Finite Group Databasebeta

← #14724960

Subgroups — #14724960

Order 2816.

600 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078696C211yesmaximal, characteristic
2#13077772C211yesmaximal, characteristic
3#13077705C211yesmaximal, characteristic, complemented
4#13067510C211yesmaximal, characteristic, complemented
5#13067503C211yesmaximal, characteristic, complemented
6#13067491C211yesmaximal, characteristic, complemented
7#13067490C211yesmaximal, characteristic, complemented
8#13067484C211yesmaximal, characteristic, complemented
9#13067476C211yesmaximal, characteristic, complemented
10#13067420C211yesmaximal, characteristic, complemented
11#13067413C211yesmaximal, characteristic, complemented
12#13067399C211yesmaximal, characteristic, complemented
13#13067077C211yesmaximal, characteristic
14#13066899C211yesmaximal, characteristic, complemented
15C2×C11×Q8⋊C8C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C11C2211yescharacteristic
17#10623010C2211yescharacteristic
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C4×C8×C11C2211yescharacteristic
20#10622841C411yescharacteristic
21#10622840C411yescharacteristic
22#10622724—21no—
23C8×C22⋊D11—21no—
24C4×#4326C2211yescharacteristic
25C4×#4326C2211yescharacteristic
26#10622641C411yescharacteristic
27#10622641C411yescharacteristic
28C4×#4325C2211yescharacteristic
29C4×#4325C2211yescharacteristic
30#10622637—21no—
31#10622637—21no—
32#10622637C2211yescharacteristic
33#10622637C2211yescharacteristic
34Q8×C11⋊C8C2211yescharacteristic
35Q8×C11⋊C8C2211yescharacteristic
36#10622635C411yescharacteristic
37#10622635C411yescharacteristic
38#10622584C411yescharacteristic
39#10622580C411yescharacteristic
40#10622539—21no—
41#10622539C2211yescharacteristic
42#10622538—21no—
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#10622093C2211yescharacteristic
65C8×C11⋊C8C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C22×Q8×C11C2×C411yescharacteristic
68C22×C8×C11—21no—
69C22×C8×C11—21no—
70C4×Q8×C11—21no—
71C4×Q8×C11—21no—
72C4×Q8×C11C2×C411yescharacteristic
73C4×Q8×C11C2×C411yescharacteristic
74C4×Q8×C11C2311yescharacteristic
75C4×Q8×C11C2311yescharacteristic
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4C2×C411yescharacteristic
78C2×C42×C11—21no—
79C2×C42×C11C2311yescharacteristic
80C2×#4326C2×C411yescharacteristic
81C2×#4326C2×C411yescharacteristic
82C2×#4325C2×C411yescharacteristic
83C2×#4325C2×C411yescharacteristic
84#66983C2×C411yescharacteristic
85#66982—21no—
86C4×C22⋊D11—21no—
87#66977C2×C411yescharacteristic
88C2×#4313—21no—
89C2×C8×D11—21no—
90#66929—21no—
91#66928C2×C411yescharacteristic
92C4×D44C2311yescharacteristic
93#66925—21no—
94#66923C2×C411yescharacteristic
95C4×Dic22C2311yescharacteristic
96C11×C4⋊C8—21no—
97C11×C4⋊C8C2311yescharacteristic
98C11×C4⋊C8C2311yescharacteristic
99C4×C8×C11—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—
138C4×C11⋊C8—21no—
139C4×C11⋊C8—21no—
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#18017—111nomaximal, Sylow
145C2×Q8×C11—21no—
146C2×Q8×C11—22no—
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
159C2×C8×C11—24no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—81no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4C22×C411yescharacteristic
171C11×C4⋊C4C22×C411yescharacteristic
172C42×C11—21no—
173C42×C11—21no—
174C42×C11—21no—
175C42×C11—21no—
176C42×C11C22×C411yescharacteristic
177C42×C11C2×D411yescharacteristic
178C42×C11#4111yescharacteristic
179C42×C11C2411yescharacteristic
180C22⋊Dic11—21no—
181#4326—22no—
182#4326—41no—
183#4325—22no—
184#4325—41no—
185(C2×D11)⋊C4—21no—
186(C2×D11)⋊C4—21no—
187(C2×D11)⋊C4—21no—
188(C2×D11)⋊C4—21no—
189C4⋊Dic11C22×C411yescharacteristic
190C4⋊Dic11C22×C411yescharacteristic
191Dic11⋊C4—21no—
192Dic11⋊C4—21no—
193Dic11⋊C4—21no—
194Dic11⋊C4—21no—
