Finite Group Databasebeta

← #14738856

Subgroups — #14738856

Order 2816.

572 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079989C211yesmaximal, characteristic
2#13079158C211yesmaximal, characteristic, complemented
3#13077621C211yesmaximal, characteristic
4#13068142C211yesmaximal, characteristic, complemented
5#13068137C211yesmaximal, characteristic, complemented
6#13068124C211yesmaximal, characteristic, complemented
7#13068117C211yesmaximal, characteristic, complemented
8#13068018C211yesmaximal, characteristic, complemented
9#13068013C211yesmaximal, characteristic, complemented
10#13068000C211yesmaximal, characteristic, complemented
11#13067993C211yesmaximal, characteristic, complemented
12#13067384C211yesmaximal, characteristic, complemented
13#13067327C211yesmaximal, characteristic, complemented
14#13067297C211yesmaximal, characteristic, complemented
15C11×#3238C211yesmaximal, characteristic
16C2×C11×C4⋊Q8C2211yescharacteristic
17C11×#529C2211yescharacteristic
18#10623001C2211yescharacteristic
19C11×#501—21no—
20C11×#489—21no—
21C11×#483—21no—
22C11×#480—21no—
23C11×#477C2211yescharacteristic
24C11×#477C2211yescharacteristic
25C11×#476C2211yescharacteristic
26C11×#476C2211yescharacteristic
27C11×#432C2211yescharacteristic
28#10622693—21no—
29#10622693—21no—
30#10622692C2211yescharacteristic
31#10622692C2211yescharacteristic
32#10622691C2211yescharacteristic
33#10622691C2211yescharacteristic
34#10622676—21no—
35#10622667—21no—
36#10622665—21no—
37#10622655—21no—
38#10622644C2211yescharacteristic
39#10622637C2211yescharacteristic
40Q8×C11⋊C8C2211yescharacteristic
41#10622634C2211yescharacteristic
42#10622632C2211yescharacteristic
43#10622625—21no—
44#10622625C2211yescharacteristic
45#10622624—21no—
46D4×C11⋊C8C2211yescharacteristic
47#10622621C2211yescharacteristic
48#10622613—21no—
49#10622610—21no—
50#10622577—21no—
51#10622577—21no—
52#10622538C2211yescharacteristic
53#10622537C2211yescharacteristic
54C4×#4318C2211yescharacteristic
55#10622184C2211yescharacteristic
56#10622184C2211yescharacteristic
57#10622184C2211yescharacteristic
58#10622184C2211yescharacteristic
59#10622120C2211yescharacteristic
60#10622120C2211yescharacteristic
61#10622119C2211yescharacteristic
62#10622119C2211yescharacteristic
63#10622118C2211yescharacteristic
64#10622118C2211yescharacteristic
65#10622117C2211yescharacteristic
66#10622117C2211yescharacteristic
67C22×Q8×C11—21no—
68C11×C4⋊Q8—21no—
69C11×C4⋊Q8—21no—
70C11×C4⋊Q8—21no—
71C11×C4⋊Q8C2311yescharacteristic
72C11×C4⋊Q8C2311yescharacteristic
73C11×#126—21no—
74C11×#125D411yescharacteristic
75C11×#124D411yescharacteristic
76C11×#123—21no—
77C11×C22⋊Q8D411yescharacteristic
78C11×#121D411yescharacteristic
79C4×Q8×C11C2311yescharacteristic
80C4×D4×C11—21no—
81C4×D4×C11C2311yescharacteristic
82C11×#117—21no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—21no—
85C2×C42×C11C2311yescharacteristic
86C2×#4326—21no—
87C2×#4324—21no—
88#66979—21no—
89#66977—21no—
90#66977—21no—
91C2×#4318—21no—
92C2×#4318—21no—
93C2×#4318D411yescharacteristic
