Finite Group Databasebeta

← #14725648

Subgroups — #14725648

Order 2816.

588 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#13079223C211yesmaximal, characteristic
2#13077621C211yesmaximal, characteristic
3#13077559C211yesmaximal, characteristic, complemented
4#13067515C211yesmaximal, characteristic, complemented
5#13067510C211yesmaximal, characteristic, complemented
6#13067497C211yesmaximal, characteristic, complemented
7#13067484C211yesmaximal, characteristic, complemented
8#13067469C211yesmaximal, characteristic, complemented
9#13067449C211yesmaximal, characteristic, complemented
10#13067432C211yesmaximal, characteristic, complemented
11#13067419C211yesmaximal, characteristic, complemented
12#13067366C211yesmaximal, characteristic, complemented
13#13067038C211yesmaximal, characteristic, complemented
14#13066919C211yesmaximal, characteristic, complemented
15C11×#1483C211yesmaximal, characteristic
16C11×#529C2211yescharacteristic
17#10623001C2211yescharacteristic
18C2×C11×C4⋊C8C2211yescharacteristic
19C4×C11×M16C2211yescharacteristic
20#10622715—21no—
21#10622714—21no—
22#10622682C411yescharacteristic
23#10622678C411yescharacteristic
24#10622673C411yescharacteristic
25#10622668C411yescharacteristic
26#10622665C411yescharacteristic
27#10622665C411yescharacteristic
28#10622655C411yescharacteristic
29#10622655C411yescharacteristic
30C4×#4326C2211yescharacteristic
31C4×#4326C2211yescharacteristic
32#10622637C2211yescharacteristic
33Q8×C11⋊C8C2211yescharacteristic
34C4×#4324C2211yescharacteristic
35C4×#4324C2211yescharacteristic
36#10622625—21no—
37#10622625C2211yescharacteristic
38#10622624—21no—
39D4×C11⋊C8C2211yescharacteristic
40#10622613—21no—
41#10622610—21no—
42#10622538C2211yescharacteristic
43C4×#4318C2211yescharacteristic
44C4×#4318C2211yescharacteristic
45#10622444C2211yescharacteristic
46#10622444C2211yescharacteristic
47#10622443C2211yescharacteristic
48#10622443C2211yescharacteristic
49#10622441—21no—
50#10622441—21no—
51C11×Q8⋊C8C2211yescharacteristic
52C11×Q8⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic
54C11×D4⋊C8C2211yescharacteristic
55#10622118C2211yescharacteristic
56#10622118C2211yescharacteristic
57#10622117C2211yescharacteristic
58#10622117C2211yescharacteristic
59#10622094C2211yescharacteristic
60#10622094C2211yescharacteristic
61#10622094C2211yescharacteristic
62#10622094C2211yescharacteristic
63#10622093C2211yescharacteristic
64#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×C11×M16—21no—
68C22×C8×C11—21no—
69C11×#126—21no—
70C11×#125C2×C411yescharacteristic
71C11×#124C2×C411yescharacteristic
72C11×#123—21no—
73C11×C22⋊Q8C2×C411yescharacteristic
74C11×#121C2×C411yescharacteristic
75C4×Q8×C11C2311yescharacteristic
76C4×D4×C11—21no—
77C4×D4×C11C2311yescharacteristic
78C11×#117—21no—
79C2×C42×C11C2311yescharacteristic
80C2×#4326C2×C411yescharacteristic
81C2×#4326C2×C411yescharacteristic
82C2×#4324C2×C411yescharacteristic
83C2×#4324C2×C411yescharacteristic
84#66979—21no—
85#66977—21no—
86#66977C2×C411yescharacteristic
87#66977C2×C411yescharacteristic
88C2×#4318—21no—
