Finite Group Databasebeta

← #14724157

Subgroups — #14724157

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#13077767C211yesmaximal, characteristic, complemented
3#13067528C211yesmaximal, characteristic, complemented
4#13067518C211yesmaximal, characteristic, complemented
5#13067504C211yesmaximal, characteristic, complemented
6#13067499C211yesmaximal, characteristic, complemented
7#13067492C211yesmaximal, characteristic, complemented
8#13067478C211yesmaximal, characteristic, complemented
9#13067457C211yesmaximal, characteristic, complemented
10#13067443C211yesmaximal, characteristic, complemented
11#13067404C211yesmaximal, characteristic, complemented
12#13067041C211yesmaximal, characteristic, complemented
13#13067022C211yesmaximal, characteristic, complemented
14#13066916C211yesmaximal, characteristic, complemented
15C11×#2975C211yesmaximal, characteristic, complemented
16C2×C4×D4×C11C2211yescharacteristic
17#10623010C2211yescharacteristic
18C11×#436—21no—
19C11×#436—21no—
20C11×#436C2211yescharacteristic
21C11×#436C2211yescharacteristic
22C11×#436C2211yescharacteristic
23C11×#436C2211yescharacteristic
24C11×#431C2211yescharacteristic
25C11×#431C2211yescharacteristic
26C11×#407—21no—
27C11×#407—21no—
28#10622831C411yescharacteristic
29#10622830C411yescharacteristic
30C4×#4324C2211yescharacteristic
31C4×#4324C2211yescharacteristic
32#10622629C411yescharacteristic
33#10622629C411yescharacteristic
34C4×#4323C2211yescharacteristic
35C4×#4323C2211yescharacteristic
36#10622622C411yescharacteristic
37#10622622C411yescharacteristic
38#10622583C411yescharacteristic
39#10622581C411yescharacteristic
40#10622538C2211yescharacteristic
41#10622538C2211yescharacteristic
42#10622537C2211yescharacteristic
43#10622453—21no—
44#10622452—21no—
45#10622342—21no—
46#10622341—21no—
47#10622301C2211yescharacteristic, complemented
48C8×D44C2211yescharacteristic, complemented
49#10622292C2211yescharacteristic, complemented
50C8×Dic22C2211yescharacteristic, complemented
51D4⋊(C11⋊C8)C2211yescharacteristic
52D4⋊(C11⋊C8)C2211yescharacteristic
53D4⋊(C11⋊C8)C2211yescharacteristic
54D4⋊(C11⋊C8)C2211yescharacteristic
55#10622122C2211yescharacteristic, complemented
56#10622122C2211yescharacteristic, complemented
57#10622121C2211yescharacteristic, complemented
58#10622121C2211yescharacteristic, complemented
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×D4×C11C2×C411yescharacteristic
68C23×C4×C11—21no—
69C2×C11×M16—21no—
70C2×C11×M16—21no—
71C2×C11×M16—21no—
72C2×C11×M16—21no—
73C4×D4×C11—21no—
74C4×D4×C11—21no—
75C4×D4×C11C2×C411yescharacteristic
76C4×D4×C11C2×C411yescharacteristic
77C4×D4×C11C2311yescharacteristic
78C4×D4×C11C2311yescharacteristic
79C2×C11×C4⋊C4C2×C411yescharacteristic
80C2×C11×C22⋊C4—21no—
81C2×C42×C11C2311yescharacteristic
82C2×#4324C2×C411yescharacteristic
83C2×#4324C2×C411yescharacteristic
84C2×#4323C2×C411yescharacteristic
85C2×#4323C2×C411yescharacteristic
86#66983C2×C411yescharacteristic
87#66982—21no—
88C4×C22⋊D11—21no—
89#66977C2×C411yescharacteristic
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⋊C8D411yescharacteristic
100C11×C4⋊C8D411yescharacteristic
101C11×C4⋊C8C2311yescharacteristic
102C11×C4⋊C8C2311yescharacteristic
103C11×C22⋊C8—21no—
104C11×C22⋊C8—21no—
105C11×C22⋊C8—21no—
106C11×C22⋊C8—21no—
107C11×C22⋊C8—21no—
108C11×C22⋊C8D411yescharacteristic
109C11×C22⋊C8D411yescharacteristic
110C4×C8×C11—21no—
111C4×C8×C11C2311yescharacteristic
112C4×C8×C11C2311yescharacteristic
113#66896C2×C411yescharacteristic
114#66896C2×C411yescharacteristic
115#66896C2×C411yescharacteristic
116#66896C2×C411yescharacteristic
117C22⋊(C11⋊C8)—21no—
118C22⋊(C11⋊C8)C2×C411yescharacteristic
119C22⋊(C11⋊C8)C2×C411yescharacteristic
120(C2×D11)⋊C8—21no—
121(C2×D11)⋊C8—21no—
122#66879—21no—
123Dic11⋊C8—21no—
124Dic11⋊C8—21no—
125C8×Dic11—21no—
126#66874C2×C411yescharacteristic
127#66874C2×C411yescharacteristic
128#66873C2×C411yescharacteristic
129#66873C2×C411yescharacteristic
130#66872C2×C411yescharacteristic
131#66872C2×C411yescharacteristic
132#66871C2×C411yescharacteristic
133#66871C2×C411yescharacteristic
134C4⋊(C11⋊C8)—21no—
135C4⋊(C11⋊C8)—21no—
136C4⋊(C11⋊C8)C2×C411yescharacteristic
137C4⋊(C11⋊C8)C2×C411yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
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—
166C11×M16—81no—
167C11×M16—81no—
168C11×M16—81no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11C2×D411yescharacteristic
172C2×C8×C11C2×D411yescharacteristic
173C2×C8×C11C2×D411yescharacteristic
174C2×C8×C11C2×D411yescharacteristic
175C11×C4⋊C4—21no—
