Finite Group Databasebeta

← #14725478

Subgroups — #14725478

Order 2816.

668 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077702C211yesmaximal, characteristic, complemented
2#13077648C211yesmaximal, characteristic
3C4×SD16×D11C211yesmaximal, characteristic
4#13067519C211yesmaximal, characteristic, complemented
5#13067462C211yesmaximal, characteristic, complemented
6#13067457C211yesmaximal, characteristic, complemented
7#13067455C211yesmaximal, characteristic, complemented
8#13067450C211yesmaximal, characteristic, complemented
9#13067430C211yesmaximal, characteristic, complemented
10#13067427C211yesmaximal, characteristic, complemented
11#13067378C211yesmaximal, characteristic, complemented
12#13067061C211yesmaximal, characteristic, complemented
13#13067057C211yesmaximal, characteristic
14#13066902C211yesmaximal, characteristic, complemented
15C11×#1592C211yesmaximal, characteristic, complemented
16C2×SD16×D11C411yescharacteristic
17C4×Q8×D11C2211yescharacteristic
18C4×D4×D11C2211yescharacteristic
19C11×#446C2211yescharacteristic, complemented
20C4×C11×SD16C2211yescharacteristic
21C11×#436C2211yescharacteristic
22SD16×Dic11C411yescharacteristic
23#10622740—21no—
24#10622739—21no—
25C4×#4325C2211yescharacteristic
26#10622637C2211yescharacteristic, complemented
27C4×#4324C2211yescharacteristic
28#10622625C2211yescharacteristic
29D11×#106C411yescharacteristic
30#10622465C411yescharacteristic
31#10622448C2211yescharacteristic
32#10622448C2211yescharacteristic
33#10622447C2211yescharacteristic
34#10622446—21no—
35#10622443C2211yescharacteristic, complemented
36#10622441—21no—
37D11×#103C411yescharacteristic
38#10622401C411yescharacteristic
39D11×#102C411yescharacteristic
40#10622371C411yescharacteristic
41#10622341—21no—
42D11×C22⋊C8—21no—
43#10622318—21no—
44#10622314—21no—
45C4×#4314C2211yescharacteristic
46C4×#4313C2211yescharacteristic
47C8×D44C2211yescharacteristic
48#10622298C2211yescharacteristic
49C4×C8×D11C2211yescharacteristic
50C8×Dic22C2211yescharacteristic, complemented
51C11×#335C2211yescharacteristic, complemented
52C11×Q8⋊C8C2211yescharacteristic, complemented
53C11×D4⋊C8C2211yescharacteristic
54C11×#322C2211yescharacteristic, complemented
55Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
56D4⋊(C11⋊C8)C2211yescharacteristic
57#10622122C2211yescharacteristic, complemented
58#10622121C2211yescharacteristic
59#10622118C2211yescharacteristic, complemented
60#10622118C2211yescharacteristic, complemented
61#10622097C2211yescharacteristic
62#10622096C2211yescharacteristic, complemented
63#10622094C2211yescharacteristic, complemented
64#10622093C2211yescharacteristic, complemented
65#10622093C2211yescharacteristic, complemented
66#10622092C2211yescharacteristic, complemented
67C2×Q8×D11C2×C411yescharacteristic
68C2×D4×D11C2×C411yescharacteristic
69C22×C4×D11—21no—
70C2×C11×SD16C2×C411yescharacteristic
71C2×C11×M16—21no—
72C4×Q8×C11C2311yescharacteristic
73C4×D4×C11C2311yescharacteristic
74Q8×Dic11C2×C411yescharacteristic
75C2×#4325C2×C411yescharacteristic
76D4×Dic11C2×C411yescharacteristic
77C2×#4324C2×C411yescharacteristic
78C4×C22⋊D11—21no—
79C2×#4318—21no—
80SD16×D11—24no—
81C2×#4314C2×C411yescharacteristic
82C2×#4313—21no—
83C2×C8×D11—21no—
84C2×C8×D11—21no—
85C2×C8×D11C2×C411yescharacteristic
86C2×C8×D11C2×C411yescharacteristic
87#66946C2×C411yescharacteristic
88C4⋊C4×D11—21no—
89C4⋊C4×D11C2×C411yescharacteristic
90C4⋊C4×D11C2×C411yescharacteristic
