Finite Group Databasebeta

← #14724166

Subgroups — #14724166

Order 2816.

568 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078696C211yesmaximal, characteristic
2#13077761C211yesmaximal, characteristic
3#13077701C211yesmaximal, characteristic, complemented
4#13067522C211yesmaximal, characteristic, complemented
5#13067521C211yesmaximal, characteristic, complemented
6#13067510C211yesmaximal, characteristic, complemented
7#13067503C211yesmaximal, characteristic, complemented
8#13067490C211yesmaximal, characteristic, complemented
9#13067476C211yesmaximal, characteristic, complemented
10#13067469C211yesmaximal, characteristic, complemented
11#13067455C211yesmaximal, characteristic, complemented
12#13067407C211yesmaximal, characteristic, complemented
13#13067025C211yesmaximal, characteristic
14#13066916C211yesmaximal, characteristic, complemented
15C11×#1487C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C11C2211yescharacteristic
17#10623010C2211yescharacteristic
18C11×#431C2211yescharacteristic
19C11×#423C2211yescharacteristic
20#10622841C411yescharacteristic
21#10622840C411yescharacteristic
22#10622741—21no—
23#10622740—21no—
24C4×#4326C2211yescharacteristic
25C4×#4326C2211yescharacteristic
26#10622641C411yescharacteristic
27#10622641C411yescharacteristic
28C4×#4325C2211yescharacteristic
29C4×#4325C2211yescharacteristic
30#10622637—21no—
31#10622637—21no—
32#10622637C2211yescharacteristic
33#10622637C2211yescharacteristic
34#10622637C2211yescharacteristic
35#10622637C2211yescharacteristic
36#10622635C411yescharacteristic
37#10622635C411yescharacteristic
38#10622584C411yescharacteristic
39#10622580C411yescharacteristic
40#10622539—21no—
41#10622539—21no—
42#10622538C2211yescharacteristic
43#10622538C2211yescharacteristic
44#10622538C2211yescharacteristic
45#10622453—21no—
46#10622452—21no—
47#10622451C2211yescharacteristic
48#10622447C2211yescharacteristic
49#10622444C2211yescharacteristic
50#10622443C2211yescharacteristic
51C11×Q8⋊C8C2211yescharacteristic
52C11×Q8⋊C8C2211yescharacteristic
53C11×Q8⋊C8C2211yescharacteristic
54C11×Q8⋊C8C2211yescharacteristic
55#10622118C2211yescharacteristic
56#10622118C2211yescharacteristic
57#10622117C2211yescharacteristic
58#10622117C2211yescharacteristic
59#10622097C2211yescharacteristic
60#10622097C2211yescharacteristic
61#10622094C2211yescharacteristic
62#10622094C2211yescharacteristic
63#10622093C2211yescharacteristic
64#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C22×Q8×C11C2×C411yescharacteristic
68C2×C11×M16—21no—
69C4×Q8×C11—21no—
70C4×Q8×C11—21no—
71C4×Q8×C11C2×C411yescharacteristic
72C4×Q8×C11C2×C411yescharacteristic
73C4×Q8×C11C2311yescharacteristic
74C4×Q8×C11C2311yescharacteristic
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4C2×C411yescharacteristic
77C2×C42×C11—21no—
78C2×C42×C11C2311yescharacteristic
79C2×#4326C2×C411yescharacteristic
80C2×#4326C2×C411yescharacteristic
81C2×#4325C2×C411yescharacteristic
82C2×#4325C2×C411yescharacteristic
83#66983C2×C411yescharacteristic
84#66982—21no—
85C4×C22⋊D11—21no—
86#66977C2×C411yescharacteristic
87C2×#4313—21no—
88C2×C8×D11—21no—
89#66929—21no—
90#66928C2×C411yescharacteristic
91C4×D44C2311yescharacteristic
92#66925—21no—
93#66923C2×C411yescharacteristic
94C4×Dic22C2311yescharacteristic
95C11×C4⋊C8—21no—
96C11×C4⋊C8—21no—
97C11×C4⋊C8C2311yescharacteristic
