Finite Group Databasebeta

← #14727416

Subgroups — #14727416

Order 2816.

1056 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078536C211yesmaximal, characteristic, complemented
2C2×#10622657C211yesmaximal, characteristic, complemented
3#13073088C211yesmaximal, characteristic, complemented
4#13067664C214yesmaximal, complemented
5#13067641C214yesmaximal, complemented
6#13067136C211yesmaximal, characteristic, complemented
7#13067107C211yesmaximal, characteristic, complemented
8#13066976C211yesmaximal, characteristic, complemented
9C11×#3536C211yesmaximal, characteristic
10C11×#562—22no—
11C11×#554—21no—
12C11×#548—21no—
13C11×#547—21no—
14C11×#546—22no—
15C11×#546—21no—
16C11×#543C2212yes—
17C11×#542—21no—
18C11×#539—21no—
19C11×#538C2212yes—
20C11×#537—21no—
21C11×#537—21no—
22C11×#525C2211yescharacteristic
23C2×C11×C22⋊Q8C2211yescharacteristic
24C2×C11×#121C2211yescharacteristic
25C2×#66988—22no—
26C22×C4⋊Dic11C2211yescharacteristic
27#10622845—21no—
28C2×#66899—21no—
29#10622834—21no—
30C4×C22⋊Dic11C2211yescharacteristic
31#10622820C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33#10622657—22no—
34#10622657C2212yes—
35#10622657C2214yes—
36#10622656—21no—
37#10622647C2212yes—
38#10622646—21no—
39#10622608—21no—
40#10622589—21no—
41C2×#66871—21no—
42#10622562C2214yes—
43#10622176C2212yes—
44#10622176C2214yes—
45#10622175C2212yes—
46#10622163C2214yes—
47C2×C11×#41—22no—
48C2×C11×#41—21no—
49C2×C11×#41D411yescharacteristic
50C22×Q8×C11D411yescharacteristic
51C22×D4×C11D412yes—
52C22×D4×C11D411yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C23×Dic11—21no—
55C11×C4⋊Q8—21no—
56C11×#126—22no—
57C11×#125—22no—
58C11×#124—21no—
59C11×#124—22no—
60C11×#124—22no—
61C11×#123—22no—
62C11×#123—22no—
63C11×#123—22no—
64C11×#123—21no—
65C11×#123—22no—
66C11×C22⋊Q8—21no—
67C11×C22⋊Q8—22no—
68C11×C22⋊Q8—22no—
69C11×C22⋊Q8—22no—
70C11×C22⋊Q8—21no—
71C11×C22⋊Q8—21no—
72C11×C22⋊Q8—22no—
73C11×C22⋊Q8—22no—
74C11×C22⋊Q8—22no—
75C11×C22⋊Q8D412yes—
76C11×C22⋊Q8D411yescharacteristic
77C11×C22⋊Q8C2312yes—
78C11×C22⋊Q8C2311yescharacteristic
79C11×#121—21no—
80C11×#121—22no—
81C11×#121—22no—
82C11×#121—22no—
83C11×#121—22no—
84C11×#121—22no—
85C11×#121—21no—
86C11×#121—21no—
87C11×#121—21no—
88C11×#121—21no—
89C11×#121D411yescharacteristic
90C11×#121C2311yescharacteristic
91C11×#120—21no—
92C11×#120—22no—
93C4×Q8×C11—21no—
94C4×D4×C11—22no—
95C4×D4×C11—21no—
96C4×D4×C11—21no—
97C4×D4×C11—21no—
98C4×D4×C11—22no—
99C11×#117D411yescharacteristic
100C2×C11×C4⋊C4—21no—
101C2×C11×C4⋊C4—21no—
102C2×C11×C4⋊C4D411yescharacteristic
103C2×C11×C4⋊C4D411yescharacteristic
104C2×C11×C22⋊C4—21no—
105C2×C11×C22⋊C4—22no—
106C2×C11×C22⋊C4C2312yes—
107C2×C22⋊Dic11—21no—
108C2×C22⋊Dic11—24no—
109#66988—48no—
110C2×C4⋊Dic11—21no—
111C2×C4⋊Dic11—21no—
112C2×C4⋊Dic11—21no—
113C2×C4⋊Dic11—21no—
114C2×C4⋊Dic11—21no—
115C2×C4⋊Dic11C2312yes—
116C2×Dic11⋊C4—24no—
117C2×C4×Dic11—21no—
118C2×#4318—21no—
119C22×C11⋊C8—21no—
120#66899—24no—
121#66899—22no—
122#66896—22no—
123C11⋊#95C2312yes—
124C22⋊(C11⋊C8)—21no—
125C22⋊(C11⋊C8)—21no—
126C22⋊(C11⋊C8)C2312yes—
127C22⋊(C11⋊C8)C2312yes—
128#66872—22no—
129#66871—24no—
