Finite Group Databasebeta

← #14910783

Subgroups — #14910783

Order 2816.

564 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13080376C211yesmaximal, characteristic, complemented
2#13070859C211yesmaximal, characteristic, complemented
3#13070807C211yesmaximal, characteristic, complemented
4#13070796C211yesmaximal, characteristic, complemented
5#13070777C211yesmaximal, characteristic, complemented
6#13070717C211yesmaximal, characteristic, complemented
7#13070700C211yesmaximal, characteristic, complemented
8#13070651C211yesmaximal, characteristic, complemented
9#13070537C211yesmaximal, characteristic, complemented
10#13070537C211yesmaximal, characteristic, complemented
11#13070480C211yesmaximal, characteristic, complemented
12#13070442C211yesmaximal, characteristic, complemented
13#13070326C211yesmaximal, characteristic, complemented
14#13070321C211yesmaximal, characteristic, complemented
15C11×#3339C211yesmaximal, characteristic, complemented
16C11×#553—21no—
17C2×#66957C2211yescharacteristic
18C2×#66957C2211yescharacteristic
19#10623084—21no—
20C11×#499C2211yescharacteristic
21C11×#482—21no—
22C11×#481—21no—
23C11×#478—21no—
24C11×#466C2211yescharacteristic
25C11×#466C2211yescharacteristic
26C4×C11×D8C2211yescharacteristic
27C8×D4×C11C2211yescharacteristic
28C11×#427C2211yescharacteristic
29C2×C11×#107C2211yescharacteristic
30C2×#66891C2211yescharacteristic
31C2×#66890C2211yescharacteristic
32C2×#66890C2211yescharacteristic
33#10622728C2211yescharacteristic
34#10622728C2211yescharacteristic
35C2×#66876C2211yescharacteristic
36C22×C11⋊C16C2211yescharacteristic
37#10622461—21no—
38#10622347—21no—
39#10622347—21no—
40C4×Dic44C2211yescharacteristic
41#10622308C2211yescharacteristic
42#10622200C2211yescharacteristic
43C22⋊(C11⋊C16)C2211yescharacteristic
44C22⋊(C11⋊C16)C2211yescharacteristic
45#10622130C2211yescharacteristic
46#10622130C2211yescharacteristic
47#10622130C2211yescharacteristic
48#10622129C2211yescharacteristic
49#10622129C2211yescharacteristic
50#10622129C2211yescharacteristic
51#10622129C2211yescharacteristic
52#10622129C2211yescharacteristic
53#10622129C2211yescharacteristic
54#10622128C2211yescharacteristic
55#10622127C2211yescharacteristic
56#10622127C2211yescharacteristic
57C4⋊(C11⋊C16)C2211yescharacteristic
58#10622099C2211yescharacteristic
59C2×#4339—21no—
60C2×#4339—21no—
61C2×C11×D8C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C11×#126—41no—
65C11×#125—21no—
66C11×#123—41no—
67C11×#121—21no—
68C11×#121—21no—
69C11×#121—41no—
70C4×D4×C11—21no—
71C4×D4×C11—41no—
72C4×D4×C11D411yescharacteristic
73C11×#117—21no—
74C2×C11×C4⋊C4—21no—
75#66993—41no—
76#66983—21no—
77#66983—21no—
78C2×Dic44C2311yescharacteristic
79#66957—22no—
80#66957—22no—
81#66957—41no—
82#66957—41no—
83C2×D88—21no—
84C2×D88C2311yescharacteristic
85C2×D88C2311yescharacteristic
86C2×#4314—21no—
87C2×#4314—21no—
88#66946—41no—
89#66937—41no—
90#66937—41no—
91#66927—21no—
92C4×Dic22—21no—
93C11×#107—21no—
94C11×#107C2311yescharacteristic
95C11×#107C2311yescharacteristic
