Finite Group Databasebeta

← #14649362

Subgroups — #14649362

Order 2816.

674 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
1C2×#10622332C211yesmaximal, characteristic, complemented
2#13076948C211yesmaximal, characteristic
3C2×#10622108C211yesmaximal, characteristic
4C2×#10622089C211yesmaximal, characteristic
5#13066840C211yesmaximal, characteristic, complemented
6#13066494C211yesmaximal, characteristic, complemented
7C11×#1294C211yesmaximal, characteristic, complemented
8C2×#66983C2211yescharacteristic
9C22×C4×Dic11C2211yescharacteristic
10C2×#66939—21no—
11C2×C11×C22⋊C8C2211yescharacteristic
12C11×#380C2211yescharacteristic
13C2×C11×#95C2211yescharacteristic
14C2×C11⋊#95—21no—
15C2×C11⋊#95—21no—
16C2×C11⋊#95C2211yescharacteristic
17C2×C22⋊(C11⋊C8)C2211yescharacteristic
18C2×#66879—21no—
19C2×Dic11⋊C8—21no—
20#10622601C411yescharacteristic, complemented
21#10622601C411yescharacteristic, complemented
22#10622598C411yescharacteristic, complemented
23#10622598C411yescharacteristic, complemented
24#10622571—21no—
25#10622332—22no—
26#10622332—22no—
27#10622283—21no—
28#10622283—21no—
29#10622108—22no—
30#10622089—22no—
31C23×C4×C11—21no—
32C23×C4×C11C2311yescharacteristic
33C22×C22⋊D11—21no—
34C23×Dic11—21no—
35C23×Dic11D411yescharacteristic
36C23×Dic11D411yescharacteristic
37C22×D44C2×C411yescharacteristic
38C22×C8×C11—21no—
39C2×C11×C4⋊C4C2×C411yescharacteristic
40C2×C11×C4⋊C4C2×C411yescharacteristic
41C2×C11×C22⋊C4—21no—
42#66983—21no—
43#66983—21no—
44#66983—21no—
45#66983—21no—
46C2×(C2×D11)⋊C4—21no—
47C2×(C2×D11)⋊C4—21no—
48C2×(C2×D11)⋊C4—21no—
49C2×(C2×D11)⋊C4—21no—
50C2×(C2×D11)⋊C4—21no—
51C2×C4⋊Dic11—21no—
52C2×C4⋊Dic11—21no—
53C2×C4⋊Dic11C2×C411yescharacteristic
54C2×C4×Dic11—21no—
55C2×C4×Dic11—21no—
56C2×C4×Dic11—21no—
57C2×C4×Dic11—21no—
58C2×C4×Dic11C2×C411yescharacteristic
59C2×C4×Dic11C2×C411yescharacteristic
60C2×C4×Dic11D411yescharacteristic
61C2×C4×Dic11D411yescharacteristic
62C22×C11⋊C8—21no—
63#66939—42no—
64#66939—42no—
65C11×C22⋊C8—21no—
66C11×C22⋊C8D412yes—
67C11×#95—21no—
68C11×#95—21no—
69C11×#95—21no—
70C11⋊#95—24no—
71C11⋊#95—21no—
72C11⋊#95—21no—
73C11⋊#95—21no—
74C11⋊#95—21no—
75C11⋊#95—42no—
76C22⋊(C11⋊C8)—21no—
77C22⋊(C11⋊C8)D412yes—
78#66879—24no—
79Dic11⋊C8—24no—
80#9118—111nomaximal, Sylow
81C24×C11C2×D411yescharacteristic
82C23×D11—21no—
83C22×C4×C11—22no—
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11—41no—
89C22×C4×C11—41no—
90C22×C4×C11—41no—
91C22×C4×C11—41no—
92C22×C4×C11—41no—
93C22×C4×C11—41no—
94C22×C4×C11C22×C411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11#4111yescharacteristic
99C22×C4×C11#4111yescharacteristic
100C2×C22⋊D11—41no—
101C2×C22⋊D11—41no—
102C2×C22⋊D11—41no—
103C2×C22⋊D11—41no—
104C2×C22⋊D11—41no—
105C2×C22⋊D11—41no—
106C22×Dic11—22no—
107C22×Dic11—22no—
108C22×Dic11—21no—
109C22×Dic11—21no—
110C22×Dic11—21no—
