Finite Group Databasebeta

← #14720465

Subgroups — #14720465

Order 2816.

920 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082043C211yesmaximal, characteristic
2#13077733C211yesmaximal, characteristic, complemented
3#13067090C212yesmaximal, complemented
4#13067082C212yesmaximal, complemented
5#13067077C212yesmaximal, complemented
6#13067072C212yesmaximal, complemented
7#13067012C211yesmaximal, characteristic, complemented
8#13067004C211yesmaximal, characteristic, complemented
9#13066999C211yesmaximal, characteristic, complemented
10C2×#10622094C211yesmaximal, characteristic, complemented
11C8×C11×#41C211yesmaximal, characteristic, complemented
12C4×C11×#41C2211yescharacteristic
13#10623364C411yescharacteristic
14#10623356C411yescharacteristic
15#10623114—21no—
16#10623109—21no—
17#10623095—22no—
18#10623092—21no—
19#10623088—21no—
20#10623069—22no—
21#10623065C412yes—
22#10623057C411yescharacteristic
23#10623050C411yescharacteristic
24#10623049C412yes—
25#10623010C2212yes—
26C4×#4339C2211yescharacteristic
27#10623001C2212yes—
28C2×C4×Dic22C2211yescharacteristic
29C8×Q8×C11—21no—
30C8×D4×C11—21no—
31C8×D4×C11—22no—
32C11×#431C2211yescharacteristic
33C11×#431C2212yes—
34C2×C4×C8×C11C2212yes—
35C2×C4×C8×C11C2211yescharacteristic
36#10622637—21no—
37#10622625—21no—
38#10622624—22no—
39#10622539C2212yes—
40#10622538C2211yescharacteristic
41#10622537C2212yes—
42C2×C4⋊(C11⋊C8)C2211yescharacteristic
43#10622097C2211yescharacteristic
44#10622097C2212yes—
45#10622097C2211yescharacteristic
46#10622094C2212yes—
47#10622094C2212yes—
48#10622094C2211yescharacteristic
49#10622094C2212yes—
50#10622094C2212yes—
51#10622094C2212yes—
52#10622094C2211yescharacteristic
53C2×C11×#41C2×C411yescharacteristic
54C2×#4339C2×C411yescharacteristic
55C22×Dic22C2×C411yescharacteristic
56C22×C8×C11—21no—
57C22×C8×C11—22no—
58C4×Q8×C11D411yescharacteristic
59C4×Q8×C11D411yescharacteristic
60C4×D4×C11D412yes—
61C4×D4×C11D411yescharacteristic
62C4×D4×C11D411yescharacteristic
63C4×D4×C11D412yes—
64C11×#117C2×C412yes—
65C11×#117C2×C411yescharacteristic
66C2×C42×C11C2311yescharacteristic
67C2×C42×C11C2312yes—
68#66999—21no—
69#66997—21no—
70#66992—22no—
71#66991—21no—
72#66989—21no—
73#66988—22no—
74#66983C2×C412yes—
75#66982—22no—
76C4×C22⋊D11—21no—
77C4×C22⋊D11—21no—
78C4×C22⋊D11—22no—
79#66979—22no—
80#66979C2×C411yescharacteristic
81C2×C4⋊Dic11C2×C411yescharacteristic
82#66977—22no—
83#66977C2×C412yes—
84#66977C2×C412yes—
85#66977C2×C412yes—
86C2×Dic11⋊C4—21no—
87C2×C4×Dic11—21no—
88C2×#4318—22no—
89C22×C11⋊C8—21no—
90#66951—22no—
91#66950—21no—
92#66950—21no—
93#66949—22no—
94#66943—21no—
95#66942—22no—
96#66942—22no—
97#66941—21no—
98#66939—22no—
99#66938—22no—
100#66936—22no—
