Finite Group Databasebeta

← #14645142

Subgroups — #14645142

Order 2816.

1088 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×D11C211yesmaximal, characteristic
2#13068593C211yesmaximal, characteristic
3C4×(C2×D11)⋊C8C211yesmaximal, characteristic
4C2×#10622094C211yesmaximal, characteristic, complemented
5C2×Q8⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
6C2×#10622122C211yesmaximal, characteristic, complemented
7C2×C11×Q8⋊C8C211yesmaximal, characteristic, complemented
8C22×Q8×D11C411yescharacteristic
9C2×C4×Q8×C11C2211yescharacteristic
10C2×Q8×Dic11C411yescharacteristic
11C4×Q8×D11—22no—
12C4×Q8×D11—22no—
13C4×Q8×D11—22no—
14C4×Q8×D11—22no—
15C2×C4⋊C4×D11—21no—
16C2×C4⋊C4×D11C411yescharacteristic
17C2×#66940—21no—
18C2×#66940C411yescharacteristic
19C2×C42×D11—21no—
20C2×C42×D11C2211yescharacteristic
21C2×C4×Dic22—21no—
22C2×C4×Dic22C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C4×C8×C11C2211yescharacteristic
25C2×(C2×D11)⋊C8—21no—
26C2×(C2×D11)⋊C8—21no—
27C2×C4⋊(C11⋊C8)C2211yescharacteristic
28C2×C4×C11⋊C8C2211yescharacteristic
29C11×Q8⋊C8—22no—
30#10622188—21no—
31#10622188—21no—
32Q8⋊(C11⋊C8)—22no—
33#10622122—22no—
34#10622094—22no—
35C22×Q8×C11C2×C411yescharacteristic
36C2×Q8×D11—22no—
37C2×Q8×D11—22no—
38C2×Q8×D11—22no—
39C2×Q8×D11—22no—
40C2×Q8×D11—22no—
41C2×Q8×D11C814yescomplemented
42C22×C4×D11—21no—
43C22×C4×D11—21no—
44C22×C4×D11C2×C411yescharacteristic
45C22×C4×D11D411yescharacteristic
46C22×C4×D11D411yescharacteristic
47C22×Dic22—21no—
48C22×Dic22C2×C411yescharacteristic
49C22×C8×C11—21no—
50C22×C8×C11—21no—
51C4×Q8×C11—21no—
52C4×Q8×C11—21no—
53C4×Q8×C11D412yes—
54C4×Q8×C11D412yes—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4C2×C411yescharacteristic
57C2×C42×C11—21no—
58C2×C42×C11C2311yescharacteristic
59Q8×Dic11—22no—
60Q8×Dic11—22no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11C2×C411yescharacteristic
63C2×Dic11⋊C4—21no—
64C2×Dic11⋊C4—21no—
65C2×Dic11⋊C4—21no—
66C2×C4×Dic11—21no—
67C2×C4×Dic11—21no—
68C2×C4×Dic11—21no—
69C2×C4×Dic11C2×C411yescharacteristic
70C2×C4×Dic11D411yescharacteristic
71C2×C4×Dic11D411yescharacteristic
72C22×C11⋊C8—21no—
73C22×C11⋊C8—21no—
74C4⋊C4×D11—24no—
75C4⋊C4×D11—24no—
76C4⋊C4×D11—22no—
77C4⋊C4×D11—22no—
78#66940—24no—
79#66940—24no—
80#66940—22no—
81#66940—22no—
82C42×D11—24no—
83C42×D11—24no—
84C42×D11—21no—
85C42×D11—21no—
86C42×D11—21no—
87C42×D11—21no—
88C4×Dic22—24no—
89C4×Dic22—24no—
90C4×Dic22—21no—
91C4×Dic22—21no—
92C4×Dic22D412yes—
93C4×Dic22D412yes—
94C11×C4⋊C8—21no—
95C11×C4⋊C8—21no—
96C4×C8×C11—21no—
97C4×C8×C11—21no—
98(C2×D11)⋊C8—24no—
99(C2×D11)⋊C8—42no—
100C4⋊(C11⋊C8)—21no—
101C4⋊(C11⋊C8)—21no—
102C4×C11⋊C8—21no—
103C4×C11⋊C8—21no—
104#8311—111nomaximal, Sylow
105C23×D11C22⋊C411yescharacteristic
106C2×Q8×C11—21no—
107C2×Q8×C11—21no—
