Finite Group Databasebeta

← #14725410

Subgroups — #14725410

Order 2816.

624 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077745C211yesmaximal, characteristic
2C4×#66995C211yesmaximal, characteristic
3#13067516C211yesmaximal, characteristic, complemented
4#13067506C211yesmaximal, characteristic, complemented
5#13067494C211yesmaximal, characteristic, complemented
6#13067485C211yesmaximal, characteristic, complemented
7#13067464C211yesmaximal, characteristic, complemented
8#13067459C211yesmaximal, characteristic, complemented
9#13067433C211yesmaximal, characteristic, complemented
10C8×#4326C211yesmaximal, characteristic, complemented
11#13067384C211yesmaximal, characteristic, complemented
12#13067048C211yesmaximal, characteristic
13#13067045C211yesmaximal, characteristic, complemented
14#13066911C211yesmaximal, characteristic, complemented
15C11×#2984C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C11C2211yescharacteristic
17C2×#66995C411yescharacteristic
18C4×#4339C2211yescharacteristic
19C11×#446—21no—
20C11×#446—21no—
21C11×#446C2211yescharacteristic
22C11×#446C2211yescharacteristic
23C8×Q8×C11C2211yescharacteristic
24C8×Q8×C11C2211yescharacteristic
25C11×#432—21no—
26C11×#432C2211yescharacteristic
27C11×#431—21no—
28C11×#431C2211yescharacteristic
29#10622838C411yescharacteristic
30#10622643C411yescharacteristic
31#10622643C411yescharacteristic
32C4×#4326C2211yescharacteristic
33C4×#4326C2211yescharacteristic
34#10622639C411yescharacteristic
35#10622639C411yescharacteristic
36C4×#4325C2211yescharacteristic
37C4×#4325C2211yescharacteristic
38#10622579C411yescharacteristic
39#10622577C411yescharacteristic
40#10622538C2211yescharacteristic
41#10622537C2211yescharacteristic
42C4×#4318C2211yescharacteristic
43#10622450—21no—
44#10622446—21no—
45#10622342—21no—
46#10622342—21no—
47#10622301C2211yescharacteristic
48#10622301C2211yescharacteristic
49C8×Dic22C2211yescharacteristic
50C8×Dic22C2211yescharacteristic
51Q8⋊(C11⋊C8)C2211yescharacteristic
52Q8⋊(C11⋊C8)C2211yescharacteristic
53Q8⋊(C11⋊C8)C2211yescharacteristic
54Q8⋊(C11⋊C8)C2211yescharacteristic
55#10622122C2211yescharacteristic
56#10622122C2211yescharacteristic
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×#4339C2×C411yescharacteristic
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×#4326C2×C411yescharacteristic
80C2×#4326C2×C411yescharacteristic
81#66995—24no—
82C2×#4325C2×C411yescharacteristic
83C2×#4325C2×C411yescharacteristic
84C4×C22⋊D11—21no—
85C4×C22⋊D11—21no—
86#66979C2×C411yescharacteristic
87C2×#4318—21no—
88C2×#4318C2×C411yescharacteristic
89C2×#4318C2×C411yescharacteristic
90C2×#4313—21no—
91C2×#4313—21no—
92C4×D44C2×C411yescharacteristic
93C4×D44C2311yescharacteristic
94#66925—21no—
95C42×D11—21no—
96C4×Dic22C2×C411yescharacteristic
97C4×Dic22C2311yescharacteristic
98C11×C4⋊C8—21no—
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⋊C8D411yescharacteristic
108C11×C22⋊C8D411yescharacteristic
109C11×#97—21no—
110C11×#97—21no—
111C11×#97—21no—
112C4×C8×C11—21no—
113C4×C8×C11—21no—
114C4×C8×C11C2311yescharacteristic
115C4×C8×C11C2311yescharacteristic
116#66899C2×C411yescharacteristic
117#66899C2×C411yescharacteristic
