Finite Group Databasebeta

← #14652914

Subgroups — #14652914

Order 2816.

650 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076919C211yesmaximal, characteristic
2#13068594C211yesmaximal, characteristic, complemented
3C2×#10622176C211yesmaximal, characteristic, complemented
4C2×#10622108C211yesmaximal, characteristic
5C2×#10622089C211yesmaximal, characteristic
6#13066841C211yesmaximal, characteristic, complemented
7C2×C11×#328C211yesmaximal, characteristic, complemented
8C2×C11×C22⋊Q8C2211yescharacteristic
9C2×#67000C411yescharacteristic, complemented
10C2×#66983C2211yescharacteristic
11C22×C4×Dic11C2211yescharacteristic
12C2×C11×C22⋊C8C2211yescharacteristic
13C2×C11×#95C2211yescharacteristic
14#10622843C411yescharacteristic, complemented
15C2×C11⋊#95—21no—
16C2×C11⋊#95—21no—
17C2×C11⋊#95C2211yescharacteristic
18C2×C22⋊(C11⋊C8)C2211yescharacteristic
19C2×Dic11⋊C8—21no—
20#10622603—21no—
21#10622603—21no—
22#10622601C411yescharacteristic, complemented
23#10622590C411yescharacteristic, complemented
24#10622571—21no—
25#10622571—21no—
26C11×#328—22no—
27#10622188—21no—
28#10622176—22no—
29#10622108—22no—
30#10622089—22no—
31C22×Q8×C11C2×C411yescharacteristic
32C23×C4×C11—21no—
33C23×C4×C11C2311yescharacteristic
34C22×C22⋊D11—21no—
35C23×Dic11—21no—
36C23×Dic11D411yescharacteristic
37C23×Dic11D411yescharacteristic
38C22×D44C2×C411yescharacteristic
39C22×C8×C11—21no—
40C11×C22⋊Q8—21no—
41C11×C22⋊Q8—21no—
42C11×C22⋊Q8—21no—
43C11×C22⋊Q8—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4C2×C411yescharacteristic
46C2×C11×C22⋊C4—21no—
47#67000—42no—
48#66983—21no—
49#66983—21no—
50#66983—21no—
51#66983—21no—
52C2×(C2×D11)⋊C4—21no—
53C2×(C2×D11)⋊C4—21no—
54C2×(C2×D11)⋊C4—21no—
55C2×(C2×D11)⋊C4—21no—
56C2×(C2×D11)⋊C4—21no—
57C2×C4⋊Dic11C2×C411yescharacteristic
58C2×C4×Dic11—42no—
59C2×C4×Dic11C2×C411yescharacteristic
60C2×C4×Dic11C2×C411yescharacteristic
61C2×C4×Dic11D411yescharacteristic
62C2×C4×Dic11D411yescharacteristic
63C22×C11⋊C8—21no—
64C11×C22⋊C8—21no—
65C11×C22⋊C8—21no—
66C11×#95—21no—
67C11×#95D412yes—
68C11⋊#95—21no—
69C11⋊#95—21no—
70C11⋊#95—21no—
71C11⋊#95—21no—
72C11⋊#95—21no—
73C11⋊#95—42no—
74C11⋊#95—42no—
75C11⋊#95D412yes—
76C22⋊(C11⋊C8)—21no—
77C22⋊(C11⋊C8)—21no—
78Dic11⋊C8—42no—
79#9716—111nomaximal, Sylow
80C24×C11C2×D411yescharacteristic
81C23×D11—21no—
82C2×Q8×C11—21no—
83C2×Q8×C11—21no—
84C2×Q8×C11—41no—
85C2×Q8×C11—41no—
86C22×C4×C11—21no—
87C22×C4×C11—21no—
88C22×C4×C11—22no—
89C22×C4×C11—41no—
90C22×C4×C11—41no—
91C22×C4×C11—41no—
92C22×C4×C11—41no—
93C22×C4×C11—41no—
94C22×C4×C11—41no—
95C22×C4×C11—41no—
96C22×C4×C11—41no—
97C22×C4×C11C22×C411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11#4111yescharacteristic
102C22×C4×C11#4111yescharacteristic
103C2×C22⋊D11—41no—
104C2×C22⋊D11—41no—
105C2×C22⋊D11—41no—
106C2×C22⋊D11—41no—
107C2×C22⋊D11—41no—
108C2×C22⋊D11—41no—
109C22×Dic11—22no—
110C22×Dic11—21no—
111C22×Dic11—22no—
112C22×Dic11—21no—
113C22×Dic11—21no—
114C22×Dic11—21no—
115C22×Dic11—21no—
116C22×Dic11—41no—
117C22×Dic11—41no—
118C22×Dic11—41no—
119C22×Dic11—41no—