108C2×Q8×C11—21no—
109C2×Q8×C11C22⋊C412yes—
110C2×Q8×C11C2×C812yes—
111C2×Q8×C11M1612yes—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11C22×C411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×Dic11—21no—
118C22×Dic11—21no—
119C22×Dic11C22⋊C411yescharacteristic
120C22×Dic11C22⋊C411yescharacteristic
121C22×Dic11C22⋊C411yescharacteristic
122Q8×D11—28no—
123Q8×D11—28no—
124Q8×D11—28no—
125Q8×D11—28no—
126C2×C4×D11—24no—
127C2×C4×D11—24no—
128C2×C4×D11—24no—
129C2×C4×D11—24no—
130C2×C4×D11—22no—
131C2×C4×D11—21no—
132C2×C4×D11—21no—
133C2×C4×D11—21no—
134C2×C4×D11—21no—
135C2×C4×D11—21no—
136C2×C4×D11—21no—
137C2×C4×D11—21no—
138C2×C4×D11—21no—
139C2×C4×D11—21no—
140C2×C4×D11—21no—
141C2×C4×D11—41no—
142C2×C4×D11—42no—
143C2×C4×D11—42no—
144C2×C4×D11C2×C812yes—
145C2×C4×D11M1612yes—
146C2×C4×D11SD1612yes—
147C2×C4×D11Q1612yes—
148C2×Dic22—24no—
149C2×Dic22—24no—
150C2×Dic22—24no—
151C2×Dic22—21no—
152C2×Dic22—21no—
153C2×Dic22—21no—
154C2×Dic22C22⋊C412yes—
155C2×Dic22C2×C812yes—
156C2×Dic22M1612yes—
157C2×C8×C11—22no—
158C2×C8×C11—41no—
159C2×C8×C11—41no—
160C2×C8×C11—41no—
161C2×C8×C11—41no—
162C2×C8×C11—41no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4C22⋊C412yes—
167C42×C11—22no—
168C42×C11—22no—
169C42×C11C2×D411yescharacteristic
170C42×C11C2×D411yescharacteristic
171C42×C11C2×D411yescharacteristic
172C42×C11C2×D411yescharacteristic
173C4⋊Dic11—24no—
174C4⋊Dic11—21no—
175C4⋊Dic11C22⋊C412yes—
176Dic11⋊C4—24no—
177Dic11⋊C4—24no—
178Dic11⋊C4—22no—
179Dic11⋊C4—22no—
180C4×Dic11—24no—
181C4×Dic11—24no—
182C4×Dic11—21no—
183C4×Dic11—21no—
184C4×Dic11—21no—
185C4×Dic11—21no—
186C4×Dic11—22no—
187C4×Dic11—22no—
188C4×Dic11—21no—
189C4×Dic11—21no—
190C2×C11⋊C8—22no—
191C2×C11⋊C8—41no—
192C2×C11⋊C8—41no—
193C2×C11⋊C8—41no—
194C2×C11⋊C8—41no—
195C2×C11⋊C8—41no—
196C22×C4×Q8—111no—
197#1797—111no—
198C4×C22⋊C8—111no—
199C2×Q8⋊C8—111no—
200C2×Q8⋊C8—111no—
201C2×Q8⋊C8—111no—
202C2×Q8⋊C8D1111yescharacteristic, complemented
203C23×C11C2×C22⋊C411yescharacteristic
204C22×D11—21no—
205C22×D11—21no—
206C22×D11—21no—
207C22×D11—21no—
208C22×D11C22⋊C812yes—
209C22×D11#10312yes—
210C22×D11#10412yes—
211Q8×C11—22no—
212Q8×C11—22no—
213Q8×C11—22no—
214Q8×C11C22⋊C814yescomplemented
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—22no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11C2×C22⋊C411yescharacteristic
224C2×C4×C11C2×C22⋊C411yescharacteristic
225C2×C4×C11#12011yescharacteristic
226C2×C4×C11#12011yescharacteristic
227C2×C4×C11#12011yescharacteristic
228C2×C4×C11#12011yescharacteristic
229C2×C4×C11C22×C811yescharacteristic
230C2×C4×C11C2×M1611yescharacteristic
231C2×C4×C11C2×M1611yescharacteristic
232C2×C4×C11C2×M1611yescharacteristic
233C2×C4×C11C2×SD1611yescharacteristic
234C2×C4×C11C2×Q1611yescharacteristic
