Finite Group Databasebeta

← #14724151

Subgroups — #14724151

Order 2816.

616 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#13078663C211yesmaximal, characteristic
2#13077761C211yesmaximal, characteristic, complemented
3#13077657C211yesmaximal, characteristic, complemented
4#13067527C211yesmaximal, characteristic, complemented
5#13067515C211yesmaximal, characteristic, complemented
6#13067509C211yesmaximal, characteristic, complemented
7#13067498C211yesmaximal, characteristic, complemented
8#13067497C211yesmaximal, characteristic, complemented
9#13067483C211yesmaximal, characteristic, complemented
10#13067462C211yesmaximal, characteristic, complemented
11#13067448C211yesmaximal, characteristic, complemented
12#13067407C211yesmaximal, characteristic, complemented
13#13067025C211yesmaximal, characteristic, complemented
14#13066916C211yesmaximal, characteristic, complemented
15C11×#1486C211yesmaximal, characteristic, complemented
16C2×C4×D4×C11C2211yescharacteristic
17#10623010C2211yescharacteristic
18C11×#431C2211yescharacteristic
19C11×#423C2211yescharacteristic
20#10622831C411yescharacteristic
21#10622830C411yescharacteristic
22#10622820—21no—
23#10622820—21no—
24#10622741—21no—
25#10622740—21no—
26C4×#4324C2211yescharacteristic
27C4×#4324C2211yescharacteristic
28#10622629C411yescharacteristic
29#10622629C411yescharacteristic
30C4×#4323C2211yescharacteristic
31C4×#4323C2211yescharacteristic
32#10622625—21no—
33#10622625—21no—
34#10622625C2211yescharacteristic
35#10622625C2211yescharacteristic
36#10622625C2211yescharacteristic
37#10622625C2211yescharacteristic
38#10622622C411yescharacteristic
39#10622622C411yescharacteristic
40#10622583C411yescharacteristic
41#10622581C411yescharacteristic
42#10622538C2211yescharacteristic
43#10622538C2211yescharacteristic
44#10622538C2211yescharacteristic
45#10622453—21no—
46#10622452—21no—
47#10622451C2211yescharacteristic, complemented
48#10622447C2211yescharacteristic, complemented
49#10622444C2211yescharacteristic, complemented
50#10622443C2211yescharacteristic, complemented
51C11×D4⋊C8C2211yescharacteristic
52C11×D4⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic
54C11×D4⋊C8C2211yescharacteristic
55#10622118C2211yescharacteristic, complemented
56#10622118C2211yescharacteristic, complemented
57#10622117C2211yescharacteristic, complemented
58#10622117C2211yescharacteristic, complemented
59#10622097C2211yescharacteristic, complemented
60#10622097C2211yescharacteristic, complemented
61#10622094C2211yescharacteristic, complemented
62#10622094C2211yescharacteristic, 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—
70C4×D4×C11—21no—
71C4×D4×C11—21no—
72C4×D4×C11C2×C411yescharacteristic
73C4×D4×C11C2×C411yescharacteristic
74C4×D4×C11C2311yescharacteristic
75C4×D4×C11C2311yescharacteristic
76C2×C11×C4⋊C4C2×C411yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C42×C11C2311yescharacteristic
79C2×#4324C2×C411yescharacteristic
80C2×#4324C2×C411yescharacteristic
81C2×#4323C2×C411yescharacteristic
82C2×#4323C2×C411yescharacteristic
83#66983C2×C411yescharacteristic
84#66982—21no—
85C4×C22⋊D11—21no—
86#66977C2×C411yescharacteristic
87C2×#4318—21no—
88C2×#4318—21no—
89C2×#4318—21no—
90C2×#4318—21no—
91C2×#4313—21no—
92C2×C8×D11—21no—
93#66929—21no—
94#66928C2×C411yescharacteristic
95C4×D44C2311yescharacteristic
96#66925—21no—
97#66923C2×C411yescharacteristic
98C4×Dic22C2311yescharacteristic
99C11×C4⋊C8—21no—
100C11×C4⋊C8—21no—
101C11×C4⋊C8C2311yescharacteristic
102C11×C4⋊C8C2311yescharacteristic
103C11×C22⋊C8—21no—
104C4×C8×C11C2311yescharacteristic
105C4×C8×C11C2311yescharacteristic
106#66896C2×C411yescharacteristic
107#66896C2×C411yescharacteristic
108#66896C2×C411yescharacteristic
109#66896C2×C411yescharacteristic
110C22⋊(C11⋊C8)—21no—
111C22⋊(C11⋊C8)—21no—
112C22⋊(C11⋊C8)—21no—
113C22⋊(C11⋊C8)—21no—
114C22⋊(C11⋊C8)—21no—
115C22⋊(C11⋊C8)C2×C411yescharacteristic
116C22⋊(C11⋊C8)C2×C411yescharacteristic
117C22⋊(C11⋊C8)D411yescharacteristic
118C22⋊(C11⋊C8)D411yescharacteristic
119(C2×D11)⋊C8—21no—
120(C2×D11)⋊C8—21no—
121#66879—21no—
122Dic11⋊C8—21no—
123Dic11⋊C8—21no—
124C8×Dic11—21no—
125#66874C2×C411yescharacteristic
126#66874C2×C411yescharacteristic
127#66873C2×C411yescharacteristic
128#66873C2×C411yescharacteristic
129#66872C2×C411yescharacteristic
130#66872C2×C411yescharacteristic
131#66871C2×C411yescharacteristic
