Finite Group Databasebeta

← #14724352

Subgroups — #14724352

Order 2816.

662 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079209C211yesmaximal, characteristic
2#13077588C211yesmaximal, characteristic, complemented
3#13077323C211yesmaximal, characteristic, complemented
4#13067530C211yesmaximal, characteristic, complemented
5#13067527C211yesmaximal, characteristic, complemented
6#13067517C211yesmaximal, characteristic, complemented
7#13067515C211yesmaximal, characteristic, complemented
8C8×#4314C211yesmaximal, characteristic, complemented
9C8×#4324C211yesmaximal, characteristic, complemented
10C8×#4323C211yesmaximal, characteristic, complemented
11#13067382C211yesmaximal, characteristic, complemented
12#13067083C211yesmaximal, characteristic, complemented
13#13067078C211yesmaximal, characteristic, complemented
14C8×#4313C211yesmaximal, characteristic, complemented
15C8×C11×D8C211yesmaximal, characteristic, complemented
16C2×#66954—21no—
17#10623088C2211yescharacteristic
18#10623079C2211yescharacteristic
19C4×C11×D8C2211yescharacteristic
20C8×D4×C11C2211yescharacteristic
21C8×D4×C11C2211yescharacteristic
22#10622772C411yescharacteristic
23#10622767C411yescharacteristic
24C8×C22⋊D11—21no—
25C8×C22⋊D11—21no—
26#10622714—21no—
27C4×#4324C2211yescharacteristic
28C4×#4323C2211yescharacteristic
29#10622625C2211yescharacteristic
30#10622625C2211yescharacteristic
31#10622499C411yescharacteristic
32#10622489C411yescharacteristic
33#10622451C2211yescharacteristic
34#10622450C2211yescharacteristic
35#10622448C2211yescharacteristic
36#10622444C2211yescharacteristic
37#10622395C411yescharacteristic
38#10622393C411yescharacteristic
39#10622378C411yescharacteristic
40#10622377C411yescharacteristic
41#10622342—21no—
42#10622341—21no—
43#10622340—21no—
44#10622333—21no—
45C4×#4314C2211yescharacteristic
46C4×#4313C2211yescharacteristic
47C8×D44C2211yescharacteristic
48#10622298C2211yescharacteristic
49C4×C8×D11C2211yescharacteristic
50C8×Dic22C2211yescharacteristic
51C11×#335C2211yescharacteristic
52C11×D4⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic
54C82×C11C2211yescharacteristic
55D4⋊(C11⋊C8)C2211yescharacteristic
56D4⋊(C11⋊C8)C2211yescharacteristic
57#10622122C2211yescharacteristic
58#10622121C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622117C2211yescharacteristic
61#10622097C2211yescharacteristic
62#10622095C2211yescharacteristic
63#10622094C2211yescharacteristic
64#10622093C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×#4339—21no—
68C2×C11×D8C2×C411yescharacteristic
69C22×C8×C11—21no—
70C22×C8×C11—21no—
71C4×D4×C11C2311yescharacteristic
72C4×D4×C11C2311yescharacteristic
73#66993C2×C411yescharacteristic
74#66991C2×C411yescharacteristic
75#66991C2×C411yescharacteristic
76#66989C2×C411yescharacteristic
77C2×#4324C2×C411yescharacteristic
78C2×#4323C2×C411yescharacteristic
79C4×C22⋊D11—21no—
