Finite Group Databasebeta

← #14725002

Subgroups — #14725002

Order 2816.

642 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078661C211yesmaximal, characteristic
2#13077771C211yesmaximal, characteristic, complemented
3#13077648C211yesmaximal, characteristic, complemented
4#13067530C211yesmaximal, characteristic, complemented
5#13067518C211yesmaximal, characteristic, complemented
6#13067462C211yesmaximal, characteristic, complemented
7#13067454C211yesmaximal, characteristic, complemented
8#13067448C211yesmaximal, characteristic, complemented
9#13067438C211yesmaximal, characteristic, complemented
10#13067427C211yesmaximal, characteristic, complemented
11#13067400C211yesmaximal, characteristic, complemented
12#13067073C211yesmaximal, characteristic, complemented
13D11×D4⋊C8C211yesmaximal, characteristic, complemented
14#13066907C211yesmaximal, characteristic, complemented
15C11×#1581C211yesmaximal, characteristic, complemented
16#10623088C2211yescharacteristic
17C4×D4×D11C2211yescharacteristic
18C4×C11×D8C2211yescharacteristic
19C11×#436C2211yescharacteristic
20C8×D4×C11C2211yescharacteristic, complemented
21#10622769C411yescharacteristic
22#10622766C411yescharacteristic
23#10622740—21no—
24#10622739—21no—
25C8×C22⋊D11—21no—
26#10622715—21no—
27C4×#4324C2211yescharacteristic
28C4×#4323C2211yescharacteristic
29#10622625C2211yescharacteristic
30#10622625C2211yescharacteristic, complemented
31#10622504C411yescharacteristic
32#10622497C411yescharacteristic
33#10622448C2211yescharacteristic
34#10622447C2211yescharacteristic
35D11×C4⋊C8C2211yescharacteristic
36#10622443C2211yescharacteristic, complemented
37#10622400C411yescharacteristic
38#10622390C411yescharacteristic
39#10622389C411yescharacteristic
40#10622376C411yescharacteristic
41#10622341—21no—
42#10622341—21no—
43D11×C22⋊C8—21no—
44#10622333—21no—
45C4×#4314C2211yescharacteristic
46C8×D44C2211yescharacteristic
47#10622298C2211yescharacteristic
48#10622298C2211yescharacteristic
49C4×C8×D11C2211yescharacteristic
50#10622292C2211yescharacteristic, complemented
51C11×#335C2211yescharacteristic, complemented
52C11×D4⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic, complemented
54C11×#322C2211yescharacteristic, complemented
55D4⋊(C11⋊C8)C2211yescharacteristic
56D4⋊(C11⋊C8)C2211yescharacteristic, complemented
57#10622122C2211yescharacteristic, complemented
58#10622121C2211yescharacteristic
59#10622118C2211yescharacteristic, complemented
60#10622117C2211yescharacteristic, complemented
61#10622097C2211yescharacteristic
62#10622095C2211yescharacteristic, complemented
63#10622094C2211yescharacteristic, complemented
64#10622093C2211yescharacteristic, complemented
65#10622092C2211yescharacteristic, complemented
66#10622092C2211yescharacteristic, complemented
67C2×D4×D11C2×C411yescharacteristic
68C22×C4×D11—21no—
69C2×C11×D8C2×C411yescharacteristic
70C2×C11×M16—21no—
71C22×C8×C11—21no—
72C4×D4×C11C2311yescharacteristic
73C4×D4×C11C2311yescharacteristic
74#66991C2×C411yescharacteristic
75#66989C2×C411yescharacteristic
76D4×Dic11C2×C411yescharacteristic
77C2×#4324C2×C411yescharacteristic
78C2×#4323C2×C411yescharacteristic
79C4×C22⋊D11—21no—
80C4×C22⋊D11—21no—
81#66979—21no—
82C2×#4318—21no—
83C2×#4318—21no—
84C2×#4314C2×C411yescharacteristic
85C2×C8×D11—21no—
86C2×C8×D11—21no—
87C2×C8×D11—21no—
88C2×C8×D11—21no—
89#66950C2×C411yescharacteristic