130#66871—22no—
131#18267—111nomaximal, Sylow
132C24×C11C2×D411yescharacteristic
133C24×C11C2×D412yes—
134C11×#41—42no—
135C11×#41—84no—
136C11×#41—82no—
137C2×Q8×C11—22no—
138C2×Q8×C11—21no—
139C2×Q8×C11—42no—
140C2×Q8×C11C2×D411yescharacteristic
141C2×Q8×C11C2×D412yes—
142C2×D4×C11—21no—
143C2×D4×C11—22no—
144C2×D4×C11—21no—
145C2×D4×C11—22no—
146C2×D4×C11—22no—
147C2×D4×C11—21no—
148C2×D4×C11—22no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—42no—
152C2×D4×C11—44no—
153C2×D4×C11C2×D411yescharacteristic
154C22×C4×C11—21no—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—42no—
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D412yes—
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2411yescharacteristic
168C22×Dic11—22no—
169C22×Dic11—22no—
170C22×Dic11—44no—
171C22×Dic11—41no—
172C22×Dic11—41no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4C2×D412yes—
185C11×C4⋊C4C2×D411yescharacteristic
186C11×C4⋊C4C2×D411yescharacteristic
187C11×C22⋊C4—22no—
188C11×C22⋊C4—22no—
189C11×C22⋊C4—22no—
190C11×C22⋊C4—22no—
191C11×C22⋊C4—22no—
192C11×C22⋊C4—22no—
193C11×C22⋊C4—21no—
194C11×C22⋊C4—21no—
195C11×C22⋊C4—22no—
196C11×C22⋊C4—21no—
197C11×C22⋊C4—21no—
198C11×C22⋊C4—22no—
199C11×C22⋊C4—22no—
200C11×C22⋊C4—21no—
201C42×C11—22no—
202C42×C11—21no—
203C22⋊Dic11—24no—
204C22⋊Dic11—48no—
205C4⋊Dic11—22no—
206C4⋊Dic11—22no—
207C4⋊Dic11—41no—
208C4⋊Dic11—41no—
209Dic11⋊C4—48no—
210C4×Dic11—42no—
211#4318—42no—
212C2×C11⋊C8—22no—
213C2×C11⋊C8—22no—
214C2×C11⋊C8—42no—
215#3536D1111yescharacteristic
216#3092—111no—
217C2×#484—111no—
218#2501—111no—
219#1618—114no—
220#1614—114no—
221#1508—111no—
222#1501—111no—
223#1471—111no—
224C23×C11—22no—
225C23×C11—22no—
226C23×C11—22no—
227C23×C11—21no—
228C23×C11—24no—
229C23×C11—41no—
230C23×C11—42no—
231C23×C11—42no—
232C23×C11#12011yescharacteristic
233C23×C11#12011yescharacteristic
234C23×C11C22×D411yescharacteristic
235Q8×C11—42no—
236Q8×C11—41no—
237Q8×C11—42no—
238Q8×C11—82no—
239D4×C11—41no—
240D4×C11—42no—
241D4×C11—44no—
242D4×C11—42no—
243D4×C11—42no—
244D4×C11—81no—
245D4×C11—82no—
246D4×C11—81no—
247D4×C11—82no—
248D4×C11—82no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—21no—
253C2×C4×C11—22no—
254C2×C4×C11—21no—
255C2×C4×C11—22no—
256C2×C4×C11—21no—
257C2×C4×C11—22no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—42no—
262C2×C4×C11—42no—
263C2×C4×C11—42no—
264C2×C4×C11—81no—
265C2×C4×C11—82no—
266C2×C4×C11—82no—
267C2×C4×C11—82no—
268C2×C4×C11#12011yescharacteristic
269C2×C4×C11#12011yescharacteristic
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11C22×D411yescharacteristic
272C2×Dic11—24no—
273C2×Dic11—42no—
274C2×Dic11—42no—
275C2×Dic11—44no—
276C2×Dic11—42no—
277C2×Dic11—82no—
278C2×Dic11—82no—
279C11⋊C8—42no—
280C11⋊C8—42no—
281#562—22no—
282#554—21no—
283#548—21no—
284#547—21no—
285#546—22no—
286#546—21no—
287#543C2×D1112yes—
288#542—21no—
289#539—21no—
290#538C2×D1112yes—
291#537—21no—
292#537—21no—
293#525C2×D1111yescharacteristic
294C2×#123—222no—
295C2×C22⋊Q8C2×D1111yescharacteristic
296C2×#121C2×D1111yescharacteristic
297C22×C4⋊C4—111no—
298#484—114no—
299#484—112no—
300#484—222no—
301#483—221no—
