Finite Group Databasebeta

← #14723884

Subgroups — #14723884

Order 2816.

598 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#13078681C211yesmaximal, characteristic
2#13077725C211yesmaximal, characteristic
3#13077711C211yesmaximal, characteristic, complemented
4#13067490C211yesmaximal, characteristic, complemented
5#13067476C211yesmaximal, characteristic, complemented
6#13067469C211yesmaximal, characteristic, complemented
7#13067455C211yesmaximal, characteristic, complemented
8#13067432C211yesmaximal, characteristic, complemented
9#13067431C211yesmaximal, characteristic, complemented
10#13067420C211yesmaximal, characteristic, complemented
11#13067413C211yesmaximal, characteristic, complemented
12#13067399C211yesmaximal, characteristic, complemented
13#13067051C211yesmaximal, characteristic
14#13066916C211yesmaximal, characteristic, complemented
15C11×#1481C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17C4×#4339C2211yescharacteristic
18C11×#431C2211yescharacteristic
19C2×C11×C4⋊C8C2211yescharacteristic
20C8×C22⋊D11—21no—
21C8×C22⋊D11—21no—
22#10622707C411yescharacteristic
23#10622703C411yescharacteristic
24#10622700C411yescharacteristic
25#10622696C411yescharacteristic
26#10622660C411yescharacteristic
27#10622660C411yescharacteristic
28#10622658C411yescharacteristic
29#10622658C411yescharacteristic
30C4×#4326C2211yescharacteristic
31C4×#4326C2211yescharacteristic
32C4×#4325C2211yescharacteristic
33C4×#4325C2211yescharacteristic
34#10622637—21no—
35#10622637—21no—
36#10622637C2211yescharacteristic
37#10622637C2211yescharacteristic
38Q8×C11⋊C8C2211yescharacteristic
39Q8×C11⋊C8C2211yescharacteristic
40#10622613—21no—
41#10622613—21no—
42#10622539C2211yescharacteristic
43#10622538C2211yescharacteristic
44#10622538C2211yescharacteristic
45#10622447C2211yescharacteristic
46#10622447C2211yescharacteristic
47#10622446—21no—
48D11×C4⋊C8—21no—
49#10622443C2211yescharacteristic
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
67C2×#4339C2×C411yescharacteristic
68C22×C8×C11—21no—
69C11×C4⋊Q8C2×C411yescharacteristic
70C11×C4⋊Q8C2×C411yescharacteristic
71C11×#125—21no—
72C11×C22⋊Q8—21no—
73C11×C22⋊Q8C2×C411yescharacteristic
74C11×C22⋊Q8C2×C411yescharacteristic
75C4×Q8×C11—21no—
76C4×Q8×C11C2311yescharacteristic
77C4×Q8×C11C2311yescharacteristic
78C11×#117—21no—
79C2×C42×C11C2311yescharacteristic
80C2×#4326C2×C411yescharacteristic
81C2×#4326C2×C411yescharacteristic
82C2×#4325C2×C411yescharacteristic
83C2×#4325C2×C411yescharacteristic
84C4×C22⋊D11—21no—
85C4×C22⋊D11—21no—
86#66979C2×C411yescharacteristic
87C2×C8×D11—21no—
88C2×C8×D11—21no—
89C4×D44C2×C411yescharacteristic
90C4×D44C2311yescharacteristic
91#66925—21no—
92C42×D11—21no—
93C4×Dic22C2×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—
113Dic11⋊C8—21no—
114Dic11⋊C8—21no—
115C8×Dic11—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#17921—111nomaximal, Sylow
145C2×Q8×C11—21no—
146C2×Q8×C11C22×C411yescharacteristic
147C2×Q8×C11C22×C411yescharacteristic
148C22×C4×C11C22×C411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11#4111yescharacteristic
151C2×C22⋊D11—21no—
152#4339—22no—
153#4339—22no—
154C2×D44C22×C411yescharacteristic
