Finite Group Databasebeta

← #14908304

Subgroups — #14908304

Order 2816.

694 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622524C211yesmaximal, characteristic, complemented
2C2×#10622514C211yesmaximal, characteristic, complemented
3#13078281C211yesmaximal, characteristic, complemented
4#13078259C211yesmaximal, characteristic, complemented
5#13070730C211yesmaximal, characteristic, complemented
6#13070727C211yesmaximal, characteristic, complemented
7#13070717C211yesmaximal, characteristic, complemented
8#13070716C211yesmaximal, characteristic, complemented
9#13070712C211yesmaximal, characteristic, complemented
10#13070711C211yesmaximal, characteristic, complemented
11#13070701C211yesmaximal, characteristic, complemented
12#13070401C211yesmaximal, characteristic, complemented
13#13070320C211yesmaximal, characteristic, complemented
14D11×#357C211yesmaximal, characteristic, complemented
15C11×#2215C211yesmaximal, characteristic, complemented
16C2×#66965C2211yescharacteristic
17C2×D8×D11C2211yescharacteristic
18C2×#66954C2211yescharacteristic
19#10623139—21no—
20#10623138—21no—
21C2×C11×D16C2211yescharacteristic
22C22×C11×C16C2211yescharacteristic, complemented
23C11×#466C2211yescharacteristic
24C11×#466C2211yescharacteristic, complemented
25#10622770C2211yescharacteristic
26#10622770C2211yescharacteristic, complemented
27C2×#66891C2211yescharacteristic
28C2×#66890C2211yescharacteristic
29#10622729C2211yescharacteristic, complemented
30#10622728C2211yescharacteristic
31C2×#66876C2211yescharacteristic, complemented
32#10622655—21no—
33#10622652—21no—
34#10622524—24no—
35C2×#66864C2211yescharacteristic
36#10622514—24no—
37C2×#66862C2211yescharacteristic
38C2×#66862C2211yescharacteristic, complemented
39C2×C16×D11C2211yescharacteristic
40C2×C16×D11C2211yescharacteristic, complemented
41#10622500C2211yescharacteristic, complemented
42#10622496C2211yescharacteristic
43#10622493C2211yescharacteristic
44D11×#107C2211yescharacteristic
45#10622395—21no—
46#10622393—21no—
47#10622384—21no—
48#10622383—21no—
49C11×#366C2211yescharacteristic, complemented
50C11×#357C2211yescharacteristic
51C11×#357C2211yescharacteristic, complemented
52#10622200C2211yescharacteristic
53#10622200C2211yescharacteristic, complemented
54#10622147C2211yescharacteristic
55#10622143C2211yescharacteristic, complemented
56#10622141C2211yescharacteristic, complemented
57#10622130C2211yescharacteristic, complemented
58#10622129C2211yescharacteristic
59#10622128C2211yescharacteristic, complemented
60#10622127C2211yescharacteristic, complemented
61C2×#4341—21no—
62C2×D4×D11—21no—
63C2×#4339D411yescharacteristic
64C2×C11×D8C2311yescharacteristic
65C2×C11×D8C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C11×#121—21no—
68C11×#121—21no—
69#66993—41no—
70#66992—41no—
71#66991—21no—
72#66991—21no—
73#66991—41no—
74#66990—41no—
75C2×#4324—21no—
76C2×#4323—21no—
77#66983—21no—
78#66977—21no—
79C2×#4318D411yescharacteristic
80#66965—22no—
81#66965—22no—
82D8×D11—22no—
83D8×D11—22no—
84C2×Dic44C2311yescharacteristic
85C2×D88C2311yescharacteristic
86#66954—22no—
87#66954—22no—
88C2×#4313D411yescharacteristic
89C2×#4313D411yescharacteristic
90C2×C8×D11C2311yescharacteristic
91C2×C8×D11C2311yescharacteristic
92#66950—21no—
93#66948—21no—
94#66945—21no—
95C4⋊C4×D11—21no—
96#66938—41no—
97#66937—41no—
98#66935—41no—
99#66931—41no—
100C11×D16—22no—
101C2×C11×C16—22no—
102C2×C11×C16C2311yescharacteristic
103C2×C11×C16C2311yescharacteristic
104C11×#107C2311yescharacteristic
105C11×#107C2311yescharacteristic
106C11×#102—21no—
107C11×#102—21no—
108#66896—21no—
109#66896—21no—
110#66891—22no—
111#66890—22no—
112#66885—21no—
113#66882C2311yescharacteristic
114#66882C2311yescharacteristic
115#66880—21no—
116#66876—22no—
117C2×C11⋊C16C2311yescharacteristic
118C2×C11⋊C16C2311yescharacteristic
119#66874—21no—
120#66873—21no—
121#66872—21no—
122#66871—21no—
123#66864—22no—
124#66862—22no—
125#66862D414yescomplemented
126C16×D11—22no—
127C16×D11—22no—
128#33612—111nomaximal, Sylow
129C23×D11—41no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—41no—
133C2×D4×C11—41no—
134C22×C4×C11C2×D411yescharacteristic
