Finite Group Databasebeta

← #14725825

Subgroups — #14725825

Order 2816.

598 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079182C211yesmaximal, characteristic
2#13077779C211yesmaximal, characteristic, complemented
3#13077771C211yesmaximal, characteristic, complemented
4#13067527C211yesmaximal, characteristic, complemented
5#13067523C211yesmaximal, characteristic, complemented
6#13067460C211yesmaximal, characteristic, complemented
7#13067458C211yesmaximal, characteristic, complemented
8#13067454C211yesmaximal, characteristic, complemented
9#13067438C211yesmaximal, characteristic, complemented
10#13067432C211yesmaximal, characteristic, complemented
11D11×#334C211yesmaximal, characteristic, complemented
12#13067028C211yesmaximal, characteristic, complemented
13#13067026C211yesmaximal, characteristic, complemented
14#13066904C211yesmaximal, characteristic, complemented
15C11×#1582C211yesmaximal, characteristic, complemented
16#10623111C2211yescharacteristic
17#10623088C2211yescharacteristic
18C11×#446C2211yescharacteristic
19C4×C11×SD16C2211yescharacteristic
20C8×D4×C11C2211yescharacteristic
21#10622784C411yescharacteristic
22#10622781C411yescharacteristic
23C8×C22⋊D11—21no—
24#10622715—21no—
25C4×#4326C2211yescharacteristic
26Q8×C11⋊C8C2211yescharacteristic
27C4×#4323C2211yescharacteristic
28#10622625C2211yescharacteristic
29#10622477C411yescharacteristic
30#10622471C411yescharacteristic
31#10622452—21no—
32#10622451C2211yescharacteristic
33#10622447—21no—
34D11×C4⋊C8C2211yescharacteristic
35D11×C4⋊C8C2211yescharacteristic
36#10622443C2211yescharacteristic
37#10622426C411yescharacteristic
38#10622413C411yescharacteristic
39#10622388C411yescharacteristic
40#10622381C411yescharacteristic
41#10622341—21no—
42#10622333—21no—
43#10622322—21no—
44#10622319—21no—
45C4×#4314C2211yescharacteristic
46C4×#4313C2211yescharacteristic
47C8×D44C2211yescharacteristic
48#10622298C2211yescharacteristic
49C4×C8×D11C2211yescharacteristic
50#10622292C2211yescharacteristic
51C11×#334C2211yescharacteristic
52C11×Q8⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic
54C11×#322C2211yescharacteristic
55Q8⋊(C11⋊C8)C2211yescharacteristic
56D4⋊(C11⋊C8)C2211yescharacteristic
57#10622122C2211yescharacteristic
58#10622121C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622118C2211yescharacteristic
61#10622097C2211yescharacteristic
62#10622095C2211yescharacteristic
63#10622094C2211yescharacteristic
64#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66#10622092C2211yescharacteristic
67C2×C11×SD16C2×C411yescharacteristic
68C22×C8×C11—21no—
69C4×Q8×C11C2311yescharacteristic
70C4×D4×C11C2311yescharacteristic
71#67000C2×C411yescharacteristic
72#66999C2×C411yescharacteristic
73C2×#4326C2×C411yescharacteristic
74#66991C2×C411yescharacteristic
75#66989C2×C411yescharacteristic
76C2×#4323C2×C411yescharacteristic
77C4×C22⋊D11—21no—
78#66979—21no—
79C2×#4318—21no—
80C2×#4314C2×C411yescharacteristic
81C2×#4313—21no—
82C2×#4313—21no—
83C2×C8×D11—21no—
84C2×C8×D11—21no—
85C2×C8×D11—21no—
86C2×C8×D11C2×C411yescharacteristic
87C2×C8×D11C2×C411yescharacteristic
88#66951—21no—
89#66950C2×C411yescharacteristic
90#66948C2×C411yescharacteristic
91#66947—21no—
92#66943C2×C411yescharacteristic
93#66943C2×C411yescharacteristic
94#66936—21no—
95#66932—21no—
96C4×D44—21no—
97C4×D44C2311yescharacteristic
98#66925—21no—
99C42×D11C2311yescharacteristic
100C4×Dic22C2311yescharacteristic
101C11×#106C2×C411yescharacteristic
