Finite Group Databasebeta

← #14909854

Subgroups — #14909854

Order 2816.

574 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079110C211yesmaximal, characteristic, complemented
2#13070888C211yesmaximal, characteristic, complemented
3#13070875C211yesmaximal, characteristic, complemented
4#13070855C211yesmaximal, characteristic, complemented
5#13070845C211yesmaximal, characteristic, complemented
6#13070678C211yesmaximal, characteristic, complemented
7#13070671C211yesmaximal, characteristic, complemented
8#13070666C211yesmaximal, characteristic, complemented
9#13070661C211yesmaximal, characteristic, complemented
10#13070554C211yesmaximal, characteristic, complemented
11#13070549C211yesmaximal, characteristic, complemented
12#13070537C211yesmaximal, characteristic
13#13070532C211yesmaximal, characteristic, complemented
14#13070423C211yesmaximal, characteristic, complemented
15C11×#3175C211yesmaximal, characteristic, complemented
16C11×#542—21no—
17C2×#66962—21no—
18C22×Dic44C2211yescharacteristic
19C2×#66957C2211yescharacteristic
20#10623057—21no—
21C11×#500C2211yescharacteristic
22C11×#495C2211yescharacteristic
23C11×#489—21no—
24C11×#468—21no—
25C11×#467C2211yescharacteristic
26C11×#466C2211yescharacteristic
27C11×#440—21no—
28C4×C11×Q16C2211yescharacteristic
29C4×C11×D8C2211yescharacteristic
30C11×#405C2211yescharacteristic
31C2×#66893C2211yescharacteristic
32C2×#66893C2211yescharacteristic
33C2×#66893C2211yescharacteristic
34C2×#66892C2211yescharacteristic
35C2×#66891C2211yescharacteristic
36C2×#66891C2211yescharacteristic
37C2×#66891C2211yescharacteristic
38C2×#66890C2211yescharacteristic
39#10622328—21no—
40#10622328—21no—
41#10622312C2211yescharacteristic
42#10622312C2211yescharacteristic
43#10622309C2211yescharacteristic
44#10622309C2211yescharacteristic
45C22⋊(C11⋊C16)C2211yescharacteristic
46C22⋊(C11⋊C16)C2211yescharacteristic
47#10622130C2211yescharacteristic
48#10622130C2211yescharacteristic
49#10622130C2211yescharacteristic
50#10622130C2211yescharacteristic
51#10622130C2211yescharacteristic
52#10622130C2211yescharacteristic
53#10622129C2211yescharacteristic
54#10622129C2211yescharacteristic
55C4⋊(C11⋊C16)C2211yescharacteristic
56C4⋊(C11⋊C16)C2211yescharacteristic
57#10622099C2211yescharacteristic
58C4×C11⋊C16C2211yescharacteristic
59C2×#4339—21no—
60C22×Dic22—21no—
61C2×C11×Q16C2311yescharacteristic
62C2×C11×SD16—21no—
63C2×C11×D8C2311yescharacteristic
64C2×C11×M16D411yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C11×C4⋊Q8—21no—
67C11×#126—41no—
68C11×#124—21no—
69C11×#124—41no—
70C11×#123—41no—
71C11×C22⋊Q8—21no—
72C11×C22⋊Q8—41no—
73C11×#121—21no—
74C4×Q8×C11—21no—
75C4×D4×C11—21no—
76C11×#117D411yescharacteristic
77#66962—44no—
78C2×Dic44—21no—
79C2×Dic44—21no—
80C2×Dic44—21no—
81C2×Dic44—41no—
82C2×Dic44—41no—
83C2×Dic44C2311yescharacteristic
84C2×Dic44C2311yescharacteristic
85C2×Dic44C2311yescharacteristic
86#66957—41no—
87#66957—41no—
88C2×D88C2311yescharacteristic
89C2×#4314—21no—
90C2×#4314—21no—
91C2×#4314—21no—
92#66950—41no—
93#66950—41no—
94#66939—41no—
95#66939—41no—
96#66928—21no—
97#66928—21no—
98#66922—21no—
99#66922—21no—
