Finite Group Databasebeta

← #14723821

Subgroups — #14723821

Order 2816.

692 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078674C211yesmaximal, characteristic
2C8×#4343C211yesmaximal, characteristic, complemented
3#13077325C211yesmaximal, characteristic, complemented
4#13067459C211yesmaximal, characteristic, complemented
5#13067447C211yesmaximal, characteristic, complemented
6#13067443C211yesmaximal, characteristic, complemented
7#13067439C211yesmaximal, characteristic, complemented
8#13067437C211yesmaximal, characteristic, complemented
9#13067431C211yesmaximal, characteristic, complemented
10SD16⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
11#13067403C211yesmaximal, characteristic, complemented
12#13067054C211yesmaximal, characteristic, complemented
13#13067031C211yesmaximal, characteristic, complemented
14#13066902C211yesmaximal, characteristic, complemented
15C11×#1583C211yesmaximal, characteristic, complemented
16C2×#66960—21no—
17C4×#4343C2211yescharacteristic
18#10623079C2211yescharacteristic
19C8×Q8×C11C2211yescharacteristic
20C4×C11×SD16C2211yescharacteristic
21C11×#436C2211yescharacteristic
22#10622785C411yescharacteristic
23#10622776C411yescharacteristic
24#10622741—21no—
25C4×#4325C2211yescharacteristic
26Q8×C11⋊C8C2211yescharacteristic
27C4×#4323C2211yescharacteristic
28D4×C11⋊C8C2211yescharacteristic
29#10622483C411yescharacteristic
30#10622479C411yescharacteristic
31#10622450C2211yescharacteristic
32#10622447—21no—
33#10622447C2211yescharacteristic
34#10622447C2211yescharacteristic
35#10622446—21no—
36#10622446C2211yescharacteristic
37#10622424C411yescharacteristic
38#10622407C411yescharacteristic
39#10622399C411yescharacteristic
40#10622397C411yescharacteristic
41#10622340—21no—
42(C22⋊D11)⋊C8—21no—
43C4×D88C2211yescharacteristic
44#10622301C2211yescharacteristic
45C4×#4313C2211yescharacteristic
46C8×D44—21no—
47C8×D44C2211yescharacteristic
48#10622298C2211yescharacteristic
49C4×C8×D11—21no—
50C4×C8×D11C2211yescharacteristic
51C11×#334C2211yescharacteristic
52C11×Q8⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic
54C11×#322C2211yescharacteristic
55Q8⋊(C11⋊C8)C2211yescharacteristic
56D4⋊(C11⋊C8)C2211yescharacteristic
57#10622121C2211yescharacteristic
58#10622121C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622117C2211yescharacteristic
61#10622097C2211yescharacteristic
62#10622097C2211yescharacteristic
63#10622096C2211yescharacteristic
64#10622093C2211yescharacteristic
65#10622093C2211yescharacteristic
66#10622092C2211yescharacteristic
67C2×#4343C2×C411yescharacteristic
68C2×#4339—21no—
69C2×C11×SD16C2×C411yescharacteristic
70C2×C11×M16—21no—
71C4×Q8×C11C2311yescharacteristic
72C4×D4×C11C2311yescharacteristic
73Q8×Dic11C2×C411yescharacteristic
74C2×#4325C2×C411yescharacteristic
75#66993C2×C411yescharacteristic
76#66991C2×C411yescharacteristic
77C2×#4323C2×C411yescharacteristic
78C4×C22⋊D11—21no—