120C22×Dic11—41no—
121C22×Dic11—41no—
122C22×Dic11—41no—
123C22×Dic11—41no—
124C22×Dic11—41no—
125C22×Dic11C22⋊C411yescharacteristic
126C22×Dic11C22⋊C411yescharacteristic
127C22×Dic11C22⋊C411yescharacteristic
128C22×Dic11C22⋊C411yescharacteristic
129C2×D44—21no—
130C2×D44—21no—
131C2×D44—41no—
132C2×D44—41no—
133C2×C8×C11—41no—
134C2×C8×C11—41no—
135C2×C8×C11—41no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—41no—
139C11×C4⋊C4—41no—
140C11×C22⋊C4—41no—
141C11×C22⋊C4—41no—
142(C2×D11)⋊C4—42no—
143(C2×D11)⋊C4—42no—
144(C2×D11)⋊C4—42no—
145(C2×D11)⋊C4—42no—
146(C2×D11)⋊C4—41no—
147(C2×D11)⋊C4—41no—
148C4⋊Dic11—21no—
149C4⋊Dic11—21no—
150C4×Dic11—22no—
151C4×Dic11—22no—
152C4×Dic11—41no—
153C4×Dic11—41no—
154C2×C11⋊C8—41no—
155C2×C11⋊C8—41no—
156C2×C11⋊C8—41no—
157#2850—111no—
158#1797—111no—
159C2×#328—111no—
160C2×#328D1111yescharacteristic, complemented
161C2×#327—111no—
162C2×#327—111no—
163#1434—111no—
164C23×C11—21no—
165C23×C11—21no—
166C23×C11—21no—
167C23×C11—21no—
168C23×C11C2×C22⋊C411yescharacteristic
169C23×C11#12111yescharacteristic
170C23×C11#12111yescharacteristic
171C23×C11#13511yescharacteristic
172C23×C11#13511yescharacteristic
173C23×C11AGL(1,ℤ/8)11yescharacteristic
174C23×C11#13711yescharacteristic
175C22×D11—41no—
176C22×D11—41no—
177C22×D11—41no—
178C22×D11—41no—
179C22×D11—41no—
180C22×D11—41no—
181C22×D11—41no—
182Q8×C11—81no—
183Q8×C11—81no—
184C2×C4×C11—21no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—42no—
201C2×C4×C11—81no—
202C2×C4×C11—81no—
203C2×C4×C11—81no—
204C2×C4×C11—81no—
205C2×C4×C11C4×D411yescharacteristic
206C2×C4×C11C4×D411yescharacteristic
207C2×C4×C11#12411yescharacteristic
208C2×C4×C11#12711yescharacteristic
209C22⋊D11—81no—
210C22⋊D11—81no—
211C22⋊D11—81no—
212C22⋊D11—81no—
213C2×Dic11—21no—
214C2×Dic11—21no—
215C2×Dic11—21no—
216C2×Dic11—21no—
217C2×Dic11—21no—
218C2×Dic11—21no—
219C2×Dic11—21no—
220C2×Dic11—21no—
221C2×Dic11—21no—
222C2×Dic11—21no—
223C2×Dic11—21no—
224C2×Dic11—42no—
225C2×Dic11—42no—
226C2×Dic11—42no—
227C2×Dic11—42no—
228C2×Dic11—42no—
229C2×Dic11—42no—
230C2×Dic11—41no—
231C2×Dic11—41no—
232C2×Dic11—41no—
233C2×Dic11—42no—
234C2×Dic11—81no—
235C2×Dic11—81no—
236C2×Dic11—81no—
237C2×Dic11—81no—
238C2×Dic11#9912yes—
239D44—81no—
240D44—81no—
241C8×C11—81no—
242C11⋊C8—81no—
243C2×#124—111no—
244C2×C22⋊Q8C2×D1111yescharacteristic
245C2×#121—111no—
246C22×C42—111no—
247C2×C4⋊C8—221no—
248C2×C22⋊C8—111no—
249C2×C22⋊C8C2×D1111yescharacteristic
250#391—111no—
251#390—111no—
252#388—221no—
253#388—221no—
254#386—221no—
255#386—221no—
256#382—111no—
257C2×#95—111no—
258C2×#95—221no—
259C2×#95—221no—
260C2×#95C2×D1111yescharacteristic
261#336—221no—
262#328—22no—
263#328—222no—
264#327—222no—
265#327—222no—
266C22×C11—21no—
267C22×C11—21no—
268C22×C11—21no—
269C22×C11—21no—
270C22×C11—21no—
271C22×C11—21no—
272C22×C11—21no—
273C22×C11—21no—
274C22×C11—21no—
275C22×C11—21no—
276C22×C11—21no—
277C22×C11—21no—
278C22×C11#39011yescharacteristic
279C22×C11C2×#9911yescharacteristic
280C22×C11#41011yescharacteristic
281C22×C11#41611yescharacteristic