80C4×C22⋊D11—21no—
81#66979—21no—
82C2×#4318—21no—
83C2×#4318—21no—
84C2×#4314C2×C411yescharacteristic
85#66954—44no—
86C2×#4313—21no—
87C2×#4313—21no—
88C2×#4313C2×C411yescharacteristic
89C2×#4313C2×C411yescharacteristic
90C2×C8×D11—21no—
91C2×C8×D11D411yescharacteristic
92C2×C8×D11D411yescharacteristic
93#66950C2×C411yescharacteristic
94#66948C2×C411yescharacteristic
95#66943C2×C411yescharacteristic
96#66941C2×C411yescharacteristic
97#66938—21no—
98#66937—21no—
99#66936—21no—
100#66932—21no—
101C4×D44C2311yescharacteristic
102C42×D11C2311yescharacteristic
103C4×Dic22C2311yescharacteristic
104C11×#107C2×C411yescharacteristic
105C11×C4⋊C8C2311yescharacteristic
106C11×C4⋊C8C2311yescharacteristic
107C11×#102C2×C411yescharacteristic
108C11×#102C2×C411yescharacteristic
109C11×C22⋊C8—21no—
110C11×C22⋊C8—21no—
111C4×C8×C11C2311yescharacteristic
112C4×C8×C11C2311yescharacteristic
113C4×C8×C11C2311yescharacteristic
114#66896C2×C411yescharacteristic
115#66896C2×C411yescharacteristic
116C22⋊(C11⋊C8)—21no—
117C22⋊(C11⋊C8)—21no—
118#66885C2×C411yescharacteristic
119(C2×D11)⋊C8—21no—
120(C2×D11)⋊C8—21no—
121(C2×D11)⋊C8—21no—
122(C2×D11)⋊C8—21no—
123#66881C2×C411yescharacteristic
124#66880C2×C411yescharacteristic
125#66879—21no—
126#66879—21no—
127#66879C2×C411yescharacteristic
128#66879C2×C411yescharacteristic
129Dic11⋊C8—21no—
130Dic11⋊C8—21no—
131Dic11⋊C8—21no—
132Dic11⋊C8—21no—
133C8×Dic11—21no—
134C8×Dic11D411yescharacteristic
135C8×Dic11D411yescharacteristic
136#66874C2×C411yescharacteristic
137#66873C2×C411yescharacteristic
138#66872C2×C411yescharacteristic
139#66871C2×C411yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#17964—111nomaximal, Sylow
146C2×D4×C11C22×C411yescharacteristic
147C2×D4×C11C22×C411yescharacteristic
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C2×C22⋊D11—21no—
151C2×C22⋊D11—21no—
152C2×C22⋊D11—21no—
153C2×C22⋊D11—21no—
154#4339—42no—
155#4339—42no—
156C2×D44—21no—
157C2×D44C22×C411yescharacteristic
158C2×C4×D11—21no—
159C2×C4×D11C22×C411yescharacteristic
160C2×C4×D11C2×D411yescharacteristic
161C2×C4×D11#4111yescharacteristic
162C2×Dic22—21no—
163C2×Dic22C22×C411yescharacteristic
164C11×D8—22no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—42no—
169C2×C8×C11—42no—
170C2×C8×C11C22×C411yescharacteristic
171C2×C8×C11C22×C411yescharacteristic
172C2×C8×C11C2×D411yescharacteristic
173C2×C8×C11C2×D411yescharacteristic
174C11×C4⋊C4C22×C411yescharacteristic
175C11×C4⋊C4C22×C411yescharacteristic
176C11×C22⋊C4—21no—
177C11×C22⋊C4—21no—
178C42×C11C2411yescharacteristic
179C22⋊Dic11—21no—
180C22⋊Dic11—21no—
181C22⋊Dic11—21no—
182C22⋊Dic11—21no—
183#4324—22no—
184#4323—22no—
185(C2×D11)⋊C4—21no—
186(C2×D11)⋊C4—21no—
187(C2×D11)⋊C4—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11C22×C411yescharacteristic
191C4⋊Dic11C22×C411yescharacteristic
192Dic11⋊C4—21no—
193Dic11⋊C4—21no—