79C22×C11⋊C8—21no—
80#66960—44no—
81C2×D88C2×C411yescharacteristic
82C2×#4313—21no—
83C2×#4313—21no—
84C2×#4313—21no—
85C2×C8×D11—21no—
86C2×C8×D11—21no—
87C2×C8×D11—21no—
88C2×C8×D11D411yescharacteristic
89C2×C8×D11D411yescharacteristic
90#66948C2×C411yescharacteristic
91#66946—21no—
92#66946C2×C411yescharacteristic
93#66945—21no—
94#66945C2×C411yescharacteristic
95#66941C2×C411yescharacteristic
96#66938—21no—
97#66937—21no—
98C4×D44—21no—
99C4×D44C2311yescharacteristic
100C4×D44C2311yescharacteristic
101C42×D11—21no—
102C42×D11C2311yescharacteristic
103C11×#106C2×C411yescharacteristic
104C11×C4⋊C8—21no—
105C11×C4⋊C8C2311yescharacteristic
106C11×C4⋊C8C2311yescharacteristic
107C11×#103C2×C411yescharacteristic
108C11×#102C2×C411yescharacteristic
109C11×C22⋊C8—21no—
110C4×C8×C11—21no—
111C4×C8×C11C2311yescharacteristic
112C4×C8×C11C2311yescharacteristic
113C4×C8×C11C2311yescharacteristic
114#66899C2×C411yescharacteristic
115#66896C2×C411yescharacteristic
116C22⋊(C11⋊C8)—21no—
117#66885C2×C411yescharacteristic
118#66885C2×C411yescharacteristic
119(C2×D11)⋊C8—21no—
120(C2×D11)⋊C8—21no—
121(C2×D11)⋊C8—21no—
122(C2×D11)⋊C8—21no—
123(C2×D11)⋊C8—21no—
124(C2×D11)⋊C8C2×C411yescharacteristic
125(C2×D11)⋊C8C2×C411yescharacteristic
126#66882C2×C411yescharacteristic
127#66879—21no—
128Dic11⋊C8—21no—
129Dic11⋊C8C2×C411yescharacteristic
130Dic11⋊C8C2×C411yescharacteristic
131C8×Dic11—21no—
132C8×Dic11D411yescharacteristic
133C8×Dic11D411yescharacteristic
134#66873C2×C411yescharacteristic
135#66873C2×C411yescharacteristic
136#66872C2×C411yescharacteristic
137#66871C2×C411yescharacteristic
138C4⋊(C11⋊C8)—21no—
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4×C11⋊C8—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#17917—111nomaximal, Sylow
146C2×Q8×C11C22×C411yescharacteristic
147C2×D4×C11C22×C411yescharacteristic
148C22×C4×C11—21no—
149C2×C22⋊D11—21no—
150C2×C22⋊D11—21no—
151C2×C22⋊D11—21no—
152#4343—22no—
153#4343—22no—
154#4339—42no—
155#4339—42no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44C22×C411yescharacteristic
159C2×D44C22×C411yescharacteristic
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×C4×D11—21no—
164C2×C4×D11C22×C411yescharacteristic
165C2×C4×D11C2×D411yescharacteristic
166C2×C4×D11#4111yescharacteristic
167C2×Dic22—21no—
168C11×SD16—22no—
169C11×M16—42no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11C22×C411yescharacteristic
174C2×C8×C11C22×C411yescharacteristic
175C2×C8×C11C2×D411yescharacteristic
176C2×C8×C11C2×D411yescharacteristic
177C11×C4⋊C4—21no—
178C11×C4⋊C4C22×C411yescharacteristic
179C11×C4⋊C4C22×C411yescharacteristic
180C11×C22⋊C4—21no—
181C42×C11—21no—
182C42×C11C2411yescharacteristic
183C22⋊Dic11—21no—
184#4325—22no—
185#4323—22no—
186(C2×D11)⋊C4—21no—
187(C2×D11)⋊C4—21no—
188(C2×D11)⋊C4—21no—
189(C2×D11)⋊C4—21no—
190(C2×D11)⋊C4—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11C22×C411yescharacteristic
