Finite Group Databasebeta

← #14816912

Subgroups — #14816912

Order 2816.

796 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
1C2×#10622704C211yesmaximal, characteristic
2C2×#10622486C211yesmaximal, characteristic
3#13072451C211yesmaximal, characteristic
4#13071530C211yesmaximal, characteristic
5#13070151C211yesmaximal, characteristic
6#13070090C211yesmaximal, characteristic
7#13070008C211yesmaximal, characteristic
8#13069348C211yesmaximal, characteristic
9#13069176C211yesmaximal, characteristic
10#13068958C211yesmaximal, characteristic
11#13068956C211yesmaximal, characteristic
12#13068871C211yesmaximal, characteristic
13#13068871C211yesmaximal, characteristic
14#13068867C211yesmaximal, characteristic
15C11×#2057C211yesmaximal, characteristic
16C2×C11×C4⋊Q8C2211yescharacteristic
17C22×Dic44C2211yescharacteristic
18C2×#66940C2211yescharacteristic
19C2×#66940C2211yescharacteristic
20C2×#66940C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22C2×C11×#107C2211yescharacteristic
23C2×C11×#107C2211yescharacteristic
24C11×#389C2211yescharacteristic
25#10622843—21no—
26#10622842—21no—
27C2×#66880C2211yescharacteristic
28C2×#66880C2211yescharacteristic
29C2×C8×Dic11C2211yescharacteristic
30#10622704—24no—
31#10622598C2211yescharacteristic
32#10622598C2211yescharacteristic
33#10622597—21no—
34#10622591—21no—
35#10622589—21no—
36#10622589C2211yescharacteristic
37#10622587C2211yescharacteristic
38#10622586C2211yescharacteristic
39#10622585—21no—
40C2×#66874C2211yescharacteristic
41C2×#66874C2211yescharacteristic
42C2×#66874C2211yescharacteristic
43C2×#66874C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46C2×#66871C2211yescharacteristic
47C4×Dic11⋊C4C2211yescharacteristic
48#10622542C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50#10622486—24no—
51#10622262—21no—
52#10622260—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#336C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11—21no—
62C22×Dic22C2311yescharacteristic
63C22×Dic22C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C11×C4⋊Q8—22no—
67C11×C4⋊Q8—41no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C42×C11C2311yescharacteristic
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×Dic11⋊C4—21no—
80C2×Dic11⋊C4—21no—
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4D411yescharacteristic
87C2×Dic11⋊C4D411yescharacteristic
88C2×C4×Dic11—21no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11C2311yescharacteristic
93C2×C4×Dic11C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C2×Dic44—22no—
97C2×Dic44—22no—
98C2×Dic44Q814yescomplemented
99#66940—22no—
100#66940—22no—
101#66940—22no—
102#66940—22no—
103#66940—41no—
104#66940—41no—
105C4×Dic22—22no—
106C4×Dic22—41no—
107C11×#107—22no—
108C11×#107—41no—
109C11×#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95D411yescharacteristic
118C11⋊#95D411yescharacteristic
119#66880—22no—
120#66880—41no—
121C8×Dic11—22no—
122#66874—22no—
123#66874—22no—
124#66874—22no—
125#66874D414yes—
126#66871—22no—
127#66871—22no—
128#66871—22no—
129C4⋊(C11⋊C8)—22no—
130#26381—111nomaximal, Sylow
131C2×Q8×C11—42no—
132C2×Q8×C11—42no—
133C2×Q8×C11—81no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2411yescharacteristic
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11C2×D411yescharacteristic
146C22×Dic11C2×D411yescharacteristic
147C22×Dic11C2×D411yescharacteristic
148C22×Dic11C2×D411yescharacteristic
149C2×Dic22—21no—
150C2×Dic22—21no—
151C2×Dic22—21no—
152C2×Dic22—21no—
153C2×Dic22—21no—
154C2×Dic22—21no—
155C2×Dic22—21no—
156C2×Dic22—21no—
157C2×Dic22C2×D412yes—
158C2×Dic22C2×Q812yes—
159C2×Dic22C2×Q812yes—
160C2×Dic22#4112yes—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11C2×Q812yes—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—42no—
174C11×C4⋊C4—81no—
175C11×C4⋊C4C2×D412yes—
176C11×C4⋊C4#4112yes—
177C42×C11—21no—
178C42×C11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—81no—
