Finite Group Databasebeta

← #14725642

Subgroups — #14725642

Order 2816.

588 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079216C211yesmaximal, characteristic
2#13077620C211yesmaximal, characteristic
3#13067516C211yesmaximal, characteristic, complemented
4#13067511C211yesmaximal, characteristic, complemented
5#13067494C211yesmaximal, characteristic, complemented
6#13067485C211yesmaximal, characteristic, complemented
7#13067466C211yesmaximal, characteristic, complemented
8#13067450C211yesmaximal, characteristic, complemented
9#13067433C211yesmaximal, characteristic, complemented
10C8×#4325C211yesmaximal, characteristic, complemented
11#13067366C211yesmaximal, characteristic, complemented
12#13067037C211yesmaximal, characteristic, complemented
13#13067027C211yesmaximal, characteristic
14#13066919C211yesmaximal, characteristic, complemented
15C11×#2962C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17#10623010C2211yescharacteristic
18C11×#446—21no—
19C11×#446—21no—
20C11×#446C2211yescharacteristic
21C11×#446C2211yescharacteristic
22C8×Q8×C11C2211yescharacteristic
23C8×Q8×C11C2211yescharacteristic
24C11×#424—21no—
25C2×C11×C4⋊C8C2211yescharacteristic
26C11×#405—21no—
27C4×C11×M16C2211yescharacteristic
28#10622741—21no—
29#10622740—21no—
30#10622702C411yescharacteristic
31#10622699C411yescharacteristic
32#10622695C411yescharacteristic
33#10622693C411yescharacteristic
34#10622665C411yescharacteristic
35#10622665C411yescharacteristic
36#10622662C411yescharacteristic
37#10622662C411yescharacteristic
38C4×#4326C2211yescharacteristic
39C4×#4326C2211yescharacteristic
40C4×#4325C2211yescharacteristic
41C4×#4325C2211yescharacteristic
42#10622538C2211yescharacteristic
43C4×#4318C2211yescharacteristic
44C4×#4318C2211yescharacteristic
45#10622322—21no—
46#10622321—21no—
47#10622301C2211yescharacteristic
48C8×D44C2211yescharacteristic
49#10622292C2211yescharacteristic
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
67C2×C11×M16D411yescharacteristic
68C2×C11×M16D411yescharacteristic
69C22×C8×C11—21no—
70C11×C4⋊Q8C2×C411yescharacteristic
71C11×C4⋊Q8C2×C411yescharacteristic
72C11×#125—21no—
73C11×C22⋊Q8—21no—
74C11×C22⋊Q8C2×C411yescharacteristic
75C11×C22⋊Q8C2×C411yescharacteristic
76C4×Q8×C11—21no—
77C4×Q8×C11C2311yescharacteristic
78C4×Q8×C11C2311yescharacteristic
79C11×#117—21no—
80C2×C42×C11C2311yescharacteristic
81C2×#4326C2×C411yescharacteristic
82C2×#4326C2×C411yescharacteristic
83C2×#4325C2×C411yescharacteristic
84C2×#4325C2×C411yescharacteristic
85#66983C2×C411yescharacteristic
86#66982—21no—
87C4×C22⋊D11—21no—
88#66977C2×C411yescharacteristic
89C2×#4318—21no—
90C2×#4318C2×C411yescharacteristic
91C2×#4318C2×C411yescharacteristic
92C2×#4313—21no—
93C2×C8×D11—21no—
94#66929—21no—
95#66928C2×C411yescharacteristic
96C4×D44C2311yescharacteristic
97#66925—21no—
98#66923C2×C411yescharacteristic
99C4×Dic22C2311yescharacteristic
100C11×C4⋊C8—21no—
101C11×C4⋊C8—21no—
102C11×C4⋊C8—21no—
103C11×C4⋊C8—21no—
104C11×C4⋊C8—21no—
105C11×C4⋊C8C2311yescharacteristic