111C22×Dic11—21no—
112C22×Dic11—21no—
113C22×Dic11—21no—
114C22×Dic11—21no—
115C22×Dic11—21no—
116C22×Dic11—21no—
117C22×Dic11—41no—
118C22×Dic11—41no—
119C22×Dic11—41no—
120C22×Dic11—41no—
121C22×Dic11—41no—
122C22×Dic11—41no—
123C22×Dic11—41no—
124C22×Dic11C22⋊C411yescharacteristic
125C22×Dic11C22⋊C411yescharacteristic
126C22×Dic11C22⋊C411yescharacteristic
127C22×Dic11C22⋊C411yescharacteristic
128C2×D44—21no—
129C2×D44—21no—
130C2×D44—41no—
131C2×D44—41no—
132C2×C8×C11—22no—
133C2×C8×C11—41no—
134C2×C8×C11—41no—
135C11×C4⋊C4—41no—
136C11×C4⋊C4—41no—
137C11×C22⋊C4—41no—
138C11×C22⋊C4—41no—
139(C2×D11)⋊C4—42no—
140(C2×D11)⋊C4—42no—
141(C2×D11)⋊C4—42no—
142(C2×D11)⋊C4—42no—
143(C2×D11)⋊C4—41no—
144(C2×D11)⋊C4—41no—
145C4⋊Dic11—21no—
146C4⋊Dic11—21no—
147C4⋊Dic11—42no—
148C4⋊Dic11—42no—
149C4×Dic11—21no—
150C4×Dic11—21no—
151C4×Dic11—21no—
152C4×Dic11—21no—
153C4×Dic11—21no—
154C4×Dic11—21no—
155C4×Dic11—21no—
156C4×Dic11—21no—
157C2×C11⋊C8—22no—
158C2×C11⋊C8—41no—
159C2×C11⋊C8—41no—
160C2×#432—111no—
161#2854—111no—
162C2×#327—111no—
163C2×#327—111no—
164#1434—111no—
165#1294—111no—
166#1294D1111yescharacteristic, complemented
167C23×C11—21no—
168C23×C11—21no—
169C23×C11—21no—
170C23×C11—21no—
171C23×C11C2×C22⋊C411yescharacteristic
172C23×C11#12111yescharacteristic
173C23×C11#12111yescharacteristic
174C23×C11AGL(1,ℤ/8)11yescharacteristic
175C23×C11AGL(1,ℤ/8)11yescharacteristic
176C23×C11AGL(1,ℤ/8)11yescharacteristic
177C23×C11#13711yescharacteristic
178C22×D11—41no—
179C22×D11—41no—
180C22×D11—41no—
181C22×D11—41no—
182C22×D11—41no—
183C22×D11—41no—
184C22×D11—41no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—81no—
203C2×C4×C11—81no—
204C2×C4×C11—81no—
205C2×C4×C11—81no—
206C2×C4×C11C4×D411yescharacteristic
207C2×C4×C11C4×D411yescharacteristic
208C2×C4×C11#12011yescharacteristic
209C2×C4×C11#12311yescharacteristic
210C22⋊D11—81no—
211C22⋊D11—81no—
212C22⋊D11—81no—
213C22⋊D11—81no—
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—21no—
225C2×Dic11—42no—
226C2×Dic11—42no—
227C2×Dic11—41no—
228C2×Dic11—41no—
229C2×Dic11—41no—
230C2×Dic11—41no—
231C2×Dic11—42no—
232C2×Dic11—42no—
233C2×Dic11—42no—
234C2×Dic11—41no—
235C2×Dic11—41no—
236C2×Dic11—41no—
237C2×Dic11—81no—
238C2×Dic11—81no—
239C2×Dic11—81no—
240C2×Dic11—81no—
241C2×Dic11#10412yes—
242D44—81no—
243D44—81no—
244C8×C11—42no—
245C11⋊C8—42no—
246C2×#123—221no—
247C2×#121—111no—
248C22×C42—111no—
249#432—222no—
250#432—222no—
251C2×C4⋊C8—221no—
252C2×C22⋊C8—111no—
253C2×C22⋊C8C2×D1111yescharacteristic
254C2×#97—221no—
255#390—111no—
256#390—111no—
257#389—111no—
258#389—111no—
259#388—221no—
260#388—221no—
261#386—221no—
262#380C2×D1111yescharacteristic
263C2×#95—111no—
264C2×#95—221no—
265C2×#95—221no—
266C2×#95C2×D1111yescharacteristic
267#327—222no—
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#38611yescharacteristic
282C22×C11#41011yescharacteristic