91#66940—21no—
92#66940C2×C411yescharacteristic
93(C22⋊D11)⋊C4—21no—
94C22⋊C4×D11—21no—
95C4×D44C2311yescharacteristic
96C42×D11—21no—
97C42×D11C2311yescharacteristic
98C4×Dic22—21no—
99C4×Dic22C2311yescharacteristic
100C11×#106C2×C411yescharacteristic
101C11×C4⋊C8—21no—
102C11×C4⋊C8C2311yescharacteristic
103C11×C4⋊C8C2311yescharacteristic
104C11×#103C2×C411yescharacteristic
105C11×#102C2×C411yescharacteristic
106C11×C22⋊C8—21no—
107C11×#97—21no—
108C4×C8×C11C2311yescharacteristic
109C4×C8×C11C2311yescharacteristic
110C4×C8×C11C2311yescharacteristic
111#66899C2×C411yescharacteristic
112#66896C2×C411yescharacteristic
113C22⋊(C11⋊C8)—21no—
114#66885C2×C411yescharacteristic
115(C2×D11)⋊C8—21no—
116(C2×D11)⋊C8—21no—
117(C2×D11)⋊C8—21no—
118(C2×D11)⋊C8—21no—
119(C2×D11)⋊C8D411yescharacteristic
120(C2×D11)⋊C8D411yescharacteristic
121#66881C2×C411yescharacteristic
122#66880C2×C411yescharacteristic
123#66879—21no—
124#66879—21no—
125#66879—21no—
126Dic11⋊C8—21no—
127Dic11⋊C8—21no—
128Dic11⋊C8D411yescharacteristic
129Dic11⋊C8D411yescharacteristic
130C8×Dic11—21no—
131C8×Dic11—21no—
132C8×Dic11C2×C411yescharacteristic
133C8×Dic11C2×C411yescharacteristic
134#66874C2×C411yescharacteristic
135#66873C2×C411yescharacteristic
136#66872C2×C411yescharacteristic
137#66872C2×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#18060—111nomaximal, Sylow
146C23×D11—21no—
147C2×Q8×C11C22×C411yescharacteristic
148C2×D4×C11C22×C411yescharacteristic
149C22×C4×C11—21no—
150C2×C22⋊D11—21no—
151C22×Dic11—21no—
152Q8×D11—22no—
153Q8×D11—41no—
154D4×D11—22no—
155D4×D11—41no—
156C2×D44C22×C411yescharacteristic
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—81no—
163C2×C4×D11—81no—
164C2×C4×D11C22×C411yescharacteristic
165C2×C4×D11C2×D411yescharacteristic
166C2×C4×D11#4111yescharacteristic
167C2×Dic22—21no—
168C2×Dic22C22×C411yescharacteristic
169C11×SD16—22no—
170C11×M16—81no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11C22×C411yescharacteristic
175C2×C8×C11C22×C411yescharacteristic
176C2×C8×C11C2×D411yescharacteristic
177C2×C8×C11C2×D411yescharacteristic
178C11×C4⋊C4—21no—
179C11×C4⋊C4C22×C411yescharacteristic
180C11×C4⋊C4C22×C411yescharacteristic
181C11×C22⋊C4—21no—
182C42×C11—21no—
183C42×C11C2411yescharacteristic
184C22⋊Dic11—21no—
185#4325—22no—
186#4324—22no—
187(C2×D11)⋊C4—21no—
188(C2×D11)⋊C4—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11C22×C411yescharacteristic
191C4⋊Dic11C22×C411yescharacteristic
192Dic11⋊C4—21no—
193Dic11⋊C4—21no—
194Dic11⋊C4—21no—
195Dic11⋊C4—21no—
196C4×Dic11—21no—
197C4×Dic11—21no—
198C4×Dic11—21no—
199C4×Dic11C22×C411yescharacteristic
200C4×Dic11C2×D411yescharacteristic
201C4×Dic11#4111yescharacteristic
202#4318—81no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8C22×C411yescharacteristic
207C2×C11⋊C8C22×C411yescharacteristic
208C2×C11⋊C8C2×D411yescharacteristic
209C2×C11⋊C8C2×D411yescharacteristic
210#4314M1614yescomplemented
211#4313—42no—
212C8×D11—22no—
213C8×D11—41no—
214C8×D11—81no—
215C8×D11—81no—
216#2984—111no—
217#2974—111no—
218C2×C4×SD16—111no—
219#1592—111no—
220#1592D1111yescharacteristic, complemented
221#1583—111no—
222#1583—111no—
223#1582—111no—
224#1582—111no—
225SD16⋊C8—111no—
226SD16⋊C8—111no—
227#1568—111no—
228#1491—111no—
229#1490—111no—
230#1451—111no—
231C23×C11—21no—
232C22×D11—21no—
233C22×D11—42no—
234C22×D11—42no—
235C22×D11—81no—
236C22×D11C4×D411yescharacteristic
237Q8×C11—21no—
238Q8×C11—21no—
239D4×C11—21no—
