Finite Group Databasebeta

← #14723933

Subgroups — #14723933

Order 2816.

620 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078628C211yesmaximal, characteristic
2#13077724C211yesmaximal, characteristic, complemented
3#13067492C211yesmaximal, characteristic, complemented
4#13067471C211yesmaximal, characteristic, complemented
5#13067464C211yesmaximal, characteristic, complemented
6#13067443C211yesmaximal, characteristic, complemented
7#13067428C211yesmaximal, characteristic, complemented
8#13067426C211yesmaximal, characteristic, complemented
9C8×#4326C211yesmaximal, characteristic, complemented
10C8×#4323C211yesmaximal, characteristic, complemented
11#13067392C211yesmaximal, characteristic, complemented
12#13067053C211yesmaximal, characteristic, complemented
13#13067029C211yesmaximal, characteristic, complemented
14#13066911C211yesmaximal, characteristic, complemented
15C11×#2993C211yesmaximal, characteristic, complemented
16C11×#529C2211yescharacteristic
17C4×#4339C2211yescharacteristic
18C11×#446C2211yescharacteristic
19C8×Q8×C11C2211yescharacteristic
20C11×#436—21no—
21C11×#436C2211yescharacteristic
22C11×#435—21no—
23C8×D4×C11C2211yescharacteristic
24C11×#433—21no—
25C11×#431C2211yescharacteristic
26C11×#424—21no—
27C11×#423C2211yescharacteristic
28#10622679C411yescharacteristic
29#10622676C411yescharacteristic
30#10622670C411yescharacteristic
31#10622667C411yescharacteristic
32#10622660C411yescharacteristic
33#10622658C411yescharacteristic
34#10622650C411yescharacteristic
35#10622648C411yescharacteristic
36C4×#4326C2211yescharacteristic
37C4×#4325C2211yescharacteristic
38C4×#4324C2211yescharacteristic
39C4×#4323C2211yescharacteristic
40#10622538C2211yescharacteristic
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42C4×#4318C2211yescharacteristic
43#10622446—21no—
44D11×C4⋊C8—21no—
45(C22⋊D11)⋊C8—21no—
46(C22⋊D11)⋊C8—21no—
47C8×D44C2211yescharacteristic
48C8×D44C2211yescharacteristic
49C8×Dic22C2211yescharacteristic
50C8×Dic22C2211yescharacteristic
51Q8⋊(C11⋊C8)C2211yescharacteristic
52Q8⋊(C11⋊C8)C2211yescharacteristic
53D4⋊(C11⋊C8)C2211yescharacteristic
54D4⋊(C11⋊C8)C2211yescharacteristic
55#10622122C2211yescharacteristic
56#10622122C2211yescharacteristic
57#10622121C2211yescharacteristic
58#10622121C2211yescharacteristic
59#10622117C2211yescharacteristic
60#10622117C2211yescharacteristic
61#10622117C2211yescharacteristic
62#10622117C2211yescharacteristic
63#10622093C2211yescharacteristic
64#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×#4339C2×C411yescharacteristic
68C2×C11×M16—21no—
69C2×C11×M16—21no—
70C22×C8×C11—21no—
71C11×#126—21no—
72C11×#125C2×C411yescharacteristic
73C11×#124C2×C411yescharacteristic
74C11×#123—21no—
75C11×C22⋊Q8C2×C411yescharacteristic
76C11×#121C2×C411yescharacteristic
77C4×Q8×C11C2311yescharacteristic
78C4×D4×C11—21no—
79C4×D4×C11C2311yescharacteristic
80C11×#117—21no—
81C2×C42×C11C2311yescharacteristic
82C2×#4326C2×C411yescharacteristic
83C2×#4325C2×C411yescharacteristic
84C2×#4324C2×C411yescharacteristic
85C2×#4323C2×C411yescharacteristic
86C4×C22⋊D11—21no—
87C4×C22⋊D11—21no—
88#66979C2×C411yescharacteristic
89C2×#4318—21no—
90C22×C11⋊C8—21no—
91C2×C8×D11—21no—
92C2×C8×D11—21no—
93C4×D44C2×C411yescharacteristic
94C4×D44C2311yescharacteristic
95#66925—21no—
96C42×D11—21no—
97C4×Dic22C2×C411yescharacteristic
98C4×Dic22C2311yescharacteristic
