Finite Group Databasebeta

← #14720835

Subgroups — #14720835

Order 2816.

934 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082231C211yesmaximal, characteristic
2#13077748C211yesmaximal, characteristic, complemented
3#13067082C212yesmaximal, complemented
4#13067072C211yesmaximal, characteristic, complemented
5#13067056C211yesmaximal, characteristic, complemented
6#13067046C212yesmaximal, complemented
7#13067038C211yesmaximal, characteristic, complemented
8#13067025C212yesmaximal, complemented
9#13067012C212yesmaximal, complemented
10#13066999C211yesmaximal, characteristic, complemented
11C11×#2922C211yesmaximal, characteristic, complemented
12C4×C11×#41C2211yescharacteristic
13#10623355—21no—
14#10623115C411yescharacteristic
15#10623109—21no—
16#10623098C411yescharacteristic
17#10623086C411yescharacteristic
18#10623083C412yes—
19#10623072C412yes—
20#10623069—22no—
21D4×Dic22C411yescharacteristic
22C4×#4341—21no—
23#10623064—21no—
24#10623062—22no—
25#10623010C2212yes—
26C4×#4339C2211yescharacteristic
27#10623001C2211yescharacteristic
28C2×C4×Dic22C2212yes—
29C11×#433—22no—
30C11×#431C2212yes—
31C11×#431C2212yes—
32C11×#424—21no—
33C11×#408—21no—
34C4×C11×M16C2211yescharacteristic
35C2×C4×C8×C11C2211yescharacteristic
36Q8×C11⋊C8—21no—
37#10622625—21no—
38#10622625—22no—
39#10622538C2212yes—
40#10622538C2211yescharacteristic
41#10622537C2212yes—
42#10622537C2211yescharacteristic
43#10622097C2211yescharacteristic
44#10622097C2212yes—
45#10622097C2211yescharacteristic
46#10622094C2211yescharacteristic
47#10622094C2212yes—
48#10622094C2212yes—
49#10622094C2212yes—
50#10622094C2212yes—
51#10622094C2212yes—
52#10622094C2211yescharacteristic
53C2×C11×#41D411yescharacteristic
54C2×#4341—21no—
55C2×#4339C2×C411yescharacteristic
56C22×Dic22C2×C412yes—
57C2×C11×M16—21no—
58C22×C8×C11—21no—
59C4×Q8×C11C2×C411yescharacteristic
60C4×Q8×C11D411yescharacteristic
61C4×D4×C11C2×C411yescharacteristic
62C4×D4×C11C2×C412yes—
63C4×D4×C11D411yescharacteristic
64C4×D4×C11D412yes—
65C11×#117D412yes—
66C11×#117D411yescharacteristic
67C2×C42×C11C2312yes—
68C2×C42×C11C2311yescharacteristic
69#66999—21no—
70#66997—21no—
71#66992—22no—
72#66988—22no—
73D4×Dic11—21no—
74#66983C2×C412yes—
75#66982—22no—
76C4×C22⋊D11—21no—
77C4×C22⋊D11—21no—
78C4×C22⋊D11—22no—
79#66979—21no—
80#66979C2×C411yescharacteristic
81C2×C4⋊Dic11C2×C412yes—
82#66977—21no—
83#66977C2×C412yes—
84#66977C2×C412yes—
85C2×Dic11⋊C4—22no—
86C2×C4×Dic11—22no—
87C2×#4318—22no—
88C2×#4318—21no—
89#66951—22no—
90#66950—21no—
91#66949—22no—
92#66945—21no—
93#66942—22no—
94#66942—22no—
95#66941—21no—
96#66940—21no—
97#66939—22no—
98#66938—22no—
99(C22⋊D11)⋊C4—22no—
100#66932—22no—
101#66931—22no—
102#66930—22no—
103#66929—22no—
104#66928C2×C412yes—