235C2×C4×C11#13711yescharacteristic
236C2×C4×C11#13711yescharacteristic
237C2×Dic11—21no—
238C2×Dic11—21no—
239C2×Dic11—22no—
240C2×Dic11—22no—
241C2×Dic11—21no—
242C2×Dic11—22no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—22no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—41no—
249C2×Dic11—41no—
250C2×Dic11C22⋊C812yes—
251C2×Dic11#10312yes—
252C4×D11—216no—
253C4×D11—22no—
254C4×D11—22no—
255C4×D11—22no—
256C4×D11—22no—
257C4×D11—22no—
258C4×D11—22no—
259C4×D11—22no—
260C4×D11—22no—
261C4×D11—42no—
262C4×D11—42no—
263C4×D11—48no—
264Dic22—216no—
265Dic22—22no—
266Dic22—22no—
267Dic22—22no—
268Dic22C22⋊C814yescomplemented
269C8×C11—42no—
270C8×C11—81no—
271C11⋊C8—42no—
272C11⋊C8—81no—
273C23×Q8—111no—
274C2×C4×Q8—111no—
275C2×C4×Q8—111no—
276C2×C4×Q8—111no—
277C2×C4×Q8—221no—
278C2×C4×Q8—221no—
279C2×C4×Q8—222no—
280C2×C4×Q8—222no—
281C2×C4×Q8—222no—
282C2×C4×Q8—222no—
283C2×C4×Q8C2×D1111yescharacteristic
284C22×C4⋊C4—111no—
285C22×C4⋊C4—221no—
286C22×C42—111no—
287C22×C42—221no—
288C2×C4⋊C8—111no—
289C2×C4⋊C8C2×D1111yescharacteristic
290C2×C22⋊C8—221no—
291C2×C22⋊C8—221no—
292C2×C4×C8—111no—
293C2×C4×C8C2×D1111yescharacteristic
294#336—221no—
295#336—221no—
296Q8⋊C8—22no—
297Q8⋊C8—222no—
298Q8⋊C8—222no—
299Q8⋊C8—222no—
300C22×C11#37911yescharacteristic
301C22×C11C2×C22⋊C811yescharacteristic
302C22×C11#40711yescharacteristic
303C22×C11C2×#10311yescharacteristic
304C22×C11#41911yescharacteristic
305C22×C11C2×#10411yescharacteristic
306C22×C11#42111yescharacteristic
307C2×D11—22no—
308C2×D11—22no—
309C2×D11—22no—
310C2×D11—22no—
311C2×D11—22no—
312C2×D11—22no—
313C2×D11Q8⋊C814yescomplemented
314C4×C11—24no—
315C4×C11—21no—
316C4×C11—21no—
317C4×C11—42no—
318C4×C11C2×C22⋊C811yescharacteristic
319C4×C11C2×C22⋊C811yescharacteristic
320C4×C11#40711yescharacteristic
321C4×C11#40711yescharacteristic
322C4×C11#44811yescharacteristic
323C4×C11#44811yescharacteristic
324C4×C11#45111yescharacteristic
325C4×C11#45111yescharacteristic
326Dic11—22no—
327Dic11—24no—
328Dic11—22no—
329Dic11—41no—
330Dic11—42no—
331C22×Q8—114no—
332C22×Q8—111no—
333C22×Q8—221no—
334C22×Q8—222no—
335C22×Q8—222no—
336C22×Q8—222no—
337C22×Q8—222no—
338C22×Q8—222no—
339C22×Q8C4×D1111yescharacteristic
340C23×C4—111no—
341C23×C4—111no—
342C23×C4—111no—
343C23×C4—221no—
344C23×C4—221no—
345C22×C8—21no—
346C22×C8—21no—
347C22×C8—221no—
348C22×C8—221no—
349C4×Q8—21no—
350C4×Q8—21no—
351C4×Q8—112no—
352C4×Q8—112no—
353C4×Q8—224no—
354C4×Q8—224no—
355C4×Q8—222no—
356C4×Q8—224no—
357C4×Q8—224no—
358C4×Q8—222no—
359C4×Q8—222no—
360C4×Q8—222no—
361C4×Q8—221no—
362C4×Q8—221no—
363C4×Q8D4412yes—
364C4×Q8C22⋊D1112yes—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—111no—
367C2×C4⋊C4—222no—
368C2×C4⋊C4—224no—
