximal, characteristic, complemented
10D11×#328C212yesmaximal, complemented
11C11×#1506C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13#10623261C412yescomplemented
14#10623258C412yescomplemented
15#10623221—22no—
16#10623165—21no—
17#10623165—21no—
18D11×C22⋊Q8C2212yes—
19D11×C22⋊Q8C2212yes—
20#10623110—22no—
21#10623110C412yescomplemented
22Q8×D44C412yescomplemented
23#10623052—21no—
24#10623050—21no—
25C2×C4×D44C2211yescharacteristic
26#10623001C2211yescharacteristic
27C11×#432C2211yescharacteristic
28C11×#376C2211yescharacteristic
29#10622553—21no—
30C4×(C2×D11)⋊C4—21no—
31#10622550C2211yescharacteristic
32#10622539C2211yescharacteristic
33#10622449—22no—
34#10622339C2212yes—
35D11×C22⋊C8C2212yes—
36#10622319—22no—
37#10622280C2211yescharacteristic
38#10622279C2211yescharacteristic
39#10622278—21no—
40#10622277C2211yescharacteristic
41D11×#95C2211yescharacteristic
42#10622267—21no—
43C11×#328C2212yes—
44C11×#328C2212yes—
45#10622176C2212yes—
46#10622176C2212yes—
47#10622105C2212yes—
48#10622105C2212yes—
49#10622090C2212yes—
50#10622090C2212yes—
51C2×Q8×D11C2×C412yes—
52C2×Q8×D11C2×C412yescomplemented
53C22×D44D411yescharacteristic
54C22×C4×D11—21no—
55C22×C4×D11C2311yescharacteristic
56C22×C4×D11C2311yescharacteristic
57C11×C4⋊Q8C2×C411yescharacteristic, complemented
58C11×C4⋊Q8C2×C411yescharacteristic, complemented
59C11×#125—21no—
60C11×C22⋊Q8—21no—
61C11×C22⋊Q8C2312yes—
62C4×Q8×C11—21no—
63C4×Q8×C11C2×C412yescomplemented
64C11×#117—21no—
65C2×C42×C11—21no—
66C2×C42×C11C2311yescharacteristic
67#66999—22no—
68#66999—22no—
69#66999C2×C412yes—
70#66999C2×C412yescomplemented
71C2×(C2×D11)⋊C4—21no—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4D411yescharacteristic
75C2×(C2×D11)⋊C4D411yescharacteristic
76#66979—21no—
77C2×C4⋊Dic11D411yescharacteristic
78#66977—21no—
79#66977C2312yes—
80C2×Dic11⋊C4—21no—
81C2×C4×Dic11—21no—
82C2×#4313—22no—
83C2×C8×D11—22no—
84#66950—22no—
85#66950—22no—
86#66950C2×C412yes—
87#66950C2×C412yescomplemented
88#66949—22no—
89#66949—22no—
90#66949—22no—
91#66949—22no—
92#66949—22no—
93#66949—22no—
94#66946—22no—
95#66946—22no—
96C4⋊C4×D11—22no—
97C4⋊C4×D11—22no—
98C4⋊C4×D11C2×C412yes—
99C4⋊C4×D11C2×C412yescomplemented
100#66943—22no—
101#66941—22no—
102C22⋊C4×D11—22no—
103C22⋊C4×D11—22no—
104#66931—22no—
105#66931—22no—
106C4×D44—22no—
107C4×D44—22no—
108C4×D44C2×C412yes—
109C4×D44C2×C412yes—
110C4×D44D412yes—
111C4×D44D412yes—
112#66923—21no—
113#66923—22no—
114#66922—22no—
115#66922C2×C411yescharacteristic, complemented
116#66922C2×C411yescharacteristic, complemented
117C4×Dic22—21no—
118C4×Dic22C2×C412yescomplemented
119C11×C4⋊C8—21no—
