Finite Group Databasebeta

← #14724803

Subgroups — #14724803

Order 2816.

670 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#13078663C211yesmaximal, characteristic
2#13077614C211yesmaximal, characteristic, complemented
3D4×#4318C211yesmaximal, characteristic, complemented
4#13067527C211yesmaximal, characteristic, complemented
5#13067509C211yesmaximal, characteristic, complemented
6#13067497C211yesmaximal, characteristic, complemented
7#13067477C211yesmaximal, characteristic, complemented
8#13067449C211yesmaximal, characteristic, complemented
9#13067448C211yesmaximal, characteristic, complemented
10#13067425C211yesmaximal, characteristic, complemented
11#13067408C211yesmaximal, characteristic, complemented
12#13067404C211yesmaximal, characteristic, complemented
13#13067082C211yesmaximal, characteristic, complemented
14#13066911C211yesmaximal, characteristic, complemented
15C11×#1478C211yesmaximal, characteristic, complemented
16C2×C4×D4×C11C2211yescharacteristic
17C22×#4318—21no—
18#10623010C2211yescharacteristic
19C11×#431C2211yescharacteristic
20C11×#431C2211yescharacteristic
21#10622831C411yescharacteristic
22#10622830C411yescharacteristic
23#10622820—21no—
24C4×#4324C2211yescharacteristic
25C4×#4324C2211yescharacteristic
26#10622629C411yescharacteristic
27#10622629C411yescharacteristic
28C4×#4323C2211yescharacteristic
29C4×#4323C2211yescharacteristic
30#10622625C2211yescharacteristic
31#10622625C2211yescharacteristic
32#10622624—21no—
33#10622624—21no—
34D4×C11⋊C8C2211yescharacteristic
35D4×C11⋊C8C2211yescharacteristic
36#10622622C411yescharacteristic
37#10622622C411yescharacteristic
38#10622583C411yescharacteristic
39#10622581C411yescharacteristic
40#10622538C2211yescharacteristic
41#10622537C2211yescharacteristic
42C4×#4318C2211yescharacteristic
43#10622451C2211yescharacteristic, complemented
44#10622447C2211yescharacteristic, complemented
45#10622444C2211yescharacteristic, complemented
46#10622443C2211yescharacteristic, complemented
47#10622342—21no—
48#10622341—21no—
49#10622303—21no—
50#10622302—21no—
51C11×D4⋊C8C2211yescharacteristic
52C11×D4⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic
54C11×D4⋊C8C2211yescharacteristic
55#10622118C2211yescharacteristic, complemented
56#10622118C2211yescharacteristic, complemented
57#10622117C2211yescharacteristic, complemented
58#10622117C2211yescharacteristic, complemented
59#10622097C2211yescharacteristic, complemented
60#10622097C2211yescharacteristic, complemented
61#10622094C2211yescharacteristic, complemented
62#10622094C2211yescharacteristic, complemented
63#10622093C2211yescharacteristic, complemented
64#10622092C2211yescharacteristic, complemented
65#10622092C2211yescharacteristic, complemented
66C8×C11⋊C8C2211yescharacteristic, complemented
67C22×D4×C11C2×C411yescharacteristic
68C23×C4×C11—21no—
69C4×D4×C11—21no—
70C4×D4×C11—21no—
71C4×D4×C11C2×C411yescharacteristic
72C4×D4×C11C2×C411yescharacteristic
73C4×D4×C11C2311yescharacteristic
74C4×D4×C11C2311yescharacteristic
75C2×C11×C4⋊C4C2×C411yescharacteristic
76C2×C11×C22⋊C4—21no—
77C2×C42×C11C2311yescharacteristic
78C2×#4324C2×C411yescharacteristic
79C2×#4324C2×C411yescharacteristic
80C2×#4323C2×C411yescharacteristic
81C2×#4323C2×C411yescharacteristic
82#66983C2×C411yescharacteristic
83#66982—21no—
84C4×C22⋊D11—21no—
85#66977C2×C411yescharacteristic
86C2×#4318—21no—
87C2×#4318—21no—
88C2×#4318—21no—
89C2×#4318—44no—