89C2×#4318C2×C411yescharacteristic
90C2×#4318C2×C411yescharacteristic
91C2×#4318D411yescharacteristic
92C2×#4318D411yescharacteristic
93C22×C11⋊C8—21no—
94#66923—21no—
95#66922C2×C411yescharacteristic
96#66922C2×C411yescharacteristic
97C4×Dic22—21no—
98C4×Dic22C2311yescharacteristic
99C4×Dic22C2311yescharacteristic
100C11×C4⋊C8—21no—
101C11×C4⋊C8C2311yescharacteristic
102C11×C4⋊C8C2311yescharacteristic
103C11×#97—21no—
104C4×C8×C11C2311yescharacteristic
105C4×C8×C11C2311yescharacteristic
106#66899C2×C411yescharacteristic
107#66899C2×C411yescharacteristic
108#66896C2×C411yescharacteristic
109#66896C2×C411yescharacteristic
110C22⋊(C11⋊C8)—21no—
111C22⋊(C11⋊C8)—21no—
112C22⋊(C11⋊C8)—21no—
113#66879—21no—
114#66879—21no—
115Dic11⋊C8—21no—
116Dic11⋊C8—21no—
117Dic11⋊C8—21no—
118Dic11⋊C8—21no—
119C8×Dic11—21no—
120C8×Dic11—21no—
121#66874C2×C411yescharacteristic
122#66874C2×C411yescharacteristic
123#66874C2×C411yescharacteristic
124#66874C2×C411yescharacteristic
125#66872C2×C411yescharacteristic
126#66872C2×C411yescharacteristic
127#66871C2×C411yescharacteristic
128#66871C2×C411yescharacteristic
129C4⋊(C11⋊C8)—21no—
130C4⋊(C11⋊C8)—21no—
131C4⋊(C11⋊C8)C2311yescharacteristic
132C4⋊(C11⋊C8)C2311yescharacteristic
133#66867—21no—
134#66867C2×C411yescharacteristic
135#66867C2×C411yescharacteristic
136#66867D411yescharacteristic
137#66867D411yescharacteristic
138C4×C11⋊C8—21no—
139C4×C11⋊C8—21no—
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#18077—111nomaximal, Sylow
145C2×Q8×C11C22×C411yescharacteristic
146C2×D4×C11—21no—
147C2×D4×C11C22×C411yescharacteristic
148C22×C4×C11—21no—
149C22×C4×C11C22×C411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11#4111yescharacteristic
152C2×Dic22—21no—
153C2×Dic22C22×C411yescharacteristic
154C2×Dic22C22×C411yescharacteristic
155C11×M16—42no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—42no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4C22×C411yescharacteristic
166C11×C4⋊C4C22×C411yescharacteristic
167C11×C22⋊C4—21no—
168C11×C22⋊C4—21no—
169C11×C22⋊C4—21no—
170C11×C22⋊C4—21no—
171C11×C22⋊C4—21no—
172C42×C11—21no—
173C42×C11C22×C411yescharacteristic
174C42×C11C2×D411yescharacteristic
175C42×C11#4111yescharacteristic
176C42×C11C2411yescharacteristic
177C22⋊Dic11—21no—
178C22⋊Dic11—21no—
179#4326—22no—
180#4326—41no—
181#4324—22no—
182#4324—41no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11C22×C411yescharacteristic
187C4⋊Dic11C22×C411yescharacteristic
188Dic11⋊C4—21no—
189Dic11⋊C4—21no—
190Dic11⋊C4—21no—
191Dic11⋊C4—21no—
192C4×Dic11—21no—
193C4×Dic11—21no—
194#4318—22no—
195#4318—22no—
196#4318—41no—
197#4318—41no—
198#4318—42no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—42no—
202C2×C11⋊C8C22×C411yescharacteristic
203C2×C11⋊C8C22×C411yescharacteristic
204C2×C11⋊C8C22×C411yescharacteristic
205C2×C11⋊C8C22×C411yescharacteristic
206C2×C11⋊C8C2×D411yescharacteristic
207C2×C11⋊C8C2×D411yescharacteristic
208C2×C11⋊C8C2×D411yescharacteristic
209C2×C11⋊C8C2×D411yescharacteristic
210#3172—111no—
211#2969—111no—
212#2962—111no—
213#1592—111no—
214#1591—111no—
215#1588—111no—