94C2×#4318D411yescharacteristic
95C22×C11⋊C8—21no—
96#66923—21no—
97#66922C2311yescharacteristic
98#66922C2311yescharacteristic
99C4×Dic22—21no—
100C4×Dic22—21no—
101C11×#107—21no—
102C11×#107—21no—
103C11×#106—21no—
104C11×#106—21no—
105C11×C4⋊C8C2311yescharacteristic
106C11×C4⋊C8C2311yescharacteristic
107C11×#103—21no—
108C11×#103—21no—
109C11×#102—21no—
110C11×#102—21no—
111C11×C22⋊C8—21no—
112C11×#97—21no—
113#66899—21no—
114#66896—21no—
115C22⋊(C11⋊C8)—21no—
116C22⋊(C11⋊C8)—21no—
117C22⋊(C11⋊C8)—21no—
118#66874—21no—
119#66874—21no—
120#66872—21no—
121#66872—21no—
122#66872—21no—
123#66872—21no—
124#66872—21no—
125#66871—21no—
126#66871—21no—
127#66871—21no—
128#66871—21no—
129#66871—21no—
130C4⋊(C11⋊C8)—21no—
131C4⋊(C11⋊C8)—21no—
132C4⋊(C11⋊C8)—21no—
133C4⋊(C11⋊C8)C2311yescharacteristic
134C4⋊(C11⋊C8)C2311yescharacteristic
135C4⋊(C11⋊C8)C2311yescharacteristic
136C4⋊(C11⋊C8)C2311yescharacteristic
137#66867—21no—
138#66867D411yescharacteristic
139#66867D411yescharacteristic
140C4×C11⋊C8—21no—
141C4×C11⋊C8—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19379—111nomaximal, Sylow
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—41no—
148C2×Q8×C11—82no—
149C2×Q8×C11C2×D411yescharacteristic
150C2×D4×C11—21no—
151C2×D4×C11C2×D411yescharacteristic
152C22×C4×C11—21no—
153C22×C4×C11—41no—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11#4111yescharacteristic
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—41no—
170C11×C4⋊C4—41no—
171C11×C4⋊C4C2×D411yescharacteristic
172C11×C4⋊C4C2×D411yescharacteristic
173C11×C22⋊C4—21no—
174C11×C22⋊C4—21no—
175C11×C22⋊C4—21no—
176C11×C22⋊C4—21no—
177C11×C22⋊C4—21no—
178C42×C11—21no—
179C42×C11C2×D411yescharacteristic
180C42×C11C2×D411yescharacteristic
181C42×C11#4111yescharacteristic
182C42×C11C2411yescharacteristic
183C22⋊Dic11—41no—
184#4326—81no—
185#4324—81no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190Dic11⋊C4—41no—
191Dic11⋊C4—41no—
192C4×Dic11—41no—
193#4318—22no—
194#4318—22no—
195#4318—42no—
196#4318—81no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—42no—
202C2×C11⋊C8C2×D411yescharacteristic
203C2×C11⋊C8C2×D411yescharacteristic
204C2×C11⋊C8C2×D411yescharacteristic
205C2×C11⋊C8C2×D411yescharacteristic
206#3252—111no—
207#3238D1111yescharacteristic
208#3165—111no—
209#2969—111no—
210#1696—111no—
211#1695—111no—
212#1692—111no—
213#1691—111no—
214#1676—111no—
215#1675—111no—
216#1672—111no—
217#1671—111no—
218#1569—111no—
219#1554—111no—
220#1548—111no—
221C23×C11—21no—
222C23×C11#12111yescharacteristic
223Q8×C11—21no—
224Q8×C11—21no—
225Q8×C11—81no—
226Q8×C11—81no—
227Q8×C11—82no—
228D4×C11—21no—
229D4×C11—21no—
230D4×C11—81no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—82no—
244C2×C4×C11#12111yescharacteristic
245C2×C4×C11#12111yescharacteristic
246C2×C4×C11#12111yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×Dic11—41no—
251C2×Dic11—41no—
252Dic22—41no—
253Dic22—41no—
254Dic22—81no—
255C8×C11—41no—
256C8×C11—41no—
257C11⋊C8—21no—
258C11⋊C8—21no—
259C11⋊C8—41no—
260C11⋊C8—41no—
