Finite Group Databasebeta

← #14724884

Subgroups — #14724884

Order 2816.

660 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078676C211yesmaximal, characteristic
2#13077362C211yesmaximal, characteristic, complemented
3#13067528C211yesmaximal, characteristic, complemented
4#13067499C211yesmaximal, characteristic, complemented
5#13067494C211yesmaximal, characteristic, complemented
6#13067478C211yesmaximal, characteristic, complemented
7#13067459C211yesmaximal, characteristic, complemented
8#13067443C211yesmaximal, characteristic, complemented
9#13067426C211yesmaximal, characteristic, complemented
10C8×#4325C211yesmaximal, characteristic, complemented
11#13067402C211yesmaximal, characteristic, complemented
12#13067084C211yesmaximal, characteristic, complemented
13#13067003C211yesmaximal, characteristic, complemented
14#13066913C211yesmaximal, characteristic, complemented
15C11×#2971C211yesmaximal, characteristic, complemented
16C4×C11×#41C2211yescharacteristic
17C2×#66960—21no—
18#10623008C2211yescharacteristic
19C8×Q8×C11C2211yescharacteristic
20C8×Q8×C11C2211yescharacteristic
21C11×#436—21no—
22C11×#436—21no—
23C11×#436C2211yescharacteristic
24C11×#436C2211yescharacteristic
25C11×#432—21no—
26C11×#432C2211yescharacteristic
27C4×C11×M16—21no—
28C4×C11×M16C2211yescharacteristic
29#10622851C411yescharacteristic
30#10622851C411yescharacteristic
31#10622742—21no—
32#10622640C411yescharacteristic
33C4×#4325C2211yescharacteristic
34C4×#4325C2211yescharacteristic
35#10622634C411yescharacteristic
36#10622628C411yescharacteristic
37C4×#4323C2211yescharacteristic
38C4×#4323C2211yescharacteristic
39#10622621C411yescharacteristic
40#10622616C411yescharacteristic
41#10622616C411yescharacteristic
42#10622538C2211yescharacteristic
43#10622538C2211yescharacteristic
44C2×C4⋊(C11⋊C8)C2211yescharacteristic
45#10622319—21no—
46#10622319—21no—
47#10622301C2211yescharacteristic
48#10622301C2211yescharacteristic
49C8×D44C2211yescharacteristic
50C8×D44C2211yescharacteristic
51Q8⋊(C11⋊C8)C2211yescharacteristic
52Q8⋊(C11⋊C8)C2211yescharacteristic
53D4⋊(C11⋊C8)C2211yescharacteristic
54D4⋊(C11⋊C8)C2211yescharacteristic
55#10622121C2211yescharacteristic
56#10622121C2211yescharacteristic
57#10622121C2211yescharacteristic
58#10622121C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622118C2211yescharacteristic
61#10622117C2211yescharacteristic
62#10622117C2211yescharacteristic
63#10622093C2211yescharacteristic
64#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×C11×#41C2×C411yescharacteristic
68C2×#4339—21no—
69C2×C11×M16—21no—
70C2×C11×M16—21no—
71C2×C11×M16D411yescharacteristic
72C2×C11×M16D411yescharacteristic
73C4×Q8×C11C2×C411yescharacteristic
74C4×Q8×C11C2311yescharacteristic
75C4×D4×C11—21no—
76C4×D4×C11—21no—
77C4×D4×C11C2×C411yescharacteristic
78C4×D4×C11C2311yescharacteristic
79C11×#117—21no—
80C11×#117C2×C411yescharacteristic
81C2×C42×C11—21no—
82C2×C42×C11C2311yescharacteristic
83C2×#4325C2×C411yescharacteristic
84C2×#4325C2×C411yescharacteristic
85C2×#4323C2×C411yescharacteristic
86C2×#4323C2×C411yescharacteristic
87#66983—21no—
88#66983C2×C411yescharacteristic
89#66983C2×C411yescharacteristic
90C22×C11⋊C8—21no—
91#66960—44no—
92C2×#4313—21no—
93C2×#4313—21no—
94C2×C8×D11—21no—
95C2×C8×D11—21no—
96#66928—21no—
97#66927C2×C411yescharacteristic
98C4×D44—21no—
99C4×D44C2311yescharacteristic
100C4×D44C2311yescharacteristic
101#66922C2×C411yescharacteristic
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#18011—111nomaximal, Sylow
146C11×#41—22no—
147C11×#41—41no—
148C2×Q8×C11C22×C411yescharacteristic
149C2×D4×C11—21no—
150C2×D4×C11C22×C411yescharacteristic
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11C22×C411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11#4111yescharacteristic
157C2×C22⋊D11—21no—
158C2×C22⋊D11—21no—
159#4339—42no—
160#4339—42no—
161C2×D44—21no—
162C2×D44—21no—
163C2×D44C22×C411yescharacteristic
164C2×D44C22×C411yescharacteristic
165C2×C4×D11—21no—
166C2×C4×D11—21no—
167C2×Dic22—21no—
168C11×M16—22no—