101#66932—22no—
102#66932—22no—
103#66931—22no—
104#66929—22no—
105#66928C2×C412yes—
106C4×D44C2×C411yescharacteristic
107C4×D44C2311yescharacteristic
108#66925—21no—
109#66925—22no—
110C42×D11—21no—
111#66923—22no—
112#66923C2×C412yes—
113#66922C2×C412yes—
114#66922C2×C412yes—
115C4×Dic22—21no—
116C4×Dic22—21no—
117C4×Dic22—22no—
118C4×Dic22C2×C412yes—
119C4×Dic22C2×C411yescharacteristic
120C4×Dic22C2312yes—
121C4×Dic22C2311yescharacteristic
122C11×C4⋊C8—21no—
123C11×C4⋊C8—22no—
124C11×C22⋊C8—21no—
125C11×C22⋊C8—22no—
126C4×C8×C11—21no—
127C4×C8×C11—22no—
128C4×C8×C11C2311yescharacteristic
129C4×C8×C11C2312yes—
130C4×C8×C11C2311yescharacteristic
131C22⋊(C11⋊C8)—21no—
132C22⋊(C11⋊C8)—22no—
133C4⋊(C11⋊C8)—21no—
134C4⋊(C11⋊C8)—22no—
135C4⋊(C11⋊C8)C2312yes—
136C4⋊(C11⋊C8)C2311yescharacteristic
137C4⋊(C11⋊C8)C2311yescharacteristic
138#66867—22no—
139C4×C11⋊C8—21no—
140#17484—111nomaximal, Sylow
141C11×#41—24no—
142C2×Q8×C11C22⋊C411yescharacteristic
143C2×D4×C11C22⋊C412yes—
144C2×D4×C11C22⋊C411yescharacteristic
145C22×C4×C11C22×C412yes—
146C22×C4×C11C22×C411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D412yes—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D412yes—
151C2×C22⋊D11—21no—
152C2×C22⋊D11—22no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155#4339—24no—
156C2×D44C22×C411yescharacteristic
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×Dic22—21no—
161C2×Dic22—22no—
162C2×Dic22—24no—
163C2×Dic22C22×C411yescharacteristic
164C2×Dic22C22×C412yes—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—22no—
168C2×C8×C11—44no—
169C2×C8×C11—42no—
170C11×C4⋊C4C22⋊C411yescharacteristic
171C11×C4⋊C4C22⋊C412yes—
172C11×C4⋊C4C22⋊C412yes—
173C11×C4⋊C4C22⋊C411yescharacteristic
174C11×C22⋊C4C22⋊C412yes—
175C11×C22⋊C4C22⋊C412yes—
176C11×C22⋊C4C22⋊C412yes—
177C42×C11C22×C411yescharacteristic
178C42×C11C22×C412yes—
179C42×C11C2×D411yescharacteristic
180C42×C11C2×D412yes—
181C42×C11C2×D411yescharacteristic
182C42×C11C2×D412yes—
183C42×C11C2411yescharacteristic
184C22⋊Dic11—21no—
185C22⋊Dic11—22no—
186C22⋊Dic11—22no—
187C22⋊Dic11—22no—
188(C2×D11)⋊C4—21no—
189(C2×D11)⋊C4—22no—
190(C2×D11)⋊C4—22no—
191(C2×D11)⋊C4—22no—
192(C2×D11)⋊C4—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—22no—
195C4⋊Dic11—22no—
196C4⋊Dic11—22no—
197C4⋊Dic11C22×C412yes—
198C4⋊Dic11C22×C411yescharacteristic
199C4⋊Dic11C22×C411yescharacteristic
200Dic11⋊C4—22no—
201Dic11⋊C4—22no—
202Dic11⋊C4—22no—
203Dic11⋊C4—21no—
204Dic11⋊C4—22no—
205Dic11⋊C4—22no—
206Dic11⋊C4—22no—
207Dic11⋊C4—22no—
208Dic11⋊C4—21no—
209C4×Dic11—22no—
210C4×Dic11—21no—
211C4×Dic11—21no—
212C4×Dic11—21no—
213C4×Dic11—22no—
214#4318—82no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—22no—