90#66946C2×C411yescharacteristic
91C4⋊C4×D11C2×C411yescharacteristic
92#66943C2×C411yescharacteristic
93#66936—21no—
94(C22⋊D11)⋊C4—21no—
95C22⋊C4×D11—21no—
96#66932—21no—
97C4×D44C2311yescharacteristic
98C42×D11C2311yescharacteristic
99C4×Dic22C2311yescharacteristic
100C11×#107C2×C411yescharacteristic
101C11×C4⋊C8C2311yescharacteristic
102C11×C4⋊C8C2311yescharacteristic
103C11×#102C2×C411yescharacteristic
104C11×#102C2×C411yescharacteristic
105C11×C22⋊C8—21no—
106C11×C22⋊C8—21no—
107C4×C8×C11C2311yescharacteristic
108C4×C8×C11C2311yescharacteristic
109C4×C8×C11C2311yescharacteristic
110#66896C2×C411yescharacteristic
111#66896C2×C411yescharacteristic
112C22⋊(C11⋊C8)—21no—
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)⋊C8C2×C411yescharacteristic
119(C2×D11)⋊C8C2×C411yescharacteristic
120(C2×D11)⋊C8D411yescharacteristic
121(C2×D11)⋊C8D411yescharacteristic
122#66881C2×C411yescharacteristic
123#66880C2×C411yescharacteristic
124#66879—21no—
125#66879—21no—
126Dic11⋊C8—21no—
127Dic11⋊C8—21no—
128Dic11⋊C8—21no—
129Dic11⋊C8C2×C411yescharacteristic
130Dic11⋊C8C2×C411yescharacteristic
131Dic11⋊C8D411yescharacteristic
132Dic11⋊C8D411yescharacteristic
133C8×Dic11—21no—
134C8×Dic11—21no—
135#66874C2×C411yescharacteristic
136#66873C2×C411yescharacteristic
137#66872C2×C411yescharacteristic
138#66871C2×C411yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#18020—111nomaximal, Sylow
145C23×D11—21no—
146C2×D4×C11C22×C411yescharacteristic
147C2×D4×C11C22×C411yescharacteristic
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C2×C22⋊D11—21no—
151C2×C22⋊D11—21no—
152C22×Dic11—21no—
153D4×D11—22no—
154D4×D11—41no—
155C2×D44C22×C411yescharacteristic
156C2×C4×D11—21no—
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×C4×D11—81no—
160C2×C4×D11—81no—
161C2×C4×D11C22×C411yescharacteristic
162C2×C4×D11C2×D411yescharacteristic
163C2×C4×D11#4111yescharacteristic
164C2×Dic22C22×C411yescharacteristic
165C11×D8—41no—
166C11×M16—81no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—81no—
171C2×C8×C11C22×C411yescharacteristic
172C2×C8×C11C22×C411yescharacteristic
173C2×C8×C11C2×D411yescharacteristic
174C2×C8×C11C2×D411yescharacteristic
175C11×C4⋊C4C22×C411yescharacteristic
176C11×C4⋊C4C22×C411yescharacteristic
177C11×C22⋊C4—21no—
178C11×C22⋊C4—21no—
179C42×C11C2411yescharacteristic
180C22⋊Dic11—21no—
181C22⋊Dic11—21no—
182C22⋊Dic11—21no—
183C22⋊Dic11—21no—
184#4324—41no—
185#4323—22no—
186(C2×D11)⋊C4—21no—
187(C2×D11)⋊C4—21no—
188(C2×D11)⋊C4—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11C22×C411yescharacteristic
192C4⋊Dic11C22×C411yescharacteristic
193Dic11⋊C4—21no—
194Dic11⋊C4—21no—
195Dic11⋊C4—21no—
196C4×Dic11—21no—
197C4×Dic11C22×C411yescharacteristic
198C4×Dic11C2×D411yescharacteristic
199C4×Dic11#4111yescharacteristic
200#4318—81no—
201#4318—81no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8C22×C411yescharacteristic
206C2×C11⋊C8C22×C411yescharacteristic
207C2×C11⋊C8C2×D411yescharacteristic
208C2×C11⋊C8C2×D411yescharacteristic
209#4314—22no—
210C8×D11—42no—
211C8×D11—81no—
212C8×D11—81no—
213C8×D11—81no—
214#3105—111no—
215#2994—111no—
216#2974—111no—
217#1594—111no—
218#1592—111no—
219#1583—111no—
220#1582—111no—
221#1581—111no—
222#1581D1111yescharacteristic, complemented
223#1580—111no—
224SD16⋊C8—111no—
225#1573—111no—
226#1494—111no—
227C2×D4⋊C8—111no—
228#1452—111no—
229C23×C11—21no—