261C11⋊C8—41no—
262C11⋊C8—41no—
263C11⋊C8#13712yes—
264C11⋊C8#13712yes—
265#533—111no—
266C2×C4⋊Q8C2×D1111yescharacteristic
267#529C2×D1111yescharacteristic
268#501—21no—
269#501—221no—
270#501—221no—
271#500—111no—
272#500—111no—
273#498—111no—
274#498—111no—
275#489—21no—
276#483—21no—
277#480—21no—
278#479—221no—
279#477—111no—
280#477C2×D1111yescharacteristic
281#477C2×D1111yescharacteristic
282#476—111no—
283#476C2×D1111yescharacteristic
284#476C2×D1111yescharacteristic
285#470—221no—
286#468—221no—
287#464—221no—
288#462—111no—
289#461—111no—
290#446—111no—
291C8×Q8—111no—
292#436—111no—
293#436—221no—
294#435—221no—
295C8×D4—111no—
296#433—221no—
297#432C2×D1111yescharacteristic
298#431—111no—
299#428—221no—
300#428—221no—
301#423—111no—
302#405—221no—
303C4×M16—111no—
304#335—111no—
305#335—111no—
306#334—111no—
307#334—111no—
308#333—111no—
309#333—111no—
310#333—111no—
311#333—111no—
312#333—111no—
313#333—111no—
314#332—111no—
315#332—111no—
316C22×C11—21no—
317C22×C11—21no—
318C22×C11—21no—
319C22×C11—41no—
320C22×C11—41no—
321C22×C11—41no—
322C22×C11C2×#12111yescharacteristic
323C4×C11—21no—
324C4×C11—21no—
325C4×C11—21no—
326C4×C11—21no—
327C4×C11—41no—
328C4×C11—41no—
329C4×C11—41no—
330C4×C11—81no—
331C4×C11—81no—
332C4×C11C2×#13711yescharacteristic
333C4×C11C2×#13711yescharacteristic
334C4×C11#57711yescharacteristic
335C4×C11#57811yescharacteristic
336Dic11—81no—
337Dic11—81no—
338C22×Q8—21no—
339C2×Q16—221no—
340C2×SD16—221no—
341C2×M16—111no—
342C2×M16—111no—
343C2×M16—221no—
344C2×M16—221no—
345C22×C8—221no—
346C4⋊Q8—21no—
347C4⋊Q8—21no—
348C4⋊Q8—21no—
349C4⋊Q8—111no—
350C4⋊Q8—111no—
351C4⋊Q8C22×D1111yescharacteristic
352C4⋊Q8C22×D1111yescharacteristic
353#126—21no—
354#125—221no—
355#125C22⋊D1111yescharacteristic
356#124C22⋊D1111yescharacteristic
357#123—21no—
358C22⋊Q8—221no—
359C22⋊Q8—221no—
360C22⋊Q8C22⋊D1111yescharacteristic
361#121C22⋊D1111yescharacteristic
362C4×Q8—221no—
363C4×Q8—221no—
364C4×Q8C22×D1111yescharacteristic
365C4×D4—21no—
366C4×D4C22×D1111yescharacteristic
367#117—21no—
368#117—221no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C42C22×D1111yescharacteristic
372#107—21no—
373#107—21no—
374#107—221no—
375#107—221no—
376#107—221no—
377#107—221no—
378#107—221no—
379#106—21no—
380#106—21no—
381#106—221no—
382#106—221no—
383#106—221no—
384#106—221no—
385#106—221no—
386C4⋊C8—111no—
387C4⋊C8—111no—
388C4⋊C8—111no—
389C4⋊C8—111no—
390C4⋊C8—221no—
391C4⋊C8—221no—
392C4⋊C8—221no—
393C4⋊C8C22×D1111yescharacteristic
394C4⋊C8C22×D1111yescharacteristic
395#103—21no—
396#103—21no—
397#103—221no—
398#103—221no—
399#103—221no—
400#102—21no—
401#102—21no—
402#102—221no—
403C22⋊C8—21no—
404C22⋊C8—221no—
405C22⋊C8—221no—
406C22⋊C8—221no—
407#97—21no—
408#97—111no—
409#97—111no—
410#97—221no—
411C4×C8—111no—
412C4×C8—111no—
413C4×C8—221no—
414C4×C8—221no—
415C2×C11—41no—
416C2×C11—81no—
417C2×C11#303911yescharacteristic
418C2×C11#306311yescharacteristic
419C2×C11#306811yescharacteristic
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—41no—
423C2×Q8—82no—