194Dic11⋊C4—21no—
195C4×Dic11—21no—
196C4×Dic11C22×C411yescharacteristic
197C4×Dic11C2×D411yescharacteristic
198C4×Dic11#4111yescharacteristic
199#4318—42no—
200#4318—42no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8C22×C411yescharacteristic
205C2×C11⋊C8C22×C411yescharacteristic
206C2×C11⋊C8C2×D411yescharacteristic
207C2×C11⋊C8C2×D411yescharacteristic
208#4314—22no—
209#4313—22no—
210#4313—22no—
211#4313—42no—
212#4313—42no—
213C8×D11—22no—
214C8×D11—41no—
215C8×D11—42no—
216#3171—111no—
217#2966—111no—
218#2931—111no—
219#1594—111no—
220#1594—111no—
221#1592—111no—
222#1592—111no—
223C8×SD16—111no—
224C8×SD16—111no—
225C8×D8—111no—
226C8×D8D1111yescharacteristic, complemented
227#1569—111no—
228#1496—111no—
229#1495—111no—
230C8×M16—111no—
231C23×C11—21no—
232C23×C11—21no—
233C22×D11—21no—
234C22×D11C4×D411yescharacteristic
235D4×C11—21no—
236D4×C11—21no—
237D4×C11—21no—
238D4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11C23×C411yescharacteristic
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C22⋊D11—42no—
249C22⋊D11—42no—
250C22⋊D11—42no—
251C22⋊D11—42no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11C4×D411yescharacteristic
256C2×Dic11C4×D411yescharacteristic
257C2×Dic11C4×D411yescharacteristic
258D44—21no—
259D44—21no—
260D44—42no—
261C4×D11—21no—
262C4×D11—21no—
263C4×D11—21no—
264C4×D11—21no—
265C4×D11—41no—
266C4×D11—41no—
267C4×D11—41no—
268Dic22—21no—
269Dic22—21no—
270Dic22—42no—
271C8×C11—21no—
272C8×C11—21no—
273C8×C11—41no—
274C8×C11—41no—
275C8×C11—41no—
276C8×C11#13112yescomplemented
277C8×C11AGL(1,ℤ/8)12yes—
278C11⋊C8—21no—
279C11⋊C8—21no—
280C11⋊C8—21no—
281C11⋊C8—41no—
282C11⋊C8—41no—
283C11⋊C8—41no—
284C11⋊C8#13112yescomplemented
285C2×#131—221no—
286#532—111no—
287#529—111no—
288#501—111no—
289#496—111no—
290#490—111no—
291#489—111no—
292#469—111no—
293#469—111no—
294#468—111no—
295#468—111no—
296#446—111no—
297C8×Q8—111no—
298C4×SD16—111no—
299C4×SD16—111no—
300C4×D8—111no—
301C4×D8C2×D1111yescharacteristic
302#436—111no—
303#436—111no—
304#436—111no—
305#436—221no—
306#435—221no—
307C8×D4—111no—
308C8×D4—221no—
309C8×D4—221no—
310C8×D4C2×D1111yescharacteristic
311C8×D4C2×D1111yescharacteristic
312#433—221no—
313#432—111no—
314#431—111no—
315#423—111no—
316#408—221no—
317#405—221no—
318C4×M16—111no—
319C2×C4×C8—111no—
320#335—111no—
321#335C2×D1111yescharacteristic
322#334—111no—
323#334—111no—
324Q8⋊C8—111no—
325Q8⋊C8—111no—
326D4⋊C8—111no—
327D4⋊C8—111no—
328D4⋊C8—111no—
329D4⋊C8—111no—
330D4⋊C8C2×D1111yescharacteristic
331D4⋊C8C2×D1111yescharacteristic
332#322—111no—
333#322—111no—
334C82—111no—
335C82C2×D1111yescharacteristic
336C22×C11—41no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11—41no—
341C22×C11—41no—
342C22×C11C2×C4×D411yescharacteristic
343C2×D11—21no—
344C2×D11—21no—
345C2×D11—21no—
346C2×D11—41no—
347C2×D11—41no—
