Finite Group Databasebeta

← #14816943

Subgroups — #14816943

Order 2816.

772 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622409C211yesmaximal, characteristic
2#13072471C211yesmaximal, characteristic
3#13071534C211yesmaximal, characteristic
4#13070162C211yesmaximal, characteristic
5#13070100C211yesmaximal, characteristic
6#13070009C211yesmaximal, characteristic
7#13069952C211yesmaximal, characteristic
8#13069349C211yesmaximal, characteristic
9#13069173C211yesmaximal, characteristic
10#13068959C211yesmaximal, characteristic
11#13068959C211yesmaximal, characteristic
12#13068884C211yesmaximal, characteristic
13#13068884C211yesmaximal, characteristic
14#13068872C211yesmaximal, characteristic
15C2×C4×C11×Q16C211yesmaximal, characteristic
16C22×C11×Q16C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×Q8×Dic11C2211yescharacteristic
20C2×Q8×Dic11C2211yescharacteristic
21C2×#66943C2211yescharacteristic
22C4×C11×Q16—24no—
23C2×C11×#107C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C4×C8×C11C2211yescharacteristic
27#10622843C2211yescharacteristic
28#10622843C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66882C2211yescharacteristic
34C2×#66882C2211yescharacteristic
35C2×Dic11⋊C8C2211yescharacteristic
36#10622599—21no—
37#10622598C2211yescharacteristic
38#10622597—21no—
39#10622590—21no—
40#10622590C2211yescharacteristic
41#10622586—21no—
42#10622586C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44C2×#66872C2211yescharacteristic
45#10622546—21no—
46C4×Dic11⋊C4—21no—
47C4×Dic11⋊C4C2211yescharacteristic
48#10622541—21no—
49#10622541—21no—
50#10622541C2211yescharacteristic
51#10622541C2211yescharacteristic
52#10622409—24no—
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C2×C11×Q16—22no—
64C2×C11×Q16—22no—
65C2×C11×Q16Q814yes—
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C4×Q8×C11—22no—
69C4×Q8×C11—22no—
70C4×Q8×C11—41no—
71C4×Q8×C11—41no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C42×C11—21no—
77C2×C42×C11—21no—
78C2×C42×C11C2311yescharacteristic
79Q8×Dic11—22no—
80Q8×Dic11—22no—
81Q8×Dic11—22no—
82Q8×Dic11—41no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4D411yescharacteristic
96C2×Dic11⋊C4D411yescharacteristic
97C2×C4×Dic11—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11C2311yescharacteristic
100C2×C4×Dic11C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103#66943—22no—
104#66943—41no—
105C11×#107—22no—
106C11×#103—22no—
107C11×#103D414yes—
108C4×C8×C11—22no—
109#66899—22no—
110#66899—22no—
111#66899—22no—
112#66899—41no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95D411yescharacteristic
124C11⋊#95D411yescharacteristic
125#66882—22no—
126#66882—22no—
127Dic11⋊C8—22no—
128#66872—22no—
129#66872—41no—
130#26383—111nomaximal, Sylow
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11C2×D412yes—
140C2×Q8×C11C2×Q812yes—
141C2×Q8×C11C2×Q812yes—
142C2×Q8×C11#4112yes—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2411yescharacteristic
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11C2×D411yescharacteristic
155C22×Dic11C2×D411yescharacteristic
156C22×Dic11C2×D411yescharacteristic
157C22×Dic11C2×D411yescharacteristic
158C11×Q16—28no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11C2×D412yes—
164C2×C8×C11C2×Q812yes—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—42no—
169C11×C4⋊C4—42no—
170C11×C4⋊C4C2×D412yes—
171C42×C11—21no—
172C42×C11—21no—
173C42×C11—42no—
174C42×C11—42no—
175C4⋊Dic11—24no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—42no—
184C4⋊Dic11—42no—
185C4⋊Dic11—42no—
186C4⋊Dic11#4112yes—
187Dic11⋊C4—22no—
188Dic11⋊C4—41no—
189Dic11⋊C4—42no—
190Dic11⋊C4—42no—
191Dic11⋊C4—42no—