169C11×M16—41no—
170C11×M16—42no—
171C11×M16—42no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11C2×D411yescharacteristic
175C2×C8×C11C2×D411yescharacteristic
176C2×C8×C11C2×D411yescharacteristic
177C2×C8×C11C2×D411yescharacteristic
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—
185C42×C11—21no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11C22×C411yescharacteristic
189C42×C11C2×D411yescharacteristic
190C42×C11#4111yescharacteristic
191C42×C11C2411yescharacteristic
192#4325—22no—
193#4325—22no—
194#4323—41no—
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
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—42no—
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#3106—111no—
217#2971D1111yescharacteristic, complemented
218#2935—111no—
219#1594—111no—
220#1589—111no—
221#1588—111no—
222#1586—111no—
223#1583—111no—
224#1581—111no—
225SD16⋊C8—111no—
226C8×SD16—111no—
227#1573—111no—
228#1496—111no—
229#1477—111no—
230#1453—111no—
231C23×C11—21no—
232C23×C11C4×D411yescharacteristic
233C22×D11—21no—
234C22×D11—21no—
235Q8×C11—21no—
236Q8×C11#13112yescomplemented
237D4×C11—21no—
238D4×C11—21no—
239D4×C11—42no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—41no—
248C2×C4×C11—42no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—81no—
252C2×C4×C11C4×D411yescharacteristic
253C2×C4×C11C4×D411yescharacteristic
254C2×C4×C11C4×D411yescharacteristic
255C2×C4×C11C23×C411yescharacteristic
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C22⋊D11—42no—
259C22⋊D11—42no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262D44—21no—
263D44—21no—
264D44—21no—
265D44—21no—
266D44—42no—
267D44—81no—
268C4×D11—41no—
269C4×D11—41no—
270C4×D11—41no—
271C4×D11—41no—
272Dic22—42no—
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—
287C2×#131—221no—
288#532—111no—
289C4×#41C2×D1111yescharacteristic
290#482—111no—
291#482—111no—
292#477—111no—
293#476—111no—
294#460—111no—
295#459—111no—
296#449—111no—
297#449—111no—
298C8×Q8C2×D1111yescharacteristic
299C8×Q8C2×D1111yescharacteristic
300C4×SD16—111no—
301C4×SD16—111no—
302C4×D8—111no—
303C4×D8—111no—
304#436—21no—
305#436—21no—
306#436—111no—
307#436—111no—
308#436C2×D1111yescharacteristic
309#436C2×D1111yescharacteristic
310#435—221no—
311#435—221no—
312C8×D4—111no—
313C8×D4—111no—
314#432—21no—
315#432C2×D1111yescharacteristic
316#431—111no—
317#431—111no—
318C2×C4⋊C8—111no—
319#408—221no—
320C4×M16—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—41no—
346C2×D11—41no—
347C2×D11—41no—
348C2×D11—41no—
349C2×D11—41no—
350C2×D11—41no—
351C4×C11—21no—
352C4×C11—22no—
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—
364C2×#41—221no—
365C2×#41C4×D1111yescharacteristic
366C2×SD16—111no—
367C2×SD16—111no—
368C2×D8—111no—
369C2×D8—111no—
370#131—444no—
371C2×M16—21no—
372C2×M16—21no—
373C2×M16—221no—
374C2×M16—221no—
375C2×M16C22⋊D1111yescharacteristic
376C2×M16C22⋊D1111yescharacteristic
377C22×C8—221no—
378C22×C8—221no—
379C22×C8—221no—
380C4⋊Q8—111no—
381#127—111no—
382#124—221no—
383#121—111no—
384#121—111no—
385#121—221no—
386C4×Q8C4×D1111yescharacteristic
387C4×Q8C22×D1111yescharacteristic
388C4×D4—21no—
389C4×D4—21no—
390C4×D4—111no—
391C4×D4—111no—
392C4×D4—221no—
393C4×D4C4×D1111yescharacteristic
394C4×D4C22×D1111yescharacteristic
395#117—21no—
396#117C4×D1111yescharacteristic
397C2×C42—21no—
398C2×C42C22×D1111yescharacteristic
399#107—111no—
400#107—111no—
401#106—111no—
402#106—111no—
403C4⋊C8—21no—
404C4⋊C8—21no—
405C4⋊C8—111no—
406C4⋊C8—111no—
407C4⋊C8—111no—
408C4⋊C8—111no—
409C4⋊C8—221no—
410C4⋊C8—221no—
411C4⋊C8C22×D1111yescharacteristic
412C4⋊C8C22×D1111yescharacteristic
413#103—111no—
414#103—111no—
415#102—111no—
416#102—111no—
417#102—111no—
418#102—111no—
419#102—111no—
420#102—111no—
421C22⋊C8—21no—
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—
431#97—21no—
432#97C22⋊D1111yescharacteristic
433#97C22⋊D1111yescharacteristic
434C4×C8—21no—
435C4×C8—21no—
436C4×C8—111no—
437C4×C8—111no—
438C4×C8—111no—
439C4×C8—111no—
440C4×C8C22×D1111yescharacteristic