106C11×C4⋊C8C2311yescharacteristic
107C11×#97—21no—
108C11×#97—21no—
109C11×#97D411yescharacteristic
110C11×#97D411yescharacteristic
111C4×C8×C11—21no—
112C4×C8×C11—21no—
113C4×C8×C11C2311yescharacteristic
114C4×C8×C11C2311yescharacteristic
115#66899C2×C411yescharacteristic
116#66899C2×C411yescharacteristic
117#66899C2×C411yescharacteristic
118#66899C2×C411yescharacteristic
119C22⋊(C11⋊C8)—21no—
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)C2311yescharacteristic
135C4⋊(C11⋊C8)C2311yescharacteristic
136#66867—21no—
137#66867C2×C411yescharacteristic
138#66867C2×C411yescharacteristic
139C4×C11⋊C8—21no—
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#18077—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—
152C2×D44C22×C411yescharacteristic
153C2×C4×D11—21no—
154C2×Dic22C22×C411yescharacteristic
155C11×M16—22no—
156C11×M16—41no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—42no—
160C2×C8×C11C2×D411yescharacteristic
161C2×C8×C11C2×D411yescharacteristic
162C2×C8×C11C2×D411yescharacteristic
163C2×C8×C11C2×D411yescharacteristic
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⋊C4—21no—
171C11×C4⋊C4C22×C411yescharacteristic
172C11×C4⋊C4C22×C411yescharacteristic
173C11×C22⋊C4—21no—
174C11×C22⋊C4—21no—
175C42×C11—21no—
176C42×C11—21no—
177C42×C11C22×C411yescharacteristic
178C42×C11C2×D411yescharacteristic
179C42×C11#4111yescharacteristic
180C42×C11C2411yescharacteristic
181C22⋊Dic11—21no—
182#4326—22no—
183#4326—41no—
184#4325—22no—
185#4325—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—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8C22×C411yescharacteristic
205C2×C11⋊C8C22×C411yescharacteristic
206C2×C11⋊C8C22×C411yescharacteristic
207C2×C11⋊C8C22×C411yescharacteristic
208#4313—42no—
209C8×D11—42no—
210#3172—111no—
211#2969—111no—
212#2962D1111yescharacteristic, complemented
213#1592—111no—
214#1591—111no—
215#1588—111no—
216#1587—111no—
217#1584—111no—
218#1582—111no—
219#1579—111no—
220C8×SD16—111no—
221#1565—111no—
222#1485—111no—
223#1483—111no—
224#1455—111no—
225C23×C11C4×D411yescharacteristic
226C22×D11—21no—
227Q8×C11—21no—
228Q8×C11—21no—
229Q8×C11—21no—
230Q8×C11—21no—
231Q8×C11—81no—
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—21no—
240C2×C4×C11—41no—
241C2×C4×C11C4×D411yescharacteristic
242C2×C4×C11C4×D411yescharacteristic
243C2×C4×C11C4×D411yescharacteristic
244C2×C4×C11C23×C411yescharacteristic
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C22⋊D11—81no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251D44—21no—
252D44—21no—
253C4×D11—41no—
254C4×D11—41no—
255Dic22—21no—
256Dic22—21no—
257C8×C11—21no—
258C8×C11—21no—
259C8×C11—21no—
260C8×C11—41no—
261C8×C11—41no—
262C8×C11#13712yes—
263C11⋊C8—22no—
264C11⋊C8—21no—
265C11⋊C8—21no—
266C11⋊C8—21no—
267C11⋊C8—41no—
268C11⋊C8—41no—
269C11⋊C8—41no—
270C11⋊C8#13112yes—
271#533C2×D1111yescharacteristic
272#529—111no—
273#501—111no—
274#497—111no—
275#491—111no—
276#489—111no—
277#470—111no—
278#470—111no—
279#468—111no—
280#468—111no—
281#446—21no—
282#446—21no—