99C11×C4⋊C8—21no—
100C11×C4⋊C8—21no—
101C11×C4⋊C8—21no—
102C11×C4⋊C8D411yescharacteristic
103C11×C4⋊C8D411yescharacteristic
104C11×C4⋊C8C2311yescharacteristic
105C11×C4⋊C8C2311yescharacteristic
106C11×C22⋊C8—21no—
107C11×C22⋊C8—21no—
108C11×C22⋊C8D411yescharacteristic
109C11×C22⋊C8D411yescharacteristic
110C11×#97—21no—
111C4×C8×C11—21no—
112C4×C8×C11C2311yescharacteristic
113C4×C8×C11C2311yescharacteristic
114#66899C2×C411yescharacteristic
115#66899C2×C411yescharacteristic
116#66896C2×C411yescharacteristic
117#66896C2×C411yescharacteristic
118C22⋊(C11⋊C8)C2×C411yescharacteristic
119C22⋊(C11⋊C8)C2×C411yescharacteristic
120(C2×D11)⋊C8—21no—
121(C2×D11)⋊C8—21no—
122Dic11⋊C8—21no—
123Dic11⋊C8—21no—
124C8×Dic11—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#66867—21no—
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#17926—111nomaximal, Sylow
145C2×Q8×C11C22×C411yescharacteristic
146C2×D4×C11—21no—
147C2×D4×C11C22×C411yescharacteristic
148C22×C4×C11—21no—
149C22×C4×C11C22×C411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11#4111yescharacteristic
152C2×C22⋊D11—21no—
153#4339—22no—
154#4339—22no—
155C2×D44C22×C411yescharacteristic
156C2×C4×D11—21no—
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×Dic22C22×C411yescharacteristic
160C11×M16—81no—
161C11×M16—81no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—81no—
165C2×C8×C11C2×D411yescharacteristic
166C2×C8×C11C2×D411yescharacteristic
167C2×C8×C11C2×D411yescharacteristic
168C2×C8×C11C2×D411yescharacteristic
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4C22×C411yescharacteristic
174C11×C4⋊C4C22×C411yescharacteristic
175C11×C22⋊C4—21no—
176C11×C22⋊C4—21no—
177C11×C22⋊C4—21no—
178C11×C22⋊C4—21no—
179C11×C22⋊C4—21no—
180C42×C11—21no—
181C42×C11C22×C411yescharacteristic
182C42×C11C2×D411yescharacteristic
183C42×C11#4111yescharacteristic
184C42×C11C2411yescharacteristic
185C22⋊Dic11—21no—
186#4326—22no—
187#4325—22no—
188#4324—22no—
189#4323—22no—
190(C2×D11)⋊C4—21no—
191(C2×D11)⋊C4—21no—
192C4⋊Dic11C22×C411yescharacteristic
193C4⋊Dic11C22×C411yescharacteristic
194Dic11⋊C4—21no—
195Dic11⋊C4—21no—
196C4×Dic11—21no—
197C4×Dic11—21no—
198C4×Dic11—21no—
199#4318—42no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—81no—
205C2×C11⋊C8C22×C411yescharacteristic
206C2×C11⋊C8C22×C411yescharacteristic
207C2×C11⋊C8C22×C411yescharacteristic
208C2×C11⋊C8C22×C411yescharacteristic
209C8×D11—81no—
210C8×D11—81no—
211#3102—111no—
212#2993D1111yescharacteristic, complemented
213#2988—111no—
214#1588—111no—
215#1585—111no—
216#1584—111no—
217#1581—111no—
218SD16⋊C8—111no—
219SD16⋊C8—111no—
220C8×Q16—111no—
221C8×D8—111no—
222#1571—111no—
223#1489—111no—
224#1483—111no—
225#1453—111no—
226C23×C11—21no—
227C23×C11C4×D411yescharacteristic
228C22×D11—21no—
229Q8×C11—21no—
230Q8×C11—21no—
231D4×C11—21no—
232D4×C11—21no—
233D4×C11—81no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11C4×D411yescharacteristic
245C2×C4×C11C4×D411yescharacteristic
246C2×C4×C11C4×D411yescharacteristic
247C2×C4×C11C23×C411yescharacteristic
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C22⋊D11—24no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254D44—21no—
255D44#13112yes—
256C4×D11—24no—
257C4×D11—41no—
258C4×D11—41no—
259C4×D11—81no—
260Dic22—21no—
261Dic22#13112yes—
262C8×C11—21no—
263C8×C11—21no—
264C8×C11—21no—
265C8×C11—21no—
266C8×C11—41no—
