Finite Group Databasebeta

← #14743991

Subgroups — #14743991

Order 2816.

580 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081522C211yesmaximal, characteristic
2Q8×#4325C211yesmaximal, characteristic
3#13080494C211yesmaximal, characteristic
4#13068292C211yesmaximal, characteristic, complemented
5#13068124C211yesmaximal, characteristic, complemented
6#13068074C211yesmaximal, characteristic, complemented
7#13068018C211yesmaximal, characteristic, complemented
8#13068012C211yesmaximal, characteristic
9#13067837C211yesmaximal, characteristic, complemented
10#13067779C211yesmaximal, characteristic
11#13067756C211yesmaximal, characteristic, complemented
12#13067749C211yesmaximal, characteristic
13#13067467C211yesmaximal, characteristic, complemented
14#13067426C211yesmaximal, characteristic
15Q8×C11×Q16C211yesmaximal, characteristic, complemented
16Q82×C11C2211yescharacteristic
17Q82×C11C2211yescharacteristic
18#10623110C2211yescharacteristic
19Q8×D44C2211yescharacteristic
20C11×#500—21no—
21C11×#500C2211yescharacteristic
22C11×#477—21no—
23C11×#477—21no—
24C11×#477C2211yescharacteristic
25C11×#477C2211yescharacteristic
26C8×Q8×C11C2211yescharacteristic
27C4×C11×Q16—21no—
28C4×C11×Q16C2211yescharacteristic
29#10622799—21no—
30#10622705C2211yescharacteristic
31#10622700—21no—
32#10622697—21no—
33#10622697C2211yescharacteristic
34#10622697C2211yescharacteristic
35#10622694C2211yescharacteristic
36#10622693—21no—
37#10622692—21no—
38#10622692C2211yescharacteristic
39#10622691C2211yescharacteristic
40#10622644C2211yescharacteristic
41#10622639—21no—
42C4×#4325—21no—
43C4×#4325C2211yescharacteristic
44#10622637C2211yescharacteristic
45Q8×C11⋊C8C2211yescharacteristic
46#10622635—21no—
47#10622634C2211yescharacteristic
48#10622634C2211yescharacteristic
49#10622633—21no—
50#10622633C2211yescharacteristic
51#10622497—21no—
52#10622426—21no—
53D11×#103—21no—
54C8×D44C2211yescharacteristic
55#10622294C2211yescharacteristic
56#10622184C2211yescharacteristic
57#10622184C2211yescharacteristic
58Q8⋊(C11⋊C8)C2211yescharacteristic
59Q8⋊(C11⋊C8)C2211yescharacteristic
60Q8⋊(C11⋊C8)C2211yescharacteristic
61#10622121C2211yescharacteristic
62#10622120C2211yescharacteristic
63#10622119C2211yescharacteristic
64#10622117C2211yescharacteristic
65#10622096C2211yescharacteristic
66#10622092C2211yescharacteristic
67C2×Q8×D11—21no—
68C2×C11×Q16D411yescharacteristic
69C11×C4⋊Q8—21no—
70C11×C4⋊Q8—21no—
71C11×C4⋊Q8—21no—
72C11×C4⋊Q8—21no—
73C11×C4⋊Q8—41no—
74C11×C4⋊Q8—41no—
75C11×C4⋊Q8C2311yescharacteristic
76C11×C4⋊Q8C2311yescharacteristic
77C4×Q8×C11—21no—
78C4×Q8×C11—21no—
79C4×Q8×C11—21no—
80C4×Q8×C11—21no—
81C4×Q8×C11C2311yescharacteristic
82C4×Q8×C11C2311yescharacteristic
83C4×Q8×C11C2311yescharacteristic
84#66999—21no—
85C2×#4326—21no—
86C2×#4326—41no—
87C2×#4325D411yescharacteristic
88C2×C8×D11—21no—
89#66950—21no—
90#66950—41no—
91#66949—41no—
92C4⋊C4×D11—21no—
93C4×D44—21no—
94C4×D44—21no—
95C4×D44C2311yescharacteristic
96#66923—21no—
97#66922—21no—
98#66922C2311yescharacteristic