90C2×#4318D411yescharacteristic
91C2×#4318D411yescharacteristic
92C22×C11⋊C8—21no—
93C22×C11⋊C8—21no—
94C2×#4313—21no—
95C2×C8×D11—21no—
96#66929—21no—
97#66928C2×C411yescharacteristic
98C4×D44C2311yescharacteristic
99#66925—21no—
100#66923C2×C411yescharacteristic
101C4×Dic22C2311yescharacteristic
102C11×C4⋊C8—21no—
103C11×C4⋊C8C2311yescharacteristic
104C11×C4⋊C8C2311yescharacteristic
105C11×C22⋊C8—21no—
106C11×C22⋊C8—21no—
107C4×C8×C11—21no—
108C4×C8×C11C2311yescharacteristic
109C4×C8×C11C2311yescharacteristic
110#66896C2×C411yescharacteristic
111#66896C2×C411yescharacteristic
112#66896C2×C411yescharacteristic
113#66896C2×C411yescharacteristic
114C22⋊(C11⋊C8)—21no—
115C22⋊(C11⋊C8)—21no—
116C22⋊(C11⋊C8)—21no—
117C22⋊(C11⋊C8)—21no—
118C22⋊(C11⋊C8)C2×C411yescharacteristic
119C22⋊(C11⋊C8)C2×C411yescharacteristic
120(C2×D11)⋊C8—21no—
121(C2×D11)⋊C8—21no—
122#66879—21no—
123Dic11⋊C8—21no—
124Dic11⋊C8—21no—
125C8×Dic11—21no—
126#66874C2×C411yescharacteristic
127#66874C2×C411yescharacteristic
128#66873C2×C411yescharacteristic
129#66873C2×C411yescharacteristic
130#66872C2×C411yescharacteristic
131#66872C2×C411yescharacteristic
132#66871C2×C411yescharacteristic
133#66871C2×C411yescharacteristic
134C4⋊(C11⋊C8)—21no—
135C4⋊(C11⋊C8)C2×C411yescharacteristic
136C4⋊(C11⋊C8)C2×C411yescharacteristic
137C4⋊(C11⋊C8)C2311yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139#66867D411yescharacteristic
140#66867D411yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#18006—111nomaximal, Sylow
146C24×C11—21no—
147C2×D4×C11—22no—
148C2×D4×C11—21no—
149C2×D4×C11—41no—
150C2×D4×C11C22×C411yescharacteristic
151C2×D4×C11C22×C411yescharacteristic
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—42no—
158C22×C4×C11—42no—
159C22×C4×C11C22×C411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11#4111yescharacteristic
162C2×C22⋊D11—21no—
163C2×D44C22×C411yescharacteristic
164C2×C4×D11—21no—
165C2×Dic22C22×C411yescharacteristic
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4C22×C411yescharacteristic
172C11×C4⋊C4C22×C411yescharacteristic
173C11×C22⋊C4—21no—
174C11×C22⋊C4—21no—
175C11×C22⋊C4—21no—
176C11×C22⋊C4—21no—
177C42×C11C22×C411yescharacteristic
178C42×C11C2×D411yescharacteristic
179C42×C11#4111yescharacteristic
180C42×C11C2411yescharacteristic
181C22⋊Dic11—21no—
182#4324—22no—
183#4324—41no—
184#4323—22no—
185#4323—41no—
186(C2×D11)⋊C4—21no—
187(C2×D11)⋊C4—21no—
188(C2×D11)⋊C4—21no—
189(C2×D11)⋊C4—21no—
190C4⋊Dic11C22×C411yescharacteristic
191C4⋊Dic11C22×C411yescharacteristic
192Dic11⋊C4—21no—
193Dic11⋊C4—21no—
194Dic11⋊C4—21no—
195Dic11⋊C4—21no—
196C4×Dic11—21no—
197#4318—22no—
198#4318—41no—
199#4318—42no—
200#4318—42no—
201#4318—42no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—42no—
205C2×C11⋊C8—42no—
206C2×C11⋊C8C22×C411yescharacteristic
207C2×C11⋊C8C22×C411yescharacteristic
208C2×C11⋊C8C22×C411yescharacteristic
209C2×C11⋊C8C22×C411yescharacteristic
210C2×C11⋊C8C2×D411yescharacteristic
211C2×C11⋊C8C2×D411yescharacteristic
212C2×C11⋊C8C2×D411yescharacteristic
213C2×C11⋊C8C2×D411yescharacteristic
214#4313—42no—
215C8×D11—42no—
216#3105—111no—
217#2969—111no—
218D4×M16—111no—
219#1594—111no—
220#1590—111no—
221#1588—111no—
222#1586—111no—
223#1582—111no—
224#1581—111no—
225SD16⋊C8—111no—
226C8×D8—111no—
227#1574—111no—
228#1495—111no—
229#1478D1111yescharacteristic, complemented
230#1453—111no—
231C23×C11—21no—
232C23×C11—21no—
233C23×C11—42no—
234C23×C11—42no—