102C11×C4⋊C8—21no—
103C11×C4⋊C8C2311yescharacteristic
104C11×C4⋊C8C2311yescharacteristic
105C11×#103C2×C411yescharacteristic
106C11×#102C2×C411yescharacteristic
107C11×C22⋊C8—21no—
108C11×#97—21no—
109C4×C8×C11C2311yescharacteristic
110C4×C8×C11C2311yescharacteristic
111C4×C8×C11C2311yescharacteristic
112#66899C2×C411yescharacteristic
113#66896C2×C411yescharacteristic
114C22⋊(C11⋊C8)—21no—
115#66885C2×C411yescharacteristic
116(C2×D11)⋊C8—21no—
117(C2×D11)⋊C8—21no—
118(C2×D11)⋊C8D411yescharacteristic
119(C2×D11)⋊C8D411yescharacteristic
120#66881C2×C411yescharacteristic
121#66880C2×C411yescharacteristic
122#66879—21no—
123#66879—21no—
124Dic11⋊C8—21no—
125Dic11⋊C8—21no—
126Dic11⋊C8—21no—
127Dic11⋊C8—21no—
128Dic11⋊C8D411yescharacteristic
129Dic11⋊C8D411yescharacteristic
130C8×Dic11—21no—
131C8×Dic11C2×C411yescharacteristic
132C8×Dic11C2×C411yescharacteristic
133#66874C2×C411yescharacteristic
134#66873C2×C411yescharacteristic
135#66871C2×C411yescharacteristic
136#66871C2×C411yescharacteristic
137C4⋊(C11⋊C8)—21no—
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4×C11⋊C8—21no—
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#18093—111nomaximal, Sylow
145C2×Q8×C11C22×C411yescharacteristic
146C2×D4×C11C22×C411yescharacteristic
147C22×C4×C11—21no—
148C2×C22⋊D11—21no—
149C2×D44—21no—
150C2×D44C22×C411yescharacteristic
151C2×C4×D11—21no—
152C2×C4×D11C22×C411yescharacteristic
153C2×C4×D11C2×D411yescharacteristic
154C2×C4×D11#4111yescharacteristic
155C2×Dic22C22×C411yescharacteristic
156C11×SD16—41no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—81no—
161C2×C8×C11C22×C411yescharacteristic
162C2×C8×C11C22×C411yescharacteristic
163C2×C8×C11C2×D411yescharacteristic
164C2×C8×C11C2×D411yescharacteristic
165C11×C4⋊C4—21no—
166C11×C4⋊C4C22×C411yescharacteristic
167C11×C4⋊C4C22×C411yescharacteristic
168C11×C22⋊C4—21no—
169C42×C11—21no—
170C42×C11C2411yescharacteristic
171C22⋊Dic11—21no—
172C22⋊Dic11—21no—
173C22⋊Dic11—21no—
174#4326—22no—
175#4323—22no—
176(C2×D11)⋊C4—21no—
177(C2×D11)⋊C4—21no—
178(C2×D11)⋊C4—21no—
179(C2×D11)⋊C4—21no—
180(C2×D11)⋊C4—21no—
181(C2×D11)⋊C4—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11C22×C411yescharacteristic
186C4⋊Dic11C22×C411yescharacteristic
187Dic11⋊C4—21no—
188Dic11⋊C4—21no—
189Dic11⋊C4—21no—
190Dic11⋊C4—21no—
191C4×Dic11—21no—
192C4×Dic11C22×C411yescharacteristic
193C4×Dic11C2×D411yescharacteristic
194C4×Dic11#4111yescharacteristic
195#4318—81no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8C22×C411yescharacteristic
200C2×C11⋊C8C22×C411yescharacteristic
201C2×C11⋊C8C2×D411yescharacteristic
202C2×C11⋊C8C2×D411yescharacteristic
203#4314—41no—
204#4313—42no—
205#4313—81no—
206C8×D11—22no—
207C8×D11—41no—
208C8×D11—81no—
209C8×D11—81no—
210C8×D11—81no—
211#3168—111no—
212#2994—111no—
213#2994—111no—
214#1594—111no—
215#1593—111no—
216#1583—111no—
217#1583—111no—
218#1582—111no—
219#1582D1111yescharacteristic, complemented
220#1580—111no—
221#1579—111no—
222C2×#334—111no—
223#1483—111no—
224#1483—111no—
225#1451—111no—
226C23×C11—21no—
227C22×D11—21no—
228C22×D11C4×D411yescharacteristic
229Q8×C11—21no—
230Q8×C11—21no—
231D4×C11—21no—
232D4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11C23×C411yescharacteristic
239C2×C4×C11C22×D411yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C22⋊D11—42no—
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11C4×D411yescharacteristic
246C2×Dic11C4×D411yescharacteristic
