Finite Group Databasebeta

← #14724805

Subgroups — #14724805

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#13078659C211yesmaximal, characteristic
2M16×D44C211yesmaximal, characteristic, complemented
3#13067528C211yesmaximal, characteristic, complemented
4#13067506C211yesmaximal, characteristic, complemented
5#13067494C211yesmaximal, characteristic, complemented
6#13067478C211yesmaximal, characteristic, complemented
7#13067450C211yesmaximal, characteristic, complemented
8#13067445C211yesmaximal, characteristic, complemented
9#13067426C211yesmaximal, characteristic, complemented
10C8×#4323C211yesmaximal, characteristic, complemented
11#13067404C211yesmaximal, characteristic, complemented
12#13067081C211yesmaximal, characteristic, complemented
13#13067006C211yesmaximal, characteristic, complemented
14#13066913C211yesmaximal, characteristic, complemented
15C11×#2969C211yesmaximal, characteristic, complemented
16C11×#529C2211yescharacteristic
17C2×M16×D11—21no—
18C2×C4×D44C2211yescharacteristic
19C11×#446C2211yescharacteristic, complemented
20C8×Q8×C11C2211yescharacteristic, complemented
21C11×#436—21no—
22C11×#436C2211yescharacteristic, complemented
23C11×#435—21no—
24C8×D4×C11C2211yescharacteristic, complemented
25C11×#433—21no—
26C11×#431C2211yescharacteristic
27C11×#405—21no—
28C4×C11×M16C2211yescharacteristic
29#10622739—21no—
30#10622679C411yescharacteristic
31#10622679C411yescharacteristic
32#10622670C411yescharacteristic
33#10622670C411yescharacteristic
34#10622659C411yescharacteristic
35#10622657C411yescharacteristic
36#10622649C411yescharacteristic
37#10622647C411yescharacteristic
38C4×#4325C2211yescharacteristic
39C4×#4325C2211yescharacteristic
40C4×#4323C2211yescharacteristic
41C4×#4323C2211yescharacteristic
42#10622538C2211yescharacteristic
43#10622538C2211yescharacteristic
44#10622537C2211yescharacteristic
45#10622319—21no—
46#10622319—21no—
47#10622301C2211yescharacteristic
48#10622301C2211yescharacteristic
49C8×D44C2211yescharacteristic
50C8×D44C2211yescharacteristic
51Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
52Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
53D4⋊(C11⋊C8)C2211yescharacteristic, complemented
54D4⋊(C11⋊C8)C2211yescharacteristic, complemented
55#10622121C2211yescharacteristic
56#10622121C2211yescharacteristic
57#10622121C2211yescharacteristic
58#10622121C2211yescharacteristic
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×D44C2×C411yescharacteristic
68C22×C4×D11—21no—
69C2×C11×M16—21no—
70C2×C11×M16D411yescharacteristic
71C2×C11×M16D411yescharacteristic
72C22×C8×C11—21no—
73C11×#126—21no—
74C11×#125C2×C411yescharacteristic
75C11×#124C2×C411yescharacteristic
76C11×#123—21no—
77C11×C22⋊Q8C2×C411yescharacteristic
78C11×#121C2×C411yescharacteristic
79C4×Q8×C11C2311yescharacteristic
80C4×D4×C11—21no—
81C4×D4×C11C2311yescharacteristic
82C11×#117—21no—
83C2×C42×C11C2311yescharacteristic
84C2×#4325C2×C411yescharacteristic
85C2×#4325C2×C411yescharacteristic
86C2×#4323C2×C411yescharacteristic
87C2×#4323C2×C411yescharacteristic
88C2×(C2×D11)⋊C4—21no—
89C2×C4⋊Dic11C2×C411yescharacteristic
90C2×#4318—21no—
91M16×D11—44no—
92C2×#4313—21no—
93C2×#4313—21no—
94C2×C8×D11—21no—
95C2×C8×D11—21no—
96C4×D44—21no—
97C4×D44—21no—
98C4×D44C2×C411yescharacteristic
99C4×D44C2×C411yescharacteristic
100C4×D44C2311yescharacteristic
101C4×D44C2311yescharacteristic
102C11×C4⋊C8—21no—
103C11×C4⋊C8—21no—
104C11×C4⋊C8C2311yescharacteristic
105C11×C4⋊C8C2311yescharacteristic
106C11×C22⋊C8—21no—
107C11×C22⋊C8—21no—
108C11×C22⋊C8—21no—
109C11×#97—21no—
110C11×#97D411yescharacteristic
111C11×#97D411yescharacteristic
112C4×C8×C11—21no—
113C4×C8×C11—21no—
114C4×C8×C11C2311yescharacteristic
115C4×C8×C11C2311yescharacteristic
116#66899C2×C411yescharacteristic
117#66899C2×C411yescharacteristic
118#66896C2×C411yescharacteristic
119#66896C2×C411yescharacteristic
120C22⋊(C11⋊C8)—21no—
121C22⋊(C11⋊C8)C2×C411yescharacteristic