302#481—112no—
303#480—221no—
304#428—221no—
305C2×#107—221no—
306#417—221no—
307C2×#103—221no—
308#407—111no—
309C2×C22⋊C8—111no—
310#399—114no—
311#390—221no—
312#384—221no—
313C4×C22⋊C4—111no—
314#328—112no—
315#328—114no—
316#327—112no—
317#323—114no—
318C22×C11—21no—
319C22×C11—21no—
320C22×C11—21no—
321C22×C11—21no—
322C22×C11—21no—
323C22×C11—21no—
324C22×C11—21no—
325C22×C11—44no—
326C22×C11—41no—
327C22×C11—42no—
328C22×C11—41no—
329C22×C11—42no—
330C22×C11—41no—
331C22×C11—42no—
332C22×C11—84no—
333C22×C11#45312yes—
334C22×C11C2×#12011yescharacteristic
335C22×C11#57812yes—
336C4×C11—21no—
337C4×C11—21no—
338C4×C11—21no—
339C4×C11—41no—
340C4×C11—42no—
341C4×C11—42no—
342C4×C11—41no—
343C4×C11—41no—
344C4×C11—42no—
345C4×C11#45812yes—
346Dic11—44no—
347Dic11—82no—
348C2×#41—22no—
349C2×#41—21no—
350C2×#41C22⋊D1111yescharacteristic
351C22×Q8C22⋊D1111yescharacteristic
352C22×D4C22⋊D1112yes—
353C22×D4C22⋊D1111yescharacteristic
354C23×C4—221no—
355C23×C4C22×D1111yescharacteristic
356C2×M16—221no—
357C22×C8—221no—
358C4⋊Q8—21no—
359#126—22no—
360#125—22no—
361#124—21no—
362#124—22no—
363#124—22no—
364#123—22no—
365#123—22no—
366#123—22no—
367#123—21no—
368#123—22no—
369#123—448no—
370C22⋊Q8—21no—
371C22⋊Q8—22no—
372C22⋊Q8—22no—
373C22⋊Q8—22no—
374C22⋊Q8—21no—
375C22⋊Q8—21no—
376C22⋊Q8—22no—
377C22⋊Q8—22no—
378C22⋊Q8—22no—
379C22⋊Q8C22⋊D1112yes—
380C22⋊Q8C22⋊D1111yescharacteristic
381C22⋊Q8C22×D1112yes—
382C22⋊Q8C22×D1111yescharacteristic
383#121—21no—
384#121—22no—
385#121—22no—
386#121—22no—
387#121—22no—
388#121—22no—
389#121—21no—
390#121—21no—
391#121—21no—
392#121—21no—
393#121C22⋊D1111yescharacteristic
394#121C22×D1111yescharacteristic
395#120—21no—
396#120—22no—
397C4×Q8—21no—
398C4×D4—22no—
399C4×D4—21no—
400C4×D4—21no—
401C4×D4—21no—
402C4×D4—22no—
403#117C22⋊D1111yescharacteristic
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—112no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4—224no—
413C2×C4⋊C4C22⋊D1111yescharacteristic
414C2×C4⋊C4C22⋊D1111yescharacteristic
415C2×C22⋊C4—21no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—221no—
418C2×C22⋊C4—224no—
419C2×C22⋊C4C22×D1112yes—
420C2×C42—221no—
421#107—224no—
422#107—222no—
423#106—222no—
424#103—224no—
425#103—222no—
426#102—222no—
427C22⋊C8—112no—
428C22⋊C8—112no—
429C22⋊C8—221no—
430C22⋊C8—221no—
431#95—112no—
432C2×C11—22no—
433C2×C11—22no—
434C2×C11—41no—
435C2×C11—81no—
436C2×C11—82no—
437C2×C11#301111yescharacteristic
438C2×C11C2×#45311yescharacteristic
439C2×C11C2×#45811yescharacteristic
440C24C2×C22⋊D1111yescharacteristic
441C24C2×C22⋊D1112yes—
442#41—42no—
443#41—84no—
444#41—82no—
445C2×Q8—22no—
446C2×Q8—21no—
447C2×Q8—42no—
448C2×Q8C2×C22⋊D1111yescharacteristic
449C2×Q8C2×C22⋊D1112yes—
450C2×D4—21no—
451C2×D4—22no—
452C2×D4—21no—
453C2×D4—22no—
454C2×D4—22no—
455C2×D4—21no—
456C2×D4—22no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—42no—
460C2×D4—44no—
461C2×D4C2×C22⋊D1111yescharacteristic
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—42no—
469C22×C4—222no—
470C22×C4—222no—
471C22×C4—444no—
472C22×C4—441no—
473C22×C4—441no—
474C22×C4C2×C22⋊D1111yescharacteristic