120C11×C22⋊C8C2312yes—
121C11×#97—21no—
122C11×#95—21no—
123C11×#95C2311yescharacteristic
124C11×#95C2311yescharacteristic
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95—21no—
129C11⋊#95C2311yescharacteristic
130C11⋊#95C2311yescharacteristic
131C22⋊(C11⋊C8)C2312yes—
132(C2×D11)⋊C8—22no—
133(C2×D11)⋊C8—22no—
134C4⋊(C11⋊C8)—21no—
135#66867—21no—
136#17621—111nomaximal, Sylow
137C23×D11C2×D411yescharacteristic
138C23×D11C2×D411yescharacteristic
139C2×Q8×C11—21no—
140C2×Q8×C11C22×C412yes—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2411yescharacteristic
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11C2×D411yescharacteristic
149C22×Dic11C2×D411yescharacteristic
150Q8×D11—82no—
151Q8×D11—82no—
152C2×D44—22no—
153C2×D44—22no—
154C2×D44C22⋊C412yes—
155C2×D44C22⋊C412yes—
156C2×C4×D11—22no—
157C2×C4×D11—22no—
158C2×C4×D11—22no—
159C2×C4×D11—22no—
160C2×C4×D11—42no—
161C2×C4×D11—42no—
162C2×C4×D11—81no—
163C2×C4×D11—81no—
164C2×C4×D11—81no—
165C2×C4×D11C22×C412yes—
166C2×C4×D11C22×C412yes—
167C2×C4×D11C2×D412yes—
168C2×C4×D11C2×D412yes—
169C2×Dic22—22no—
170C2×Dic22—22no—
171C2×Dic22—21no—
172C2×Dic22C22×C412yes—
173C2×C8×C11—22no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4C22×C412yes—
180C11×C22⋊C4—22no—
181C42×C11—22no—
182C42×C11—42no—
183C42×C11C22×C411yescharacteristic
184C42×C11C22×C411yescharacteristic
185C42×C11C2×D411yescharacteristic
186C42×C11C2×D411yescharacteristic
187C22⋊Dic11—22no—
188(C2×D11)⋊C4—22no—
189(C2×D11)⋊C4—22no—
190(C2×D11)⋊C4—22no—
191(C2×D11)⋊C4—22no—
192(C2×D11)⋊C4—42no—
193(C2×D11)⋊C4—42no—
194(C2×D11)⋊C4—81no—
195(C2×D11)⋊C4C22⋊C412yes—
196(C2×D11)⋊C4C22⋊C412yes—
197(C2×D11)⋊C4C22⋊C412yes—
198(C2×D11)⋊C4C22⋊C412yes—
199C4⋊Dic11—22no—
200C4⋊Dic11—22no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11C22⋊C412yes—
205C4⋊Dic11C22⋊C412yes—
206C4⋊Dic11C22×C412yes—
207Dic11⋊C4—22no—
208Dic11⋊C4—22no—
209Dic11⋊C4—22no—
210Dic11⋊C4—22no—
211Dic11⋊C4—22no—
212Dic11⋊C4—22no—
213Dic11⋊C4—81no—
214C4×Dic11—22no—
215C4×Dic11—81no—
216C2×C11⋊C8—22no—
217#4313—82no—
218C8×D11—82no—
219#3501—111no—
220#2973—111no—
221#2353—111no—
222#1520—112no—
223#1515—111no—
224#1515—111no—
225#1511—112no—
226#1508—112no—
227#1506—111no—
228#1506D1111yescharacteristic, complemented
229C2×#328—112no—
230C23×C11C22×D411yescharacteristic
231C22×D11—21no—
232C22×D11—21no—
233C22×D11—41no—
234C22×D11—41no—
235C22×D11—41no—
236C22×D11—41no—
237C22×D11C2×C22⋊C412yes—
238C22×D11C2×C22⋊C412yes—
239C22×D11#13712yes—
240C22×D11#13712yes—
241Q8×C11—42no—
242Q8×C11—81no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