135C2×C22⋊D11—41no—
136C2×C22⋊D11—41no—
137C2×C22⋊D11—41no—
138C2×C22⋊D11—41no—
139C2×C22⋊D11—41no—
140C2×C22⋊D11D811yescharacteristic
141C2×C22⋊D11D811yescharacteristic
142C22×Dic11—41no—
143#4341—42no—
144#4341—42no—
145D4×D11—42no—
146D4×D11—42no—
147#4339—22no—
148#4339—22no—
149C2×D44—21no—
150C2×D44—41no—
151C2×D44D811yescharacteristic
152C2×C4×D11—41no—
153C2×C4×D11C2×D411yescharacteristic
154C2×C4×D11C2×D411yescharacteristic
155C2×Dic22—21no—
156C2×Dic22D811yescharacteristic
157C11×D8—21no—
158C11×D8—21no—
159C11×D8—21no—
160C11×D8—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11C2×D411yescharacteristic
164C2×C8×C11C2411yescharacteristic
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C22⋊C4—41no—
168C11×C22⋊C4—41no—
169C22⋊Dic11—41no—
170C22⋊Dic11—41no—
171C22⋊Dic11—41no—
172#4324—42no—
173#4323—42no—
174(C2×D11)⋊C4—41no—
175(C2×D11)⋊C4—41no—
176(C2×D11)⋊C4—41no—
177(C2×D11)⋊C4—41no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—41no—
181Dic11⋊C4—41no—
182Dic11⋊C4—41no—
183C4×Dic11—41no—
184#4318—22no—
185C2×C11⋊C8C2×D411yescharacteristic
186C2×C11⋊C8C2×D411yescharacteristic
187Dic44—21no—
188Dic44—21no—
189D88—21no—
190D88—21no—
191#4313—22no—
192#4313—22no—
193C8×D11—21no—
194C8×D11—21no—
195C8×D11C2×D412yes—
196C8×D11#4112yes—
197C11×C16—21no—
198C11×C16C2×D412yes—
199C11⋊C16—21no—
200C11⋊C16C2×D412yes—
201C2×#509—111no—
202C2×#504—111no—
203#3061—111no—
204#3058—111no—
205#2220—111no—
206#2220—111no—
207#2218—111no—
208#2218—111no—
209#2217—111no—
210#2217—111no—
211#2215—111no—
212#2215D1111yescharacteristic, complemented
213#2159—111no—
214#2138—111no—
215C2×#357—111no—
216C23×C11—41no—
217C23×C11—41no—
218C23×C11C2×D811yescharacteristic
219C22×D11—41no—
220C22×D11—82no—
221C22×D11—161no—
222C22×D11—161no—
223C22×D11C2×D811yescharacteristic
224C22×D11C2×D811yescharacteristic
225D4×C11—41no—
226D4×C11—41no—
227D4×C11—41no—
228D4×C11—41no—
229D4×C11—161no—
230D4×C11—161no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11C2×D811yescharacteristic
236C2×C4×C11C22×D411yescharacteristic
237C22⋊D11—22no—
238C22⋊D11—22no—
239C22⋊D11—82no—
240C22⋊D11—82no—
241C22⋊D11—161no—
242C22⋊D11—161no—
243C22⋊D11—161no—
244C2×Dic11—41no—
245C2×Dic11—41no—
246C2×Dic11—41no—
247C2×Dic11—82no—
248C2×Dic11C2×D811yescharacteristic
249C2×Dic11C2×D811yescharacteristic
250D44—22no—
251D44—41no—
252D44—41no—
253D44—161no—
254C4×D11—21no—
255C4×D11—21no—
256C4×D11—161no—
257C4×D11#12112yes—
258C4×D11#13512yes—
259Dic22—22no—
260Dic22—41no—
261Dic22—41no—
262C8×C11—21no—
263C8×C11C22×D411yescharacteristic
264C8×C11C2×#4111yescharacteristic
265C11⋊C8—21no—
266C11⋊C8#12112yes—
267C2×#135—111no—
268C22×D8—111no—
269C2×#131—111no—
270#537—221no—
271#535—221no—
272#509—224no—
273C2×SD32—111no—
274C2×SD32—111no—
275C2×D16—111no—
276C2×D16C2×D1111yescharacteristic
277#504—224no—
278C2×M32—111no—
279C2×M32—111no—
280C2×M32—111no—
281C22×C16—111no—
282C22×C16—111no—
283C22×C16C2×D1111yescharacteristic, complemented
284#469—221no—
285#469—221no—
286#468—221no—
287#468—221no—
288#467—111no—
289#467—111no—
290#466—111no—
291#466—111no—
292#466—111no—
293#466—111no—
294#466C2×D1111yescharacteristic
295#466C2×D1111yescharacteristic, complemented
296#427—111no—
297C2×#107—111no—
298#418—221no—
299#417—221no—
300#367—111no—
301#367—111no—
302#366—111no—
303#366C2×D1111yescharacteristic, complemented
304#358—111no—
305#358—111no—
306#357—111no—
307#357—111no—
308#357—111no—
309#357—111no—
310#357C2×D1111yescharacteristic
311#357C2×D1111yescharacteristic, complemented
312C22×C11—21no—
313C22×C11—21no—
314C22×C11—21no—
315C22×C11—81no—
316C22×C11—81no—
317C22×C11—81no—
318C22×C11—81no—
319C22×C11—81no—
320C22×C11—81no—
321C22×C11C22×D811yescharacteristic
322C2×D11—21no—
323C2×D11—21no—
324C2×D11—21no—
325C2×D11—21no—
326C2×D11—21no—
327C2×D11—81no—
328C2×D11—81no—
329C2×D11—81no—
330C2×D11—164no—
331C2×D11#46612yes—
332C4×C11—21no—
333C4×C11—81no—
334C4×C11—81no—
335C4×C11C2×#12111yescharacteristic
336C4×C11C2×#13511yescharacteristic
337Dic11—21no—
338Dic11—81no—
339Dic11—81no—
340Dic11—81no—
341Dic11#46612yes—
342C2×#41—111no—
343C2×#41—221no—
