Finite Group Databasebeta

← #14910789

Subgroups — #14910789

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#13081019C211yesmaximal, characteristic, complemented
2#13070857C211yesmaximal, characteristic, complemented
3#13070804C211yesmaximal, characteristic, complemented
4#13070794C211yesmaximal, characteristic, complemented
5#13070780C211yesmaximal, characteristic, complemented
6#13070717C211yesmaximal, characteristic, complemented
7#13070700C211yesmaximal, characteristic, complemented
8#13070648C211yesmaximal, characteristic, complemented
9#13070539C211yesmaximal, characteristic, complemented
10#13070539C211yesmaximal, characteristic, complemented
11#13070478C211yesmaximal, characteristic, complemented
12#13070442C211yesmaximal, characteristic, complemented
13#13070328C211yesmaximal, characteristic, complemented
14#13070323C211yesmaximal, characteristic, complemented
15C11×#3287C211yesmaximal, characteristic, complemented
16C2×C11×#135C2211yescharacteristic
17C2×C11×#135C2211yescharacteristic
18C11×#550—21no—
19#10623096—21no—
20C11×#493C2211yescharacteristic
21C11×#466C2211yescharacteristic
22C11×#466C2211yescharacteristic
23C11×#460—21no—
24C11×#449—21no—
25C11×#449—21no—
26C4×C11×Q16C2211yescharacteristic
27C8×D4×C11C2211yescharacteristic
28C2×#66892C2211yescharacteristic
29C2×#66890C2211yescharacteristic
30C2×#66890C2211yescharacteristic
31#10622728C2211yescharacteristic
32#10622728C2211yescharacteristic
33#10622719C2211yescharacteristic
34C2×#66882C2211yescharacteristic
35C2×#66876C2211yescharacteristic
36C22×C11⋊C16C2211yescharacteristic
37#10622460—21no—
38#10622350—21no—
39#10622348—21no—
40C4×D88C2211yescharacteristic
41#10622296C2211yescharacteristic
42#10622202C2211yescharacteristic
43#10622202C2211yescharacteristic
44#10622202C2211yescharacteristic
45#10622200C2211yescharacteristic
46#10622200C2211yescharacteristic
47#10622200C2211yescharacteristic
48#10622200C2211yescharacteristic
49#10622200C2211yescharacteristic
50#10622200C2211yescharacteristic
51C22⋊(C11⋊C16)C2211yescharacteristic
52C22⋊(C11⋊C16)C2211yescharacteristic
53#10622129C2211yescharacteristic
54#10622128C2211yescharacteristic
55#10622127C2211yescharacteristic
56#10622127C2211yescharacteristic
57C4⋊(C11⋊C16)C2211yescharacteristic
58#10622099C2211yescharacteristic
59C2×C11×#41—21no—
60C2×C11×#41—21no—
61C11×#135—22no—
62C11×#135—22no—
63C11×#135—41no—
64C11×#135—41no—
65C2×C11×Q16C2311yescharacteristic
66C2×C11×SD16—21no—
67C2×C11×SD16—21no—
68C2×C11×D8—21no—
69C2×C11×D8C2311yescharacteristic
70C2×C11×D8C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C11×#127—21no—
74C11×#127—41no—
75C11×#121—21no—
76C11×#121—21no—
77C11×#121—41no—
78C11×#121—41no—
79C4×Q8×C11—21no—
80C4×D4×C11—41no—
81C4×D4×C11D411yescharacteristic
82#66992—41no—
83#66983—21no—
84#66983—21no—
85#66979—21no—
86C2×C4⋊Dic11—21no—
87C2×D88C2311yescharacteristic
88#66951—41no—
89#66936—41no—
90(C22⋊D11)⋊C4—41no—
91C4×D44—21no—
92#66923—21no—
93C11×#107C2311yescharacteristic
94C11×C4⋊C8D411yescharacteristic
95C11×#103—21no—
96C11×#102—21no—
97C11×#102—21no—
98C11×C22⋊C8D411yescharacteristic
99C11×C22⋊C8D411yescharacteristic
100C4×C8×C11C2311yescharacteristic
101#66892—22no—
102#66890—41no—
103#66890—41no—
104#66885—21no—
105#66885—21no—
106#66885—21no—
107#66882—21no—
108#66882C2311yescharacteristic
109#66882C2311yescharacteristic
110#66882C2311yescharacteristic
111#66881—21no—
112#66881—21no—
113#66876—41no—
114C2×C11⋊C16—41no—
115C2×C11⋊C16C2311yescharacteristic
116C2×C11⋊C16C2311yescharacteristic
117C2×C11⋊C16C2311yescharacteristic
118C2×C11⋊C16C2311yescharacteristic
119#33876—111nomaximal, Sylow
