Finite Group Databasebeta

← #14724802

Subgroups — #14724802

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#13078661C211yesmaximal, characteristic
2#13077617C211yesmaximal, characteristic, complemented
3D4×#4313C211yesmaximal, characteristic, complemented
4#13067527C211yesmaximal, characteristic, complemented
5#13067508C211yesmaximal, characteristic, complemented
6#13067493C211yesmaximal, characteristic, complemented
7#13067481C211yesmaximal, characteristic, complemented
8#13067452C211yesmaximal, characteristic, complemented
9#13067445C211yesmaximal, characteristic, complemented
10#13067425C211yesmaximal, characteristic, complemented
11#13067406C211yesmaximal, characteristic, complemented
12#13067078C211yesmaximal, characteristic, complemented
13#13067005C211yesmaximal, characteristic, complemented
14#13066910C211yesmaximal, characteristic, complemented
15C8×C11×D8C211yesmaximal, characteristic, complemented
16C22×#4313—21no—
17#10623088C2211yescharacteristic
18C4×D4×D11C2211yescharacteristic
19C4×C11×D8C2211yescharacteristic
20C8×D4×C11C2211yescharacteristic
21C8×D4×C11C2211yescharacteristic, complemented
22#10622769C411yescharacteristic
23#10622766C411yescharacteristic
24#10622724—21no—
25#10622724—21no—
26#10622714—21no—
27C4×#4324C2211yescharacteristic
28C4×#4323C2211yescharacteristic
29#10622625C2211yescharacteristic, complemented
30D4×C11⋊C8C2211yescharacteristic
31#10622504C411yescharacteristic
32#10622497C411yescharacteristic
33#10622451C2211yescharacteristic
34#10622450C2211yescharacteristic
35#10622446C2211yescharacteristic
36#10622443C2211yescharacteristic, complemented
37#10622400C411yescharacteristic
38#10622390C411yescharacteristic
39#10622389C411yescharacteristic
40#10622376C411yescharacteristic
41#10622343—21no—
42#10622342—21no—
43#10622339—21no—
44#10622333—21no—
45C4×#4314C2211yescharacteristic
46#10622301C2211yescharacteristic
47C4×#4313C2211yescharacteristic
48#10622298C2211yescharacteristic
49#10622298C2211yescharacteristic
50#10622292C2211yescharacteristic, complemented
51C11×#335C2211yescharacteristic, complemented
52C11×D4⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic, complemented
54C82×C11C2211yescharacteristic, complemented
55D4⋊(C11⋊C8)C2211yescharacteristic
56D4⋊(C11⋊C8)C2211yescharacteristic, complemented
57#10622122C2211yescharacteristic, complemented
58#10622121C2211yescharacteristic
59#10622118C2211yescharacteristic, complemented
60#10622117C2211yescharacteristic, complemented
61#10622097C2211yescharacteristic
62#10622095C2211yescharacteristic, complemented
63#10622094C2211yescharacteristic, complemented
64#10622093C2211yescharacteristic, complemented
65#10622092C2211yescharacteristic, complemented
66#10622092C2211yescharacteristic, complemented
67C2×D4×D11C2×C411yescharacteristic
68C22×C4×D11—21no—
69C2×C11×D8C2×C411yescharacteristic
70C22×C8×C11—21no—
71C22×C8×C11—21no—
72C4×D4×C11C2311yescharacteristic
73C4×D4×C11C2311yescharacteristic
74#66991C2×C411yescharacteristic
75#66989C2×C411yescharacteristic
76D4×Dic11C2×C411yescharacteristic
77C2×#4324C2×C411yescharacteristic
78C2×#4323C2×C411yescharacteristic
79C4×C22⋊D11—21no—
80C4×C22⋊D11—21no—
81#66979—21no—
82C2×#4318—21no—
83C22×C11⋊C8—21no—
84C2×#4314C2×C411yescharacteristic
85C2×#4313—21no—
86C2×#4313—21no—
87C2×#4313—21no—
88C2×#4313—44no—
89C2×#4313D411yescharacteristic
90C2×#4313D411yescharacteristic
91#66950C2×C411yescharacteristic
92#66946C2×C411yescharacteristic
93C4⋊C4×D11C2×C411yescharacteristic
94#66943C2×C411yescharacteristic
95#66936—21no—
96(C22⋊D11)⋊C4—21no—
97C22⋊C4×D11—21no—
98#66932—21no—
99C4×D44C2311yescharacteristic
100C42×D11C2311yescharacteristic
101C4×Dic22C2311yescharacteristic
102C11×#107C2×C411yescharacteristic
103C11×C4⋊C8C2311yescharacteristic
104C11×C4⋊C8C2311yescharacteristic
105C11×#102C2×C411yescharacteristic
106C11×#102C2×C411yescharacteristic
107C11×C22⋊C8—21no—
108C11×C22⋊C8—21no—
109C4×C8×C11C2311yescharacteristic
110C4×C8×C11C2311yescharacteristic
111C4×C8×C11C2311yescharacteristic
112#66896C2×C411yescharacteristic
113#66896C2×C411yescharacteristic
114C22⋊(C11⋊C8)—21no—
115C22⋊(C11⋊C8)—21no—
116#66885C2×C411yescharacteristic
117(C2×D11)⋊C8—21no—