369C2×C4⋊C4—224no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4—221no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4—221no—
374C2×C4⋊C4—222no—
375C2×C4⋊C4C4×D1111yescharacteristic
376C2×C42—21no—
377C2×C42—111no—
378C2×C42—111no—
379C2×C42—111no—
380C2×C42—224no—
381C2×C42—224no—
382C2×C42—221no—
383C2×C42—221no—
384C2×C42—221no—
385C2×C42—221no—
386C2×C42—221no—
387C2×C42—221no—
388C2×C42—221no—
389C2×C42C22×D1111yescharacteristic
390C4⋊C8—21no—
391C4⋊C8—21no—
392C4⋊C8—221no—
393C4⋊C8—221no—
394C22⋊C8—224no—
395C22⋊C8—442no—
396C4×C8—21no—
397C4×C8—21no—
398C4×C8—221no—
399C4×C8—221no—
400C2×C11C2×Q8⋊C811yescharacteristic
401C2×C11#147911yescharacteristic
402C2×C11#148711yescharacteristic
403C2×C11#149111yescharacteristic
404C2×C11#177911yescharacteristic
405C2×C11#178711yescharacteristic
406C2×C11#178911yescharacteristic
407D11—24no—
408C24—111no—
409C2×Q8—21no—
410C2×Q8—21no—
411C2×Q8—21no—
412C2×Q8—112no—
413C2×Q8—112no—
414C2×Q8—112no—
415C2×Q8—224no—
416C2×Q8—224no—
417C2×Q8—224no—
418C2×Q8—228no—
419C2×Q8—228no—
420C2×Q8—228no—
421C2×Q8—228no—
422C2×Q8—221no—
423C2×Q8—221no—
424C2×Q8—221no—
425C2×Q8C8×D1112yes—
426C2×Q8#431312yes—
427C2×Q8(C2×D11)⋊C412yes—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—111no—
431C22×C4—111no—
432C22×C4—112no—
433C22×C4—112no—
434C22×C4—112no—
435C22×C4—112no—
436C22×C4—111no—
437C22×C4—224no—
438C22×C4—224no—
439C22×C4—224no—
440C22×C4—222no—
441C22×C4—224no—
442C22×C4—221no—
443C22×C4—221no—
444C22×C4—221no—
445C22×C4—221no—
446C22×C4—221no—
447C22×C4—221no—
448C22×C4—221no—
449C22×C4—221no—
450C22×C4—221no—
451C22×C4—221no—
452C22×C4—221no—
453C22×C4—221no—
454C22×C4—441no—
455C22×C4—442no—
456C22×C4—442no—
457C22×C4C2×C4×D1111yescharacteristic
458C22×C4D4×D1111yescharacteristic
459C22×C4D4×D1111yescharacteristic
460C2×C8—22no—
461C2×C8—41no—
462C2×C8—41no—
463C2×C8—41no—
464C2×C8—41no—
465C2×C8—41no—
466C2×C8—222no—
467C2×C8—441no—
468C2×C8—441no—
469C2×C8—441no—
470C2×C8—441no—
471C2×C8—441no—
472C4⋊C4—21no—
473C4⋊C4—22no—
474C4⋊C4—22no—
475C4⋊C4—112no—
476C4⋊C4—224no—
477C4⋊C4—224no—
478C4⋊C4—224no—
479C4⋊C4—222no—
480C4⋊C4—221no—
481C4⋊C4—222no—
482C4⋊C4(C2×D11)⋊C412yes—
483C42—22no—
484C42—22no—
485C42—224no—
486C42—224no—
487C42—221no—
488C42—221no—
489C42—221no—
490C42—222no—
491C42—221no—
492C42—221no—
493C42—221no—
494C42—222no—
495C42C2×D4411yescharacteristic
496C42D4×D1111yescharacteristic
497C42D4×D1111yescharacteristic
498C42C2×C22⋊D1111yescharacteristic
499C11#831111yescharacteristic, complemented, Sylow
500C23—112no—
501C23—112no—
502C23—112no—
503C23—221no—
504C23—221no—
505C23—221no—
506C23—221no—
507C23C22⋊C4×D1111yescharacteristic
508Q8—22no—
509Q8—22no—
510Q8—22no—
511Q8—114no—
512Q8—2216no—
513Q8—222no—
514Q8—222no—
515Q8—222no—
516Q8(C2×D11)⋊C814yescomplemented