267C8×C11—41no—
268C11⋊C8—22no—
269C11⋊C8—21no—
270C11⋊C8—21no—
271C11⋊C8—21no—
272C11⋊C8—21no—
273C11⋊C8—41no—
274C11⋊C8—41no—
275C11⋊C8—41no—
276#529C2×D1111yescharacteristic
277C4×#41—111no—
278#485—111no—
279#482—111no—
280#479—111no—
281#478—111no—
282#464—111no—
283#463—111no—
284#452—111no—
285#449—111no—
286#446C2×D1111yescharacteristic
287C8×Q8—111no—
288C8×Q8—111no—
289C8×Q8C2×D1111yescharacteristic
290C4×Q16—111no—
291C4×SD16—111no—
292C4×SD16—111no—
293C4×D8—111no—
294#436—21no—
295#436C2×D1111yescharacteristic
296#435—21no—
297C8×D4—111no—
298C8×D4—111no—
299C8×D4—221no—
300C8×D4—221no—
301C8×D4C2×D1111yescharacteristic
302#433—21no—
303#431—111no—
304#431—221no—
305#431C2×D1111yescharacteristic
306#424—21no—
307#423C2×D1111yescharacteristic
308C2×C4⋊C8—111no—
309C2×C4⋊C8—221no—
310C4×M16—111no—
311#335—111no—
312#335—111no—
313#335—111no—
314#335—111no—
315Q8⋊C8—111no—
316Q8⋊C8—111no—
317Q8⋊C8—111no—
318Q8⋊C8—111no—
319D4⋊C8—111no—
320D4⋊C8—111no—
321D4⋊C8—111no—
322D4⋊C8—111no—
323#322—111no—
324#322—111no—
325#322—111no—
326C82—111no—
327C22×C11—21no—
328C22×C11—21no—
329C22×C11—21no—
330C22×C11—41no—
331C22×C11—41no—
332C22×C11—41no—
333C22×C11C2×C4×D411yescharacteristic
334C2×D11—22no—
335C2×D11—41no—
336C2×D11—41no—
337C4×C11—21no—
338C4×C11—21no—
339C4×C11—21no—
340C4×C11—21no—
341C4×C11—41no—
342C4×C11—41no—
343C4×C11—41no—
344C4×C11C2×#13111yescharacteristic
345C4×C11C2×#13111yescharacteristic
346C4×C11#57611yescharacteristic
347C4×C11#57811yescharacteristic
348Dic11—22no—
349Dic11—41no—
350Dic11—41no—
351C2×#41—111no—
352C2×Q16—111no—
353C2×SD16—111no—
354C2×SD16—111no—
355C2×D8—111no—
356C2×M16—21no—
357C2×M16—21no—
358C2×M16—221no—
359C22×C8—21no—
360C22×C8—221no—
361C22×C8—221no—
362C22×C8—221no—
363#126—21no—
364#125C4×D1111yescharacteristic
365#124C4×D1111yescharacteristic
366#123—21no—
367C22⋊Q8C4×D1111yescharacteristic
368#121C4×D1111yescharacteristic
369C4×Q8—111no—
370C4×Q8—111no—
371C4×Q8C22×D1111yescharacteristic
372C4×D4—21no—
373C4×D4—111no—
374C4×D4—111no—
375C4×D4—221no—
376C4×D4—221no—
377C4×D4C22×D1111yescharacteristic
378#117—21no—
379#117—111no—
380#117—221no—
381C2×C42—221no—
382C2×C42C22×D1111yescharacteristic
383#107—111no—
384#107—111no—
385#106—111no—
386#106—111no—
387C4⋊C8—21no—
388C4⋊C8—21no—
389C4⋊C8—21no—
390C4⋊C8—111no—
391C4⋊C8—111no—
392C4⋊C8—111no—
393C4⋊C8—111no—
394C4⋊C8—221no—
395C4⋊C8—221no—
396C4⋊C8—221no—
397C4⋊C8C22⋊D1111yescharacteristic
398C4⋊C8C22⋊D1111yescharacteristic
399C4⋊C8C22×D1111yescharacteristic
400C4⋊C8C22×D1111yescharacteristic
401#103—111no—
402#103—111no—
403#103—111no—
404#103—111no—
405#102—111no—
406#102—111no—
407#102—111no—
408#102—111no—
409C22⋊C8—21no—
410C22⋊C8—21no—
411C22⋊C8—111no—
412C22⋊C8—111no—
413C22⋊C8—221no—
414C22⋊C8—221no—
415C22⋊C8C22⋊D1111yescharacteristic
416C22⋊C8C22⋊D1111yescharacteristic
417#97—21no—
418#97—221no—
419C4×C8—21no—
420C4×C8—111no—
421C4×C8—111no—
422C4×C8—111no—
423C4×C8—111no—
424C4×C8—221no—
425C4×C8—221no—
426C4×C8C22×D1111yescharacteristic
427C4×C8C22×D1111yescharacteristic
428C2×C11—41no—
429C2×C11—81no—
430C2×C11#292911yescharacteristic
431C2×C11#295111yescharacteristic
432C2×C11#295611yescharacteristic
433D11—42no—
434#41—222no—
435#41—222no—
436C2×Q8—111no—
437C2×Q8C2×C4×D1111yescharacteristic
438C2×D4—21no—
439C2×D4—111no—
440C2×D4—221no—
441C2×D4C2×C4×D1111yescharacteristic
