Finite Group Databasebeta

← #14725137

Subgroups — #14725137

Order 2816.

606 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
1#13078647C211yesmaximal, characteristic
2#13077682C211yesmaximal, characteristic
3#13067516C211yesmaximal, characteristic, complemented
4#13067506C211yesmaximal, characteristic, complemented
5#13067494C211yesmaximal, characteristic, complemented
6#13067471C211yesmaximal, characteristic, complemented
7#13067459C211yesmaximal, characteristic, complemented
8#13067450C211yesmaximal, characteristic, complemented
9#13067426C211yesmaximal, characteristic, complemented
10C8×#4325C211yesmaximal, characteristic, complemented
11#13067397C211yesmaximal, characteristic, complemented
12#13067084C211yesmaximal, characteristic
13#13067011C211yesmaximal, characteristic, complemented
14#13066916C211yesmaximal, characteristic, complemented
15C11×#2984C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C11C2211yescharacteristic
17#10623008C2211yescharacteristic
18C11×#446—21no—
19C11×#446—21no—
20C11×#446C2211yescharacteristic
21C11×#446C2211yescharacteristic
22C8×Q8×C11C2211yescharacteristic
23C8×Q8×C11C2211yescharacteristic
24C11×#432—21no—
25C11×#432C2211yescharacteristic
26C11×#431—21no—
27C11×#431C2211yescharacteristic
28#10622840C411yescharacteristic
29#10622840C411yescharacteristic
30#10622640C411yescharacteristic
31#10622640C411yescharacteristic
32C4×#4325C2211yescharacteristic
33C4×#4325C2211yescharacteristic
34C4×#4325C2211yescharacteristic
35C4×#4325C2211yescharacteristic
36#10622633C411yescharacteristic
37#10622633C411yescharacteristic
38#10622581C411yescharacteristic
39#10622581C411yescharacteristic
40#10622538C2211yescharacteristic
41#10622538C2211yescharacteristic
42#10622538C2211yescharacteristic
43#10622451—21no—
44#10622447—21no—
45#10622340—21no—
46#10622340—21no—
47#10622301C2211yescharacteristic
48#10622301C2211yescharacteristic
49C8×D44C2211yescharacteristic
50C8×D44C2211yescharacteristic
51Q8⋊(C11⋊C8)C2211yescharacteristic
52Q8⋊(C11⋊C8)C2211yescharacteristic
53Q8⋊(C11⋊C8)C2211yescharacteristic
54Q8⋊(C11⋊C8)C2211yescharacteristic
55#10622121C2211yescharacteristic
56#10622121C2211yescharacteristic
57#10622121C2211yescharacteristic
58#10622121C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622118C2211yescharacteristic
61#10622117C2211yescharacteristic
62#10622117C2211yescharacteristic
63#10622093C2211yescharacteristic
64#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C22×Q8×C11C2×C411yescharacteristic
68C2×#4339—21no—
69C4×Q8×C11—21no—
70C4×Q8×C11—21no—
71C4×Q8×C11C2×C411yescharacteristic
72C4×Q8×C11C2×C411yescharacteristic
73C4×Q8×C11C2311yescharacteristic
74C4×Q8×C11C2311yescharacteristic
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4C2×C411yescharacteristic
77C2×C42×C11—21no—
78C2×C42×C11C2311yescharacteristic
79C2×#4325C2×C411yescharacteristic
80C2×#4325C2×C411yescharacteristic
81C2×#4325C2×C411yescharacteristic
82C2×#4325C2×C411yescharacteristic
83#66983—21no—
84#66983C2×C411yescharacteristic
85#66983C2×C411yescharacteristic
86C2×#4313—21no—
87C2×#4313—21no—
88C2×C8×D11—21no—
89C2×C8×D11—21no—
90#66928—21no—
91#66927C2×C411yescharacteristic
92C4×D44—21no—
93C4×D44C2311yescharacteristic
94C4×D44C2311yescharacteristic
95#66922C2×C411yescharacteristic
96C11×C4⋊C8—21no—
97C11×C4⋊C8—21no—
98C11×C4⋊C8—21no—
99C11×C4⋊C8—21no—
100C11×C4⋊C8D411yescharacteristic
101C11×C4⋊C8D411yescharacteristic
102C11×C4⋊C8C2311yescharacteristic
103C11×C4⋊C8C2311yescharacteristic
