Finite Group Databasebeta

← #14724407

Subgroups — #14724407

Order 2816.

622 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079211C211yesmaximal, characteristic
2#13077767C211yesmaximal, characteristic, complemented
3#13077691C211yesmaximal, characteristic, complemented
4#13067531C211yesmaximal, characteristic, complemented
5#13067520C211yesmaximal, characteristic, complemented
6#13067508C211yesmaximal, characteristic, complemented
7#13067502C211yesmaximal, characteristic, complemented
8#13067441C211yesmaximal, characteristic, complemented
9#13067430C211yesmaximal, characteristic, complemented
10C8×#4314C211yesmaximal, characteristic, complemented
11C8×D88C211yesmaximal, characteristic, complemented
12#13067383C211yesmaximal, characteristic, complemented
13#13067077C211yesmaximal, characteristic, complemented
14#13067068C211yesmaximal, characteristic, complemented
15C8×C11×M16C211yesmaximal, characteristic, complemented
16#10623010C2211yescharacteristic
17#10623008C2211yescharacteristic
18C11×#431C2211yescharacteristic
19C4×C11×M16C2211yescharacteristic
20C2×C4×C8×C11C2211yescharacteristic
21#10622748C411yescharacteristic
22#10622748C411yescharacteristic
23#10622747C411yescharacteristic
24#10622747C411yescharacteristic
25#10622539C2211yescharacteristic
26#10622537C2211yescharacteristic
27#10622453—21no—
28#10622452—21no—
29#10622449—21no—
30#10622449—21no—
31#10622342—21no—
32#10622341—21no—
33#10622340—21no—
34#10622340—21no—
35#10622327C411yescharacteristic
36#10622326C411yescharacteristic
37#10622325C411yescharacteristic
38#10622315C411yescharacteristic
39C4×D88C2211yescharacteristic
40C4×D88C2211yescharacteristic
41C4×#4314C2211yescharacteristic
42C4×#4314C2211yescharacteristic
43#10622301C2211yescharacteristic
44#10622301C2211yescharacteristic
45#10622301C2211yescharacteristic
46C8×D44C2211yescharacteristic
47C8×D44C2211yescharacteristic
48C8×D44C2211yescharacteristic
49#10622292C2211yescharacteristic
50C8×Dic22C2211yescharacteristic
51C11×#322C2211yescharacteristic
52C11×#322C2211yescharacteristic
53C82×C11C2211yescharacteristic
54C82×C11C2211yescharacteristic
55#10622097C2211yescharacteristic
56#10622097C2211yescharacteristic
57#10622097C2211yescharacteristic
58#10622097C2211yescharacteristic
59#10622097C2211yescharacteristic
60#10622097C2211yescharacteristic
61#10622096C2211yescharacteristic
62#10622096C2211yescharacteristic
63#10622095C2211yescharacteristic
64#10622095C2211yescharacteristic
65#10622094C2211yescharacteristic
66#10622094C2211yescharacteristic
67C2×#4339—21no—
68C2×C11×M16C2×C411yescharacteristic
69C2×C11×M16C2×C411yescharacteristic
70C22×C8×C11—21no—
71C2×C42×C11C2311yescharacteristic
72#66983—21no—
73#66983C2×C411yescharacteristic
74#66983C2×C411yescharacteristic
75#66983C2×C411yescharacteristic
76#66982—21no—
77C4×C22⋊D11—21no—
78#66977C2×C411yescharacteristic
79C2×#4318—21no—
