Finite Group Databasebeta

← #14730430

Subgroups — #14730430

Order 2816.

866 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
1#13079834C211yesmaximal, characteristic
2#13078998C211yesmaximal, characteristic, complemented
3C2×#10622634C211yesmaximal, characteristic, complemented
4#13067788C212yesmaximal, complemented
5#13067781C212yesmaximal, complemented
6#13067774C212yesmaximal, complemented
7#13067774C212yesmaximal, complemented
8#13067316C211yesmaximal, characteristic, complemented
9#13067063C211yesmaximal, characteristic, complemented
10#13067029C211yesmaximal, characteristic
11C11×#3523C211yesmaximal, characteristic
12C11×#557—21no—
13C11×#557C2211yescharacteristic
14C11×#557C2211yescharacteristic
15C11×#556—21no—
16C11×#556C2211yescharacteristic
17C11×#552—22no—
18C11×#552—21no—
19D4×Q8×C11—21no—
20D4×Q8×C11C2211yescharacteristic
21C11×#541—22no—
22C11×#541—21no—
23C11×#533—21no—
24C11×#533C2211yescharacteristic
25C11×#529—21no—
26C11×#529C2211yescharacteristic
27C11×#519—21no—
28C2×C4×Q8×C11C2211yescharacteristic
29C2×#66922C2211yescharacteristic
30C2×#66899—21no—
31#10622706C2212yes—
32#10622706C2212yes—
33#10622682—22no—
34#10622678—21no—
35#10622668—21no—
36#10622656—21no—
37#10622646—21no—
38#10622634—21no—
39#10622634—21no—
40#10622634C2212yes—
41#10622634C2212yes—
42#10622634C2212yes—
43#10622621C2212yes—
44#10622617—22no—
45C2×#66871—21no—
46#10622539C2211yescharacteristic
47C2×C4⋊(C11⋊C8)C2211yescharacteristic
48C4×#4318C2211yescharacteristic
49#10622185C2212yes—
50#10622185C2212yes—
51Q8⋊(C11⋊C8)C2212yes—
52Q8⋊(C11⋊C8)C2212yes—
53Q8⋊(C11⋊C8)C2212yes—
54D4⋊(C11⋊C8)C2212yes—
55C22×Q8×C11—21no—
56C22×Q8×C11D411yescharacteristic
57C22×Dic22—21no—
58C11×C4⋊Q8—22no—
59C11×C4⋊Q8—21no—
60C11×C4⋊Q8—21no—
61C11×C4⋊Q8—21no—
62C11×C4⋊Q8C2311yescharacteristic
63C11×C4⋊Q8C2311yescharacteristic
64C11×#126—22no—
65C11×#126—22no—
66C11×#126—22no—
67C11×#126—22no—
68C11×#126—21no—
69C11×#125—22no—
70C11×#125—22no—
71C11×#125—22no—
72C11×#125—21no—
73C11×#125—22no—
74C11×#125—22no—
75C11×#125—21no—
76C11×#125D411yescharacteristic
77C11×#125D412yes—
78C11×#124—21no—
79C11×#124D411yescharacteristic
80C11×#123—22no—
81C11×#123—21no—
82C11×C22⋊Q8—22no—
83C11×C22⋊Q8—22no—
84C11×C22⋊Q8—21no—
85C11×C22⋊Q8—21no—
86C11×C22⋊Q8—21no—
87C11×C22⋊Q8—21no—
88C11×C22⋊Q8—22no—
89C11×C22⋊Q8D411yescharacteristic
90C11×#121D411yescharacteristic
91C4×Q8×C11—22no—
92C4×Q8×C11—22no—
93C4×Q8×C11—21no—
94C4×Q8×C11—21no—
95C4×Q8×C11—21no—
96C4×Q8×C11—21no—
97C4×Q8×C11—21no—
98C4×Q8×C11—21no—
99C4×Q8×C11—21no—
100C4×Q8×C11—21no—
101C4×Q8×C11—21no—
102C4×Q8×C11D411yescharacteristic
103C4×Q8×C11D411yescharacteristic
104C4×Q8×C11C2311yescharacteristic
105C4×Q8×C11C2311yescharacteristic
106C4×Q8×C11C2311yescharacteristic
107C4×D4×C11—22no—
108C4×D4×C11—21no—
109C4×D4×C11—21no—
110C4×D4×C11C2311yescharacteristic
111C11×#117—22no—
112C11×#117—22no—
113C11×#117—22no—
114C11×#117—21no—
115C11×#117—21no—
116C11×#117D412yes—
117C2×C11×C4⋊C4—21no—
118C2×C11×C4⋊C4D411yescharacteristic
119C2×C42×C11—21no—
120C2×C42×C11C2311yescharacteristic
121C2×C4⋊Dic11—21no—
122C2×C4⋊Dic11—21no—
123C2×#4318—21no—
124C22×C11⋊C8—21no—