442C22×C4—21no—
443C22×C4—221no—
444C22×C4—221no—
445C22×C4—221no—
446C22×C4C2×C4×D1111yescharacteristic
447C22×C4#433911yescharacteristic
448C22×C4C2×C22⋊D1111yescharacteristic
449Q16—222no—
450SD16—222no—
451SD16—222no—
452D8—222no—
453M16—81no—
454M16—81no—
455M16—442no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—81no—
459C2×C8—111no—
460C2×C8—111no—
461C2×C8—111no—
462C2×C8—111no—
463C2×C8—221no—
464C2×C8—221no—
465C2×C8—221no—
466C2×C8—221no—
467C2×C8—881no—
468C2×C8—881no—
469C2×C8—881no—
470C2×C8C2×C22⋊D1111yescharacteristic
471C2×C8C2×C22⋊D1111yescharacteristic
472C2×C8C2×C22⋊D1111yescharacteristic
473C2×C8C2×C22⋊D1111yescharacteristic
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—111no—
479C4⋊C4—111no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4C2×C4×D1111yescharacteristic
483C4⋊C4C2×C4×D1111yescharacteristic
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—221no—
490C22⋊C4—221no—
491C22⋊C4—221no—
492C42—21no—
493C42—221no—
494C42—221no—
495C42—221no—
496C42C2×C4×D1111yescharacteristic
497C42#433911yescharacteristic
498C42C2×C22⋊D1111yescharacteristic
499C42C23×D1111yescharacteristic
500C11#1792611yescharacteristic, complemented, Sylow
501C23—21no—
502C23—221no—
503C23C4×C22⋊D1111yescharacteristic
504Q8—21no—
505Q8—21no—
506Q8—112no—
507Q8—221no—
508D4—21no—
509D4—21no—
510D4—81no—
511D4—112no—
512D4—224no—
513D4—221no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—224no—
525C2×C4—221no—
526C2×C4—221no—
527C2×C4—221no—
528C2×C4—441no—
529C2×C4—441no—
530C2×C4—881no—
531C2×C4C4×C22⋊D1111yescharacteristic
532C2×C4C4×C22⋊D1111yescharacteristic
533C2×C4C4×C22⋊D1111yescharacteristic
534C2×C4C22×C4×D1111yescharacteristic
535C2×C4C2×#433911yescharacteristic
536C2×C4C22×C22⋊D1111yescharacteristic
537C8—21no—
538C8—21no—
539C8—21no—
540C8—21no—
541C8—41no—
542C8—41no—
543C8—222no—
544C8—221no—
545C8—221no—
546C8—221no—
547C8—221no—
548C8—441no—
549C8—441no—
550C8—441no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—222no—
558C22—441no—
559C22—441no—
560C22C2×C4×C22⋊D1111yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—222no—
569C4—441no—
570C4—441no—
571C4D11×#13111yescharacteristic
572C4D11×#13111yescharacteristic
573C4#1062336611yescharacteristic
574C4#1062336911yescharacteristic
575C2—41no—
576C2—81no—
577C2—442no—
578C2#1307730811yescharacteristic
579C2#1307748911yescharacteristic
580C2#1307752311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2993C2
socleC22×C11C2×C4×D4
prime radical#10622650C4
cosocleC42×C11C24
hypercenter#2993D11
hypocenterC11#17926
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2993

Complements

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

NH ≅ G/Ntype
2. #13077724C2semidirect
3. #13067492C2semidirect
4. #13067471C2semidirect
5. #13067464C2semidirect
6. #13067443C2semidirect
7. #13067428C2semidirect
8. #13067426C2semidirect
9. C8×#4326C2semidirect
10. C8×#4323C2semidirect
11. #13067392C2semidirect
12. #13067053C2semidirect
13. #13067029C2semidirect
14. #13066911C2semidirect
15. C11×#2993C2semidirect
212. #2993D11semidirect
500. C11#17926semidirect

Maximal subgroups

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

subgroupindex
#130786282
#130777242
#130674922
#130674712
#130674642
#130674432
#130674282
#130674262
C8×#43262
C8×#43232
#130673922
#130670532
#130670292
#130669112
C11×#29932
#1792611