122C22⋊(C11⋊C8)C2×C411yescharacteristic
123(C2×D11)⋊C8—21no—
124(C2×D11)⋊C8—21no—
125(C2×D11)⋊C8—21no—
126(C2×D11)⋊C8—21no—
127#66873C2×C411yescharacteristic
128#66873C2×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)—21no—
137C4⋊(C11⋊C8)C2×C411yescharacteristic
138C4⋊(C11⋊C8)C2×C411yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#18006—111nomaximal, Sylow
146C23×D11—21no—
147C2×Q8×C11C22×C411yescharacteristic
148C2×D4×C11—21no—
149C2×D4×C11C22×C411yescharacteristic
150C22×C4×C11—21no—
151C22×C4×C11C22×C411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11#4111yescharacteristic
154C22×Dic11—21no—
155C2×D44—22no—
156C2×D44—21no—
157C2×D44—41no—
158C2×D44C22×C411yescharacteristic
159C2×D44C22×C411yescharacteristic
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×C4×D11—21no—
164C2×C4×D11—42no—
165C2×C4×D11—42no—
166C11×M16—22no—
167C11×M16—41no—
168C11×M16—42no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—42no—
172C2×C8×C11C2×D411yescharacteristic
173C2×C8×C11C2×D411yescharacteristic
174C2×C8×C11C2×D411yescharacteristic
175C2×C8×C11C2×D411yescharacteristic
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
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—
186C11×C22⋊C4—21no—
187C42×C11—21no—
188C42×C11C22×C411yescharacteristic
189C42×C11C2×D411yescharacteristic
190C42×C11#4111yescharacteristic
191C42×C11C2411yescharacteristic
192#4325—22no—
193#4325—41no—
194#4323—22no—
195#4323—41no—
196(C2×D11)⋊C4—21no—
197(C2×D11)⋊C4—21no—
198(C2×D11)⋊C4—21no—
199(C2×D11)⋊C4—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11C22×C411yescharacteristic
202C4⋊Dic11C22×C411yescharacteristic
203#4318—42no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8C22×C411yescharacteristic
209C2×C11⋊C8C22×C411yescharacteristic
210C2×C11⋊C8C22×C411yescharacteristic
211C2×C11⋊C8C22×C411yescharacteristic
212#4313—42no—
213#4313—42no—
214C8×D11—42no—
215C8×D11—42no—
216#3105—111no—
217#2969D1111yescharacteristic, complemented
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×D8—111no—
227#1574—111no—
228#1495—111no—
229#1478—111no—
230#1453—111no—
231C23×C11—21no—
232C23×C11C4×D411yescharacteristic
233C22×D11—21no—
234C22×D11—21no—
235C22×D11—42no—
236C22×D11—42no—
237C22×D11—81no—
238Q8×C11—21no—
239Q8×C11—21no—
240D4×C11—21no—
241D4×C11—21no—
242D4×C11—81no—
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—21no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11C4×D411yescharacteristic
254C2×C4×C11C4×D411yescharacteristic
255C2×C4×C11C4×D411yescharacteristic
256C2×C4×C11C23×C411yescharacteristic
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—42no—
262D44—21no—
263D44—21no—
264D44—21no—
265D44—42no—
266D44#13112yes—
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—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—221no—
288#529C2×D1111yescharacteristic
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#446C2×D1111yescharacteristic, complemented
299C8×Q8C2×D1111yescharacteristic, complemented
300C4×SD16—111no—
301C4×SD16—111no—
302C4×D8—111no—
303C4×D8—111no—
304#436—21no—
305#436—111no—
306#436—111no—
307#436C2×D1111yescharacteristic, complemented
308#435—21no—
309#435—221no—
310#435—221no—
311C8×D4—111no—
312C8×D4—111no—
313C8×D4C2×D1111yescharacteristic, complemented
314#433—21no—
315#431—111no—
316#431—111no—
317#431C2×D1111yescharacteristic
318#423—111no—
319#407—221no—
320#405—21no—
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—21no—
340C22×C11—21no—
341C22×C11—41no—
342C22×C11—41no—
343C22×C11—41no—
344C22×C11C2×C4×D411yescharacteristic
345C2×D11—22no—
346C2×D11—41no—
347C2×D11—41no—
348C2×D11—41no—
349C2×D11—41no—
350C2×D11—41no—
351C2×D11—84no—
352C4×C11—21no—
353C4×C11—21no—
354C4×C11—21no—
355C4×C11—21no—
356C4×C11—41no—
357C4×C11—41no—
358C4×C11—41no—
359C4×C11C2×#13111yescharacteristic
360C4×C11#56811yescharacteristic
361C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
362C4×C11#57511yescharacteristic