344C22×D4—221no—
345#135—222no—
346#135—222no—
347C2×Q16—111no—
348C2×SD16—221no—
349C2×D8—111no—
350C2×D8—222no—
351C2×D8—222no—
352C2×D8—221no—
353C2×D8C22×D1111yescharacteristic
354C2×D8C22×D1111yescharacteristic
355#131—222no—
356#131—222no—
357C2×M16—111no—
358C2×M16—111no—
359C2×M16—111no—
360C22×C8—111no—
361C22×C8—111no—
362C22×C8C22×D1111yescharacteristic
363#127—441no—
364#124—441no—
365C22⋊Q8—221no—
366C22⋊Q8—221no—
367C22⋊Q8—441no—
368#121—21no—
369#121—21no—
370#121—221no—
371#121—221no—
372#121—221no—
373#121—221no—
374#121—441no—
375#121—441no—
376#121—441no—
377#120—441no—
378#120—441no—
379#117—221no—
380C2×C4⋊C4—221no—
381SD32—222no—
382SD32—222no—
383D16—22no—
384D16—222no—
385M32—114no—
386M32—222no—
387M32—222no—
388C2×C16—22no—
389C2×C16—111no—
390C2×C16—111no—
391C2×C16—222no—
392C2×C16—222no—
393C2×C16C22×D1111yescharacteristic
394C2×C16C22×D1111yescharacteristic
395#107—111no—
396#107—111no—
397#107—221no—
398#107C22×D1111yescharacteristic
399#107C22×D1111yescharacteristic
400#106—221no—
401#103—221no—
402#103—221no—
403#102—21no—
404#102—21no—
405#102—221no—
406#102—221no—
407#102—221no—
408#102—221no—
409C2×C11—41no—
410C2×C11—161no—
411C2×C11—161no—
412C2×C11C2×#46611yescharacteristic
413C2×C11#341511yescharacteristic
414C2×C11#341611yescharacteristic
415D11—22no—
416D11—41no—
417D11—161no—
418C24—441no—
419#41—222no—
420#41—222no—
421#41—442no—
422#41—442no—
423C2×Q8—111no—
424C2×Q8—221no—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—41no—
428C2×D4—41no—
429C2×D4—111no—
430C2×D4—111no—
431C2×D4—111no—
432C2×D4—221no—
433C2×D4—441no—
434C2×D4—442no—
435C2×D4—442no—
436C2×D4—441no—
437C2×D4—441no—
438C2×D4—441no—
439C2×D4—441no—
440C2×D4—441no—
441C22×C4—111no—
442C22×C4—111no—
443C22×C4—441no—
444C22×C4—441no—
445C22×C4D4×D1111yescharacteristic
446Q16—221no—
447Q16—221no—
448SD16—442no—
449D8—21no—
450D8—21no—
451D8—21no—
452D8—21no—
453D8—221no—
454D8—221no—
455D8—442no—
456M16—222no—
457M16—222no—
458M16—222no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—111no—
462C2×C8—112no—
463C2×C8—112no—
464C2×C8—111no—
465C2×C8—221no—
466C2×C8—221no—
467C2×C8D4×D1111yescharacteristic
468C2×C8C23×D1111yescharacteristic
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4—441no—
474C4⋊C4—441no—
475C4⋊C4—441no—
476C22⋊C4—41no—
477C22⋊C4—41no—
478C22⋊C4—441no—
479C22⋊C4—441no—
480C22⋊C4—441no—
481C22⋊C4—441no—
482C22⋊C4—441no—
483C22⋊C4—441no—
484C22⋊C4—441no—
485C42—441no—
486C16—21no—
487C16—112no—
488C16—221no—
489C16D4×D1112yes—
490C11#3361211yescharacteristic, complemented, Sylow
491C23—41no—
492C23—41no—
493C23—111no—
494C23—111no—
495C23—441no—
496C23—882no—
497C23—1761no—
498C23—1761no—
499C23D8×D1111yescharacteristic
500Q8—222no—
501Q8—441no—
502Q8—441no—
503D4—41no—
504D4—41no—
505D4—41no—
506D4—41no—
507D4—161no—
508D4—161no—
509D4—222no—
510D4—222no—
511D4—222no—
512D4—441no—
513D4—441no—
514D4—882no—
515D4—882no—
516D4—1761no—
517D4—1761no—
518D4—1761no—
519D4—1761no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—111no—
525C2×C4—112no—
526C2×C4—112no—
527C2×C4—111no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4—882no—
534C2×C4—1761no—
535C2×C4D8×D1111yescharacteristic
536C2×C4C2×D4×D1111yescharacteristic
537C8—21no—
538C8—112no—
539C8—221no—
540C8C2×D4×D1111yescharacteristic
541C8#41×D1111yescharacteristic
542C22—21no—
543C22—21no—
544C22—21no—
545C22—81no—
546C22—81no—
547C22—81no—
548C22—81no—
549C22—81no—
550C22—81no—
551C22—112no—
552C22—221no—
553C22—221no—
554C22—221no—
555C22—221no—
556C22—221no—
557C22—881no—
558C22—881no—
559C22—881no—
560C22—1764no—
561C22C2×D8×D1111yescharacteristic
562C4—21no—
563C4—81no—
564C4—81no—
565C4—112no—
566C4—221no—
567C4—881no—
568C4—881no—
569C4—881no—
570C4D11×#12111yescharacteristic
571C4D11×#13511yescharacteristic
572C2—41no—
573C2—161no—
574C2—161no—
575C2—222no—
576C2—441no—
577C2—1761no—
578C2D11×#46611yescharacteristic
579C2#1308175311yescharacteristic
580C2#1308175911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2215C2
socleC22×C11C22×D8
hypercenter#2215D11
hypocenterC11#33612
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2215

