Finite Group Databasebeta

← #14727434

Subgroups — #14727434

Order 2816.

924 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078536C211yesmaximal, characteristic
2C2×#10622657C211yesmaximal, characteristic, complemented
3#13073102C211yesmaximal, characteristic, complemented
4#13067658C214yesmaximal, complemented
5#13067647C214yesmaximal, complemented
6#13067136C211yesmaximal, characteristic, complemented
7#13067107C211yesmaximal, characteristic
8#13066980C211yesmaximal, characteristic, complemented
9C11×#3538C211yesmaximal, characteristic
10C11×#563—22no—
11C11×#552—21no—
12C11×#552—21no—
13C11×#551—22no—
14D4×Q8×C11—21no—
15D4×Q8×C11—21no—
16C11×#544—21no—
17C11×#544C2212yes—
18C11×#541—21no—
19C11×#539—21no—
20C11×#539C2212yes—
21C11×#536—21no—
22C11×#525C2211yescharacteristic
23C2×C11×C22⋊Q8C2211yescharacteristic
24C2×C11×C22⋊Q8C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26#10622845—21no—
27#10622843—21no—
28C2×#66899—21no—
29C4×C22⋊Dic11C2211yescharacteristic
30#10622820C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32#10622657—22no—
33#10622657C2212yes—
34#10622657C2214yes—
35#10622656—21no—
36#10622647C2212yes—
37#10622646—21no—
38#10622608—21no—
39#10622599C2214yes—
40#10622590—21no—
41C2×#66871—21no—
42#10622556—22no—
43#10622176C2212yes—
44#10622176C2214yes—
45#10622175C2212yes—
46#10622166C2214yes—
47C2×C11×#41D411yescharacteristic
48C22×Q8×C11—21no—
49C22×Q8×C11D411yescharacteristic
50C22×Q8×C11D411yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C23×Dic11—21no—
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8—22no—
55C11×C4⋊Q8—22no—
56C11×C4⋊Q8—22no—
57C11×#126—22no—
58C11×#126—22no—
59C11×#126—22no—
60C11×#126—22no—
61C11×#125—21no—
62C11×#125—22no—
63C11×#125—22no—
64C11×#125—22no—
65C11×#125—22no—
66C11×#124—22no—
67C11×#123—22no—
68C11×#123—22no—
69C11×#123—22no—
70C11×#123—21no—
71C11×#123—22no—
72C11×C22⋊Q8—21no—
73C11×C22⋊Q8—21no—
74C11×C22⋊Q8—22no—
75C11×C22⋊Q8—22no—
76C11×C22⋊Q8—22no—
77C11×C22⋊Q8—21no—
78C11×C22⋊Q8—21no—
79C11×C22⋊Q8—21no—
80C11×C22⋊Q8—21no—
81C11×C22⋊Q8—21no—
82C11×C22⋊Q8—21no—
83C11×C22⋊Q8—22no—
84C11×C22⋊Q8D412yes—
85C11×C22⋊Q8D411yescharacteristic
86C11×C22⋊Q8C2312yes—
87C11×C22⋊Q8C2311yescharacteristic
88C11×#121D411yescharacteristic
89C11×#121C2311yescharacteristic
90C11×#120—21no—
91C4×Q8×C11—21no—
92C4×Q8×C11—21no—
93C4×D4×C11—22no—
94C4×D4×C11—21no—
95C4×D4×C11—21no—
96C4×D4×C11—22no—
97C11×#117—21no—
98C11×#117—22no—
99C11×#117—22no—
100C11×#117D411yescharacteristic
101C2×C11×C4⋊C4—21no—
102C2×C11×C4⋊C4D411yescharacteristic
103C2×C11×C4⋊C4D411yescharacteristic
104C2×C11×C4⋊C4C2312yes—
105C2×C11×C22⋊C4—21no—
106C2×C11×C22⋊C4D412yes—
107C2×C22⋊Dic11—21no—
108C2×C4⋊Dic11—21no—
109C2×C4⋊Dic11—21no—
110C2×C4⋊Dic11—21no—
111C2×C4⋊Dic11—21no—
112C2×C4⋊Dic11—21no—
113C2×C4⋊Dic11C2312yes—
114C2×C4×Dic11—21no—
115C2×#4318—21no—
116C22×C11⋊C8—21no—
117#66899—24no—
118#66899—22no—
119#66896—22no—