193C4⋊Dic11C22×C411yescharacteristic
194Dic11⋊C4—21no—
195C4×Dic11—21no—
196C4×Dic11—21no—
197C4×Dic11C22×C411yescharacteristic
198C4×Dic11C2×D411yescharacteristic
199C4×Dic11#4111yescharacteristic
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—42no—
204C2×C11⋊C8C22×C411yescharacteristic
205C2×C11⋊C8C22×C411yescharacteristic
206C2×C11⋊C8C2×D411yescharacteristic
207C2×C11⋊C8C2×D411yescharacteristic
208D88—22no—
209#4313—42no—
210#4313—42no—
211#4313—42no—
212C8×D11—22no—
213C8×D11—41no—
214C8×D11—42no—
215C8×D11—42no—
216C8×D11—42no—
217#3106—111no—
218C8×#41—111no—
219#2931—111no—
220#1583—111no—
221#1583D1111yescharacteristic, complemented
222#1581—111no—
223#1581—111no—
224#1580—111no—
225#1580—111no—
226SD16⋊C8—111no—
227SD16⋊C8—111no—
228#1574—111no—
229#1489—111no—
230#1484—111no—
231#1451—111no—
232C23×C11—21no—
233C22×D11—21no—
234C22×D11—21no—
235C22×D11C4×D411yescharacteristic
236Q8×C11—21no—
237Q8×C11#13112yescomplemented
238D4×C11—21no—
239D4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
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—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11C4×D411yescharacteristic
254C2×Dic11C4×D411yescharacteristic
255C2×Dic11C4×D411yescharacteristic
256D44—24no—
257D44—21no—
258D44—21no—
259D44—21no—
260D44—42no—
261D44#13112yescomplemented
262C4×D11—24no—
263C4×D11—21no—
264C4×D11—21no—
265C4×D11—21no—
266C4×D11—21no—
267C4×D11—22no—
268C4×D11—41no—
269C4×D11—41no—
270C4×D11—41no—
271C4×D11—41no—
272C4×D11—42no—
273Dic22—42no—
274C8×C11—21no—
275C8×C11—21no—
276C8×C11—21no—
277C8×C11—41no—
278C8×C11—41no—
279C8×C11—41no—
280C8×C11AGL(1,ℤ/8)12yes—
281C11⋊C8—21no—
282C11⋊C8—21no—
283C11⋊C8—21no—
284C11⋊C8—21no—
285C11⋊C8—41no—
286C11⋊C8—41no—
287C11⋊C8—41no—
288C2×#131—221no—
289#532—111no—
290C4×#41—111no—
291#482—111no—
292#482—111no—
293#477—111no—
294#476—111no—
295#460—111no—
296#459—111no—
297#449—111no—
298#449—111no—
299C8×Q8—111no—
300C8×Q8C2×D1111yescharacteristic
301C4×SD16—111no—
302C4×SD16C2×D1111yescharacteristic
303C4×D8—111no—
304C4×D8—111no—
305#436—111no—
306#436—221no—
307#436C2×D1111yescharacteristic
308C8×D4—111no—
309C8×D4—111no—
310C8×D4—111no—
311C8×D4—111no—
312C8×D4—221no—
313C8×D4—221no—
314C8×D4—221no—
315#431—111no—
316#431—111no—
317#431—221no—
318#423—111no—
319#408—221no—
320C4×M16—111no—
321C2×C4×C8—111no—
322C2×C4×C8—221no—
323#335—111no—
324#335—111no—
325#334—111no—
326#334C2×D1111yescharacteristic
327Q8⋊C8—111no—
328Q8⋊C8C2×D1111yescharacteristic
329D4⋊C8—111no—
330D4⋊C8—111no—
331D4⋊C8—111no—
332D4⋊C8—111no—
333D4⋊C8—111no—
334D4⋊C8C2×D1111yescharacteristic
335#322—111no—
336#322—111no—
337#322—111no—
338#322C2×D1111yescharacteristic
339C22×C11—41no—
340C22×C11—41no—
341C22×C11—41no—
342C22×C11C2×C4×D411yescharacteristic
343C2×D11—22no—
344C2×D11—21no—
345C2×D11—21no—
346C2×D11—21no—
347C2×D11—41no—
348C2×D11—41no—
349C2×D11—41no—