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—22no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—112no—
526C2×C4—112no—
527C2×C4—2216no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—222no—
531C2×C4—222no—
532C2×C4—221no—
533C2×C4—222no—
534C2×C4—221no—
535C2×C4—222no—
536C2×C4—222no—
537C2×C4—222no—
538C2×C4—222no—
539C2×C4—222no—
540C2×C4—222no—
541C2×C4—222no—
542C2×C4—222no—
543C2×C4—222no—
544C2×C4—221no—
545C2×C4—221no—
546C2×C4—221no—
547C2×C4—442no—
548C2×C4—442no—
549C2×C4—448no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4C22⋊C4×D1111yescharacteristic
553C2×C4#6693511yescharacteristic
554C2×C4#6693511yescharacteristic
555C2×C4C2×C8×D1111yescharacteristic
556C2×C4C2×#431311yescharacteristic
557C2×C4M16×D1111yescharacteristic
558C2×C4M16×D1111yescharacteristic
559C2×C4SD16×D1111yescharacteristic
560C2×C4#6696811yescharacteristic
561C2×C4Q16×D1111yescharacteristic
562C2×C4#6697111yescharacteristic
563C2×C4C2×(C2×D11)⋊C411yescharacteristic
564C2×C4#6699011yescharacteristic
565C2×C4#6699011yescharacteristic
566C8—42no—
567C8—81no—
568C8—442no—
569C8—881no—
570C22—114no—
571C22—222no—
572C22—222no—
573C22—222no—
574C22—222no—
575C22—222no—
576C22—222no—
577C22D11×C22⋊C811yescharacteristic
578C22#1062233911yescharacteristic
579C22D11×#10311yescharacteristic
580C22#1062241511yescharacteristic
581C22D11×#10411yescharacteristic
582C22#1062243411yescharacteristic
583C22#1062256811yescharacteristic
584C4—21no—
585C4—21no—
586C4—24no—
587C4—42no—
588C4—222no—
589C4—222no—
590C4—224no—
591C4—441no—
592C4—442no—
593C4D11×C22⋊C811yescharacteristic
594C4#1062233911yescharacteristic
595C4#1062241911yescharacteristic
596C4#1062242111yescharacteristic
597C4C2×(C2×D11)⋊C811yescharacteristic
598C4#1062273911yescharacteristic
599C4#1062278311yescharacteristic
600C4#1062279911yescharacteristic
601C2—224no—
602C2D11×Q8⋊C811yescharacteristic
603C2#1306700911yescharacteristic
604C2#1306704311yescharacteristic
605C2#1306706111yescharacteristic
606C2#1306852511yescharacteristic
607C2#1306854911yescharacteristic
608C2#1306855811yescharacteristic
subgroupG/H
centerC22×C4D4×D11
commutatorC2×C4×C11C22×C8
FrattiniC2×C42C22×D11
FittingC2×C11×Q8⋊C8C2
socleC23×C11C2×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC2×C42×C11C23
hypercenterC2×Q8⋊C8D11
hypocenterC11#8311
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
4. C2×#10622094C2semidirect
5. C2×Q8⋊(C11⋊C8)C2semidirect
6. C2×#10622122C2semidirect
7. C2×C11×Q8⋊C8C2semidirect
41. C2×Q8×D11C8semidirect
202. C2×Q8⋊C8D11semidirect
214. Q8×C11C22⋊C8semidirect
268. Dic22C22⋊C8semidirect
313. C2×D11Q8⋊C8semidirect
499. C11#8311semidirect
516. Q8(C2×D11)⋊C8semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D112
#130685932
C4×(C2×D11)⋊C82
C2×#106220942
C2×Q8⋊(C11⋊C8)2
C2×#106221222
C2×C11×Q8⋊C82
#831111