184C4⋊Dic11—81no—
185Dic11⋊C4—24no—
186Dic11⋊C4—41no—
187Dic11⋊C4—42no—
188Dic11⋊C4—42no—
189Dic11⋊C4—42no—
190Dic11⋊C4—42no—
191Dic11⋊C4—81no—
192Dic11⋊C4—81no—
193Dic11⋊C4Q1614yescomplemented
194C4×Dic11—24no—
195C4×Dic11—21no—
196C4×Dic11—21no—
197C4×Dic11—21no—
198C4×Dic11—21no—
199C4×Dic11—42no—
200C4×Dic11—42no—
201C4×Dic11—42no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8C2×D412yes—
208Dic44—28no—
209C2×#477—111no—
210C2×C4×Q16—111no—
211#2451—111no—
212Q8×C4⋊C4—111no—
213#2095—111no—
214#2083—111no—
215#2068—111no—
216#2057D1111yescharacteristic
217#1942—111no—
218#1916—111no—
219#1878—111no—
220#1878—111no—
221#1863—111no—
222#1863—111no—
223#1863—111no—
224C23×C11C22×D411yescharacteristic
225Q8×C11—84no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11C2×Q1612yes—
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C22×Q811yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C2×C4×C11H(5,𝔽2)11yescharacteristic
249C2×C4×C112−1+411yescharacteristic
250C2×Dic11—21no—
251C2×Dic11—22no—
252C2×Dic11—21no—
253C2×Dic11—22no—
254C2×Dic11—22no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—22no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11C2×Q1612yes—
273C2×Dic11C2×Q1612yes—
274Dic22—22no—
275Dic22—22no—
276Dic22—22no—
277Dic22—22no—
278Dic22—22no—
279Dic22—41no—
280Dic22—41no—
281Dic22C22⋊Q814yes—
282C8×C11—22no—
283C8×C11—41no—
284C11⋊C8—22no—
285C11⋊C8—41no—
286C22×Q16—111no—
287C2×C4⋊Q8C2×D1111yescharacteristic
288C2×C4×Q8—111no—
289C2×C4×Q8—111no—
290C2×C4×Q8—111no—
291C2×C4×Q8—111no—
292#477—224no—
293C4×Q16—224no—
294C2×#107—111no—
295C2×#107—111no—
296C2×#107—111no—
297C2×#107C2×D1111yescharacteristic
298C2×#107C2×D1111yescharacteristic
299C2×C4⋊C8—111no—
300C2×#103—111no—
301C2×#103—111no—
302C2×#103—111no—
303C2×#103—111no—
304C2×#103—111no—
305C2×#103—111no—
306C2×C4×C8—111no—
307#398—221no—
308#395—221no—
309#391—111no—
310#391—111no—
311#391—221no—
312#389—111no—
313#389—111no—
314#389—111no—
315#389—221no—
316#389—221no—
317#389C2×D1111yescharacteristic
318#387—221no—
319#384—111no—
320#384—221no—
321C4×C4⋊C4—111no—
322C4×C4⋊C4—221no—
323#340—111no—
324#340—111no—
325#340C2×D1111yescharacteristic
326#340C2×D1111yescharacteristic
327#336—111no—
328#336—111no—
329#336—111no—
330#336C2×D1111yescharacteristic
331C22×C11#52511yescharacteristic
332C22×C11D4211yescharacteristic
333C22×C11D4×Q811yescharacteristic
334C22×C11C22×Q1611yescharacteristic
335C22×C11#57511yescharacteristic
336C22×C11#57611yescharacteristic
337C22×C11#57811yescharacteristic
338C4×C11—22no—
339C4×C11—42no—
340C4×C11—41no—
341C4×C11—42no—
342C4×C11—81no—
343C4×C11—81no—
344C4×C11C2×C22⋊Q811yescharacteristic
345C4×C11#53911yescharacteristic
346C4×C11#54711yescharacteristic
347C4×C11#55411yescharacteristic
348Dic11—22no—
349Dic11—24no—
350Dic11—22no—
351Dic11—41no—
352Dic11—42no—
353Dic11—41no—
354Dic11—81no—
355Dic11—81no—
356C22×Q8—21no—
357C22×Q8—111no—
358C22×Q8—111no—
359C2×Q16—114no—
360C2×Q16—222no—
361C2×Q16—222no—
362C22×C8—111no—
363C22×C8—111no—
364C22×C8C22×D1111yescharacteristic
365C22×C8C22×D1111yescharacteristic
366C4⋊Q8—22no—
367C4⋊Q8—41no—
368C4×Q8—222no—
369C4×Q8—222no—
370C4×Q8—222no—
371C4×Q8—222no—
372C4×Q8—222no—
373C4×Q8—441no—
374C4×Q8—441no—
375C4×Q8—441no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—111no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—111no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4—221no—
389C2×C4⋊C4—221no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4C22×D1111yescharacteristic
392C2×C4⋊C4C22×D1111yescharacteristic
393C2×C4⋊C4C22×D1111yescharacteristic
394C2×C4⋊C4C22×D1111yescharacteristic
395C2×C42—111no—
396C2×C42—111no—
397C2×C42—221no—
398C2×C42—221no—
399C2×C42—221no—
400C2×C42—221no—
401C2×C42C22×D1111yescharacteristic
402#107—22no—
403#107—41no—
404#107—222no—
405#107—222no—
406#107—222no—
407C4⋊C8—222no—
408#103—114no—
409#103—222no—
410#103—222no—