348C2×D11—41no—
349C4×C11—21no—
350C4×C11—41no—
351C4×C11—41no—
352C4×C11C2×#13111yescharacteristic
353C4×C11C2×#13111yescharacteristic
354C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
355C4×C11#57511yescharacteristic
356Dic11—21no—
357Dic11—21no—
358Dic11—21no—
359Dic11—41no—
360Dic11—41no—
361Dic11—41no—
362C2×#41—221no—
363C2×SD16—111no—
364C2×SD16—111no—
365C2×D8—111no—
366C2×D8C4×D1111yescharacteristic
367#131—444no—
368C2×M16—111no—
369C2×M16—111no—
370C2×M16—221no—
371C2×M16—221no—
372C2×M16—221no—
373C2×M16—221no—
374C22×C8—21no—
375C22×C8—21no—
376C22×C8—111no—
377C22×C8—111no—
378C22×C8—221no—
379C4⋊Q8—111no—
380#127—111no—
381#126—221no—
382#125—111no—
383#124—111no—
384#124—221no—
385#123—221no—
386C22⋊Q8—111no—
387#121—111no—
388#121—111no—
389#121—111no—
390#121—221no—
391C4×Q8—111no—
392C4×D4—111no—
393C4×D4—221no—
394C4×D4—221no—
395C4×D4C22×D1111yescharacteristic
396C4×D4C22×D1111yescharacteristic
397#117—221no—
398C2×C42—111no—
399#107—111no—
400#107C4×D1111yescharacteristic
401#106—111no—
402#106—111no—
403C4⋊C8—111no—
404C4⋊C8—111no—
405C4⋊C8—221no—
406C4⋊C8—221no—
407C4⋊C8—221no—
408C4⋊C8—221no—
409C4⋊C8C22×D1111yescharacteristic
410C4⋊C8C22×D1111yescharacteristic
411#103—111no—
412#103—111no—
413#102—111no—
414#102—111no—
415#102—111no—
416#102—111no—
417#102C4×D1111yescharacteristic
418#102C4×D1111yescharacteristic
419C22⋊C8—21no—
420C22⋊C8—21no—
421C22⋊C8—221no—
422C22⋊C8—221no—
423C22⋊C8—221no—
424C22⋊C8—221no—
425C22⋊C8—221no—
426C22⋊C8—221no—
427#97—111no—
428#97—111no—
429#97—221no—
430#97—221no—
431C4×C8—111no—
432C4×C8—111no—
433C4×C8—111no—
434C4×C8—111no—
435C4×C8—111no—
436C4×C8—221no—
437C4×C8C22×D1111yescharacteristic
438C4×C8C22×D1111yescharacteristic
439C4×C8C22×D1111yescharacteristic
440C2×C11—81no—
441C2×C11—81no—
442C2×C11#293111yescharacteristic
443C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
444C2×C11#295511yescharacteristic
445D11—41no—
446D11—81no—
447#41—442no—
448#41—442no—
449C2×Q8—111no—
450C2×Q8—221no—
451C2×D4—111no—
452C2×D4—221no—
453C2×D4—221no—
454C2×D4—221no—
455C2×D4—221no—
456C2×D4—221no—
457C2×D4C2×C4×D1111yescharacteristic
458C2×D4C2×C4×D1111yescharacteristic
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—111no—
462C22×C4—111no—
463C22×C4—111no—
464C22×C4—221no—
465SD16—222no—
466SD16—222no—
467D8—22no—
468D8—222no—
469M16—222no—
470M16—222no—
471M16—442no—
472M16—442no—
473M16—442no—
474M16—442no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—42no—
479C2×C8—42no—
480C2×C8—111no—
481C2×C8—111no—
482C2×C8—111no—
483C2×C8—111no—
484C2×C8—222no—
485C2×C8—221no—
486C2×C8—221no—
487C2×C8—221no—
488C2×C8—441no—
489C2×C8—442no—
490C2×C8C2×C4×D1111yescharacteristic
491C2×C8C2×C4×D1111yescharacteristic
492C2×C8D4×D1111yescharacteristic
493C2×C8D4×D1111yescharacteristic
494C4⋊C4—111no—
495C4⋊C4—111no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4—221no—