176C11×C4⋊C4C22×C411yescharacteristic
177C11×C4⋊C4C22×C411yescharacteristic
178C11×C22⋊C4—21no—
179C11×C22⋊C4—21no—
180C11×C22⋊C4—21no—
181C11×C22⋊C4—21no—
182C42×C11C22×C411yescharacteristic
183C42×C11C2×D411yescharacteristic
184C42×C11#4111yescharacteristic
185C42×C11C2411yescharacteristic
186C22⋊Dic11—21no—
187#4324—41no—
188#4324—41no—
189#4323—41no—
190#4323—41no—
191(C2×D11)⋊C4—21no—
192(C2×D11)⋊C4—21no—
193(C2×D11)⋊C4—21no—
194(C2×D11)⋊C4—21no—
195C4⋊Dic11C22×C411yescharacteristic
196C4⋊Dic11C22×C411yescharacteristic
197Dic11⋊C4—21no—
198Dic11⋊C4—21no—
199Dic11⋊C4—21no—
200Dic11⋊C4—21no—
201C4×Dic11—21no—
202#4318—81no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8C22×C411yescharacteristic
208C2×C11⋊C8C22×C411yescharacteristic
209C2×C11⋊C8C22×C411yescharacteristic
210C2×C11⋊C8C22×C411yescharacteristic
211#4313—81no—
212C8×D11—81no—
213#3105—111no—
214#2993—111no—
215#2975D1111yescharacteristic, complemented
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#1486—111no—
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—21no—
271C8×C11—21no—
272C8×C11—21no—
273C8×C11—21no—
274C8×C11—41no—
275C8×C11—41no—
276C11⋊C8—21no—
277C11⋊C8—21no—
278C11⋊C8—21no—
279C11⋊C8—21no—
280C11⋊C8—41no—
281C11⋊C8—41no—
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—21no—
301#436—21no—
302#436—111no—
303#436—221no—
304#436C2×D1111yescharacteristic
305#436C2×D1111yescharacteristic
306#436C2×D1111yescharacteristic
307#436C2×D1111yescharacteristic
308#435—221no—
309C8×D4—111no—
310#433—221no—
311#431—111no—
312#431—111no—
313#431C2×D1111yescharacteristic
314#431C2×D1111yescharacteristic
315#424—221no—
316#423—111no—
317#407—21no—
318#407—21no—
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⋊C8—111no—
328D4⋊C8—111no—
329D4⋊C8—111no—
330D4⋊C8—111no—
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—21no—
370C2×M16—21no—
371C2×M16—21no—
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—111no—
399C4⋊C8—111no—
400C4⋊C8—111no—
401C4⋊C8—111no—
402C4⋊C8—221no—
403C4⋊C8—221no—
404C4⋊C8—221no—
405C4⋊C8—221no—
406C4⋊C8C22⋊D1111yescharacteristic
407C4⋊C8C22⋊D1111yescharacteristic
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—21no—
420C22⋊C8—21no—
421C22⋊C8—21no—
422C22⋊C8—21no—
423C22⋊C8—111no—
424C22⋊C8—111no—
425C22⋊C8—221no—
426C22⋊C8—221no—
427C22⋊C8—221no—
428C22⋊C8C22⋊D1111yescharacteristic
429C22⋊C8C22⋊D1111yescharacteristic
430#97—221no—
431C4×C8—21no—
432C4×C8—111no—
433C4×C8—111no—
434C4×C8—111no—
435C4×C8—111no—
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×C4#433911yescharacteristic
465C22×C4C2×C22⋊D1111yescharacteristic
466SD16—441no—
467SD16—441no—
468D8—441no—
469D8—441no—
470M16—81no—
471M16—81no—
472M16—81no—
473M16—81no—
474M16—881no—
475M16—881no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—111no—
479C2×C8—111no—
480C2×C8—111no—
481C2×C8—111no—
482C2×C8—221no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—881no—
487C2×C8C2×C22⋊D1111yescharacteristic
488C2×C8C2×C22⋊D1111yescharacteristic
489C2×C8C2×C22⋊D1111yescharacteristic
490C2×C8C2×C22⋊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—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
511C42#433911yescharacteristic
512C42C2×C22⋊D1111yescharacteristic
513C42C23×D1111yescharacteristic
514C11#1794611yescharacteristic, complemented, Sylow
515C23—21no—
516C23—21no—
517C23—42no—
518C23—81no—
519C23—81no—
520C23—221no—
521C23C4×C22⋊D1111yescharacteristic
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×C4C4×C22⋊D1111yescharacteristic
552C2×C4C4×C22⋊D1111yescharacteristic
553C2×C4C4×C22⋊D1111yescharacteristic
554C2×C4C22×C4×D1111yescharacteristic
555C2×C4C2×#433911yescharacteristic
556C2×C4C22×C22⋊D1111yescharacteristic
557C8—21no—
558C8—21no—
559C8—21no—
560C8—21no—
561C8—41no—
562C8—41no—
563C8—221no—
564C8—221no—
565C8—221no—
566C8—221no—
567C8—441no—
568C8—441no—
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×C4×C22⋊D1111yescharacteristic
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—41no—
590C4—41no—
591C4—441no—
592C4—441no—
593C4—441no—
594C4#1062327611yescharacteristic
595C4#1062327611yescharacteristic
596C4#1062336611yescharacteristic
597C4#1062336711yescharacteristic
598C2—41no—
599C2—81no—
600C2—81no—
601C2—881no—
602C2#1307731911yescharacteristic
603C2#1307744811yescharacteristic
604C2#1307753111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2975C2
socleC22×C11C2×C4×D4
prime radical#10622830C4
cosocleC42×C11C24
hypercenter#2975D11
hypocenterC11#17946
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2975

