Finite Group Databasebeta

← #14652903

Subgroups — #14652903

Order 2816.

742 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076915C211yesmaximal, characteristic
2#13068594C211yesmaximal, characteristic, complemented
3C2×#10622105C211yesmaximal, characteristic, complemented
4C2×#10622090C211yesmaximal, characteristic, complemented
5C2×#10622175C211yesmaximal, characteristic
6#95×Dic11C211yesmaximal, characteristic, complemented
7C2×C11×#327C211yesmaximal, characteristic
8C2×C11×#121C2211yescharacteristic
9C2×#66989C411yescharacteristic, complemented
10C2×#66977C2211yescharacteristic
11C22×C4×Dic11—21no—
12C22×C4×Dic11C2211yescharacteristic
13C2×C11×C22⋊C8C2211yescharacteristic
14C2×C11×#95C2211yescharacteristic
15#10622834C411yescharacteristic, complemented
16#10622833—21no—
17#10622833—21no—
18C2×C11⋊#95—21no—
19C2×C11⋊#95C2211yescharacteristic
20C2×C22⋊(C11⋊C8)C2211yescharacteristic
21C2×Dic11⋊C8—21no—
22#10622590C411yescharacteristic, complemented
23#10622587C411yescharacteristic, complemented
24#10622558—21no—
25#10622558—21no—
26C11×#327—22no—
27#10622188—21no—
28#10622175—22no—
29#10622105—22no—
30#10622090—22no—
31C22×D4×C11—21no—
32C22×D4×C11C2×C411yescharacteristic
33C23×C4×C11—21no—
34C23×C4×C11C2311yescharacteristic
35C23×Dic11—21no—
36C23×Dic11D411yescharacteristic
37C23×Dic11D411yescharacteristic
38C22×Dic22C2×C411yescharacteristic
39C22×C8×C11—21no—
40C11×#121—21no—
41C11×#121—21no—
42C11×#121—21no—
43C11×#121—21no—
44C2×C11×C4⋊C4C2×C411yescharacteristic
45C2×C11×C22⋊C4—21no—
46C2×C22⋊Dic11—21no—
47C2×C22⋊Dic11—21no—
48C2×C22⋊Dic11—21no—
49C2×C22⋊Dic11—21no—
50C2×C22⋊Dic11—21no—
51#66989—42no—
52C2×C4⋊Dic11C2×C411yescharacteristic
53#66977—21no—
54#66977—21no—
55#66977—21no—
56#66977—21no—
57C2×Dic11⋊C4—21no—
58C2×C4×Dic11—24no—
59C2×C4×Dic11—42no—
60C2×C4×Dic11—42no—
61C2×C4×Dic11—42no—
62C2×C4×Dic11C2×C411yescharacteristic
63C2×C4×Dic11C2×C411yescharacteristic
64C2×C4×Dic11D411yescharacteristic
65C2×C4×Dic11D411yescharacteristic
66C22×C11⋊C8—21no—
67C11×C22⋊C8—21no—
68C11×C22⋊C8—21no—
69C11×#95—21no—
70C11×#95D412yes—
71C11⋊#95—24no—
72C11⋊#95—21no—
73C11⋊#95—21no—
74C11⋊#95—21no—
75C11⋊#95—21no—
76C11⋊#95—21no—
77C11⋊#95D412yes—
78C22⋊(C11⋊C8)—21no—
79C22⋊(C11⋊C8)—21no—
80Dic11⋊C8—42no—
81#9713—111nomaximal, Sylow
82C24×C11—21no—
83C24×C11C2×D411yescharacteristic
84C2×D4×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—41no—
87C2×D4×C11—41no—
88C2×D4×C11—41no—
89C2×D4×C11—41no—
90C2×D4×C11—41no—
91C2×D4×C11—41no—
92C2×D4×C11—41no—
93C2×D4×C11—41no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—21no—
98C22×C4×C11—41no—
99C22×C4×C11—41no—
100C22×C4×C11—41no—
101C22×C4×C11—41no—
102C22×C4×C11—41no—
103C22×C4×C11—41no—
104C22×C4×C11C22×C411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11#4111yescharacteristic
109C22×C4×C11#4111yescharacteristic
110C22×Dic11—22no—
111C22×Dic11—22no—
112C22×Dic11—22no—
113C22×Dic11—22no—
114C22×Dic11—22no—
115C22×Dic11—21no—
116C22×Dic11—21no—
117C22×Dic11—22no—
118C22×Dic11—21no—
119C22×Dic11—21no—
