Finite Group Databasebeta

← #14823716

Subgroups — #14823716

Order 2816.

758 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622682C211yesmaximal, characteristic
2C2×#10622643C211yesmaximal, characteristic
3#13072392C211yesmaximal, characteristic
4#13069994C211yesmaximal, characteristic
5#13069951C211yesmaximal, characteristic
6#13069938C211yesmaximal, characteristic
7#13069715C211yesmaximal, characteristic
8#13069476C211yesmaximal, characteristic
9#13069309C211yesmaximal, characteristic
10#13069305C211yesmaximal, characteristic
11#13069291C211yesmaximal, characteristic
12#13068957C211yesmaximal, characteristic
13#13068869C211yesmaximal, characteristic
14#13068485C211yesmaximal, characteristic
15C11×#2453C211yesmaximal, characteristic
16C2×C11×#125C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C22×#4326C2211yescharacteristic
19C22×#4326C2211yescharacteristic
20C2×#66922C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22C11×#400—21no—
23C11×#398—21no—
24C11×#391C2211yescharacteristic
25C11×#391C2211yescharacteristic
26C11×#389—21no—
27C11×#389C2211yescharacteristic
28C11×#389C2211yescharacteristic
29C11×#387—21no—
30C4×C11×C4⋊C4C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33#10622682—24no—
34#10622643—24no—
35#10622597—21no—
36#10622594—21no—
37C2×#66874C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C2×#66874C2211yescharacteristic
42C2×#66874C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45#10622542C2211yescharacteristic
46#10622542C2211yescharacteristic
47#10622542C2211yescharacteristic
48#10622541C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×#66867C2211yescharacteristic
51C2×#66867C2211yescharacteristic
52C2×C4×C11⋊C8C2211yescharacteristic
53#10622273—21no—
54#10622268—21no—
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×Dic22C2311yescharacteristic
63C22×Dic22C2311yescharacteristic
64C11×#125—22no—
65C11×#125—41no—
66C4×Q8×C11—22no—
67C4×Q8×C11—41no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4D411yescharacteristic
74C2×C11×C4⋊C4D411yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C42×C11—21no—
79C2×C42×C11C2311yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C2×C42×C11C2311yescharacteristic
82C2×#4326—22no—
83C2×#4326—22no—
84C2×#4326—22no—
85C2×#4326—22no—
86C2×#4326—22no—
87C2×#4326—41no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×C4×Dic11—21no—
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99#66922—22no—
100#66922—41no—
101C4×Dic22—22no—
102C4×Dic22—41no—
103C11×#95—21no—
104C11×#95—21no—
105C11×#95—21no—
106C11×#95—21no—
107C11×#95—21no—
108C11×#95—21no—
109C11×#95D411yescharacteristic
110C11×#95D411yescharacteristic
111#66899—22no—
112#66899—22no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120#66874—22no—
121#66874—22no—
122#66874—22no—
123#66874—22no—
124#66874—22no—
125#66874D414yes—
126#66872—22no—
127#66871—41no—
128C4⋊(C11⋊C8)—22no—
129#66867—22no—
130#66867—22no—
131C4×C11⋊C8—22no—
132#26847—111nomaximal, Sylow
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11#4112yes—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2411yescharacteristic
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C2×Dic22—21no—
155C2×Dic22—21no—
156C2×Dic22—21no—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22—21no—
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22C2×D412yes—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—41no—
173C11×C4⋊C4—42no—
174C11×C4⋊C4—42no—
175C11×C4⋊C4—42no—
176C11×C4⋊C4—42no—
177C11×C4⋊C4—42no—
178C11×C4⋊C4C2×D412yes—
179C42×C11—21no—
180C42×C11—21no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11—21no—
185C42×C11—42no—
186#4326—28no—