Complements

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

NH ≅ G/Ntype
2. #13077767C2semidirect
3. #13067528C2semidirect
4. #13067518C2semidirect
5. #13067504C2semidirect
6. #13067499C2semidirect
7. #13067492C2semidirect
8. #13067478C2semidirect
9. #13067457C2semidirect
10. #13067443C2semidirect
11. #13067404C2semidirect
12. #13067041C2semidirect
13. #13067022C2semidirect
14. #13066916C2semidirect
15. C11×#2975C2semidirect
47. #10622301C22semidirect
48. C8×D44C22semidirect
49. #10622292C22semidirect
50. C8×Dic22C22semidirect
55. #10622122C22semidirect
56. #10622122C22semidirect
57. #10622121C22semidirect
58. #10622121C22semidirect
59. #10622118C22semidirect
60. #10622118C22semidirect
61. #10622117C22semidirect
62. #10622117C22semidirect
63. #10622093C22semidirect
64. #10622092C22semidirect
65. #10622092C22semidirect
66. C8×C11⋊C8C22semidirect
215. #2975D11semidirect
514. C11#17946semidirect

Maximal subgroups

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

subgroupindex
#130786632
#130777672
#130675282
#130675182
#130675042
#130674992
#130674922
#130674782
#130674572
#130674432
#130674042
#130670412
#130670222
#130669162
C11×#29752
#1794611