Finite Group Databasebeta

← #14647752

Subgroups — #14647752

Order 2816.

764 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071229C211yesmaximal, characteristic
2#13068809C211yesmaximal, characteristic, complemented
3C2×#10622106C211yesmaximal, characteristic
4#13066858C211yesmaximal, characteristic
5#13066496C211yesmaximal, characteristic, complemented
6#13066494C211yesmaximal, characteristic, complemented
7C11×#1853C211yesmaximal, characteristic, complemented
8C22×C11×C4⋊C4C2211yescharacteristic
9C22×(C2×D11)⋊C4—21no—
10C22×(C2×D11)⋊C4C2211yescharacteristic
11C2×C22⋊C4×D11—21no—
12C2×C11×#106—21no—
13C2×C11×C22⋊C8C2211yescharacteristic
14C11×#380C2211yescharacteristic
15#10622825C2211yescharacteristic
16C2×C11⋊#95—21no—
17C2×C11⋊#95C2211yescharacteristic
18C2×C22⋊(C11⋊C8)C2211yescharacteristic
19#10622602—21no—
20#10622602—21no—
21C2×#66872—21no—
22#10622555—21no—
23#10622281—21no—
24#10622281—21no—
25C11×#340—21no—
26#10622167—21no—
27#10622106C414yescomplemented
28C24×D11D411yescharacteristic
29C23×C4×C11—21no—
30C23×C4×C11C2311yescharacteristic
31C23×Dic11—21no—
32C23×Dic11D411yescharacteristic
33C22×C4×D11—21no—
34C22×C4×D11—21no—
35C22×C8×C11—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—42no—
39C2×C11×C4⋊C4D411yescharacteristic
40C2×C11×C4⋊C4D411yescharacteristic
41C2×C11×C22⋊C4—21no—
42C2×C22⋊Dic11—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×(C2×D11)⋊C4—21no—
46C2×(C2×D11)⋊C4—21no—
47C2×(C2×D11)⋊C4—21no—
48C2×(C2×D11)⋊C4—21no—
49C2×(C2×D11)⋊C4—42no—
50C2×(C2×D11)⋊C4—42no—
51C2×(C2×D11)⋊C4—42no—
52C2×(C2×D11)⋊C4C2×C412yes—
53C2×(C2×D11)⋊C4Q812yes—
54C2×C4⋊Dic11D411yescharacteristic
55C2×C4⋊Dic11D411yescharacteristic
56C2×Dic11⋊C4—21no—
57C2×Dic11⋊C4—21no—
58C22×C11⋊C8—21no—
59C22⋊C4×D11—42no—
60C22⋊C4×D11—42no—
61C11×#106—42no—
62C11×C22⋊C8—21no—
63C11×C22⋊C8C2×C412yescomplemented
64C11×#95—21no—
65C11⋊#95—21no—
66C11⋊#95—21no—
67C11⋊#95—21no—
68C11⋊#95—21no—
69C11⋊#95—21no—
70C11⋊#95—42no—
71C22⋊(C11⋊C8)—21no—
72C22⋊(C11⋊C8)C2×C412yescomplemented
73#66872—42no—
74#8854—111nomaximal, Sylow
75C24×C11C2×D411yescharacteristic
76C23×D11—21no—
77C23×D11—21no—
78C23×D11—21no—
79C23×D11—21no—
80C23×D11—41no—
81C23×D11—41no—
82C23×D11—41no—
83C23×D11—41no—
84C23×D11C4⋊C412yes—
85C23×D11SD1612yes—
86C23×D11SD1612yes—
87C22×C4×C11—22no—
88C22×C4×C11—21no—
89C22×C4×C11—21no—
90C22×C4×C11—41no—
91C22×C4×C11—41no—
92C22×C4×C11—41no—
93C22×C4×C11—41no—
94C22×C4×C11—41no—
95C22×C4×C11—41no—
96C22×C4×C11—41no—
97C22×C4×C11—41no—
98C22×C4×C11C22×C411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×Q811yescharacteristic
102C22×C4×C11#4111yescharacteristic
103C22×C4×C11#4111yescharacteristic
104C22×Dic11—22no—
105C22×Dic11—21no—
106C22×Dic11—21no—
107C22×Dic11—21no—
108C22×Dic11—21no—
109C22×Dic11—41no—
110C22×Dic11—41no—
111C22×Dic11—41no—
112C22×Dic11—41no—
113C22×Dic11—41no—
114C22×Dic11—41no—
115C22×Dic11—41no—
116C22×Dic11—41no—
117C22×Dic11C4⋊C412yes—
118C2×C4×D11—42no—
119C2×C4×D11—42no—
120C2×C4×D11—81no—
121C2×C4×D11—81no—
122C2×C4×D11—81no—
