Finite Group Databasebeta

← #14723828

Subgroups — #14723828

Order 2816.

648 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#13078667C211yesmaximal, characteristic
2#13077768C211yesmaximal, characteristic, complemented
3#13077637C211yesmaximal, characteristic, complemented
4#13067480C211yesmaximal, characteristic, complemented
5#13067471C211yesmaximal, characteristic, complemented
6#13067447C211yesmaximal, characteristic, complemented
7#13067439C211yesmaximal, characteristic, complemented
8SD16⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
9#13067413C211yesmaximal, characteristic, complemented
10#13067408C211yesmaximal, characteristic, complemented
11#13067403C211yesmaximal, characteristic, complemented
12#13067039C211yesmaximal, characteristic, complemented
13#13067023C211yesmaximal, characteristic, complemented
14#13066917C211yesmaximal, characteristic, complemented
15C11×#1582C211yesmaximal, characteristic, complemented
16#10623111C2211yescharacteristic
17C4×D4×D11C2211yescharacteristic
18C11×#446C2211yescharacteristic, complemented
19C4×C11×SD16C2211yescharacteristic
20C8×D4×C11C2211yescharacteristic
21#10622782C411yescharacteristic
22#10622778C411yescharacteristic
23C8×C22⋊D11—21no—
24C2×(C2×D11)⋊C8—21no—
25C4×#4325C2211yescharacteristic
26Q8×C11⋊C8C2211yescharacteristic, complemented
27C4×#4323C2211yescharacteristic
28D4×C11⋊C8C2211yescharacteristic
29#10622484C411yescharacteristic
30#10622476C411yescharacteristic
31#10622452—21no—
32#10622451—21no—
33#10622450C2211yescharacteristic
34#10622447C2211yescharacteristic
35#10622447C2211yescharacteristic, complemented
36#10622446C2211yescharacteristic
37#10622432C411yescharacteristic
38#10622422C411yescharacteristic
39#10622386C411yescharacteristic
40#10622379C411yescharacteristic
41(C22⋊D11)⋊C8—21no—
42D11×C22⋊C8—21no—
43#10622322—21no—
44#10622319—21no—
45C4×D88C2211yescharacteristic
46#10622301C2211yescharacteristic, complemented
47C8×D44C2211yescharacteristic
48#10622298C2211yescharacteristic
49#10622298C2211yescharacteristic
50#10622298C2211yescharacteristic
51C11×#334C2211yescharacteristic, complemented
52C11×Q8⋊C8C2211yescharacteristic, complemented
53C11×D4⋊C8C2211yescharacteristic
54C11×#322C2211yescharacteristic, complemented
55Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
56D4⋊(C11⋊C8)C2211yescharacteristic
57#10622121C2211yescharacteristic
58#10622121C2211yescharacteristic, complemented
59#10622118C2211yescharacteristic, complemented
60#10622117C2211yescharacteristic, complemented
61#10622097C2211yescharacteristic
62#10622097C2211yescharacteristic, complemented
63#10622096C2211yescharacteristic, complemented
64#10622093C2211yescharacteristic, complemented
65#10622092C2211yescharacteristic, complemented
66C8×C11⋊C8C2211yescharacteristic, complemented
67C2×D4×D11C2×C411yescharacteristic
68C22×C4×D11—21no—
69C2×C11×SD16C2×C411yescharacteristic
70C22×C8×C11—21no—
71C4×Q8×C11C2311yescharacteristic
72C4×D4×C11C2311yescharacteristic
73#67000C2×C411yescharacteristic
74#66999C2×C411yescharacteristic
75C2×#4325C2×C411yescharacteristic
76D4×Dic11C2×C411yescharacteristic
77C2×#4323C2×C411yescharacteristic
78C4×C22⋊D11—21no—
79C22×C11⋊C8—21no—
80C2×D88C2×C411yescharacteristic
81C2×#4313—21no—
82C2×#4313—21no—
83C2×C8×D11—21no—
84C2×C8×D11—21no—
85C2×C8×D11—21no—
86#66951—21no—
87#66948C2×C411yescharacteristic
88#66947—21no—
89#66946C2×C411yescharacteristic
90C4⋊C4×D11C2×C411yescharacteristic
