Finite Group Databasebeta

← #14724809

Subgroups — #14724809

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#13078663C211yesmaximal, characteristic
2#13077620C211yesmaximal, characteristic, complemented
3#13067528C211yesmaximal, characteristic, complemented
4#13067504C211yesmaximal, characteristic, complemented
5#13067492C211yesmaximal, characteristic, complemented
6#13067480C211yesmaximal, characteristic, complemented
7#13067452C211yesmaximal, characteristic, complemented
8#13067443C211yesmaximal, characteristic, complemented
9#13067428C211yesmaximal, characteristic, complemented
10C8×#4323C211yesmaximal, characteristic, complemented
11#13067407C211yesmaximal, characteristic, complemented
12#13067079C211yesmaximal, characteristic, complemented
13#13067007C211yesmaximal, characteristic, complemented
14#13066913C211yesmaximal, characteristic, complemented
15D4×C11×M16C211yesmaximal, characteristic, complemented
16C22×C11×M16—21no—
17C2×C4×D4×C11C2211yescharacteristic
18#10623010C2211yescharacteristic
19C11×#436C2211yescharacteristic
20C11×#436C2211yescharacteristic
21C11×#435—21no—
22C11×#435—21no—
23C8×D4×C11C2211yescharacteristic
24C8×D4×C11C2211yescharacteristic
25C11×#423C2211yescharacteristic
26C11×#407—21no—
27C4×C11×M16C2211yescharacteristic
28#10622831C411yescharacteristic
29#10622830C411yescharacteristic
30#10622741—21no—
31#10622740—21no—
32C4×#4324C2211yescharacteristic
33C4×#4324C2211yescharacteristic
34#10622629C411yescharacteristic
35#10622629C411yescharacteristic
36C4×#4323C2211yescharacteristic
37C4×#4323C2211yescharacteristic
38#10622622C411yescharacteristic
39#10622622C411yescharacteristic
40#10622583C411yescharacteristic
41#10622581C411yescharacteristic
42#10622538C2211yescharacteristic
43#10622538C2211yescharacteristic
44#10622538C2211yescharacteristic
45#10622322—21no—
46#10622321—21no—
47#10622301C2211yescharacteristic, complemented
48C8×D44C2211yescharacteristic, complemented
49#10622292C2211yescharacteristic, complemented
50C8×Dic22C2211yescharacteristic, complemented
51D4⋊(C11⋊C8)C2211yescharacteristic
52D4⋊(C11⋊C8)C2211yescharacteristic
53D4⋊(C11⋊C8)C2211yescharacteristic
54D4⋊(C11⋊C8)C2211yescharacteristic
55#10622122C2211yescharacteristic, complemented
56#10622122C2211yescharacteristic, complemented
57#10622121C2211yescharacteristic, complemented
58#10622121C2211yescharacteristic, complemented
59#10622118C2211yescharacteristic, complemented
60#10622118C2211yescharacteristic, complemented
61#10622117C2211yescharacteristic, complemented
62#10622117C2211yescharacteristic, complemented
63#10622093C2211yescharacteristic, complemented
64#10622092C2211yescharacteristic, complemented
65#10622092C2211yescharacteristic, complemented
66C8×C11⋊C8C2211yescharacteristic, complemented
67C22×D4×C11C2×C411yescharacteristic
68C23×C4×C11—21no—
69C2×C11×M16—21no—
70C2×C11×M16—21no—
71C2×C11×M16—21no—
72C2×C11×M16—44no—
73C2×C11×M16D411yescharacteristic
74C2×C11×M16D411yescharacteristic
75C22×C8×C11—21no—
76C22×C8×C11—21no—
77C4×D4×C11—21no—
78C4×D4×C11—21no—
79C4×D4×C11C2×C411yescharacteristic
80C4×D4×C11C2×C411yescharacteristic
81C4×D4×C11C2311yescharacteristic
82C4×D4×C11C2311yescharacteristic
83C2×C11×C4⋊C4C2×C411yescharacteristic
84C2×C11×C22⋊C4—21no—
85C2×C42×C11C2311yescharacteristic
86C2×#4324C2×C411yescharacteristic
87C2×#4324C2×C411yescharacteristic
88C2×#4323C2×C411yescharacteristic
89C2×#4323C2×C411yescharacteristic
90#66983C2×C411yescharacteristic
91#66982—21no—
92C4×C22⋊D11—21no—
93#66977C2×C411yescharacteristic
94C2×#4313—21no—
95C2×C8×D11—21no—
96#66929—21no—
97#66928C2×C411yescharacteristic
98C4×D44C2311yescharacteristic
99#66925—21no—
100#66923C2×C411yescharacteristic
101C4×Dic22C2311yescharacteristic
102C11×C4⋊C8—21no—
103C11×C4⋊C8C2311yescharacteristic
104C11×C4⋊C8C2311yescharacteristic
105C11×C22⋊C8—21no—
106C11×C22⋊C8—21no—
107C11×C22⋊C8—21no—
108C11×C22⋊C8—21no—
109C11×#97D411yescharacteristic
110C11×#97D411yescharacteristic
111C4×C8×C11C2311yescharacteristic
112C4×C8×C11C2311yescharacteristic
113#66896C2×C411yescharacteristic
114#66896C2×C411yescharacteristic
115#66896C2×C411yescharacteristic
116#66896C2×C411yescharacteristic
117C22⋊(C11⋊C8)—21no—
118C22⋊(C11⋊C8)—21no—
119C22⋊(C11⋊C8)C2×C411yescharacteristic
120C22⋊(C11⋊C8)C2×C411yescharacteristic
121(C2×D11)⋊C8—21no—
122(C2×D11)⋊C8—21no—
123#66879—21no—
124Dic11⋊C8—21no—