283C22×C11#41011yescharacteristic
284C22×C11#41711yescharacteristic
285C22×C11#41811yescharacteristic
286C22×C11C2×#10411yescharacteristic
287C22×C11#42111yescharacteristic
288C22×C11#46811yescharacteristic
289C22×C11#46811yescharacteristic
290C22×C11#46911yescharacteristic
291C22×C11#46911yescharacteristic
292C2×D11—81no—
293C2×D11—81no—
294C2×D11—81no—
295C2×D11—81no—
296C2×D11—81no—
297C2×D11—81no—
298C2×D11—81no—
299C4×C11—21no—
300C4×C11—21no—
301C4×C11—21no—
302C4×C11—21no—
303C4×C11—82no—
304C4×C11—81no—
305C4×C11—81no—
306Dic11—22no—
307Dic11—41no—
308Dic11—41no—
309Dic11—41no—
310Dic11—82no—
311Dic11—81no—
312C22×D4—111no—
313C22×D4—221no—
314C23×C4—21no—
315C23×C4—111no—
316C23×C4—111no—
317C23×C4—221no—
318C23×C4C22×D1111yescharacteristic
319C22×C8—21no—
320C22×C8—221no—
321#123—442no—
322#123—442no—
323#121—221no—
324#121—221no—
325#121—221no—
326#121—221no—
327C2×C4⋊C4—111no—
328C2×C4⋊C4—221no—
329C2×C4⋊C4—221no—
330C2×C4⋊C4C4×D1111yescharacteristic
331C2×C4⋊C4C4×D1111yescharacteristic
332C2×C22⋊C4—21no—
333C2×C22⋊C4—221no—
334C2×C22⋊C4—221no—
335C2×C22⋊C4—221no—
336C2×C22⋊C4—221no—
337C2×C22⋊C4—221no—
338C2×C42—111no—
339C2×C42—111no—
340C2×C42—111no—
341C2×C42—111no—
342C2×C42—221no—
343C2×C42—221no—
344C2×C42—221no—
345C2×C42—221no—
346C4⋊C8—224no—
347C22⋊C8—21no—
348C22⋊C8—112no—
349C22⋊C8—221no—
350C22⋊C8D4412yes—
351#97—224no—
352#95—21no—
353#95—21no—
354#95—21no—
355#95—221no—
356#95—221no—
357#95—224no—
358#95—221no—
359#95—221no—
360#95—442no—
361C2×C11—21no—
362C2×C11—21no—
363C2×C11—21no—
364C2×C11—21no—
365C2×C11#150511yescharacteristic
366C2×C11#150911yescharacteristic
367C2×C11#151211yescharacteristic
368C2×C11#151411yescharacteristic
369C2×C11#187111yescharacteristic
370C2×C11#189511yescharacteristic
371C2×C11#189911yescharacteristic
372D11—161no—
373C24—221no—
374C24D4×D1111yescharacteristic
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—22no—
386C22×C4—21no—
387C22×C4—21no—
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—221no—
407C22×C4—221no—
408C22×C4—221no—
409C22×C4—222no—
410C22×C4—221no—
411C22×C4—441no—
412C22×C4—441no—
413C22×C4—441no—
414C22×C4—441no—
415C22×C4—441no—
416C22×C4—441no—
417C22×C4—441no—
418C22×C4C2×C4×D1111yescharacteristic
419C22×C4C2×D4411yescharacteristic
420C22×C4#433911yescharacteristic
421C22×C4D4×D1111yescharacteristic
422C22×C4D4×D1111yescharacteristic
423C22×C4#434311yescharacteristic
424C2×C8—22no—
425C2×C8—41no—
426C2×C8—41no—
427C2×C8—222no—
428C2×C8—441no—
429C2×C8—441no—
430C4⋊C4—41no—
431C4⋊C4—41no—
432C4⋊C4—221no—
433C4⋊C4—221no—
434C4⋊C4—442no—
435C4⋊C4—442no—
436C22⋊C4—41no—
437C22⋊C4—41no—
438C22⋊C4—442no—
439C22⋊C4—442no—
440C22⋊C4—442no—
441C22⋊C4—442no—
442C22⋊C4—441no—
443C22⋊C4—441no—
444C42—221no—
445C42—221no—
446C42—221no—
447C42—221no—
448C42—221no—
449C42—221no—
450C42—221no—
451C42—221no—