283#446—111no—
284#446C2×D1111yescharacteristic
285#446C2×D1111yescharacteristic
286C8×Q8—111no—
287C8×Q8C2×D1111yescharacteristic
288C8×Q8C2×D1111yescharacteristic
289C4×Q16—111no—
290C4×Q16—111no—
291C4×SD16—111no—
292C4×SD16—111no—
293#436—111no—
294#436—221no—
295#435—221no—
296C8×D4—111no—
297#433—221no—
298#431—111no—
299#424—21no—
300C2×C4⋊C8C2×D1111yescharacteristic
301#405—21no—
302#405—221no—
303C4×M16—111no—
304C4×M16—111no—
305C4×M16C2×D1111yescharacteristic
306#335—111no—
307#335—111no—
308#334—111no—
309#334—111no—
310Q8⋊C8—111no—
311Q8⋊C8—111no—
312Q8⋊C8—111no—
313Q8⋊C8—111no—
314Q8⋊C8—111no—
315Q8⋊C8—111no—
316D4⋊C8—111no—
317D4⋊C8—111no—
318#322—111no—
319#322—111no—
320#322—111no—
321C82—111no—
322C22×C11—21no—
323C22×C11—21no—
324C22×C11—21no—
325C22×C11C2×C4×D411yescharacteristic
326C2×D11—41no—
327C2×D11—41no—
328C2×D11—41no—
329C4×C11—21no—
330C4×C11—21no—
331C4×C11—21no—
332C4×C11—21no—
333C4×C11—41no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11—41no—
337C4×C11C2×#13111yescharacteristic
338C4×C11#56811yescharacteristic
339C4×C11C2×#13711yescharacteristic
340C4×C11#57511yescharacteristic
341Dic11—41no—
342Dic11—41no—
343Dic11—41no—
344C2×Q16—111no—
345C2×Q16—111no—
346C2×SD16—111no—
347C2×SD16—111no—
348C2×M16—111no—
349C2×M16—111no—
350C2×M16—221no—
351C2×M16—221no—
352C2×M16C22⋊D1111yescharacteristic
353C2×M16C22⋊D1111yescharacteristic
354C22×C8—21no—
355C22×C8—221no—
356C4⋊Q8C4×D1111yescharacteristic
357C4⋊Q8C4×D1111yescharacteristic
358#126—221no—
359#125—21no—
360#125—111no—
361#124—111no—
362#123—221no—
363C22⋊Q8—21no—
364C22⋊Q8—111no—
365C22⋊Q8C4×D1111yescharacteristic
366C22⋊Q8C4×D1111yescharacteristic
367#121—111no—
368C4×Q8—21no—
369C4×Q8—111no—
370C4×Q8C22×D1111yescharacteristic
371C4×Q8C22×D1111yescharacteristic
372C4×D4—111no—
373C4×D4—221no—
374#117—21no—
375#117—221no—
376C2×C42C22×D1111yescharacteristic
377#107—111no—
378#107—111no—
379#106—111no—
380#106—111no—
381C4⋊C8—21no—
382C4⋊C8—21no—
383C4⋊C8—21no—
384C4⋊C8—21no—
385C4⋊C8—21no—
386C4⋊C8—111no—
387C4⋊C8—111no—
388C4⋊C8—221no—
389C4⋊C8—221no—
390C4⋊C8C22×D1111yescharacteristic
391C4⋊C8C22×D1111yescharacteristic
392#103—111no—
393#103—111no—
394#103—111no—
395#103—111no—
396#103—111no—
397#103—111no—
398#102—111no—
399#102—111no—
400C22⋊C8—221no—
401C22⋊C8—221no—
402C22⋊C8—221no—
403#97—21no—
404#97—21no—
405#97—111no—
406#97—111no—
407#97—221no—
408#97—221no—
409#97C22⋊D1111yescharacteristic
410#97C22⋊D1111yescharacteristic
411C4×C8—21no—
412C4×C8—21no—
413C4×C8—111no—
414C4×C8—111no—
415C4×C8—111no—
416C4×C8—111no—
417C4×C8—221no—
418C4×C8—221no—
419C4×C8C22×D1111yescharacteristic
420C4×C8C22×D1111yescharacteristic
421C2×C11—41no—
422C2×C11#293511yescharacteristic
423C2×C11C4×#13711yescharacteristic
424C2×C11#295611yescharacteristic
425D11—81no—
426C2×Q8—21no—
427C2×Q8—111no—
428C2×Q8C2×C4×D1111yescharacteristic
429C2×Q8C2×C4×D1111yescharacteristic
430C2×D4—111no—
431C2×D4—221no—
432C22×C4—221no—
433C22×C4C2×C4×D1111yescharacteristic
434C22×C4#433911yescharacteristic