96C11×#107C2311yescharacteristic
97C11×#106—21no—
98C11×#106—21no—
99C11×C4⋊C8D411yescharacteristic
100C11×#102—21no—
101C11×#102—21no—
102C11×#102—21no—
103C11×C22⋊C8D411yescharacteristic
104C11×C22⋊C8D411yescharacteristic
105C4×C8×C11C2311yescharacteristic
106#66891—22no—
107#66890—41no—
108#66890—41no—
109#66885—21no—
110#66885—21no—
111#66882C2311yescharacteristic
112#66880—21no—
113#66876—41no—
114C2×C11⋊C16—41no—
115C2×C11⋊C16C2311yescharacteristic
116C2×C11⋊C16C2311yescharacteristic
117C2×C11⋊C16C2311yescharacteristic
118C2×C11⋊C16C2311yescharacteristic
119#33876—111nomaximal, Sylow
120C2×D4×C11—21no—
121C2×D4×C11—41no—
122C2×D4×C11—41no—
123C2×D4×C11D811yescharacteristic
124C22×C4×C11—41no—
125C22×C4×C11—41no—
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C2×C22⋊D11—41no—
129C2×C22⋊D11—41no—
130C2×C22⋊D11—41no—
131C2×C22⋊D11—41no—
132#4339—42no—
133#4339—42no—
134#4339—81no—
135#4339—81no—
136C2×D44—21no—
137C2×D44—21no—
138C2×D44—41no—
139C2×D44—41no—
140C2×C4×D11—41no—
141C2×C4×D11—41no—
142C2×Dic22—21no—
143C11×D8—21no—
144C11×D8—21no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11C2×D411yescharacteristic
150C2×C8×C11C2×D411yescharacteristic
151C2×C8×C11C2×D411yescharacteristic
152C2×C8×C11C2411yescharacteristic
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—41no—
157C11×C4⋊C4—41no—
158C11×C4⋊C4—41no—
159C11×C4⋊C4D811yescharacteristic
160C11×C22⋊C4—41no—
161C11×C22⋊C4—41no—
162C11×C22⋊C4—41no—
163C11×C22⋊C4—41no—
164C11×C22⋊C4D811yescharacteristic
165C11×C22⋊C4D811yescharacteristic
166C42×C11—41no—
167C42×C11C2×D411yescharacteristic
168(C2×D11)⋊C4—41no—
169(C2×D11)⋊C4—41no—
170C4⋊Dic11—21no—
171Dic11⋊C4—41no—
172C4×Dic11—41no—
173Dic44—21no—
174Dic44#4112yes—
175D88—21no—
176D88—21no—
177D88—21no—
178D88—21no—
179D88—81no—
180#4314—42no—
181#4314—42no—
182C11⋊C16—21no—
183C11⋊C16—21no—
184C11⋊C16—21no—
185C11⋊C16—21no—
186#3339D1111yescharacteristic, complemented
187#3287—111no—
188#2244—111no—
189#2234—111no—
190#2232—111no—
191#2229—111no—
192#2218—111no—
193#2215—111no—
194#2206—111no—
195#2186—111no—
196#2186—111no—
197#2175—111no—
198#2168—111no—
199#2139—111no—
200#2138—111no—
201C23×C11—41no—
202C23×C11C2×D811yescharacteristic
203C23×C11C2×D811yescharacteristic
204C22×D11—41no—
205C22×D11—41no—
206D4×C11—41no—
207D4×C11—41no—
208D4×C11—41no—
209D4×C11—82no—
210D4×C11—161no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—161no—
219C2×C4×C11—161no—
220C2×C4×C11C2×D811yescharacteristic
221C2×C4×C11C2×D811yescharacteristic
222C2×C4×C11C2×D811yescharacteristic
223C2×C4×C11C2×D811yescharacteristic
224C2×C4×C11C22×D411yescharacteristic
225C22⋊D11—82no—
226C22⋊D11—82no—
227C22⋊D11—161no—
228C22⋊D11—161no—
229C2×Dic11—41no—
230C2×Dic11—41no—
231D44—41no—
232D44—41no—
233D44—41no—
234D44—41no—
235D44—82no—
236D44—161no—
237C4×D11—82no—
238C4×D11—82no—
239Dic22—22no—
240Dic22—41no—
241C8×C11—21no—
242C8×C11—21no—
243C8×C11—21no—
244C8×C11C2×#4111yescharacteristic
245C8×C11H(5,𝔽2)11yescharacteristic
246C2×#135—111no—
247C2×#135—111no—
248#553—21no—