230C23×C11—21no—
231C22×D11—21no—
232C22×D11—42no—
233C22×D11—42no—
234C22×D11—81no—
235C22×D11C4×D411yescharacteristic
236D4×C11—21no—
237D4×C11—21no—
238D4×C11—21no—
239D4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11C23×C411yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C22⋊D11—42no—
250C22⋊D11—42no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—81no—
255C2×Dic11C4×D411yescharacteristic
256C2×Dic11C4×D411yescharacteristic
257C2×Dic11C4×D411yescharacteristic
258D44—21no—
259D44#13112yes—
260C4×D11—22no—
261C4×D11—21no—
262C4×D11—21no—
263C4×D11—21no—
264C4×D11—21no—
265C4×D11—41no—
266C4×D11—41no—
267C4×D11—81no—
268C4×D11—81no—
269Dic22—21no—
270Dic22—21no—
271C8×C11—21no—
272C8×C11—21no—
273C8×C11—21no—
274C8×C11—21no—
275C8×C11—41no—
276C8×C11—41no—
277C8×C11—41no—
278C11⋊C8—21no—
279C11⋊C8—21no—
280C11⋊C8—21no—
281C11⋊C8—21no—
282C11⋊C8—41no—
283C11⋊C8—41no—
284C11⋊C8—41no—
285#529—111no—
286C2×C4×D4—111no—
287#484—111no—
288#481—111no—
289#478—111no—
290#478—111no—
291#463—111no—
292#463—111no—
293#450—111no—
294#447—111no—
295#446—111no—
296C8×Q8—111no—
297C4×SD16—111no—
298C4×SD16—111no—
299C4×D8—111no—
300C4×D8C2×D1111yescharacteristic
301#436—111no—
302#436—111no—
303#436C2×D1111yescharacteristic
304#435—221no—
305#435—221no—
306#435—221no—
307C8×D4—111no—
308C8×D4—111no—
309C8×D4—221no—
310C8×D4C2×D1111yescharacteristic, complemented
311#433—221no—
312#432—111no—
313#431—111no—
314#431—111no—
315#424—221no—
316C2×C4⋊C8—111no—
317#407—221no—
318C2×C22⋊C8—221no—
319C2×C4×C8—111no—
320#335—111no—
321#335C2×D1111yescharacteristic, complemented
322#334—111no—
323#334—111no—
324Q8⋊C8—111no—
325Q8⋊C8—111no—
326D4⋊C8—111no—
327D4⋊C8—111no—
328D4⋊C8—111no—
329D4⋊C8—111no—
330D4⋊C8C2×D1111yescharacteristic
331D4⋊C8C2×D1111yescharacteristic, complemented
332#322—111no—
333#322—111no—
334#322—111no—
335#322C2×D1111yescharacteristic, complemented
336C22×C11—41no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11—41no—
341C22×C11—41no—
342C22×C11C2×C4×D411yescharacteristic
343C2×D11—21no—
344C2×D11—21no—
345C2×D11—22no—
346C2×D11—41no—
347C2×D11—41no—
348C2×D11—84no—
349C2×D11#44412yes—
350C4×C11—21no—
351C4×C11—41no—
352C4×C11—41no—
353C4×C11C2×#13111yescharacteristic
354C4×C11#56811yescharacteristic
355C4×C11#57611yescharacteristic
356C4×C11#57711yescharacteristic
357Dic11—21no—
358Dic11—21no—
359Dic11—21no—
360Dic11—41no—
361Dic11—41no—
362Dic11—41no—
363C22×D4—111no—
364C23×C4—221no—
365C2×SD16—111no—
366C2×SD16—111no—
367C2×D8—111no—
368C2×D8C4×D1111yescharacteristic
369C2×M16—21no—
370C2×M16—221no—
371C2×M16—221no—
372C22×C8—21no—
373C22×C8—221no—
374C22×C8—221no—
375C22×C8—221no—
376C22×C8—221no—
377#126—221no—
378#125—111no—
379#124—111no—
380#123—221no—
381C22⋊Q8—111no—
382#121—111no—
383C4×Q8—111no—
384C4×D4—111no—
385C4×D4—111no—
386C4×D4—111no—
387C4×D4—221no—
388C4×D4—221no—
389C4×D4—221no—
390C4×D4C22×D1111yescharacteristic
391C4×D4C22×D1111yescharacteristic
392#117—221no—
393C2×C4⋊C4—111no—
394C2×C22⋊C4—221no—
395C2×C42—111no—
396#107—111no—
397#107C4×D1111yescharacteristic
398#106—111no—
399#106—111no—
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⋊C8—221no—
409C4⋊C8C22×D1111yescharacteristic
410C4⋊C8C22×D1111yescharacteristic
411#103—111no—
412#103—111no—
413#102—111no—
414#102—111no—
415#102—111no—
416#102—111no—
417#102C4×D1111yescharacteristic