235C23×C11—81no—
236C23×C11C4×D411yescharacteristic
237C22×D11—21no—
238D4×C11—21no—
239D4×C11—21no—
240D4×C11—21no—
241D4×C11—42no—
242D4×C11#13112yes—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—41no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11C4×D411yescharacteristic
258C2×C4×C11C4×D411yescharacteristic
259C2×C4×C11C4×D411yescharacteristic
260C2×C4×C11C23×C411yescharacteristic
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C22⋊D11—81no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267D44—21no—
268D44—21no—
269C4×D11—41no—
270C4×D11—41no—
271Dic22—21no—
272Dic22—21no—
273C8×C11—41no—
274C8×C11—41no—
275C8×C11—41no—
276C8×C11—41no—
277C11⋊C8—21no—
278C11⋊C8—21no—
279C11⋊C8—21no—
280C11⋊C8—21no—
281C11⋊C8—21no—
282C11⋊C8—21no—
283C11⋊C8—21no—
284C11⋊C8—41no—
285C11⋊C8—41no—
286C11⋊C8AGL(1,ℤ/8)12yes—
287C22×M16—221no—
288#529—111no—
289C2×C4×D4C2×D1111yescharacteristic
290#484—111no—
291#481—111no—
292#478—111no—
293#478—111no—
294#463—111no—
295#463—111no—
296#450—111no—
297#447—111no—
298#446—111no—
299C8×Q8—111no—
300C4×SD16—111no—
301C4×SD16—111no—
302C4×D8—111no—
303C4×D8—111no—
304#436—111no—
305#436—111no—
306#436—111no—
307#436—221no—
308#435—221no—
309#435—221no—
310#435—221no—
311C8×D4—111no—
312C8×D4—111no—
313C8×D4—111no—
314#433—221no—
315#431—111no—
316#431C2×D1111yescharacteristic
317#431C2×D1111yescharacteristic
318#423—111no—
319#407—221no—
320#405—221no—
321C4×M16—111no—
322#335—111no—
323#335—111no—
324#334—111no—
325#334—111no—
326Q8⋊C8—111no—
327Q8⋊C8—111no—
328D4⋊C8—111no—
329D4⋊C8—111no—
330D4⋊C8C2×D1111yescharacteristic
331D4⋊C8C2×D1111yescharacteristic
332D4⋊C8C2×D1111yescharacteristic
333D4⋊C8C2×D1111yescharacteristic
334#322—111no—
335#322—111no—
336#322—111no—
337C82—111no—
338C22×C11—21no—
339C22×C11—22no—
340C22×C11—21no—
341C22×C11—21no—
342C22×C11—41no—
343C22×C11—41no—
344C22×C11—41no—
345C22×C11—41no—
346C22×C11—41no—
347C22×C11—84no—
348C22×C11C2×C4×D411yescharacteristic
349C2×D11—41no—
350C2×D11—41no—
351C2×D11—41no—
352C4×C11—21no—
353C4×C11—21no—
354C4×C11—21no—
355C4×C11—21no—
356C4×C11—41no—
357C4×C11—41no—
358C4×C11C2×#13111yescharacteristic
359C4×C11#56811yescharacteristic
360C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
361C4×C11#57511yescharacteristic
362Dic11—41no—
363Dic11—41no—
364Dic11—41no—
365C22×D4C4×D1111yescharacteristic
366C23×C4—21no—
367C2×SD16—111no—
368C2×SD16—111no—
369C2×D8—111no—
370C2×D8—111no—
371C2×M16—111no—
372C2×M16—111no—
373C2×M16—221no—
374C2×M16—221no—
375C2×M16—221no—
376C2×M16—221no—
377C2×M16—444no—
378C22×C8—221no—
379C22×C8—221no—
380C22×C8—221no—
381#126—221no—
382#125—111no—
383#124—111no—
384#123—221no—
385C22⋊Q8—111no—
386#121—111no—
387C4×Q8—111no—
388C4×D4—21no—
389C4×D4—21no—
390C4×D4—111no—
391C4×D4—221no—
392C4×D4C4×D1111yescharacteristic
393C4×D4C4×D1111yescharacteristic
394C4×D4C22×D1111yescharacteristic
395C4×D4C22×D1111yescharacteristic
396#117—221no—
397C2×C4⋊C4C4×D1111yescharacteristic
398C2×C22⋊C4—21no—
399C2×C42C22×D1111yescharacteristic
400#107—111no—
401#107—111no—
402#106—111no—
403#106—111no—
404C4⋊C8—21no—
405C4⋊C8—111no—
406C4⋊C8—111no—
407C4⋊C8—111no—
408C4⋊C8—111no—
409C4⋊C8—221no—
410C4⋊C8—221no—
411C4⋊C8—221no—
412C4⋊C8C22×D1111yescharacteristic
413C4⋊C8C22×D1111yescharacteristic
414#103—111no—
415#103—111no—
416#102—111no—
417#102—111no—
418#102—111no—
419#102—111no—
420#102—111no—
421#102—111no—
422C22⋊C8—21no—