118#66899C2×C411yescharacteristic
119#66899C2×C411yescharacteristic
120C22⋊(C11⋊C8)—21no—
121(C2×D11)⋊C8—21no—
122(C2×D11)⋊C8—21no—
123Dic11⋊C8—21no—
124Dic11⋊C8—21no—
125C8×Dic11—21no—
126C8×Dic11—21no—
127#66874C2×C411yescharacteristic
128#66874C2×C411yescharacteristic
129#66873C2×C411yescharacteristic
130#66873C2×C411yescharacteristic
131#66872C2×C411yescharacteristic
132#66872C2×C411yescharacteristic
133#66871C2×C411yescharacteristic
134#66871C2×C411yescharacteristic
135C4⋊(C11⋊C8)—21no—
136C4⋊(C11⋊C8)—21no—
137C4⋊(C11⋊C8)C2311yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139#66867C2×C411yescharacteristic
140#66867C2×C411yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#18053—111nomaximal, Sylow
146C2×Q8×C11—21no—
147C2×Q8×C11—22no—
148C2×Q8×C11—41no—
149C2×Q8×C11C22×C411yescharacteristic
150C2×Q8×C11C22×C411yescharacteristic
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11C22×C411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11#4111yescharacteristic
156C2×C22⋊D11—21no—
157#4339—22no—
158#4339—41no—
159C2×D44C22×C411yescharacteristic
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×Dic22C22×C411yescharacteristic
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11C2×D411yescharacteristic
167C2×C8×C11C2×D411yescharacteristic
168C2×C8×C11C2×D411yescharacteristic
169C2×C8×C11C2×D411yescharacteristic
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4C22×C411yescharacteristic
176C11×C4⋊C4C22×C411yescharacteristic
177C42×C11—21no—
178C42×C11—21no—
179C42×C11—21no—
180C42×C11—21no—
181C42×C11C22×C411yescharacteristic
182C42×C11C2×D411yescharacteristic
183C42×C11#4111yescharacteristic
184C42×C11C2411yescharacteristic
185C22⋊Dic11—21no—
186#4326—22no—
187#4326M1614yescomplemented
188#4325—22no—
189#4325—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—22no—
200#4318—41no—
201#4318—81no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8C22×C411yescharacteristic
207C2×C11⋊C8C22×C411yescharacteristic
208C2×C11⋊C8C22×C411yescharacteristic
209C2×C11⋊C8C22×C411yescharacteristic
210#4313—81no—
211#4313—81no—
212#2991—111no—
213#2984D1111yescharacteristic, complemented
214C4×#137—111no—
215#1592—111no—
216#1590—111no—
217#1588—111no—
218#1587—111no—
219#1584—111no—
220#1583—111no—
221#1579—111no—
222C8×Q16—111no—
223#1569—111no—
224#1488—111no—
225#1487—111no—
226#1453—111no—
227C23×C11C4×D411yescharacteristic
228C22×D11—21no—
229Q8×C11—21no—
230Q8×C11—21no—
231Q8×C11—21no—
232Q8×C11—42no—
233Q8×C11C2×M1612yes—
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—21no—
242C2×C4×C11—41no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11C4×D411yescharacteristic
246C2×C4×C11C4×D411yescharacteristic
247C2×C4×C11C4×D411yescharacteristic
248C2×C4×C11C23×C411yescharacteristic
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C22⋊D11—42no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255D44—21no—
256D44—21no—
257C4×D11—42no—
258C4×D11—42no—
259C4×D11—41no—
260C4×D11—41no—
261Dic22—21no—
262Dic22C2×M1612yes—
263C8×C11—21no—
264C8×C11—21no—
265C8×C11—21no—
266C8×C11—21no—
267C8×C11—41no—
268C8×C11—41no—
269C11⋊C8—21no—
270C11⋊C8—21no—