192Dic11⋊C4—42no—
193C4×Dic11—24no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11—21no—
197C4×Dic11—21no—
198C4×Dic11—42no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×#479—111no—
206C2×C4×Q16D1111yescharacteristic
207#2453—111no—
208#2351—111no—
209#2097—111no—
210#2085—111no—
211#2068—111no—
212#2059—111no—
213#1942—111no—
214#1916—111no—
215#1878—111no—
216#1878—111no—
217#1865—111no—
218#1865—111no—
219#1863—111no—
220C23×C11C22×D411yescharacteristic
221Q8×C11—22no—
222Q8×C11—22no—
223Q8×C11—22no—
224Q8×C11—22no—
225Q8×C11—22no—
226Q8×C11—41no—
227Q8×C11—41no—
228Q8×C11C22⋊Q814yes—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—21no—
232C2×C4×C11—22no—
233C2×C4×C11—21no—
234C2×C4×C11—22no—
235C2×C4×C11—21no—
236C2×C4×C11—22no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11#13512yes—
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C22×Q811yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C2×C4×C11H(5,𝔽2)11yescharacteristic
252C2×C4×C112−1+411yescharacteristic
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—22no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C8×C11—22no—
278C8×C11—22no—
279C11⋊C8—41no—
280C11⋊C8—41no—
281C22×Q16C2×D1111yescharacteristic
282C2×#125—111no—
283C2×C4×Q8—111no—
284C2×C4×Q8—111no—
285C2×C4×Q8C2×D1111yescharacteristic
286C2×C4×Q8C2×D1111yescharacteristic
287#479—224no—
288C4×Q16—24no—
289C2×#107—111no—
290C2×#107—111no—
291C2×#107C2×D1111yescharacteristic
292C2×#106—111no—
293C2×#106—111no—
294C2×C4⋊C8—111no—
295C2×#103—111no—
296C2×#103—111no—
297C2×#103—111no—
298C2×#103—111no—
299C2×#103C2×D1111yescharacteristic
300C2×#103C2×D1111yescharacteristic
301C2×C4×C8C2×D1111yescharacteristic
302#400—221no—
303#398—221no—
304#391—111no—
305#391—111no—
306#389—111no—
307#389—111no—
308#389—111no—
309#389—111no—
310#389—221no—
311#389—221no—
312#389—221no—
313#387—221no—
314#382—111no—
315#382—221no—
316C4×C4⋊C4—111no—
317C4×C4⋊C4—221no—
318#340—111no—
319#340—111no—
320#340—111no—
321#340—111no—
322#336—111no—
323#336—111no—
324#336—111no—
325#336—111no—
326C22×C11#52511yescharacteristic
327C22×C11D4211yescharacteristic
328C22×C11D4×Q811yescharacteristic
329C22×C11C2×#13511yescharacteristic
330C22×C11#57511yescharacteristic
331C22×C11#57811yescharacteristic
332C22×C11#57811yescharacteristic
333C4×C11—24no—
334C4×C11—22no—
335C4×C11—42no—
336C4×C11—41no—
337C4×C11—42no—
338C4×C11—81no—
339C4×C11C2×C22⋊Q811yescharacteristic
340C4×C11#53911yescharacteristic
341C4×C11#54711yescharacteristic
342C4×C11#55411yescharacteristic
343Dic11—41no—
344Dic11—42no—
345Dic11—41no—
346Dic11—41no—
347Dic11—41no—
348Dic11—81no—
349Dic11—81no—
350Dic11—81no—
351C22×Q8C22×D1111yescharacteristic
352C22×Q8C22×D1111yescharacteristic
353C2×Q16—22no—
354C2×Q16—22no—
355C2×Q16Dic2214yes—
356C22×C8—111no—
357C22×C8—111no—
358C22×C8C22×D1111yescharacteristic
359C22×C8C22×D1111yescharacteristic
360#125—222no—
361#125—441no—
362C4×Q8—22no—
363C4×Q8—22no—
364C4×Q8—41no—
365C4×Q8—41no—
366C4×Q8—222no—
367C4×Q8—222no—
368C4×Q8—222no—
369C4×Q8—441no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—111no—
373C2×C4⋊C4—111no—
374C2×C4⋊C4—111no—
375C2×C4⋊C4—111no—
376C2×C4⋊C4—111no—
377C2×C4⋊C4—111no—
378C2×C4⋊C4—221no—
379C2×C4⋊C4—221no—
380C2×C4⋊C4—221no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4C22×D1111yescharacteristic
387C2×C4⋊C4C22×D1111yescharacteristic
388C2×C42—21no—
389C2×C42—21no—
390C2×C42—111no—
391C2×C42—111no—
392C2×C42—221no—
393C2×C42—221no—
394C2×C42C22×D1111yescharacteristic
395#107—22no—
396#107—222no—
397#107—222no—
398#106—222no—
399#106—441no—
400C4⋊C8—222no—
401#103—22no—
402#103—222no—
403#103—222no—
404#103—222no—
405#103—441no—