411#103—222no—
412#103—222no—
413#103—441no—
414C4×C8—222no—
415#95—21no—
416#95—111no—
417#95—111no—
418#95—221no—
419#95—221no—
420#95—221no—
421#95—221no—
422#95—221no—
423#95—221no—
424#95—221no—
425C2×C11#244911yescharacteristic
426C2×C11#310411yescharacteristic
427C2×C11#312411yescharacteristic
428C2×C11#326811yescharacteristic
429C2×C11D4×Q1611yescharacteristic
430C2×C11Q8×Q1611yescharacteristic
431C2×C11#339011yescharacteristic
432C2×Q8—42no—
433C2×Q8—42no—
434C2×Q8—81no—
435C2×Q8—112no—
436C2×Q8—112no—
437C2×Q8—112no—
438C2×Q8—112no—
439C2×Q8—221no—
440C2×Q8—221no—
441C2×Q8—221no—
442C2×Q8—221no—
443C2×Q8—221no—
444C2×Q8—221no—
445C2×Q8—221no—
446C2×Q8—221no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—111no—
452C22×C4—111no—
453C22×C4—111no—
454C22×C4—111no—
455C22×C4—221no—
456C22×C4—221no—
457C22×C4—221no—
458C22×C4—221no—
459C22×C4D4×D1111yescharacteristic
460C22×C4D4×D1111yescharacteristic
461C22×C4C23×D1111yescharacteristic
462Q16—228no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—112no—
469C2×C8—221no—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8—221no—
474C2×C8Q8×D1112yes—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—42no—
482C4⋊C4—81no—
483C4⋊C4—114no—
484C4⋊C4—224no—
485C4⋊C4—221no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4—441no—
490C4⋊C4—442no—
491C4⋊C4—442no—
492C4⋊C4—442no—
493C4⋊C4—442no—
494C4⋊C4—881no—
495C4⋊C4—881no—
496C4⋊C4—881no—
497C4⋊C4—881no—
498C4⋊C4D4×D1112yes—
499C4⋊C4#434312yes—
500C42—21no—
501C42—21no—
502C42—224no—
503C42—221no—
504C42—221no—
505C42—221no—
506C42—221no—
507C42—442no—
508C42—442no—
509C42—442no—
510C11#2638111yescharacteristic, complemented, Sylow
511C23C2×D4×D1111yescharacteristic
512Q8—84no—
513Q8—114no—
514Q8—222no—
515Q8—222no—
516Q8—222no—
517Q8—222no—
518Q8—222no—
519Q8—441no—
520Q8—441no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—112no—
539C2×C4—112no—
540C2×C4—222no—
541C2×C4—221no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—222no—
545C2×C4—221no—
546C2×C4—222no—
547C2×C4—222no—
548C2×C4—221no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—221no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4—441no—
558C2×C4—441no—
559C2×C4—441no—
560C2×C4—441no—
561C2×C4—441no—
562C2×C4Q16×D1112yes—
563C2×C4C2×D4×D1111yescharacteristic
564C2×C4#6703711yescharacteristic
565C2×C4C2×Q8×D1111yescharacteristic
566C2×C4C2×#434311yescharacteristic
567C2×C4#6704011yescharacteristic
568C2×C4#41×D1111yescharacteristic
569C8—22no—
570C8—41no—
571C8—222no—
572C8—441no—
573C22#1062312111yescharacteristic
574C22#1062315811yescharacteristic
575C22#1062325811yescharacteristic
576C22#1062328811yescharacteristic
577C22C2×Q16×D1111yescharacteristic
578C22#1062330411yescharacteristic
579C22#1062331011yescharacteristic
580C4—22no—
581C4—41no—
582C4—42no—
583C4—42no—
584C4—81no—
585C4—81no—
586C4—224no—
587C4—222no—
588C4—222no—
589C4—442no—
590C4—441no—
591C4—441no—
592C4—881no—
593C4—881no—
594C4D11×C22⋊Q811yescharacteristic
595C4#1062316911yescharacteristic
596C4#1062325711yescharacteristic
597C4#1062326111yescharacteristic
598C2#1307241811yescharacteristic
599C2#1307865711yescharacteristic
600C2#1307888311yescharacteristic
601C2#1308015411yescharacteristic
602C2#1308036111yescharacteristic
603C2#1308149911yescharacteristic
604C2#1308158011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2057C2
socle, prime radicalC23×C11C22×D4
hypercenter#2057D11
hypocenterC11#26381
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2057

Complements

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

NH ≅ G/Ntype
98. C2×Dic44Q8semidirect
193. Dic11⋊C4Q16semidirect
510. C11#26381semidirect

Maximal subgroups

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

subgroupindex
C2×#106227042
C2×#106224862
#130724512
#130715302
#130701512
#130700902
#130700082
#130693482
#130691762
#130689582
#130689562
#130688712
#130688672
C11×#20572
#2638111