271C11⋊C8—21no—
272C11⋊C8—41no—
273C11⋊C8—41no—
274C11⋊C8—41no—
275C11⋊C8—41no—
276C11⋊C8C2×M1612yes—
277C2×#137—111no—
278C4×#41—111no—
279C2×C4×Q8C2×D1111yescharacteristic
280#446—21no—
281#446—21no—
282#446C2×D1111yescharacteristic
283#446C2×D1111yescharacteristic
284C8×Q8—111no—
285C8×Q8—111no—
286C8×Q8C2×D1111yescharacteristic
287C8×Q8C2×D1111yescharacteristic
288#441—111no—
289#441—111no—
290#440—111no—
291#440—111no—
292C4×Q16—111no—
293C4×Q16—111no—
294C4×SD16—111no—
295C4×SD16—111no—
296#436—111no—
297#436—111no—
298#436—221no—
299#436—221no—
300#432—21no—
301#432C2×D1111yescharacteristic
302#431—21no—
303#431—111no—
304#431—221no—
305#431C2×D1111yescharacteristic
306#428—111no—
307#423—111no—
308#423—221no—
309#419—111no—
310#417—111no—
311C4×M16—111no—
312#335—111no—
313#335—111no—
314#334—111no—
315#334—111no—
316Q8⋊C8—111no—
317Q8⋊C8—111no—
318Q8⋊C8—111no—
319Q8⋊C8—111no—
320Q8⋊C8—111no—
321Q8⋊C8—111no—
322D4⋊C8—111no—
323D4⋊C8—111no—
324#322—111no—
325#322—111no—
326#322—111no—
327C82—111no—
328C22×C11—21no—
329C22×C11—21no—
330C22×C11—21no—
331C22×C11C2×C4×D411yescharacteristic
332C2×D11—41no—
333C2×D11—41no—
334C2×D11—41no—
335C4×C11—21no—
336C4×C11—22no—
337C4×C11—21no—
338C4×C11—21no—
339C4×C11—21no—
340C4×C11—41no—
341C4×C11—41no—
342C4×C11—41no—
343C4×C11C22×M1611yescharacteristic
344C4×C11#56811yescharacteristic
345C4×C11#57711yescharacteristic
346C4×C11#57811yescharacteristic
347Dic11—22no—
348Dic11—41no—
349Dic11—41no—
350C2×#41—111no—
351C22×Q8C4×D1111yescharacteristic
352#137—224no—
353C2×Q16—111no—
354C2×Q16—111no—
355C2×SD16—111no—
356C2×SD16—111no—
357C2×M16—111no—
358C2×M16—111no—
359C2×M16—221no—
360C2×M16—221no—
361C2×M16—221no—
362C4×Q8—21no—
363C4×Q8—21no—
364C4×Q8—111no—
365C4×Q8—111no—
366C4×Q8C4×D1111yescharacteristic
367C4×Q8C4×D1111yescharacteristic
368C4×Q8C22×D1111yescharacteristic
369C4×Q8C22×D1111yescharacteristic
370C4×D4—111no—
371C4×D4—111no—
372C4×D4—221no—
373C4×D4—221no—
374#117—111no—
375#117—221no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4C4×D1111yescharacteristic
378C2×C42—21no—
379C2×C42—221no—
380C2×C42C22×D1111yescharacteristic
381#107—111no—
382#107—111no—
383#106—111no—
384#106—111no—
385C4⋊C8—21no—
386C4⋊C8—21no—
387C4⋊C8—21no—
388C4⋊C8—21no—
389C4⋊C8—111no—
390C4⋊C8—111no—
391C4⋊C8—221no—
392C4⋊C8—221no—
393C4⋊C8—221no—
394C4⋊C8—221no—
395C4⋊C8C22⋊D1111yescharacteristic
396C4⋊C8C22⋊D1111yescharacteristic
397C4⋊C8C22×D1111yescharacteristic
398C4⋊C8C22×D1111yescharacteristic
399#103—111no—
400#103—111no—
401#103—111no—
402#103—111no—
403#103—111no—
404#103—111no—
405#102—111no—
406#102—111no—
407C22⋊C8—21no—
408C22⋊C8—221no—
409C22⋊C8—221no—
410C22⋊C8—221no—
411C22⋊C8C22⋊D1111yescharacteristic
412C22⋊C8C22⋊D1111yescharacteristic
413#97—21no—
414#97—21no—
415#97—21no—
416#97—111no—
417#97—111no—
418C4×C8—21no—
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×C11D4×M1611yescharacteristic
430C2×C11#294711yescharacteristic
431C2×C11#295511yescharacteristic
432D11—81no—
433#41—222no—
434#41—441no—
435C2×Q8—21no—
436C2×Q8—22no—
437C2×Q8—41no—
438C2×Q8—111no—
439C2×Q8C2×C4×D1111yescharacteristic
440C2×Q8C2×C4×D1111yescharacteristic