125#66922—21no—
126#66922—21no—
127#66922—21no—
128#66922C2312yes—
129#66899—22no—
130#66899—22no—
131#66899—22no—
132#66896—22no—
133C22⋊(C11⋊C8)—21no—
134#66874—24no—
135#66874—24no—
136#66872—22no—
137#66871—22no—
138#66871—22no—
139#66871—22no—
140C4⋊(C11⋊C8)—21no—
141C4⋊(C11⋊C8)C2312yes—
142C4⋊(C11⋊C8)C2312yes—
143#66867—21no—
144#66867—21no—
145C4×C11⋊C8C2312yes—
146#18581—111nomaximal, Sylow
147C2×Q8×C11—22no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11—22no—
152C2×Q8×C11—41no—
153C2×Q8×C11—42no—
154C2×Q8×C11—42no—
155C2×Q8×C11C2×D411yescharacteristic
156C2×Q8×C11C2×D411yescharacteristic
157C2×Q8×C11C2×D411yescharacteristic
158C2×D4×C11—21no—
159C2×D4×C11C2×D411yescharacteristic
160C22×C4×C11—22no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D411yescharacteristic
167C22×Dic11—41no—
168C2×Dic22—22no—
169C2×Dic22—44no—
170C2×Dic22—41no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—22no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4C2×D411yescharacteristic
193C11×C4⋊C4C2×D411yescharacteristic
194C11×C4⋊C4C2×D411yescharacteristic
195C11×C4⋊C4C2×D411yescharacteristic
196C11×C4⋊C4C2×D412yes—
197C11×C4⋊C4C2×D412yes—
198C11×C22⋊C4—22no—
199C11×C22⋊C4—22no—
200C11×C22⋊C4—22no—
201C11×C22⋊C4—21no—
202C11×C22⋊C4—22no—
203C11×C22⋊C4—21no—
204C11×C22⋊C4—21no—
205C11×C22⋊C4—21no—
206C11×C22⋊C4—21no—
207C42×C11—22no—
208C42×C11—22no—
209C42×C11—22no—
210C42×C11—21no—
211C42×C11—21no—
212C42×C11—22no—
213C42×C11—21no—
214C42×C11—21no—
215C42×C11—21no—
216C42×C11C2×D411yescharacteristic
217C42×C11C2×D411yescharacteristic
218C42×C11C2×D411yescharacteristic
219C42×C11C2411yescharacteristic
220C4⋊Dic11—22no—
221C4⋊Dic11—22no—
222C4⋊Dic11—41no—
223C4⋊Dic11—41no—
224#4318—42no—
225C2×C11⋊C8—22no—
226C2×C11⋊C8—22no—
227C2×C11⋊C8—22no—
228C2×C11⋊C8—42no—
229#3523D1111yescharacteristic
230#3238—111no—
231#3139—111no—
232C2×#477—111no—
233#1638—112no—
234#1637—112no—
235#1636—112no—
236#1636—112no—
237#1552—111no—
238#1491—111no—
239#1483—111no—
240C23×C11—21no—
241C23×C11#12011yescharacteristic
242Q8×C11—21no—
243Q8×C11—21no—
244Q8×C11—21no—
245Q8×C11—22no—
246Q8×C11—42no—
247Q8×C11—44no—
248Q8×C11—41no—
249Q8×C11—41no—
250Q8×C11—42no—
251Q8×C11#13712yes—
252D4×C11—22no—
253D4×C11—42no—
254C2×C4×C11—21no—
255C2×C4×C11—22no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—22no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—22no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—22no—
267C2×C4×C11—42no—
268C2×C4×C11—44no—
269C2×C4×C11—42no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11#12011yescharacteristic
273C2×C4×C11#12011yescharacteristic
274C2×C4×C11#12011yescharacteristic
275C2×C4×C11C22×D411yescharacteristic
276C2×C4×C11C22×D411yescharacteristic
277C2×C4×C11C22×D411yescharacteristic
278C2×Dic11—42no—
279C2×Dic11—82no—
280Dic22—44no—
281Dic22—82no—
282C11⋊C8—42no—
283C11⋊C8—42no—
284C11⋊C8—42no—
285#557—21no—
286#557C2×D1111yescharacteristic
287#557C2×D1111yescharacteristic
288#556—21no—
289#556C2×D1111yescharacteristic
290#552—22no—
291#552—21no—
292D4×Q8—21no—
293D4×Q8C2×D1111yescharacteristic
294#541—22no—
295#541—21no—
296#533—21no—
297#533C2×D1111yescharacteristic
