Finite Group Databasebeta

← #14724804

Subgroups — #14724804

Order 2816.

670 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#13078667C211yesmaximal, characteristic
2#13077619C211yesmaximal, characteristic, complemented
3D4×#4313C211yesmaximal, characteristic, complemented
4#13067531C211yesmaximal, characteristic, complemented
5#13067503C211yesmaximal, characteristic, complemented
6#13067494C211yesmaximal, characteristic, complemented
7#13067480C211yesmaximal, characteristic, complemented
8#13067453C211yesmaximal, characteristic, complemented
9#13067444C211yesmaximal, characteristic, complemented
10#13067408C211yesmaximal, characteristic, complemented
11#13067406C211yesmaximal, characteristic, complemented
12#13067080C211yesmaximal, characteristic, complemented
13#13067005C211yesmaximal, characteristic, complemented
14#13066912C211yesmaximal, characteristic, complemented
15C11×SD16⋊C8C211yesmaximal, characteristic, complemented
16C22×#4313—21no—
17#10623111C2211yescharacteristic
18C4×D4×D11C2211yescharacteristic
19C8×Q8×C11C2211yescharacteristic, complemented
20C4×C11×SD16C2211yescharacteristic
21C8×D4×C11C2211yescharacteristic
22#10622782C411yescharacteristic
23#10622778C411yescharacteristic
24#10622724—21no—
25C4×#4325C2211yescharacteristic
26#10622637C2211yescharacteristic, complemented
27C4×#4323C2211yescharacteristic
28D4×C11⋊C8C2211yescharacteristic
29#10622484C411yescharacteristic
30#10622476C411yescharacteristic
31#10622453—21no—
32#10622451C2211yescharacteristic
33#10622450C2211yescharacteristic
34#10622449—21no—
35#10622447C2211yescharacteristic, complemented
36#10622446C2211yescharacteristic
37#10622432C411yescharacteristic
38#10622422C411yescharacteristic
39#10622386C411yescharacteristic
40#10622379C411yescharacteristic
41#10622343—21no—
42#10622339—21no—
43C4×D88C2211yescharacteristic
44#10622302—21no—
45#10622301—21no—
46#10622301C2211yescharacteristic
47#10622301C2211yescharacteristic, complemented
48C4×#4313C2211yescharacteristic
49#10622298C2211yescharacteristic
50#10622298C2211yescharacteristic
51C11×#335C2211yescharacteristic, complemented
52C11×Q8⋊C8C2211yescharacteristic, complemented
53C11×D4⋊C8C2211yescharacteristic
54C11×#322C2211yescharacteristic, complemented
55Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
56D4⋊(C11⋊C8)C2211yescharacteristic
57#10622121C2211yescharacteristic
58#10622121C2211yescharacteristic, complemented
59#10622118C2211yescharacteristic, complemented
60#10622117C2211yescharacteristic, complemented
61#10622097C2211yescharacteristic
62#10622097C2211yescharacteristic, complemented
63#10622095C2211yescharacteristic, complemented
64#10622092C2211yescharacteristic, complemented
65#10622092C2211yescharacteristic, complemented
66C8×C11⋊C8C2211yescharacteristic, complemented
67C2×D4×D11C2×C411yescharacteristic
68C22×C4×D11—21no—
69C2×C11×SD16C2×C411yescharacteristic
70C22×C8×C11—21no—
71C4×Q8×C11C2311yescharacteristic
72C4×D4×C11C2311yescharacteristic
73#67000C2×C411yescharacteristic
74#66999C2×C411yescharacteristic
75C2×#4325C2×C411yescharacteristic
76D4×Dic11C2×C411yescharacteristic
77C2×#4323C2×C411yescharacteristic
78C4×C22⋊D11—21no—
79C22×C11⋊C8—21no—
80C2×D88C2×C411yescharacteristic
81C2×#4313—21no—
82C2×#4313—21no—
83C2×#4313—21no—
84C2×#4313—21no—
85C2×#4313—44no—