120C22×Dic11—21no—
121C22×Dic11—21no—
122C22×Dic11—41no—
123C22×Dic11—41no—
124C22×Dic11—41no—
125C22×Dic11—41no—
126C22×Dic11—41no—
127C22×Dic11C22⋊C411yescharacteristic
128C22×Dic11C22⋊C411yescharacteristic
129C22×Dic11C22⋊C411yescharacteristic
130C22×Dic11C22⋊C411yescharacteristic
131C2×Dic22—21no—
132C2×Dic22—21no—
133C2×Dic22—41no—
134C2×Dic22—41no—
135C2×C8×C11—41no—
136C2×C8×C11—41no—
137C2×C8×C11—41no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—21no—
140C11×C22⋊C4—41no—
141C11×C22⋊C4—41no—
142C22⋊Dic11—42no—
143C22⋊Dic11—42no—
144C22⋊Dic11—42no—
145C22⋊Dic11—42no—
146C22⋊Dic11—41no—
147C22⋊Dic11—41no—
148C4⋊Dic11—21no—
149C4⋊Dic11—21no—
150Dic11⋊C4—41no—
151Dic11⋊C4—41no—
152C4×Dic11—22no—
153C4×Dic11—22no—
154C4×Dic11—41no—
155C4×Dic11—41no—
156C4×Dic11—48no—
157C2×C11⋊C8—41no—
158C2×C11⋊C8—41no—
159C2×C11⋊C8—41no—
160#2850—111no—
161#1797—111no—
162C2×#328—111no—
163C2×#328—111no—
164C2×#327—111no—
165C2×#327D1111yescharacteristic
166C4×#95—111no—
167C23×C11—21no—
168C23×C11—21no—
169C23×C11—21no—
170C23×C11—21no—
171C23×C11—41no—
172C23×C11—41no—
173C23×C11—41no—
174C23×C11—41no—
175C23×C11—41no—
176C23×C11—41no—
177C23×C11—41no—
178C23×C11C2×C22⋊C411yescharacteristic
179C23×C11#12111yescharacteristic
180C23×C11#12111yescharacteristic
181C23×C11#13511yescharacteristic
182C23×C11#13511yescharacteristic
183C23×C11AGL(1,ℤ/8)11yescharacteristic
184C23×C11#13711yescharacteristic
185D4×C11—81no—
186D4×C11—81no—
187D4×C11—81no—
188D4×C11—81no—
189D4×C11—81no—
190D4×C11—81no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—24no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11C4×D411yescharacteristic
210C2×C4×C11C4×D411yescharacteristic
211C2×C4×C11#12411yescharacteristic
212C2×C4×C11#12711yescharacteristic
213C2×Dic11—24no—
214C2×Dic11—24no—
215C2×Dic11—21no—
216C2×Dic11—21no—
217C2×Dic11—21no—
218C2×Dic11—21no—
219C2×Dic11—21no—
220C2×Dic11—21no—
221C2×Dic11—24no—
222C2×Dic11—21no—
223C2×Dic11—21no—
224C2×Dic11—21no—
225C2×Dic11—42no—
226C2×Dic11—42no—
227C2×Dic11—42no—
228C2×Dic11—42no—
229C2×Dic11—42no—
230C2×Dic11—42no—
231C2×Dic11—42no—
232C2×Dic11—42no—
233C2×Dic11—41no—
234C2×Dic11—41no—
235C2×Dic11—41no—
236C2×Dic11—41no—
237C2×Dic11—41no—
238C2×Dic11—41no—
239C2×Dic11#9912yes—
240C2×Dic11#10412yes—
241C2×Dic11#10412yes—
242Dic22—81no—
243Dic22—81no—
244C8×C11—81no—
245C11⋊C8—81no—
246C2×#124—111no—
247C2×C22⋊Q8—111no—
248C2×#121C2×D1111yescharacteristic
249C22×C42—111no—
250C22×C42—221no—
251C2×C4⋊C8—221no—
252C2×C22⋊C8—111no—
253C2×C22⋊C8C2×D1111yescharacteristic
254#391—111no—
255#390—111no—
256#388—221no—
257#388—221no—
258#386—221no—
259#386—221no—
260#382—111no—
261C2×#95—111no—
262C2×#95—221no—
263C2×#95C2×D1111yescharacteristic
264#336—221no—
265#328—222no—
266#328—222no—
267#327—22no—
268#327—222no—
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—21no—
279C22×C11—21no—
280C22×C11—21no—
281C22×C11—81no—
282C22×C11—81no—
283C22×C11—81no—
284C22×C11—81no—
285C22×C11—81no—
286C22×C11—81no—
287C22×C11—81no—