435C22×C4C2×C22⋊D1111yescharacteristic
436Q16—222no—
437Q16—441no—
438SD16—222no—
439SD16—441no—
440M16—22no—
441M16—41no—
442M16—222no—
443M16—442no—
444M16—441no—
445M16—442no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—42no—
449C2×C8—111no—
450C2×C8—111no—
451C2×C8—111no—
452C2×C8—111no—
453C2×C8—221no—
454C2×C8—221no—
455C2×C8—221no—
456C2×C8—221no—
457C2×C8—442no—
458C2×C8C2×C22⋊D1111yescharacteristic
459C2×C8C2×C22⋊D1111yescharacteristic
460C2×C8C2×C22⋊D1111yescharacteristic
461C2×C8C2×C22⋊D1111yescharacteristic
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—111no—
470C4⋊C4—111no—
471C4⋊C4—221no—
472C4⋊C4—221no—
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—
482C22⋊C4—221no—
483C22⋊C4—221no—
484C42—21no—
485C42—21no—
486C42—221no—
487C42C2×C4×D1111yescharacteristic
488C42#433911yescharacteristic
489C42C2×C22⋊D1111yescharacteristic
490C42C23×D1111yescharacteristic
491C11#1807711yescharacteristic, complemented, Sylow
492C23—221no—
493C23C4×C22⋊D1111yescharacteristic
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—21no—
498Q8—81no—
499Q8—221no—
500Q8—221no—
501D4—221no—
502D4—221no—
503D4—881no—
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—441no—
517C2×C4—441no—
518C2×C4C4×C22⋊D1111yescharacteristic
519C2×C4C4×C22⋊D1111yescharacteristic
520C2×C4C4×C22⋊D1111yescharacteristic
521C2×C4C22×C4×D1111yescharacteristic
522C2×C4C2×#433911yescharacteristic
523C2×C4C22×C22⋊D1111yescharacteristic
524C8—21no—
525C8—21no—
526C8—21no—
527C8—41no—
528C8—41no—
529C8—112no—
530C8—222no—
531C8—221no—
532C8—221no—
533C8—221no—
534C8—441no—
535C8—441no—
536C8—441no—
537C8#6699512yes—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—441no—
542C22—441no—
543C22—441no—
544C22C2×C4×C22⋊D1111yescharacteristic
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—441no—
554C4—441no—
555C4—441no—
556C4D11×#13111yescharacteristic
557C4#1062328111yescharacteristic
558C4C2×#6699511yescharacteristic
559C4#1062335311yescharacteristic
560C2—41no—
561C2—881no—
562C2#1307735811yescharacteristic
563C2C4×#6699511yescharacteristic
564C2#1307752311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2962C2
socleC22×C11C2×C4×D4
prime radical#66983C2×C4
cosocleC42×C11C24
hypercenter#2962D11
hypocenterC11#18077
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #2962

Complements

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

NH ≅ G/Ntype
3. #13067516C2semidirect
4. #13067511C2semidirect
5. #13067494C2semidirect
6. #13067485C2semidirect
7. #13067466C2semidirect
8. #13067450C2semidirect
9. #13067433C2semidirect
10. C8×#4325C2semidirect
11. #13067366C2semidirect
12. #13067037C2semidirect
14. #13066919C2semidirect
15. C11×#2962C2semidirect
212. #2962D11semidirect
491. C11#18077semidirect

Maximal subgroups

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

subgroupindex
#130792162
#130776202
#130675162
#130675112
#130674942
#130674852
#130674662
#130674502
#130674332
C8×#43252
#130673662
#130670372
#130670272
#130669192
C11×#29622
#1807711