Finite Group Databasebeta

← #14720473

Subgroups — #14720473

Order 2816.

1026 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
1D11×#533C211yesmaximal, characteristic
2D11×#431C211yesmaximal, characteristic
3C2×#10622450C211yesmaximal, characteristic
4#13067069C214yesmaximal, complemented
5#13067043C214yesmaximal, complemented
6#13067020C211yesmaximal, characteristic, complemented
7#13067019C211yesmaximal, characteristic, complemented
8#13067018C211yesmaximal, characteristic, complemented
9C11×#1481C211yesmaximal, characteristic, complemented
10C11×#533C2211yescharacteristic
11C22×#4313—21no—
12#10623259C411yescharacteristic
13#10623259C411yescharacteristic
14D11×C4⋊Q8C411yescharacteristic
15D11×C4⋊Q8C411yescharacteristic
16#10623219—21no—
17D11×#125—21no—
18D11×C22⋊Q8—21no—
19D11×C22⋊Q8C412yes—
20#10623153—21no—
21#10623153C412yes—
22#10623109—21no—
23#10623109C2212yes—
24C4×Q8×D11—21no—
25C4×Q8×D11C2212yes—
26D11×#117—21no—
27#10623048—21no—
28C2×C42×D11C2211yescharacteristic
29#10623001C2211yescharacteristic
30C11×#431C2211yescharacteristic
31C2×C11×C4⋊C8C2211yescharacteristic
32C2×Dic11⋊C8—21no—
33#10622538C2211yescharacteristic
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35#10622450—21no—
36#10622450—21no—
37#10622450C2212yes—
38#10622450C2212yes—
39#10622446—21no—
40D11×C4⋊C8—21no—
41D11×C22⋊C8—21no—
42#10622331—21no—
43#10622298C2212yes—
44C4×C8×D11C2212yes—
45C11×Q8⋊C8C2214yescomplemented
46Q8⋊(C11⋊C8)C2214yescomplemented
47#10622122C2214yescomplemented
48#10622094C2214yescomplemented
49C2×Q8×D11—21no—
50C2×Q8×D11C2×C412yes—
51C22×C4×D11C2×C411yescharacteristic
52C22×C4×D11D411yescharacteristic
53C22×C4×D11D411yescharacteristic
54C22×C8×C11—21no—
55C11×C4⋊Q8C2×C411yescharacteristic
56C11×C4⋊Q8C2×C411yescharacteristic
57C11×#125—21no—
58C11×C22⋊Q8—21no—
59C11×C22⋊Q8C2×C412yes—
60C4×Q8×C11—21no—
61C4×Q8×C11C2312yes—
62C11×#117—21no—
63C2×C42×C11C2311yescharacteristic
64#66999—21no—
65#66999C2×C412yes—
66Q8×Dic11—21no—
67Q8×Dic11C2×C412yes—
68#66997—21no—
69#66997C2×C412yes—
70#66979—21no—
71#66977—21no—
72#66977C2×C412yes—
73C2×C4×Dic11C2×C411yescharacteristic
74C2×C4×Dic11D411yescharacteristic
75C2×C4×Dic11D411yescharacteristic
76C22×C11⋊C8—21no—
77C2×#4313—22no—
78C2×#4313—22no—
79C2×#4313—44no—
80C2×C8×D11—22no—
81#66950—21no—
82#66950C2×C412yes—
83#66949—22no—
84#66949—22no—
85#66945—21no—
86#66945—21no—
87C4⋊C4×D11—21no—
88C4⋊C4×D11—21no—
89C4⋊C4×D11—21no—
90C4⋊C4×D11—22no—
91C4⋊C4×D11—22no—
92C4⋊C4×D11C2×C412yes—
93#66943—21no—
94#66943—21no—
95#66942—22no—
96#66942—22no—
97#66941—21no—
98#66941—21no—
99#66941—21no—
100#66941C2×C412yes—
101#66940—21no—
102#66940—22no—
103#66940—22no—
104#66940C2×C412yes—
105C22⋊C4×D11—22no—
106#66931—22no—
107#66931—22no—
108#66930—22no—
109#66925—22no—
110C42×D11—22no—
111C42×D11C2×C411yescharacteristic