501C4⋊C4C2×C4×D1111yescharacteristic
502C4⋊C4C2×C4×D1111yescharacteristic
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—221no—
506C22⋊C4—221no—
507C22⋊C4—221no—
508C22⋊C4—221no—
509C22⋊C4—221no—
510C22⋊C4—221no—
511C22⋊C4—221no—
512C42—111no—
513C42—111no—
514C42—111no—
515C42—221no—
516C42C23×D1111yescharacteristic
517C11#1796411yescharacteristic, complemented, Sylow
518C23—21no—
519C23—21no—
520C23—111no—
521C23—221no—
522Q8—221no—
523Q8—221no—
524Q8—442no—
525D4—21no—
526D4—21no—
527D4—21no—
528D4—21no—
529D4—221no—
530D4—221no—
531D4—442no—
532D4—442no—
533D4—442no—
534D4—442no—
535D4—442no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—111no—
543C2×C4—111no—
544C2×C4—111no—
545C2×C4—221no—
546C2×C4—221no—
547C2×C4—221no—
548C2×C4—221no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—221no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4C22×C4×D1111yescharacteristic
556C2×C4C2×D4×D1111yescharacteristic
557C2×C4#41×D1111yescharacteristic
558C8—21no—
559C8—21no—
560C8—41no—
561C8—41no—
562C8—41no—
563C8—112no—
564C8—221no—
565C8—221no—
566C8—221no—
567C8—441no—
568C8—441no—
569C8—441no—
570C8#6695412yescomplemented
571C8#6696412yes—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—221no—
579C22—221no—
580C22—221no—
581C22—441no—
582C22—441no—
583C22—441no—
584C22C4×D4×D1111yescharacteristic
585C4—21no—
586C4—41no—
587C4—41no—
588C4—221no—
589C4—221no—
590C4—221no—
591C4—441no—
592C4—441no—
593C4—441no—
594C4C2×#6695411yescharacteristic
595C4D11×#13111yescharacteristic
596C4C2×#6696411yescharacteristic
597C4#1062329911yescharacteristic
598C2—81no—
599C2—81no—
600C2—441no—
601C2—881no—
602C2#1307732311yescharacteristic
603C2C4×#6696411yescharacteristic
604C2#1307751411yescharacteristic
subgroupG/H
centerC2×C8D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC8×C11×D8C2
socleC22×C11C2×C4×D4
prime radical#13079209C2
cosocleC42×C11C24
hypercenterC8×D8D11
hypocenterC11#17964
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C8 ◁ C4×C8 ◁ C8×D8

Complements

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

NH ≅ G/Ntype
2. #13077588C2semidirect
3. #13077323C2semidirect
4. #13067530C2semidirect
5. #13067527C2semidirect
6. #13067517C2semidirect
7. #13067515C2semidirect
8. C8×#4314C2semidirect
9. C8×#4324C2semidirect
10. C8×#4323C2semidirect
11. #13067382C2semidirect
12. #13067083C2semidirect
13. #13067078C2semidirect
14. C8×#4313C2semidirect
15. C8×C11×D8C2semidirect
226. C8×D8D11semidirect
276. C8×C11#131semidirect
284. C11⋊C8#131semidirect
517. C11#17964semidirect
570. C8#66954semidirect

Maximal subgroups

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

subgroupindex
#130792092
#130775882
#130773232
#130675302
#130675272
#130675172
#130675152
C8×#43142
C8×#43242
C8×#43232
#130673822
#130670832
#130670782
C8×#43132
C8×C11×D82
#1796411