216#1587—111no—
217#1584—111no—
218#1582—111no—
219#1579—111no—
220C8×SD16—111no—
221#1565—111no—
222#1485—111no—
223#1483D1111yescharacteristic
224#1455—111no—
225C23×C11—21no—
226C23×C11C4×D411yescharacteristic
227Q8×C11—21no—
228Q8×C11—21no—
229D4×C11—21no—
230D4×C11—21no—
231D4×C11—81no—
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—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11C4×D411yescharacteristic
243C2×C4×C11C4×D411yescharacteristic
244C2×C4×C11C4×D411yescharacteristic
245C2×C4×C11C23×C411yescharacteristic
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252Dic22—21no—
253Dic22—21no—
254Dic22—21no—
255Dic22—21no—
256Dic22—81no—
257C8×C11—22no—
258C8×C11—41no—
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—41no—
268C11⋊C8—41no—
269C11⋊C8#13112yes—
270C11⋊C8#13712yes—
271#533—111no—
272#529C2×D1111yescharacteristic
273#501—111no—
274#497—111no—
275#491—111no—
276#489—111no—
277#470—111no—
278#470—111no—
279#468—111no—
280#468—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#436—221no—
295#435—221no—
296C8×D4—111no—
297#433—221no—
298#431—111no—
299#424—221no—
300C2×C4⋊C8C2×D1111yescharacteristic
301#405—221no—
302#405—221no—
303C4×M16—111no—
304C4×M16—111no—
305C4×M16C2×D1111yescharacteristic
306#335—111no—
307#335—111no—
308#334—111no—
309#334—111no—
310Q8⋊C8—111no—
311Q8⋊C8—111no—
312Q8⋊C8—111no—
313Q8⋊C8—111no—
314Q8⋊C8C2×D1111yescharacteristic
315Q8⋊C8C2×D1111yescharacteristic
316D4⋊C8C2×D1111yescharacteristic
317D4⋊C8C2×D1111yescharacteristic
318#322—111no—
319#322—111no—
320#322—111no—
321C82—111no—
322C22×C11—21no—
323C22×C11—21no—
324C22×C11—21no—
325C22×C11—41no—
326C22×C11—41no—
327C22×C11—41no—
328C22×C11C2×C4×D411yescharacteristic
329C4×C11—21no—
330C4×C11—21no—
331C4×C11—21no—
332C4×C11—21no—
333C4×C11—41no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11C2×#13111yescharacteristic
337C4×C11#56811yescharacteristic
338C4×C11C2×#13711yescharacteristic
339C4×C11#57511yescharacteristic
340Dic11—41no—
341Dic11—41no—
342Dic11—41no—
343Dic11—41no—
344C2×Q16—111no—
345C2×Q16—111no—
346C2×SD16—111no—
347C2×SD16—111no—
348C2×M16—21no—
349C2×M16—111no—
350C2×M16—111no—
351C2×M16—111no—
352C2×M16—111no—
353C2×M16—221no—
354C22×C8—21no—
355C22×C8—221no—
356C4⋊Q8—111no—
357C4⋊Q8—111no—
358#126—21no—
359#125—221no—
360#125C4×D1111yescharacteristic
361#124C4×D1111yescharacteristic
362#123—21no—
363C22⋊Q8—111no—
364C22⋊Q8—111no—
365C22⋊Q8—221no—
366C22⋊Q8C4×D1111yescharacteristic
367#121C4×D1111yescharacteristic
368C4×Q8—111no—
369C4×Q8—111no—
370C4×Q8—221no—
371C4×Q8C22×D1111yescharacteristic
372C4×D4—21no—
373C4×D4C22×D1111yescharacteristic
374#117—21no—
375#117—221no—
376C2×C42C22×D1111yescharacteristic
377#107—111no—
378#107—111no—
379#106—111no—
380#106—111no—
381C4⋊C8—21no—
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—221no—
401C22⋊C8—221no—
402C22⋊C8—221no—
403#97—21no—
404#97—111no—
405#97—111no—
406#97—111no—
407#97—111no—
408#97—221no—
409#97—221no—
410#97—221no—
411C4×C8—111no—
412C4×C8—111no—
413C4×C8—111no—
414C4×C8—111no—
415C4×C8—221no—
416C4×C8—221no—