132#66871C2×C411yescharacteristic
133C4⋊(C11⋊C8)C2×C411yescharacteristic
134C4⋊(C11⋊C8)C2×C411yescharacteristic
135C4⋊(C11⋊C8)D411yescharacteristic
136C4⋊(C11⋊C8)D411yescharacteristic
137C4⋊(C11⋊C8)C2311yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4×C11⋊C8—21no—
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#17946—111nomaximal, Sylow
145C24×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—41no—
148C2×D4×C11—41no—
149C2×D4×C11C22×C411yescharacteristic
150C2×D4×C11C22×C411yescharacteristic
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—81no—
157C22×C4×C11—81no—
158C22×C4×C11C22×C411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11#4111yescharacteristic
161C2×C22⋊D11—21no—
162C2×D44C22×C411yescharacteristic
163C2×C4×D11—21no—
164C2×Dic22C22×C411yescharacteristic
165C11×M16—81no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4C22×C411yescharacteristic
172C11×C4⋊C4C22×C411yescharacteristic
173C11×C22⋊C4—21no—
174C11×C22⋊C4—21no—
175C11×C22⋊C4—21no—
176C11×C22⋊C4—21no—
177C42×C11C22×C411yescharacteristic
178C42×C11C2×D411yescharacteristic
179C42×C11#4111yescharacteristic
180C42×C11C2411yescharacteristic
181C22⋊Dic11—21no—
182#4324—41no—
183#4324—41no—
184#4323—41no—
185#4323—41no—
186(C2×D11)⋊C4—21no—
187(C2×D11)⋊C4—21no—
188(C2×D11)⋊C4—21no—
189(C2×D11)⋊C4—21no—
190C4⋊Dic11C22×C411yescharacteristic
191C4⋊Dic11C22×C411yescharacteristic
192Dic11⋊C4—21no—
193Dic11⋊C4—21no—
194Dic11⋊C4—21no—
195Dic11⋊C4—21no—
196C4×Dic11—21no—
197#4318—81no—
198#4318—81no—
199#4318—81no—
200#4318—81no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8C22×C411yescharacteristic
204C2×C11⋊C8C22×C411yescharacteristic
205C2×C11⋊C8C22×C411yescharacteristic
206C2×C11⋊C8C22×C411yescharacteristic
207C2×C11⋊C8C2×D411yescharacteristic
208C2×C11⋊C8C2×D411yescharacteristic
209C2×C11⋊C8C2×D411yescharacteristic
210C2×C11⋊C8C2×D411yescharacteristic
211#4313—81no—
212C8×D11—81no—
213#3105—111no—
214#2993—111no—
215#2975—111no—
216#1594—111no—
217#1592—111no—
218#1590—111no—
219#1589—111no—
220#1588—111no—
221#1586—111no—
222#1583—111no—
223#1581—111no—
224#1574—111no—
225#1486D1111yescharacteristic, complemented
226#1482—111no—
227#1454—111no—
228C23×C11—21no—
229C23×C11—21no—
230C23×C11—42no—
231C23×C11—81no—
232C23×C11—81no—
233C23×C11C4×D411yescharacteristic
234C22×D11—21no—
235D4×C11—21no—
236D4×C11—21no—
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—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—81no—
252C2×C4×C11—81no—
253C2×C4×C11—81no—
254C2×C4×C11C4×D411yescharacteristic
255C2×C4×C11C4×D411yescharacteristic
256C2×C4×C11C4×D411yescharacteristic
257C2×C4×C11C23×C411yescharacteristic
258C2×C4×C11C22×D411yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C22⋊D11—81no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264D44—21no—
265D44—21no—
266C4×D11—41no—
267C4×D11—41no—
268Dic22—21no—
269Dic22—21no—
270C8×C11—41no—
271C8×C11—41no—
272C8×C11—41no—
273C8×C11—41no—
274C11⋊C8—21no—
275C11⋊C8—21no—
276C11⋊C8—21no—
277C11⋊C8—21no—
278C11⋊C8—21no—
279C11⋊C8—21no—
280C11⋊C8—21no—
281C11⋊C8—21no—
282C11⋊C8—41no—
283C11⋊C8—41no—
284#529—111no—
285C2×C4×D4C2×D1111yescharacteristic
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#446—111no—
295C8×Q8—111no—
296C4×SD16—111no—
297C4×SD16—111no—
298C4×D8—111no—
299C4×D8—111no—
300#436—111no—
301#436—111no—
302#436—111no—
303#436—111no—
304#436—111no—
305#436—221no—
306#436—221no—
307#436—221no—
308#435—221no—
309C8×D4—111no—
310#433—221no—
311#431—111no—
312#431—111no—
313#431—111no—
314#431C2×D1111yescharacteristic
315#424—221no—
316#423C2×D1111yescharacteristic
317#407—221no—
318#407—221no—
319#335—111no—
320#335—111no—
321#334—111no—
322#334—111no—
323Q8⋊C8—111no—
324Q8⋊C8—111no—
325D4⋊C8—111no—
326D4⋊C8—111no—
327D4⋊C8C2×D1111yescharacteristic
328D4⋊C8C2×D1111yescharacteristic
329D4⋊C8C2×D1111yescharacteristic
330D4⋊C8C2×D1111yescharacteristic
331#322—111no—
332#322—111no—
333#322—111no—
334C82—111no—
335C22×C11—21no—
336C22×C11—21no—
337C22×C11—21no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11—41no—
341C22×C11—41no—
342C22×C11—41no—
343C22×C11—41no—
344C22×C11—84no—
345C22×C11C2×C4×D411yescharacteristic
346C2×D11—41no—
347C2×D11—41no—
348C2×D11—41no—
349C4×C11—21no—
350C4×C11—21no—
351C4×C11—21no—
352C4×C11—21no—
353C4×C11—41no—
354C4×C11—41no—
355C4×C11#56811yescharacteristic