423C22⋊C8—21no—
424C22⋊C8—111no—
425C22⋊C8—111no—
426C22⋊C8—221no—
427C22⋊C8—221no—
428C22⋊C8—221no—
429C22⋊C8—221no—
430C22⋊C8—221no—
431C22⋊C8—221no—
432#97—111no—
433#97—111no—
434#97—221no—
435C4×C8—21no—
436C4×C8—111no—
437C4×C8—111no—
438C4×C8—111no—
439C4×C8—111no—
440C4×C8—221no—
441C4×C8C22×D1111yescharacteristic
442C4×C8C22×D1111yescharacteristic
443C2×C11—41no—
444C2×C11—42no—
445C2×C11—81no—
446C2×C11#293311yescharacteristic
447C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
448C2×C11#295711yescharacteristic
449D11—81no—
450C24—21no—
451C2×Q8—111no—
452C2×D4—22no—
453C2×D4—21no—
454C2×D4—41no—
455C2×D4—111no—
456C2×D4—221no—
457C2×D4C2×C4×D1111yescharacteristic
458C2×D4C2×C4×D1111yescharacteristic
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—221no—
467C22×C4C2×C4×D1111yescharacteristic
468C22×C4D4×D1111yescharacteristic
469C22×C4#434111yescharacteristic
470SD16—222no—
471SD16—441no—
472D8—222no—
473D8—441no—
474M16—222no—
475M16—442no—
476M16—442no—
477M16—441no—
478M16—442no—
479M16—442no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—111no—
485C2×C8—111no—
486C2×C8—111no—
487C2×C8—111no—
488C2×C8—111no—
489C2×C8—111no—
490C2×C8—111no—
491C2×C8—111no—
492C2×C8—221no—
493C2×C8—221no—
494C2×C8—442no—
495C2×C8—442no—
496C2×C8—442no—
497C4⋊C4—21no—
498C4⋊C4—111no—
499C4⋊C4—111no—
500C4⋊C4—221no—
501C4⋊C4—221no—
502C4⋊C4—221no—
503C4⋊C4—221no—
504C4⋊C4C2×C4×D1111yescharacteristic
505C4⋊C4C2×C4×D1111yescharacteristic
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—221no—
511C22⋊C4—221no—
512C22⋊C4—221no—
513C22⋊C4—221no—
514C22⋊C4—221no—
515C42—221no—
516C42C2×C4×D1111yescharacteristic
517C42D4×D1111yescharacteristic
518C42#434111yescharacteristic
519C42C23×D1111yescharacteristic
520C11#1800611yescharacteristic, complemented, Sylow
521C23—21no—
522C23—21no—
523C23—42no—
524C23—42no—
525C23—81no—
526C23—221no—
527C23(C22⋊D11)⋊C411yescharacteristic
528Q8—221no—
529Q8—221no—
530D4—21no—
531D4—21no—
532D4—21no—
533D4—42no—
534D4—221no—
535D4—221no—
536D4—881no—
537D4#6695412yes—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—41no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—221no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4(C22⋊D11)⋊C411yescharacteristic
558C2×C4(C22⋊D11)⋊C411yescharacteristic
559C2×C4(C22⋊D11)⋊C411yescharacteristic
560C2×C4C22×C4×D1111yescharacteristic
561C2×C4C2×D4×D1111yescharacteristic
562C2×C4C2×#434111yescharacteristic
563C8—41no—
564C8—41no—
565C8—41no—
566C8—41no—
567C8—112no—
568C8—221no—
569C8—221no—
570C8—221no—
571C8—221no—
572C8—221no—
573C8—221no—
574C8—221no—
575C8—441no—
576C8—441no—
577C22—21no—
578C22—21no—
579C22—22no—
580C22—21no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—84no—
587C22—441no—
588C22—441no—
589C22—441no—
590C22C2×(C22⋊D11)⋊C411yescharacteristic
591C4—21no—
592C4—21no—
593C4—21no—
594C4—21no—
595C4—41no—
596C4—41no—
597C4—441no—
598C4—441no—
599C4—441no—
600C4C2×#6695411yescharacteristic
601C4#1062327611yescharacteristic
602C4D11×AGL(1,ℤ/8)11yescharacteristic
603C4#1062330411yescharacteristic
604C2—41no—
605C2—42no—
606C2—81no—
607C2—881no—
608C2#1307733711yescharacteristic
609C2#1307742011yescharacteristic
610C2#1307752911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1478C2
socleC22×C11C2×C4×D4
prime radical#10622830C4
cosocleC42×C11C24
hypercenter#1478D11
hypocenterC11#18006
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1478