218C2×C11⋊C8—81no—
219#3461—111no—
220#2989—111no—
221C8×#41D1111yescharacteristic, complemented
222#1497—112no—
223#1495—112no—
224#1494—112no—
225#1493—112no—
226#1479—111no—
227#1477—111no—
228#1476—111no—
229C2×Q8⋊C8—111no—
230C23×C11C2×C22⋊C412yes—
231C23×C11C2×C22⋊C411yescharacteristic
232C22×D11—21no—
233Q8×C11—22no—
234D4×C11—24no—
235D4×C11—22no—
236C2×C4×C11—24no—
237C2×C4×C11—21no—
238C2×C4×C11—22no—
239C2×C4×C11—21no—
240C2×C4×C11—22no—
241C2×C4×C11—42no—
242C2×C4×C11—41no—
243C2×C4×C11C2×C22⋊C411yescharacteristic
244C2×C4×C11C2×C22⋊C411yescharacteristic
245C2×C4×C11C2×C22⋊C412yes—
246C2×C4×C11C2×C22⋊C412yes—
247C2×C4×C11C2×C22⋊C412yes—
248C2×C4×C11C2×C22⋊C411yescharacteristic
249C2×C4×C11#13114yes—
250C2×C4×C11C23×C411yescharacteristic
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C22×D411yescharacteristic
253C22⋊D11—42no—
254C22⋊D11—82no—
255C2×Dic11—21no—
256C2×Dic11—22no—
257C2×Dic11—21no—
258C2×Dic11—22no—
259C2×Dic11—21no—
260C2×Dic11—42no—
261C2×Dic11—81no—
262D44—22no—
263C4×D11—41no—
264C4×D11—41no—
265C4×D11—42no—
266C4×D11—81no—
267Dic22—24no—
268Dic22—22no—
269Dic22—42no—
270Dic22—82no—
271C8×C11—22no—
272C8×C11—41no—
273C8×C11—42no—
274C11⋊C8—42no—
275C11⋊C8—41no—
276C11⋊C8—41no—
277#544—111no—
278#542—112no—
279#542—221no—
280#541—112no—
281#541—221no—
282#539—222no—
283#537—111no—
284#536—111no—
285#536—111no—
286#533—112no—
287#533—221no—
288#529—112no—
289#529—222no—
290#529—221no—
291C4×#41—111no—
292C4×#41C2×D1111yescharacteristic
293C2×C4×Q8—111no—
294#446—221no—
295C8×Q8—21no—
296#436—221no—
297#435—222no—
298C8×D4—22no—
299C8×D4—21no—
300#432—112no—
301#431—111no—
302#431C2×D1111yescharacteristic
303#431C2×D1112yes—
304#423—112no—
305C2×C4⋊C8—111no—
306C2×C4×C8C2×D1111yescharacteristic
307C2×C4×C8C2×D1112yes—
308Q8⋊C8—112no—
309Q8⋊C8—112no—
310Q8⋊C8—111no—
311Q8⋊C8—111no—
312Q8⋊C8—112no—
313Q8⋊C8—112no—
314Q8⋊C8—112no—
315D4⋊C8—111no—
316D4⋊C8—111no—
317D4⋊C8—112no—
318C22×C11—21no—
319C22×C11—21no—
320C22×C11—22no—
321C22×C11—22no—
322C22×C11—22no—
323C22×C11#40812yes—
324C22×C11C22×C22⋊C411yescharacteristic
325C2×D11—41no—
326C2×D11—41no—
327C2×D11—41no—
328C4×C11—22no—
329C4×C11—21no—
330C4×C11—22no—
331C4×C11—21no—
332C4×C11—22no—
333C4×C11—21no—
334C4×C11#40812yes—
335C4×C11C2×#13112yes—
336C4×C11#57711yescharacteristic
337C4×C11#57811yescharacteristic
338Dic11—42no—
339Dic11—41no—
340Dic11—41no—
341Dic11—41no—
342Dic11—42no—
343C2×#41—111no—
344C2×#41C4×D1111yescharacteristic
345C22×Q8—111no—
346C2×M16—222no—
347C22×C8—21no—
348C22×C8—22no—
349C22×C8—221no—
350C4⋊Q8—112no—
351C4⋊Q8—112no—
352C4⋊Q8—221no—
353C4⋊Q8—221no—
354#126—222no—
355#126—222no—
356#126—222no—
357#126—222no—
358#125—112no—
359#125—222no—