91#66943C2×C411yescharacteristic
92(C22⋊D11)⋊C4—21no—
93C22⋊C4×D11—21no—
94C4×D44—21no—
95C4×D44C2311yescharacteristic
96C4×D44C2311yescharacteristic
97#66925—21no—
98C42×D11C2311yescharacteristic
99C11×#106C2×C411yescharacteristic
100C11×C4⋊C8—21no—
101C11×C4⋊C8C2311yescharacteristic
102C11×C4⋊C8C2311yescharacteristic
103C11×#103C2×C411yescharacteristic
104C11×#102C2×C411yescharacteristic
105C11×C22⋊C8—21no—
106C11×#97—21no—
107C4×C8×C11C2311yescharacteristic
108C4×C8×C11C2311yescharacteristic
109C4×C8×C11C2311yescharacteristic
110#66899C2×C411yescharacteristic
111#66896C2×C411yescharacteristic
112C22⋊(C11⋊C8)—21no—
113#66885C2×C411yescharacteristic
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)⋊C8—21no—
120(C2×D11)⋊C8—21no—
121(C2×D11)⋊C8C2×C411yescharacteristic
122(C2×D11)⋊C8C2×C411yescharacteristic
123(C2×D11)⋊C8D411yescharacteristic
124(C2×D11)⋊C8D411yescharacteristic
125#66882C2×C411yescharacteristic
126Dic11⋊C8—21no—
127Dic11⋊C8—21no—
128Dic11⋊C8C2×C411yescharacteristic
129Dic11⋊C8C2×C411yescharacteristic
130Dic11⋊C8D411yescharacteristic
131Dic11⋊C8D411yescharacteristic
132C8×Dic11—21no—
133#66873C2×C411yescharacteristic
134#66873C2×C411yescharacteristic
135#66872C2×C411yescharacteristic
136#66871C2×C411yescharacteristic
137C4⋊(C11⋊C8)—21no—
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4×C11⋊C8—21no—
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#17918—111nomaximal, Sylow
145C23×D11—21no—
146C2×Q8×C11C22×C411yescharacteristic
147C2×D4×C11C22×C411yescharacteristic
148C22×C4×C11—21no—
149C2×C22⋊D11—21no—
150C22×Dic11—21no—
151D4×D11—22no—
152D4×D11—22no—
153C2×D44—21no—
154C2×D44C22×C411yescharacteristic
155C2×D44C22×C411yescharacteristic
156C2×C4×D11—21no—
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×C4×D11—81no—
161C2×C4×D11—81no—
162C2×C4×D11C22×C411yescharacteristic
163C2×C4×D11C2×D411yescharacteristic
164C2×C4×D11#4111yescharacteristic
165C11×SD16—22no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—81no—
170C2×C8×C11C22×C411yescharacteristic
171C2×C8×C11C22×C411yescharacteristic
172C2×C8×C11C2×D411yescharacteristic
173C2×C8×C11C2×D411yescharacteristic
174C11×C4⋊C4—21no—
175C11×C4⋊C4C22×C411yescharacteristic
176C11×C4⋊C4C22×C411yescharacteristic
177C11×C22⋊C4—21no—
178C42×C11—21no—
179C42×C11C2411yescharacteristic
180C22⋊Dic11—21no—
181#4325—22no—
182#4323—22no—
183(C2×D11)⋊C4—21no—
184(C2×D11)⋊C4—21no—
185(C2×D11)⋊C4—21no—
186(C2×D11)⋊C4—21no—
187(C2×D11)⋊C4—21no—
188(C2×D11)⋊C4—21no—
189(C2×D11)⋊C4—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11C22×C411yescharacteristic
192C4⋊Dic11C22×C411yescharacteristic
193Dic11⋊C4—21no—
194Dic11⋊C4—21no—
195Dic11⋊C4—21no—
196C4×Dic11C22×C411yescharacteristic
197C4×Dic11C2×D411yescharacteristic
198C4×Dic11#4111yescharacteristic
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—81no—
203C2×C11⋊C8C22×C411yescharacteristic
204C2×C11⋊C8C22×C411yescharacteristic
205C2×C11⋊C8C2×D411yescharacteristic
206C2×C11⋊C8C2×D411yescharacteristic
207D88—22no—
208#4313—81no—
209#4313—81no—
210C8×D11—81no—
211C8×D11—81no—
212C8×D11—81no—
213#3105—111no—
214#2993—111no—
215#2972—111no—
216#1586—111no—
217#1585—111no—
218#1582D1111yescharacteristic, complemented
219#1581—111no—
220#1580—111no—
221SD16⋊C8—111no—
222C8×SD16—111no—
223C8×D8—111no—
224#1574—111no—
225#1486—111no—
226#1482—111no—
227#1454—111no—
228C23×C11—21no—
229C22×D11—21no—
230C22×D11—24no—