Complements

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

NH ≅ G/Ntype
2. #13077614C2semidirect
3. D4×#4318C2semidirect
4. #13067527C2semidirect
5. #13067509C2semidirect
6. #13067497C2semidirect
7. #13067477C2semidirect
8. #13067449C2semidirect
9. #13067448C2semidirect
10. #13067425C2semidirect
11. #13067408C2semidirect
12. #13067404C2semidirect
13. #13067082C2semidirect
14. #13066911C2semidirect
15. C11×#1478C2semidirect
43. #10622451C22semidirect
44. #10622447C22semidirect
45. #10622444C22semidirect
46. #10622443C22semidirect
55. #10622118C22semidirect
56. #10622118C22semidirect
57. #10622117C22semidirect
58. #10622117C22semidirect
59. #10622097C22semidirect
60. #10622097C22semidirect
61. #10622094C22semidirect
62. #10622094C22semidirect
63. #10622093C22semidirect
64. #10622092C22semidirect
65. #10622092C22semidirect
66. C8×C11⋊C8C22semidirect
229. #1478D11semidirect
520. C11#18006semidirect

Maximal subgroups

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

subgroupindex
#130786632
#130776142
D4×#43182
#130675272
#130675092
#130674972
#130674772
#130674492
#130674482
#130674252
#130674082
#130674042
#130670822
#130669112
C11×#14782
#1800611