120C11×#41—42no—
121C11×#41—42no—
122C11×#41—81no—
123C11×#41—81no—
124C2×Q8×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—41no—
128C2×D4×C11—41no—
129C2×D4×C11—41no—
130C2×D4×C11—41no—
131C2×D4×C11—41no—
132C2×D4×C11—41no—
133C2×D4×C11D811yescharacteristic
134C22×C4×C11—41no—
135C22×C4×C11—41no—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C2×C22⋊D11—41no—
139C2×C22⋊D11—41no—
140C22×Dic11—41no—
141C2×D44—21no—
142C2×C4×D11—41no—
143C11×Q16—21no—
144C11×Q16#4112yes—
145C11×SD16—42no—
146C11×SD16—42no—
147C11×D8—21no—
148C11×D8—21no—
149C11×D8—21no—
150C11×D8—21no—
151C11×D8—81no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11C2×D411yescharacteristic
157C2×C8×C11C2×D411yescharacteristic
158C2×C8×C11C2×D411yescharacteristic
159C2×C8×C11C2411yescharacteristic
160C11×C4⋊C4—21no—
161C11×C4⋊C4—41no—
162C11×C4⋊C4D811yescharacteristic
163C11×C22⋊C4—41no—
164C11×C22⋊C4—41no—
165C11×C22⋊C4D811yescharacteristic
166C11×C22⋊C4D811yescharacteristic
167C42×C11—41no—
168C42×C11C2×D411yescharacteristic
169C22⋊Dic11—41no—
170(C2×D11)⋊C4—41no—
171(C2×D11)⋊C4—41no—
172(C2×D11)⋊C4—41no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—41no—
177Dic11⋊C4—41no—
178Dic11⋊C4—41no—
179C4×Dic11—41no—
180D88—21no—
181D88—21no—
182C11⋊C16—21no—
183C11⋊C16—21no—
184C11⋊C16—21no—
185C11⋊C16—21no—
186#3339—111no—
187#3287D1111yescharacteristic, complemented
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×C11—41no—
203C23×C11C2×D811yescharacteristic
204C23×C11C2×D811yescharacteristic
205C22×D11—41no—
206Q8×C11—22no—
207Q8×C11—41no—
208D4×C11—41no—
209D4×C11—41no—
210D4×C11—41no—
211D4×C11—41no—
212D4×C11—41no—
213D4×C11—82no—
214D4×C11—82no—
215D4×C11—82no—
216D4×C11—161no—
217D4×C11—161no—
218D4×C11—161no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—82no—
226C2×C4×C11—82no—
227C2×C4×C11C2×D811yescharacteristic
228C2×C4×C11C2×D811yescharacteristic
229C2×C4×C11C2×D811yescharacteristic
230C2×C4×C11C2×D811yescharacteristic
231C2×C4×C11C22×D411yescharacteristic
232C22⋊D11—82no—
233C22⋊D11—161no—
234C2×Dic11—41no—
235C2×Dic11—41no—
236C2×Dic11—41no—
237C2×Dic11—161no—
238D44—41no—
239D44—41no—
240C4×D11—161no—
241C8×C11—21no—
242C8×C11—21no—
243C8×C11—21no—
244C8×C11C2×#4111yescharacteristic
245C8×C11H(5,𝔽2)11yescharacteristic
246C2×#135C2×D1111yescharacteristic
247C2×#135C2×D1111yescharacteristic
248#553—221no—
249#550—21no—
250C2×SD32—111no—
251C2×D16—111no—
252C2×D16—111no—
253C2×M32—111no—
254C22×C16—111no—
255#499—111no—
256#493C2×D1111yescharacteristic
257#482—221no—
258#481—221no—
259#478—221no—
260#466—111no—
261#466—111no—
262#466C2×D1111yescharacteristic
263#466C2×D1111yescharacteristic
264#460—21no—
265#449—21no—
266#449—21no—
267C4×Q16C2×D1111yescharacteristic
268C4×D8—111no—
269C8×D4C2×D1111yescharacteristic
270#427—111no—
271C2×#107—111no—
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×C11—81no—
299C22×C11—81no—
300C22×C11—81no—
301C22×C11C22×D811yescharacteristic
302C2×D11—81no—
303C2×D11—81no—
304C2×D11—81no—
305C4×C11—21no—
306C4×C11—21no—
307C4×C11—21no—
308C4×C11—21no—
309C4×C11—42no—
310C4×C11—81no—
311C4×C11#54611yescharacteristic
312C4×C11#57711yescharacteristic
313Dic11—81no—
314Dic11—81no—
315Dic11—81no—
316C2×#41—21no—
317C2×#41—21no—
318#135—22no—
319#135—22no—
320#135—41no—
321#135—41no—
322C2×Q16C22×D1111yescharacteristic
323C2×SD16—21no—
324C2×SD16—21no—
325C2×D8—21no—
326C2×D8—111no—
327C2×D8C22×D1111yescharacteristic
328C2×D8C22×D1111yescharacteristic
329C22×C8C22×D1111yescharacteristic
330C22×C8C22×D1111yescharacteristic
331#127—21no—
332#127—41no—
333#126—441no—
334#125—221no—
335#123—441no—