231C22×D11—21no—
232C22×D11—81no—
233C22×D11—81no—
234C22×D11C4×D411yescharacteristic
235Q8×C11—21no—
236Q8×C11—21no—
237D4×C11—21no—
238D4×C11#13112yes—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11C23×C411yescharacteristic
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C22⋊D11—24no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—81no—
251C2×Dic11C4×D411yescharacteristic
252C2×Dic11C4×D411yescharacteristic
253C2×Dic11C4×D411yescharacteristic
254D44—21no—
255D44—21no—
256D44—21no—
257D44—81no—
258D44#13112yes—
259C4×D11—21no—
260C4×D11—21no—
261C4×D11—21no—
262C4×D11—21no—
263C4×D11—41no—
264C4×D11—41no—
265C4×D11—41no—
266C4×D11—41no—
267C4×D11—41no—
268C4×D11—81no—
269C4×D11—81no—
270C8×C11—21no—
271C8×C11—21no—
272C8×C11—21no—
273C8×C11—21no—
274C8×C11—41no—
275C8×C11—41no—
276C8×C11—41no—
277C11⋊C8—21no—
278C11⋊C8—21no—
279C11⋊C8—21no—
280C11⋊C8—21no—
281C11⋊C8—41no—
282C11⋊C8—41no—
283C11⋊C8—41no—
284#529—111no—
285C2×C4×D4—111no—
286#484—111no—
287#481—111no—
288#478—111no—
289#478—111no—
290#463—111no—
291#463—111no—
292#450—111no—
293#447—111no—
294#446C2×D1111yescharacteristic, complemented
295C8×Q8—111no—
296C4×SD16—111no—
297C4×SD16C2×D1111yescharacteristic
298C4×D8—111no—
299C4×D8—111no—
300#436—111no—
301#436—221no—
302#435—221no—
303C8×D4—111no—
304C8×D4—111no—
305C8×D4—111no—
306C8×D4—111no—
307C8×D4—221no—
308C8×D4—221no—
309C8×D4C2×D1111yescharacteristic
310#433—221no—
311#431—111no—
312#431—111no—
313#431—111no—
314#431—111no—
315#424—221no—
316#423—111no—
317C2×C22⋊C8—221no—
318C2×C22⋊C8—221no—
319#335—111no—
320#335—111no—
321#334—111no—
322#334C2×D1111yescharacteristic, complemented
323Q8⋊C8—111no—
324Q8⋊C8C2×D1111yescharacteristic, complemented
325D4⋊C8—111no—
326D4⋊C8—111no—
327D4⋊C8—111no—
328D4⋊C8—111no—
329D4⋊C8—111no—
330D4⋊C8C2×D1111yescharacteristic
331#322—111no—
332#322—111no—
333#322C2×D1111yescharacteristic, complemented
334C82—111no—
335C22×C11—22no—
336C22×C11—41no—
337C22×C11—41no—
338C22×C11C2×C4×D411yescharacteristic
339C2×D11—21no—
340C2×D11—22no—
341C2×D11—21no—
342C2×D11—21no—
343C2×D11—41no—
344C2×D11—41no—
345C2×D11—41no—
346C2×D11—41no—
347C2×D11—41no—
348C2×D11—84no—
349C4×C11—21no—
350C4×C11—41no—
351C4×C11—41no—
352C4×C11—41no—
353C4×C11C2×#13111yescharacteristic
354C4×C11C2×#13111yescharacteristic
355C4×C11#57611yescharacteristic
356C4×C11#57711yescharacteristic
357Dic11—21no—
358Dic11—21no—
359Dic11—21no—
360Dic11—41no—
361Dic11—41no—
362C22×D4—111no—
363C23×C4—221no—
364C2×SD16—111no—
365C2×SD16C4×D1111yescharacteristic
366C2×D8—111no—
367C2×D8—111no—
368C2×M16—221no—
369C2×M16—221no—
370C22×C8—21no—
371C22×C8—221no—
372C22×C8—221no—
373C22×C8—221no—
374C22×C8—221no—
375#126—221no—
376#125—111no—
377#124—111no—
378#123—221no—
379C22⋊Q8—111no—
380#121—111no—
381C4×Q8C22×D1111yescharacteristic
382C4×D4—111no—
383C4×D4—111no—
384C4×D4—111no—
385C4×D4—111no—
386C4×D4—221no—
387C4×D4—221no—
388C4×D4—221no—
389C4×D4C22×D1111yescharacteristic
390#117—221no—
391C2×C4⋊C4—111no—
392C2×C22⋊C4—221no—
393C2×C42—111no—
394#107—111no—
395#107—111no—
396#106—111no—
397#106C4×D1111yescharacteristic
398C4⋊C8—21no—
399C4⋊C8—111no—
400C4⋊C8—111no—
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#103C4×D1111yescharacteristic
412#102—111no—
413#102—111no—
414#102—111no—
415#102—111no—
416#102—111no—
417#102C4×D1111yescharacteristic
418C22⋊C8—21no—
419C22⋊C8—111no—
420C22⋊C8—111no—
421C22⋊C8—111no—