247C2×Dic11C4×D411yescharacteristic
248D44—21no—
249D44—21no—
250D44—42no—
251C4×D11—22no—
252C4×D11—21no—
253C4×D11—21no—
254C4×D11—21no—
255C4×D11—21no—
256C4×D11—41no—
257C4×D11—41no—
258Dic22—21no—
259Dic22—21no—
260C8×C11—21no—
261C8×C11—21no—
262C8×C11—21no—
263C8×C11—21no—
264C8×C11—41no—
265C8×C11—41no—
266C8×C11—41no—
267C11⋊C8—21no—
268C11⋊C8—21no—
269C11⋊C8—21no—
270C11⋊C8—41no—
271C11⋊C8—41no—
272C11⋊C8—41no—
273C11⋊C8#13112yes—
274#529—111no—
275#529—111no—
276#499—111no—
277#495—111no—
278#488—111no—
279#488—111no—
280#467—111no—
281#466—111no—
282#465—111no—
283#465—111no—
284#446—111no—
285#446C2×D1111yescharacteristic
286C8×Q8—111no—
287C8×Q8—111no—
288C4×Q16—111no—
289C4×SD16—111no—
290C4×SD16C2×D1111yescharacteristic
291C4×D8—111no—
292#436—111no—
293#436—111no—
294#435—221no—
295#435—221no—
296C8×D4—111no—
297C8×D4—221no—
298C8×D4—221no—
299C8×D4C2×D1111yescharacteristic
300#433—221no—
301#433—221no—
302#431—111no—
303#424—221no—
304#424—221no—
305C2×C4⋊C8—111no—
306C2×C4⋊C8—111no—
307C4×M16—111no—
308C2×C4×C8—111no—
309#334—111no—
310#334—111no—
311#334—111no—
312#334C2×D1111yescharacteristic
313Q8⋊C8—111no—
314Q8⋊C8—111no—
315Q8⋊C8—111no—
316Q8⋊C8C2×D1111yescharacteristic
317D4⋊C8—111no—
318D4⋊C8—111no—
319D4⋊C8—111no—
320D4⋊C8C2×D1111yescharacteristic
321#322—111no—
322#322—111no—
323#322—111no—
324#322C2×D1111yescharacteristic
325C22×C11—41no—
326C22×C11—41no—
327C22×C11—41no—
328C22×C11C2×C4×D411yescharacteristic
329C2×D11—21no—
330C2×D11—21no—
331C2×D11—41no—
332C2×D11—41no—
333C2×D11—41no—
334C2×D11#44412yes—
335C4×C11—21no—
336C4×C11—41no—
337C4×C11—41no—
338C4×C11—41no—
339C4×C11C2×#13111yescharacteristic
340C4×C11#56811yescharacteristic
341C4×C11#57711yescharacteristic
342C4×C11#57711yescharacteristic
343Dic11—21no—
344Dic11—21no—
345Dic11—21no—
346Dic11—41no—
347Dic11—41no—
348Dic11—41no—
349C2×Q16—111no—
350C2×SD16—111no—
351C2×SD16C4×D1111yescharacteristic
352C2×D8—111no—
353C2×M16—221no—
354C2×M16—221no—
355C2×M16—221no—
356C22×C8—21no—
357C22×C8—111no—
358C22×C8—111no—
359C22×C8—221no—
360C22×C8—221no—
361C22×C8—221no—
362#126—221no—
363#126—221no—
364#125—111no—
365#125—111no—
366#124—111no—
367#124—111no—
368#123—221no—
369#123—221no—
370C22⋊Q8—111no—
371C22⋊Q8—111no—
372#121—111no—
373#121—111no—
374C4×Q8—111no—
375C4×Q8C22×D1111yescharacteristic
376C4×D4—111no—
377C4×D4—221no—
378C4×D4—221no—
379C4×D4C22×D1111yescharacteristic
380#117—221no—
381#117—221no—
382C2×C42—111no—
383#107—111no—
384#107—111no—
385#106—111no—
386#106C4×D1111yescharacteristic
387C4⋊C8—21no—
388C4⋊C8—111no—
389C4⋊C8—111no—
390C4⋊C8—111no—
391C4⋊C8—111no—
392C4⋊C8—221no—
393C4⋊C8—221no—
394C4⋊C8—221no—
395C4⋊C8—221no—
396C4⋊C8—221no—
397C4⋊C8C22×D1111yescharacteristic
398C4⋊C8C22×D1111yescharacteristic
399#103—111no—
400#103—111no—
401#103—111no—
402#103C4×D1111yescharacteristic
403#102—111no—
404#102—111no—
405#102—111no—
406#102C4×D1111yescharacteristic
407C22⋊C8—21no—
408C22⋊C8—111no—
409C22⋊C8—111no—
410C22⋊C8—221no—
411C22⋊C8—221no—
412C22⋊C8—221no—
413#97—21no—
414#97—221no—
415#97—221no—
416C4×C8—111no—
417C4×C8—111no—
418C4×C8—111no—
419C4×C8—111no—
420C4×C8—111no—
421C4×C8—221no—
422C4×C8—221no—
423C4×C8C22×D1111yescharacteristic
424C4×C8C22×D1111yescharacteristic
425C4×C8C22×D1111yescharacteristic
426C2×C11—81no—
427C2×C11#293511yescharacteristic
428C2×C11#295211yescharacteristic
429C2×C11C2×#44411yescharacteristic
430D11—22no—
431D11—81no—