118(C2×D11)⋊C8—21no—
119(C2×D11)⋊C8—21no—
120(C2×D11)⋊C8—21no—
121(C2×D11)⋊C8C2×C411yescharacteristic
122(C2×D11)⋊C8C2×C411yescharacteristic
123#66881C2×C411yescharacteristic
124#66880C2×C411yescharacteristic
125#66879—21no—
126#66879D411yescharacteristic
127#66879D411yescharacteristic
128Dic11⋊C8—21no—
129Dic11⋊C8—21no—
130Dic11⋊C8—21no—
131Dic11⋊C8—21no—
132Dic11⋊C8C2×C411yescharacteristic
133Dic11⋊C8C2×C411yescharacteristic
134C8×Dic11—21no—
135C8×Dic11—21no—
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#18006—111nomaximal, Sylow
146C23×D11—21no—
147C2×D4×C11C22×C411yescharacteristic
148C2×D4×C11C22×C411yescharacteristic
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C2×C22⋊D11—21no—
152C2×C22⋊D11—21no—
153C22×Dic11—21no—
154D4×D11—22no—
155D4×D11—41no—
156C2×D44C22×C411yescharacteristic
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×C4×D11—42no—
161C2×C4×D11—42no—
162C2×C4×D11C22×C411yescharacteristic
163C2×C4×D11C2×D411yescharacteristic
164C2×C4×D11#4111yescharacteristic
165C2×Dic22C22×C411yescharacteristic
166C11×D8—22no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—42no—
171C2×C8×C11—42no—
172C2×C8×C11C22×C411yescharacteristic
173C2×C8×C11C22×C411yescharacteristic
174C2×C8×C11C2×D411yescharacteristic
175C2×C8×C11C2×D411yescharacteristic
176C11×C4⋊C4C22×C411yescharacteristic
177C11×C4⋊C4C22×C411yescharacteristic
178C11×C22⋊C4—21no—
179C11×C22⋊C4—21no—
180C42×C11C2411yescharacteristic
181C22⋊Dic11—21no—
182C22⋊Dic11—21no—
183C22⋊Dic11—21no—
184C22⋊Dic11—21no—
185#4324—22no—
186#4323—41no—
187(C2×D11)⋊C4—21no—
188(C2×D11)⋊C4—21no—
189(C2×D11)⋊C4—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11C22×C411yescharacteristic
193C4⋊Dic11C22×C411yescharacteristic
194Dic11⋊C4—21no—
195Dic11⋊C4—21no—
196Dic11⋊C4—21no—
197C4×Dic11—21no—
198C4×Dic11C22×C411yescharacteristic
199C4×Dic11C2×D411yescharacteristic
200C4×Dic11#4111yescharacteristic
201#4318—42no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—42no—
206C2×C11⋊C8C22×C411yescharacteristic
207C2×C11⋊C8C22×C411yescharacteristic
208C2×C11⋊C8C2×D411yescharacteristic
209C2×C11⋊C8C2×D411yescharacteristic
210#4314—41no—
211#4313—22no—
212#4313—41no—
213#4313—42no—
214#4313—42no—
215#4313—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⋊C8—111no—
226C8×D8D1111yescharacteristic, complemented
227#1574—111no—
228#1495—111no—
229#1478—111no—
230#1453—111no—
231C23×C11—21no—
232C23×C11—21no—
233C22×D11—21no—
234C22×D11—42no—
235C22×D11—42no—
236C22×D11—81no—
237C22×D11C4×D411yescharacteristic
238D4×C11—21no—
239D4×C11—21no—
240D4×C11—21no—
241D4×C11#13112yes—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11C23×C411yescharacteristic
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C22⋊D11—42no—
252C22⋊D11—81no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—42no—
257C2×Dic11C4×D411yescharacteristic
258C2×Dic11C4×D411yescharacteristic
259C2×Dic11C4×D411yescharacteristic
260D44—21no—
261D44—21no—
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—
271Dic22—21no—
272Dic22—21no—
273C8×C11—21no—
274C8×C11—21no—
275C8×C11—21no—
276C8×C11—41no—
277C8×C11—41no—
278C8×C11—41no—
279C8×C11AGL(1,ℤ/8)12yes—
280C11⋊C8—21no—
281C11⋊C8—21no—
282C11⋊C8—21no—
283C11⋊C8—21no—
284C11⋊C8—41no—
285C11⋊C8—41no—
286C11⋊C8—41no—
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×Q8—111no—
300C4×SD16—111no—
301C4×SD16—111no—
302C4×D8—111no—
303C4×D8C2×D1111yescharacteristic
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×D4C2×D1111yescharacteristic
313C8×D4C2×D1111yescharacteristic, complemented
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⋊C8—111no—
328D4⋊C8—111no—
329D4⋊C8—111no—
330D4⋊C8—111no—
331D4⋊C8—111no—
332D4⋊C8C2×D1111yescharacteristic
333D4⋊C8C2×D1111yescharacteristic, complemented
334#322—111no—
335#322—111no—
336#322—111no—
337C82C2×D1111yescharacteristic, complemented
338C22×C11—22no—
339C22×C11—41no—
340C22×C11—41no—
341C22×C11—41no—
342C22×C11—41no—
343C22×C11—41no—
344C22×C11C2×C4×D411yescharacteristic
345C2×D11—21no—
346C2×D11—21no—
347C2×D11—21no—
348C2×D11—41no—
349C2×D11—41no—
350C2×D11—41no—
351C2×D11—84no—
352C4×C11—21no—
353C4×C11—41no—
354C4×C11—41no—
355C4×C11C2×#13111yescharacteristic