105C4×D44C2×C411yescharacteristic
106C4×D44C2311yescharacteristic
107#66925—21no—
108#66925—22no—
109C42×D11—21no—
110#66923—21no—
111#66923C2×C412yes—
112#66922C2×C411yescharacteristic
113#66922C2×C411yescharacteristic
114C4×Dic22—22no—
115C4×Dic22—22no—
116C4×Dic22—21no—
117C4×Dic22C2×C412yes—
118C4×Dic22C2×C412yes—
119C4×Dic22C2×C411yescharacteristic
120C4×Dic22C2311yescharacteristic
121C4×Dic22C2312yes—
122C11×C4⋊C8—22no—
123C11×C4⋊C8—22no—
124C11×C22⋊C8—22no—
125C11×C22⋊C8—22no—
126C11×#97—21no—
127C4×C8×C11—21no—
128C4×C8×C11C2311yescharacteristic
129C4×C8×C11C2311yescharacteristic
130C4×C8×C11C2312yes—
131C22⋊(C11⋊C8)—22no—
132C22⋊(C11⋊C8)—21no—
133C4⋊(C11⋊C8)—21no—
134C4⋊(C11⋊C8)—22no—
135C4⋊(C11⋊C8)C2311yescharacteristic
136C4⋊(C11⋊C8)C2312yes—
137C4⋊(C11⋊C8)C2311yescharacteristic
138C4×C11⋊C8—21no—
139C4×C11⋊C8—22no—
140#17525—111nomaximal, Sylow
141C11×#41—42no—
142C2×Q8×C11C22⋊C411yescharacteristic
143C2×D4×C11C22⋊C411yescharacteristic
144C2×D4×C11C22⋊C412yes—
145C22×C4×C11C22×C411yescharacteristic
146C22×C4×C11C22×C412yes—
147C22×C4×C11C2×D412yes—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D412yes—
151C2×C22⋊D11—22no—
152C2×C22⋊D11—21no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155#4341—44no—
156#4339—22no—
157#4339—41no—
158C2×D44C22×C411yescharacteristic
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×Dic22—24no—
163C2×Dic22—22no—
164C2×Dic22—21no—
165C2×Dic22—42no—
166C2×Dic22C22×C412yes—
167C2×Dic22C22×C411yescharacteristic
168C11×M16—42no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—22no—
172C2×C8×C11—42no—
173C11×C4⋊C4C22⋊C411yescharacteristic
174C11×C4⋊C4C22⋊C411yescharacteristic
175C11×C4⋊C4C22⋊C412yes—
176C11×C4⋊C4C22⋊C412yes—
177C11×C22⋊C4C22⋊C412yes—
178C11×C22⋊C4C22⋊C412yes—
179C11×C22⋊C4C22⋊C412yes—
180C42×C11C22×C412yes—
181C42×C11C22×C411yescharacteristic
182C42×C11C2×D411yescharacteristic
183C42×C11C2×D412yes—
184C42×C11C2×D411yescharacteristic
185C42×C11C2×D412yes—
186C42×C11C2411yescharacteristic
187C22⋊Dic11—22no—
188C22⋊Dic11—21no—
189C22⋊Dic11—22no—
190(C2×D11)⋊C4—21no—
191(C2×D11)⋊C4—22no—
192(C2×D11)⋊C4—22no—
193(C2×D11)⋊C4—22no—
194(C2×D11)⋊C4—21no—
195C4⋊Dic11—22no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11C22×C411yescharacteristic
200C4⋊Dic11C22×C412yes—
201C4⋊Dic11C22×C411yescharacteristic
202Dic11⋊C4—22no—
203Dic11⋊C4—22no—
204Dic11⋊C4—22no—
205Dic11⋊C4—21no—
206Dic11⋊C4—22no—
207Dic11⋊C4—22no—
208Dic11⋊C4—22no—
209Dic11⋊C4—21no—
210Dic11⋊C4—22no—
211C4×Dic11—22no—
212C4×Dic11—22no—
213C4×Dic11—21no—
214C4×Dic11—21no—
215C4×Dic11—21no—
216C4×Dic11—22no—
217#4318—82no—
218#4318—81no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—22no—
222#3482—111no—
223#2991—111no—
224#2922D1111yescharacteristic, complemented