99#66922C2311yescharacteristic
100C11×#107—21no—
101C11×#107—21no—
102C11×#107—21no—
103C11×#107—21no—
104C11×#107D411yescharacteristic
105C11×C4⋊C8—21no—
106C11×C4⋊C8C2311yescharacteristic
107C11×#103—21no—
108C11×#103—21no—
109C11×#103D411yescharacteristic
110C11×#103D411yescharacteristic
111C4×C8×C11—21no—
112C4×C8×C11C2311yescharacteristic
113#66899—21no—
114#66899—21no—
115#66899—21no—
116#66899—41no—
117#66899D411yescharacteristic
118(C2×D11)⋊C8—21no—
119#66880—21no—
120#66880—21no—
121#66874—21no—
122#66873—21no—
123#66873—21no—
124#66873D411yescharacteristic
125#66872—21no—
126#66872—21no—
127#66872—21no—
128#66872—21no—
129#66872—21no—
130#66872D411yescharacteristic
131#66871—21no—
132#66871—21no—
133#66871—21no—
134#66871—21no—
135C4⋊(C11⋊C8)—21no—
136C4⋊(C11⋊C8)—21no—
137C4⋊(C11⋊C8)C2311yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140#66867—21no—
141C4×C11⋊C8—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19813—111nomaximal, Sylow
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—41no—
148C2×Q8×C11—41no—
149C2×Q8×C11C2×D411yescharacteristic
150C2×Q8×C11C2×D411yescharacteristic
151C2×Q8×C11C2×D411yescharacteristic
152Q8×D11—42no—
153Q8×D11—81no—
154C2×D44C2×D411yescharacteristic
155C2×C4×D11—21no—
156C2×C4×D11—41no—
157C2×C4×D11—41no—
158C2×Dic22—21no—
159C2×Dic22—21no—
160C2×Dic22—41no—
161C11×Q16—22no—
162C2×C8×C11—21no—
163C2×C8×C11C2×D411yescharacteristic
164C2×C8×C11C2×D411yescharacteristic
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
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—41no—
174C11×C4⋊C4—41no—
175C11×C4⋊C4—41no—
176C11×C4⋊C4C2×D411yescharacteristic
177C11×C4⋊C4C2×D411yescharacteristic
178C11×C4⋊C4C2×D411yescharacteristic
179C42×C11—21no—
180C42×C11—21no—
181C42×C11—21no—
182C42×C11—41no—
183C42×C11—41no—
184C42×C11C2411yescharacteristic
185#4326—81no—
186#4326—82no—
187#4325Q1614yescomplemented
188(C2×D11)⋊C4—21no—
189(C2×D11)⋊C4—41no—
190(C2×D11)⋊C4—41no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—41no—
196C4⋊Dic11C2×D411yescharacteristic
197Dic11⋊C4—41no—
198Dic11⋊C4—41no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8C2×D411yescharacteristic
204C2×C11⋊C8C2×D411yescharacteristic
205C8×D11—81no—
206#3385—111no—
207Q8×Q16D1111yescharacteristic, complemented
208Q8×SD16—111no—
209#3299—111no—
210#1723—111no—
211#1692—111no—
212#1684—111no—
213#1676—111no—
214#1675—111no—
215#1645—111no—
216#1637—111no—
217#1633—111no—
218#1632—111no—
219#1584—111no—
220SD16⋊C8—111no—
221C22×D11—21no—
222Q8×C11—21no—
223Q8×C11—21no—
224Q8×C11—21no—
225Q8×C11—21no—
226Q8×C11—81no—
227Q8×C11—81no—
228Q8×C11—161no—
229Q8×C11—161no—
230Q8×C11C2×Q1612yes—
231Q8×C11#13712yes—
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×C11C22×D411yescharacteristic
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11H(5,𝔽2)11yescharacteristic
243C2×Dic11—21no—
244C2×Dic11—41no—
245C2×Dic11—41no—
246D44—21no—
247D44C2×Q1612yes—
248C4×D11—41no—
249C4×D11—41no—
250C4×D11—82no—
251C4×D11—161no—
252Dic22—41no—
253Dic22—41no—
254Dic22—82no—
