Finite Group Databasebeta

← #14724920

Subgroups — #14724920

Order 2816.

592 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078681C211yesmaximal, characteristic
2#13077633C211yesmaximal, characteristic
3#13077565C211yesmaximal, characteristic, complemented
4#13067521C211yesmaximal, characteristic, complemented
5#13067503C211yesmaximal, characteristic, complemented
6#13067491C211yesmaximal, characteristic, complemented
7#13067490C211yesmaximal, characteristic, complemented
8#13067469C211yesmaximal, characteristic, complemented
9#13067456C211yesmaximal, characteristic, complemented
10#13067432C211yesmaximal, characteristic, complemented
11#13067420C211yesmaximal, characteristic, complemented
12#13067402C211yesmaximal, characteristic, complemented
13#13067004C211yesmaximal, characteristic
14#13066911C211yesmaximal, characteristic, complemented
15C11×#1497C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17C4×#4339C2211yescharacteristic
18C11×#432C2211yescharacteristic
19C11×#431C2211yescharacteristic
20#10622707C411yescharacteristic
21#10622703C411yescharacteristic
22#10622700C411yescharacteristic
23#10622696C411yescharacteristic
24#10622660C411yescharacteristic
25#10622660C411yescharacteristic
26#10622658C411yescharacteristic
27#10622658C411yescharacteristic
28C4×#4326C2211yescharacteristic
29C4×#4326C2211yescharacteristic
30C4×#4325C2211yescharacteristic
31C4×#4325C2211yescharacteristic
32#10622637—21no—
33#10622637—21no—
34#10622637C2211yescharacteristic
35#10622637C2211yescharacteristic
36Q8×C11⋊C8C2211yescharacteristic
37Q8×C11⋊C8C2211yescharacteristic
38#10622612—21no—
39#10622610—21no—
40#10622538C2211yescharacteristic
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42C4×#4318C2211yescharacteristic
43#10622451C2211yescharacteristic
44#10622451C2211yescharacteristic
45#10622443C2211yescharacteristic
46#10622443C2211yescharacteristic
47#10622342—21no—
48#10622342—21no—
49#10622320—21no—
50#10622318—21no—
51C11×Q8⋊C8C2211yescharacteristic
52C11×Q8⋊C8C2211yescharacteristic
53C11×Q8⋊C8C2211yescharacteristic
54C11×Q8⋊C8C2211yescharacteristic
55#10622118C2211yescharacteristic
56#10622118C2211yescharacteristic
57#10622117C2211yescharacteristic
58#10622117C2211yescharacteristic
59#10622097C2211yescharacteristic
60#10622097C2211yescharacteristic
61#10622094C2211yescharacteristic
62#10622094C2211yescharacteristic
63#10622093C2211yescharacteristic
64#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×#4339C2×C411yescharacteristic
68C11×C4⋊Q8C2×C411yescharacteristic
69C11×C4⋊Q8C2×C411yescharacteristic
70C11×#125—21no—
71C11×C22⋊Q8—21no—
72C11×C22⋊Q8C2×C411yescharacteristic
73C11×C22⋊Q8C2×C411yescharacteristic
74C4×Q8×C11—21no—
75C4×Q8×C11C2311yescharacteristic
76C4×Q8×C11C2311yescharacteristic
77C11×#117—21no—
78C2×C42×C11C2311yescharacteristic
79C2×#4326C2×C411yescharacteristic
80C2×#4326C2×C411yescharacteristic
81C2×#4325C2×C411yescharacteristic
82C2×#4325C2×C411yescharacteristic
83C4×C22⋊D11—21no—
84C4×C22⋊D11—21no—
85#66979C2×C411yescharacteristic
86C2×#4318D411yescharacteristic
87C2×#4318D411yescharacteristic
88C22×C11⋊C8—21no—
89C2×#4313—21no—
90C2×#4313—21no—
91C4×D44C2×C411yescharacteristic
92C4×D44C2311yescharacteristic
93#66925—21no—
94C42×D11—21no—
95C4×Dic22C2×C411yescharacteristic
96C4×Dic22C2311yescharacteristic
97C11×C4⋊C8—21no—
98C11×C4⋊C8C2311yescharacteristic