298C2×C4⋊Q8—111no—
299#529—21no—
300#529C2×D1111yescharacteristic
301#519—21no—
302C2×C4×Q8C2×D1111yescharacteristic
303#501—221no—
304#491—222no—
305#489—221no—
306#487—112no—
307#487—112no—
308#483—221no—
309#480—221no—
310#477—112no—
311#477—112no—
312#477—112no—
313#477—221no—
314#477—221no—
315#476—112no—
316#432—111no—
317C2×#107—221no—
318C2×C4⋊C8—111no—
319#419—222no—
320C2×#103—221no—
321C4×M16—111no—
322#332—112no—
323#332—112no—
324Q8⋊C8—112no—
325Q8⋊C8—112no—
326Q8⋊C8—112no—
327D4⋊C8—112no—
328C22×C11—21no—
329C22×C11—21no—
330C22×C11—41no—
331C22×C11—41no—
332C22×C11—41no—
333C22×C11#45412yes—
334C22×C11C2×#12011yescharacteristic
335C4×C11—21no—
336C4×C11—22no—
337C4×C11—21no—
338C4×C11—21no—
339C4×C11—21no—
340C4×C11—41no—
341C4×C11—42no—
342C4×C11—41no—
343C4×C11—41no—
344C4×C11—42no—
345C4×C11—41no—
346C4×C11—41no—
347C4×C11—41no—
348C4×C11C2×#13711yescharacteristic
349C4×C11#57511yescharacteristic
350C4×C11#57812yes—
351Dic11—82no—
352C22×Q8—21no—
353C22×Q8—221no—
354C22×Q8C22⋊D1111yescharacteristic
355C2×M16—221no—
356C22×C8—221no—
357C4⋊Q8—22no—
358C4⋊Q8—21no—
359C4⋊Q8—21no—
360C4⋊Q8—21no—
361C4⋊Q8—112no—
362C4⋊Q8—221no—
363C4⋊Q8—221no—
364C4⋊Q8—221no—
365C4⋊Q8C22×D1111yescharacteristic
366C4⋊Q8C22×D1111yescharacteristic
367#126—22no—
368#126—22no—
369#126—22no—
370#126—22no—
371#126—21no—
372#125—22no—
373#125—22no—
374#125—22no—
375#125—21no—
376#125—22no—
377#125—22no—
378#125—21no—
379#125C22⋊D1111yescharacteristic
380#125C22⋊D1112yes—
381#124—21no—
382#124C22⋊D1111yescharacteristic
383#123—22no—
384#123—21no—
385C22⋊Q8—22no—
386C22⋊Q8—22no—
387C22⋊Q8—21no—
388C22⋊Q8—21no—
389C22⋊Q8—21no—
390C22⋊Q8—21no—
391C22⋊Q8—22no—
392C22⋊Q8C22⋊D1111yescharacteristic
393#121C22⋊D1111yescharacteristic
394C4×Q8—22no—
395C4×Q8—22no—
396C4×Q8—21no—
397C4×Q8—21no—
398C4×Q8—21no—
399C4×Q8—21no—
400C4×Q8—21no—
401C4×Q8—21no—
402C4×Q8—21no—
403C4×Q8—21no—
404C4×Q8—21no—
405C4×Q8C22⋊D1111yescharacteristic
406C4×Q8C22⋊D1111yescharacteristic
407C4×Q8C22×D1111yescharacteristic
408C4×Q8C22×D1111yescharacteristic
409C4×Q8C22×D1111yescharacteristic
410C4×D4—22no—
411C4×D4—21no—
412C4×D4—21no—
413C4×D4C22×D1111yescharacteristic
414#117—22no—
415#117—22no—
416#117—22no—
417#117—21no—
418#117—21no—
419#117C22⋊D1112yes—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—221no—
422C2×C4⋊C4—221no—
423C2×C4⋊C4C22⋊D1111yescharacteristic
424C2×C42—21no—
425C2×C42C22×D1111yescharacteristic
426#107—222no—
427#107—222no—
428#107—222no—
429#106—222no—
430C4⋊C8—112no—
431C4⋊C8—112no—
432C4⋊C8—221no—
433#103—222no—
434#103—222no—
435#103—222no—
436#103—224no—
437#103—224no—
438#102—222no—
439C22⋊C8—221no—
440#97—221no—
441#97—221no—
442C4×C8—112no—
443C2×C11—22no—
444C2×C11—81no—
445C2×C11#300711yescharacteristic
446C2×C11#301111yescharacteristic
447C2×C11C2×#45411yescharacteristic
448C2×Q8—22no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—22no—
453C2×Q8—41no—
454C2×Q8—42no—
455C2×Q8—42no—
456C2×Q8—222no—
457C2×Q8—444no—
458C2×Q8—441no—
459C2×Q8C2×C22⋊D1111yescharacteristic
460C2×Q8C2×C22⋊D1111yescharacteristic
461C2×Q8C2×C22⋊D1111yescharacteristic
462C2×D4—21no—
463C2×D4C2×C22⋊D1111yescharacteristic