100C11×#107—21no—
101C11×#107C2311yescharacteristic
102C11×#107C2311yescharacteristic
103C11×#103—21no—
104C11×#103—21no—
105C11×#102—21no—
106C11×#102—21no—
107C11×#97D411yescharacteristic
108C11×#97D411yescharacteristic
109C4×C8×C11C2311yescharacteristic
110C4×C8×C11C2311yescharacteristic
111#66893—41no—
112#66893—41no—
113#66893—41no—
114#66892—41no—
115#66891—41no—
116#66891—41no—
117#66891—41no—
118#66890—41no—
119C2×C11⋊C16C2311yescharacteristic
120C2×C11⋊C16C2311yescharacteristic
121C2×C11⋊C16C2311yescharacteristic
122C2×C11⋊C16C2311yescharacteristic
123#33791—111nomaximal, Sylow
124C2×Q8×C11—21no—
125C2×Q8×C11—41no—
126C2×D4×C11—21no—
127C2×D4×C11—41no—
128C22×C4×C11—41no—
129C22×C4×C11C2×D411yescharacteristic
130C2×C22⋊D11—41no—
131C22×Dic11—41no—
132#4339—42no—
133#4339—42no—
134C2×D44—21no—
135C2×C4×D11—41no—
136C2×Dic22—21no—
137C2×Dic22—21no—
138C2×Dic22—21no—
139C2×Dic22—42no—
140C2×Dic22—42no—
141C2×Dic22—41no—
142C11×Q16—21no—
143C11×Q16—21no—
144C11×SD16—42no—
145C11×D8—21no—
146C11×D8—21no—
147C11×M16—22no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11C2×D411yescharacteristic
151C2×C8×C11C2×D411yescharacteristic
152C2×C8×C11C2×D411yescharacteristic
153C2×C8×C11C2411yescharacteristic
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—41no—
157C11×C4⋊C4—41no—
158C11×C4⋊C4—41no—
159C11×C4⋊C4D811yescharacteristic
160C11×C4⋊C4D811yescharacteristic
161C11×C22⋊C4—41no—
162C11×C22⋊C4—41no—
163C11×C22⋊C4—41no—
164C11×C22⋊C4—41no—
165C11×C22⋊C4—41no—
166C11×C22⋊C4D811yescharacteristic
167C11×C22⋊C4D811yescharacteristic
168C42×C11—41no—
169C42×C11C2×D411yescharacteristic
170C42×C11C2×D411yescharacteristic
171(C2×D11)⋊C4—41no—
172(C2×D11)⋊C4—41no—
173(C2×D11)⋊C4—41no—
174(C2×D11)⋊C4—41no—
175C4⋊Dic11—41no—
176C4⋊Dic11—41no—
177C4⋊Dic11—41no—
178C4⋊Dic11—41no—
179Dic44—21no—
180Dic44—21no—
181Dic44—21no—
182Dic44—21no—
183Dic44—21no—
184Dic44—21no—
185Dic44—42no—
186Dic44—42no—
187Dic44—42no—
188D88—21no—
189D88—21no—
190#4314—42no—
191#4314—42no—
192#4314—42no—
193C11⋊C16—21no—
194C11⋊C16—21no—
195C11⋊C16—21no—
196C11⋊C16—21no—
197#3175D1111yescharacteristic, complemented
198#3156—111no—
199#2251—111no—
200#2249—111no—
201#2243—111no—
202#2241—111no—
203#2211—111no—
204#2210—111no—
205#2209—111no—
206#2208—111no—
207#2189—111no—
208#2188—111no—
209#2186—111no—
210#2185—111no—
211#2164—111no—
212C23×C11—41no—
213C23×C11C2×D811yescharacteristic
214C22×D11—41no—
215Q8×C11—41no—
216Q8×C11—41no—
217Q8×C11—161no—
218D4×C11—41no—
219D4×C11—41no—
220D4×C11—161no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—161no—
227C2×C4×C11C2×D811yescharacteristic
228C2×C4×C11C2×D811yescharacteristic
229C2×C4×C11C2×D811yescharacteristic
230C2×C4×C11C2×D811yescharacteristic
231C2×C4×C11C2×D811yescharacteristic
232C2×C4×C11C22×D411yescharacteristic
233C22⋊D11—82no—
234C2×Dic11—41no—
235C2×Dic11—41no—
236C2×Dic11—41no—
237C2×Dic11—82no—
238D44—41no—
239D44—41no—
240C4×D11—82no—
241Dic22—41no—
242Dic22—41no—
243Dic22—41no—
244Dic22—41no—
245Dic22—41no—
246Dic22—41no—
247Dic22—82no—
248C8×C11—21no—
249C8×C11—21no—
250C8×C11AGL(1,ℤ/8)12yes—