98C11×C4⋊C8C2311yescharacteristic
99C11×C22⋊C8—21no—
100C4×C8×C11C2311yescharacteristic
101C4×C8×C11C2311yescharacteristic
102#66899C2×C411yescharacteristic
103#66899C2×C411yescharacteristic
104#66899C2×C411yescharacteristic
105#66899C2×C411yescharacteristic
106C22⋊(C11⋊C8)—21no—
107C22⋊(C11⋊C8)C2×C411yescharacteristic
108C22⋊(C11⋊C8)C2×C411yescharacteristic
109C22⋊(C11⋊C8)D411yescharacteristic
110C22⋊(C11⋊C8)D411yescharacteristic
111(C2×D11)⋊C8—21no—
112(C2×D11)⋊C8—21no—
113#66879—21no—
114Dic11⋊C8—21no—
115Dic11⋊C8—21no—
116C8×Dic11—21no—
117#66874C2×C411yescharacteristic
118#66874C2×C411yescharacteristic
119#66873C2×C411yescharacteristic
120#66873C2×C411yescharacteristic
121#66872C2×C411yescharacteristic
122#66872C2×C411yescharacteristic
123#66871C2×C411yescharacteristic
124#66871C2×C411yescharacteristic
125C4⋊(C11⋊C8)—21no—
126C4⋊(C11⋊C8)—21no—
127C4⋊(C11⋊C8)—21no—
128C4⋊(C11⋊C8)—21no—
129C4⋊(C11⋊C8)C2×C411yescharacteristic
130C4⋊(C11⋊C8)C2×C411yescharacteristic
131C4⋊(C11⋊C8)D411yescharacteristic
132C4⋊(C11⋊C8)D411yescharacteristic
133C4⋊(C11⋊C8)C2311yescharacteristic
134C4⋊(C11⋊C8)C2311yescharacteristic
135#66867—21no—
136#66867—21no—
137#66867—21no—
138#66867—21no—
139C4×C11⋊C8—21no—
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#17947—111nomaximal, Sylow
145C2×Q8×C11—21no—
146C2×Q8×C11—41no—
147C2×Q8×C11—41no—
148C2×Q8×C11C22×C411yescharacteristic
149C2×Q8×C11C22×C411yescharacteristic
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11C22×C411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11#4111yescharacteristic
155C2×C22⋊D11—21no—
156C2×D44C22×C411yescharacteristic
157C2×C4×D11—21no—
158C2×Dic22C22×C411yescharacteristic
159C11×M16—81no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4C22×C411yescharacteristic
170C11×C4⋊C4C22×C411yescharacteristic
171C42×C11—21no—
172C42×C11—21no—
173C42×C11—21no—
174C42×C11—21no—
175C42×C11C22×C411yescharacteristic
176C42×C11C2×D411yescharacteristic
177C42×C11#4111yescharacteristic
178C42×C11C2411yescharacteristic
179C22⋊Dic11—21no—
180#4326—41no—
181#4326—41no—
182#4325—41no—
183#4325—41no—
184(C2×D11)⋊C4—21no—
185(C2×D11)⋊C4—21no—
186(C2×D11)⋊C4—21no—
187(C2×D11)⋊C4—21no—
188C4⋊Dic11C22×C411yescharacteristic
189C4⋊Dic11C22×C411yescharacteristic
190Dic11⋊C4—21no—
191Dic11⋊C4—21no—
192Dic11⋊C4—21no—
193Dic11⋊C4—21no—
194C4×Dic11—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8C22×C411yescharacteristic
198C2×C11⋊C8C22×C411yescharacteristic
199C2×C11⋊C8C22×C411yescharacteristic
200C2×C11⋊C8C22×C411yescharacteristic
201C2×C11⋊C8C2×D411yescharacteristic
202C2×C11⋊C8C2×D411yescharacteristic
203C2×C11⋊C8C2×D411yescharacteristic
204C2×C11⋊C8C2×D411yescharacteristic
205#4313—81no—
206C8×D11—81no—
207#3108—111no—
208#2993—111no—
209#2983—111no—
210#1593—111no—
211#1592—111no—
212#1591—111no—
213#1590—111no—
214#1587—111no—
215#1585—111no—
216#1584—111no—
217#1582—111no—
218#1574—111no—
219#1487D1111yescharacteristic, complemented
220#1482—111no—
221#1454—111no—
222C23×C11C4×D411yescharacteristic
223C22×D11—21no—
224Q8×C11—21no—
225Q8×C11—21no—
226Q8×C11—21no—
227Q8×C11—21no—
228Q8×C11—42no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
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—41no—
238C2×C4×C11—42no—
239C2×C4×C11—81no—
240C2×C4×C11C4×D411yescharacteristic
241C2×C4×C11C4×D411yescharacteristic
242C2×C4×C11C4×D411yescharacteristic