195C4×Dic11—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8C22×C411yescharacteristic
199C2×C11⋊C8C22×C411yescharacteristic
200C2×C11⋊C8C22×C411yescharacteristic
201C2×C11⋊C8C22×C411yescharacteristic
202C2×C11⋊C8C2×D411yescharacteristic
203C2×C11⋊C8C2×D411yescharacteristic
204C2×C11⋊C8C2×D411yescharacteristic
205C2×C11⋊C8C2×D411yescharacteristic
206#4313—81no—
207C8×D11—81no—
208#3108—111no—
209#2994—111no—
210#2984—111no—
211#1591—111no—
212#1590—111no—
213#1588—111no—
214#1587—111no—
215#1587—111no—
216#1585—111no—
217C8×Q16—111no—
218C8×SD16—111no—
219#1573—111no—
220#1494—111no—
221C2×Q8⋊C8D1111yescharacteristic, complemented
222#1450—111no—
223C23×C11C4×D411yescharacteristic
224C22×D11—21no—
225Q8×C11—21no—
226Q8×C11—21no—
227Q8×C11—21no—
228Q8×C11—42no—
229Q8×C11#13112yes—
230C2×C4×C11—21no—
231C2×C4×C11—22no—
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—21no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11C4×D411yescharacteristic
242C2×C4×C11C4×D411yescharacteristic
243C2×C4×C11C4×D411yescharacteristic
244C2×C4×C11C23×C411yescharacteristic
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C22⋊D11—42no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251D44—21no—
252D44—21no—
253C4×D11—41no—
254C4×D11—41no—
255Dic22—21no—
256Dic22—21no—
257C8×C11—22no—
258C8×C11—22no—
259C8×C11—41no—
260C8×C11—41no—
261C11⋊C8—21no—
262C11⋊C8—21no—
263C11⋊C8—21no—
264C11⋊C8—21no—
265C11⋊C8—21no—
266C11⋊C8—21no—
267C11⋊C8—21no—
268C11⋊C8—21no—
269C11⋊C8—41no—
270C11⋊C8—41no—
271#529—111no—
272C2×C4×Q8C2×D1111yescharacteristic
273#483—111no—
274#480—111no—
275#479—111no—
276#479—111no—
277#464—111no—
278#464—111no—
279#451—111no—
280#448—111no—
281#446—111no—
282#446—111no—
283#446—111no—
284#446—221no—
285#446—221no—
286C8×Q8—111no—
287C8×Q8—111no—
288C8×Q8—111no—
289C4×Q16—111no—
290C4×Q16—111no—
291C4×SD16—111no—
292C4×SD16—111no—
293#436—111no—
294#435—221no—
295C8×D4—111no—
296C8×D4—221no—
297#433—221no—
298#432—111no—
299#432—221no—
300#431—111no—
301#431—111no—
302#431—221no—
303#424—221no—
304C2×C4⋊C8C2×D1111yescharacteristic
305C2×C4×C8C2×D1111yescharacteristic
306#335—111no—
307#335—111no—
308#334—111no—
309#334—111no—
310Q8⋊C8—111no—
311Q8⋊C8—111no—
312Q8⋊C8C2×D1111yescharacteristic
313Q8⋊C8C2×D1111yescharacteristic
314Q8⋊C8C2×D1111yescharacteristic
315Q8⋊C8C2×D1111yescharacteristic
316D4⋊C8—111no—
317D4⋊C8—111no—
318#322—111no—
319#322—111no—
320C82—111no—
321C82—111no—
322C22×C11—21no—
323C22×C11—21no—
324C22×C11#44312yes—
325C22×C11C2×C4×D411yescharacteristic
326C2×D11—41no—
327C2×D11—41no—
328C2×D11—41no—
329C4×C11—21no—
330C4×C11—22no—
331C4×C11—21no—
332C4×C11—21no—
333C4×C11—21no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11—41no—
337C4×C11C2×#13111yescharacteristic
338C4×C11#56811yescharacteristic
339C4×C11#57711yescharacteristic
340C4×C11#57811yescharacteristic
341Dic11—41no—
342Dic11—41no—
343Dic11—41no—
344C22×Q8C4×D1111yescharacteristic
345C2×Q16—111no—
346C2×Q16—111no—
347C2×SD16—111no—
348C2×SD16—111no—
349C2×M16—221no—
350C22×C8—21no—
351C22×C8—21no—
352C22×C8—221no—
353#126—221no—
354#125—111no—
355#124—111no—
356#123—221no—
357C22⋊Q8—111no—
358#121—111no—
359C4×Q8—21no—
360C4×Q8—21no—
361C4×Q8—111no—
362C4×Q8C4×D1111yescharacteristic
363C4×Q8C4×D1111yescharacteristic
364C4×Q8C22×D1111yescharacteristic
365C4×Q8C22×D1111yescharacteristic
366C4×D4—111no—
367C4×D4—221no—
368#117—221no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4C4×D1111yescharacteristic
371C2×C42—21no—
372C2×C42C22×D1111yescharacteristic
373#107—111no—
374#107—111no—
375#106—111no—
376#106—111no—
377C4⋊C8—21no—
378C4⋊C8—111no—
379C4⋊C8—111no—
380C4⋊C8—111no—
381C4⋊C8—111no—
382C4⋊C8—111no—
383C4⋊C8—111no—
384C4⋊C8—221no—
385C4⋊C8—221no—
386C4⋊C8—221no—
387C4⋊C8—221no—
388C4⋊C8—221no—
389C4⋊C8—221no—
390C4⋊C8C22×D1111yescharacteristic
391C4⋊C8C22×D1111yescharacteristic