112C42×D11C2×C411yescharacteristic
113C42×D11D411yescharacteristic
114C42×D11D411yescharacteristic
115C42×D11D411yescharacteristic
116C42×D11D411yescharacteristic
117C42×D11C2311yescharacteristic
118C42×D11C2311yescharacteristic
119#66923—21no—
120#66922C2×C411yescharacteristic
121#66922C2×C411yescharacteristic
122C4×Dic22—21no—
123C4×Dic22—22no—
124C4×Dic22—22no—
125C4×Dic22C2312yes—
126C11×C4⋊C8—21no—
127C11×C4⋊C8—21no—
128C11×C4⋊C8C2312yes—
129C11×C22⋊C8—21no—
130C4×C8×C11C2312yes—
131C22⋊(C11⋊C8)—21no—
132(C2×D11)⋊C8—22no—
133Dic11⋊C8—22no—
134Dic11⋊C8—22no—
135Dic11⋊C8—22no—
136C8×Dic11—22no—
137C4⋊(C11⋊C8)—21no—
138C4⋊(C11⋊C8)—21no—
139C4⋊(C11⋊C8)C2312yes—
140C4×C11⋊C8C2312yes—
141#17486—111nomaximal, Sylow
142C23×D11C22⋊C411yescharacteristic
143C2×Q8×C11—21no—
144C2×Q8×C11C22×C412yes—
145C22×C4×C11C22×C411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×Dic11C22⋊C411yescharacteristic
149C22×Dic11C22⋊C411yescharacteristic
150C22×Dic11C22⋊C411yescharacteristic
151Q8×D11—44no—
152Q8×D11—44no—
153C2×C4×D11—22no—
154C2×C4×D11—22no—
155C2×C4×D11—42no—
156C2×C4×D11—42no—
157C2×C4×D11C22⋊C411yescharacteristic
158C2×C4×D11C22⋊C411yescharacteristic
159C2×C4×D11C22⋊C411yescharacteristic
160C2×C4×D11C22⋊C411yescharacteristic
161C2×C4×D11C22⋊C411yescharacteristic
162C2×C4×D11C22⋊C411yescharacteristic
163C2×C4×D11SD1614yes—
164C2×C4×D11Q1614yes—
165C2×C4×D11C22×C411yescharacteristic
166C2×C4×D11C22×C411yescharacteristic
167C2×C4×D11C2×D411yescharacteristic
168C2×C4×D11C2×D411yescharacteristic
169C2×C4×D11C2×D411yescharacteristic
170C2×C4×D11C2×D411yescharacteristic
171C2×Dic22—22no—
172C2×Dic22—22no—
173C2×Dic22—21no—
174C2×Dic22C22×C412yes—
175C2×C8×C11—22no—
176C2×C8×C11—22no—
177C2×C8×C11—42no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4C22×C412yes—
184C11×C22⋊C4—22no—
185C42×C11—22no—
186C42×C11C22×C411yescharacteristic
187C42×C11C2×D411yescharacteristic
188C42×C11C2×D411yescharacteristic
189C42×C11C2411yescharacteristic
190C22⋊Dic11—22no—
191(C2×D11)⋊C4—22no—
192(C2×D11)⋊C4—22no—
193C4⋊Dic11—22no—
194C4⋊Dic11—22no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11C22×C412yes—
199Dic11⋊C4—22no—
200Dic11⋊C4—22no—
201Dic11⋊C4—22no—
202Dic11⋊C4—22no—
203Dic11⋊C4—22no—
204Dic11⋊C4—22no—
205Dic11⋊C4—22no—
206Dic11⋊C4—22no—
207C4×Dic11—22no—
208C4×Dic11—22no—
209C4×Dic11—22no—
210C4×Dic11C22⋊C411yescharacteristic
211C4×Dic11C22⋊C411yescharacteristic
212C4×Dic11C22⋊C411yescharacteristic
213C4×Dic11C22⋊C411yescharacteristic
214C4×Dic11C22⋊C411yescharacteristic
215C4×Dic11C22⋊C411yescharacteristic
216C4×Dic11C22×C411yescharacteristic
217C4×Dic11C22×C411yescharacteristic
218C4×Dic11C2×D411yescharacteristic
219C4×Dic11C2×D411yescharacteristic
220C4×Dic11C2×D411yescharacteristic
221C4×Dic11C2×D411yescharacteristic
222C2×C11⋊C8—22no—
223C2×C11⋊C8—22no—
224C2×C11⋊C8—42no—
225#4313—44no—