187#4326—44no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—42no—
193C4⋊Dic11—42no—
194Dic11⋊C4—42no—
195Dic11⋊C4—42no—
196C4×Dic11—42no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
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×C11⋊C8—21no—
206C2×C11⋊C8C2×D412yes—
207C2×C11⋊C8#4112yes—
208C2×C11⋊C8#4112yes—
209C2×#491—111no—
210C2×#441—111no—
211#2453D1111yescharacteristic
212#2446—111no—
213#2066—111no—
214#2059—111no—
215#2056—111no—
216#2016—111no—
217#1969—111no—
218#1935—111no—
219#1935—111no—
220#1933—111no—
221#1878—111no—
222#1863—111no—
223#1770—111no—
224C23×C11C22×D411yescharacteristic
225Q8×C11—22no—
226Q8×C11—22no—
227Q8×C11—41no—
228Q8×C11—41no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
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—21no—
247C2×C4×C11—21no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11#13712yes—
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11H(5,𝔽2)11yescharacteristic
264C2×C4×C112−1+411yescharacteristic
265C2×Dic11—22no—
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—
277Dic22—22no—
278Dic22—22no—
279Dic22—41no—
280Dic22—41no—
281Dic22—41no—
282Dic22—41no—
283Dic22—41no—
284Dic22—41no—
285C11⋊C8—22no—
286C11⋊C8—22no—
287C11⋊C8—22no—
288C11⋊C8—41no—
289C22×Q16—111no—
290C22×Q16—111no—
291C2×C4⋊Q8—111no—
292C2×#125C2×D1111yescharacteristic
293C2×C4×Q8—111no—
294C2×C4×Q8C2×D1111yescharacteristic
295#491—224no—
296#441—224no—
297C2×#107—111no—
298C2×#106—111no—
299C2×C4⋊C8—111no—
300C2×#103—111no—
301C2×#103—111no—
302C2×#103—111no—
303C2×#103—111no—
304C2×#103—111no—
305C2×#103—111no—
306C2×#103—111no—
307C2×#103—111no—
308C2×#97—111no—
309C2×#97—111no—
310C2×C4×C8—111no—
311#400—21no—
312#400—221no—
313#398—21no—
314#398—221no—
315#391—111no—
316#391—111no—
317#391—111no—
318#391C2×D1111yescharacteristic
319#391C2×D1111yescharacteristic
320#389—21no—
321#389—111no—
322#389C2×D1111yescharacteristic
323#389C2×D1111yescharacteristic
324#387—21no—
325#387—221no—
326#387—221no—
327C4×C4⋊C4C2×D1111yescharacteristic
328#340—111no—
329#340—111no—
330#340—111no—
331#340—111no—
332#336—111no—
333#336—111no—
334C22×C11#53211yescharacteristic
335C22×C11D4211yescharacteristic
336C22×C11#54811yescharacteristic
337C22×C11C2×#13711yescharacteristic
338C22×C11#57511yescharacteristic
339C22×C11#57811yescharacteristic
340C22×C11#57811yescharacteristic
341C4×C11—22no—
342C4×C11—41no—
343C4×C11—42no—
344C4×C11—41no—
345C4×C11—41no—
346C4×C11—42no—
347C4×C11—41no—
348C4×C11—41no—
349C4×C11—81no—
350C4×C11—81no—
351C4×C11#52511yescharacteristic
352C4×C11#54211yescharacteristic
353C4×C11#54711yescharacteristic
354C4×C11#55111yescharacteristic
355Dic11—42no—
356Dic11—81no—
357Dic11—81no—
358Dic11—81no—
359C22×Q8—111no—
360C22×Q8—111no—
361C22×Q8C22×D1111yescharacteristic
362C2×Q16—222no—
363C2×Q16—222no—
364C2×Q16—222no—
365C2×Q16—222no—
366C2×Q16—222no—
367C2×Q16—441no—
368C22×C8—111no—
369C22×C8—111no—
370C22×C8—111no—
371C22×C8—111no—
372C4⋊Q8—222no—
373C4⋊Q8—441no—
374#125—22no—
375#125—41no—
376C4×Q8—22no—
377C4×Q8—41no—
378C4×Q8—222no—
379C4×Q8—441no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—111no—
386C2×C4⋊C4—111no—
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×C4⋊C4C22×D1111yescharacteristic
396C2×C42—21no—
397C2×C42—221no—
398C2×C42C22×D1111yescharacteristic
399C2×C42C22×D1111yescharacteristic
400C2×C42C22×D1111yescharacteristic
401#107—441no—
402#106—222no—
403C4⋊C8—222no—
404#103—114no—
405#103—222no—
406#103—222no—
407#103—222no—
408#103—222no—
409#103—222no—
410#103—222no—
411#103—222no—
412#97—222no—
413#97—222no—
414C4×C8—222no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—221no—
422#95—221no—
423#95—221no—