86C2×#4313D411yescharacteristic
87C2×#4313D411yescharacteristic
88C2×C8×D11—21no—
89#66951—21no—
90#66948C2×C411yescharacteristic
91#66947—21no—
92#66946C2×C411yescharacteristic
93C4⋊C4×D11C2×C411yescharacteristic
94#66943C2×C411yescharacteristic
95(C22⋊D11)⋊C4—21no—
96C22⋊C4×D11—21no—
97C4×D44—21no—
98C4×D44C2311yescharacteristic
99C4×D44C2311yescharacteristic
100#66925—21no—
101C42×D11C2311yescharacteristic
102C11×#106C2×C411yescharacteristic
103C11×C4⋊C8—21no—
104C11×C4⋊C8C2311yescharacteristic
105C11×C4⋊C8C2311yescharacteristic
106C11×#103C2×C411yescharacteristic
107C11×#102C2×C411yescharacteristic
108C11×C22⋊C8—21no—
109C4×C8×C11—21no—
110C4×C8×C11C2311yescharacteristic
111C4×C8×C11C2311yescharacteristic
112C4×C8×C11C2311yescharacteristic
113#66899C2×C411yescharacteristic
114#66896C2×C411yescharacteristic
115C22⋊(C11⋊C8)—21no—
116#66885C2×C411yescharacteristic
117#66885C2×C411yescharacteristic
118(C2×D11)⋊C8—21no—
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#66879D411yescharacteristic
128#66879D411yescharacteristic
129Dic11⋊C8—21no—
130Dic11⋊C8—21no—
131Dic11⋊C8C2×C411yescharacteristic
132Dic11⋊C8C2×C411yescharacteristic
133C8×Dic11—21no—
134#66873C2×C411yescharacteristic
135#66873C2×C411yescharacteristic
136#66872C2×C411yescharacteristic
137#66871C2×C411yescharacteristic
138C4⋊(C11⋊C8)—21no—
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141#66867—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#18006—111nomaximal, Sylow
146C23×D11—21no—
147C2×Q8×C11C22×C411yescharacteristic
148C2×D4×C11C22×C411yescharacteristic
149C22×C4×C11—21no—
150C2×C22⋊D11—21no—
151C22×Dic11—21no—
152D4×D11—22no—
153D4×D11—41no—
154C2×D44—21no—
155C2×D44C22×C411yescharacteristic
156C2×D44C22×C411yescharacteristic
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11—42no—
162C2×C4×D11—42no—
163C2×C4×D11C22×C411yescharacteristic
164C2×C4×D11C2×D411yescharacteristic
165C2×C4×D11#4111yescharacteristic
166C11×SD16—22no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—42no—
171C2×C8×C11C22×C411yescharacteristic
172C2×C8×C11C22×C411yescharacteristic
173C2×C8×C11C2×D411yescharacteristic
174C2×C8×C11C2×D411yescharacteristic
175C11×C4⋊C4—21no—
176C11×C4⋊C4C22×C411yescharacteristic
177C11×C4⋊C4C22×C411yescharacteristic
178C11×C22⋊C4—21no—
179C42×C11—21no—
180C42×C11C2411yescharacteristic
181C22⋊Dic11—21no—
182#4325—41no—
183#4323—22no—
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—
189(C2×D11)⋊C4—21no—
190(C2×D11)⋊C4—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11C22×C411yescharacteristic
193C4⋊Dic11C22×C411yescharacteristic
194Dic11⋊C4—21no—
195Dic11⋊C4—21no—
196Dic11⋊C4—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—41no—
209#4313—22no—
210#4313—41no—
211#4313—42no—
212#4313—42no—
213#4313—42no—
214#4313—42no—
215C8×D11—42no—
216#3105—111no—
217#2969—111no—
218D4×M16—111no—
219#1594—111no—
220#1590—111no—
221#1588—111no—
222#1586—111no—
223#1582—111no—
224#1581—111no—
225SD16⋊C8D1111yescharacteristic, complemented
226C8×D8—111no—
227#1574—111no—
228#1495—111no—
229#1478—111no—
230#1453—111no—
231C23×C11—21no—
232C22×D11—21no—
233C22×D11—21no—
234C22×D11—42no—
235C22×D11—42no—
236C22×D11—81no—
237C22×D11C4×D411yescharacteristic
238Q8×C11—21no—
239Q8×C11—21no—
240D4×C11—21no—