240D4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11C23×C411yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C22⋊D11—42no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—81no—
254C2×Dic11C4×D411yescharacteristic
255C2×Dic11C4×D411yescharacteristic
256C2×Dic11C4×D411yescharacteristic
257D44—21no—
258D44C2×M1612yes—
259C4×D11—22no—
260C4×D11—21no—
261C4×D11—21no—
262C4×D11—21no—
263C4×D11—21no—
264C4×D11—42no—
265C4×D11—42no—
266C4×D11—41no—
267C4×D11—41no—
268C4×D11—81no—
269C4×D11—81no—
270Dic22—21no—
271Dic22—42no—
272Dic22C2×M1612yes—
273C8×C11—21no—
274C8×C11—21no—
275C8×C11—21no—
276C8×C11—41no—
277C8×C11—41no—
278C8×C11—41no—
279C8×C11C2×M1612yes—
280C11⋊C8—21no—
281C11⋊C8—21no—
282C11⋊C8—21no—
283C11⋊C8—21no—
284C11⋊C8—41no—
285C11⋊C8—41no—
286C11⋊C8—41no—
287C22×SD16—111no—
288C2×C4×Q8—111no—
289C2×C4×D4—111no—
290#446—111no—
291#446—221no—
292#446—221no—
293#446C2×D1111yescharacteristic, complemented
294C8×Q8—111no—
295C8×Q8—111no—
296C4×SD16—111no—
297C4×SD16—111no—
298C4×SD16—111no—
299C4×SD16—111no—
300C4×SD16—111no—
301C4×SD16—111no—
302C4×SD16—111no—
303C4×SD16C2×D1111yescharacteristic
304#436—111no—
305#436C2×D1111yescharacteristic
306#435—221no—
307#435—221no—
308C8×D4—111no—
309C8×D4—111no—
310#432—111no—
311#432—111no—
312#432—221no—
313#431—111no—
314#431—221no—
315C2×#106—111no—
316C2×#103—111no—
317C2×#102—111no—
318#407—221no—
319C2×C22⋊C8—221no—
320C4×M16—111no—
321C2×C4×C8—111no—
322#335—111no—
323#335C2×D1111yescharacteristic, complemented
324#334—111no—
325#334—111no—
326Q8⋊C8—111no—
327Q8⋊C8—111no—
328Q8⋊C8—111no—
329Q8⋊C8C2×D1111yescharacteristic, complemented
330D4⋊C8—111no—
331D4⋊C8—111no—
332D4⋊C8—111no—
333D4⋊C8C2×D1111yescharacteristic
334#322—111no—
335#322—111no—
336#322—111no—
337#322C2×D1111yescharacteristic, complemented
338C22×C11—41no—
339C22×C11—41no—
340C22×C11—41no—
341C22×C11C2×C4×D411yescharacteristic
342C2×D11—21no—
343C2×D11—21no—
344C2×D11—22no—
345C2×D11—41no—
346C2×D11—41no—
347C2×D11—84no—
348C2×D11#44412yes—
349C4×C11—21no—
350C4×C11—41no—
351C4×C11—41no—
352C4×C11—41no—
353C4×C11C22×M1611yescharacteristic
354C4×C11#56811yescharacteristic
355C4×C11#57711yescharacteristic
356C4×C11#57711yescharacteristic
357Dic11—22no—
358Dic11—21no—
359Dic11—21no—
360Dic11—21no—
361Dic11—41no—
362Dic11—41no—
363C22×Q8—111no—
364C22×D4—111no—
365C23×C4—221no—
366C2×SD16—111no—
367C2×SD16—111no—
368C2×SD16—111no—
369C2×SD16—224no—
370C2×SD16C4×D1111yescharacteristic
371C2×M16—21no—
372C2×M16—221no—
373C2×M16—221no—
374C22×C8—111no—
375C22×C8—111no—
376C22×C8—221no—
377C22×C8—221no—
378C4×Q8—111no—
379C4×Q8—111no—
380C4×Q8—111no—
381C4×Q8—221no—
382C4×Q8—221no—
383C4×Q8C22×D1111yescharacteristic
384C4×D4—111no—
385C4×D4—111no—
386C4×D4—111no—
387C4×D4—221no—
388C4×D4—221no—
389C4×D4C22×D1111yescharacteristic
390C2×C4⋊C4—111no—
391C2×C4⋊C4—111no—
392C2×C4⋊C4—221no—
393C2×C22⋊C4—221no—
394C2×C42—111no—
395C2×C42—221no—
396#106—111no—
397#106—111no—
398#106—111no—
399#106C4×D1111yescharacteristic
400C4⋊C8—21no—
401C4⋊C8—111no—
402C4⋊C8—111no—
403C4⋊C8—111no—
404C4⋊C8—111no—
405C4⋊C8—221no—
406C4⋊C8—221no—
407C4⋊C8—221no—
408C4⋊C8C22×D1111yescharacteristic
409C4⋊C8C22×D1111yescharacteristic
410#103—111no—
411#103—111no—
412#103—111no—
413#103C4×D1111yescharacteristic
414#102—111no—
415#102—111no—
416#102—111no—
417#102C4×D1111yescharacteristic
418C22⋊C8—21no—
419C22⋊C8—111no—
420C22⋊C8—111no—
421C22⋊C8—221no—
422C22⋊C8—221no—
423C22⋊C8—221no—