356C4×C11#56811yescharacteristic
357C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
358C4×C11#57511yescharacteristic
359Dic11—21no—
360Dic11—21no—
361Dic11—21no—
362Dic11—41no—
363Dic11—41no—
364Dic11—41no—
365C22×D4—111no—
366C23×C4—221no—
367C2×SD16—111no—
368C2×SD16—111no—
369C2×D8—111no—
370C2×D8C4×D1111yescharacteristic
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—21no—
380C22×C8—221no—
381#126—221no—
382#125—111no—
383#124—111no—
384#123—221no—
385C22⋊Q8—111no—
386#121—111no—
387C4×Q8—111no—
388C4×D4—111no—
389C4×D4—111no—
390C4×D4—111no—
391C4×D4—221no—
392C4×D4—221no—
393C4×D4—221no—
394C4×D4C22×D1111yescharacteristic
395C4×D4C22×D1111yescharacteristic
396#117—221no—
397C2×C4⋊C4—111no—
398C2×C22⋊C4—221no—
399C2×C42—111no—
400#107—111no—
401#107C4×D1111yescharacteristic
402#106—111no—
403#106—111no—
404C4⋊C8—111no—
405C4⋊C8—111no—
406C4⋊C8—111no—
407C4⋊C8—111no—
408C4⋊C8—221no—
409C4⋊C8—221no—
410C4⋊C8—221no—
411C4⋊C8—221no—
412C4⋊C8C22×D1111yescharacteristic
413C4⋊C8C22×D1111yescharacteristic
414#103—111no—
415#103—111no—
416#102—111no—
417#102—111no—
418#102—111no—
419#102—111no—
420#102C4×D1111yescharacteristic
421#102C4×D1111yescharacteristic
422C22⋊C8—21no—
423C22⋊C8—21no—
424C22⋊C8—111no—
425C22⋊C8—111no—
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—111no—
436C4×C8—111no—
437C4×C8—111no—
438C4×C8—221no—
439C4×C8—221no—
440C4×C8C22×D1111yescharacteristic
441C4×C8C22×D1111yescharacteristic
442C4×C8C22×D1111yescharacteristic
443C2×C11—42no—
444C2×C11—81no—
445C2×C11#293311yescharacteristic
446C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
447C2×C11#295711yescharacteristic
448D11—41no—
449D11—81no—
450C24—221no—
451C2×Q8—111no—
452C2×D4—111no—
453C2×D4—221no—
454C2×D4—222no—
455C2×D4—221no—
456C2×D4—441no—
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—
465C22×C4—221no—
466C22×C4—221no—
467C22×C4—221no—
468C22×C4—442no—
469C22×C4—442no—
470SD16—222no—
471SD16—441no—
472D8—22no—
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—42no—
485C2×C8—111no—
486C2×C8—111no—
487C2×C8—111no—
488C2×C8—111no—
489C2×C8—221no—
490C2×C8—221no—
491C2×C8—221no—
492C2×C8—442no—
493C2×C8C2×C4×D1111yescharacteristic
494C2×C8C2×C4×D1111yescharacteristic
495C2×C8D4×D1111yescharacteristic
496C2×C8D4×D1111yescharacteristic
497C4⋊C4—111no—
498C4⋊C4—111no—
499C4⋊C4—221no—
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—21no—
508C22⋊C4—221no—
509C22⋊C4—221no—
510C22⋊C4—221no—
511C22⋊C4—221no—
512C22⋊C4—221no—
513C22⋊C4—221no—
514C22⋊C4—221no—
515C42—111no—
516C42—111no—
517C42—111no—
518C42—221no—
519C42C23×D1111yescharacteristic
520C11#1800611yescharacteristic, complemented, Sylow
521C23—21no—
522C23—21no—
523C23—111no—
524C23—221no—
525C23—442no—
526C23—442no—
527C23—881no—
528Q8—221no—
529Q8—221no—
530D4—21no—
531D4—21no—
532D4—21no—
533D4—221no—
534D4—221no—
535D4—442no—
536D4—881no—
537D4#6695412yes—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—111no—
545C2×C4—111no—
546C2×C4—111no—
547C2×C4—221no—
548C2×C4—221no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—221no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—441no—
555C2×C4—442no—
556C2×C4—442no—
557C2×C4—442no—
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—41no—
567C8—41no—
568C8—41no—
569C8—221no—
570C8—221no—
571C8—221no—
572C8—221no—
573C8—441no—
574C8—441no—
575C8—441no—
576C8#6696412yes—
577C22—22no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—221no—
584C22—221no—
585C22—221no—
586C22—441no—
587C22—441no—
588C22—441no—
589C22—884no—
590C22C4×D4×D1111yescharacteristic
591C4—21no—
592C4—41no—
593C4—41no—
594C4—221no—
595C4—221no—
596C4—221no—
597C4—441no—
598C4—441no—
599C4—441no—
600C4C2×#6695411yescharacteristic
601C4#1062328111yescharacteristic
602C4C2×#6696411yescharacteristic
603C4#1062329911yescharacteristic
604C2—42no—
605C2—81no—
606C2—441no—
607C2—881no—
608C2#1307733611yescharacteristic
609C2C4×#6696411yescharacteristic
610C2#1307752811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC8×C11×D8C2
socleC22×C11C2×C4×D4
prime radical#10622769C4
cosocleC42×C11C24
hypercenterC8×D8D11
hypocenterC11#18006
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×D8