356C4×C11#56811yescharacteristic
357C4×C11#57611yescharacteristic
358C4×C11#57711yescharacteristic
359Dic11—41no—
360Dic11—41no—
361Dic11—41no—
362C22×D4C4×D1111yescharacteristic
363C23×C4—21no—
364C2×SD16—111no—
365C2×SD16—111no—
366C2×D8—111no—
367C2×D8—111no—
368C2×M16—21no—
369C2×M16—221no—
370C2×M16—221no—
371C2×M16—221no—
372C2×M16—221no—
373C2×M16—221no—
374C22×C8—221no—
375#126—221no—
376#125—111no—
377#124—111no—
378#123—221no—
379C22⋊Q8—111no—
380#121—111no—
381C4×Q8—111no—
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—111no—
385C4×D4—221no—
386C4×D4C4×D1111yescharacteristic
387C4×D4C4×D1111yescharacteristic
388C4×D4C22×D1111yescharacteristic
389C4×D4C22×D1111yescharacteristic
390#117—221no—
391C2×C4⋊C4C4×D1111yescharacteristic
392C2×C22⋊C4—21no—
393C2×C42C22×D1111yescharacteristic
394#107—111no—
395#107—111no—
396#106—111no—
397#106—111no—
398C4⋊C8—21no—
399C4⋊C8—21no—
400C4⋊C8—111no—
401C4⋊C8—111no—
402C4⋊C8—111no—
403C4⋊C8—111no—
404C4⋊C8—111no—
405C4⋊C8—111no—
406C4⋊C8—221no—
407C4⋊C8—221no—
408C4⋊C8C22×D1111yescharacteristic
409C4⋊C8C22×D1111yescharacteristic
410#103—111no—
411#103—111no—
412#102—111no—
413#102—111no—
414#102—111no—
415#102—111no—
416#102—111no—
417#102—111no—
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—221no—
431C4×C8—111no—
432C4×C8—111no—
433C4×C8—111no—
434C4×C8—111no—
435C4×C8—221no—
436C4×C8—221no—
437C4×C8C22×D1111yescharacteristic
438C4×C8C22×D1111yescharacteristic
439C2×C11—41no—
440C2×C11—81no—
441C2×C11—81no—
442C2×C11#293011yescharacteristic
443C2×C11#294611yescharacteristic
444C2×C11#295711yescharacteristic
445D11—81no—
446C24—21no—
447C2×Q8—111no—
448C2×D4—21no—
449C2×D4—41no—
450C2×D4—41no—
451C2×D4—111no—
452C2×D4—221no—
453C2×D4C2×C4×D1111yescharacteristic
454C2×D4C2×C4×D1111yescharacteristic
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—81no—
461C22×C4—81no—
462C22×C4—221no—
463C22×C4C2×C4×D1111yescharacteristic
464C22×C4D4×D1111yescharacteristic
465C22×C4#434111yescharacteristic
466SD16—441no—
467SD16—441no—
468D8—441no—
469D8—441no—
470M16—81no—
471M16—881no—
472M16—881no—
473M16—881no—
474M16—881no—
475M16—881no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—111no—
481C2×C8—111no—
482C2×C8—111no—
483C2×C8—111no—
484C2×C8—111no—
485C2×C8—111no—
486C2×C8—111no—
487C2×C8—111no—
488C2×C8—221no—
489C2×C8—221no—
490C2×C8—881no—
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—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—221no—
505C22⋊C4—221no—
506C22⋊C4—221no—
507C22⋊C4—221no—
508C22⋊C4—221no—
509C42—221no—
510C42C2×C4×D1111yescharacteristic
511C42D4×D1111yescharacteristic
512C42#434111yescharacteristic
513C42C23×D1111yescharacteristic
514C11#1794611yescharacteristic, complemented, Sylow
515C23—21no—
516C23—21no—
517C23—42no—
518C23—81no—
519C23—81no—
520C23—221no—
521C23(C22⋊D11)⋊C411yescharacteristic
522Q8—221no—
523Q8—221no—
524D4—21no—
525D4—21no—
526D4—21no—
527D4—21no—
528D4—42no—
529D4—221no—
530D4—221no—
531D4—881no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—81no—
544C2×C4—81no—
545C2×C4—81no—
546C2×C4—221no—
547C2×C4—221no—
548C2×C4—221no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4(C22⋊D11)⋊C411yescharacteristic
552C2×C4(C22⋊D11)⋊C411yescharacteristic
553C2×C4(C22⋊D11)⋊C411yescharacteristic
554C2×C4C22×C4×D1111yescharacteristic
555C2×C4C2×D4×D1111yescharacteristic
556C2×C4C2×#434111yescharacteristic
557C8—41no—
558C8—41no—
559C8—41no—
560C8—41no—
561C8—221no—
562C8—221no—
563C8—221no—
564C8—221no—
565C8—221no—
566C8—221no—
567C8—221no—
568C8—221no—
569C8—441no—
570C8—441no—
571C22—21no—
572C22—21no—
573C22—21no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—84no—
581C22—441no—
582C22—441no—
583C22—441no—
584C22C2×(C22⋊D11)⋊C411yescharacteristic
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—41no—
590C4—41no—
591C4—441no—
592C4—441no—
593C4—441no—
594C4#1062327611yescharacteristic
595C4#1062327611yescharacteristic
596C4#1062328811yescharacteristic
597C4#1062329311yescharacteristic
598C2—41no—
599C2—81no—
600C2—81no—
601C2—881no—
602C2#1307731511yescharacteristic
603C2#1307744211yescharacteristic
604C2#1307752911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1486C2
socleC22×C11C2×C4×D4
prime radical#10622830C4
cosocleC42×C11C24
hypercenter#1486D11
hypocenterC11#17946
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1486