350C2×D11—41no—
351C2×D11—41no—
352C4×C11—22no—
353C4×C11—21no—
354C4×C11—41no—
355C4×C11—41no—
356C4×C11C2×#13111yescharacteristic
357C4×C11C2×#13111yescharacteristic
358C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
359C4×C11#57511yescharacteristic
360Dic11—21no—
361Dic11—21no—
362Dic11—41no—
363Dic11—41no—
364Dic11#44412yes—
365C2×#41—111no—
366C2×#41—221no—
367C2×SD16—111no—
368C2×SD16C4×D1111yescharacteristic
369C2×D8—111no—
370C2×D8—111no—
371#131—444no—
372C2×M16—21no—
373C2×M16—221no—
374C2×M16—221no—
375C2×M16—221no—
376C22×C8—111no—
377C22×C8—111no—
378C22×C8—221no—
379C22×C8—221no—
380C22×C8—221no—
381C22×C8—221no—
382C4⋊Q8—111no—
383#127—111no—
384#124—221no—
385#121—111no—
386#121—111no—
387#121—221no—
388C4×Q8—111no—
389C4×Q8C22×D1111yescharacteristic
390C4×D4—111no—
391C4×D4—111no—
392C4×D4—111no—
393C4×D4—221no—
394C4×D4—221no—
395C4×D4—221no—
396C4×D4C22×D1111yescharacteristic
397#117—111no—
398#117—221no—
399C2×C42—111no—
400C2×C42—221no—
401#107—111no—
402#107—111no—
403#106—111no—
404#106C4×D1111yescharacteristic
405C4⋊C8—21no—
406C4⋊C8—111no—
407C4⋊C8—111no—
408C4⋊C8—111no—
409C4⋊C8—111no—
410C4⋊C8—221no—
411C4⋊C8—221no—
412C4⋊C8C22×D1111yescharacteristic
413C4⋊C8C22×D1111yescharacteristic
414#103—111no—
415#103C4×D1111yescharacteristic
416#102—111no—
417#102—111no—
418#102—111no—
419#102—111no—
420#102—111no—
421#102C4×D1111yescharacteristic
422C22⋊C8—21no—
423C22⋊C8—111no—
424C22⋊C8—111no—
425C22⋊C8—221no—
426C22⋊C8—221no—
427C22⋊C8—221no—
428C22⋊C8—221no—
429C22⋊C8—221no—
430C22⋊C8—221no—
431#97—221no—
432C4×C8—21no—
433C4×C8—111no—
434C4×C8—111no—
435C4×C8—111no—
436C4×C8—111no—
437C4×C8—111no—
438C4×C8—221no—
439C4×C8—221no—
440C4×C8C22×D1111yescharacteristic
441C4×C8C22×D1111yescharacteristic
442C4×C8C22×D1111yescharacteristic
443C2×C11—81no—
444C2×C11#292911yescharacteristic
445C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
446C2×C11C2×#44411yescharacteristic
447D11—41no—
448D11—42no—
449D11—81no—
450#41—222no—
451#41—222no—
452#41—442no—
453#41—442no—
454C2×Q8—221no—
455C2×Q8C2×C4×D1111yescharacteristic
456C2×D4—111no—
457C2×D4—111no—
458C2×D4—221no—
459C2×D4—221no—
460C2×D4—221no—
461C2×D4—221no—
462C2×D4—221no—
463C2×D4C2×C4×D1111yescharacteristic
464C22×C4—21no—
465C22×C4—111no—
466C22×C4—111no—
467C22×C4—111no—
468C22×C4—221no—
469C22×C4—221no—
470C22×C4—221no—
471C22×C4—221no—
472SD16—22no—
473SD16—222no—
474D8—222no—
475D8—222no—
476M16—42no—
477M16—442no—
478M16—442no—
479M16—442no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—111no—
484C2×C8—111no—
485C2×C8—111no—
486C2×C8—111no—
487C2×C8—222no—
488C2×C8—221no—
489C2×C8—221no—
490C2×C8—221no—
491C2×C8—441no—
492C2×C8—442no—
493C2×C8—442no—
494C2×C8—442no—
495C2×C8—442no—
496C2×C8C2×C4×D1111yescharacteristic
497C2×C8C2×C4×D1111yescharacteristic
498C2×C8D4×D1111yescharacteristic
499C2×C8D4×D1111yescharacteristic
500C4⋊C4—21no—
501C4⋊C4—111no—