255Dic22—81no—
256C8×C11—21no—
257C8×C11—21no—
258C8×C11—41no—
259C11⋊C8—21no—
260C11⋊C8—41no—
261C11⋊C8—41no—
262C11⋊C8—41no—
263C11⋊C8—41no—
264C11⋊C8C2×Q1612yes—
265Q82C2×D1111yescharacteristic
266Q82C2×D1111yescharacteristic
267#554—111no—
268D4×Q8—111no—
269#501—221no—
270#500—21no—
271#500—111no—
272#500C2×D1111yescharacteristic
273#498—111no—
274#498—221no—
275#494—111no—
276#487—111no—
277#487—111no—
278#484—221no—
279#479—221no—
280#477—21no—
281#477—21no—
282#477—111no—
283#477—111no—
284#477C2×D1111yescharacteristic
285#477C2×D1111yescharacteristic
286#476—111no—
287#476—111no—
288#476—221no—
289#475—111no—
290#475—221no—
291#474—221no—
292#467—221no—
293#462—111no—
294#451—221no—
295#446—111no—
296C8×Q8—111no—
297C8×Q8C2×D1111yescharacteristic
298#440—221no—
299C4×Q16—21no—
300C4×Q16C2×D1111yescharacteristic
301C4×SD16—111no—
302C4×SD16—221no—
303C8×D4—111no—
304C2×#103—221no—
305#335—111no—
306#335—111no—
307#333—111no—
308#333—111no—
309#333—111no—
310#332—111no—
311Q8⋊C8—111no—
312Q8⋊C8—111no—
313Q8⋊C8—111no—
314D4⋊C8—111no—
315#322—111no—
316C22×C11D4211yescharacteristic
317C2×D11—22no—
318C2×D11—41no—
319C2×D11—41no—
320C4×C11—22no—
321C4×C11—22no—
322C4×C11—21no—
323C4×C11—41no—
324C4×C11—41no—
325C4×C11—41no—
326C4×C11—41no—
327C4×C11—81no—
328C4×C11—81no—
329C4×C11C22×Q1611yescharacteristic
330C4×C11C2×#13711yescharacteristic
331C4×C11#57711yescharacteristic
332C4×C11#57811yescharacteristic
333Dic11—41no—
334Dic11—81no—
335Dic11—81no—
336C22×Q8—221no—
337C2×Q16—221no—
338C2×Q16—441no—
339C2×Q16C22⋊D1111yescharacteristic
340C2×SD16—111no—
341C22×C8—221no—
342C4⋊Q8—21no—
343C4⋊Q8—21no—
344C4⋊Q8—21no—
345C4⋊Q8—21no—
346C4⋊Q8—41no—
347C4⋊Q8—41no—
348C4⋊Q8—111no—
349C4⋊Q8—111no—
350C4⋊Q8—221no—
351C4⋊Q8C22×D1111yescharacteristic
352C4⋊Q8C22×D1111yescharacteristic
353#125—221no—
354C22⋊Q8—221no—
355C22⋊Q8—221no—
356C22⋊Q8—441no—
357C22⋊Q8—441no—
358C4×Q8—21no—
359C4×Q8—21no—
360C4×Q8—21no—
361C4×Q8—21no—
362C4×Q8C22×D1111yescharacteristic
363C4×Q8C22×D1111yescharacteristic
364C4×Q8C22×D1111yescharacteristic
365C4×D4—111no—
366C4×D4—221no—
367C4×D4—221no—
368C2×C4⋊C4—221no—
369#107—21no—
370#107—21no—
371#107—21no—
372#107—21no—
373#107—221no—
374#107—221no—
375#107—221no—
376#107—221no—
377#107C22⋊D1111yescharacteristic
378#106—111no—
379#106—221no—
380#106—221no—
381#106—221no—
382#106—221no—
383#106—221no—
384C4⋊C8—21no—
385C4⋊C8—111no—
386C4⋊C8—111no—
387C4⋊C8—111no—
388C4⋊C8—221no—
389C4⋊C8—221no—
390C4⋊C8C22×D1111yescharacteristic
391#103—21no—
392#103—21no—
393#103—111no—
394#103—221no—
395#103—221no—
396#103—221no—
397#103—221no—
398#103—221no—
399#103—221no—
400#103—441no—
401#103C22⋊D1111yescharacteristic
402#103C22⋊D1111yescharacteristic
403#102—111no—
404#102—221no—
405#102—221no—
406C22⋊C8—221no—
407#97—221no—
408C4×C8—21no—
409C4×C8—111no—
410C4×C8—111no—
411C4×C8—221no—
412C4×C8C22×D1111yescharacteristic
413C2×C11#326611yescharacteristic
414C2×C11D4×Q1611yescharacteristic
415C2×C11#328811yescharacteristic
416D11—42no—