125Dic11⋊C8—21no—
126C8×Dic11—21no—
127#66874C2×C411yescharacteristic
128#66874C2×C411yescharacteristic
129#66873C2×C411yescharacteristic
130#66873C2×C411yescharacteristic
131#66872C2×C411yescharacteristic
132#66872C2×C411yescharacteristic
133#66871C2×C411yescharacteristic
134#66871C2×C411yescharacteristic
135C4⋊(C11⋊C8)—21no—
136C4⋊(C11⋊C8)C2×C411yescharacteristic
137C4⋊(C11⋊C8)C2×C411yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4×C11⋊C8—21no—
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#18006—111nomaximal, Sylow
146C24×C11—21no—
147C2×D4×C11—22no—
148C2×D4×C11—21no—
149C2×D4×C11—41no—
150C2×D4×C11C22×C411yescharacteristic
151C2×D4×C11C22×C411yescharacteristic
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—42no—
158C22×C4×C11—42no—
159C22×C4×C11C22×C411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11#4111yescharacteristic
162C2×C22⋊D11—21no—
163C2×D44C22×C411yescharacteristic
164C2×C4×D11—21no—
165C2×Dic22C22×C411yescharacteristic
166C11×M16—22no—
167C11×M16—41no—
168C11×M16—42no—
169C11×M16—42no—
170C11×M16—42no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—42no—
174C2×C8×C11—42no—
175C2×C8×C11C2×D411yescharacteristic
176C2×C8×C11C2×D411yescharacteristic
177C2×C8×C11C2×D411yescharacteristic
178C2×C8×C11C2×D411yescharacteristic
179C11×C4⋊C4—21no—
180C11×C4⋊C4C22×C411yescharacteristic
181C11×C4⋊C4C22×C411yescharacteristic
182C11×C22⋊C4—21no—
183C11×C22⋊C4—21no—
184C11×C22⋊C4—21no—
185C11×C22⋊C4—21no—
186C42×C11C22×C411yescharacteristic
187C42×C11C2×D411yescharacteristic
188C42×C11#4111yescharacteristic
189C42×C11C2411yescharacteristic
190C22⋊Dic11—21no—
191#4324—22no—
192#4324—41no—
193#4323—22no—
194#4323—41no—
195(C2×D11)⋊C4—21no—
196(C2×D11)⋊C4—21no—
197(C2×D11)⋊C4—21no—
198(C2×D11)⋊C4—21no—
199C4⋊Dic11C22×C411yescharacteristic
200C4⋊Dic11C22×C411yescharacteristic
201Dic11⋊C4—21no—
202Dic11⋊C4—21no—
203Dic11⋊C4—21no—
204Dic11⋊C4—21no—
205C4×Dic11—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8C22×C411yescharacteristic
211C2×C11⋊C8C22×C411yescharacteristic
212C2×C11⋊C8C22×C411yescharacteristic
213C2×C11⋊C8C22×C411yescharacteristic
214#4313—42no—
215C8×D11—42no—
216#3105—111no—
217#2969—111no—
218D4×M16D1111yescharacteristic, complemented
219#1594—111no—
220#1590—111no—
221#1588—111no—
222#1586—111no—
223#1582—111no—
224#1581—111no—
225SD16⋊C8—111no—
226C8×D8—111no—
227#1574—111no—
228#1495—111no—
229#1478—111no—
230#1453—111no—
231C23×C11—21no—
232C23×C11—21no—
233C23×C11—42no—
234C23×C11—42no—
235C23×C11—81no—
236C23×C11C4×D411yescharacteristic
237C22×D11—21no—
238D4×C11—21no—
239D4×C11—21no—
240D4×C11—21no—
241D4×C11—42no—
242D4×C11#13112yes—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—41no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11C4×D411yescharacteristic
258C2×C4×C11C4×D411yescharacteristic
259C2×C4×C11C4×D411yescharacteristic
260C2×C4×C11C23×C411yescharacteristic
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C22⋊D11—81no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267D44—21no—
268D44—21no—
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×C11AGL(1,ℤ/8)12yes—
279C11⋊C8—21no—
280C11⋊C8—21no—
281C11⋊C8—21no—
282C11⋊C8—21no—
283C11⋊C8—41no—
284C11⋊C8—41no—
285C11⋊C8—41no—
286C11⋊C8—41no—
287C22×M16—21no—
288#529—111no—
289C2×C4×D4C2×D1111yescharacteristic
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×D8—111no—
304#436—111no—
305#436—221no—
306#436C2×D1111yescharacteristic
307#436C2×D1111yescharacteristic
308#435—21no—
309#435—21no—
310#435—221no—
311C8×D4—111no—
312C8×D4C2×D1111yescharacteristic
313C8×D4C2×D1111yescharacteristic
314#433—221no—
315#431—111no—
316#431—111no—
317#431—111no—
318#423C2×D1111yescharacteristic
319#407—21no—
320#405—221no—
321C4×M16C2×D1111yescharacteristic
322#335—111no—
323#335—111no—
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⋊C8—111no—
333D4⋊C8—111no—
334#322—111no—
335#322—111no—
336#322—111no—
337C82—111no—
338C22×C11—21no—
339C22×C11—22no—
340C22×C11—21no—
341C22×C11—21no—
342C22×C11—41no—
343C22×C11—41no—
344C22×C11—41no—
345C22×C11—41no—
346C22×C11—41no—
347C22×C11—84no—
348C22×C11C2×C4×D411yescharacteristic
349C2×D11—41no—
350C2×D11—41no—
351C2×D11—41no—
352C4×C11—21no—
353C4×C11—21no—
354C4×C11—21no—
355C4×C11—21no—
356C4×C11—41no—
357C4×C11—41no—
358C4×C11C2×#13111yescharacteristic
359C4×C11#56811yescharacteristic