225#1495—112no—
226#1493—111no—
227#1489—111no—
228#1487—112no—
229#1485—111no—
230#1482—112no—
231#1479—112no—
232#1476—111no—
233C23×C11C2×C22⋊C411yescharacteristic
234C23×C11C2×C22⋊C412yes—
235C22×D11—21no—
236Q8×C11—22no—
237D4×C11—22no—
238D4×C11—42no—
239C2×C4×C11—22no—
240C2×C4×C11—21no—
241C2×C4×C11—22no—
242C2×C4×C11—21no—
243C2×C4×C11—22no—
244C2×C4×C11—21no—
245C2×C4×C11—22no—
246C2×C4×C11—21no—
247C2×C4×C11—22no—
248C2×C4×C11—42no—
249C2×C4×C11C2×C22⋊C412yes—
250C2×C4×C11C2×C22⋊C411yescharacteristic
251C2×C4×C11C2×C22⋊C412yes—
252C2×C4×C11C2×C22⋊C411yescharacteristic
253C2×C4×C11C2×C22⋊C412yes—
254C2×C4×C11C2×C22⋊C411yescharacteristic
255C2×C4×C11C23×C411yescharacteristic
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C22×D411yescharacteristic
258C22⋊D11—42no—
259C22⋊D11—44no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—22no—
264C2×Dic11—22no—
265C2×Dic11—44no—
266C2×Dic11—44no—
267D44—21no—
268D44—21no—
269C4×D11—42no—
270C4×D11—41no—
271C4×D11—41no—
272C4×D11—42no—
273Dic22—21no—
274Dic22—22no—
275Dic22—22no—
276Dic22—44no—
277Dic22—42no—
278Dic22#13112yes—
279C8×C11—41no—
280C8×C11—41no—
281C8×C11—42no—
282C11⋊C8—41no—
283C11⋊C8—42no—
284C11⋊C8—41no—
285#557—111no—
286#556—111no—
287#556—221no—
288#552—112no—
289#552—222no—
290D4×Q8—111no—
291#548—112no—
292#547—111no—
293#547—221no—
294#533—111no—
295#533—221no—
296#529—112no—
297#529—222no—
298C4×#41—111no—
299C4×#41—221no—
300C4×#41C2×D1111yescharacteristic
301C2×C4×Q8—112no—
302C8×Q8—221no—
303#436—221no—
304#436—222no—
305#433—22no—
306#431—111no—
307#431—112no—
308#431C2×D1112yes—
309#431C2×D1112yes—
310#424—21no—
311#423—112no—
312#423—111no—
313#408—21no—
314C4×M16C2×D1111yescharacteristic
315C2×C4×C8C2×D1111yescharacteristic
316Q8⋊C8—111no—
317Q8⋊C8—111no—
318Q8⋊C8—112no—
319Q8⋊C8—112no—
320Q8⋊C8—112no—
321Q8⋊C8—112no—
322Q8⋊C8—112no—
323D4⋊C8—111no—
324D4⋊C8—111no—
325D4⋊C8—112no—
326C22×C11—22no—
327C22×C11—21no—
328C22×C11—21no—
329C22×C11—22no—
330C22×C11—21no—
331C22×C11—22no—
332C22×C11C22×C22⋊C411yescharacteristic
333C2×D11—41no—
334C2×D11—41no—
335C2×D11—41no—
336C4×C11—22no—
337C4×C11—21no—
338C4×C11—22no—
339C4×C11—21no—
340C4×C11—21no—
341C4×C11—22no—
342C4×C11#42112yes—
343C4×C11C2×#13111yescharacteristic
344C4×C11#56811yescharacteristic
345C4×C11#57711yescharacteristic
346C4×C11#57811yescharacteristic
347Dic11—22no—
348Dic11—42no—
349Dic11—41no—
350Dic11—42no—
351Dic11—41no—
352C2×#41—111no—
353C2×#41—221no—
354C2×#41C22⋊D1111yescharacteristic
355C22×Q8—112no—
356C2×M16—21no—
357C2×M16—222no—
358C2×M16—221no—
359C22×C8—21no—
360C4⋊Q8—111no—
361C4⋊Q8—111no—
362C4⋊Q8—221no—
363C4⋊Q8—221no—
364#126—222no—
365#126—222no—
366#126—222no—
367#125—112no—
368#125—222no—
369#125—222no—