80C2×D88C2×C411yescharacteristic
81C2×D88C2×C411yescharacteristic
82C2×#4314C2×C411yescharacteristic
83C2×#4314C2×C411yescharacteristic
84C2×#4313—21no—
85C2×#4313—21no—
86C2×#4313—21no—
87C2×C8×D11—21no—
88C2×C8×D11—21no—
89C2×C8×D11—21no—
90#66929—21no—
91#66928—21no—
92#66928C2×C411yescharacteristic
93#66927C2×C411yescharacteristic
94C4×D44—21no—
95C4×D44C2311yescharacteristic
96C4×D44C2311yescharacteristic
97C4×D44C2311yescharacteristic
98#66925—21no—
99#66923C2×C411yescharacteristic
100#66922C2×C411yescharacteristic
101C4×Dic22C2311yescharacteristic
102C11×C4⋊C8D411yescharacteristic
103C11×C4⋊C8D411yescharacteristic
104C11×C22⋊C8D411yescharacteristic
105C11×C22⋊C8D411yescharacteristic
106C11×#97C2×C411yescharacteristic
107C11×#97C2×C411yescharacteristic
108C4×C8×C11—21no—
109C4×C8×C11C2311yescharacteristic
110C4×C8×C11C2311yescharacteristic
111C4×C8×C11C2311yescharacteristic
112C4×C8×C11C2311yescharacteristic
113C4×C8×C11C2311yescharacteristic
114C4×C8×C11C2311yescharacteristic
115C22⋊(C11⋊C8)—21no—
116#66885C2×C411yescharacteristic
117#66885C2×C411yescharacteristic
118#66885C2×C411yescharacteristic
119#66885C2×C411yescharacteristic
120#66885C2×C411yescharacteristic
121#66885C2×C411yescharacteristic
122(C2×D11)⋊C8—21no—
123(C2×D11)⋊C8—21no—
124(C2×D11)⋊C8—21no—
125(C2×D11)⋊C8—21no—
126(C2×D11)⋊C8—21no—
127(C2×D11)⋊C8—21no—
128#66882C2×C411yescharacteristic
129#66882C2×C411yescharacteristic
130#66881C2×C411yescharacteristic
131#66881C2×C411yescharacteristic
132#66880C2×C411yescharacteristic
133#66880C2×C411yescharacteristic
134#66879—21no—
135Dic11⋊C8—21no—
136Dic11⋊C8—21no—
137C8×Dic11—21no—
138C4⋊(C11⋊C8)—21no—
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143#66867—21no—
144#17968—111nomaximal, Sylow
145C22×C4×C11C22×C411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11#4111yescharacteristic
148C2×C22⋊D11—21no—
149C2×C22⋊D11—21no—
150C2×C22⋊D11—21no—
151#4339—81no—
152#4339—81no—
153C2×D44—21no—
154C2×D44—21no—
155C2×D44C22×C411yescharacteristic
156C2×D44C22×C411yescharacteristic
157C2×D44C22×C411yescharacteristic
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×Dic22—21no—
162C2×Dic22C22×C411yescharacteristic
163C11×M16—22no—
164C11×M16—22no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—42no—
168C2×C8×C11C22×C411yescharacteristic
169C2×C8×C11C22×C411yescharacteristic
170C2×C8×C11C22×C411yescharacteristic
171C2×C8×C11C22×C411yescharacteristic
172C2×C8×C11C2×D411yescharacteristic
173C2×C8×C11C2×D411yescharacteristic
174C2×C8×C11C2×D411yescharacteristic
175C2×C8×C11C2×D411yescharacteristic
176C42×C11C22×C411yescharacteristic
177C42×C11C2×D411yescharacteristic
178C42×C11#4111yescharacteristic
179C42×C11C2411yescharacteristic
180C22⋊Dic11—21no—
181(C2×D11)⋊C4—21no—
182(C2×D11)⋊C4—21no—
183(C2×D11)⋊C4—21no—
184(C2×D11)⋊C4—21no—
185(C2×D11)⋊C4—21no—
186(C2×D11)⋊C4—21no—
187(C2×D11)⋊C4—21no—