418#102C4×D1111yescharacteristic
419C22⋊C8—21no—
420C22⋊C8—21no—
421C22⋊C8—111no—
422C22⋊C8—111no—
423C22⋊C8—111no—
424C22⋊C8—111no—
425C22⋊C8—221no—
426C22⋊C8—221no—
427C22⋊C8—221no—
428C22⋊C8—221no—
429C22⋊C8—221no—
430#97—221no—
431#97—221no—
432C4×C8—111no—
433C4×C8—111no—
434C4×C8—111no—
435C4×C8—221no—
436C4×C8—221no—
437C4×C8C22×D1111yescharacteristic
438C4×C8C22×D1111yescharacteristic
439C4×C8C22×D1111yescharacteristic
440C2×C11—81no—
441C2×C11—81no—
442C2×C11#293311yescharacteristic
443C2×C11#294611yescharacteristic
444C2×C11C2×#44411yescharacteristic
445D11—22no—
446D11—42no—
447C24—221no—
448C2×Q8—111no—
449C2×D4—111no—
450C2×D4—221no—
451C2×D4—222no—
452C2×D4—221no—
453C2×D4—441no—
454C2×D4C2×C4×D1111yescharacteristic
455C2×D4C2×C4×D1111yescharacteristic
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—111no—
459C22×C4—111no—
460C22×C4—111no—
461C22×C4—221no—
462C22×C4—221no—
463C22×C4—221no—
464C22×C4—221no—
465C22×C4—881no—
466C22×C4—881no—
467SD16—222no—
468SD16—441no—
469D8—41no—
470D8—222no—
471M16—81no—
472M16—881no—
473M16—881no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—81no—
478C2×C8—111no—
479C2×C8—111no—
480C2×C8—111no—
481C2×C8—111no—
482C2×C8—221no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8—442no—
486C2×C8—881no—
487C2×C8—881no—
488C2×C8—881no—
489C2×C8C2×C4×D1111yescharacteristic
490C2×C8C2×C4×D1111yescharacteristic
491C2×C8D4×D1111yescharacteristic
492C2×C8D4×D1111yescharacteristic
493C4⋊C4—111no—
494C4⋊C4—111no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4C2×C4×D1111yescharacteristic
501C4⋊C4C2×C4×D1111yescharacteristic
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—221no—
505C22⋊C4—221no—
506C22⋊C4—221no—
507C22⋊C4—221no—
508C22⋊C4—221no—
509C22⋊C4—221no—
510C22⋊C4—221no—
511C42—111no—
512C42—111no—
513C42—111no—
514C42—221no—
515C42C23×D1111yescharacteristic
516C11#1802011yescharacteristic, complemented, Sylow
517C23—21no—
518C23—21no—
519C23—111no—
520C23—221no—
521C23—442no—
522C23—442no—
523C23—881no—
524Q8—221no—
525Q8—221no—
526D4—21no—
527D4—21no—
528D4—21no—
529D4—21no—
530D4—112no—
531D4—221no—
532D4—442no—
533D4—442no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—111no—
541C2×C4—111no—
542C2×C4—111no—
543C2×C4—222no—
544C2×C4—221no—
545C2×C4—221no—
546C2×C4—221no—
547C2×C4—221no—
548C2×C4—221no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4—881no—
554C2×C4—881no—
555C2×C4—881no—
556C2×C4C22×C4×D1111yescharacteristic
557C2×C4C2×D4×D1111yescharacteristic
558C2×C4#41×D1111yescharacteristic
559C8—21no—
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—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—112no—
580C22—221no—
581C22—221no—
582C22—222no—
583C22—441no—
584C22—441no—
585C22—884no—
586C22C4×D4×D1111yescharacteristic
587C4—21no—
588C4—41no—
589C4—41no—
590C4—221no—
591C4—221no—
592C4—221no—
593C4—441no—
594C4—441no—
595C4—441no—
596C4#1062327611yescharacteristic
597C4D11×#13111yescharacteristic
598C4#1062328811yescharacteristic
599C4#1062330111yescharacteristic
600C2—81no—
601C2—81no—
602C2—222no—
603C2—442no—
604C2#1307733911yescharacteristic
605C2#1307744111yescharacteristic
606C2D11×#44411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1581C2
socleC22×C11C2×C4×D4
prime radical#10622769C4
cosocleC42×C11C24
hypercenter#1581D11
hypocenterC11#18020
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1581