360C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
361C4×C11#57511yescharacteristic
362Dic11—41no—
363Dic11—41no—
364Dic11—41no—
365C22×D4C4×D1111yescharacteristic
366C23×C4—21no—
367C2×SD16—111no—
368C2×SD16—111no—
369C2×D8—111no—
370C2×D8—111no—
371C2×M16—21no—
372C2×M16—21no—
373C2×M16—21no—
374C2×M16—44no—
375C2×M16—221no—
376C2×M16C22⋊D1111yescharacteristic
377C2×M16C22⋊D1111yescharacteristic
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—21no—
389C4×D4—21no—
390C4×D4—111no—
391C4×D4—221no—
392C4×D4C4×D1111yescharacteristic
393C4×D4C4×D1111yescharacteristic
394C4×D4C22×D1111yescharacteristic
395C4×D4C22×D1111yescharacteristic
396#117—221no—
397C2×C4⋊C4C4×D1111yescharacteristic
398C2×C22⋊C4—21no—
399C2×C42C22×D1111yescharacteristic
400#107—111no—
401#107—111no—
402#106—111no—
403#106—111no—
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#103—111no—
416#102—111no—
417#102—111no—
418#102—111no—
419#102—111no—
420#102—111no—
421#102—111no—
422C22⋊C8—21no—
423C22⋊C8—21no—
424C22⋊C8—21no—
425C22⋊C8—21no—
426C22⋊C8—111no—
427C22⋊C8—111no—
428C22⋊C8—221no—
429C22⋊C8—221no—
430C22⋊C8—221no—
431C22⋊C8—221no—
432#97—221no—
433#97C22⋊D1111yescharacteristic
434#97C22⋊D1111yescharacteristic
435C4×C8—111no—
436C4×C8—111no—
437C4×C8—111no—
438C4×C8—111no—
439C4×C8—221no—
440C4×C8—221no—
441C4×C8C22×D1111yescharacteristic
442C4×C8C22×D1111yescharacteristic
443C2×C11—41no—
444C2×C11—42no—
445C2×C11—81no—
446C2×C11#293311yescharacteristic
447C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
448C2×C11#295711yescharacteristic
449D11—81no—
450C24—21no—
451C2×Q8—111no—
452C2×D4—22no—
453C2×D4—21no—
454C2×D4—41no—
455C2×D4—111no—
456C2×D4—221no—
457C2×D4C2×C4×D1111yescharacteristic
458C2×D4C2×C4×D1111yescharacteristic
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—221no—
467C22×C4C2×C4×D1111yescharacteristic
468C22×C4#433911yescharacteristic
469C22×C4C2×C22⋊D1111yescharacteristic
470SD16—222no—
471SD16—441no—
472D8—222no—
473D8—441no—
474M16—22no—
475M16—41no—
476M16—42no—
477M16—42no—
478M16—42no—
479M16—442no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—42no—
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—221no—
492C2×C8—442no—
493C2×C8C2×C22⋊D1111yescharacteristic
494C2×C8C2×C22⋊D1111yescharacteristic
495C2×C8C2×C22⋊D1111yescharacteristic
496C2×C8C2×C22⋊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—21no—
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—221no—
511C22⋊C4—221no—
512C22⋊C4—221no—
513C22⋊C4—221no—
514C22⋊C4—221no—
515C42—221no—
516C42C2×C4×D1111yescharacteristic
517C42#433911yescharacteristic
518C42C2×C22⋊D1111yescharacteristic
519C42C23×D1111yescharacteristic
520C11#1800611yescharacteristic, complemented, Sylow
521C23—21no—
522C23—21no—
523C23—42no—
524C23—42no—
525C23—81no—
526C23—221no—
527C23C4×C22⋊D1111yescharacteristic
528Q8—221no—
529Q8—221no—
530D4—21no—
531D4—21no—
532D4—21no—
533D4—42no—
534D4—221no—
535D4—221no—
536D4—881no—
537D4#6696012yes—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—41no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—221no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4C4×C22⋊D1111yescharacteristic
558C2×C4C4×C22⋊D1111yescharacteristic
559C2×C4C4×C22⋊D1111yescharacteristic
560C2×C4C22×C4×D1111yescharacteristic
561C2×C4C2×#433911yescharacteristic
562C2×C4C22×C22⋊D1111yescharacteristic
563C8—21no—
564C8—21no—
565C8—21no—
566C8—41no—
567C8—41no—
568C8—221no—
569C8—221no—
570C8—221no—
571C8—221no—
572C8—441no—
573C8—441no—
574C8—441no—
575C8—441no—
576C8#6698512yes—
577C22—21no—
578C22—21no—
579C22—22no—
580C22—21no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—84no—
587C22—441no—
588C22—441no—
589C22—441no—
590C22C2×C4×C22⋊D1111yescharacteristic
591C4—21no—
592C4—21no—
593C4—21no—
594C4—21no—
595C4—41no—
596C4—41no—
597C4—441no—
598C4—441no—
599C4—441no—
600C4C2×#6696011yescharacteristic
601C4#1062327611yescharacteristic
602C4C2×#6698511yescharacteristic
603C4#1062335311yescharacteristic
604C2—41no—
605C2—42no—
606C2—81no—
607C2—881no—
608C2#1307734111yescharacteristic
609C2C4×#6698511yescharacteristic
610C2#1307753111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingD4×C11×M16C2
socleC22×C11C2×C4×D4
prime radical#10622830C4
cosocleC42×C11C24
hypercenterD4×M16D11
hypocenterC11#18006
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ D4×M16

