Finite Group Databasebeta

← #14720475

Subgroups — #14720475

Order 2816.

1026 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#533C211yesmaximal, characteristic
2C2×#10622298C211yesmaximal, characteristic
3D11×#423C211yesmaximal, characteristic
4#13067072C211yesmaximal, characteristic, complemented
5#13067071C211yesmaximal, characteristic, complemented
6#13067070C211yesmaximal, characteristic, complemented
7#13067043C214yesmaximal, complemented
8#13067017C214yesmaximal, complemented
9C11×#1493C211yesmaximal, characteristic, complemented
10C11×#533C2211yescharacteristic
11C2×M16×D11—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×#423C2211yescharacteristic
31C2×C4×C8×C11C2211yescharacteristic
32#10622731—21no—
33C2×(C2×D11)⋊C8—21no—
34C2×Dic11⋊C8—21no—
35#10622537C2211yescharacteristic
36C2×C4×C11⋊C8C2211yescharacteristic
37#10622450—21no—
38#10622450C2212yes—
39D11×C4⋊C8—21no—
40D11×C4⋊C8C2212yes—
41#10622298—21no—
42#10622298—21no—
43#10622298C2212yes—
44#10622298C2212yes—
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
54C2×C11×M16—21no—
55C22×C8×C11—21no—
56C11×C4⋊Q8C2×C411yescharacteristic
57C11×C4⋊Q8C2×C411yescharacteristic
58C11×#125—21no—
59C11×C22⋊Q8—21no—
60C11×C22⋊Q8C2×C412yes—
61C4×Q8×C11—21no—
62C4×Q8×C11C2312yes—
63C11×#117—21no—
64C2×C42×C11C2311yescharacteristic
65#66999—21no—
66#66999C2×C412yes—
67Q8×Dic11—21no—
68Q8×Dic11C2×C412yes—
69#66997—21no—
70#66997C2×C412yes—
71#66979—21no—
72#66977—21no—
73#66977C2×C412yes—
74C2×C4×Dic11C2×C411yescharacteristic
75C2×C4×Dic11D411yescharacteristic
76C2×C4×Dic11D411yescharacteristic
77C2×#4318—21no—
78C22×C11⋊C8—21no—
79M16×D11—44no—
80C2×#4313—22no—
81C2×C8×D11—22no—
82#66950—21no—
83#66950C2×C412yes—
84#66949—22no—
85#66949—22no—
86#66945—21no—
87#66945—21no—
88C4⋊C4×D11—21no—
89C4⋊C4×D11—21no—
90C4⋊C4×D11—21no—
91C4⋊C4×D11—22no—
92C4⋊C4×D11—22no—
93C4⋊C4×D11C2×C412yes—
94#66943—21no—
95#66943—21no—
96#66942—22no—
97#66942—22no—
98#66941—21no—
99#66941—21no—
100#66941—21no—
101#66941C2×C412yes—
102#66940—21no—
103#66940—22no—
104#66940—22no—
105#66940C2×C412yes—
106C22⋊C4×D11—22no—
107#66931—22no—
108#66931—22no—
109#66930—22no—
110#66925—22no—
111C42×D11—22no—
112C42×D11C2×C411yescharacteristic
113C42×D11C2×C411yescharacteristic
114C42×D11D411yescharacteristic
115C42×D11D411yescharacteristic
116C42×D11D411yescharacteristic
117C42×D11D411yescharacteristic
118C42×D11C2311yescharacteristic
119C42×D11C2311yescharacteristic
120#66923—21no—
121#66922C2×C411yescharacteristic
122#66922C2×C411yescharacteristic
123C4×Dic22—21no—
124C4×Dic22—22no—
125C4×Dic22—22no—
126C4×Dic22C2312yes—
127C11×C4⋊C8—21no—
128C11×C4⋊C8C2312yes—
129C4×C8×C11—21no—
130C4×C8×C11C2312yes—
131(C2×D11)⋊C8—22no—
132(C2×D11)⋊C8—22no—
133Dic11⋊C8—22no—
134Dic11⋊C8—22no—
135Dic11⋊C8—22no—
136Dic11⋊C8—22no—
137C4⋊(C11⋊C8)—21no—
138C4⋊(C11⋊C8)C2312yes—
139C4×C11⋊C8—21no—
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—
175C11×M16—42no—
176C2×C8×C11—22no—
177C2×C8×C11—22no—
178C2×C8×C11—42no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4C22×C412yes—
185C11×C22⋊C4—22no—