424C2×Q8—221no—
425C2×Q8—221no—
426C2×Q8C2×C22⋊D1111yescharacteristic
427C2×D4—21no—
428C2×D4C2×C22⋊D1111yescharacteristic
429C22×C4—21no—
430C22×C4—41no—
431C22×C4D4×D1111yescharacteristic
432C22×C4#434111yescharacteristic
433C22×C4C2×C22⋊D1111yescharacteristic
434Q16—881no—
435SD16—881no—
436M16—222no—
437M16—222no—
438M16—442no—
439M16—881no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—111no—
443C2×C8—111no—
444C2×C8—111no—
445C2×C8—111no—
446C2×C8—221no—
447C2×C8—221no—
448C2×C8—221no—
449C2×C8—221no—
450C2×C8—442no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4—221no—
462C4⋊C4—221no—
463C4⋊C4—221no—
464C4⋊C4—221no—
465C4⋊C4—441no—
466C4⋊C4—441no—
467C4⋊C4C2×C22⋊D1111yescharacteristic
468C4⋊C4C2×C22⋊D1111yescharacteristic
469C22⋊C4—21no—
470C22⋊C4—21no—
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—441no—
475C42—21no—
476C42—441no—
477C42D4×D1111yescharacteristic
478C42#434111yescharacteristic
479C42C2×C22⋊D1111yescharacteristic
480C42C23×D1111yescharacteristic
481C11#1937911yescharacteristic, complemented, Sylow
482C23—21no—
483C23#6699211yescharacteristic
484Q8—21no—
485Q8—21no—
486Q8—81no—
487Q8—81no—
488Q8—82no—
489Q8—441no—
490Q8—441no—
491Q8—881no—
492D4—21no—
493D4—21no—
494D4—81no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—82no—
508C2×C4—441no—
509C2×C4—441no—
510C2×C4#6699211yescharacteristic
511C2×C4#6699211yescharacteristic
512C2×C4#6699211yescharacteristic
513C2×C4C2×D4×D1111yescharacteristic
514C2×C4C2×#434111yescharacteristic
515C2×C4C22×C22⋊D1111yescharacteristic
516C8—41no—
517C8—41no—
518C8—112no—
519C8—112no—
520C8—221no—
521C8—221no—
522C8—441no—
523C8—441no—
524C8—441no—
525C8—441no—
526C22—21no—
527C22—21no—
528C22—21no—
529C22—41no—
530C22—41no—
531C22—41no—
532C22C2×#6699211yescharacteristic
533C4—21no—
534C4—21no—
535C4—21no—
536C4—21no—
537C4—41no—
538C4—41no—
539C4—41no—
540C4—81no—
541C4—81no—
542C4—881no—
543C4—881no—
544C4D11×#13711yescharacteristic
545C4D11×#13711yescharacteristic
546C4#1062336811yescharacteristic
547C4#1062336911yescharacteristic
548C2—41no—
549C2—81no—
550C2#1307810111yescharacteristic
551C2#1307830311yescharacteristic
552C2#1307834111yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3238C2
socleC22×C11C2×#121
prime radicalC11×#121D4
hypercenter#3238D11
hypocenterC11#19379
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3238

Complements

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

NH ≅ G/Ntype
2. #13079158C2semidirect
4. #13068142C2semidirect
5. #13068137C2semidirect
6. #13068124C2semidirect
7. #13068117C2semidirect
8. #13068018C2semidirect
9. #13068013C2semidirect
10. #13068000C2semidirect
11. #13067993C2semidirect
12. #13067384C2semidirect
13. #13067327C2semidirect
14. #13067297C2semidirect
481. C11#19379semidirect

Maximal subgroups

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

subgroupindex
#130799892
#130791582
#130776212
#130681422
#130681372
#130681242
#130681172
#130680182
#130680132
#130680002
#130679932
#130673842
#130673272
#130672972
C11×#32382
#1937911