123C2×C4×D11—81no—
124C2×C8×C11—22no—
125C2×C8×C11—41no—
126C2×C8×C11—41no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—41no—
130C11×C4⋊C4—41no—
131C11×C4⋊C4—41no—
132C11×C4⋊C4—41no—
133C11×C22⋊C4—41no—
134C11×C22⋊C4—41no—
135C22⋊Dic11—41no—
136C22⋊Dic11—41no—
137(C2×D11)⋊C4—22no—
138(C2×D11)⋊C4—22no—
139(C2×D11)⋊C4—22no—
140(C2×D11)⋊C4—22no—
141(C2×D11)⋊C4—42no—
142(C2×D11)⋊C4—42no—
143(C2×D11)⋊C4—48no—
144C4⋊Dic11—41no—
145C4⋊Dic11—41no—
146Dic11⋊C4—81no—
147Dic11⋊C4—81no—
148C2×C11⋊C8—22no—
149C2×C11⋊C8—41no—
150C2×C11⋊C8—41no—
151#2315—111no—
152#1853—111no—
153#1853D1111yescharacteristic, complemented
154C2×#323—111no—
155#1439—111no—
156#1294—111no—
157#1294—111no—
158C23×C11—21no—
159C23×C11—21no—
160C23×C11—21no—
161C23×C11—21no—
162C23×C11C2×C4⋊C411yescharacteristic
163C23×C11#12011yescharacteristic
164C23×C11#12311yescharacteristic
165C23×C11C2×SD1611yescharacteristic
166C23×C11C2×SD1611yescharacteristic
167C23×C11AGL(1,ℤ/8)11yescharacteristic
168C23×C11#13711yescharacteristic
169C22×D11—22no—
170C22×D11—22no—
171C22×D11—22no—
172C22×D11—22no—
173C22×D11—22no—
174C22×D11—22no—
175C22×D11—41no—
176C22×D11—41no—
177C22×D11—41no—
178C22×D11—41no—
179C22×D11—42no—
180C22×D11—42no—
181C22×D11—42no—
182C22×D11—42no—
183C22×D11—42no—
184C22×D11—42no—
185C22×D11—81no—
186C22×D11—81no—
187C22×D11—81no—
188C22×D11—81no—
189C22×D11—81no—
190C22×D11—81no—
191C22×D11#10614yescomplemented
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—42no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—81no—
210C2×C4×C11—81no—
211C2×C4×C11—81no—
212C2×C4×C11—81no—
213C2×C4×C11C4×D411yescharacteristic
214C2×C4×C11C4×D411yescharacteristic
215C2×C4×C11C22⋊Q811yescharacteristic
216C2×C4×C11C22⋊Q811yescharacteristic
217C2×Dic11—22no—
218C2×Dic11—41no—
219C2×Dic11—41no—
220C2×Dic11—42no—
221C2×Dic11—42no—
222C2×Dic11—42no—
223C2×Dic11—42no—
224C2×Dic11—41no—
225C2×Dic11—41no—
226C2×Dic11—41no—
227C2×Dic11—41no—
228C2×Dic11—41no—
229C2×Dic11—41no—
230C2×Dic11—81no—
231C2×Dic11—81no—
232C2×Dic11—81no—
233C2×Dic11—81no—
234C2×Dic11—81no—
235C4×D11—84no—
236C4×D11—84no—
237C8×C11—42no—
238C11⋊C8—42no—
239C22×C4⋊C4C2×D1111yescharacteristic
240C22×C22⋊C4—111no—
241C22×C22⋊C4—221no—
242C22×C22⋊C4—221no—
243C2×#106—21no—
244C2×#106—221no—
245C2×C22⋊C8—111no—
246C2×C22⋊C8C2×D1111yescharacteristic
247#385—221no—
248#385—221no—
249#385—221no—
250#385—221no—
251#380—111no—
252#380—221no—
253#380C2×D1111yescharacteristic
254C2×#95—111no—
255C2×#95—221no—
256#340—21no—
257#340—221no—
258#323—114no—
259C22×C11—21no—
260C22×C11—21no—
261C22×C11—21no—
262C22×C11—21no—
263C22×C11—21no—
264C22×C11—21no—
265C22×C11—21no—
266C22×C11—21no—
267C22×C11—21no—
268C22×C11—21no—
269C22×C11—21no—
270C22×C11—21no—
271C22×C11#38511yescharacteristic
272C22×C11C2×#10611yescharacteristic
273C22×C11#42811yescharacteristic
274C22×C11#44811yescharacteristic
275C22×C11#45011yescharacteristic
276C22×C11#45311yescharacteristic
277C22×C11#45511yescharacteristic
278C22×C11B(4,𝔽2)11yescharacteristic
279C22×C11#45811yescharacteristic
