Finite Group Databasebeta

← #14776289

Subgroups — #14776289

Order 2816.

880 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078073C211yesmaximal, characteristic
2C2×#10622507C212yesmaximal, complemented
3#13077362C211yesmaximal, characteristic, complemented
4#13077185C211yesmaximal, characteristic, complemented
5#13069443C211yesmaximal, characteristic, complemented
6#13069325C212yesmaximal, complemented
7#13068944C212yesmaximal, complemented
8#13068888C212yesmaximal, complemented
9#13068471C211yesmaximal, characteristic, complemented
10C4×#66889C211yesmaximal, characteristic, complemented
11C11×#1950C211yesmaximal, characteristic, complemented
12C2×#66960C2212yes—
13C2×#66960C2212yes—
14C2×#66957C2212yes—
15#10623008C2211yescharacteristic
16C4×#4339C2211yescharacteristic
17C2×C11×#108C2212yes—
18C11×#423C2211yescharacteristic
19C2×C11×C4⋊C8C2211yescharacteristic
20C4×C11×M16C2211yescharacteristic
21C2×#66889C2212yes—
22C2×#66889C2211yescharacteristic
23C2×#66889C2212yes—
24C2×#66889C2211yescharacteristic
25#10622742C2212yes—
26#10622732C2212yes—
27#10622726C2212yes—
28C2×#66879C2212yes—
29C42×Dic11C2211yescharacteristic
30C2×C4⋊(C11⋊C8)C2211yescharacteristic
31#10622507—28no—
32#10622462C411yescharacteristic, complemented
33#10622461C411yescharacteristic, complemented
34#10622458C412yescomplemented
35#10622457C412yescomplemented
36#10622456C411yescharacteristic, complemented
37#10622454C411yescharacteristic, complemented
38#10622452—22no—
39#10622450—21no—
40D11×C4⋊C8—21no—
41#10622319—22no—
42#10622301—21no—
43C8×D44—21no—
44C11×#341C2212yes—
45#10622193C2211yescharacteristic
46#10622193C2211yescharacteristic
47#10622188C2212yes—
48C2×#4339C2312yes—
49C2×#4339C2311yescharacteristic
50C2×C11×M16C2312yes—
51C2×C11×M16C2311yescharacteristic
52C2×C11×M16C2311yescharacteristic
53C22×C8×C11C2312yes—
54C2×C42×C11C2311yescharacteristic
55#66983—21no—
56#66983—21no—
57C4×C22⋊D11—21no—
58C4×C22⋊D11—21no—
59#66979C2311yescharacteristic
60C2×C4×Dic11—21no—
61C2×C4×Dic11—21no—
62C2×C4×Dic11C2311yescharacteristic
63C2×C4×Dic11C2311yescharacteristic
64C22×C11⋊C8C2312yes—
65#66960—24no—
66#66960—24no—
67#66960—42no—
68#66960—42no—
69C2×Dic44C2×C412yes—
70#66957—24no—
71#66957—24no—
72C2×D88C2×C412yes—
73C2×#4314C2×C412yes—
74C2×#4314C2×C412yes—
75C2×#4313—22no—
76C2×#4313—22no—
77C2×C8×D11—22no—
78C2×C8×D11—22no—
79#66928C2×C412yes—
80#66927C2×C411yescharacteristic
81C4×D44—21no—
82C4×D44—21no—
83C4×D44C2×C411yescharacteristic
84C4×D44C2×C411yescharacteristic
85#66925—21no—
86C42×D11—21no—
87#66922C2×C411yescharacteristic
88C4×Dic22C2×C411yescharacteristic
89C4×Dic22C2×C411yescharacteristic
90C11×#108—24no—
91C11×C4⋊C8—21no—
92C11×C4⋊C8—21no—
93C11×C4⋊C8C2×C411yescharacteristic
94C11×C4⋊C8C2×C411yescharacteristic
95C11×C4⋊C8C2×C412yes—
96C11×#97—21no—
97C4×C8×C11—21no—
98#66889—22no—
99#66889—24no—
100#66889—42no—
101#66889D414yescomplemented