186C42×C11—22no—
187C42×C11C22×C411yescharacteristic
188C42×C11C2×D411yescharacteristic
189C42×C11C2×D411yescharacteristic
190C42×C11C2411yescharacteristic
191C22⋊Dic11—22no—
192(C2×D11)⋊C4—22no—
193(C2×D11)⋊C4—22no—
194C4⋊Dic11—22no—
195C4⋊Dic11—22no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11C22×C412yes—
200Dic11⋊C4—22no—
201Dic11⋊C4—22no—
202Dic11⋊C4—22no—
203Dic11⋊C4—22no—
204Dic11⋊C4—22no—
205Dic11⋊C4—22no—
206Dic11⋊C4—22no—
207Dic11⋊C4—22no—
208C4×Dic11—22no—
209C4×Dic11—22no—
210C4×Dic11—22no—
211C4×Dic11C22⋊C411yescharacteristic
212C4×Dic11C22⋊C411yescharacteristic
213C4×Dic11C22⋊C411yescharacteristic
214C4×Dic11C22⋊C411yescharacteristic
215C4×Dic11C22⋊C411yescharacteristic
216C4×Dic11C22⋊C411yescharacteristic
217C4×Dic11C22×C411yescharacteristic
218C4×Dic11C22×C411yescharacteristic
219C4×Dic11C2×D411yescharacteristic
220C4×Dic11C2×D411yescharacteristic
221C4×Dic11C2×D411yescharacteristic
222C4×Dic11C2×D411yescharacteristic
223#4318—42no—
224C2×C11⋊C8—22no—
225C2×C11⋊C8—22no—
226C2×C11⋊C8—42no—
227#4313—44no—
228C8×D11—44no—
229C2×#533—111no—
230C2×#431—111no—
231C2×#423—111no—
232#1493—111no—
233#1493—111no—
234#1493—111no—
235#1493D1111yescharacteristic, complemented
236#1487—114no—
237#1481—114no—
238C23×C11C2×C22⋊C411yescharacteristic
239C22×D11—41no—
240C22×D11—41no—
241C22×D11#10314yes—
242C22×D11C2×C22⋊C411yescharacteristic
243C22×D11C2×C22⋊C411yescharacteristic
244Q8×C11—24no—
245Q8×C11—42no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11C2×C22⋊C411yescharacteristic
251C2×C4×C11C2×C22⋊C411yescharacteristic
252C2×C4×C11C2×C22⋊C411yescharacteristic
253C2×C4×C11C2×SD1612yes—
254C2×C4×C11C2×Q1612yes—
255C2×C4×C11C23×C411yescharacteristic
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C22×D411yescharacteristic
258C2×Dic11—22no—
259C2×Dic11—22no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11#10314yes—
263C2×Dic11C2×C22⋊C411yescharacteristic
264C2×Dic11C2×C22⋊C411yescharacteristic
265C2×Dic11C2×C22⋊C411yescharacteristic
266C2×Dic11C2×C22⋊C411yescharacteristic
267C2×Dic11C2×C22⋊C411yescharacteristic
268C2×Dic11C2×C22⋊C411yescharacteristic
269C4×D11—22no—
270C4×D11—22no—
271C4×D11—22no—
272C4×D11—22no—
273C4×D11—41no—
274C4×D11—41no—
275C4×D11—41no—
276C4×D11—41no—
277C4×D11—44no—
278C4×D11—44no—
279C4×D11#10314yes—
280C4×D11#10314yes—
281C4×D11C2×SD1612yes—
282C4×D11C2×SD1612yes—
283C4×D11C2×Q1612yes—
284C4×D11C2×Q1612yes—
285Dic22—24no—
286Dic22—44no—
287Dic22—44no—
288Dic22—42no—
289C8×C11—42no—
290C8×C11—42no—
291C11⋊C8—42no—
292C11⋊C8—42no—
293C22×M16—221no—
294#533—111no—
295#533—111no—
296#533—112no—
297#533—112no—
298#533—111no—
299#533—221no—
300#533—221no—
301#533—221no—
302#533—221no—
303#533C2×D1111yescharacteristic
304C2×C4⋊Q8—111no—
305C2×C4⋊Q8—111no—
306C2×#125—221no—
307C2×C22⋊Q8—112no—
308C2×C22⋊Q8—221no—
309C2×C4×Q8—112no—
310C2×C4×Q8—221no—
311C2×#117—221no—
312C22×C42—111no—
313#431—112no—
314#431—112no—
315#431—221no—
316#431—221no—
317#423—111no—
318#423—112no—
319#423—221no—
320#423—221no—
321#423C2×D1111yescharacteristic
322C2×C4⋊C8—112no—
323C2×C4⋊C8—221no—
324C2×C4⋊C8—221no—