424C22⋊C8—221no—
425C22⋊C8—221no—
426#97—21no—
427#97—221no—
428#97—221no—
429#97—221no—
430#97—221no—
431C4×C8—111no—
432C4×C8—111no—
433C4×C8—111no—
434C4×C8—111no—
435C4×C8—111no—
436C4×C8—221no—
437C4×C8—221no—
438C4×C8C22×D1111yescharacteristic
439C4×C8C22×D1111yescharacteristic
440C4×C8C22×D1111yescharacteristic
441C2×C11—81no—
442C2×C11D4×M1611yescharacteristic
443C2×C11#294911yescharacteristic
444C2×C11C2×#44411yescharacteristic
445D11—22no—
446D11—42no—
447C24—221no—
448C2×Q8—111no—
449C2×Q8—221no—
450C2×Q8—222no—
451C2×Q8—441no—
452C2×Q8C2×C4×D1111yescharacteristic
453C2×D4—111no—
454C2×D4—221no—
455C2×D4—222no—
456C2×D4—441no—
457C2×D4C2×C4×D1111yescharacteristic
458C22×C4—21no—
459C22×C4—111no—
460C22×C4—111no—
461C22×C4—111no—
462C22×C4—221no—
463C22×C4—221no—
464C22×C4—221no—
465C22×C4—221no—
466C22×C4—221no—
467C22×C4—221no—
468C22×C4—881no—
469C22×C4—881no—
470SD16—22no—
471SD16—114no—
472SD16—222no—
473SD16—222no—
474M16—81no—
475M16—442no—
476M16—881no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—111no—
481C2×C8—111no—
482C2×C8—111no—
483C2×C8—111no—
484C2×C8—222no—
485C2×C8—221no—
486C2×C8—221no—
487C2×C8—221no—
488C2×C8—441no—
489C2×C8—881no—
490C2×C8—881no—
491C2×C8C2×C4×D1111yescharacteristic
492C2×C8C2×C4×D1111yescharacteristic
493C2×C8D4×D1111yescharacteristic
494C2×C8D4×D1111yescharacteristic
495C4⋊C4—21no—
496C4⋊C4—111no—
497C4⋊C4—111no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4—221no—
501C4⋊C4—221no—
502C4⋊C4—221no—
503C4⋊C4C2×C4×D1111yescharacteristic
504C4⋊C4C2×C4×D1111yescharacteristic
505C22⋊C4—21no—
506C22⋊C4—221no—
507C22⋊C4—221no—
508C22⋊C4—221no—
509C42—21no—
510C42—111no—
511C42—111no—
512C42—111no—
513C42—221no—
514C42—221no—
515C42—221no—
516C42C23×D1111yescharacteristic
517C11#1806011yescharacteristic, complemented, Sylow
518C23—21no—
519C23—111no—
520C23—221no—
521C23—442no—
522C23—442no—
523C23—881no—
524Q8—21no—
525Q8—21no—
526Q8—112no—
527Q8—221no—
528Q8—442no—
529D4—21no—
530D4—21no—
531D4—112no—
532D4—221no—
533D4—442no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—111no—
540C2×C4—111no—
541C2×C4—111no—
542C2×C4—222no—
543C2×C4—221no—
544C2×C4—221no—
545C2×C4—221no—
546C2×C4—221no—
547C2×C4—221no—
548C2×C4—221no—
549C2×C4—221no—
550C2×C4—442no—
551C2×C4—442no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—881no—
555C2×C4—881no—
556C2×C4—881no—
557C2×C4C22×C4×D1111yescharacteristic
558C2×C4C2×D4×D1111yescharacteristic
559C2×C4#41×D1111yescharacteristic
560C8—21no—
561C8—21no—
562C8—21no—
563C8—41no—
564C8—41no—
565C8—41no—
566C8—221no—
567C8—221no—
568C8—221no—
569C8—221no—
570C8—441no—
571C8—441no—
572C8—441no—
573C8M16×D1112yes—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—112no—
578C22—221no—
579C22—221no—
580C22—222no—
581C22—441no—
582C22—441no—
583C22—884no—
584C22C4×D4×D1111yescharacteristic
585C4—21no—
586C4—41no—
587C4—41no—
588C4—41no—
589C4—221no—
590C4—221no—
591C4—222no—
592C4—221no—
593C4—441no—
594C4—441no—
595C4C2×M16×D1111yescharacteristic
596C4#1062328111yescharacteristic
597C4#1062330611yescharacteristic
598C4#1062330911yescharacteristic
599C2—81no—
600C2—222no—
601C2—442no—
602C2#1307735211yescharacteristic
603C2#1307747211yescharacteristic
604C2D11×#44411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1592C2
socleC22×C11C2×C4×D4
prime radicalC2×D4×D11C2×C4
cosocleC42×C11C24
hypercenter#1592D11
hypocenterC11#18060
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1592