241D4×C11#13112yes—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11C23×C411yescharacteristic
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C22⋊D11—42no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—42no—
254C2×Dic11C4×D411yescharacteristic
255C2×Dic11C4×D411yescharacteristic
256C2×Dic11C4×D411yescharacteristic
257D44—21no—
258D44—21no—
259D44—21no—
260D44—21no—
261D44—81no—
262C4×D11—21no—
263C4×D11—21no—
264C4×D11—21no—
265C4×D11—21no—
266C4×D11—41no—
267C4×D11—42no—
268C4×D11—42no—
269C4×D11—41no—
270C4×D11—41no—
271C4×D11—41no—
272C4×D11—41no—
273C8×C11—21no—
274C8×C11—21no—
275C8×C11—21no—
276C8×C11—21no—
277C8×C11—41no—
278C8×C11—41no—
279C8×C11—41no—
280C11⋊C8—21no—
281C11⋊C8—21no—
282C11⋊C8—21no—
283C11⋊C8—41no—
284C11⋊C8—41no—
285C11⋊C8—41no—
286C11⋊C8AGL(1,ℤ/8)12yes—
287C22×M16—221no—
288#529—111no—
289C2×C4×D4—111no—
290#484—111no—
291#481—111no—
292#478—111no—
293#478—111no—
294#463—111no—
295#463—111no—
296#450—111no—
297#447—111no—
298#446—111no—
299C8×Q8C2×D1111yescharacteristic, complemented
300C4×SD16—111no—
301C4×SD16C2×D1111yescharacteristic
302C4×D8—111no—
303C4×D8—111no—
304#436—111no—
305#436—111no—
306#436—111no—
307#436—221no—
308#435—221no—
309#435—221no—
310#435—221no—
311C8×D4—111no—
312C8×D4—111no—
313C8×D4C2×D1111yescharacteristic
314#433—221no—
315#431—111no—
316#431—111no—
317#431—111no—
318#423—111no—
319#407—221no—
320#405—221no—
321C4×M16—111no—
322#335—111no—
323#335C2×D1111yescharacteristic, complemented
324#334—111no—
325#334—111no—
326Q8⋊C8—111no—
327Q8⋊C8C2×D1111yescharacteristic, complemented
328D4⋊C8—111no—
329D4⋊C8—111no—
330D4⋊C8—111no—
331D4⋊C8—111no—
332D4⋊C8—111no—
333D4⋊C8C2×D1111yescharacteristic
334#322—111no—
335#322—111no—
336#322C2×D1111yescharacteristic, complemented
337C82—111no—
338C22×C11—22no—
339C22×C11—41no—
340C22×C11—41no—
341C22×C11C2×C4×D411yescharacteristic
342C2×D11—21no—
343C2×D11—21no—
344C2×D11—21no—
345C2×D11—41no—
346C2×D11—41no—
347C2×D11—41no—
348C2×D11—41no—
349C2×D11—41no—
350C2×D11—41no—
351C2×D11—84no—
352C4×C11—21no—
353C4×C11—41no—
354C4×C11—41no—
355C4×C11—41no—
356C4×C11C2×#13111yescharacteristic
357C4×C11#56811yescharacteristic
358C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
359C4×C11#57511yescharacteristic
360Dic11—21no—
361Dic11—21no—
362Dic11—21no—
363Dic11—41no—
364Dic11—41no—
365C22×D4—111no—
366C23×C4—221no—
367C2×SD16—111no—
368C2×SD16C4×D1111yescharacteristic
369C2×D8—111no—
370C2×D8—111no—
371C2×M16—111no—
372C2×M16—111no—
373C2×M16—221no—
374C2×M16—221no—
375C2×M16—221no—
376C2×M16—221no—
377C2×M16—444no—
378C22×C8—21no—
379C22×C8—221no—
380C22×C8—221no—
381#126—221no—
382#125—111no—
383#124—111no—
384#123—221no—
385C22⋊Q8—111no—
386#121—111no—
387C4×Q8C22×D1111yescharacteristic
388C4×D4—111no—
389C4×D4—111no—
390C4×D4—111no—
391C4×D4—111no—
392C4×D4—221no—
393C4×D4—221no—
394C4×D4—221no—
395C4×D4C22×D1111yescharacteristic
396#117—221no—
397C2×C4⋊C4—111no—
398C2×C22⋊C4—221no—
399C2×C42—111no—
400#107—111no—
401#107—111no—
402#106—111no—
403#106C4×D1111yescharacteristic
404C4⋊C8—21no—
405C4⋊C8—111no—
406C4⋊C8—111no—
407C4⋊C8—111no—
408C4⋊C8—111no—
409C4⋊C8—221no—
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—
431C22⋊C8—221no—
432#97—111no—
433#97—111no—
434#97—221no—
435C4×C8—21no—
436C4×C8—111no—
437C4×C8—111no—
438C4×C8—111no—
439C4×C8—221no—