280C22×C11#48111yescharacteristic
281C22×C11#48311yescharacteristic
282C2×D11—24no—
283C2×D11—42no—
284C2×D11—42no—
285C2×D11—42no—
286C2×D11—42no—
287C2×D11—42no—
288C2×D11—42no—
289C2×D11—44no—
290C2×D11—82no—
291C2×D11—82no—
292C2×D11—82no—
293C4×C11—21no—
294C4×C11—21no—
295C4×C11—21no—
296C4×C11—21no—
297C4×C11—82no—
298C4×C11—81no—
299C4×C11—81no—
300Dic11—42no—
301Dic11—82no—
302Dic11—81no—
303Dic11—81no—
304C25—111no—
305C23×C4—21no—
306C23×C4—111no—
307C23×C4—221no—
308C23×C4—221no—
309C23×C4—221no—
310C23×C4C22×D1111yescharacteristic
311C22×C8—21no—
312C22×C8—221no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4—111no—
317C2×C4⋊C4—111no—
318C2×C4⋊C4—221no—
319C2×C4⋊C4—221no—
320C2×C4⋊C4C22⋊D1111yescharacteristic
321C2×C4⋊C4C22⋊D1111yescharacteristic
322C2×C22⋊C4—21no—
323C2×C22⋊C4—112no—
324C2×C22⋊C4—112no—
325C2×C22⋊C4—221no—
326C2×C22⋊C4—221no—
327C2×C22⋊C4—221no—
328C2×C22⋊C4—221no—
329C2×C22⋊C4—221no—
330C2×C22⋊C4—221no—
331C2×C22⋊C4—221no—
332C2×C22⋊C4—442no—
333C2×C22⋊C4—442no—
334C2×C22⋊C4—442no—
335C2×C22⋊C4—442no—
336C2×C22⋊C4—442no—
337#106—42no—
338#106—442no—
339C22⋊C8—21no—
340C22⋊C8—112no—
341C22⋊C8—221no—
342C22⋊C8C4×D1112yescomplemented
343#95—21no—
344#95—221no—
345#95—221no—
346#95—221no—
347#95—221no—
348#95—221no—
349#95—442no—
350C2×C11—21no—
351C2×C11—21no—
352C2×C11—21no—
353C2×C11—21no—
354C2×C11#159611yescharacteristic
355C2×C11#160111yescharacteristic
356C2×C11#160811yescharacteristic
357C2×C11#161311yescharacteristic
358C2×C11#185311yescharacteristic
359C2×C11#185611yescharacteristic
360C2×C11#186711yescharacteristic
361D11—44no—
362C24—112no—
363C24—112no—
364C24—112no—
365C24—221no—
366C24—221no—
367C24—221no—
368C24—221no—
369C24—441no—
370C24—441no—
371C24—441no—
372C24—441no—
373C24D4×D1111yescharacteristic
374C22×C4—22no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4—41no—
385C22×C4—112no—
386C22×C4—221no—
387C22×C4—221no—
388C22×C4—222no—
389C22×C4—221no—
390C22×C4—221no—
391C22×C4—442no—
392C22×C4—442no—
393C22×C4—441no—
394C22×C4—441no—
395C22×C4—441no—
396C22×C4—441no—
397C22×C4—441no—
398C22×C4—441no—
399C22×C4—441no—
400C22×C4—441no—
401C22×C4—881no—
402C22×C4—881no—
403C22×C4—881no—
404C22×C4—881no—
405C22×C4C2×C4×D1111yescharacteristic
406C22×C4#433911yescharacteristic
407C22×C4D4×D1111yescharacteristic
408C22×C4Q8×D1111yescharacteristic
409C22×C4#434311yescharacteristic
410C22×C4C2×C22⋊D1111yescharacteristic
411C2×C8—22no—
412C2×C8—41no—
413C2×C8—41no—
414C2×C8—222no—
415C2×C8—441no—
416C2×C8—441no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—41no—
420C4⋊C4—41no—
421C4⋊C4—41no—
422C4⋊C4—41no—
423C4⋊C4—441no—
424C4⋊C4—441no—
425C4⋊C4—881no—
426C4⋊C4—881no—
427C22⋊C4—41no—
428C22⋊C4—41no—
429C22⋊C4—222no—
430C22⋊C4—222no—
431C22⋊C4—222no—
432C22⋊C4—222no—
433C22⋊C4—442no—
434C22⋊C4—442no—
435C22⋊C4—448no—
436C22⋊C4—441no—
437C22⋊C4—441no—
438C11#885411yescharacteristic, complemented, Sylow
439C23—21no—
440C23—21no—
441C23—21no—
442C23—21no—
443C23—114no—
444C23—222no—
445C23—222no—
446C23—222no—