363Dic11—41no—
364Dic11—41no—
365C22×D4—111no—
366C23×C4—221no—
367C2×SD16—111no—
368C2×SD16—111no—
369C2×D8—111no—
370C2×D8—111no—
371C2×M16—21no—
372C2×M16—221no—
373C2×M16—221no—
374C2×M16—221no—
375C2×M16—444no—
376C2×M16C22⋊D1111yescharacteristic
377C2×M16C22⋊D1111yescharacteristic
378C22×C8—21no—
379C22×C8—221no—
380C22×C8—221no—
381#126—21no—
382#125C4×D1111yescharacteristic
383#124C4×D1111yescharacteristic
384#123—21no—
385C22⋊Q8C4×D1111yescharacteristic
386#121C4×D1111yescharacteristic
387C4×Q8C22×D1111yescharacteristic
388C4×D4—21no—
389C4×D4—111no—
390C4×D4—111no—
391C4×D4—111no—
392C4×D4—111no—
393C4×D4—221no—
394C4×D4—221no—
395C4×D4C22×D1111yescharacteristic
396#117—21no—
397C2×C4⋊C4—111no—
398C2×C22⋊C4—221no—
399C2×C42C22×D1111yescharacteristic
400#107—111no—
401#107—111no—
402#106—111no—
403#106—111no—
404C4⋊C8—21no—
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#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—111no—
426C22⋊C8—111no—
427C22⋊C8—221no—
428C22⋊C8—221no—
429C22⋊C8—221no—
430C22⋊C8—221no—
431C22⋊C8—221no—
432#97—21no—
433#97C22⋊D1111yescharacteristic
434#97C22⋊D1111yescharacteristic
435C4×C8—21no—
436C4×C8—21no—
437C4×C8—111no—
438C4×C8—111no—
439C4×C8—111no—
440C4×C8—111no—
441C4×C8C22×D1111yescharacteristic
442C4×C8C22×D1111yescharacteristic
443C2×C11—41no—
444C2×C11—81no—
445C2×C11#293311yescharacteristic
446C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
447C2×C11#295711yescharacteristic
448D11—42no—
449D11—81no—
450C24—221no—
451C2×Q8C2×C4×D1111yescharacteristic
452C2×D4—21no—
453C2×D4—111no—
454C2×D4—111no—
455C2×D4—222no—
456C2×D4—221no—
457C2×D4—441no—
458C2×D4C2×C4×D1111yescharacteristic
459C22×C4—21no—
460C22×C4—221no—
461C22×C4—221no—
462C22×C4—221no—
463C22×C4—221no—
464C22×C4—221no—
465C22×C4—442no—
466C22×C4—442no—
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—442no—
478M16—442no—
479M16—442no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—42no—
483C2×C8—111no—
484C2×C8—111no—
485C2×C8—111no—
486C2×C8—111no—
487C2×C8—221no—
488C2×C8—221no—
489C2×C8—221no—
490C2×C8—221no—
491C2×C8—442no—
492C2×C8—442no—
493C2×C8C2×C22⋊D1111yescharacteristic
494C2×C8C2×C22⋊D1111yescharacteristic
495C2×C8C2×C22⋊D1111yescharacteristic
496C2×C8C2×C22⋊D1111yescharacteristic
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—111no—
502C4⋊C4—111no—
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—21no—
511C22⋊C4—221no—
512C22⋊C4—221no—
513C22⋊C4—221no—
514C22⋊C4—221no—
515C42—21no—
516C42C2×C4×D1111yescharacteristic
517C42#433911yescharacteristic
518C42C2×C22⋊D1111yescharacteristic
519C42C23×D1111yescharacteristic
520C11#1800611yescharacteristic, complemented, Sylow
521C23—21no—
522C23—221no—
523C23—221no—
524C23—442no—
525C23—442no—
526C23—881no—
527C23C4×C22⋊D1111yescharacteristic
528Q8—21no—
529Q8—21no—
530D4—21no—
531D4—21no—
532D4—81no—
533D4—112no—
534D4—221no—
535D4—221no—
536D4—221no—
537D4—442no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—221no—
549C2×C4—221no—
550C2×C4—442no—
551C2×C4—442no—
552C2×C4—442no—
553C2×C4—441no—
554C2×C4—441no—
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#6700212yes—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—222no—
584C22—441no—
585C22—441no—
586C22—441no—
587C22—441no—
588C22—441no—
589C22—884no—
590C22C2×C4×C22⋊D1111yescharacteristic
591C4—21no—
592C4—21no—
593C4—21no—
594C4—21no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—441no—
599C4—441no—
600C4D11×#13111yescharacteristic
601C4#1062328111yescharacteristic
602C4C2×#6700211yescharacteristic
603C4#1062335311yescharacteristic
604C2—41no—
605C2—81no—
606C2—442no—
607C2—881no—
608C2#1307733811yescharacteristic
609C2C4×#6700211yescharacteristic
610C2#1307753111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2969C2
socleC22×C11C2×C4×D4
prime radical#10622649C4
cosocleC42×C11C24
hypercenter#2969D11
hypocenterC11#18006
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #2969