360#125—221no—
361#125—222no—
362#125—222no—
363#124—112no—
364#124—221no—
365#124—222no—
366#123—222no—
367#123—222no—
368#123—222no—
369#123—222no—
370C22⋊Q8—112no—
371C22⋊Q8—112no—
372C22⋊Q8—112no—
373C22⋊Q8—221no—
374C22⋊Q8—222no—
375C22⋊Q8—221no—
376C22⋊Q8—221no—
377C22⋊Q8—222no—
378C22⋊Q8—222no—
379#121—112no—
380#121—222no—
381#121—221no—
382C4×Q8—112no—
383C4×Q8—111no—
384C4×Q8—112no—
385C4×Q8—111no—
386C4×Q8—221no—
387C4×Q8—222no—
388C4×Q8—221no—
389C4×Q8D4411yescharacteristic
390C4×Q8C22⋊D1111yescharacteristic
391C4×D4—111no—
392C4×D4—111no—
393C4×D4—221no—
394C4×D4—222no—
395C4×D4—221no—
396C4×D4D4412yes—
397C4×D4D4411yescharacteristic
398C4×D4C22⋊D1112yes—
399C4×D4C22⋊D1111yescharacteristic
400#117—111no—
401#117—222no—
402#117—222no—
403#117—221no—
404#117C4×D1111yescharacteristic
405#117C4×D1112yes—
406C2×C4⋊C4—111no—
407C2×C4⋊C4—221no—
408C2×C42—221no—
409C2×C42—221no—
410C2×C42C22×D1111yescharacteristic
411C2×C42C22×D1112yes—
412C4⋊C8—21no—
413C4⋊C8—22no—
414C4⋊C8—112no—
415C4⋊C8—111no—
416C4⋊C8—111no—
417C4⋊C8—221no—
418C4⋊C8—222no—
419C22⋊C8—21no—
420C22⋊C8—22no—
421C22⋊C8—221no—
422C22⋊C8—222no—
423#97—222no—
424C4×C8—21no—
425C4×C8—22no—
426C4×C8—221no—
427C4×C8C22×D1111yescharacteristic
428C4×C8C22×D1111yescharacteristic
429C4×C8C22×D1112yes—
430C2×C11—22no—
431C2×C11—42no—
432C2×C11C2×#40811yescharacteristic
433C2×C11#289811yescharacteristic
434C2×C11#290111yescharacteristic
435D11—81no—
436#41—24no—
437#41—224no—
438C2×Q8—112no—
439C2×Q8—111no—
440C2×Q8—221no—
441C2×Q8—222no—
442C2×Q8—224no—
443C2×Q8(C2×D11)⋊C411yescharacteristic
444C2×D4—111no—
445C2×D4—221no—
446C2×D4—222no—
447C2×D4(C2×D11)⋊C412yes—
448C2×D4(C2×D11)⋊C411yescharacteristic
449C22×C4—221no—
450C22×C4—221no—
451C22×C4—221no—
452C22×C4—221no—
453C22×C4—221no—
454C22×C4C2×C4×D1112yes—
455C22×C4C2×C4×D1111yescharacteristic
456C22×C4C2×D4411yescharacteristic
457C22×C4C2×D4412yes—
458C22×C4C2×C22⋊D1111yescharacteristic
459C22×C4C2×C22⋊D1112yes—
460M16—882no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—22no—
464C2×C8—42no—
465C2×C8—44no—
466C2×C8—221no—
467C2×C8—221no—
468C2×C8—222no—
469C2×C8—881no—
470C4⋊C4—112no—
471C4⋊C4—111no—
472C4⋊C4—111no—
473C4⋊C4—221no—
474C4⋊C4—222no—
475C4⋊C4—221no—
476C4⋊C4—222no—
477C4⋊C4—222no—
478C4⋊C4—222no—
479C4⋊C4—222no—
480C4⋊C4—222no—
481C4⋊C4—222no—
482C4⋊C4—222no—
483C4⋊C4—222no—
484C4⋊C4—222no—
485C4⋊C4—221no—
486C4⋊C4(C2×D11)⋊C411yescharacteristic
487C4⋊C4(C2×D11)⋊C412yes—
488C4⋊C4(C2×D11)⋊C412yes—
489C4⋊C4(C2×D11)⋊C411yescharacteristic
490C22⋊C4—221no—
491C22⋊C4—222no—
492C22⋊C4—222no—
493C22⋊C4—222no—
494C22⋊C4—221no—
495C22⋊C4—222no—
496C22⋊C4—222no—
497C22⋊C4—222no—
498C22⋊C4—221no—
499C22⋊C4(C2×D11)⋊C412yes—