288C22×C11#39011yescharacteristic
289C22×C11C2×#9911yescharacteristic
290C22×C11#41011yescharacteristic
291C22×C11#41611yescharacteristic
292C22×C11#41711yescharacteristic
293C22×C11C2×#10411yescharacteristic
294C22×C11C2×#10411yescharacteristic
295C22×C11#46311yescharacteristic
296C22×C11#46311yescharacteristic
297C22×C11#46411yescharacteristic
298C22×C11#46411yescharacteristic
299C4×C11—21no—
300C4×C11—21no—
301C4×C11—21no—
302C4×C11—21no—
303C4×C11—44no—
304C4×C11—81no—
305Dic11—22no—
306Dic11—22no—
307Dic11—22no—
308Dic11—44no—
309Dic11—41no—
310Dic11—81no—
311Dic11—81no—
312C22×Q8—111no—
313C22×D4—21no—
314C22×D4C4×D1111yescharacteristic
315C23×C4—21no—
316C23×C4—111no—
317C23×C4—111no—
318C23×C4—221no—
319C23×C4C22×D1111yescharacteristic
320C22×C8—21no—
321C22×C8—221no—
322#124—442no—
323C22⋊Q8—221no—
324C22⋊Q8—221no—
325C22⋊Q8—221no—
326C22⋊Q8—221no—
327#121—21no—
328#121—21no—
329#121—21no—
330#121—21no—
331C2×C4⋊C4—111no—
332C2×C4⋊C4—221no—
333C2×C4⋊C4C4×D1111yescharacteristic
334C2×C22⋊C4—21no—
335C2×C22⋊C4—221no—
336C2×C22⋊C4—221no—
337C2×C22⋊C4—221no—
338C2×C22⋊C4—221no—
339C2×C22⋊C4—221no—
340C2×C42—111no—
341C2×C42—111no—
342C2×C42—111no—
343C2×C42—111no—
344C2×C42—224no—
345C2×C42—442no—
346C2×C42—442no—
347C2×C42—442no—
348C4⋊C8—442no—
349C22⋊C8—21no—
350C22⋊C8—21no—
351C22⋊C8—221no—
352C22⋊C8—221no—
353#95—21no—
354#95—112no—
355#95—221no—
356#95—221no—
357#95—221no—
358#95—221no—
359#95—224no—
360#95—221no—
361#95C22⋊D1112yes—
362C2×C11—21no—
363C2×C11—21no—
364C2×C11—21no—
365C2×C11—21no—
366C2×C11—161no—
367C2×C11#150011yescharacteristic
368C2×C11#150111yescharacteristic
369C2×C11#150411yescharacteristic
370C2×C11#150911yescharacteristic
371C2×C11#196211yescharacteristic
372C2×C11#196411yescharacteristic
373C2×C11#198311yescharacteristic
374C24—21no—
375C24D4×D1111yescharacteristic
376C2×Q8—221no—
377C2×Q8—221no—
378C2×Q8—441no—
379C2×Q8—441no—
380C2×D4—21no—
381C2×D4—21no—
382C2×D4—41no—
383C2×D4—41no—
384C2×D4—41no—
385C2×D4—41no—
386C2×D4—41no—
387C2×D4—41no—
388C2×D4—41no—
389C2×D4—41no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—21no—
394C22×C4—41no—
395C22×C4—41no—
396C22×C4—41no—
397C22×C4—41no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—111no—
401C22×C4—111no—
402C22×C4—111no—
403C22×C4—111no—
404C22×C4—222no—
405C22×C4—222no—
406C22×C4—222no—
407C22×C4—221no—
408C22×C4—221no—
409C22×C4—222no—
410C22×C4—222no—
411C22×C4—222no—
412C22×C4—221no—
413C22×C4—221no—
414C22×C4—221no—
415C22×C4—221no—
416C22×C4—441no—
417C22×C4—441no—
418C22×C4—441no—
419C22×C4—441no—
420C22×C4—441no—
421C22×C4C2×C4×D1111yescharacteristic
422C22×C4#433911yescharacteristic
423C22×C4D4×D1111yescharacteristic
424C22×C4D4×D1111yescharacteristic
425C22×C4#434111yescharacteristic
426C22×C4C2×C22⋊D1111yescharacteristic
427C2×C8—41no—
428C2×C8—41no—
429C2×C8—41no—
430C2×C8—441no—
431C2×C8—441no—
432C2×C8—441no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—221no—
436C4⋊C4—221no—
437C4⋊C4—441no—
438C4⋊C4—441no—
439C22⋊C4—41no—
440C22⋊C4—41no—
441C22⋊C4—442no—