475C22×C4C2×C22⋊D1111yescharacteristic
476C22×C4C2×C22⋊D1111yescharacteristic
477C22×C4C2×C22⋊D1112yes—
478C22×C4C2×C22⋊D1111yescharacteristic
479C22×C4C2×C22⋊D1111yescharacteristic
480C22×C4C23×D1111yescharacteristic
481M16—442no—
482C2×C8—222no—
483C2×C8—222no—
484C2×C8—442no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—22no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—22no—
495C4⋊C4—21no—
496C4⋊C4—222no—
497C4⋊C4—222no—
498C4⋊C4—448no—
499C4⋊C4—441no—
500C4⋊C4—441no—
501C4⋊C4C2×C22⋊D1111yescharacteristic
502C4⋊C4C2×C22⋊D1112yes—
503C4⋊C4C2×C22⋊D1111yescharacteristic
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—22no—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—22no—
510C22⋊C4—21no—
511C22⋊C4—21no—
512C22⋊C4—22no—
513C22⋊C4—21no—
514C22⋊C4—21no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—21no—
518C22⋊C4—224no—
519C22⋊C4—448no—
520C42—22no—
521C42—21no—
522C42—442no—
523C11#1826711yescharacteristic, complemented, Sylow
524C23—22no—
525C23—22no—
526C23—22no—
527C23—21no—
528C23—24no—
529C23—41no—
530C23—42no—
531C23—42no—
532C23#6700611yescharacteristic
533C23#6700611yescharacteristic
534C23C22×C22⋊D1111yescharacteristic
535Q8—42no—
536Q8—41no—
537Q8—42no—
538Q8—82no—
539D4—41no—
540D4—44no—
541D4—42no—
542D4—42no—
543D4—42no—
544D4—81no—
545D4—82no—
546D4—81no—
547D4—82no—
548D4—82no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—21no—
553C2×C4—22no—
554C2×C4—21no—
555C2×C4—22no—
556C2×C4—21no—
557C2×C4—22no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—81no—
565C2×C4—82no—
566C2×C4—82no—
567C2×C4—82no—
568C2×C4—224no—
569C2×C4—442no—
570C2×C4—442no—
571C2×C4—444no—
572C2×C4—442no—
573C2×C4—882no—
574C2×C4—882no—
575C2×C4#6700611yescharacteristic
576C2×C4#6700611yescharacteristic
577C2×C4C22×C22⋊D1111yescharacteristic
578C2×C4C22×C22⋊D1111yescharacteristic
579C8—442no—
580C8—442no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—21no—
585C22—21no—
586C22—21no—
587C22—21no—
588C22—44no—
589C22—41no—
590C22—42no—
591C22—41no—
592C22—42no—
593C22—41no—
594C22—42no—
595C22—84no—
596C22#1062285412yes—
597C22#1062336912yes—
598C22C2×#6700611yescharacteristic
599C4—21no—
600C4—21no—
601C4—21no—
602C4—41no—
603C4—42no—
604C4—42no—
605C4—41no—
606C4—41no—
607C4—42no—
608C4—444no—
609C4—882no—
610C4#1062285612yes—
611C2—22no—
612C2—22no—
613C2—41no—
614C2—82no—
615C2—81no—
616C2#1307791111yescharacteristic
617C2C2×#1062285411yescharacteristic
618C2C2×#1062285611yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#3536C2
socleC22×C11C2×#120
hypercenter#3536D11
hypocenterC11#18267
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3536

Complements

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

NH ≅ G/Ntype
1. #13078536C2semidirect
2. C2×#10622657C2semidirect
3. #13073088C2semidirect
4. #13067664C2semidirect
5. #13067641C2semidirect
6. #13067136C2semidirect
7. #13067107C2semidirect
8. #13066976C2semidirect
523. C11#18267semidirect

Maximal subgroups

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

subgroupindex
#130785362
C2×#106226572
#130730882
#130676642
#130676412
#130671362
#130671072
#130669762
C11×#35362
#1826711