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×C11C2×C22⋊C411yescharacteristic
256C2×C4×C11C2×C22⋊C411yescharacteristic
257C2×C4×C11C2×C22⋊C411yescharacteristic
258C2×C4×C11C2×C22⋊C411yescharacteristic
259C2×C4×C11C23×C411yescharacteristic
260C2×C4×C11C22×D411yescharacteristic
261C2×Dic11—22no—
262C2×Dic11—22no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11C2×C22⋊C412yes—
272C2×Dic11C2×C22⋊C412yes—
273D44—24no—
274D44—24no—
275C4×D11—42no—
276C4×D11—42no—
277C4×D11—42no—
278C4×D11—42no—
279C4×D11—82no—
280C4×D11—82no—
281C4×D11—82no—
282C4×D11—82no—
283C4×D11—84no—
284Dic22—42no—
285Dic22—82no—
286Dic22—82no—
287Dic22—81no—
288C8×C11—42no—
289C11⋊C8—42no—
290#554—112no—
291#554—112no—
292#554—222no—
293#554—222no—
294D4×Q8—112no—
295D4×Q8—112no—
296#544—221no—
297#543—221no—
298#543—221no—
299#533—111no—
300#533C2×D1111yescharacteristic
301C2×C22⋊Q8—112no—
302C2×C22⋊Q8—112no—
303#518—221no—
304C2×C4×D4—111no—
305#435—222no—
306#435—222no—
307#432—111no—
308#432C2×D1111yescharacteristic
309#407—112no—
310C2×C22⋊C8—112no—
311#388—221no—
312#387—221no—
313#386—221no—
314#383—111no—
315#381—111no—
316#380—111no—
317C4×C22⋊C4—111no—
318C4×C22⋊C4—221no—
319#376C2×D1111yescharacteristic
320C2×#95—111no—
321#328—112no—
322#328—112no—
323#328—112no—
324#328—112no—
325#328—112no—
326#328—112no—
327#328C2×D1112yes—
328#328C2×D1112yes—
329C22×C11—21no—
330C22×C11—21no—
331C22×C11C22×C22⋊C411yescharacteristic
332C22×C11C2×#13711yescharacteristic
333C22×C11C2×#13711yescharacteristic
334C2×D11—22no—
335C2×D11—22no—
336C2×D11—22no—
337C2×D11—22no—
338C2×D11—22no—
339C2×D11—42no—
340C2×D11—42no—
341C2×D11—81no—
342C2×D11—81no—
343C2×D11#41914yes—
344C4×C11—21no—
345C4×C11—21no—
346C4×C11—21no—
347C4×C11—21no—
348C4×C11—21no—
349C4×C11—21no—
350C4×C11—42no—
351C4×C11—42no—
352C4×C11—42no—
353C4×C11—81no—
354Dic11—22no—
355Dic11—22no—
356Dic11—42no—
357Dic11—42no—
358Dic11—81no—
359Dic11—81no—
360C22×Q8—112no—
361C22×Q8—112no—
362C22×D4—111no—
363C23×C4—111no—
364C23×C4—111no—
365C23×C4—221no—
366C2×M16—222no—
367C22×C8—222no—
368C4⋊Q8—111no—
369C4⋊Q8—111no—
370C4⋊Q8—222no—
371C4⋊Q8—222no—
372C4⋊Q8C4×D1111yescharacteristic, complemented
373C4⋊Q8C4×D1111yescharacteristic, complemented
374#125—21no—
375#125—222no—
376#125—222no—
377#125—221no—
378C22⋊Q8—21no—
379C22⋊Q8—112no—
380C22⋊Q8—112no—
381C22⋊Q8—112no—
382C22⋊Q8—112no—
383C22⋊Q8—112no—
384C22⋊Q8—222no—
385C22⋊Q8—222no—
386C22⋊Q8—222no—
387C22⋊Q8—222no—
388C22⋊Q8—222no—
389C22⋊Q8—222no—
390C22⋊Q8—222no—
391C22⋊Q8—222no—
392C22⋊Q8—222no—
393C22⋊Q8—222no—
394C22⋊Q8—222no—
395C22⋊Q8—222no—
396C22⋊Q8—221no—
397C22⋊Q8C22×D1112yes—
398C4×Q8—21no—
399C4×Q8—112no—