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—41no—
420C2×Q8—41no—
421C2×Q8—221no—
422C2×Q8—221no—
423C2×Q8—441no—
424C2×Q8—442no—
425C2×Q8—881no—
426C2×Q8D4×D1111yescharacteristic
427C2×Q8C2×C22⋊D1111yescharacteristic
428C2×Q8C2×C22⋊D1111yescharacteristic
429C2×D4—111no—
430C22×C4—221no—
431C22×C4—441no—
432C22×C4—441no—
433Q16—22no—
434Q16—881no—
435Q16—882no—
436SD16—114no—
437C2×C8—21no—
438C2×C8—111no—
439C2×C8—111no—
440C2×C8—221no—
441C2×C8—221no—
442C2×C8—221no—
443C2×C8—221no—
444C2×C8—881no—
445C2×C8C2×C22⋊D1111yescharacteristic
446C2×C8C2×C22⋊D1111yescharacteristic
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—41no—
455C4⋊C4—41no—
456C4⋊C4—41no—
457C4⋊C4—41no—
458C4⋊C4—111no—
459C4⋊C4—221no—
460C4⋊C4—221no—
461C4⋊C4—221no—
462C4⋊C4—221no—
463C4⋊C4—441no—
464C4⋊C4—441no—
465C4⋊C4—441no—
466C4⋊C4D4×D1111yescharacteristic
467C4⋊C4C2×C22⋊D1111yescharacteristic
468C4⋊C4C2×C22⋊D1111yescharacteristic
469C22⋊C4—221no—
470C22⋊C4—441no—
471C22⋊C4—441no—
472C42—21no—
473C42—21no—
474C42—21no—
475C42—41no—
476C42—41no—
477C42C23×D1111yescharacteristic
478C11#1981311yescharacteristic, complemented, Sylow
479C23—221no—
480Q8—21no—
481Q8—21no—
482Q8—21no—
483Q8—21no—
484Q8—81no—
485Q8—81no—
486Q8—161no—
487Q8—161no—
488Q8—441no—
489Q8—441no—
490Q8—882no—
491Q8—881no—
492Q8Q16×D1112yes—
493Q8#6699512yes—
494D4—112no—
495D4—221no—
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—221no—
505C2×C4—441no—
506C2×C4—441no—
507C2×C4—441no—
508C2×C4—441no—
509C2×C4—882no—
510C2×C4—1761no—
511C2×C4C2×D4×D1111yescharacteristic
512C2×C4#6703711yescharacteristic
513C2×C4C22×C22⋊D1111yescharacteristic
514C8—21no—
515C8—21no—
516C8—41no—
517C8—112no—
518C8—221no—
519C8—441no—
520C8—441no—
521C8—441no—
522C8—441no—
523C22—222no—
524C22—441no—
525C22—441no—
526C22D4×C22⋊D1111yescharacteristic
527C4—22no—
528C4—21no—
529C4—22no—
530C4—41no—
531C4—41no—
532C4—41no—
533C4—41no—
534C4—81no—
535C4—81no—
536C4—441no—
537C4—881no—
538C4—881no—
539C4C2×Q16×D1111yescharacteristic
540C4#1062329711yescharacteristic
541C4C2×#6699511yescharacteristic
542C4#1062336811yescharacteristic
543C2—442no—
544C2#1308012711yescharacteristic
545C2Q16×C22⋊D1111yescharacteristic
546C2#1308038011yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingQ8×C11×Q16C2
socleC22×C11D42
prime radicalC2×D44C2×D4
hypercenterQ8×Q16D11
hypocenterC11#19813
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ Q8×Q16

Complements

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

NH ≅ G/Ntype
4. #13068292C2semidirect
5. #13068124C2semidirect
6. #13068074C2semidirect
7. #13068018C2semidirect
9. #13067837C2semidirect
11. #13067756C2semidirect
13. #13067467C2semidirect
15. Q8×C11×Q16C2semidirect
187. #4325Q16semidirect
207. Q8×Q16D11semidirect
478. C11#19813semidirect

Maximal subgroups

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

subgroupindex
#130815222
Q8×#43252
#130804942
#130682922
#130681242
#130680742
#130680182
#130680122
#130678372
#130677792
#130677562
#130677492
#130674672
#130674262
Q8×C11×Q162
#1981311