440C4×C8C22×D1111yescharacteristic
441C4×C8C22×D1111yescharacteristic
442C4×C8C22×D1111yescharacteristic
443C2×C11—42no—
444C2×C11#293311yescharacteristic
445C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
446C2×C11#295711yescharacteristic
447D11—41no—
448D11—81no—
449D11—81no—
450C24—221no—
451C2×Q8C2×C4×D1111yescharacteristic
452C2×D4—111no—
453C2×D4—111no—
454C2×D4—221no—
455C2×D4—221no—
456C2×D4—222no—
457C2×D4—441no—
458C2×D4C2×C4×D1111yescharacteristic
459C22×C4—21no—
460C22×C4—111no—
461C22×C4—111no—
462C22×C4—111no—
463C22×C4—221no—
464C22×C4—221no—
465C22×C4—221no—
466C22×C4—221no—
467C22×C4—221no—
468C22×C4—442no—
469C22×C4—442no—
470SD16—22no—
471SD16—441no—
472D8—222no—
473D8—441no—
474M16—222no—
475M16—441no—
476M16—442no—
477M16—442no—
478M16—442no—
479M16—442no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—42no—
484C2×C8—111no—
485C2×C8—111no—
486C2×C8—111no—
487C2×C8—111no—
488C2×C8—221no—
489C2×C8—221no—
490C2×C8—221no—
491C2×C8—442no—
492C2×C8—442no—
493C2×C8C2×C4×D1111yescharacteristic
494C2×C8C2×C4×D1111yescharacteristic
495C2×C8D4×D1111yescharacteristic
496C2×C8D4×D1111yescharacteristic
497C4⋊C4—21no—
498C4⋊C4—111no—
499C4⋊C4—111no—
500C4⋊C4—221no—
501C4⋊C4—221no—
502C4⋊C4—221no—
503C4⋊C4—221no—
504C4⋊C4C2×C4×D1111yescharacteristic
505C4⋊C4C2×C4×D1111yescharacteristic
506C22⋊C4—21no—
507C22⋊C4—221no—
508C22⋊C4—221no—
509C22⋊C4—221no—
510C22⋊C4—221no—
511C22⋊C4—221no—
512C22⋊C4—221no—
513C22⋊C4—221no—
514C22⋊C4—221no—
515C42—21no—
516C42—111no—
517C42—111no—
518C42—111no—
519C42C23×D1111yescharacteristic
520C11#1800611yescharacteristic, complemented, Sylow
521C23—21no—
522C23—111no—
523C23—221no—
524C23—221no—
525C23—442no—
526C23—442no—
527C23—881no—
528Q8—21no—
529Q8—21no—
530D4—21no—
531D4—221no—
532D4—221no—
533D4—221no—
534D4—221no—
535D4—442no—
536D4—881no—
537D4#6695412yes—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—111no—
544C2×C4—111no—
545C2×C4—111no—
546C2×C4—221no—
547C2×C4—221no—
548C2×C4—221no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—221no—
552C2×C4—441no—
553C2×C4—442no—
554C2×C4—442no—
555C2×C4—442no—
556C2×C4—441no—
557C2×C4—441no—
558C2×C4—441no—
559C2×C4—441no—
560C2×C4C22×C4×D1111yescharacteristic
561C2×C4C2×D4×D1111yescharacteristic
562C2×C4#41×D1111yescharacteristic
563C8—21no—
564C8—21no—
565C8—21no—
566C8—21no—
567C8—41no—
568C8—41no—
569C8—41no—
570C8—112no—
571C8—221no—
572C8—221no—
573C8—221no—
574C8—441no—
575C8—441no—
576C8—441no—
577C22—22no—
578C22—41no—
579C22—41no—
580C22—221no—
581C22—221no—
582C22—221no—
583C22—441no—
584C22—441no—
585C22—441no—
586C22—441no—
587C22—441no—
588C22—441no—
589C22—884no—
590C22C4×D4×D1111yescharacteristic
591C4—21no—
592C4—41no—
593C4—41no—
594C4—41no—
595C4—221no—
596C4—221no—
597C4—221no—
598C4—441no—
599C4—441no—
600C4C2×#6695411yescharacteristic
601C4#1062328111yescharacteristic
602C4D11×AGL(1,ℤ/8)11yescharacteristic
603C4#1062330811yescharacteristic
604C2—42no—
605C2—441no—
606C2—881no—
607C2—881no—
608C2#1307733611yescharacteristic
609C2#1307742111yescharacteristic
610C2#1307753011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×SD16⋊C8C2
socleC22×C11C2×C4×D4
prime radical#10622386C4
cosocleC42×C11C24
hypercenterSD16⋊C8D11
hypocenterC11#18006
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ SD16⋊C8