441C4×C8C22×D1111yescharacteristic
442C2×C11—41no—
443C2×C11—81no—
444C2×C11#293311yescharacteristic
445C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
446C2×C11#295711yescharacteristic
447D11—81no—
448D11—81no—
449#41—22no—
450#41—41no—
451#41—442no—
452#41—442no—
453C2×Q8—221no—
454C2×Q8C2×C4×D1111yescharacteristic
455C2×D4—21no—
456C2×D4—111no—
457C2×D4—111no—
458C2×D4—221no—
459C2×D4—221no—
460C2×D4—221no—
461C2×D4—221no—
462C2×D4C2×C4×D1111yescharacteristic
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—221no—
467C22×C4—221no—
468C22×C4C2×C4×D1111yescharacteristic
469C22×C4#433911yescharacteristic
470C22×C4C2×C22⋊D1111yescharacteristic
471SD16—222no—
472SD16—222no—
473D8—441no—
474D8—441no—
475M16—22no—
476M16—41no—
477M16—42no—
478M16—42no—
479M16—442no—
480M16—442no—
481C2×C8—21no—
482C2×C8—21no—
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×C8—442no—
494C2×C8C2×C22⋊D1111yescharacteristic
495C2×C8C2×C22⋊D1111yescharacteristic
496C2×C8C2×C22⋊D1111yescharacteristic
497C2×C8C2×C22⋊D1111yescharacteristic
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—111no—
501C4⋊C4—111no—
502C4⋊C4—221no—
503C4⋊C4C2×C4×D1111yescharacteristic
504C4⋊C4C2×C4×D1111yescharacteristic
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—221no—
509C22⋊C4—221no—
510C22⋊C4—221no—
511C22⋊C4—221no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42C2×C4×D1111yescharacteristic
516C42#433911yescharacteristic
517C42C2×C22⋊D1111yescharacteristic
518C42C23×D1111yescharacteristic
519C11#1801111yescharacteristic, complemented, Sylow
520C23—21no—
521C23—221no—
522C23—221no—
523C23C4×C22⋊D1111yescharacteristic
524Q8—21no—
525Q8—442no—
526Q8#6696012yescomplemented
527D4—21no—
528D4—21no—
529D4—42no—
530D4—221no—
531D4—221no—
532D4—221no—
533D4—221no—
534D4—442no—
535D4—442no—
536D4—442no—
537D4—881no—
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—42no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—81no—
550C2×C4—221no—
551C2×C4—221no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4C4×C22⋊D1111yescharacteristic
557C2×C4C4×C22⋊D1111yescharacteristic
558C2×C4C4×C22⋊D1111yescharacteristic
559C2×C4C22×C4×D1111yescharacteristic
560C2×C4C2×#433911yescharacteristic
561C2×C4C22×C22⋊D1111yescharacteristic
562C8—21no—
563C8—21no—
564C8—21no—
565C8—41no—
566C8—41no—
567C8—221no—
568C8—221no—
569C8—221no—
570C8—221no—
571C8—441no—
572C8—441no—
573C8—441no—
574C8—441no—
575C8#6700212yes—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—441no—
583C22—441no—
584C22—441no—
585C22—441no—
586C22—441no—
587C22—441no—
588C22C2×C4×C22⋊D1111yescharacteristic
589C4—21no—
590C4—21no—
591C4—21no—
592C4—22no—
593C4—21no—
594C4—41no—
595C4—41no—
596C4—441no—
597C4—441no—
598C4C2×#6696011yescharacteristic
599C4#1062327611yescharacteristic
600C4C2×#6700211yescharacteristic
601C4#1062335311yescharacteristic
602C2—41no—
603C2—81no—
604C2—881no—
605C2—881no—
606C2#1307734111yescharacteristic
607C2C4×#6700211yescharacteristic
608C2#1307753111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2971C2
socleC22×C11C2×C4×D4
prime radical#13078676C2
cosocleC42×C11C24
hypercenter#2971D11
hypocenterC11#18011
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #2971

Complements

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

NH ≅ G/Ntype
2. #13077362C2semidirect
3. #13067528C2semidirect
4. #13067499C2semidirect
5. #13067494C2semidirect
6. #13067478C2semidirect
7. #13067459C2semidirect
8. #13067443C2semidirect
9. #13067426C2semidirect
10. C8×#4325C2semidirect
11. #13067402C2semidirect
12. #13067084C2semidirect
13. #13067003C2semidirect
14. #13066913C2semidirect
15. C11×#2971C2semidirect
217. #2971D11semidirect
236. Q8×C11#131semidirect
519. C11#18011semidirect
526. Q8#66960semidirect

Maximal subgroups

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

subgroupindex
#130786762
#130773622
#130675282
#130674992
#130674942
#130674782
#130674592
#130674432
#130674262
C8×#43252
#130674022
#130670842
#130670032
#130669132
C11×#29712
#1801111