226#4313—44no—
227C8×D11—44no—
228C2×#533—111no—
229C2×#431—111no—
230C2×#423—111no—
231#1493—114no—
232#1487—114no—
233#1481—111no—
234#1481—111no—
235#1481—111no—
236#1481D1111yescharacteristic, complemented
237C23×C11C2×C22⋊C411yescharacteristic
238C22×D11—41no—
239C22×D11—41no—
240C22×D11#10314yes—
241C22×D11C2×C22⋊C411yescharacteristic
242C22×D11C2×C22⋊C411yescharacteristic
243Q8×C11—24no—
244Q8×C11—42no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—41no—
249C2×C4×C11C2×C22⋊C411yescharacteristic
250C2×C4×C11C2×C22⋊C411yescharacteristic
251C2×C4×C11C2×C22⋊C411yescharacteristic
252C2×C4×C11C2×SD1612yes—
253C2×C4×C11C2×Q1612yes—
254C2×C4×C11C23×C411yescharacteristic
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C22×D411yescharacteristic
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—22no—
260C2×Dic11—41no—
261C2×Dic11#10314yes—
262C2×Dic11C2×C22⋊C411yescharacteristic
263C2×Dic11C2×C22⋊C411yescharacteristic
264C2×Dic11C2×C22⋊C411yescharacteristic
265C2×Dic11C2×C22⋊C411yescharacteristic
266C2×Dic11C2×C22⋊C411yescharacteristic
267C2×Dic11C2×C22⋊C411yescharacteristic
268C4×D11—22no—
269C4×D11—22no—
270C4×D11—22no—
271C4×D11—22no—
272C4×D11—41no—
273C4×D11—41no—
274C4×D11—41no—
275C4×D11—41no—
276C4×D11—44no—
277C4×D11—44no—
278C4×D11#10314yes—
279C4×D11#10314yes—
280C4×D11C2×SD1612yes—
281C4×D11C2×SD1612yes—
282C4×D11C2×Q1612yes—
283C4×D11C2×Q1612yes—
284Dic22—24no—
285Dic22—44no—
286Dic22—42no—
287Dic22—44no—
288C8×C11—42no—
289C8×C11—42no—
290C11⋊C8—42no—
291C11⋊C8—42no—
292C22×M16—221no—
293#533—111no—
294#533—111no—
295#533—112no—
296#533—112no—
297#533—111no—
298#533—221no—
299#533—221no—
300#533—221no—
301#533—221no—
302#533C2×D1111yescharacteristic
303C2×C4⋊Q8—111no—
304C2×C4⋊Q8—111no—
305C2×#125—221no—
306C2×C22⋊Q8—112no—
307C2×C22⋊Q8—221no—
308C2×C4×Q8—112no—
309C2×C4×Q8—221no—
310C2×#117—221no—
311C22×C42—111no—
312#431—111no—
313#431—112no—
314#431—221no—
315#431—221no—
316#431C2×D1111yescharacteristic
317#423—112no—
318#423—112no—
319#423—221no—
320#423—221no—
321C2×C4⋊C8—111no—
322C2×C4⋊C8—221no—
323C2×C4⋊C8—221no—
324C2×C4⋊C8C2×D1111yescharacteristic
325C2×C22⋊C8—221no—
326C2×C4×C8—112no—
327Q8⋊C8—114no—
328Q8⋊C8—114no—
329Q8⋊C8—114no—
330Q8⋊C8C2×D1114yescomplemented
331C22×C11—21no—
332C22×C11—21no—
333C22×C11C2×#10312yes—
334C22×C11C22×C22⋊C411yescharacteristic
335C2×D11—21no—
336C2×D11—21no—
337C2×D11—21no—
338C2×D11—21no—
339C2×D11—44no—
340C2×D11C2×#10312yes—
341C2×D11C2×#10312yes—
342C4×C11—21no—
343C4×C11—21no—
344C4×C11—21no—
345C4×C11—42no—
346C4×C11—42no—
347C4×C11C2×#10312yes—
348C4×C11#56812yes—
349C4×C11C22×SD1611yescharacteristic
350C4×C11C22×Q1611yescharacteristic
351Dic11—21no—
352Dic11—21no—
353Dic11—21no—
354Dic11—42no—
355Dic11—42no—
356Dic11C2×#10312yes—
357Dic11C2×#10312yes—
358Dic11#42112yes—
359C22×Q8—112no—
360C22×Q8—221no—