400C4×Q8—221no—
401C4×Q8C4×D1112yescomplemented
402C4×D4—112no—
403C4×D4—112no—
404C4×D4—112no—
405C4×D4—112no—
406C4×D4—222no—
407C4×D4—222no—
408C4×D4—222no—
409C4×D4—222no—
410#117—21no—
411#117—221no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4—112no—
414C2×C4⋊C4—112no—
415C2×C4⋊C4—222no—
416C2×C4⋊C4—222no—
417C2×C4⋊C4—221no—
418C2×C22⋊C4—111no—
419C2×C22⋊C4—111no—
420C2×C22⋊C4—222no—
421C2×C22⋊C4—222no—
422C2×C22⋊C4—221no—
423C2×C22⋊C4—221no—
424C2×C22⋊C4—221no—
425C2×C42—21no—
426C2×C42—221no—
427C2×C42C22×D1111yescharacteristic
428C4⋊C8—21no—
429C4⋊C8—221no—
430C22⋊C8—112no—
431C22⋊C8—222no—
432C22⋊C8—222no—
433C22⋊C8C22×D1112yes—
434#97—21no—
435#97—221no—
436#95—21no—
437#95—111no—
438#95—111no—
439#95—221no—
440#95—221no—
441#95—221no—
442#95—221no—
443#95C22×D1111yescharacteristic
444#95C22×D1111yescharacteristic
445C2×C11—21no—
446C2×C11—21no—
447C2×C11#288311yescharacteristic
448C2×C11C2×#41911yescharacteristic
449C2×C11#290111yescharacteristic
450D11—24no—
451D11—42no—
452C24—111no—
453C24—111no—
454C2×Q8—21no—
455C2×Q8—112no—
456C2×Q8—222no—
457C2×Q8—222no—
458C2×Q8—221no—
459C2×Q8—882no—
460C2×Q8—882no—
461C2×Q8C2×C4×D1112yes—
462C2×D4—112no—
463C2×D4—112no—
464C2×D4—222no—
465C2×D4—222no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—111no—
469C22×C4—111no—
470C22×C4—112no—
471C22×C4—112no—
472C22×C4—112no—
473C22×C4—112no—
474C22×C4—222no—
475C22×C4—222no—
476C22×C4—222no—
477C22×C4—222no—
478C22×C4—221no—
479C22×C4—221no—
480C22×C4—442no—
481C22×C4—442no—
482C22×C4—881no—
483C22×C4—881no—
484C22×C4—881no—
485C22×C4D4×D1111yescharacteristic
486C22×C4D4×D1111yescharacteristic
487C22×C4C23×D1111yescharacteristic
488M16—882no—
489C2×C8—22no—
490C2×C8—222no—
491C2×C8—882no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—112no—
498C4⋊C4—112no—
499C4⋊C4—112no—
500C4⋊C4—222no—
501C4⋊C4—222no—
502C4⋊C4—222no—
503C4⋊C4—222no—
504C4⋊C4—222no—
505C4⋊C4—222no—
506C4⋊C4—221no—
507C4⋊C4—221no—
508C4⋊C4—222no—
509C4⋊C4—221no—
510C4⋊C4—222no—
511C4⋊C4—881no—
512C4⋊C4C2×C4×D1112yes—
513C22⋊C4—22no—
514C22⋊C4—112no—
515C22⋊C4—112no—
516C22⋊C4—112no—
517C22⋊C4—112no—
518C22⋊C4—222no—
519C22⋊C4—222no—
520C22⋊C4—222no—
521C22⋊C4—222no—
522C22⋊C4—222no—
523C22⋊C4—442no—
524C22⋊C4—442no—
525C22⋊C4—881no—
526C42—22no—
527C42—42no—
528C42—222no—
529C42—881no—
530C42C2×C4×D1111yescharacteristic
531C42C2×C4×D1111yescharacteristic
532C42D4×D1111yescharacteristic
533C42D4×D1111yescharacteristic
534C11#1762111yescharacteristic, complemented, Sylow
535C23—112no—
536C23—112no—
537C23—112no—
538C23—112no—
539C23—221no—
540C23—221no—
541C23—441no—
542C23—441no—
543C23—441no—