Complements

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

NH ≅ G/Ntype
1. #13077702C2semidirect
4. #13067519C2semidirect
5. #13067462C2semidirect
6. #13067457C2semidirect
7. #13067455C2semidirect
8. #13067450C2semidirect
9. #13067430C2semidirect
10. #13067427C2semidirect
11. #13067378C2semidirect
12. #13067061C2semidirect
14. #13066902C2semidirect
15. C11×#1592C2semidirect
19. C11×#446C22semidirect
26. #10622637C22semidirect
35. #10622443C22semidirect
50. C8×Dic22C22semidirect
51. C11×#335C22semidirect
52. C11×Q8⋊C8C22semidirect
54. C11×#322C22semidirect
55. Q8⋊(C11⋊C8)C22semidirect
57. #10622122C22semidirect
59. #10622118C22semidirect
60. #10622118C22semidirect
62. #10622096C22semidirect
63. #10622094C22semidirect
64. #10622093C22semidirect
65. #10622093C22semidirect
66. #10622092C22semidirect
210. #4314M16semidirect
220. #1592D11semidirect
293. #446C2×D11semidirect
323. #335C2×D11semidirect
329. Q8⋊C8C2×D11semidirect
337. #322C2×D11semidirect
517. C11#18060semidirect

Maximal subgroups

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

subgroupindex
#130777022
#130776482
C4×SD16×D112
#130675192
#130674622
#130674572
#130674552
#130674502
#130674302
#130674272
#130673782
#130670612
#130670572
#130669022
C11×#15922
#1806011