325C2×C22⋊C8—221no—
326C2×C4×C8—111no—
327C2×C4×C8C2×D1111yescharacteristic
328Q8⋊C8—114no—
329Q8⋊C8—114no—
330Q8⋊C8—114no—
331Q8⋊C8C2×D1114yescomplemented
332C22×C11—21no—
333C22×C11—21no—
334C22×C11C2×#10312yes—
335C22×C11C22×C22⋊C411yescharacteristic
336C2×D11—21no—
337C2×D11—21no—
338C2×D11—21no—
339C2×D11—21no—
340C2×D11—44no—
341C2×D11C2×#10312yes—
342C2×D11C2×#10312yes—
343C4×C11—21no—
344C4×C11—21no—
345C4×C11—42no—
346C4×C11—42no—
347C4×C11C2×#10312yes—
348C4×C11#42112yes—
349C4×C11#56812yes—
350C4×C11C22×SD1611yescharacteristic
351C4×C11C22×Q1611yescharacteristic
352Dic11—21no—
353Dic11—21no—
354Dic11—21no—
355Dic11—21no—
356Dic11—42no—
357Dic11—42no—
358Dic11C2×#10312yes—
359Dic11C2×#10312yes—
360C22×Q8—112no—
361C22×Q8—221no—
362C23×C4—111no—
363C23×C4—111no—
364C23×C4—111no—
365C2×M16—21no—
366C2×M16—222no—
367C2×M16—221no—
368C2×M16—444no—
369C22×C8—21no—
370C22×C8—222no—
371C22×C8—221no—
372C4⋊Q8—112no—
373C4⋊Q8—112no—
374C4⋊Q8—111no—
375C4⋊Q8—111no—
376C4⋊Q8—221no—
377C4⋊Q8—221no—
378C4⋊Q8—221no—
379C4⋊Q8—221no—
380C4⋊Q8C4×D1111yescharacteristic
381C4⋊Q8C4×D1111yescharacteristic
382#125—21no—
383#125—222no—
384#125—222no—
385#125—221no—
386#125—221no—
387#125—221no—
388C22⋊Q8—21no—
389C22⋊Q8—112no—
390C22⋊Q8—112no—
391C22⋊Q8—112no—
392C22⋊Q8—222no—
393C22⋊Q8—222no—
394C22⋊Q8—222no—
395C22⋊Q8—222no—
396C22⋊Q8—221no—
397C22⋊Q8—221no—
398C22⋊Q8—221no—
399C22⋊Q8C4×D1112yes—
400C4×Q8—21no—
401C4×Q8—112no—
402C4×Q8—112no—
403C4×Q8—112no—
404C4×Q8—222no—
405C4×Q8—222no—
406C4×Q8—222no—
407C4×Q8—221no—
408C4×Q8—222no—
409C4×Q8—221no—
410C4×Q8—221no—
411C4×Q8C22×D1112yes—
412#117—21no—
413#117—222no—
414#117—222no—
415#117—221no—
416#117—221no—
417#117—221no—
418C2×C4⋊C4—112no—
419C2×C4⋊C4—221no—
420C2×C4⋊C4—221no—
421C2×C4⋊C4—222no—
422C2×C4⋊C4—222no—
423C2×C4⋊C4—221no—
424C2×C22⋊C4—222no—
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—111no—
435C2×C42—111no—
436C2×C42—222no—
437C2×C42C22×D1111yescharacteristic
438C4⋊C8—21no—
439C4⋊C8—112no—
440C4⋊C8—222no—
441C4⋊C8—222no—
442C4⋊C8—222no—
443C4⋊C8—222no—
444C4⋊C8—221no—
445C4⋊C8C22×D1112yes—
446C22⋊C8—222no—
447C22⋊C8—222no—
448C4×C8—21no—
449C4×C8—112no—
450C4×C8—221no—
451C4×C8C22×D1112yes—
452C2×C11—22no—
453C2×C11#287911yescharacteristic
454C2×C11C22×#10311yescharacteristic
455C2×C11C2×#42111yescharacteristic
456D11—22no—
457D11—22no—
458C24—111no—
459C2×Q8—21no—
460C2×Q8—112no—
461C2×Q8—222no—
462C2×Q8—222no—
463C2×Q8—221no—
464C2×Q8—444no—
465C2×Q8—444no—
466C2×Q8C2×C4×D1112yes—
467C22×C4—111no—
468C22×C4—111no—
469C22×C4—111no—
470C22×C4—114no—
471C22×C4—114no—
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—111no—
484C22×C4—222no—
485C22×C4—222no—
486C22×C4—442no—
487C22×C4—442no—
488C22×C4C2×C4×D1111yescharacteristic
489C22×C4D4×D1111yescharacteristic
490C22×C4D4×D1111yescharacteristic
491M16—42no—
492M16—444no—
493M16—442no—
494C2×C8—22no—
495C2×C8—22no—
496C2×C8—42no—
497C2×C8—222no—
498C2×C8—222no—
499C2×C8—444no—
500C2×C8—442no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—112no—
507C4⋊C4—222no—
508C4⋊C4—222no—
509C4⋊C4—222no—