Complements

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

NH ≅ G/Ntype
2. #13077761C2semidirect
3. #13077657C2semidirect
4. #13067527C2semidirect
5. #13067515C2semidirect
6. #13067509C2semidirect
7. #13067498C2semidirect
8. #13067497C2semidirect
9. #13067483C2semidirect
10. #13067462C2semidirect
11. #13067448C2semidirect
12. #13067407C2semidirect
13. #13067025C2semidirect
14. #13066916C2semidirect
15. C11×#1486C2semidirect
47. #10622451C22semidirect
48. #10622447C22semidirect
49. #10622444C22semidirect
50. #10622443C22semidirect
55. #10622118C22semidirect
56. #10622118C22semidirect
57. #10622117C22semidirect
58. #10622117C22semidirect
59. #10622097C22semidirect
60. #10622097C22semidirect
61. #10622094C22semidirect
62. #10622094C22semidirect
63. #10622093C22semidirect
64. #10622092C22semidirect
65. #10622092C22semidirect
66. C8×C11⋊C8C22semidirect
225. #1486D11semidirect
514. C11#17946semidirect

Maximal subgroups

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

subgroupindex
#130786632
#130777612
#130776572
#130675272
#130675152
#130675092
#130674982
#130674972
#130674832
#130674622
#130674482
#130674072
#130670252
#130669162
C11×#14862
#1794611