99C11×C4⋊C8C2311yescharacteristic
100C11×C22⋊C8—21no—
101C11×C22⋊C8—21no—
102C11×#97—21no—
103C4×C8×C11C2311yescharacteristic
104C4×C8×C11C2311yescharacteristic
105#66899C2×C411yescharacteristic
106#66899C2×C411yescharacteristic
107#66899C2×C411yescharacteristic
108#66899C2×C411yescharacteristic
109C22⋊(C11⋊C8)C2×C411yescharacteristic
110C22⋊(C11⋊C8)C2×C411yescharacteristic
111(C2×D11)⋊C8—21no—
112(C2×D11)⋊C8—21no—
113Dic11⋊C8—21no—
114Dic11⋊C8—21no—
115C8×Dic11—21no—
116C8×Dic11—21no—
117#66874C2×C411yescharacteristic
118#66874C2×C411yescharacteristic
119#66873C2×C411yescharacteristic
120#66873C2×C411yescharacteristic
121#66872C2×C411yescharacteristic
122#66872C2×C411yescharacteristic
123#66871C2×C411yescharacteristic
124#66871C2×C411yescharacteristic
125C4⋊(C11⋊C8)—21no—
126C4⋊(C11⋊C8)—21no—
127C4⋊(C11⋊C8)—21no—
128C4⋊(C11⋊C8)—21no—
129C4⋊(C11⋊C8)—21no—
130C4⋊(C11⋊C8)C2×C411yescharacteristic
131C4⋊(C11⋊C8)C2×C411yescharacteristic
132C4⋊(C11⋊C8)C2311yescharacteristic
133C4⋊(C11⋊C8)C2311yescharacteristic
134#66867—21no—
135#66867—21no—
136#66867D411yescharacteristic
137#66867D411yescharacteristic
138C4×C11⋊C8—21no—
139C4×C11⋊C8—21no—
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#18013—111nomaximal, Sylow
145C2×Q8×C11—21no—
146C2×Q8×C11C22×C411yescharacteristic
147C2×Q8×C11C22×C411yescharacteristic
148C22×C4×C11C22×C411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11#4111yescharacteristic
151C2×C22⋊D11—21no—
152#4339—22no—
153#4339—41no—
154C2×D44C22×C411yescharacteristic
155C2×C4×D11—21no—
156C2×C4×D11—21no—
157C2×C4×D11—21no—
158C2×Dic22C22×C411yescharacteristic
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4C22×C411yescharacteristic
171C11×C4⋊C4C22×C411yescharacteristic
172C11×C22⋊C4—21no—
173C11×C22⋊C4—21no—
174C42×C11—21no—
175C42×C11—21no—
176C42×C11C22×C411yescharacteristic
177C42×C11C2×D411yescharacteristic
178C42×C11#4111yescharacteristic
179C42×C11C2411yescharacteristic
180C22⋊Dic11—21no—
181#4326—22no—
182#4326—22no—
183#4325—41no—
184#4325—41no—
185(C2×D11)⋊C4—21no—
186(C2×D11)⋊C4—21no—
187C4⋊Dic11C22×C411yescharacteristic
188C4⋊Dic11C22×C411yescharacteristic
189Dic11⋊C4—21no—
190Dic11⋊C4—21no—
191C4×Dic11—21no—
192C4×Dic11—21no—
193C4×Dic11—21no—
194#4318—22no—
195#4318—41no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—42no—
199C2×C11⋊C8C22×C411yescharacteristic
200C2×C11⋊C8C22×C411yescharacteristic
201C2×C11⋊C8C22×C411yescharacteristic
202C2×C11⋊C8C22×C411yescharacteristic
203C2×C11⋊C8C2×D411yescharacteristic
204C2×C11⋊C8C2×D411yescharacteristic
205C2×C11⋊C8C2×D411yescharacteristic
206C2×C11⋊C8C2×D411yescharacteristic
207#4313—42no—
208#4313—42no—
209#3107—111no—
210#2971—111no—
211#2962—111no—
212#1592—111no—
213#1590—111no—
214#1588—111no—
215#1587—111no—
216#1584—111no—
217#1583—111no—
218#1579—111no—
219C8×Q16—111no—
220#1573—111no—
221#1497D1111yescharacteristic, complemented
222#1477—111no—
223#1453—111no—
224C23×C11C4×D411yescharacteristic
225C22×D11—21no—
226Q8×C11—21no—
227Q8×C11—21no—
228Q8×C11—21no—
229Q8×C11—21no—
230Q8×C11—81no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
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—41no—
240C2×C4×C11C4×D411yescharacteristic
241C2×C4×C11C4×D411yescharacteristic
242C2×C4×C11C4×D411yescharacteristic
243C2×C4×C11C23×C411yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C2×#4111yescharacteristic