452C11#911811yescharacteristic, complemented, Sylow
453C23—21no—
454C23—21no—
455C23—21no—
456C23—21no—
457C23—441no—
458C23—441no—
459C23—441no—
460C23—441no—
461C23—441no—
462C23—441no—
463C23—441no—
464C23C22⋊C4×D1111yescharacteristic
465C23#6693711yescharacteristic
466C23#6694811yescharacteristic
467C23#6696411yescharacteristic
468C23#6696711yescharacteristic
469C23#6696711yescharacteristic
470C23#6697111yescharacteristic
471D4—881no—
472D4—881no—
473D4—881no—
474D4—881no—
475D4—881no—
476D4—881no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—81no—
495C2×C4—81no—
496C2×C4—81no—
497C2×C4—81no—
498C2×C4—112no—
499C2×C4—221no—
500C2×C4—221no—
501C2×C4—221no—
502C2×C4—221no—
503C2×C4—221no—
504C2×C4—221no—
505C2×C4—221no—
506C2×C4—221no—
507C2×C4—221no—
508C2×C4—221no—
509C2×C4—221no—
510C2×C4—442no—
511C2×C4—442no—
512C2×C4—441no—
513C2×C4—441no—
514C2×C4—441no—
515C2×C4—441no—
516C2×C4—442no—
517C2×C4—442no—
518C2×C4—442no—
519C2×C4—441no—
520C2×C4—441no—
521C2×C4—441no—
522C2×C4—881no—
523C2×C4—881no—
524C2×C4—881no—
525C2×C4—881no—
526C2×C4C4×D4411yescharacteristic
527C2×C4#6693511yescharacteristic
528C2×C4#6694611yescharacteristic
529C2×C4#6694711yescharacteristic
530C8—42no—
531C8—442no—
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—881no—
545C22—881no—
546C22—881no—
547C22—881no—
548C22—881no—
549C22—881no—
550C22—881no—
551C22#1062227811yescharacteristic
552C22#1062235311yescharacteristic
553C22#1062235311yescharacteristic
554C22#1062238311yescharacteristic
555C22#1062239511yescharacteristic
556C22#1062241611yescharacteristic
557C22#1062242511yescharacteristic
558C22D11×#10411yescharacteristic
559C22#1062243411yescharacteristic
560C22#1062247811yescharacteristic
561C22#1062249911yescharacteristic
562C4—21no—
563C4—21no—
564C4—21no—
565C4—21no—
566C4—82no—
567C4—81no—
568C4—81no—
569C4—222no—
570C4—441no—
571C4—441no—
572C4—441no—
573C4—882no—
574C4—881no—
575C2—21no—
576C2—21no—
577C2—21no—
578C2—21no—
579C2—1761no—
580C2#1306712211yescharacteristic
581C2#1306714011yescharacteristic
582C2#1306715311yescharacteristic
583C2#1306716111yescharacteristic
584C2#1306891711yescharacteristic
585C2#1306905311yescharacteristic
586C2#1306907311yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1294C2
socleC23×C11C2×C22⋊C4
prime radicalC2×#66983C22
cosocleC23×C4×C11C23
hypercenter#1294D11
hypocenterC11#9118
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
1. C2×#10622332C2semidirect
5. #13066840C2semidirect
6. #13066494C2semidirect
7. C11×#1294C2semidirect
20. #10622601C4semidirect
21. #10622601C4semidirect
22. #10622598C4semidirect
23. #10622598C4semidirect
166. #1294D11semidirect
452. C11#9118semidirect

Maximal subgroups

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

subgroupindex
C2×#106223322
#130769482
C2×#106221082
C2×#106220892
#130668402
#130664942
C11×#12942
#911811