188(C2×D11)⋊C4—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11C22×C411yescharacteristic
191C4⋊Dic11C22×C411yescharacteristic
192C4⋊Dic11C22×C411yescharacteristic
193C4⋊Dic11C22×C411yescharacteristic
194Dic11⋊C4—21no—
195Dic11⋊C4—21no—
196Dic11⋊C4—21no—
197Dic11⋊C4—21no—
198C4×Dic11—21no—
199#4318—81no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204D88—22no—
205D88—22no—
206#4314—22no—
207#4314—22no—
208#4313—81no—
209#4313—81no—
210#4313—81no—
211C8×D11—81no—
212C8×D11—81no—
213C8×D11—81no—
214#3171—111no—
215#2993—111no—
216#2981—111no—
217#1594—111no—
218#1592—111no—
219#1590—111no—
220#1589—111no—
221#1580—111no—
222SD16⋊C8—111no—
223C8×SD16—111no—
224C8×D8—111no—
225#1569—111no—
226#1494—111no—
227#1492—111no—
228C8×M16D1111yescharacteristic, complemented
229C23×C11C4×D411yescharacteristic
230C22×D11—21no—
231C22×D11—21no—
232C22×D11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—41no—
238C2×C4×C11C4×D411yescharacteristic
239C2×C4×C11C4×D411yescharacteristic
240C2×C4×C11C4×D411yescharacteristic
241C2×C4×C11C23×C411yescharacteristic
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C22⋊D11—81no—
245C22⋊D11—81no—
246C22⋊D11—81no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252D44—21no—
253D44—21no—
254D44—21no—
255D44—21no—
256D44—21no—
257D44—21no—
258D44—81no—
259D44—81no—
260C4×D11—41no—
261C4×D11—41no—
262C4×D11—41no—
263C4×D11—41no—
264C4×D11—41no—
265C4×D11—41no—
266Dic22—21no—
267Dic22—21no—
268Dic22—81no—
269C8×C11—22no—
270C8×C11—21no—
271C8×C11—21no—
272C8×C11—21no—
273C8×C11—21no—
274C8×C11—21no—
275C8×C11—21no—
276C8×C11—41no—
277C8×C11#13112yes—
278C8×C11#13112yes—
279C11⋊C8—41no—
280C11⋊C8—41no—
281C11⋊C8—41no—
282C11⋊C8—41no—
283#532—111no—
284#529—111no—
285#501—111no—
286#496—111no—
287#490—111no—
288#489—111no—
289#469—111no—
290#469—111no—
291#468—111no—
292#468—111no—
293#446—111no—
294C8×Q8—111no—
295C4×SD16—111no—
296C4×SD16—111no—
297C4×D8—111no—
298C4×D8—111no—
299#436—111no—
300#436—111no—
301#436—111no—
302#436—221no—
303#435—221no—
304#435—221no—
305#435—221no—
306C8×D4—111no—
307C8×D4—111no—
308C8×D4—111no—
309#433—221no—
310#432—111no—
311#431C2×D1111yescharacteristic
312#424—221no—
313#423—111no—
314#408—221no—
315#408—221no—
316C4×M16C2×D1111yescharacteristic
317C2×C4×C8C2×D1111yescharacteristic
318#335—111no—
319#335—111no—
320#334—111no—
321#334—111no—
322Q8⋊C8—111no—
323Q8⋊C8—111no—
324D4⋊C8—111no—
325D4⋊C8—111no—
326D4⋊C8—111no—
327D4⋊C8—111no—
328D4⋊C8—111no—
329D4⋊C8—111no—
330#322C2×D1111yescharacteristic
331#322C2×D1111yescharacteristic
332C82C2×D1111yescharacteristic
333C82C2×D1111yescharacteristic
334C22×C11—21no—
335C22×C11—21no—
336C22×C11—21no—
337C22×C11C2×C4×D411yescharacteristic
338C2×D11—41no—
339C2×D11—41no—
340C2×D11—41no—
341C2×D11—41no—
342C2×D11—41no—
343C2×D11—41no—
344C2×D11—41no—
345C2×D11—41no—
346C2×D11—41no—
347C4×C11—21no—
348C4×C11—21no—