510C4⋊C4—222no—
511C4⋊C4—222no—
512C4⋊C4—222no—
513C4⋊C4—222no—
514C4⋊C4—222no—
515C4⋊C4—221no—
516C4⋊C4—221no—
517C4⋊C4—222no—
518C4⋊C4—221no—
519C4⋊C4—222no—
520C4⋊C4C2×C4×D1112yes—
521C22⋊C4—22no—
522C22⋊C4—222no—
523C22⋊C4—222no—
524C22⋊C4—222no—
525C42—22no—
526C42—111no—
527C42—111no—
528C42—111no—
529C42—111no—
530C42—111no—
531C42—111no—
532C42—111no—
533C42—111no—
534C42—111no—
535C42—111no—
536C42—111no—
537C42—111no—
538C42—222no—
539C42—222no—
540C42—222no—
541C42C2×C4×D1111yescharacteristic
542C42D4×D1111yescharacteristic
543C42D4×D1111yescharacteristic
544C42C23×D1111yescharacteristic
545C11#1748611yescharacteristic, complemented, Sylow
546C23—111no—
547C23—111no—
548C23—114no—
549C23—441no—
550C23—441no—
551C23C22⋊C4×D1111yescharacteristic
552Q8—24no—
553Q8—42no—
554Q8—224no—
555Q8—444no—
556Q8—444no—
557Q8—442no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—111no—
563C2×C4—111no—
564C2×C4—114no—
565C2×C4—112no—
566C2×C4—112no—
567C2×C4—112no—
568C2×C4—112no—
569C2×C4—114no—
570C2×C4—114no—
571C2×C4—111no—
572C2×C4—111no—
573C2×C4—111no—
574C2×C4—111no—
575C2×C4—222no—
576C2×C4—222no—
577C2×C4—222no—
578C2×C4—222no—
579C2×C4—222no—
580C2×C4—222no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4—444no—
586C2×C4—444no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4C22⋊C4×D1111yescharacteristic
590C2×C4C22⋊C4×D1111yescharacteristic
591C2×C4C22⋊C4×D1111yescharacteristic
592C2×C4SD16×D1112yes—
593C2×C4Q16×D1112yes—
594C2×C4C22×C4×D1111yescharacteristic
595C2×C4C2×D4×D1111yescharacteristic
596C2×C4C2×D4×D1111yescharacteristic
597C8—42no—
598C8—42no—
599C8—442no—
600C8—442no—
601C22—21no—
602C22—21no—
603C22—112no—
604C22—112no—
605C22—221no—
606C22—221no—
607C22—221no—
608C22—221no—
609C22—444no—
610C22D11×#10312yes—
611C22C2×C22⋊C4×D1111yescharacteristic
612C4—21no—
613C4—21no—
614C4—42no—
615C4—42no—
616C4—112no—
617C4—112no—
618C4—221no—
619C4—221no—
620C4—221no—
621C4—221no—
622C4—442no—
623C4—442no—
624C4D11×#10312yes—
625C4#1062243412yes—
626C4#1062328112yes—
627C4C2×SD16×D1111yescharacteristic
628C4C2×Q16×D1111yescharacteristic
629C2—22no—
630C2—222no—
631C2—222no—
632C2#1307705811yescharacteristic
633C2C2×D11×#10311yescharacteristic
634C2C2×#1062243411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1493C2
socleC22×C11C22×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC42×C11C24
hypercenter#1493D11
hypocenterC11#17486
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1493

Complements

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

NH ≅ G/Ntype
4. #13067072C2semidirect
5. #13067071C2semidirect
6. #13067070C2semidirect
7. #13067043C2semidirect
8. #13067017C2semidirect
9. C11×#1493C2semidirect
45. C11×Q8⋊C8C22semidirect
46. Q8⋊(C11⋊C8)C22semidirect
47. #10622122C22semidirect
48. #10622094C22semidirect
235. #1493D11semidirect
331. Q8⋊C8C2×D11semidirect
545. C11#17486semidirect

Maximal subgroups

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

subgroupindex
D11×#5332
C2×#106222982
D11×#4232
#130670722
#130670712
#130670702
#130670432
#130670172
C11×#14932
#1748611