282C22×C11#41711yescharacteristic
283C22×C11#42111yescharacteristic
284C22×C11#42111yescharacteristic
285C22×C11#46311yescharacteristic
286C22×C11#46311yescharacteristic
287C22×C11#46411yescharacteristic
288C22×C11#46411yescharacteristic
289C2×D11—81no—
290C2×D11—81no—
291C2×D11—81no—
292C2×D11—81no—
293C2×D11—81no—
294C2×D11—81no—
295C2×D11—81no—
296C4×C11—21no—
297C4×C11—21no—
298C4×C11—21no—
299C4×C11—21no—
300C4×C11—82no—
301C4×C11—81no—
302C4×C11—81no—
303Dic11—22no—
304Dic11—41no—
305Dic11—41no—
306Dic11—41no—
307Dic11—82no—
308Dic11—81no—
309C22×Q8C4×D1111yescharacteristic
310C22×D4—111no—
311C22×D4—221no—
312C23×C4—21no—
313C23×C4—111no—
314C23×C4—111no—
315C23×C4—221no—
316C23×C4C22×D1111yescharacteristic
317C22×C8—21no—
318C22×C8—221no—
319#124—442no—
320C22⋊Q8—21no—
321C22⋊Q8—21no—
322C22⋊Q8—21no—
323C22⋊Q8—21no—
324#121—221no—
325#121—221no—
326#121—221no—
327#121—221no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—111no—
330C2×C4⋊C4C4×D1111yescharacteristic
331C2×C22⋊C4—21no—
332C2×C22⋊C4—221no—
333C2×C22⋊C4—221no—
334C2×C22⋊C4—221no—
335C2×C22⋊C4—221no—
336C2×C22⋊C4—221no—
337C2×C42—111no—
338C2×C42—111no—
339C2×C42—111no—
340C2×C42—111no—
341C2×C42—442no—
342C4⋊C8—442no—
343C22⋊C8—21no—
344C22⋊C8—21no—
345C22⋊C8—221no—
346C22⋊C8—221no—
347#95—21no—
348#95—112no—
349#95—221no—
350#95—221no—
351#95—221no—
352#95—221no—
353#95—221no—
354#95—442no—
355#95—442no—
356#95C22⋊D1112yes—
357C2×C11—21no—
358C2×C11—21no—
359C2×C11—21no—
360C2×C11—21no—
361C2×C11#151211yescharacteristic
362C2×C11#151311yescharacteristic
363C2×C11#151611yescharacteristic
364C2×C11#152111yescharacteristic
365C2×C11#196311yescharacteristic
366C2×C11#196411yescharacteristic
367C2×C11#198311yescharacteristic
368D11—161no—
369C24—221no—
370C24D4×D1111yescharacteristic
371C2×Q8—21no—
372C2×Q8—21no—
373C2×Q8—41no—
374C2×Q8—41no—
375C2×D4—221no—
376C2×D4—221no—
377C2×D4—441no—
378C2×D4—441no—
379C2×D4—441no—
380C2×D4—441no—
381C2×D4—441no—
382C2×D4—441no—
383C2×D4—441no—
384C2×D4—441no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—22no—
388C22×C4—41no—
389C22×C4—41no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4—41no—
393C22×C4—41no—
394C22×C4—41no—
395C22×C4—41no—
396C22×C4—111no—
397C22×C4—111no—
398C22×C4—111no—
399C22×C4—111no—
400C22×C4—222no—
401C22×C4—221no—
402C22×C4—221no—
403C22×C4—221no—
404C22×C4—221no—
405C22×C4—221no—
406C22×C4—222no—
407C22×C4—441no—
408C22×C4—441no—
409C22×C4—441no—
410C22×C4—441no—
411C22×C4—441no—
412C22×C4—441no—
413C22×C4—441no—
414C22×C4—441no—
415C22×C4—441no—
416C22×C4C2×C4×D1111yescharacteristic
417C22×C4#433911yescharacteristic
418C22×C4D4×D1111yescharacteristic
419C22×C4D4×D1111yescharacteristic
420C22×C4#434111yescharacteristic
421C22×C4C2×C22⋊D1111yescharacteristic
422C2×C8—41no—
423C2×C8—41no—
424C2×C8—41no—
425C2×C8—441no—
426C2×C8—441no—
427C2×C8—441no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—41no—
431C4⋊C4—41no—
432C4⋊C4—221no—
433C4⋊C4—221no—
434C22⋊C4—41no—
435C22⋊C4—41no—
436C22⋊C4—442no—
437C22⋊C4—442no—
438C22⋊C4—442no—