424#95—221no—
425#95—221no—
426#95—221no—
427#95—221no—
428#95C22⋊D1111yescharacteristic
429#95C22⋊D1111yescharacteristic
430C2×C11#246111yescharacteristic
431C2×C11#317711yescharacteristic
432C2×C11#318111yescharacteristic
433C2×C11#327611yescharacteristic
434C2×C11#327711yescharacteristic
435C2×C11#337411yescharacteristic
436C2×C11#337711yescharacteristic
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—112no—
443C2×Q8—221no—
444C2×Q8—221no—
445C2×Q8—221no—
446C2×Q8—221no—
447C2×Q8—221no—
448C2×Q8—221no—
449C2×Q8—221no—
450C2×Q8—221no—
451C2×Q8—221no—
452C2×Q8—221no—
453C2×Q8—221no—
454C2×Q8#434312yes—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—221no—
460C22×C4—221no—
461C22×C4—221no—
462C22×C4—221no—
463C22×C4C2×C22⋊D1111yescharacteristic
464C22×C4C2×C22⋊D1111yescharacteristic
465C22×C4C2×C22⋊D1111yescharacteristic
466C22×C4C2×C22⋊D1111yescharacteristic
467C22×C4C2×C22⋊D1111yescharacteristic
468C22×C4C2×C22⋊D1111yescharacteristic
469C22×C4C23×D1111yescharacteristic
470Q16—228no—
471Q16—444no—
472C2×C8—112no—
473C2×C8—112no—
474C2×C8—112no—
475C2×C8—221no—
476C2×C8—221no—
477C2×C8—221no—
478C2×C8—221no—
479C2×C8—221no—
480C2×C8—221no—
481C2×C8—221no—
482C2×C8—221no—
483C2×C8—221no—
484C4⋊C4—22no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—41no—
491C4⋊C4—42no—
492C4⋊C4—42no—
493C4⋊C4—42no—
494C4⋊C4—42no—
495C4⋊C4—42no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4—442no—
501C4⋊C4—442no—
502C4⋊C4—442no—
503C4⋊C4—442no—
504C4⋊C4D4×D1112yes—
505C42—21no—
506C42—21no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42—21no—
511C42—42no—
512C42—442no—
513C11#2684711yescharacteristic, complemented, Sylow
514C23C22×C22⋊D1111yescharacteristic
515Q8—22no—
516Q8—22no—
517Q8—41no—
518Q8—41no—
519Q8—222no—
520Q8—222no—
521Q8—441no—
522Q8—441no—
523Q8—441no—
524Q8—441no—
525Q8—441no—
526Q8—441no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—222no—
557C2×C4—441no—
558C2×C4—441no—
559C2×C4—441no—
560C2×C4—441no—
561C2×C4—441no—
562C2×C4—441no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4#6700412yes—
569C2×C4C2×D4×D1111yescharacteristic
570C2×C4#6703711yescharacteristic
571C2×C4C2×#434311yescharacteristic
572C2×C4#6704011yescharacteristic
573C2×C4#41×D1111yescharacteristic
574C2×C4#41×D1111yescharacteristic
575C8—222no—
576C8—222no—
577C8—222no—
578C8—441no—
579C22D4×C22⋊D1111yescharacteristic
580C22#1062334811yescharacteristic
581C22#1062335311yescharacteristic
582C22C2×#6700411yescharacteristic
583C22#1062336311yescharacteristic
584C22#1062336911yescharacteristic
585C22#1062336911yescharacteristic
586C4—22no—
587C4—41no—
588C4—41no—
589C4—42no—
590C4—41no—
591C4—41no—
592C4—42no—
593C4—41no—
594C4—81no—
595C4—81no—
596C4—442no—
597C4—881no—
598C4—881no—
599C4—881no—
600C4#1062315811yescharacteristic
601C4#1062316211yescharacteristic
602C4#1062316811yescharacteristic
603C4#1062317111yescharacteristic
604C2#1307259011yescharacteristic
605C2#1307926911yescharacteristic
606C2#1307932611yescharacteristic
607C2#1308025811yescharacteristic
608C2#1308026911yescharacteristic
609C2#1308141911yescharacteristic
610C2#1308145811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2453C2
socle, prime radicalC23×C11C22×D4
hypercenter#2453D11
hypocenterC11#26847
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2453

Complements

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

NH ≅ G/Ntype
513. C11#26847semidirect

Maximal subgroups

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

subgroupindex
C2×#106226822
C2×#106226432
#130723922
#130699942
#130699512
#130699382
#130697152
#130694762
#130693092
#130693052
#130692912
#130689572
#130688692
#130684852
C11×#24532
#2684711