120C11⋊#95—24no—
121C11⋊#95—24no—
122C11⋊#95C2312yes—
123C22⋊(C11⋊C8)—21no—
124C22⋊(C11⋊C8)—21no—
125C22⋊(C11⋊C8)C2312yes—
126C22⋊(C11⋊C8)C2312yes—
127#66872—22no—
128#66871—24no—
129#66871—22no—
130#18269—111nomaximal, Sylow
131C24×C11C2×D411yescharacteristic
132C11×#41—42no—
133C2×Q8×C11—22no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—42no—
138C2×Q8×C11—42no—
139C2×Q8×C11—82no—
140C2×Q8×C11C2×D412yes—
141C2×Q8×C11C2×D411yescharacteristic
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11C2×D411yescharacteristic
146C22×C4×C11—21no—
147C22×C4×C11—22no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—42no—
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D412yes—
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2411yescharacteristic
159C22×Dic11—22no—
160C22×Dic11—22no—
161C22×Dic11—44no—
162C22×Dic11—41no—
163C22×Dic11—41no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4C2×D412yes—
182C11×C4⋊C4C2×D411yescharacteristic
183C11×C4⋊C4C2×D411yescharacteristic
184C11×C22⋊C4—22no—
185C11×C22⋊C4—22no—
186C11×C22⋊C4—22no—
187C11×C22⋊C4—22no—
188C11×C22⋊C4—22no—
189C11×C22⋊C4—22no—
190C11×C22⋊C4—21no—
191C11×C22⋊C4—21no—
192C11×C22⋊C4—22no—
193C11×C22⋊C4—21no—
194C11×C22⋊C4—21no—
195C11×C22⋊C4—21no—
196C42×C11—22no—
197C42×C11—22no—
198C42×C11—22no—
199C42×C11—21no—
200C22⋊Dic11—42no—
201C4⋊Dic11—22no—
202C4⋊Dic11—22no—
203C4⋊Dic11—41no—
204C4⋊Dic11—41no—
205C4×Dic11—42no—
206#4318—42no—
207C2×C11⋊C8—22no—
208C2×C11⋊C8—22no—
209C2×C11⋊C8—42no—
210#3538D1111yescharacteristic
211#3092—111no—
212C2×#484—111no—
213#2503—111no—
214#1617—114no—
215#1615—114no—
216#1508—111no—
217#1501—111no—
218#1472—111no—
219C23×C11—22no—
220C23×C11—22no—
221C23×C11—21no—
222C23×C11—41no—
223C23×C11#12011yescharacteristic
224C23×C11#12011yescharacteristic
225C23×C11C22×D411yescharacteristic
226Q8×C11—42no—
227Q8×C11—41no—
228Q8×C11—42no—
229Q8×C11—42no—
230Q8×C11—81no—
231Q8×C11—82no—
232D4×C11—41no—
233D4×C11—42no—
234D4×C11—42no—
235D4×C11—81no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—21no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—24no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—81no—
254C2×C4×C11—82no—
255C2×C4×C11#12011yescharacteristic
256C2×C4×C11#12011yescharacteristic
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C22×D411yescharacteristic
259C2×Dic11—42no—
260C2×Dic11—42no—
261C2×Dic11—44no—
262C2×Dic11—42no—
263C2×Dic11—42no—
264C2×Dic11—82no—
265C2×Dic11—82no—
266C11⋊C8—42no—
267C11⋊C8—42no—
268#563—22no—
269#552—21no—
270#552—21no—
271#551—22no—
272D4×Q8—21no—
273D4×Q8—21no—
274#544—21no—
275#544C2×D1112yes—
276#541—21no—
277#539—21no—
278#539C2×D1112yes—
279#536—21no—
280#525C2×D1111yescharacteristic
281C2×C22⋊Q8C2×D1111yescharacteristic
282C2×C22⋊Q8C2×D1111yescharacteristic
283C22×C4⋊C4—111no—
284#484—114no—
285#484—112no—
286#484—222no—
287#483—221no—
288#481—112no—
289#480—221no—
290#428—221no—