155C2×C4×D11—21no—
156C2×C4×D11—21no—
157C2×C4×D11—21no—
158C2×Dic22C22×C411yescharacteristic
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—81no—
164C11×C4⋊C4—21no—
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⋊C4C22×C411yescharacteristic
172C11×C4⋊C4C22×C411yescharacteristic
173C11×C22⋊C4—21no—
174C11×C22⋊C4—21no—
175C42×C11—21no—
176C42×C11—21no—
177C42×C11C22×C411yescharacteristic
178C42×C11C2×D411yescharacteristic
179C42×C11#4111yescharacteristic
180C42×C11C2411yescharacteristic
181C22⋊Dic11—21no—
182#4326—22no—
183#4326—22no—
184#4325—22no—
185#4325—22no—
186(C2×D11)⋊C4—21no—
187(C2×D11)⋊C4—21no—
188C4⋊Dic11C22×C411yescharacteristic
189C4⋊Dic11C22×C411yescharacteristic
190Dic11⋊C4—21no—
191Dic11⋊C4—21no—
192C4×Dic11—21no—
193C4×Dic11—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
205C8×D11—81no—
206C8×D11—81no—
207#3107—111no—
208#2988—111no—
209#2985—111no—
210#1587—111no—
211#1585—111no—
212#1584—111no—
213#1582—111no—
214#1579—111no—
215SD16⋊C8—111no—
216C8×Q16—111no—
217C8×SD16—111no—
218#1573—111no—
219#1488—111no—
220#1481D1111yescharacteristic, complemented
221#1454—111no—
222C23×C11C4×D411yescharacteristic
223C22×D11—21no—
224Q8×C11—21no—
225Q8×C11—21no—
226Q8×C11—21no—
227Q8×C11—21no—
228Q8×C11—81no—
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×C11C4×D411yescharacteristic
239C2×C4×C11C4×D411yescharacteristic
240C2×C4×C11C4×D411yescharacteristic
241C2×C4×C11C23×C411yescharacteristic
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C22⋊D11—24no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248D44—21no—
249D44#13112yes—
250C4×D11—24no—
251C4×D11—41no—
252C4×D11—41no—
253C4×D11—81no—
254Dic22—21no—
255Dic22#13112yes—
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#533C2×D1111yescharacteristic
271C4×#41—111no—
272#485—111no—
273#485—111no—
274#475—111no—
275#474—111no—
276#462—111no—
277#461—111no—
278#452—111no—
279#452—111no—
280#446—111no—
281#446—111no—
282#446—221no—
283#446—221no—
284C8×Q8—111no—
285C8×Q8—111no—
286C8×Q8—111no—
287C8×Q8—111no—
288C4×Q16—111no—
289C4×Q16—111no—
290C4×SD16—111no—
291C4×SD16—111no—
292C8×D4—111no—
293C8×D4—111no—
294C8×D4—221no—
295C8×D4—221no—
296#433—221no—
297#433—221no—
298#432—111no—
299#431—111no—
300#431—111no—
301#431—221no—
302#431C2×D1111yescharacteristic
303C2×C4⋊C8—221no—
304C2×C4⋊C8C2×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—22no—
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×C11C2×#13111yescharacteristic
337C4×C11C2×#13111yescharacteristic
338C4×C11#57711yescharacteristic
339C4×C11#57811yescharacteristic
340Dic11—22no—
341Dic11—41no—
342Dic11—41no—
343C2×#41—111no—
344C2×Q16—111no—
345C2×Q16—111no—
346C2×SD16—111no—
347C2×SD16—111no—
348C22×C8—21no—
349C22×C8—221no—
350C22×C8—221no—
351C4⋊Q8C4×D1111yescharacteristic
352C4⋊Q8C4×D1111yescharacteristic
353#125—21no—
354C22⋊Q8—21no—
355C22⋊Q8C4×D1111yescharacteristic
356C22⋊Q8C4×D1111yescharacteristic
357C4×Q8—21no—
358C4×Q8—111no—
359C4×Q8—111no—
360C4×Q8C22×D1111yescharacteristic
361C4×Q8C22×D1111yescharacteristic
362C4×D4—111no—
363C4×D4—111no—
364C4×D4—221no—
365C4×D4—221no—
366#117—21no—
367#117—111no—
368#117—221no—
369C2×C42—221no—