104C11×C22⋊C8—21no—
105C11×C22⋊C8D411yescharacteristic
106C11×C22⋊C8D411yescharacteristic
107C11×#97—21no—
108C11×#97—21no—
109C11×#97—21no—
110C4×C8×C11—21no—
111C4×C8×C11—21no—
112C4×C8×C11C2311yescharacteristic
113C4×C8×C11C2311yescharacteristic
114#66899C2×C411yescharacteristic
115#66899C2×C411yescharacteristic
116#66899C2×C411yescharacteristic
117#66899C2×C411yescharacteristic
118C22⋊(C11⋊C8)—21no—
119C22⋊(C11⋊C8)—21no—
120C22⋊(C11⋊C8)C2×C411yescharacteristic
121C22⋊(C11⋊C8)C2×C411yescharacteristic
122(C2×D11)⋊C8—21no—
123(C2×D11)⋊C8—21no—
124(C2×D11)⋊C8—21no—
125(C2×D11)⋊C8—21no—
126#66873C2×C411yescharacteristic
127#66873C2×C411yescharacteristic
128#66873C2×C411yescharacteristic
129#66873C2×C411yescharacteristic
130#66872C2×C411yescharacteristic
131#66872C2×C411yescharacteristic
132#66872C2×C411yescharacteristic
133#66872C2×C411yescharacteristic
134C4⋊(C11⋊C8)—21no—
135C4⋊(C11⋊C8)C2×C411yescharacteristic
136C4⋊(C11⋊C8)C2×C411yescharacteristic
137C4⋊(C11⋊C8)C2311yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4×C11⋊C8—21no—
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#18030—111nomaximal, Sylow
145C2×Q8×C11—21no—
146C2×Q8×C11—22no—
147C2×Q8×C11—41no—
148C2×Q8×C11C22×C411yescharacteristic
149C2×Q8×C11C22×C411yescharacteristic
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11C22×C411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11#4111yescharacteristic
155C2×C22⋊D11—21no—
156C2×C22⋊D11—21no—
157#4339—81no—
158#4339—81no—
159C2×D44—21no—
160C2×D44—21no—
161C2×D44C22×C411yescharacteristic
162C2×D44C22×C411yescharacteristic
163C2×C4×D11—21no—
164C2×C4×D11—21no—
165C2×Dic22—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11C2×D411yescharacteristic
169C2×C8×C11C2×D411yescharacteristic
170C2×C8×C11C2×D411yescharacteristic
171C2×C8×C11C2×D411yescharacteristic
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4C22×C411yescharacteristic
178C11×C4⋊C4C22×C411yescharacteristic
179C42×C11—21no—
180C42×C11—21no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11C22×C411yescharacteristic
184C42×C11C2×D411yescharacteristic
185C42×C11#4111yescharacteristic
186C42×C11C2411yescharacteristic
187#4325—22no—
188#4325—22no—
189#4325—41no—
190#4325—41no—
191(C2×D11)⋊C4—21no—
192(C2×D11)⋊C4—21no—
193(C2×D11)⋊C4—21no—
194(C2×D11)⋊C4—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11C22×C411yescharacteristic
197C4⋊Dic11C22×C411yescharacteristic
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8C22×C411yescharacteristic
203C2×C11⋊C8C22×C411yescharacteristic
204C2×C11⋊C8C22×C411yescharacteristic
205C2×C11⋊C8C22×C411yescharacteristic
206#4313—81no—
207#4313—81no—
208C8×D11—81no—
209C8×D11—81no—
210#3103—111no—
211#2984D1111yescharacteristic, complemented
212#2979—111no—
213#1592—111no—
214#1590—111no—
215#1588—111no—
216#1585—111no—
217#1583—111no—
218#1582—111no—
219SD16⋊C8—111no—
220C8×SD16—111no—
221#1572—111no—
222#1496—111no—
223#1479—111no—
224#1454—111no—
225C23×C11C4×D411yescharacteristic
226C22×D11—21no—
227C22×D11—21no—
228Q8×C11—21no—
229Q8×C11—21no—
230Q8×C11—21no—
231Q8×C11—42no—
232Q8×C11#13112yes—
233C2×C4×C11—21no—
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—42no—
243C2×C4×C11—42no—
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—81no—
251C22⋊D11—81no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254D44—21no—
255D44—21no—
256D44—21no—
257D44—21no—
258D44—42no—
259D44—81no—
260C4×D11—41no—
261C4×D11—41no—
262C4×D11—41no—
263C4×D11—41no—
264Dic22—81no—