370#125—221no—
371#124—112no—
372#124—222no—
373#123—222no—
374#123—222no—
375#123—222no—
376C22⋊Q8—112no—
377C22⋊Q8—112no—
378C22⋊Q8—221no—
379C22⋊Q8—221no—
380C22⋊Q8—221no—
381C22⋊Q8—222no—
382C22⋊Q8—222no—
383#121—112no—
384#121—222no—
385C4×Q8—112no—
386C4×Q8—112no—
387C4×Q8—111no—
388C4×Q8—111no—
389C4×Q8—112no—
390C4×Q8—221no—
391C4×Q8—222no—
392C4×Q8—221no—
393C4×Q8—222no—
394C4×Q8C4×D1111yescharacteristic
395C4×Q8D4411yescharacteristic
396C4×D4—111no—
397C4×D4—111no—
398C4×D4—221no—
399C4×D4—221no—
400C4×D4—222no—
401C4×D4—221no—
402C4×D4—222no—
403C4×D4C4×D1111yescharacteristic
404C4×D4C4×D1112yes—
405C4×D4D4411yescharacteristic
406C4×D4D4412yes—
407#117—111no—
408#117—221no—
409#117—221no—
410#117—222no—
411#117—222no—
412#117—221no—
413#117C22⋊D1112yes—
414#117C22⋊D1111yescharacteristic
415C2×C4⋊C4—112no—
416C2×C4⋊C4—222no—
417C2×C42—222no—
418C2×C42—221no—
419C2×C42C22×D1112yes—
420C2×C42C22×D1111yescharacteristic
421C4⋊C8—22no—
422C4⋊C8—22no—
423C4⋊C8—111no—
424C4⋊C8—112no—
425C4⋊C8—111no—
426C4⋊C8—221no—
427C4⋊C8—222no—
428C22⋊C8—22no—
429C22⋊C8—22no—
430C22⋊C8—222no—
431C22⋊C8—221no—
432#97—21no—
433C4×C8—21no—
434C4×C8—221no—
435C4×C8—222no—
436C4×C8C22×D1111yescharacteristic
437C4×C8C22×D1111yescharacteristic
438C4×C8C22×D1112yes—
439C2×C11—42no—
440C2×C11—41no—
441C2×C11#288011yescharacteristic
442C2×C11#289811yescharacteristic
443C2×C11C2×#42111yescharacteristic
444D11—81no—
445#41—42no—
446#41—222no—
447#41—441no—
448#41—444no—
449C2×Q8—111no—
450C2×Q8—112no—
451C2×Q8—224no—
452C2×Q8—222no—
453C2×Q8—221no—
454C2×Q8—442no—
455C2×Q8(C2×D11)⋊C411yescharacteristic
456C2×D4—111no—
457C2×D4—222no—
458C2×D4—221no—
459C2×D4(C2×D11)⋊C411yescharacteristic
460C2×D4(C2×D11)⋊C412yes—
461C22×C4—222no—
462C22×C4—222no—
463C22×C4—221no—
464C22×C4—221no—
465C22×C4—221no—
466C22×C4C2×C4×D1112yes—
467C22×C4C2×C4×D1111yescharacteristic
468C22×C4C2×D4412yes—
469C22×C4C2×D4411yescharacteristic
470C22×C4C2×C22⋊D1111yescharacteristic
471C22×C4C2×C22⋊D1112yes—
472M16—42no—
473M16—882no—
474M16—881no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—22no—
478C2×C8—42no—
479C2×C8—221no—
480C2×C8—221no—
481C2×C8—222no—
482C4⋊C4—111no—
483C4⋊C4—112no—
484C4⋊C4—111no—
485C4⋊C4—222no—
486C4⋊C4—222no—
487C4⋊C4—222no—
488C4⋊C4—221no—
489C4⋊C4—222no—
490C4⋊C4—221no—
491C4⋊C4—222no—
492C4⋊C4—222no—
493C4⋊C4—221no—
494C4⋊C4—222no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—222no—
498C4⋊C4(C2×D11)⋊C411yescharacteristic
499C4⋊C4(C2×D11)⋊C412yes—
500C4⋊C4(C2×D11)⋊C411yescharacteristic
501C4⋊C4(C2×D11)⋊C412yes—
502C22⋊C4—221no—
503C22⋊C4—222no—
504C22⋊C4—222no—
505C22⋊C4—221no—
506C22⋊C4—222no—
507C22⋊C4—222no—
508C22⋊C4—222no—
509C22⋊C4—221no—
510C22⋊C4(C2×D11)⋊C412yes—
511C22⋊C4(C2×D11)⋊C412yes—