361C23×C4—111no—
362C23×C4—111no—
363C23×C4—111no—
364C2×M16—222no—
365C2×M16—222no—
366C2×M16—444no—
367C22×C8—21no—
368C22×C8—222no—
369C22×C8—221no—
370C4⋊Q8—112no—
371C4⋊Q8—112no—
372C4⋊Q8—111no—
373C4⋊Q8—111no—
374C4⋊Q8—221no—
375C4⋊Q8—221no—
376C4⋊Q8—221no—
377C4⋊Q8—221no—
378C4⋊Q8C4×D1111yescharacteristic
379C4⋊Q8C4×D1111yescharacteristic
380#125—21no—
381#125—222no—
382#125—222no—
383#125—221no—
384#125—221no—
385#125—221no—
386C22⋊Q8—21no—
387C22⋊Q8—112no—
388C22⋊Q8—112no—
389C22⋊Q8—112no—
390C22⋊Q8—222no—
391C22⋊Q8—222no—
392C22⋊Q8—222no—
393C22⋊Q8—222no—
394C22⋊Q8—221no—
395C22⋊Q8—221no—
396C22⋊Q8—221no—
397C22⋊Q8C4×D1112yes—
398C4×Q8—21no—
399C4×Q8—112no—
400C4×Q8—112no—
401C4×Q8—112no—
402C4×Q8—222no—
403C4×Q8—222no—
404C4×Q8—222no—
405C4×Q8—221no—
406C4×Q8—222no—
407C4×Q8—221no—
408C4×Q8—221no—
409C4×Q8C22×D1112yes—
410#117—21no—
411#117—222no—
412#117—222no—
413#117—221no—
414#117—221no—
415#117—221no—
416C2×C4⋊C4—112no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4—221no—
419C2×C4⋊C4—222no—
420C2×C4⋊C4—222no—
421C2×C4⋊C4—221no—
422C2×C22⋊C4—222no—
423C2×C42—111no—
424C2×C42—111no—
425C2×C42—111no—
426C2×C42—111no—
427C2×C42—111no—
428C2×C42—111no—
429C2×C42—111no—
430C2×C42—111no—
431C2×C42—111no—
432C2×C42—111no—
433C2×C42—111no—
434C2×C42—222no—
435C2×C42C22×D1111yescharacteristic
436C4⋊C8—21no—
437C4⋊C8—21no—
438C4⋊C8—112no—
439C4⋊C8—222no—
440C4⋊C8—222no—
441C4⋊C8—222no—
442C4⋊C8—221no—
443C4⋊C8—221no—
444C4⋊C8C22×D1112yes—
445C22⋊C8—21no—
446C22⋊C8—222no—
447C22⋊C8—221no—
448C4×C8—112no—
449C4×C8—222no—
450C4×C8C22×D1112yes—
451C2×C11—22no—
452C2×C11#287911yescharacteristic
453C2×C11C22×#10311yescharacteristic
454C2×C11C2×#42111yescharacteristic
455D11—22no—
456D11—22no—
457C24—111no—
458C2×Q8—21no—
459C2×Q8—112no—
460C2×Q8—222no—
461C2×Q8—222no—
462C2×Q8—221no—
463C2×Q8—444no—
464C2×Q8—444no—
465C2×Q8C2×C4×D1112yes—
466C22×C4—111no—
467C22×C4—111no—
468C22×C4—111no—
469C22×C4—114no—
470C22×C4—114no—
471C22×C4—111no—
472C22×C4—111no—
473C22×C4—111no—
474C22×C4—111no—
475C22×C4—111no—
476C22×C4—111no—
477C22×C4—111no—
478C22×C4—111no—
479C22×C4—111no—
480C22×C4—111no—
481C22×C4—111no—
482C22×C4—111no—
483C22×C4—222no—
484C22×C4—222no—
485C22×C4—442no—
486C22×C4—442no—
487C22×C4C2×C4×D1111yescharacteristic
488C22×C4D4×D1111yescharacteristic
489C22×C4D4×D1111yescharacteristic
490M16—444no—
491M16—444no—
492C2×C8—22no—
493C2×C8—22no—
494C2×C8—42no—
495C2×C8—222no—
496C2×C8—222no—
497C2×C8—444no—
498C2×C8—442no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—112no—
505C4⋊C4—222no—
506C4⋊C4—222no—
507C4⋊C4—222no—
508C4⋊C4—222no—
509C4⋊C4—222no—
510C4⋊C4—222no—
511C4⋊C4—222no—
512C4⋊C4—222no—
513C4⋊C4—221no—
514C4⋊C4—221no—
515C4⋊C4—222no—
516C4⋊C4—221no—
517C4⋊C4—222no—
518C4⋊C4C2×C4×D1112yes—
519C22⋊C4—22no—
520C22⋊C4—222no—
521C22⋊C4—222no—