Complements

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

NH ≅ G/Ntype
1. C2×#10622524C2semidirect
2. C2×#10622514C2semidirect
3. #13078281C2semidirect
4. #13078259C2semidirect
5. #13070730C2semidirect
6. #13070727C2semidirect
7. #13070717C2semidirect
8. #13070716C2semidirect
9. #13070712C2semidirect
10. #13070711C2semidirect
11. #13070701C2semidirect
12. #13070401C2semidirect
13. #13070320C2semidirect
14. D11×#357C2semidirect
15. C11×#2215C2semidirect
22. C22×C11×C16C22semidirect
24. C11×#466C22semidirect
26. #10622770C22semidirect
29. #10622729C22semidirect
31. C2×#66876C22semidirect
38. C2×#66862C22semidirect
40. C2×C16×D11C22semidirect
41. #10622500C22semidirect
49. C11×#366C22semidirect
51. C11×#357C22semidirect
53. #10622200C22semidirect
55. #10622143C22semidirect
56. #10622141C22semidirect
57. #10622130C22semidirect
59. #10622128C22semidirect
60. #10622127C22semidirect
125. #66862D4semidirect
212. #2215D11semidirect
283. C22×C16C2×D11semidirect
295. #466C2×D11semidirect
303. #366C2×D11semidirect
311. #357C2×D11semidirect
490. C11#33612semidirect

Maximal subgroups

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

subgroupindex
C2×#106225242
C2×#106225142
#130782812
#130782592
#130707302
#130707272
#130707172
#130707162
#130707122
#130707112
#130707012
#130704012
#130703202
D11×#3572
C11×#22152
#3361211