336#121—21no—
337#121—21no—
338#121—41no—
339#121—41no—
340#121—221no—
341#121—221no—
342#121—441no—
343C4×Q8—21no—
344C4×D4—41no—
345C4×D4—221no—
346C4×D4—441no—
347C4×D4C22⋊D1111yescharacteristic
348#117—221no—
349C2×C4⋊C4—221no—
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—111no—
360#107—111no—
361#107—111no—
362#107—221no—
363#107C22×D1111yescharacteristic
364#106—221no—
365#106—221no—
366C4⋊C8C22⋊D1111yescharacteristic
367#103—21no—
368#102—21no—
369#102—21no—
370#102—221no—
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—161no—
380C2×C11#329411yescharacteristic
381C2×C11#341411yescharacteristic
382C2×C11#341511yescharacteristic
383D11—161no—
384#41—42no—
385#41—42no—
386#41—81no—
387#41—81no—
388C2×Q8—21no—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—41no—
392C2×D4—41no—
393C2×D4—41no—
394C2×D4—41no—
395C2×D4—41no—
396C2×D4—41no—
397C2×D4—221no—
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—21no—
408Q16#434112yes—
409SD16—42no—
410SD16—42no—
411D8—21no—
412D8—21no—
413D8—21no—
414D8—21no—
415D8—81no—
416D8—221no—
417D8—221no—
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—41no—
428C4⋊C4—221no—
429C4⋊C4—221no—
430C4⋊C4—221no—
431C4⋊C4—441no—
432C4⋊C4—441no—
433C4⋊C4—441no—
434C4⋊C4#432311yescharacteristic
435C22⋊C4—41no—
436C22⋊C4—41no—
437C22⋊C4—441no—
438C22⋊C4—441no—
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—41no—
453C23—441no—
454C23C2×#432311yescharacteristic
455C23C2×#432311yescharacteristic
456Q8—22no—
457Q8—41no—
458D4—41no—
459D4—41no—
460D4—41no—
461D4—41no—
462D4—41no—
463D4—82no—
464D4—82no—
465D4—82no—
466D4—161no—
467D4—161no—
468D4—161no—
469D4—441no—
470D4—441no—
471D4—882no—
472D4—1761no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—82no—
480C2×C4—82no—
481C2×C4—441no—
482C2×C4—441no—
483C2×C4—441no—
484C2×C4—1761no—
485C2×C4—1761no—
486C2×C4C2×#432311yescharacteristic
487C2×C4C2×#432311yescharacteristic
488C2×C4C2×#432311yescharacteristic
489C2×C4C2×#432311yescharacteristic
490C2×C4C22×C22⋊D1111yescharacteristic
491C8—21no—
492C8—21no—
493C8—21no—
494C8C2×#434111yescharacteristic
495C8#6703711yescharacteristic
496C22—21no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—81no—
503C22—81no—
504C22—81no—
505C22—81no—
506C22—81no—
507C22—81no—
508C22—881no—
509C22—881no—
510C22—881no—
511C22C22×#432311yescharacteristic
512C4—21no—
513C4—21no—
514C4—21no—
515C4—21no—
516C4—42no—
517C4—81no—
518C4—881no—
519C4—881no—
520C4—881no—
521C4#1062333711yescharacteristic
522C4#1062336711yescharacteristic
523C2—41no—
524C2—41no—
525C2—161no—
526C2—161no—
527C2—1761no—
528C2#1308042911yescharacteristic
529C2#1308175011yescharacteristic
530C2#1308175511yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3287C2
socleC22×C11C22×D8
hypercenter#3287D11
hypocenterC11#33876
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3287

Complements

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

NH ≅ G/Ntype
1. #13081019C2semidirect
2. #13070857C2semidirect
3. #13070804C2semidirect
4. #13070794C2semidirect
5. #13070780C2semidirect
6. #13070717C2semidirect
7. #13070700C2semidirect
8. #13070648C2semidirect
9. #13070539C2semidirect
10. #13070539C2semidirect
11. #13070478C2semidirect
12. #13070442C2semidirect
13. #13070328C2semidirect
14. #13070323C2semidirect
15. C11×#3287C2semidirect
187. #3287D11semidirect
450. C11#33876semidirect

Maximal subgroups

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

subgroupindex
#130810192
#130708572
#130708042
#130707942
#130707802
#130707172
#130707002
#130706482
#130705392
#130704782
#130704422
#130703282
#130703232
C11×#32872
#3387611