Complements

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

NH ≅ G/Ntype
2. #13077771C2semidirect
3. #13077648C2semidirect
4. #13067530C2semidirect
5. #13067518C2semidirect
6. #13067462C2semidirect
7. #13067454C2semidirect
8. #13067448C2semidirect
9. #13067438C2semidirect
10. #13067427C2semidirect
11. #13067400C2semidirect
12. #13067073C2semidirect
13. D11×D4⋊C8C2semidirect
14. #13066907C2semidirect
15. C11×#1581C2semidirect
20. C8×D4×C11C22semidirect
30. #10622625C22semidirect
36. #10622443C22semidirect
50. #10622292C22semidirect
51. C11×#335C22semidirect
53. C11×D4⋊C8C22semidirect
54. C11×#322C22semidirect
56. D4⋊(C11⋊C8)C22semidirect
57. #10622122C22semidirect
59. #10622118C22semidirect
60. #10622117C22semidirect
62. #10622095C22semidirect
63. #10622094C22semidirect
64. #10622093C22semidirect
65. #10622092C22semidirect
66. #10622092C22semidirect
222. #1581D11semidirect
310. C8×D4C2×D11semidirect
321. #335C2×D11semidirect
331. D4⋊C8C2×D11semidirect
335. #322C2×D11semidirect
516. C11#18020semidirect

Maximal subgroups

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

subgroupindex
#130786612
#130777712
#130776482
#130675302
#130675182
#130674622
#130674542
#130674482
#130674382
#130674272
#130674002
#130670732
D11×D4⋊C82
#130669072
C11×#15812
#1802011