243C2×C4×C11C23×C411yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C2×#4111yescharacteristic
246C22⋊D11—81no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250D44—21no—
251D44—21no—
252C4×D11—41no—
253C4×D11—41no—
254Dic22—21no—
255Dic22—21no—
256C8×C11—41no—
257C8×C11—41no—
258C8×C11—41no—
259C8×C11—41no—
260C11⋊C8—21no—
261C11⋊C8—21no—
262C11⋊C8—21no—
263C11⋊C8—21no—
264C11⋊C8—21no—
265C11⋊C8—21no—
266C11⋊C8—21no—
267C11⋊C8—21no—
268C11⋊C8—41no—
269C11⋊C8—41no—
270#529—111no—
271C2×C4×Q8C2×D1111yescharacteristic
272#483—111no—
273#480—111no—
274#479—111no—
275#479—111no—
276#464—111no—
277#464—111no—
278#451—111no—
279#448—111no—
280#446—111no—
281#446—111no—
282#446—111no—
283#446—111no—
284#446—111no—
285#446—221no—
286#446—221no—
287C8×Q8—111no—
288C4×Q16—111no—
289C4×Q16—111no—
290C4×SD16—111no—
291C4×SD16—111no—
292#436—111no—
293#436—221no—
294#435—221no—
295C8×D4—111no—
296#433—221no—
297#432—221no—
298#432—221no—
299#431—111no—
300#431—111no—
301#431—111no—
302#431C2×D1111yescharacteristic
303#424—221no—
304#423C2×D1111yescharacteristic
305#335—111no—
306#335—111no—
307#334—111no—
308#334—111no—
309Q8⋊C8—111no—
310Q8⋊C8—111no—
311Q8⋊C8C2×D1111yescharacteristic
312Q8⋊C8C2×D1111yescharacteristic
313Q8⋊C8C2×D1111yescharacteristic
314Q8⋊C8C2×D1111yescharacteristic
315D4⋊C8—111no—
316D4⋊C8—111no—
317#322—111no—
318#322—111no—
319#322—111no—
320C82—111no—
321C22×C11—21no—
322C22×C11—21no—
323C22×C11—21no—
324C22×C11C2×C4×D411yescharacteristic
325C2×D11—41no—
326C2×D11—41no—
327C2×D11—41no—
328C4×C11—21no—
329C4×C11—21no—
330C4×C11—21no—
331C4×C11—21no—
332C4×C11—41no—
333C4×C11—41no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11#56811yescharacteristic
337C4×C11#56811yescharacteristic
338C4×C11#57711yescharacteristic
339C4×C11#57811yescharacteristic
340Dic11—41no—
341Dic11—41no—
342Dic11—41no—
343C22×Q8C4×D1111yescharacteristic
344C2×Q16—111no—
345C2×Q16—111no—
346C2×SD16—111no—
347C2×SD16—111no—
348C2×M16—21no—
349C2×M16—221no—
350C22×C8—221no—
351#126—221no—
352#125—111no—
353#124—111no—
354#123—221no—
355C22⋊Q8—111no—
356#121—111no—
357C4×Q8—21no—
358C4×Q8—21no—
359C4×Q8—111no—
360C4×Q8C4×D1111yescharacteristic
361C4×Q8C4×D1111yescharacteristic
362C4×Q8C22×D1111yescharacteristic
363C4×Q8C22×D1111yescharacteristic
364C4×D4—111no—
365C4×D4—221no—
366#117—221no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4C4×D1111yescharacteristic
369C2×C42—21no—
370C2×C42C22×D1111yescharacteristic
371#107—111no—
372#107—111no—
373#106—111no—
374#106—111no—
375C4⋊C8—21no—
376C4⋊C8—21no—
377C4⋊C8—111no—
378C4⋊C8—111no—
379C4⋊C8—111no—
380C4⋊C8—111no—
381C4⋊C8—111no—
382C4⋊C8—111no—
383C4⋊C8—221no—
384C4⋊C8—221no—
385C4⋊C8—221no—
386C4⋊C8—221no—
387C4⋊C8—221no—
388C4⋊C8—221no—
389C4⋊C8C22×D1111yescharacteristic
390C4⋊C8C22×D1111yescharacteristic
391#103—111no—
392#103—111no—
393#103—111no—
394#103—111no—
395#103—111no—
396#103—111no—
397#102—111no—
398#102—111no—
399C22⋊C8—21no—
400C22⋊C8—111no—
401C22⋊C8—111no—
402C22⋊C8—111no—
403C22⋊C8—111no—
404C22⋊C8—221no—
405C22⋊C8—221no—
406C22⋊C8—221no—
407#97—221no—
408#97—221no—
409#97—221no—
410#97—221no—
411#97—221no—
412C4×C8—111no—
413C4×C8—111no—
414C4×C8—111no—
415C4×C8—111no—
416C4×C8—221no—
417C4×C8—221no—
418C4×C8C22×D1111yescharacteristic
419C4×C8C22×D1111yescharacteristic
420C2×C11—41no—
421C2×C11#293011yescharacteristic