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—
410C4×C8—111no—
411C4×C8—111no—
412C4×C8—111no—
413C4×C8—111no—
414C4×C8—221no—
415C4×C8—221no—
416C4×C8—221no—
417C4×C8—221no—
418C4×C8C22×D1111yescharacteristic
419C4×C8C22×D1111yescharacteristic
420C2×C11—41no—
421C2×C11#292911yescharacteristic
422C2×C11#294711yescharacteristic
423C2×C11#295711yescharacteristic
424D11—42no—
425#41—222no—
426#41—222no—
427C2×Q8—21no—
428C2×Q8—111no—
429C2×Q8C2×C4×D1111yescharacteristic
430C2×Q8C2×C4×D1111yescharacteristic
431C2×D4—111no—
432C2×D4—221no—
433C22×C4—221no—
434C22×C4—221no—
435C22×C4—221no—
436C22×C4C2×C4×D1111yescharacteristic
437C22×C4D4×D1111yescharacteristic
438C22×C4#434111yescharacteristic
439Q16—222no—
440Q16—222no—
441SD16—222no—
442SD16—222no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—81no—
448C2×C8—111no—
449C2×C8—111no—
450C2×C8—111no—
451C2×C8—111no—
452C2×C8—111no—
453C2×C8—111no—
454C2×C8—111no—
455C2×C8—111no—
456C2×C8—221no—
457C2×C8—221no—
458C2×C8—881no—
459C2×C8—881no—
460C4⋊C4—21no—
461C4⋊C4—21no—
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⋊C4C2×C4×D1111yescharacteristic
472C4⋊C4C2×C4×D1111yescharacteristic
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—221no—
476C22⋊C4—221no—
477C22⋊C4—221no—
478C42—21no—
479C42—21no—
480C42—221no—
481C42—221no—
482C42—221no—
483C42C2×C4×D1111yescharacteristic
484C42D4×D1111yescharacteristic
485C42#434111yescharacteristic
486C42C23×D1111yescharacteristic
487C11#1792111yescharacteristic, complemented, Sylow
488C23—221no—
489C23(C22⋊D11)⋊C411yescharacteristic
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—81no—
495Q8—112no—
496Q8—221no—
497D4—112no—
498D4—224no—
499D4—221no—
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—224no—
510C2×C4—221no—
511C2×C4—221no—
512C2×C4—221no—
513C2×C4—441no—
514C2×C4—441no—
515C2×C4—881no—
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—222no—
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—222no—
552C4—441no—
553C4—441no—
554C4D11×#13111yescharacteristic
555C4D11×#13111yescharacteristic
556C4#1062329311yescharacteristic
557C4#1062329711yescharacteristic
558C2—41no—
559C2—442no—
560C2#1307731311yescharacteristic
561C2#1307745311yescharacteristic
562C2#1307752911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1481C2
socleC22×C11C2×C4×D4
prime radicalC2×#4339C2×C4
cosocleC42×C11C24
hypercenter#1481D11
hypocenterC11#17921
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1481

Complements

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

NH ≅ G/Ntype
3. #13077711C2semidirect
4. #13067490C2semidirect
5. #13067476C2semidirect
6. #13067469C2semidirect
7. #13067455C2semidirect
8. #13067432C2semidirect
9. #13067431C2semidirect
10. #13067420C2semidirect
11. #13067413C2semidirect
12. #13067399C2semidirect
14. #13066916C2semidirect
15. C11×#1481C2semidirect
220. #1481D11semidirect
487. C11#17921semidirect

Maximal subgroups

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

subgroupindex
#130786812
#130777252
#130777112
#130674902
#130674762
#130674692
#130674552
#130674322
#130674312
#130674202
#130674132
#130673992
#130670512
#130669162
C11×#14812
#1792111