442C22⋊C4—442no—
443C22⋊C4—442no—
444C22⋊C4—442no—
445C22⋊C4—441no—
446C22⋊C4—441no—
447C42—222no—
448C42—222no—
449C42—441no—
450C42—441no—
451C42—448no—
452C11#971311yescharacteristic, complemented, Sylow
453C23—21no—
454C23—21no—
455C23—21no—
456C23—21no—
457C23—41no—
458C23—41no—
459C23—41no—
460C23—41no—
461C23—41no—
462C23—41no—
463C23—41no—
464C23C22⋊C4×D1111yescharacteristic
465C23#6693711yescharacteristic
466C23#6696411yescharacteristic
467C23#6696511yescharacteristic
468C23#6696811yescharacteristic
469C23#6696911yescharacteristic
470C23#6699211yescharacteristic
471Q8—881no—
472Q8—881no—
473D4—81no—
474D4—81no—
475D4—81no—
476D4—81no—
477D4—81no—
478D4—81no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—24no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—112no—
498C2×C4—112no—
499C2×C4—112no—
500C2×C4—224no—
501C2×C4—224no—
502C2×C4—221no—
503C2×C4—221no—
504C2×C4—221no—
505C2×C4—221no—
506C2×C4—221no—
507C2×C4—221no—
508C2×C4—224no—
509C2×C4—221no—
510C2×C4—221no—
511C2×C4—221no—
512C2×C4—442no—
513C2×C4—442no—
514C2×C4—442no—
515C2×C4—442no—
516C2×C4—442no—
517C2×C4—442no—
518C2×C4—442no—
519C2×C4—442no—
520C2×C4—441no—
521C2×C4—441no—
522C2×C4—441no—
523C2×C4—441no—
524C2×C4—441no—
525C2×C4—441no—
526C2×C4(C22⋊D11)⋊C411yescharacteristic
527C2×C4#6693811yescharacteristic
528C2×C4C4×C22⋊D1111yescharacteristic
529C2×C4#6699311yescharacteristic
530C8—81no—
531C8—881no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—81no—
545C22—81no—
546C22—81no—
547C22—81no—
548C22—81no—
549C22—81no—
550C22—81no—
551C22#1062235311yescharacteristic
552C22D11×#9911yescharacteristic
553C22#1062238011yescharacteristic
554C22#1062238411yescharacteristic
555C22#1062238511yescharacteristic
556C22#1062240011yescharacteristic
557C22D11×#10411yescharacteristic
558C22D11×#10411yescharacteristic
559C22#1062257011yescharacteristic
560C22#1062276611yescharacteristic
561C22#1062277911yescharacteristic
562C4—21no—
563C4—21no—
564C4—21no—
565C4—21no—
566C4—44no—
567C4—81no—
568C4—222no—
569C4—222no—
570C4—222no—
571C4—444no—
572C4—441no—
573C4—881no—
574C4—881no—
575C2—21no—
576C2—21no—
577C2—21no—
578C2—21no—
579C2—161no—
580C2#1306709911yescharacteristic
581C2#1306710411yescharacteristic
582C2#1306711711yescharacteristic
583C2#1306713811yescharacteristic
584C2#1306944211yescharacteristic
585C2#1306945011yescharacteristic
586C2#1306954711yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C11×#327C2
socleC23×C11C2×C22⋊C4
prime radicalC2×C11×#121C22
cosocleC23×C4×C11C23
hypercenterC2×#327D11
hypocenterC11#9713
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
2. #13068594C2semidirect
3. C2×#10622105C2semidirect
4. C2×#10622090C2semidirect
6. #95×Dic11C2semidirect
9. C2×#66989C4semidirect
15. #10622834C4semidirect
22. #10622590C4semidirect
23. #10622587C4semidirect
452. C11#9713semidirect

Maximal subgroups

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

subgroupindex
#130769152
#130685942
C2×#106221052
C2×#106220902
C2×#106221752
#95×Dic112
C2×C11×#3272
#971311