249#550—221no—
250C2×SD32—111no—
251C2×D16—111no—
252C2×D16—111no—
253C2×M32—111no—
254C22×C16—111no—
255#499C2×D1111yescharacteristic
256#493—111no—
257#482—21no—
258#481—21no—
259#478—21no—
260#466—111no—
261#466—111no—
262#466C2×D1111yescharacteristic
263#466C2×D1111yescharacteristic
264#460—221no—
265#449—221no—
266#449—221no—
267C4×Q16—111no—
268C4×D8C2×D1111yescharacteristic
269C8×D4C2×D1111yescharacteristic
270#427C2×D1111yescharacteristic
271C2×#107C2×D1111yescharacteristic
272#367—111no—
273#366—111no—
274#366—111no—
275C4⋊C16—111no—
276#358—111no—
277#358—111no—
278#358—111no—
279#357—111no—
280#357—111no—
281#357—111no—
282#357—111no—
283#357—111no—
284#357—111no—
285#357—111no—
286C22⋊C16—111no—
287C22⋊C16—111no—
288#346—111no—
289C22×C11—21no—
290C22×C11—21no—
291C22×C11—21no—
292C22×C11—21no—
293C22×C11—21no—
294C22×C11—21no—
295C22×C11—81no—
296C22×C11—81no—
297C22×C11—81no—
298C22×C11C22×D811yescharacteristic
299C2×D11—81no—
300C2×D11—81no—
301C2×D11—81no—
302C2×D11—81no—
303C2×D11—81no—
304C2×D11—81no—
305C4×C11—21no—
306C4×C11—21no—
307C4×C11—21no—
308C4×C11—21no—
309C4×C11—81no—
310C4×C11—81no—
311C4×C11—81no—
312C4×C11#54611yescharacteristic
313C4×C11#57711yescharacteristic
314Dic11—42no—
315Dic11—81no—
316C2×#41—221no—
317C2×#41—221no—
318#135—222no—
319#135—222no—
320#135—441no—
321#135—441no—
322C2×Q16—111no—
323C2×SD16—221no—
324C2×SD16—221no—
325C2×D8—111no—
326C2×D8—111no—
327C2×D8—221no—
328C2×D8C22×D1111yescharacteristic
329C22×C8C22×D1111yescharacteristic
330C22×C8C22×D1111yescharacteristic
331#127—221no—
332#127—441no—
333#126—41no—
334#125—21no—
335#123—41no—
336#121—21no—
337#121—21no—
338#121—41no—
339#121—221no—
340#121—221no—
341#121—441no—
342#121—441no—
343C4×Q8—221no—
344C4×D4—21no—
345C4×D4—41no—
346C4×D4—441no—
347C4×D4C22⋊D1111yescharacteristic
348#117—21no—
349C2×C4⋊C4—21no—
350SD32—222no—
351D16—441no—
352D16—441no—
353M32—441no—
354C2×C16—111no—
355C2×C16—111no—
356C2×C16—111no—
357C2×C16—111no—
358C2×C16—441no—
359#107—21no—
360#107—111no—
361#107C22×D1111yescharacteristic
362#107C22×D1111yescharacteristic
363#107C22×D1111yescharacteristic
364#106—21no—
365#106—21no—
366C4⋊C8C22⋊D1111yescharacteristic
367#103—221no—
368#102—21no—
369#102—21no—
370#102—21no—
371#102—221no—
372#102—221no—
373C22⋊C8C22⋊D1111yescharacteristic
374C22⋊C8C22⋊D1111yescharacteristic
375C4×C8C22×D1111yescharacteristic
376C2×C11—41no—
377C2×C11—41no—
378C2×C11—161no—
379C2×C11#329411yescharacteristic
380C2×C11#341411yescharacteristic
381C2×C11#341511yescharacteristic
382D11—161no—
383D11—161no—
384#41—442no—
385#41—442no—
386#41—881no—
387#41—881no—
388C2×Q8—221no—
389C2×D4—21no—
390C2×D4—41no—
391C2×D4—41no—
392C2×D4—221no—
393C2×D4—221no—
394C2×D4—441no—
395C2×D4—441no—
396C2×D4—441no—
397C2×D4—441no—
398C2×D4—441no—
399C2×D4—441no—
400C2×D4#432311yescharacteristic
401C22×C4—41no—
402C22×C4—41no—
403C22×C4—441no—
404C22×C4—441no—
405C22×C4C2×C22⋊D1111yescharacteristic
406C22×C4C2×C22⋊D1111yescharacteristic
407Q16—112no—
408Q16—221no—
409SD16—442no—
410SD16—442no—