246C22⋊D11—42no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250D44—21no—
251D44—21no—
252C4×D11—42no—
253C4×D11—41no—
254C4×D11—41no—
255C4×D11—81no—
256Dic22—21no—
257Dic22#13112yes—
258C8×C11—41no—
259C8×C11—41no—
260C8×C11—41no—
261C8×C11—41no—
262C11⋊C8—21no—
263C11⋊C8—21no—
264C11⋊C8—21no—
265C11⋊C8—21no—
266C11⋊C8—21no—
267C11⋊C8—21no—
268C11⋊C8—21no—
269C11⋊C8—41no—
270C11⋊C8—41no—
271C11⋊C8#13712yes—
272#533C2×D1111yescharacteristic
273C4×#41—111no—
274#485—111no—
275#485—111no—
276#475—111no—
277#474—111no—
278#462—111no—
279#461—111no—
280#452—111no—
281#452—111no—
282#446—111no—
283#446—111no—
284#446—221no—
285#446—221no—
286C8×Q8—111no—
287C8×Q8—111no—
288C8×Q8—111no—
289C8×Q8—111no—
290C4×Q16—111no—
291C4×Q16—111no—
292C4×SD16—111no—
293C4×SD16—111no—
294#436—111no—
295#436—111no—
296#436—221no—
297#436—221no—
298#432—221no—
299#432C2×D1111yescharacteristic
300#431—111no—
301#431C2×D1111yescharacteristic
302#424—221no—
303C2×C4⋊C8—111no—
304#405—221no—
305C4×M16—111no—
306C4×M16—221no—
307#335—111no—
308#335—111no—
309#334—111no—
310#334—111no—
311Q8⋊C8—111no—
312Q8⋊C8—111no—
313Q8⋊C8C2×D1111yescharacteristic
314Q8⋊C8C2×D1111yescharacteristic
315Q8⋊C8C2×D1111yescharacteristic
316Q8⋊C8C2×D1111yescharacteristic
317D4⋊C8—111no—
318D4⋊C8—111no—
319#322—111no—
320#322—111no—
321#322—111no—
322C82—111no—
323C22×C11—21no—
324C22×C11—21no—
325C22×C11—21no—
326C22×C11C2×C4×D411yescharacteristic
327C2×D11—41no—
328C2×D11—41no—
329C2×D11—41no—
330C4×C11—21no—
331C4×C11—21no—
332C4×C11—21no—
333C4×C11—21no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11—41no—
337C4×C11—41no—
338C4×C11C2×#13111yescharacteristic
339C4×C11#56811yescharacteristic
340C4×C11C2×#13711yescharacteristic
341C4×C11#57511yescharacteristic
342Dic11—22no—
343Dic11—41no—
344Dic11—41no—
345C2×#41—111no—
346C2×Q16—111no—
347C2×Q16—111no—
348C2×SD16—111no—
349C2×SD16—111no—
350C2×M16—111no—
351C2×M16—111no—
352C2×M16—221no—
353C2×M16—221no—
354C22×C8—221no—
355C4⋊Q8C4×D1111yescharacteristic
356C4⋊Q8C4×D1111yescharacteristic
357#125—21no—
358C22⋊Q8—21no—
359C22⋊Q8C4×D1111yescharacteristic
360C22⋊Q8C4×D1111yescharacteristic
361C4×Q8—21no—
362C4×Q8—111no—
363C4×Q8—111no—
364C4×Q8C22×D1111yescharacteristic
365C4×Q8C22×D1111yescharacteristic
366C4×D4—111no—
367C4×D4—111no—
368C4×D4—221no—
369C4×D4—221no—
370#117—21no—
371#117—111no—
372#117—221no—
373C2×C42—221no—
374C2×C42C22×D1111yescharacteristic
375#107—111no—
376#107—111no—
377#106—111no—
378#106—111no—
379C4⋊C8—21no—
380C4⋊C8—111no—
381C4⋊C8—111no—
382C4⋊C8—111no—
383C4⋊C8—111no—
384C4⋊C8—221no—
385C4⋊C8—221no—
386C4⋊C8—221no—
387C4⋊C8—221no—
388C4⋊C8—221no—
389C4⋊C8—221no—
390C4⋊C8—221no—
391C4⋊C8C22×D1111yescharacteristic
392C4⋊C8C22×D1111yescharacteristic
393#103—111no—
394#103—111no—
395#103—111no—
396#103—111no—
397#103—111no—
398#103—111no—
399#102—111no—
400#102—111no—
401C22⋊C8—21no—
402C22⋊C8—21no—
403C22⋊C8—111no—
404C22⋊C8—111no—
405C22⋊C8—221no—
406C22⋊C8—221no—
407#97—21no—
408#97—111no—
409#97—111no—
410#97—221no—
411#97—221no—
412C4×C8—111no—
413C4×C8—111no—
414C4×C8—111no—
415C4×C8—111no—
416C4×C8—221no—
417C4×C8—221no—
418C4×C8—221no—
419C4×C8—221no—
420C4×C8C22×D1111yescharacteristic
421C4×C8C22×D1111yescharacteristic
422C2×C11—41no—
423C2×C11#293311yescharacteristic
424C2×C11C4×#13711yescharacteristic
425C2×C11#295711yescharacteristic