439C22⋊C4—442no—
440C22⋊C4—441no—
441C22⋊C4—441no—
442C42—222no—
443C42—222no—
444C42—441no—
445C42—441no—
446C11#971611yescharacteristic, complemented, Sylow
447C23—21no—
448C23—21no—
449C23—21no—
450C23—21no—
451C23—441no—
452C23—441no—
453C23—441no—
454C23—441no—
455C23—441no—
456C23—441no—
457C23—441no—
458C23C22⋊C4×D1111yescharacteristic
459C23#6693711yescharacteristic
460C23#6696711yescharacteristic
461C23#6696911yescharacteristic
462C23#6697111yescharacteristic
463C23#6697211yescharacteristic
464C23#6699211yescharacteristic
465Q8—81no—
466Q8—81no—
467D4—881no—
468D4—881no—
469D4—881no—
470D4—881no—
471D4—881no—
472D4—881no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—81no—
491C2×C4—81no—
492C2×C4—81no—
493C2×C4—81no—
494C2×C4—112no—
495C2×C4—221no—
496C2×C4—221no—
497C2×C4—221no—
498C2×C4—221no—
499C2×C4—221no—
500C2×C4—221no—
501C2×C4—221no—
502C2×C4—221no—
503C2×C4—221no—
504C2×C4—221no—
505C2×C4—221no—
506C2×C4—442no—
507C2×C4—442no—
508C2×C4—442no—
509C2×C4—442no—
510C2×C4—442no—
511C2×C4—442no—
512C2×C4—441no—
513C2×C4—441no—
514C2×C4—441no—
515C2×C4—442no—
516C2×C4—881no—
517C2×C4—881no—
518C2×C4—881no—
519C2×C4—881no—
520C2×C4(C22⋊D11)⋊C411yescharacteristic
521C2×C4#6693811yescharacteristic
522C2×C4C4×C22⋊D1111yescharacteristic
523C2×C4#6699311yescharacteristic
524C8—81no—
525C8—881no—
526C22—21no—
527C22—21no—
528C22—21no—
529C22—21no—
530C22—21no—
531C22—21no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—21no—
538C22—881no—
539C22—881no—
540C22—881no—
541C22—881no—
542C22—881no—
543C22—881no—
544C22—881no—
545C22#1062235311yescharacteristic
546C22D11×#9911yescharacteristic
547C22#1062241111yescharacteristic
548C22#1062241611yescharacteristic
549C22#1062241711yescharacteristic
550C22#1062243211yescharacteristic
551C22#1062243411yescharacteristic
552C22#1062243411yescharacteristic
553C22#1062257011yescharacteristic
554C22#1062277811yescharacteristic
555C22#1062279811yescharacteristic
556C4—21no—
557C4—21no—
558C4—21no—
559C4—21no—
560C4—82no—
561C4—81no—
562C4—81no—
563C4—222no—
564C4—441no—
565C4—441no—
566C4—441no—
567C4—882no—
568C4—881no—
569C2—21no—
570C2—21no—
571C2—21no—
572C2—21no—
573C2—1761no—
574C2#1306715311yescharacteristic
575C2#1306715811yescharacteristic
576C2#1306717111yescharacteristic
577C2#1306719211yescharacteristic
578C2#1306944611yescharacteristic
579C2#1306945011yescharacteristic
580C2#1306954511yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C11×#328C2
socleC23×C11C2×C22⋊C4
prime radicalC2×#66983C22
cosocleC23×C4×C11C23
hypercenterC2×#328D11
hypocenterC11#9716
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
2. #13068594C2semidirect
3. C2×#10622176C2semidirect
6. #13066841C2semidirect
7. C2×C11×#328C2semidirect
9. C2×#67000C4semidirect
14. #10622843C4semidirect
22. #10622601C4semidirect
23. #10622590C4semidirect
160. C2×#328D11semidirect
446. C11#9716semidirect

Maximal subgroups

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

subgroupindex
#130769192
#130685942
C2×#106221762
C2×#106221082
C2×#106220892
#130668412
C2×C11×#3282
#971611