Complements

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

NH ≅ G/Ntype
2. #13077617C2semidirect
3. D4×#4313C2semidirect
4. #13067527C2semidirect
5. #13067508C2semidirect
6. #13067493C2semidirect
7. #13067481C2semidirect
8. #13067452C2semidirect
9. #13067445C2semidirect
10. #13067425C2semidirect
11. #13067406C2semidirect
12. #13067078C2semidirect
13. #13067005C2semidirect
14. #13066910C2semidirect
15. C8×C11×D8C2semidirect
21. C8×D4×C11C22semidirect
29. #10622625C22semidirect
36. #10622443C22semidirect
50. #10622292C22semidirect
51. C11×#335C22semidirect
53. C11×D4⋊C8C22semidirect
54. C82×C11C22semidirect
56. D4⋊(C11⋊C8)C22semidirect
57. #10622122C22semidirect
59. #10622118C22semidirect
60. #10622117C22semidirect
62. #10622095C22semidirect
63. #10622094C22semidirect
64. #10622093C22semidirect
65. #10622092C22semidirect
66. #10622092C22semidirect
226. C8×D8D11semidirect
313. C8×D4C2×D11semidirect
323. #335C2×D11semidirect
333. D4⋊C8C2×D11semidirect
337. C82C2×D11semidirect
520. C11#18006semidirect

Maximal subgroups

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

subgroupindex
#130786612
#130776172
D4×#43132
#130675272
#130675082
#130674932
#130674812
#130674522
#130674452
#130674252
#130674062
#130670782
#130670052
#130669102
C8×C11×D82
#1800611