Complements

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

NH ≅ G/Ntype
2. #13077620C2semidirect
3. #13067528C2semidirect
4. #13067504C2semidirect
5. #13067492C2semidirect
6. #13067480C2semidirect
7. #13067452C2semidirect
8. #13067443C2semidirect
9. #13067428C2semidirect
10. C8×#4323C2semidirect
11. #13067407C2semidirect
12. #13067079C2semidirect
13. #13067007C2semidirect
14. #13066913C2semidirect
15. D4×C11×M16C2semidirect
47. #10622301C22semidirect
48. C8×D44C22semidirect
49. #10622292C22semidirect
50. C8×Dic22C22semidirect
55. #10622122C22semidirect
56. #10622122C22semidirect
57. #10622121C22semidirect
58. #10622121C22semidirect
59. #10622118C22semidirect
60. #10622118C22semidirect
61. #10622117C22semidirect
62. #10622117C22semidirect
63. #10622093C22semidirect
64. #10622092C22semidirect
65. #10622092C22semidirect
66. C8×C11⋊C8C22semidirect
218. D4×M16D11semidirect
520. C11#18006semidirect

Maximal subgroups

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

subgroupindex
#130786632
#130776202
#130675282
#130675042
#130674922
#130674802
#130674522
#130674432
#130674282
C8×#43232
#130674072
#130670792
#130670072
#130669132
D4×C11×M162
#1800611