251C8×C11H(5,𝔽2)11yescharacteristic
252C8×C11H(5,𝔽2)11yescharacteristic
253C2×#137—221no—
254C2×#135—111no—
255C22×Q16—111no—
256#542—21no—
257#536—221no—
258C2×Q32—111no—
259C2×Q32—111no—
260C2×Q32—111no—
261C2×SD32—111no—
262C2×SD32—111no—
263C2×SD32—111no—
264C2×SD32—111no—
265C2×D16—111no—
266#500C2×D1111yescharacteristic
267#497—221no—
268#497—221no—
269#495—111no—
270#495—111no—
271#495C2×D1111yescharacteristic
272#494—111no—
273#494—111no—
274#489—21no—
275#468—21no—
276#467C2×D1111yescharacteristic
277#466C2×D1111yescharacteristic
278#440—21no—
279C4×Q16C2×D1111yescharacteristic
280C4×D8C2×D1111yescharacteristic
281#405C2×D1111yescharacteristic
282C4⋊C16—111no—
283C4⋊C16—111no—
284#358—111no—
285#358—111no—
286#358—111no—
287#358—111no—
288#358—111no—
289#358—111no—
290#357—111no—
291#357—111no—
292C22⋊C16—111no—
293C22⋊C16—111no—
294#346—111no—
295C4×C16—111no—
296C22×C11—21no—
297C22×C11—21no—
298C22×C11—21no—
299C22×C11—81no—
300C22×C11—81no—
301C22×C11—81no—
302C22×C11C22×D811yescharacteristic
303C2×D11—81no—
304C2×D11—81no—
305C2×D11—81no—
306C4×C11—21no—
307C4×C11—21no—
308C4×C11—21no—
309C4×C11—21no—
310C4×C11—21no—
311C4×C11—81no—
312C4×C11—81no—
313C4×C11—81no—
314C4×C11#53511yescharacteristic
315C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
316Dic11—81no—
317Dic11—81no—
318Dic11—81no—
319C2×#41—221no—
320C22×Q8—221no—
321#137—444no—
322#135—441no—
323#135—441no—
324C2×Q16—111no—
325C2×Q16—111no—
326C2×Q16—111no—
327C2×Q16—221no—
328C2×Q16—221no—
329C2×Q16—221no—
330C2×Q16—441no—
331C2×Q16—441no—
332C2×Q16C22×D1111yescharacteristic
333C2×SD16—21no—
334C2×SD16—221no—
335C2×SD16—221no—
336C2×SD16—221no—
337C2×D8—111no—
338C2×D8C22×D1111yescharacteristic
339C2×M16C22⋊D1111yescharacteristic
340C22×C8C22×D1111yescharacteristic
341C4⋊Q8—21no—
342C4⋊Q8—221no—
343C4⋊Q8—221no—
344#126—41no—
345#124—21no—
346#124—41no—
347#124—221no—
348#124—221no—
349#123—41no—
350#123—441no—
351#123—441no—
352C22⋊Q8—21no—
353C22⋊Q8—41no—
354C22⋊Q8—441no—
355C22⋊Q8—441no—
356#121—21no—
357C4×Q8—21no—
358C4×D4—21no—
359#117C22⋊D1111yescharacteristic
360Q32—441no—
361Q32—441no—
362Q32—441no—
363SD32—441no—
364SD32—441no—
365SD32—441no—
366SD32—441no—
367D16—441no—
368C2×C16—111no—
369C2×C16—111no—
370C2×C16—111no—
371C2×C16—111no—
372#107—21no—
373#107C22×D1111yescharacteristic
374#107C22×D1111yescharacteristic
375#103—21no—
376#103—21no—
377#102—21no—
378#102—21no—
379#97C22⋊D1111yescharacteristic
380#97C22⋊D1111yescharacteristic
381C4×C8C22×D1111yescharacteristic
382C4×C8C22×D1111yescharacteristic
383C2×C11—41no—
384C2×C11—161no—
385C2×C11#320511yescharacteristic
386C2×C11#341611yescharacteristic
387C2×C11#341711yescharacteristic
388D11—161no—
389#41—442no—
390#41—442no—
391C2×Q8—21no—
392C2×Q8—41no—
393C2×Q8—221no—
394C2×Q8—221no—
395C2×Q8—221no—
396C2×Q8—442no—
397C2×Q8—442no—
398C2×Q8—441no—
399C2×D4—21no—
400C2×D4—41no—
401C2×D4—221no—
402C2×D4—441no—
403C22×C4—41no—
404C22×C4—441no—
405C22×C4—441no—
406C22×C4C2×C22⋊D1111yescharacteristic
407Q16—21no—
408Q16—21no—
409Q16—221no—
410Q16—221no—
411Q16—221no—
412Q16—221no—
413Q16—221no—
414Q16—221no—
415Q16—442no—