422C2×C11#294711yescharacteristic
423C2×C11#295711yescharacteristic
424D11—81no—
425C2×Q8—21no—
426C2×Q8—41no—
427C2×Q8—41no—
428C2×Q8—111no—
429C2×Q8C2×C4×D1111yescharacteristic
430C2×Q8C2×C4×D1111yescharacteristic
431C2×D4—111no—
432C2×D4—221no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—221no—
436C22×C4C2×C4×D1111yescharacteristic
437C22×C4D4×D1111yescharacteristic
438C22×C4#434111yescharacteristic
439Q16—441no—
440Q16—441no—
441SD16—441no—
442SD16—441no—
443M16—81no—
444M16—881no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—111no—
450C2×C8—111no—
451C2×C8—111no—
452C2×C8—111no—
453C2×C8—111no—
454C2×C8—111no—
455C2×C8—111no—
456C2×C8—111no—
457C2×C8—221no—
458C2×C8—221no—
459C2×C8—881no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—111no—
466C4⋊C4—111no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4C2×C4×D1111yescharacteristic
472C4⋊C4C2×C4×D1111yescharacteristic
473C22⋊C4—221no—
474C22⋊C4—221no—
475C22⋊C4—221no—
476C22⋊C4—221no—
477C22⋊C4—221no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—221no—
483C42C2×C4×D1111yescharacteristic
484C42D4×D1111yescharacteristic
485C42#434111yescharacteristic
486C42C23×D1111yescharacteristic
487C11#1794711yescharacteristic, complemented, Sylow
488C23—221no—
489C23(C22⋊D11)⋊C411yescharacteristic
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—42no—
495Q8—221no—
496Q8—221no—
497D4—221no—
498D4—221no—
499D4—881no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—42no—
510C2×C4—81no—
511C2×C4—221no—
512C2×C4—221no—
513C2×C4—221no—
514C2×C4—441no—
515C2×C4—441no—
516C2×C4(C22⋊D11)⋊C411yescharacteristic
517C2×C4(C22⋊D11)⋊C411yescharacteristic
518C2×C4(C22⋊D11)⋊C411yescharacteristic
519C2×C4C22×C4×D1111yescharacteristic
520C2×C4C2×D4×D1111yescharacteristic
521C2×C4C2×#434111yescharacteristic
522C8—41no—
523C8—41no—
524C8—41no—
525C8—41no—
526C8—221no—
527C8—221no—
528C8—221no—
529C8—221no—
530C8—221no—
531C8—221no—
532C8—221no—
533C8—221no—
534C8—441no—
535C8—441no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—441no—
540C22—441no—
541C22—441no—
542C22C2×(C22⋊D11)⋊C411yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—441no—
552C4—441no—
553C4—441no—
554C4#1062327611yescharacteristic
555C4#1062327611yescharacteristic
556C4#1062329311yescharacteristic
557C4#1062329711yescharacteristic
558C2—41no—
559C2—881no—
560C2#1307731511yescharacteristic
561C2#1307745311yescharacteristic
562C2#1307752911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1487C2
socleC22×C11C2×C4×D4
prime radical#66983C2×C4
cosocleC42×C11C24
hypercenter#1487D11
hypocenterC11#17947
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1487

Complements

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

NH ≅ G/Ntype
3. #13077701C2semidirect
4. #13067522C2semidirect
5. #13067521C2semidirect
6. #13067510C2semidirect
7. #13067503C2semidirect
8. #13067490C2semidirect
9. #13067476C2semidirect
10. #13067469C2semidirect
11. #13067455C2semidirect
12. #13067407C2semidirect
14. #13066916C2semidirect
15. C11×#1487C2semidirect
219. #1487D11semidirect
487. C11#17947semidirect

Maximal subgroups

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

subgroupindex
#130786962
#130777612
#130777012
#130675222
#130675212
#130675102
#130675032
#130674902
#130674762
#130674692
#130674552
#130674072
#130670252
#130669162
C11×#14872
#1794711