265C8×C11—21no—
266C8×C11—21no—
267C8×C11—21no—
268C8×C11—21no—
269C8×C11—41no—
270C8×C11—41no—
271C11⋊C8—21no—
272C11⋊C8—21no—
273C11⋊C8—21no—
274C11⋊C8—21no—
275C11⋊C8—41no—
276C11⋊C8—41no—
277C11⋊C8—41no—
278C11⋊C8—41no—
279#532—111no—
280C2×C4×Q8C2×D1111yescharacteristic
281#481—111no—
282#481—111no—
283#475—111no—
284#475—111no—
285#460—111no—
286#460—111no—
287#448—111no—
288#448—111no—
289#446—21no—
290#446—21no—
291#446C2×D1111yescharacteristic
292#446C2×D1111yescharacteristic
293C8×Q8C2×D1111yescharacteristic
294C8×Q8C2×D1111yescharacteristic
295C4×SD16—111no—
296C4×SD16—111no—
297C4×SD16—111no—
298C4×SD16—111no—
299#436—111no—
300#436—111no—
301#436—221no—
302C8×D4—111no—
303C8×D4—111no—
304C8×D4—221no—
305#432—21no—
306#432C2×D1111yescharacteristic
307#431—21no—
308#431—111no—
309#431—111no—
310#431—111no—
311#431C2×D1111yescharacteristic
312#408—221no—
313#408—221no—
314#335—111no—
315#335—111no—
316#334—111no—
317#334—111no—
318Q8⋊C8—111no—
319Q8⋊C8—111no—
320Q8⋊C8—111no—
321Q8⋊C8—111no—
322D4⋊C8—111no—
323D4⋊C8—111no—
324D4⋊C8—111no—
325D4⋊C8—111no—
326#322—111no—
327#322—111no—
328#322—111no—
329C82—111no—
330C22×C11—21no—
331C22×C11—21no—
332C22×C11—21no—
333C22×C11C2×C4×D411yescharacteristic
334C2×D11—41no—
335C2×D11—41no—
336C2×D11—41no—
337C2×D11—41no—
338C2×D11—41no—
339C2×D11—41no—
340C4×C11—21no—
341C4×C11—22no—
342C4×C11—21no—
343C4×C11—21no—
344C4×C11—21no—
345C4×C11—41no—
346C4×C11—41no—
347C4×C11—41no—
348C4×C11C2×#13111yescharacteristic
349C4×C11#56811yescharacteristic
350C4×C11#57711yescharacteristic
351C4×C11#57711yescharacteristic
352Dic11—41no—
353Dic11—41no—
354C2×#41—221no—
355C22×Q8C4×D1111yescharacteristic
356C2×SD16—111no—
357C2×SD16—111no—
358C2×SD16—111no—
359C2×SD16—111no—
360C2×M16—221no—
361C2×M16—221no—
362C22×C8—221no—
363C22×C8—221no—
364C4⋊Q8—111no—
365#127—111no—
366#124—221no—
367#121—111no—
368#121—111no—
369#121—221no—
370C4×Q8—21no—
371C4×Q8—21no—
372C4×Q8C4×D1111yescharacteristic
373C4×Q8C4×D1111yescharacteristic
374C4×Q8C22×D1111yescharacteristic
375C4×Q8C22×D1111yescharacteristic
376C4×D4—111no—
377C4×D4—111no—
378C4×D4—221no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4C4×D1111yescharacteristic
381C2×C42—21no—
382C2×C42C22×D1111yescharacteristic
383#106—111no—
384#106—111no—
385#106—111no—
386#106—111no—
387C4⋊C8—21no—
388C4⋊C8—21no—
389C4⋊C8—21no—
390C4⋊C8—21no—
391C4⋊C8—111no—
392C4⋊C8—111no—
393C4⋊C8—111no—
394C4⋊C8—111no—
395C4⋊C8—221no—
396C4⋊C8C22⋊D1111yescharacteristic
397C4⋊C8C22⋊D1111yescharacteristic
398C4⋊C8C22×D1111yescharacteristic
399C4⋊C8C22×D1111yescharacteristic
400#103—111no—
401#103—111no—
402#103—111no—
403#103—111no—
404#102—111no—
405#102—111no—
406#102—111no—
407#102—111no—
408C22⋊C8—21no—
409C22⋊C8—111no—
410C22⋊C8—111no—
411C22⋊C8—221no—
412C22⋊C8—221no—
413C22⋊C8—221no—
414C22⋊C8—221no—
415C22⋊C8—221no—
416C22⋊C8—221no—
417C22⋊C8C22⋊D1111yescharacteristic
418C22⋊C8C22⋊D1111yescharacteristic
419#97—21no—
420#97—21no—
421#97—21no—
422C4×C8—21no—
423C4×C8—21no—
424C4×C8—111no—
425C4×C8—111no—
426C4×C8—111no—
427C4×C8—111no—
428C4×C8—221no—
429C4×C8C22×D1111yescharacteristic
430C4×C8C22×D1111yescharacteristic
431C2×C11—41no—
432C2×C11#293311yescharacteristic
433C2×C11#294911yescharacteristic
434C2×C11#295511yescharacteristic
435D11—81no—
436D11—81no—
437#41—881no—
438#41—881no—
439C2×Q8—21no—
440C2×Q8—22no—
441C2×Q8—41no—
442C2×Q8—221no—
443C2×Q8C2×C4×D1111yescharacteristic
444C2×Q8C2×C4×D1111yescharacteristic
445C2×D4—111no—
446C2×D4—111no—