416Q16—442no—
417Q16—442no—
418SD16—42no—
419SD16—442no—
420SD16—442no—
421SD16—442no—
422D8—21no—
423D8—21no—
424D8—221no—
425D8—221no—
426M16—22no—
427C2×C8—21no—
428C2×C8—21no—
429C2×C8C2×C22⋊D1111yescharacteristic
430C2×C8C2×C22⋊D1111yescharacteristic
431C2×C8C2×C22⋊D1111yescharacteristic
432C2×C8C23×D1111yescharacteristic
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—41no—
436C4⋊C4—41no—
437C4⋊C4—41no—
438C4⋊C4—441no—
439C4⋊C4—441no—
440C4⋊C4—441no—
441C4⋊C4—441no—
442C4⋊C4#432311yescharacteristic
443C4⋊C4#432311yescharacteristic
444C22⋊C4—41no—
445C22⋊C4—41no—
446C22⋊C4—41no—
447C22⋊C4—41no—
448C22⋊C4—41no—
449C22⋊C4—441no—
450C22⋊C4—441no—
451C22⋊C4—441no—
452C22⋊C4—441no—
453C22⋊C4#432311yescharacteristic
454C22⋊C4#432311yescharacteristic
455C42—41no—
456C42C2×C22⋊D1111yescharacteristic
457C42C2×C22⋊D1111yescharacteristic
458C16—221no—
459C16—221no—
460C16—221no—
461C16—221no—
462C11#3379111yescharacteristic, complemented, Sylow
463C23—41no—
464C23—441no—
465C23C2×#432311yescharacteristic
466Q8—41no—
467Q8—41no—
468Q8—161no—
469Q8—441no—
470Q8—441no—
471Q8—441no—
472Q8—441no—
473Q8—441no—
474Q8—441no—
475Q8—882no—
476D4—41no—
477D4—41no—
478D4—161no—
479D4—441no—
480D4—441no—
481D4—882no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—161no—
488C2×C4—441no—
489C2×C4—441no—
490C2×C4—441no—
491C2×C4—882no—
492C2×C4—882no—
493C2×C4C2×#432311yescharacteristic
494C2×C4C2×#432311yescharacteristic
495C2×C4C2×#432311yescharacteristic
496C2×C4C2×#432311yescharacteristic
497C2×C4C2×#432311yescharacteristic
498C2×C4C22×C22⋊D1111yescharacteristic
499C8—21no—
500C8—21no—
501C8#6700212yes—
502C8#6704211yescharacteristic
503C8#6704211yescharacteristic
504C22—21no—
505C22—21no—
506C22—21no—
507C22—81no—
508C22—81no—
509C22—81no—
510C22—881no—
511C22—881no—
512C22—881no—
513C22C22×#432311yescharacteristic
514C4—21no—
515C4—21no—
516C4—21no—
517C4—21no—
518C4—21no—
519C4—81no—
520C4—81no—
521C4—81no—
522C4—881no—
523C4—881no—
524C4—881no—
525C4C2×#6700211yescharacteristic
526C4#1062336111yescharacteristic
527C2—41no—
528C2—161no—
529C2—1761no—
530C2#1307953111yescharacteristic
531C2#1308176311yescharacteristic
532C2#1308176711yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3175C2
socleC22×C11C22×D8
prime radical#13070537C2
hypercenter#3175D11
hypocenterC11#33791
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #3175

Complements

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

NH ≅ G/Ntype
1. #13079110C2semidirect
2. #13070888C2semidirect
3. #13070875C2semidirect
4. #13070855C2semidirect
5. #13070845C2semidirect
6. #13070678C2semidirect
7. #13070671C2semidirect
8. #13070666C2semidirect
9. #13070661C2semidirect
10. #13070554C2semidirect
11. #13070549C2semidirect
13. #13070532C2semidirect
14. #13070423C2semidirect
15. C11×#3175C2semidirect
197. #3175D11semidirect
462. C11#33791semidirect

Maximal subgroups

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

subgroupindex
#130791102
#130708882
#130708752
#130708552
#130708452
#130706782
#130706712
#130706662
#130706612
#130705542
#130705492
#130705372
#130705322
#130704232
C11×#31752
#3379111