Complements

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

NH ≅ G/Ntype
2. #13077619C2semidirect
3. D4×#4313C2semidirect
4. #13067531C2semidirect
5. #13067503C2semidirect
6. #13067494C2semidirect
7. #13067480C2semidirect
8. #13067453C2semidirect
9. #13067444C2semidirect
10. #13067408C2semidirect
11. #13067406C2semidirect
12. #13067080C2semidirect
13. #13067005C2semidirect
14. #13066912C2semidirect
15. C11×SD16⋊C8C2semidirect
19. C8×Q8×C11C22semidirect
26. #10622637C22semidirect
35. #10622447C22semidirect
47. #10622301C22semidirect
51. C11×#335C22semidirect
52. C11×Q8⋊C8C22semidirect
54. C11×#322C22semidirect
55. Q8⋊(C11⋊C8)C22semidirect
58. #10622121C22semidirect
59. #10622118C22semidirect
60. #10622117C22semidirect
62. #10622097C22semidirect
63. #10622095C22semidirect
64. #10622092C22semidirect
65. #10622092C22semidirect
66. C8×C11⋊C8C22semidirect
225. SD16⋊C8D11semidirect
299. C8×Q8C2×D11semidirect
323. #335C2×D11semidirect
327. Q8⋊C8C2×D11semidirect
336. #322C2×D11semidirect
520. C11#18006semidirect

Maximal subgroups

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

subgroupindex
#130786672
#130776192
D4×#43132
#130675312
#130675032
#130674942
#130674802
#130674532
#130674442
#130674082
#130674062
#130670802
#130670052
#130669122
C11×SD16⋊C82
#1800611