441C2×D4—111no—
442C2×D4—221no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—221no—
446C22×C4—221no—
447C22×C4—221no—
448C22×C4C2×C4×D1111yescharacteristic
449C22×C4#433911yescharacteristic
450C22×C4C2×C22⋊D1111yescharacteristic
451Q16—114no—
452Q16—222no—
453SD16—222no—
454SD16—222no—
455M16—222no—
456M16—441no—
457M16—881no—
458M16—881no—
459M16—881no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—111no—
463C2×C8—111no—
464C2×C8—111no—
465C2×C8—111no—
466C2×C8—221no—
467C2×C8—221no—
468C2×C8—221no—
469C2×C8—221no—
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—21no—
479C4⋊C4—111no—
480C4⋊C4—111no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4C2×C4×D1111yescharacteristic
484C4⋊C4C2×C4×D1111yescharacteristic
485C22⋊C4—221no—
486C22⋊C4—221no—
487C22⋊C4—221no—
488C42—21no—
489C42—21no—
490C42—21no—
491C42—21no—
492C42—221no—
493C42—221no—
494C42—221no—
495C42C2×C4×D1111yescharacteristic
496C42#433911yescharacteristic
497C42C2×C22⋊D1111yescharacteristic
498C42C23×D1111yescharacteristic
499C11#1805311yescharacteristic, complemented, Sylow
500C23—221no—
501C23C4×C22⋊D1111yescharacteristic
502Q8—21no—
503Q8—21no—
504Q8—21no—
505Q8—42no—
506Q8—112no—
507Q8—221no—
508Q8M16×D1112yes—
509D4—221no—
510D4—221no—
511D4—442no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—41no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—221no—
524C2×C4—221no—
525C2×C4—221no—
526C2×C4—442no—
527C2×C4—442no—
528C2×C4—441no—
529C2×C4—441no—
530C2×C4C4×C22⋊D1111yescharacteristic
531C2×C4C4×C22⋊D1111yescharacteristic
532C2×C4C4×C22⋊D1111yescharacteristic
533C2×C4C22×C4×D1111yescharacteristic
534C2×C4C2×#433911yescharacteristic
535C2×C4C22×C22⋊D1111yescharacteristic
536C8—21no—
537C8—21no—
538C8—21no—
539C8—21no—
540C8—41no—
541C8—41no—
542C8—112no—
543C8—221no—
544C8—221no—
545C8—221no—
546C8—441no—
547C8—441no—
548C8—441no—
549C8—441no—
550C22—21no—
551C22—21no—
552C22—21no—
553C22—441no—
554C22—441no—
555C22—441no—
556C22C2×C4×C22⋊D1111yescharacteristic
557C4—21no—
558C4—21no—
559C4—21no—
560C4—22no—
561C4—21no—
562C4—41no—
563C4—41no—
564C4—41no—
565C4—222no—
566C4—441no—
567C4—441no—
568C4C2×M16×D1111yescharacteristic
569C4#1062327611yescharacteristic
570C4#1062336811yescharacteristic
571C4#1062336911yescharacteristic
572C2—41no—
573C2—881no—
574C2M16×C22⋊D1111yescharacteristic
575C2#1307745911yescharacteristic
576C2#1307751711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2984C2
socleC22×C11C2×C4×D4
prime radicalC2×#4339C2×C4
cosocleC42×C11C24
hypercenter#2984D11
hypocenterC11#18053
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. #13067485C2semidirect
7. #13067464C2semidirect
8. #13067459C2semidirect
9. #13067433C2semidirect
10. C8×#4326C2semidirect
11. #13067384C2semidirect
13. #13067045C2semidirect
14. #13066911C2semidirect
15. C11×#2984C2semidirect
187. #4326M16semidirect
213. #2984D11semidirect
499. C11#18053semidirect

Maximal subgroups

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

subgroupindex
#130777452
C4×#669952
#130675162
#130675062
#130674942
#130674852
#130674642
#130674592
#130674332
C8×#43262
#130673842
#130670482
#130670452
#130669112
C11×#29842
#1805311