Complements

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

NH ≅ G/Ntype
2. M16×D44C2semidirect
3. #13067528C2semidirect
4. #13067506C2semidirect
5. #13067494C2semidirect
6. #13067478C2semidirect
7. #13067450C2semidirect
8. #13067445C2semidirect
9. #13067426C2semidirect
10. C8×#4323C2semidirect
11. #13067404C2semidirect
12. #13067081C2semidirect
13. #13067006C2semidirect
14. #13066913C2semidirect
15. C11×#2969C2semidirect
19. C11×#446C22semidirect
20. C8×Q8×C11C22semidirect
22. C11×#436C22semidirect
24. C8×D4×C11C22semidirect
51. Q8⋊(C11⋊C8)C22semidirect
52. Q8⋊(C11⋊C8)C22semidirect
53. D4⋊(C11⋊C8)C22semidirect
54. D4⋊(C11⋊C8)C22semidirect
59. #10622118C22semidirect
60. #10622118C22semidirect
61. #10622117C22semidirect
62. #10622117C22semidirect
63. #10622093C22semidirect
64. #10622092C22semidirect
65. #10622092C22semidirect
66. C8×C11⋊C8C22semidirect
217. #2969D11semidirect
298. #446C2×D11semidirect
299. C8×Q8C2×D11semidirect
307. #436C2×D11semidirect
313. C8×D4C2×D11semidirect
520. C11#18006semidirect

Maximal subgroups

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

subgroupindex
#130786592
M16×D442
#130675282
#130675062
#130674942
#130674782
#130674502
#130674452
#130674262
C8×#43232
#130674042
#130670812
#130670062
#130669132
C11×#29692
#1800611