291C2×#107—221no—
292#417—221no—
293C2×#103—221no—
294#407—111no—
295C2×C22⋊C8—111no—
296#400—114no—
297#391—221no—
298#382—221no—
299#381—222no—
300C4×C22⋊C4—111no—
301#328—114no—
302#328—112no—
303#327—112no—
304#324—114no—
305C22×C11—21no—
306C22×C11—21no—
307C22×C11—21no—
308C22×C11—21no—
309C22×C11—21no—
310C22×C11—21no—
311C22×C11—21no—
312C22×C11—44no—
313C22×C11—41no—
314C22×C11—41no—
315C22×C11—41no—
316C22×C11#45412yes—
317C22×C11C2×#12011yescharacteristic
318C22×C11#57812yes—
319C4×C11—21no—
320C4×C11—21no—
321C4×C11—21no—
322C4×C11—42no—
323C4×C11—41no—
324C4×C11—42no—
325C4×C11—41no—
326C4×C11—41no—
327C4×C11—42no—
328C4×C11—42no—
329C4×C11#45812yes—
330Dic11—82no—
331Dic11—82no—
332C2×#41C22⋊D1111yescharacteristic
333C22×Q8—21no—
334C22×Q8C22⋊D1111yescharacteristic
335C22×Q8C22⋊D1111yescharacteristic
336C23×C4—221no—
337C23×C4C22×D1111yescharacteristic
338C2×M16—221no—
339C22×C8—221no—
340C4⋊Q8—21no—
341C4⋊Q8—22no—
342C4⋊Q8—22no—
343C4⋊Q8—22no—
344#126—22no—
345#126—22no—
346#126—22no—
347#126—22no—
348#125—21no—
349#125—22no—
350#125—22no—
351#125—22no—
352#125—22no—
353#124—22no—
354#123—22no—
355#123—22no—
356#123—22no—
357#123—21no—
358#123—22no—
359C22⋊Q8—21no—
360C22⋊Q8—21no—
361C22⋊Q8—22no—
362C22⋊Q8—22no—
363C22⋊Q8—22no—
364C22⋊Q8—21no—
365C22⋊Q8—21no—
366C22⋊Q8—21no—
367C22⋊Q8—21no—
368C22⋊Q8—21no—
369C22⋊Q8—21no—
370C22⋊Q8—22no—
371C22⋊Q8C22⋊D1112yes—
372C22⋊Q8C22⋊D1111yescharacteristic
373C22⋊Q8C22×D1112yes—
374C22⋊Q8C22×D1111yescharacteristic
375#121C22⋊D1111yescharacteristic
376#121C22×D1111yescharacteristic
377#120—21no—
378C4×Q8—21no—
379C4×Q8—21no—
380C4×D4—22no—
381C4×D4—21no—
382C4×D4—21no—
383C4×D4—22no—
384#117—21no—
385#117—22no—
386#117—22no—
387#117C22⋊D1111yescharacteristic
388C2×C4⋊C4—21no—
389C2×C4⋊C4—112no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4—221no—
395C2×C4⋊C4C22⋊D1111yescharacteristic
396C2×C4⋊C4C22⋊D1111yescharacteristic
397C2×C4⋊C4C22×D1112yes—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—221no—
400C2×C22⋊C4C22⋊D1112yes—
401C2×C42—221no—
402#107—224no—
403#107—222no—
404#106—222no—
405#103—224no—
406#103—222no—
407#102—222no—
408C22⋊C8—112no—
409C22⋊C8—112no—
410C22⋊C8—221no—
411C22⋊C8—221no—
412#95—112no—
413#95—224no—
414#95—224no—
415C2×C11—22no—
416C2×C11—22no—
417C2×C11—41no—
418C2×C11—81no—
419C2×C11#301111yescharacteristic
420C2×C11C2×#45411yescharacteristic
421C2×C11C2×#45811yescharacteristic
422C24C2×C22⋊D1111yescharacteristic
423#41—42no—
424C2×Q8—22no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—42no—
429C2×Q8—42no—
430C2×Q8—82no—
431C2×Q8C2×C22⋊D1112yes—
432C2×Q8C2×C22⋊D1111yescharacteristic
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4C2×C22⋊D1111yescharacteristic
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—42no—
442C22×C4—222no—
443C22×C4—222no—
444C22×C4—444no—
445C22×C4—441no—
446C22×C4—441no—
447C22×C4C2×C22⋊D1112yes—
448C22×C4C2×C22⋊D1111yescharacteristic