447C2×D4—221no—
448C2×D4—221no—
449C2×D4—221no—
450C2×D4—221no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—221no—
454C22×C4—221no—
455C22×C4C2×C4×D1111yescharacteristic
456C22×C4#433911yescharacteristic
457C22×C4C2×C22⋊D1111yescharacteristic
458SD16—222no—
459SD16—222no—
460SD16—441no—
461SD16—441no—
462M16—881no—
463M16—881no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—111no—
467C2×C8—111no—
468C2×C8—111no—
469C2×C8—111no—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8—221no—
474C2×C8—881no—
475C2×C8—881no—
476C2×C8C2×C22⋊D1111yescharacteristic
477C2×C8C2×C22⋊D1111yescharacteristic
478C2×C8C2×C22⋊D1111yescharacteristic
479C2×C8C2×C22⋊D1111yescharacteristic
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—111no—
486C4⋊C4—111no—
487C4⋊C4—221no—
488C4⋊C4C2×C4×D1111yescharacteristic
489C4⋊C4C2×C4×D1111yescharacteristic
490C22⋊C4—221no—
491C22⋊C4—221no—
492C22⋊C4—221no—
493C22⋊C4—221no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—21no—
498C42C2×C4×D1111yescharacteristic
499C42#433911yescharacteristic
500C42C2×C22⋊D1111yescharacteristic
501C42C23×D1111yescharacteristic
502C11#1803011yescharacteristic, complemented, Sylow
503C23—221no—
504C23—221no—
505C23C4×C22⋊D1111yescharacteristic
506Q8—21no—
507Q8—21no—
508Q8—21no—
509Q8—42no—
510Q8—881no—
511Q8#6696012yes—
512D4—221no—
513D4—221no—
514D4—221no—
515D4—221no—
516D4—442no—
517D4—881no—
518D4—881no—
519D4—881no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—41no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—221no—
532C2×C4—221no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4C4×C22⋊D1111yescharacteristic
538C2×C4C4×C22⋊D1111yescharacteristic
539C2×C4C4×C22⋊D1111yescharacteristic
540C2×C4C22×C4×D1111yescharacteristic
541C2×C4C2×#433911yescharacteristic
542C2×C4C22×C22⋊D1111yescharacteristic
543C8—21no—
544C8—21no—
545C8—21no—
546C8—21no—
547C8—41no—
548C8—41no—
549C8—221no—
550C8—221no—
551C8—221no—
552C8—221no—
553C8—441no—
554C8—441no—
555C8—441no—
556C8—441no—
557C22—21no—
558C22—21no—
559C22—21no—
560C22—441no—
561C22—441no—
562C22—441no—
563C22—441no—
564C22—441no—
565C22—441no—
566C22C2×C4×C22⋊D1111yescharacteristic
567C4—21no—
568C4—21no—
569C4—21no—
570C4—22no—
571C4—21no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—441no—
576C4—441no—
577C4C2×#6696011yescharacteristic
578C4#1062327611yescharacteristic
579C4#1062336811yescharacteristic
580C4#1062336811yescharacteristic
581C2—41no—
582C2—881no—
583C2—881no—
584C2#1307734111yescharacteristic
585C2#1307747511yescharacteristic
586C2#1307751711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2984C2
socleC22×C11C2×C4×D4
prime radical#10623008C22
cosocleC42×C11C24
hypercenter#2984D11
hypocenterC11#18030
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2984

Complements

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

NH ≅ G/Ntype
3. #13067516C2semidirect
4. #13067506C2semidirect
5. #13067494C2semidirect
6. #13067471C2semidirect
7. #13067459C2semidirect
8. #13067450C2semidirect
9. #13067426C2semidirect
10. C8×#4325C2semidirect
11. #13067397C2semidirect
13. #13067011C2semidirect
14. #13066916C2semidirect
15. C11×#2984C2semidirect
211. #2984D11semidirect
502. C11#18030semidirect

Maximal subgroups

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

subgroupindex
#130786472
#130776822
#130675162
#130675062
#130674942
#130674712
#130674592
#130674502
#130674262
C8×#43252
#130673972
#130670842
#130670112
#130669162
C11×#29842
#1803011