447C23—222no—
448C23—222no—
449C23—222no—
450C23—442no—
451C23—442no—
452C23—442no—
453C23—442no—
454C23—442no—
455C23—442no—
456C23—441no—
457C23—441no—
458C23—441no—
459C23—441no—
460C23—881no—
461C23—881no—
462C23—881no—
463C23—881no—
464C23—881no—
465C23—881no—
466C23C4⋊C4×D1111yescharacteristic
467C23#6694711yescharacteristic
468C23SD16×D1111yescharacteristic
469C23SD16×D1111yescharacteristic
470C23#6696711yescharacteristic
471C23#6696811yescharacteristic
472C23#6699011yescharacteristic
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—42no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—81no—
491C2×C4—81no—
492C2×C4—81no—
493C2×C4—81no—
494C2×C4—222no—
495C2×C4—441no—
496C2×C4—441no—
497C2×C4—442no—
498C2×C4—442no—
499C2×C4—442no—
500C2×C4—442no—
501C2×C4—441no—
502C2×C4—441no—
503C2×C4—441no—
504C2×C4—441no—
505C2×C4—441no—
506C2×C4—441no—
507C2×C4—884no—
508C2×C4—884no—
509C2×C4—881no—
510C2×C4—881no—
511C2×C4—881no—
512C2×C4—881no—
513C2×C4—881no—
514C2×C4#6694611yescharacteristic
515C2×C4#6694911yescharacteristic
516C2×C4C4×C22⋊D1111yescharacteristic
517C2×C4#6699911yescharacteristic
518C8—42no—
519C8—442no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22—21no—
527C22—21no—
528C22—21no—
529C22—21no—
530C22—21no—
531C22—21no—
532C22—224no—
533C22—444no—
534C22—442no—
535C22—442no—
536C22—442no—
537C22—442no—
538C22—442no—
539C22—442no—
540C22—882no—
541C22—882no—
542C22—882no—
543C22D11×#10611yescharacteristic
544C22#1062247411yescharacteristic
545C22#1062247511yescharacteristic
546C22#1062247611yescharacteristic
547C22#1062260211yescharacteristic
548C22#1062264511yescharacteristic
549C22#1062266611yescharacteristic
550C22#1062278211yescharacteristic
551C22#1062278311yescharacteristic
552C22#1062281111yescharacteristic
553C22#1062281511yescharacteristic
554C4—21no—
555C4—21no—
556C4—21no—
557C4—21no—
558C4—82no—
559C4—81no—
560C4—81no—
561C4—442no—
562C4—882no—
563C4—881no—
564C4—881no—
565C2—21no—
566C2—21no—
567C2—21no—
568C2—21no—
569C2—444no—
570C2#1306753711yescharacteristic
571C2#1306756611yescharacteristic
572C2#1306760511yescharacteristic
573C2#1306763411yescharacteristic
574C2#1306880711yescharacteristic
575C2#1306882411yescharacteristic
576C2#1306889511yescharacteristic
subgroupG/H
centerC23#66990
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1853C2
socleC23×C11#120
prime radicalC24×D11D4
cosocleC23×C4×C11C23
hypercenter#1853D11
hypocenterC11#8854
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1853

Complements

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

NH ≅ G/Ntype
2. #13068809C2semidirect
5. #13066496C2semidirect
6. #13066494C2semidirect
7. C11×#1853C2semidirect
27. #10622106C4semidirect
63. C11×C22⋊C8C2×C4semidirect
72. C22⋊(C11⋊C8)C2×C4semidirect
153. #1853D11semidirect
191. C22×D11#106semidirect
342. C22⋊C8C4×D11semidirect
438. C11#8854semidirect

Maximal subgroups

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

subgroupindex
#130712292
#130688092
C2×#106221062
#130668582
#130664962
#130664942
C11×#18532
#885411