449C22×C4C2×C22⋊D1111yescharacteristic
450C22×C4C2×C22⋊D1111yescharacteristic
451C22×C4C2×C22⋊D1112yes—
452C22×C4C2×C22⋊D1111yescharacteristic
453C22×C4C2×C22⋊D1111yescharacteristic
454C22×C4C23×D1111yescharacteristic
455M16—442no—
456C2×C8—222no—
457C2×C8—222no—
458C2×C8—442no—
459C4⋊C4—22no—
460C4⋊C4—22no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—22no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—22no—
473C4⋊C4—22no—
474C4⋊C4—22no—
475C4⋊C4—21no—
476C4⋊C4—222no—
477C4⋊C4—222no—
478C4⋊C4—441no—
479C4⋊C4—441no—
480C4⋊C4C2×C22⋊D1111yescharacteristic
481C4⋊C4C2×C22⋊D1112yes—
482C4⋊C4C2×C22⋊D1111yescharacteristic
483C22⋊C4—22no—
484C22⋊C4—22no—
485C22⋊C4—22no—
486C22⋊C4—22no—
487C22⋊C4—22no—
488C22⋊C4—22no—
489C22⋊C4—21no—
490C22⋊C4—21no—
491C22⋊C4—22no—
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—442no—
496C42—22no—
497C42—22no—
498C42—22no—
499C42—21no—
500C42—442no—
501C11#1826911yescharacteristic, complemented, Sylow
502C23—22no—
503C23—22no—
504C23—21no—
505C23—41no—
506C23#6700611yescharacteristic
507C23#6700611yescharacteristic
508C23C22×C22⋊D1111yescharacteristic
509Q8—42no—
510Q8—41no—
511Q8—42no—
512Q8—42no—
513Q8—81no—
514Q8—82no—
515D4—41no—
516D4—42no—
517D4—42no—
518D4—81no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—24no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—21no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—81no—
537C2×C4—82no—
538C2×C4—442no—
539C2×C4—442no—
540C2×C4—444no—
541C2×C4—442no—
542C2×C4—442no—
543C2×C4—882no—
544C2×C4—882no—
545C2×C4#6700611yescharacteristic
546C2×C4#6700611yescharacteristic
547C2×C4C22×C22⋊D1111yescharacteristic
548C2×C4C22×C22⋊D1111yescharacteristic
549C8—442no—
550C8—442no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—21no—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—44no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22#1062285812yes—
563C22#1062336912yes—
564C22C2×#6700611yescharacteristic
565C4—21no—
566C4—21no—
567C4—21no—
568C4—42no—
569C4—41no—
570C4—42no—
571C4—41no—
572C4—41no—
573C4—42no—
574C4—42no—
575C4—882no—
576C4—882no—
577C4#1062285612yes—
578C2—22no—
579C2—22no—
580C2—41no—
581C2—81no—
582C2#1307791111yescharacteristic
583C2C2×#1062285811yescharacteristic
584C2C2×#1062285611yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3538C2
socleC22×C11C2×#120
prime radicalC11×#525C22
hypercenter#3538D11
hypocenterC11#18269
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3538

Complements

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

NH ≅ G/Ntype
2. C2×#10622657C2semidirect
3. #13073102C2semidirect
4. #13067658C2semidirect
5. #13067647C2semidirect
6. #13067136C2semidirect
8. #13066980C2semidirect
501. C11#18269semidirect

Maximal subgroups

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

subgroupindex
#130785362
C2×#106226572
#130731022
#130676582
#130676472
#130671362
#130671072
#130669802
C11×#35382
#1826911