349C4×C11—21no—
350C4×C11—21no—
351C4×C11C2×#13111yescharacteristic
352C4×C11C2×#13111yescharacteristic
353C4×C11#57611yescharacteristic
354C4×C11#57711yescharacteristic
355Dic11—41no—
356Dic11—41no—
357Dic11—41no—
358Dic11—41no—
359Dic11—41no—
360C2×#41—221no—
361C2×SD16—111no—
362C2×SD16—111no—
363C2×D8—111no—
364C2×D8—111no—
365C2×M16—221no—
366C2×M16—221no—
367C2×M16—221no—
368C2×M16—221no—
369C2×M16C4×D1111yescharacteristic
370C2×M16C4×D1111yescharacteristic
371C22×C8—21no—
372C22×C8—221no—
373C22×C8—221no—
374C22×C8—221no—
375C4⋊Q8—111no—
376#127—111no—
377#126—221no—
378#125—111no—
379#124—111no—
380#124—221no—
381#123—221no—
382C22⋊Q8—111no—
383#121—111no—
384#121—111no—
385#121—111no—
386#121—221no—
387C4×Q8—111no—
388C4×D4—111no—
389C4×D4—111no—
390C4×D4—111no—
391C4×D4—221no—
392C4×D4—221no—
393#117—221no—
394C2×C42C22×D1111yescharacteristic
395#107—111no—
396#107—111no—
397#106—111no—
398#106—111no—
399C4⋊C8—111no—
400C4⋊C8—111no—
401C4⋊C8—111no—
402C4⋊C8—111no—
403C4⋊C8—221no—
404C4⋊C8—221no—
405C4⋊C8—221no—
406C4⋊C8D4411yescharacteristic
407C4⋊C8D4411yescharacteristic
408#103—111no—
409#103—111no—
410#102—111no—
411#102—111no—
412#102—111no—
413#102—111no—
414#102—111no—
415#102—111no—
416C22⋊C8—221no—
417C22⋊C8—221no—
418C22⋊C8—221no—
419C22⋊C8—221no—
420C22⋊C8—221no—
421C22⋊C8—221no—
422C22⋊C8—221no—
423C22⋊C8D4411yescharacteristic
424C22⋊C8D4411yescharacteristic
425#97—221no—
426#97—221no—
427#97C4×D1111yescharacteristic
428#97C4×D1111yescharacteristic
429C4×C8—21no—
430C4×C8—221no—
431C4×C8C22×D1111yescharacteristic
432C4×C8C22×D1111yescharacteristic
433C4×C8C22×D1111yescharacteristic
434C4×C8C22×D1111yescharacteristic
435C4×C8C22×D1111yescharacteristic
436C4×C8C22×D1111yescharacteristic
437C2×C11—41no—
438C2×C11#293111yescharacteristic
439C2×C11#294611yescharacteristic
440C2×C11#295611yescharacteristic
441D11—81no—
442D11—81no—
443D11—81no—
444#41—881no—
445#41—881no—
446C2×Q8—111no—
447C2×Q8—221no—
448C2×D4—111no—
449C2×D4—111no—
450C2×D4—111no—
451C2×D4—221no—
452C2×D4—221no—
453C2×D4—221no—
454C2×D4—221no—
455C2×D4—221no—
456C22×C4—221no—
457C22×C4—221no—
458C22×C4—221no—
459C22×C4C2×C4×D1111yescharacteristic
460C22×C4C2×D4411yescharacteristic
461C22×C4#433911yescharacteristic
462SD16—222no—
463SD16—222no—
464D8—222no—
465D8—222no—
466M16—22no—
467M16—22no—
468M16—881no—
469M16—881no—
470M16—881no—
471M16—881no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—42no—
475C2×C8—221no—
476C2×C8—221no—
477C2×C8—221no—
478C2×C8—221no—
479C2×C8—881no—
480C2×C8—881no—
481C2×C8—881no—
482C2×C8C2×C4×D1111yescharacteristic
483C2×C8C2×C4×D1111yescharacteristic
484C2×C8C2×C4×D1111yescharacteristic
485C2×C8C2×C4×D1111yescharacteristic
486C2×C8C2×D4411yescharacteristic
487C2×C8C2×D4411yescharacteristic
488C2×C8C2×D4411yescharacteristic
489C2×C8C2×D4411yescharacteristic
490C4⋊C4—111no—
491C4⋊C4—111no—