422C22⋊C8—111no—
423C22⋊C8—221no—
424C22⋊C8—221no—
425C22⋊C8—221no—
426C22⋊C8—221no—
427C22⋊C8—221no—
428C22⋊C8—221no—
429C22⋊C8—221no—
430#97—21no—
431C4×C8—111no—
432C4×C8—111no—
433C4×C8—111no—
434C4×C8—221no—
435C4×C8—221no—
436C4×C8C22×D1111yescharacteristic
437C4×C8C22×D1111yescharacteristic
438C4×C8C22×D1111yescharacteristic
439C2×C11—42no—
440C2×C11#292911yescharacteristic
441C2×C11#294611yescharacteristic
442C2×C11#295711yescharacteristic
443D11—41no—
444D11—42no—
445D11—81no—
446C24—221no—
447C2×Q8C2×C4×D1111yescharacteristic
448C2×D4—111no—
449C2×D4—111no—
450C2×D4—221no—
451C2×D4—221no—
452C2×D4—222no—
453C2×D4—222no—
454C2×D4C2×C4×D1111yescharacteristic
455C22×C4—21no—
456C22×C4—111no—
457C22×C4—111no—
458C22×C4—111no—
459C22×C4—221no—
460C22×C4—221no—
461C22×C4—221no—
462C22×C4—221no—
463C22×C4—221no—
464C22×C4—881no—
465C22×C4—881no—
466SD16—22no—
467SD16—222no—
468D8—222no—
469D8—222no—
470M16—881no—
471M16—881no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—81no—
476C2×C8—111no—
477C2×C8—111no—
478C2×C8—111no—
479C2×C8—111no—
480C2×C8—221no—
481C2×C8—221no—
482C2×C8—221no—
483C2×C8—881no—
484C2×C8—881no—
485C2×C8—881no—
486C2×C8—881no—
487C2×C8C2×C4×D1111yescharacteristic
488C2×C8C2×C4×D1111yescharacteristic
489C2×C8D4×D1111yescharacteristic
490C2×C8D4×D1111yescharacteristic
491C4⋊C4—21no—
492C4⋊C4—111no—
493C4⋊C4—111no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4C2×C4×D1111yescharacteristic
499C4⋊C4C2×C4×D1111yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—221no—
502C22⋊C4—221no—
503C22⋊C4—221no—
504C22⋊C4—221no—
505C22⋊C4—221no—
506C22⋊C4—221no—
507C22⋊C4—221no—
508C22⋊C4—221no—
509C42—21no—
510C42—111no—
511C42—111no—
512C42—111no—
513C42C23×D1111yescharacteristic
514C11#1791811yescharacteristic, complemented, Sylow
515C23—21no—
516C23—111no—
517C23—224no—
518C23—221no—
519C23—221no—
520C23—881no—
521C23—881no—
522Q8—21no—
523Q8—21no—
524D4—21no—
525D4—112no—
526D4—224no—
527D4—221no—
528D4—221no—
529D4—221no—
530D4—881no—
531D4#6696012yes—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—111no—
538C2×C4—111no—
539C2×C4—111no—
540C2×C4—221no—
541C2×C4—221no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—221no—
545C2×C4—221no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—881no—
552C2×C4—881no—
553C2×C4—881no—
554C2×C4C22×C4×D1111yescharacteristic
555C2×C4C2×D4×D1111yescharacteristic
556C2×C4#41×D1111yescharacteristic
557C8—21no—
558C8—21no—
559C8—21no—
560C8—21no—
561C8—41no—
562C8—41no—
563C8—41no—
564C8—221no—
565C8—221no—
566C8—221no—
567C8—221no—
568C8—441no—
569C8—441no—
570C8—441no—
571C22—22no—
572C22—41no—
573C22—41no—
574C22—221no—
575C22—221no—
576C22—222no—
577C22—221no—
578C22—441no—
579C22—441no—
580C22—441no—
581C22—441no—
582C22—441no—
583C22—884no—
584C22C4×D4×D1111yescharacteristic
585C4—21no—
586C4—41no—
587C4—41no—
588C4—41no—
589C4—221no—
590C4—221no—
591C4—221no—
592C4—441no—
593C4—441no—
594C4C2×#6696011yescharacteristic
595C4D11×#13111yescharacteristic
596C4#1062329311yescharacteristic
597C4#1062330011yescharacteristic
598C2—42no—
599C2—441no—
600C2—442no—
601C2—881no—
602C2#1307730711yescharacteristic
603C2#1307744311yescharacteristic
604C2#1307753011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1582C2
socleC22×C11C2×C4×D4
prime radical#10622386C4
cosocleC42×C11C24
hypercenter#1582D11
hypocenterC11#17918
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1582