406#103C22⋊D1114yes—
407C4×C8—22no—
408#95—111no—
409#95—111no—
410#95—221no—
411#95—221no—
412#95—221no—
413#95—221no—
414#95—221no—
415#95—221no—
416#95—221no—
417#95—221no—
418#95—221no—
419#95—221no—
420C2×C11#244911yescharacteristic
421C2×C11#310211yescharacteristic
422C2×C11#312711yescharacteristic
423C2×C11#326911yescharacteristic
424C2×C11#328511yescharacteristic
425C2×C11#338311yescharacteristic
426C2×C11#339011yescharacteristic
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8C2×Dic2212yes—
436C2×Q8C2×Dic2212yes—
437C2×Q8#433912yes—
438C2×Q8C2×C22⋊D1112yes—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—111no—
444C22×C4—111no—
445C22×C4—111no—
446C22×C4—111no—
447C22×C4—221no—
448C22×C4—221no—
449C22×C4—221no—
450C22×C4—221no—
451C22×C4D4×D1111yescharacteristic
452C22×C4D4×D1111yescharacteristic
453C22×C4C23×D1111yescharacteristic
454Q16—28no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—221no—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8—221no—
465C2×C8C2×Dic2212yes—
466C2×C8C2×C22⋊D1112yes—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—42no—
471C4⋊C4—42no—
472C4⋊C4—112no—
473C4⋊C4—224no—
474C4⋊C4—222no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4—441no—
483C4⋊C4—442no—
484C4⋊C4—442no—
485C4⋊C4—442no—
486C4⋊C4—442no—
487C4⋊C4—442no—
488C4⋊C4—442no—
489C4⋊C4—442no—
490C4⋊C4C2×C22⋊D1112yes—
491C42—21no—
492C42—21no—
493C42—42no—
494C42—42no—
495C42—224no—
496C42—221no—
497C42—221no—
498C42—221no—
499C42—221no—
500C42—442no—
501C11#2638311yescharacteristic, complemented, Sylow
502C23C2×D4×D1111yescharacteristic
503Q8—22no—
504Q8—22no—
505Q8—22no—
506Q8—22no—
507Q8—22no—
508Q8—41no—
509Q8—41no—
510Q8#6697714yes—
511C2×C4—21no—
512C2×C4—22no—
513C2×C4—21no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—21no—
520C2×C4—22no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—221no—
531C2×C4—221no—
532C2×C4—221no—
533C2×C4—221no—
534C2×C4—221no—
535C2×C4—221no—
536C2×C4—221no—
537C2×C4—221no—
538C2×C4—221no—
539C2×C4—222no—
540C2×C4—221no—
541C2×C4—441no—
542C2×C4—441no—
543C2×C4—441no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4#6697212yes—
553C2×C4C22×Dic2211yescharacteristic
554C2×C4C2×#433911yescharacteristic
555C2×C4#6703711yescharacteristic
556C2×C4#41×D1111yescharacteristic
557C2×C4#6704311yescharacteristic
558C2×C4C22×C22⋊D1111yescharacteristic
559C8—22no—
560C8—22no—
561C8—441no—
562C8—441no—
563C22D4×Dic2211yescharacteristic
564C22#1062307811yescharacteristic
565C22C2×#6697211yescharacteristic
566C22#1062329711yescharacteristic
567C22#1062329911yescharacteristic
568C22#1062330211yescharacteristic
569C22D4×C22⋊D1111yescharacteristic
570C4—24no—
571C4—22no—
572C4—42no—
573C4—41no—
574C4—42no—
575C4—81no—
576C4—441no—
577C4—441no—
578C4—441no—
579C4—442no—
580C4—441no—
581C4—881no—
582C4—881no—
583C4—881no—
584C4#1062307011yescharacteristic
585C4#1062309511yescharacteristic
586C4C2×#6697711yescharacteristic
587C4#1062335511yescharacteristic
588C2#1307241911yescharacteristic
589C2#1307864011yescharacteristic
590C2#1307891311yescharacteristic
591C2#1308017111yescharacteristic
592C2#1308035711yescharacteristic
593C2#1308150511yescharacteristic
594C2#1308158111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C4×C11×Q16C2
socle, prime radicalC23×C11C22×D4
hypercenterC2×C4×Q16D11
hypocenterC11#26383
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
501. C11#26383semidirect

Maximal subgroups

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

subgroupindex
C2×#106224092
#130724712
#130715342
#130701622
#130701002
#130700092
#130699522
#130693492
#130691732
#130689592
#130688842
#130688722
C2×C4×C11×Q162
#2638311