500C22⋊C4(C2×D11)⋊C412yes—
501C22⋊C4(C2×D11)⋊C412yes—
502C42—221no—
503C42—221no—
504C42—222no—
505C42—221no—
506C42—222no—
507C42C2×C4×D1111yescharacteristic
508C42C2×C4×D1112yes—
509C42C2×D4411yescharacteristic
510C42C2×D4412yes—
511C42C2×C22⋊D1111yescharacteristic
512C42C2×C22⋊D1112yes—
513C42C23×D1111yescharacteristic
514C11#1748411yescharacteristic, complemented, Sylow
515C23—221no—
516C23C2×(C2×D11)⋊C412yes—
517C23C2×(C2×D11)⋊C411yescharacteristic
518Q8—22no—
519Q8—224no—
520Q8—222no—
521Q8—442no—
522Q8—882no—
523D4—24no—
524D4—22no—
525D4—222no—
526D4—442no—
527D4—882no—
528C2×C4—24no—
529C2×C4—21no—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—22no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—221no—
536C2×C4—221no—
537C2×C4—222no—
538C2×C4—222no—
539C2×C4—221no—
540C2×C4—442no—
541C2×C4—442no—
542C2×C4—441no—
543C2×C4—441no—
544C2×C4—881no—
545C2×C4—881no—
546C2×C4#6695414yes—
547C2×C4C2×(C2×D11)⋊C411yescharacteristic
548C2×C4C2×(C2×D11)⋊C411yescharacteristic
549C2×C4C2×(C2×D11)⋊C412yes—
550C2×C4C2×(C2×D11)⋊C412yes—
551C2×C4C2×(C2×D11)⋊C412yes—
552C2×C4C2×(C2×D11)⋊C411yescharacteristic
553C2×C4C22×C4×D1111yescharacteristic
554C2×C4C22×D4411yescharacteristic
555C2×C4C22×C22⋊D1111yescharacteristic
556C8—22no—
557C8—41no—
558C8—42no—
559C8—442no—
560C8—441no—
561C8—441no—
562C22—21no—
563C22—21no—
564C22—22no—
565C22—22no—
566C22—22no—
567C22—441no—
568C22—441no—
569C22—441no—
570C22#1062272312yes—
571C22C22×(C2×D11)⋊C411yescharacteristic
572C4—22no—
573C4—21no—
574C4—22no—
575C4—21no—
576C4—21no—
577C4—22no—
578C4—441no—
579C4—442no—
580C4—441no—
581C4—442no—
582C4—441no—
583C4#1062272312yes—
584C4C2×#6695412yes—
585C4#1062328211yescharacteristic
586C4#1062328411yescharacteristic
587C2—22no—
588C2—42no—
589C2—881no—
590C2C2×#1062272311yescharacteristic
591C2#1307715011yescharacteristic
592C2#1307716411yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC8×C11×#41C2
socleC22×C11C22×C22⋊C4
prime radical#10623364C4
cosocleC42×C11C24
hypercenterC8×#41D11
hypocenterC11#17484
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ C8×#41

Complements

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

NH ≅ G/Ntype
2. #13077733C2semidirect
3. #13067090C2semidirect
4. #13067082C2semidirect
5. #13067077C2semidirect
6. #13067072C2semidirect
7. #13067012C2semidirect
8. #13067004C2semidirect
9. #13066999C2semidirect
10. C2×#10622094C2semidirect
11. C8×C11×#41C2semidirect
221. C8×#41D11semidirect
514. C11#17484semidirect

Maximal subgroups

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

subgroupindex
#130820432
#130777332
#130670902
#130670822
#130670772
#130670722
#130670122
#130670042
#130669992
C2×#106220942
C8×C11×#412
#1748411