392#103—111no—
393#103—111no—
394#103—111no—
395#103—111no—
396#103—111no—
397#103—111no—
398#102—111no—
399#102—111no—
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—
411C4×C8—21no—
412C4×C8—111no—
413C4×C8—111no—
414C4×C8—111no—
415C4×C8—111no—
416C4×C8—221no—
417C4×C8—221no—
418C4×C8—221no—
419C4×C8C22×D1111yescharacteristic
420C4×C8C22×D1111yescharacteristic
421C2×C11—22no—
422C2×C11#293311yescharacteristic
423C2×C11#294711yescharacteristic
424C2×C11C2×#44311yescharacteristic
425D11—81no—
426C2×Q8—21no—
427C2×Q8—22no—
428C2×Q8—41no—
429C2×Q8—111no—
430C2×Q8C2×C4×D1111yescharacteristic
431C2×Q8C2×C4×D1111yescharacteristic
432C2×D4—111no—
433C2×D4—221no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—221no—
437C22×C4C2×C4×D1111yescharacteristic
438C22×C4D4×D1111yescharacteristic
439C22×C4#434111yescharacteristic
440Q16—222no—
441Q16—441no—
442SD16—222no—
443SD16—441no—
444M16—881no—
445C2×C8—24no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—81no—
451C2×C8—111no—
452C2×C8—111no—
453C2×C8—111no—
454C2×C8—111no—
455C2×C8—111no—
456C2×C8—111no—
457C2×C8—111no—
458C2×C8—111no—
459C2×C8—221no—
460C2×C8—221no—
461C2×C8—881no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—111no—
468C4⋊C4—111no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4C2×C4×D1111yescharacteristic
474C4⋊C4C2×C4×D1111yescharacteristic
475C22⋊C4—221no—
476C22⋊C4—221no—
477C22⋊C4—221no—
478C22⋊C4—221no—
479C22⋊C4—221no—
480C42—21no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42—221no—
485C42C2×C4×D1111yescharacteristic
486C42D4×D1111yescharacteristic
487C42#434111yescharacteristic
488C42C23×D1111yescharacteristic
489C11#1801711yescharacteristic, complemented, Sylow
490C23—221no—
491C23(C22⋊D11)⋊C411yescharacteristic
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8—42no—
496Q8—221no—
497Q8—221no—
498Q8#6695412yes—
499D4—221no—
500D4—221no—
501D4—442no—
502C2×C4—21no—
503C2×C4—22no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—221no—
514C2×C4—221no—
515C2×C4—221no—
516C2×C4—441no—
517C2×C4—441no—
518C2×C4(C22⋊D11)⋊C411yescharacteristic
519C2×C4(C22⋊D11)⋊C411yescharacteristic
520C2×C4(C22⋊D11)⋊C411yescharacteristic
521C2×C4C22×C4×D1111yescharacteristic
522C2×C4C2×D4×D1111yescharacteristic
523C2×C4C2×#434111yescharacteristic
524C8—22no—
525C8—22no—
526C8—41no—
527C8—41no—
528C8—221no—
529C8—221no—
530C8—221no—
531C8—221no—
532C8—221no—
533C8—221no—
534C8—221no—
535C8—221no—
536C8—441no—
537C8—441no—
538C22—21no—
539C22—21no—
540C22—441no—
541C22—441no—
542C22—441no—
543C22#1062243712yes—
544C22C2×(C22⋊D11)⋊C411yescharacteristic
545C4—21no—
546C4—22no—
547C4—21no—
548C4—21no—
549C4—21no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—441no—
554C4—441no—
555C4—441no—
556C4C2×#6695411yescharacteristic
557C4#1062327611yescharacteristic
558C4#1062329311yescharacteristic
559C4#1062329711yescharacteristic
560C2—22no—
561C2—881no—
562C2#1307733711yescharacteristic
563C2#1307745311yescharacteristic
564C2C2×#1062243711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC2×C11×Q8⋊C8C2
socleC22×C11C2×C4×D4
prime radical#66983C2×C4
cosocleC42×C11C24
hypercenterC2×Q8⋊C8D11
hypocenterC11#18017
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
3. #13077705C2semidirect
4. #13067510C2semidirect
5. #13067503C2semidirect
6. #13067491C2semidirect
7. #13067490C2semidirect
8. #13067484C2semidirect
9. #13067476C2semidirect
10. #13067420C2semidirect
11. #13067413C2semidirect
12. #13067399C2semidirect
14. #13066899C2semidirect
15. C2×C11×Q8⋊C8C2semidirect
221. C2×Q8⋊C8D11semidirect
489. C11#18017semidirect

Maximal subgroups

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

subgroupindex
#130786962
#130777722
#130777052
#130675102
#130675032
#130674912
#130674902
#130674842
#130674762
#130674202
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