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—441no—
469C22×C4C2×C22⋊D1111yescharacteristic
470C22×C4C2×C22⋊D1111yescharacteristic
471C22×C4C2×C22⋊D1111yescharacteristic
472M16—442no—
473C2×C8—222no—
474C2×C8—222no—
475C2×C8—222no—
476C2×C8—442no—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—22no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—22no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—222no—
499C4⋊C4—222no—
500C4⋊C4—441no—
501C4⋊C4—441no—
502C4⋊C4C2×C22⋊D1112yes—
503C4⋊C4C2×C22⋊D1112yes—
504C4⋊C4C2×C22⋊D1111yescharacteristic
505C4⋊C4C2×C22⋊D1111yescharacteristic
506C4⋊C4C2×C22⋊D1111yescharacteristic
507C4⋊C4C2×C22⋊D1111yescharacteristic
508C22⋊C4—22no—
509C22⋊C4—22no—
510C22⋊C4—22no—
511C22⋊C4—21no—
512C22⋊C4—22no—
513C22⋊C4—21no—
514C22⋊C4—21no—
515C22⋊C4—21no—
516C22⋊C4—21no—
517C42—22no—
518C42—22no—
519C42—22no—
520C42—21no—
521C42—21no—
522C42—22no—
523C42—21no—
524C42—21no—
525C42—21no—
526C42C2×C22⋊D1111yescharacteristic
527C42C2×C22⋊D1111yescharacteristic
528C42C2×C22⋊D1111yescharacteristic
529C42C23×D1111yescharacteristic
530C11#1858111yescharacteristic, complemented, Sylow
531C23—21no—
532C23#6700611yescharacteristic
533Q8—21no—
534Q8—21no—
535Q8—21no—
536Q8—22no—
537Q8—42no—
538Q8—44no—
539Q8—41no—
540Q8—41no—
541Q8—42no—
542Q8—444no—
543Q8—882no—
544Q8#6700412yes—
545D4—22no—
546D4—42no—
547C2×C4—22no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—22no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—22no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—22no—
560C2×C4—42no—
561C2×C4—44no—
562C2×C4—42no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—442no—
566C2×C4—882no—
567C2×C4#6700611yescharacteristic
568C2×C4#6700611yescharacteristic
569C2×C4#6700611yescharacteristic
570C2×C4C22×C22⋊D1111yescharacteristic
571C2×C4C22×C22⋊D1111yescharacteristic
572C2×C4C22×C22⋊D1111yescharacteristic
573C8—442no—
574C8—442no—
575C8—442no—
576C22—21no—
577C22—21no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22#1062285812yes—
582C22C2×#6700611yescharacteristic
583C4—21no—
584C4—22no—
585C4—21no—
586C4—21no—
587C4—21no—
588C4—41no—
589C4—42no—
590C4—41no—
591C4—41no—
592C4—42no—
593C4—41no—
594C4—41no—
595C4—41no—
596C4—882no—
597C4#1062335311yescharacteristic
598C4C2×#6700411yescharacteristic
599C4#1062336912yes—
600C2—22no—
601C2—81no—
602C2#1307787611yescharacteristic
603C2#1307791111yescharacteristic
604C2C2×#1062285811yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3523C2
socleC22×C11C2×#120
prime radicalC11×#121D4
hypercenter#3523D11
hypocenterC11#18581
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3523

Complements

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

NH ≅ G/Ntype
2. #13078998C2semidirect
3. C2×#10622634C2semidirect
4. #13067788C2semidirect
5. #13067781C2semidirect
6. #13067774C2semidirect
7. #13067774C2semidirect
8. #13067316C2semidirect
9. #13067063C2semidirect
530. C11#18581semidirect

Maximal subgroups

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

subgroupindex
#130798342
#130789982
C2×#106226342
#130677882
#130677812
#130677742
#130673162
#130670632
#130670292
C11×#35232
#1858111