522C22⋊C4—222no—
523C42—22no—
524C42—111no—
525C42—111no—
526C42—111no—
527C42—111no—
528C42—111no—
529C42—111no—
530C42—111no—
531C42—111no—
532C42—111no—
533C42—111no—
534C42—111no—
535C42—111no—
536C42—222no—
537C42—222no—
538C42—222no—
539C42C2×C4×D1111yescharacteristic
540C42D4×D1111yescharacteristic
541C42D4×D1111yescharacteristic
542C42C23×D1111yescharacteristic
543C11#1748611yescharacteristic, complemented, Sylow
544C23—111no—
545C23—111no—
546C23—114no—
547C23—441no—
548C23—441no—
549C23C22⋊C4×D1111yescharacteristic
550Q8—24no—
551Q8—42no—
552Q8—224no—
553Q8—442no—
554Q8—444no—
555Q8—444no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—41no—
560C2×C4—111no—
561C2×C4—111no—
562C2×C4—111no—
563C2×C4—114no—
564C2×C4—112no—
565C2×C4—112no—
566C2×C4—112no—
567C2×C4—112no—
568C2×C4—114no—
569C2×C4—114no—
570C2×C4—111no—
571C2×C4—111no—
572C2×C4—111no—
573C2×C4—222no—
574C2×C4—222no—
575C2×C4—222no—
576C2×C4—222no—
577C2×C4—222no—
578C2×C4—222no—
579C2×C4—222no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4—444no—
585C2×C4—444no—
586C2×C4—441no—
587C2×C4C22⋊C4×D1111yescharacteristic
588C2×C4C22⋊C4×D1111yescharacteristic
589C2×C4C22⋊C4×D1111yescharacteristic
590C2×C4SD16×D1112yes—
591C2×C4Q16×D1112yes—
592C2×C4C22×C4×D1111yescharacteristic
593C2×C4C2×D4×D1111yescharacteristic
594C2×C4C2×D4×D1111yescharacteristic
595C8—42no—
596C8—42no—
597C8—442no—
598C8—442no—
599C22—21no—
600C22—21no—
601C22—112no—
602C22—112no—
603C22—221no—
604C22—221no—
605C22—221no—
606C22—221no—
607C22—444no—
608C22D11×#10312yes—
609C22C2×C22⋊C4×D1111yescharacteristic
610C4—21no—
611C4—21no—
612C4—21no—
613C4—42no—
614C4—42no—
615C4—112no—
616C4—112no—
617C4—112no—
618C4—221no—
619C4—221no—
620C4—221no—
621C4—442no—
622C4—442no—
623C4D11×#10312yes—
624C4#1062328112yes—
625C4C2×SD16×D1111yescharacteristic
626C4C2×Q16×D1111yescharacteristic
627C2—22no—
628C2—222no—
629C2—222no—
630C2#1307705811yescharacteristic
631C2C2×D11×#10311yescharacteristic
632C2D11×#42111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1481C2
socleC22×C11C22×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC42×C11C24
hypercenter#1481D11
hypocenterC11#17486
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1481

Complements

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

NH ≅ G/Ntype
4. #13067069C2semidirect
5. #13067043C2semidirect
6. #13067020C2semidirect
7. #13067019C2semidirect
8. #13067018C2semidirect
9. C11×#1481C2semidirect
45. C11×Q8⋊C8C22semidirect
46. Q8⋊(C11⋊C8)C22semidirect
47. #10622122C22semidirect
48. #10622094C22semidirect
236. #1481D11semidirect
330. Q8⋊C8C2×D11semidirect
543. C11#17486semidirect

Maximal subgroups

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

subgroupindex
D11×#5332
D11×#4312
C2×#106224502
#130670692
#130670432
#130670202
#130670192
#130670182
C11×#14812
#1748611