492C4⋊C4—111no—
493C4⋊C4—111no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C22⋊C4—221no—
500C22⋊C4—221no—
501C22⋊C4—221no—
502C22⋊C4—221no—
503C22⋊C4—221no—
504C22⋊C4—221no—
505C22⋊C4—221no—
506C22⋊C4—221no—
507C22⋊C4—221no—
508C42—221no—
509C42C2×C4×D1111yescharacteristic
510C42C2×D4411yescharacteristic
511C42#433911yescharacteristic
512C42C23×D1111yescharacteristic
513C11#1796811yescharacteristic, complemented, Sylow
514C23—221no—
515C23—221no—
516C23—221no—
517C23C4×D4411yescharacteristic
518Q8—221no—
519Q8—221no—
520Q8—881no—
521D4—221no—
522D4—221no—
523D4—221no—
524D4—221no—
525D4—221no—
526D4—221no—
527D4—881no—
528D4—881no—
529D4—881no—
530D4—881no—
531D4—881no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—41no—
537C2×C4—221no—
538C2×C4—221no—
539C2×C4—221no—
540C2×C4—221no—
541C2×C4—221no—
542C2×C4—441no—
543C2×C4—441no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4C4×D4411yescharacteristic
549C2×C4C4×D4411yescharacteristic
550C2×C4C4×D4411yescharacteristic
551C2×C4C22×C4×D1111yescharacteristic
552C2×C4C22×D4411yescharacteristic
553C2×C4C2×#433911yescharacteristic
554C8—22no—
555C8—21no—
556C8—21no—
557C8—21no—
558C8—21no—
559C8—21no—
560C8—21no—
561C8—41no—
562C8—441no—
563C8—441no—
564C8—441no—
565C8—441no—
566C8#6695412yes—
567C8#6695412yes—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—441no—
572C22—441no—
573C22—441no—
574C22—441no—
575C22—441no—
576C22—441no—
577C22—441no—
578C22—441no—
579C22—441no—
580C22C2×C4×D4411yescharacteristic
581C4—21no—
582C4—21no—
583C4—21no—
584C4—21no—
585C4—441no—
586C4—441no—
587C4—441no—
588C4—441no—
589C4—441no—
590C4C2×#6695411yescharacteristic
591C4C2×#6695411yescharacteristic
592C4#1062328211yescharacteristic
593C4#1062328311yescharacteristic
594C2—41no—
595C2—881no—
596C2—881no—
597C2—881no—
598C2#1307732911yescharacteristic
599C2#1307745011yescharacteristic
600C2#1307752711yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC8×C11×M16C2
socleC22×C11C2×C4×D4
prime radical#13079211C2
cosocleC42×C11C24
hypercenterC8×M16D11
hypocenterC11#17968
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #431 ◁ C8×M16

Complements

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

NH ≅ G/Ntype
2. #13077767C2semidirect
3. #13077691C2semidirect
4. #13067531C2semidirect
5. #13067520C2semidirect
6. #13067508C2semidirect
7. #13067502C2semidirect
8. #13067441C2semidirect
9. #13067430C2semidirect
10. C8×#4314C2semidirect
11. C8×D88C2semidirect
12. #13067383C2semidirect
13. #13067077C2semidirect
14. #13067068C2semidirect
15. C8×C11×M16C2semidirect
228. C8×M16D11semidirect
513. C11#17968semidirect

Maximal subgroups

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

subgroupindex
#130792112
#130777672
#130776912
#130675312
#130675202
#130675082
#130675022
#130674412
#130674302
C8×#43142
C8×D882
#130673832
#130670772
#130670682
C8×C11×M162
#1796811