502C4⋊C4—111no—
503C4⋊C4—221no—
504C4⋊C4—221no—
505C4⋊C4C2×C4×D1111yescharacteristic
506C4⋊C4C2×C4×D1111yescharacteristic
507C22⋊C4—21no—
508C22⋊C4—221no—
509C22⋊C4—221no—
510C22⋊C4—221no—
511C22⋊C4—221no—
512C22⋊C4—221no—
513C22⋊C4—221no—
514C42—21no—
515C42—111no—
516C42—111no—
517C42—111no—
518C42—221no—
519C42—221no—
520C42C23×D1111yescharacteristic
521C11#1791711yescharacteristic, complemented, Sylow
522C23—21no—
523C23—111no—
524C23—221no—
525C23—221no—
526Q8—21no—
527Q8—442no—
528Q8#6696012yescomplemented
529D4—21no—
530D4—21no—
531D4—112no—
532D4—224no—
533D4—221no—
534D4—221no—
535D4—221no—
536D4—442no—
537D4—442no—
538D4—442no—
539D4—442no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—111no—
546C2×C4—111no—
547C2×C4—111no—
548C2×C4—222no—
549C2×C4—224no—
550C2×C4—221no—
551C2×C4—221no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—221no—
555C2×C4—221no—
556C2×C4—442no—
557C2×C4—441no—
558C2×C4—441no—
559C2×C4—441no—
560C2×C4—441no—
561C2×C4C22×C4×D1111yescharacteristic
562C2×C4C2×D4×D1111yescharacteristic
563C2×C4#41×D1111yescharacteristic
564C8—21no—
565C8—21no—
566C8—21no—
567C8—41no—
568C8—41no—
569C8—41no—
570C8—221no—
571C8—221no—
572C8—221no—
573C8—221no—
574C8—441no—
575C8—441no—
576C8—441no—
577C8#6696712yes—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—221no—
582C22—222no—
583C22—221no—
584C22—221no—
585C22—441no—
586C22—441no—
587C22—441no—
588C22—441no—
589C22—441no—
590C22C4×D4×D1111yescharacteristic
591C4—21no—
592C4—22no—
593C4—41no—
594C4—41no—
595C4—112no—
596C4—221no—
597C4—221no—
598C4—441no—
599C4—441no—
600C4C2×#6696011yescharacteristic
601C4D11×#13111yescharacteristic
602C4C2×#6696711yescharacteristic
603C4#1062329911yescharacteristic
604C2—81no—
605C2—441no—
606C2—442no—
607C2—881no—
608C2#1307730711yescharacteristic
609C2C4×#6696711yescharacteristic
610C2D11×#44411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1583C2
socleC22×C11C2×C4×D4
prime radical#13078674C2
cosocleC42×C11C24
hypercenter#1583D11
hypocenterC11#17917
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1583

Complements

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

NH ≅ G/Ntype
2. C8×#4343C2semidirect
3. #13077325C2semidirect
4. #13067459C2semidirect
5. #13067447C2semidirect
6. #13067443C2semidirect
7. #13067439C2semidirect
8. #13067437C2semidirect
9. #13067431C2semidirect
10. SD16⋊(C11⋊C8)C2semidirect
11. #13067403C2semidirect
12. #13067054C2semidirect
13. #13067031C2semidirect
14. #13066902C2semidirect
15. C11×#1583C2semidirect
221. #1583D11semidirect
237. Q8×C11#131semidirect
261. D44#131semidirect
521. C11#17917semidirect
528. Q8#66960semidirect

Maximal subgroups

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

subgroupindex
#130786742
C8×#43432
#130773252
#130674592
#130674472
#130674432
#130674392
#130674372
#130674312
SD16⋊(C11⋊C8)2
#130674032
#130670542
#130670312
#130669022
C11×#15832
#1791711