426D11—81no—
427#41—222no—
428#41—441no—
429C2×Q8—21no—
430C2×Q8—111no—
431C2×Q8C2×C4×D1111yescharacteristic
432C2×Q8C2×C4×D1111yescharacteristic
433C2×D4—111no—
434C2×D4—221no—
435C22×C4—221no—
436C22×C4—221no—
437C22×C4—221no—
438C22×C4C2×C4×D1111yescharacteristic
439C22×C4D4×D1111yescharacteristic
440C22×C4#434111yescharacteristic
441Q16—222no—
442Q16—222no—
443SD16—441no—
444SD16—441no—
445M16—222no—
446M16—442no—
447M16—442no—
448M16—441no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—111no—
454C2×C8—111no—
455C2×C8—111no—
456C2×C8—111no—
457C2×C8—111no—
458C2×C8—111no—
459C2×C8—111no—
460C2×C8—111no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—442no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—111no—
472C4⋊C4—111no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4C2×C4×D1111yescharacteristic
476C4⋊C4C2×C4×D1111yescharacteristic
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—221no—
480C22⋊C4—221no—
481C22⋊C4—221no—
482C42—21no—
483C42—21no—
484C42—221no—
485C42—221no—
486C42—221no—
487C42C2×C4×D1111yescharacteristic
488C42D4×D1111yescharacteristic
489C42#434111yescharacteristic
490C42C23×D1111yescharacteristic
491C11#1801311yescharacteristic, complemented, Sylow
492C23—221no—
493C23(C22⋊D11)⋊C411yescharacteristic
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—21no—
498Q8—81no—
499Q8—112no—
500Q8—221no—
501D4—221no—
502D4—221no—
503D4—442no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—41no—
513C2×C4—221no—
514C2×C4—221no—
515C2×C4—221no—
516C2×C4—442no—
517C2×C4—441no—
518C2×C4—441no—
519C2×C4—881no—
520C2×C4(C22⋊D11)⋊C411yescharacteristic
521C2×C4(C22⋊D11)⋊C411yescharacteristic
522C2×C4(C22⋊D11)⋊C411yescharacteristic
523C2×C4C22×C4×D1111yescharacteristic
524C2×C4C2×D4×D1111yescharacteristic
525C2×C4C2×#434111yescharacteristic
526C8—41no—
527C8—41no—
528C8—41no—
529C8—41no—
530C8—112no—
531C8—221no—
532C8—221no—
533C8—221no—
534C8—221no—
535C8—221no—
536C8—221no—
537C8—221no—
538C8—441no—
539C8—441no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—441no—
544C22—441no—
545C22—441no—
546C22C2×(C22⋊D11)⋊C411yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—222no—
556C4—441no—
557C4—441no—
558C4D11×#13111yescharacteristic
559C4#1062328111yescharacteristic
560C4D11×#13711yescharacteristic
561C4#1062330811yescharacteristic
562C2—41no—
563C2—881no—
564C2#1307734611yescharacteristic
565C2#1307743111yescharacteristic
566C2#1307752911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1497C2
socleC22×C11C2×C4×D4
prime radicalC2×#4339C2×C4
cosocleC42×C11C24
hypercenter#1497D11
hypocenterC11#18013
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1497

Complements

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

NH ≅ G/Ntype
3. #13077565C2semidirect
4. #13067521C2semidirect
5. #13067503C2semidirect
6. #13067491C2semidirect
7. #13067490C2semidirect
8. #13067469C2semidirect
9. #13067456C2semidirect
10. #13067432C2semidirect
11. #13067420C2semidirect
12. #13067402C2semidirect
14. #13066911C2semidirect
15. C11×#1497C2semidirect
221. #1497D11semidirect
491. C11#18013semidirect

Maximal subgroups

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

subgroupindex
#130786812
#130776332
#130775652
#130675212
#130675032
#130674912
#130674902
#130674692
#130674562
#130674322
#130674202
#130674022
#130670042
#130669112
C11×#14972
#1801311