Complements

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

NH ≅ G/Ntype
2. #13077768C2semidirect
3. #13077637C2semidirect
4. #13067480C2semidirect
5. #13067471C2semidirect
6. #13067447C2semidirect
7. #13067439C2semidirect
8. SD16⋊(C11⋊C8)C2semidirect
9. #13067413C2semidirect
10. #13067408C2semidirect
11. #13067403C2semidirect
12. #13067039C2semidirect
13. #13067023C2semidirect
14. #13066917C2semidirect
15. C11×#1582C2semidirect
18. C11×#446C22semidirect
26. Q8×C11⋊C8C22semidirect
35. #10622447C22semidirect
46. #10622301C22semidirect
51. C11×#334C22semidirect
52. C11×Q8⋊C8C22semidirect
54. C11×#322C22semidirect
55. Q8⋊(C11⋊C8)C22semidirect
58. #10622121C22semidirect
59. #10622118C22semidirect
60. #10622117C22semidirect
62. #10622097C22semidirect
63. #10622096C22semidirect
64. #10622093C22semidirect
65. #10622092C22semidirect
66. C8×C11⋊C8C22semidirect
218. #1582D11semidirect
294. #446C2×D11semidirect
322. #334C2×D11semidirect
324. Q8⋊C8C2×D11semidirect
333. #322C2×D11semidirect
514. C11#17918semidirect

Maximal subgroups

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

subgroupindex
#130786672
#130777682
#130776372
#130674802
#130674712
#130674472
#130674392
SD16⋊(C11⋊C8)2
#130674132
#130674082
#130674032
#130670392
#130670232
#130669172
C11×#15822
#1791811