432C2×Q8—111no—
433C2×Q8C2×C4×D1111yescharacteristic
434C2×D4—111no—
435C2×D4—221no—
436C2×D4—221no—
437C2×D4C2×C4×D1111yescharacteristic
438C22×C4—21no—
439C22×C4—111no—
440C22×C4—111no—
441C22×C4—111no—
442C22×C4—221no—
443Q16—222no—
444SD16—41no—
445SD16—441no—
446D8—222no—
447M16—442no—
448M16—881no—
449M16—881no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—81no—
454C2×C8—111no—
455C2×C8—111no—
456C2×C8—111no—
457C2×C8—111no—
458C2×C8—222no—
459C2×C8—221no—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—441no—
463C2×C8—881no—
464C2×C8—881no—
465C2×C8—881no—
466C2×C8C2×C4×D1111yescharacteristic
467C2×C8C2×C4×D1111yescharacteristic
468C2×C8D4×D1111yescharacteristic
469C2×C8D4×D1111yescharacteristic
470C4⋊C4—21no—
471C4⋊C4—111no—
472C4⋊C4—111no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4C2×C4×D1111yescharacteristic
481C4⋊C4C2×C4×D1111yescharacteristic
482C22⋊C4—21no—
483C22⋊C4—221no—
484C22⋊C4—221no—
485C22⋊C4—221no—
486C22⋊C4—221no—
487C22⋊C4—221no—
488C22⋊C4—221no—
489C22⋊C4—221no—
490C22⋊C4—221no—
491C22⋊C4—221no—
492C42—21no—
493C42—111no—
494C42—111no—
495C42—111no—
496C42—221no—
497C42C23×D1111yescharacteristic
498C11#1809311yescharacteristic, complemented, Sylow
499C23—21no—
500C23—111no—
501C23—221no—
502Q8—21no—
503Q8—21no—
504Q8—221no—
505Q8—221no—
506D4—21no—
507D4—21no—
508D4—221no—
509D4—221no—
510D4—442no—
511D4—442no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—111no—
518C2×C4—111no—
519C2×C4—111no—
520C2×C4—222no—
521C2×C4—221no—
522C2×C4—221no—
523C2×C4—221no—
524C2×C4—221no—
525C2×C4—221no—
526C2×C4—221no—
527C2×C4—221no—
528C2×C4—441no—
529C2×C4—441no—
530C2×C4C22×C4×D1111yescharacteristic
531C2×C4C2×D4×D1111yescharacteristic
532C2×C4#41×D1111yescharacteristic
533C8—21no—
534C8—21no—
535C8—21no—
536C8—21no—
537C8—41no—
538C8—41no—
539C8—41no—
540C8—112no—
541C8—221no—
542C8—221no—
543C8—221no—
544C8—441no—
545C8—441no—
546C8—441no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—112no—
551C22—221no—
552C22—221no—
553C22—441no—
554C22—441no—
555C22—441no—
556C22C4×D4×D1111yescharacteristic
557C4—21no—
558C4—41no—
559C4—41no—
560C4—41no—
561C4—221no—
562C4—221no—
563C4—221no—
564C4—441no—
565C4—441no—
566C4—441no—
567C4#1062327611yescharacteristic
568C4D11×#13111yescharacteristic
569C4#1062329311yescharacteristic
570C4#1062330111yescharacteristic
571C2—81no—
572C2—222no—
573C2—881no—
574C2#1307735711yescharacteristic
575C2#1307749411yescharacteristic
576C2D11×#44411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1582C2
socleC22×C11C2×C4×D4
prime radical#10622388C4
cosocleC42×C11C24
hypercenter#1582D11
hypocenterC11#18093
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1582

Complements

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

NH ≅ G/Ntype
2. #13077779C2semidirect
3. #13077771C2semidirect
4. #13067527C2semidirect
5. #13067523C2semidirect
6. #13067460C2semidirect
7. #13067458C2semidirect
8. #13067454C2semidirect
9. #13067438C2semidirect
10. #13067432C2semidirect
11. D11×#334C2semidirect
12. #13067028C2semidirect
13. #13067026C2semidirect
14. #13066904C2semidirect
15. C11×#1582C2semidirect
219. #1582D11semidirect
498. C11#18093semidirect

Maximal subgroups

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

subgroupindex
#130791822
#130777792
#130777712
#130675272
#130675232
#130674602
#130674582
#130674542
#130674382
#130674322
D11×#3342
#130670282
#130670262
#130669042
C11×#15822
#1809311