512C22⋊C4(C2×D11)⋊C412yes—
513C42—221no—
514C42—222no—
515C42—221no—
516C42—222no—
517C42—221no—
518C42—222no—
519C42C2×C4×D1111yescharacteristic
520C42C2×C4×D1112yes—
521C42C2×D4411yescharacteristic
522C42C2×D4412yes—
523C42C2×C22⋊D1111yescharacteristic
524C42C2×C22⋊D1112yes—
525C42C23×D1111yescharacteristic
526C11#1752511yescharacteristic, complemented, Sylow
527C23—221no—
528C23C2×(C2×D11)⋊C411yescharacteristic
529C23C2×(C2×D11)⋊C412yes—
530Q8—22no—
531Q8—112no—
532Q8—221no—
533Q8—222no—
534Q8—222no—
535Q8—444no—
536Q8—442no—
537D4—22no—
538D4—42no—
539D4—221no—
540D4—221no—
541D4—442no—
542D4—444no—
543C2×C4—22no—
544C2×C4—21no—
545C2×C4—22no—
546C2×C4—21no—
547C2×C4—22no—
548C2×C4—21no—
549C2×C4—22no—
550C2×C4—21no—
551C2×C4—22no—
552C2×C4—42no—
553C2×C4—221no—
554C2×C4—221no—
555C2×C4—221no—
556C2×C4—222no—
557C2×C4—222no—
558C2×C4—442no—
559C2×C4—444no—
560C2×C4—444no—
561C2×C4—441no—
562C2×C4—441no—
563C2×C4—442no—
564C2×C4C2×(C2×D11)⋊C412yes—
565C2×C4C2×(C2×D11)⋊C411yescharacteristic
566C2×C4C2×(C2×D11)⋊C412yes—
567C2×C4C2×(C2×D11)⋊C411yescharacteristic
568C2×C4C2×(C2×D11)⋊C412yes—
569C2×C4C2×(C2×D11)⋊C411yescharacteristic
570C2×C4C22×C4×D1111yescharacteristic
571C2×C4C22×D4411yescharacteristic
572C2×C4C22×C22⋊D1111yescharacteristic
573C8—41no—
574C8—41no—
575C8—42no—
576C8—441no—
577C8—442no—
578C8—441no—
579C22—22no—
580C22—21no—
581C22—21no—
582C22—22no—
583C22—21no—
584C22—22no—
585C22—441no—
586C22—441no—
587C22—441no—
588C22C22×(C2×D11)⋊C411yescharacteristic
589C4—21no—
590C4—22no—
591C4—22no—
592C4—21no—
593C4—21no—
594C4—22no—
595C4—222no—
596C4—442no—
597C4—441no—
598C4—441no—
599C4—442no—
600C4#1062261812yes—
601C4D11×#13111yescharacteristic
602C4#1062328111yescharacteristic
603C4#1062328211yescharacteristic
604C4#1062328411yescharacteristic
605C2—42no—
606C2—41no—
607C2—881no—
608C2#1307706311yescharacteristic
609C2#1307715011yescharacteristic
610C2C2×#1062261811yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2922C2
socleC22×C11C22×C22⋊C4
prime radical#13082231C2
cosocleC42×C11C24
hypercenter#2922D11
hypocenterC11#17525
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2922

Complements

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

NH ≅ G/Ntype
2. #13077748C2semidirect
3. #13067082C2semidirect
4. #13067072C2semidirect
5. #13067056C2semidirect
6. #13067046C2semidirect
7. #13067038C2semidirect
8. #13067025C2semidirect
9. #13067012C2semidirect
10. #13066999C2semidirect
11. C11×#2922C2semidirect
224. #2922D11semidirect
526. C11#17525semidirect

Maximal subgroups

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

subgroupindex
#130822312
#130777482
#130670822
#130670722
#130670562
#130670462
#130670382
#130670252
#130670122
#130669992
C11×#29222
#1752511