411D8—21no—
412D8—21no—
413D8—221no—
414D8—221no—
415D8—221no—
416D8—221no—
417D8—881no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—21no—
422C2×C8C2×C22⋊D1111yescharacteristic
423C2×C8C2×C22⋊D1111yescharacteristic
424C2×C8C2×C22⋊D1111yescharacteristic
425C2×C8C23×D1111yescharacteristic
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—41no—
430C4⋊C4—41no—
431C4⋊C4—41no—
432C4⋊C4—221no—
433C4⋊C4—441no—
434C4⋊C4#432311yescharacteristic
435C22⋊C4—41no—
436C22⋊C4—41no—
437C22⋊C4—41no—
438C22⋊C4—41no—
439C22⋊C4—441no—
440C22⋊C4—441no—
441C22⋊C4#432311yescharacteristic
442C22⋊C4#432311yescharacteristic
443C42—41no—
444C42—441no—
445C42C2×C22⋊D1111yescharacteristic
446C16—221no—
447C16—221no—
448C16—221no—
449C16—221no—
450C11#3387611yescharacteristic, complemented, Sylow
451C23—41no—
452C23—441no—
453C23—441no—
454C23C2×#432311yescharacteristic
455C23C2×#432311yescharacteristic
456Q8—222no—
457Q8—441no—
458D4—41no—
459D4—41no—
460D4—41no—
461D4—82no—
462D4—161no—
463D4—441no—
464D4—441no—
465D4—441no—
466D4—441no—
467D4—882no—
468D4—882no—
469D4—882no—
470D4—1761no—
471D4—1761no—
472D4—1761no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—161no—
481C2×C4—161no—
482C2×C4—441no—
483C2×C4—441no—
484C2×C4—882no—
485C2×C4—882no—
486C2×C4C2×#432311yescharacteristic
487C2×C4C2×#432311yescharacteristic
488C2×C4C2×#432311yescharacteristic
489C2×C4C2×#432311yescharacteristic
490C2×C4C22×C22⋊D1111yescharacteristic
491C8—21no—
492C8—21no—
493C8—21no—
494C8#41×D1111yescharacteristic
495C8#6704211yescharacteristic
496C22—21no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—81no—
503C22—81no—
504C22—81no—
505C22—881no—
506C22—881no—
507C22—881no—
508C22—881no—
509C22—881no—
510C22—881no—
511C22C22×#432311yescharacteristic
512C4—21no—
513C4—21no—
514C4—21no—
515C4—21no—
516C4—81no—
517C4—81no—
518C4—81no—
519C4—442no—
520C4—881no—
521C4#1062336011yescharacteristic
522C4#1062336811yescharacteristic
523C2—41no—
524C2—41no—
525C2—161no—
526C2—1761no—
527C2—1761no—
528C2#1308042311yescharacteristic
529C2#1308175011yescharacteristic
530C2#1308175511yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3339C2
socleC22×C11C22×D8
hypercenter#3339D11
hypocenterC11#33876
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3339

Complements

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

NH ≅ G/Ntype
1. #13080376C2semidirect
2. #13070859C2semidirect
3. #13070807C2semidirect
4. #13070796C2semidirect
5. #13070777C2semidirect
6. #13070717C2semidirect
7. #13070700C2semidirect
8. #13070651C2semidirect
9. #13070537C2semidirect
10. #13070537C2semidirect
11. #13070480C2semidirect
12. #13070442C2semidirect
13. #13070326C2semidirect
14. #13070321C2semidirect
15. C11×#3339C2semidirect
186. #3339D11semidirect
450. C11#33876semidirect

Maximal subgroups

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

subgroupindex
#130803762
#130708592
#130708072
#130707962
#130707772
#130707172
#130707002
#130706512
#130705372
#130704802
#130704422
#130703262
#130703212
C11×#33392
#3387611