544C23—441no—
545C23C2×D4×D1111yescharacteristic
546Q8—42no—
547Q8—81no—
548Q8—442no—
549Q8—881no—
550Q8—882no—
551Q8—882no—
552D4—224no—
553D4—224no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—112no—
567C2×C4—112no—
568C2×C4—222no—
569C2×C4—222no—
570C2×C4—442no—
571C2×C4—442no—
572C2×C4—442no—
573C2×C4—442no—
574C2×C4—441no—
575C2×C4—441no—
576C2×C4—441no—
577C2×C4—441no—
578C2×C4—441no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—882no—
583C2×C4—882no—
584C2×C4—882no—
585C2×C4—882no—
586C2×C4—884no—
587C2×C4C22⋊C4×D1111yescharacteristic
588C2×C4C22⋊C4×D1111yescharacteristic
589C2×C4C22⋊C4×D1111yescharacteristic
590C2×C4C22⋊C4×D1111yescharacteristic
591C2×C4C22×C4×D1111yescharacteristic
592C2×C4C2×D4×D1111yescharacteristic
593C8—42no—
594C8—442no—
595C22—21no—
596C22—21no—
597C22—114no—
598C22—222no—
599C22—222no—
600C22—222no—
601C22—222no—
602C22—222no—
603C22—442no—
604C22—442no—
605C22—881no—
606C22—881no—
607C22C2×C22⋊C4×D1111yescharacteristic
608C22D11×#13711yescharacteristic
609C22D11×#13711yescharacteristic
610C4—21no—
611C4—21no—
612C4—21no—
613C4—21no—
614C4—21no—
615C4—21no—
616C4—42no—
617C4—42no—
618C4—42no—
619C4—81no—
620C4—222no—
621C4—222no—
622C4—442no—
623C4—442no—
624C4—881no—
625C4—881no—
626C2—21no—
627C2—21no—
628C2—224no—
629C2—442no—
630C2#1307707511yescharacteristic
631C2D11×#41911yescharacteristic
632C2#1307716011yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1506C2
socleC22×C11C22×C22⋊C4
prime radicalC22×D44D4
cosocleC22×C4×C11C24
hypercenter#1506D11
hypocenterC11#17621
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1506

Complements

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

NH ≅ G/Ntype
4. #13067186C2semidirect
5. #13067168C2semidirect
6. #13067167C2semidirect
7. #13067147C2semidirect
8. #13067134C2semidirect
9. #13067127C2semidirect
10. D11×#328C2semidirect
11. C11×#1506C2semidirect
13. #10623261C4semidirect
14. #10623258C4semidirect
21. #10623110C4semidirect
22. Q8×D44C4semidirect
52. C2×Q8×D11C2×C4semidirect
57. C11×C4⋊Q8C2×C4semidirect
58. C11×C4⋊Q8C2×C4semidirect
63. C4×Q8×C11C2×C4semidirect
70. #66999C2×C4semidirect
87. #66950C2×C4semidirect
99. C4⋊C4×D11C2×C4semidirect
115. #66922C2×C4semidirect
116. #66922C2×C4semidirect
118. C4×Dic22C2×C4semidirect
228. #1506D11semidirect
372. C4⋊Q8C4×D11semidirect
373. C4⋊Q8C4×D11semidirect
401. C4×Q8C4×D11semidirect
534. C11#17621semidirect

Maximal subgroups

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

subgroupindex
#130824172
#130776442
#130715572
#130671862
#130671682
#130671672
#130671472
#130671342
#130671272
D11×#3282
C11×#15062
#1762111