417C4×C8—221no—
418C4×C8—221no—
419C4×C8C22×D1111yescharacteristic
420C4×C8C22×D1111yescharacteristic
421C2×C11—41no—
422C2×C11—81no—
423C2×C11#293511yescharacteristic
424C2×C11C4×#13711yescharacteristic
425C2×C11#295611yescharacteristic
426C2×Q8—111no—
427C2×Q8—111no—
428C2×Q8—221no—
429C2×Q8C2×C4×D1111yescharacteristic
430C2×D4—21no—
431C2×D4C2×C4×D1111yescharacteristic
432C22×C4—21no—
433C22×C4C2×C4×D1111yescharacteristic
434C22×C4D4×D1111yescharacteristic
435C22×C4#434111yescharacteristic
436Q16—222no—
437Q16—441no—
438SD16—222no—
439SD16—441no—
440M16—42no—
441M16—222no—
442M16—222no—
443M16—441no—
444M16—441no—
445M16—442no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—42no—
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—442no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—111no—
467C4⋊C4—111no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4C2×C4×D1111yescharacteristic
476C4⋊C4C2×C4×D1111yescharacteristic
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—221no—
483C22⋊C4—221no—
484C42—21no—
485C42—221no—
486C42—221no—
487C42C2×C4×D1111yescharacteristic
488C42D4×D1111yescharacteristic
489C42#434111yescharacteristic
490C42C23×D1111yescharacteristic
491C11#1807711yescharacteristic, complemented, Sylow
492C23—21no—
493C23(C22⋊D11)⋊C411yescharacteristic
494Q8—21no—
495Q8—21no—
496Q8—221no—
497Q8—221no—
498Q8—221no—
499Q8—221no—
500Q8—881no—
501D4—21no—
502D4—21no—
503D4—81no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—221no—
515C2×C4—221no—
516C2×C4—221no—
517C2×C4—221no—
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—41no—
526C8—41no—
527C8—41no—
528C8—112no—
529C8—112no—
530C8—221no—
531C8—221no—
532C8—221no—
533C8—221no—
534C8—221no—
535C8—221no—
536C8—441no—
537C8—441no—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22C2×(C22⋊D11)⋊C411yescharacteristic
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—441no—
553C4—441no—
554C4—441no—
555C4—441no—
556C4D11×#13111yescharacteristic
557C4#1062328111yescharacteristic
558C4#1062330411yescharacteristic
559C4D11×#13711yescharacteristic
560C2—41no—
561C2—81no—
562C2#1307735611yescharacteristic
563C2#1307744011yescharacteristic
564C2#1307752211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1483C2
socleC22×C11C2×C4×D4
prime radicalC11×#121C2×C4
cosocleC42×C11C24
hypercenter#1483D11
hypocenterC11#18077
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1483

Complements

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

NH ≅ G/Ntype
3. #13077559C2semidirect
4. #13067515C2semidirect
5. #13067510C2semidirect
6. #13067497C2semidirect
7. #13067484C2semidirect
8. #13067469C2semidirect
9. #13067449C2semidirect
10. #13067432C2semidirect
11. #13067419C2semidirect
12. #13067366C2semidirect
13. #13067038C2semidirect
14. #13066919C2semidirect
491. C11#18077semidirect

Maximal subgroups

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

subgroupindex
#130792232
#130776212
#130775592
#130675152
#130675102
#130674972
#130674842
#130674692
#130674492
#130674322
#130674192
#130673662
#130670382
#130669192
C11×#14832
#1807711