102#66885C2×C412yes—
103#66885C2×C412yes—
104(C2×D11)⋊C8—22no—
105(C2×D11)⋊C8—22no—
106#66880C2×C412yes—
107#66880C2×C412yes—
108#66879—24no—
109Dic11⋊C8—22no—
110Dic11⋊C8—22no—
111C4⋊(C11⋊C8)D411yescharacteristic
112C4⋊(C11⋊C8)D411yescharacteristic
113C4⋊(C11⋊C8)D412yes—
114#23016—111nomaximal, Sylow
115C22×C4×C11#4111yescharacteristic
116C22×C4×C11#4111yescharacteristic
117C22×C4×C11C2411yescharacteristic
118C2×C22⋊D11—21no—
119C2×C22⋊D11—22no—
120C22×Dic11—21no—
121C22×Dic11—21no—
122#4339—22no—
123#4339—22no—
124#4339—21no—
125#4339—22no—
126#4339—21no—
127#4339—22no—
128#4339C2×D412yes—
129#4339#4112yes—
130C2×D44—21no—
131C2×D44—21no—
132C2×D44C22×C412yes—
133C2×D44C22×C411yescharacteristic
134C2×C4×D11—21no—
135C2×C4×D11—21no—
136C2×C4×D11—21no—
137C2×C4×D11—22no—
138C2×Dic22C22×C412yes—
139C2×Dic22C22×C411yescharacteristic
140C11×M16—22no—
141C11×M16—21no—
142C11×M16—21no—
143C11×M16—22no—
144C11×M16—21no—
145C11×M16C2×D412yes—
146C2×C8×C11—22no—
147C2×C8×C11—21no—
148C2×C8×C11—22no—
149C2×C8×C11—21no—
150C2×C8×C11—22no—
151C2×C8×C11C22×C412yes—
152C2×C8×C11C22×C412yes—
153C42×C11C22×C411yescharacteristic
154C42×C11C22×C411yescharacteristic
155C42×C11C2×D411yescharacteristic
156C42×C11C2×D411yescharacteristic
157C22⋊Dic11—21no—
158(C2×D11)⋊C4—21no—
159(C2×D11)⋊C4—21no—
160(C2×D11)⋊C4—22no—
161(C2×D11)⋊C4—22no—
162C4⋊Dic11—21no—
163C4⋊Dic11—21no—
164C4⋊Dic11C22×C411yescharacteristic
165C4⋊Dic11C22×C411yescharacteristic
166Dic11⋊C4—21no—
167Dic11⋊C4—21no—
168C4×Dic11—21no—
169C4×Dic11—21no—
170C4×Dic11—21no—
171C4×Dic11—21no—
172C4×Dic11—21no—
173C4×Dic11—21no—
174C4×Dic11—42no—
175C4×Dic11—42no—
176C4×Dic11C2×D412yes—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—22no—
179C2×C11⋊C8C2×D412yes—
180C2×C11⋊C8C2×D412yes—
181Dic44—24no—
182D88—24no—
183#4314—24no—
184#4314—24no—
185#4313—44no—
186#4313—44no—
187C8×D11—44no—
188C8×D11—44no—
189#3035—111no—
190C2×#444—112no—
191#2935—111no—
192#2906—111no—
193#1962—111no—
194#1950D1111yescharacteristic, complemented
195#1938—112no—
196#1876—112no—
197#1866—112no—
198#1767—111no—
199C4×#104—111no—
200C23×C11C2×#4111yescharacteristic
201C22×D11—21no—
202C22×D11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—41no—
205C2×C4×C11C4×D411yescharacteristic
206C2×C4×C11C4×D411yescharacteristic
207C2×C4×C11C4×D411yescharacteristic
208C2×C4×C11C4×D411yescharacteristic
209C2×C4×C11C23×C411yescharacteristic
210C2×C4×C11C22×D411yescharacteristic
211C2×C4×C11C22×D411yescharacteristic
212C2×C4×C11C2×#4111yescharacteristic
213C2×C4×C11H(5,𝔽2)11yescharacteristic
214C2×C4×C112−1+411yescharacteristic
215C22⋊D11—22no—
216C22⋊D11—22no—
217C22⋊D11—42no—
218C22⋊D11—42no—
219C2×Dic11—21no—
220C2×Dic11—22no—
221C2×Dic11—21no—
222C2×Dic11—21no—
223C2×Dic11—22no—
224C2×Dic11—22no—
225C2×Dic11—41no—
226C2×Dic11—41no—
227C2×Dic11—41no—
228C2×Dic11—41no—
229D44—22no—
230D44—21no—
231D44—22no—
232D44—42no—
233D44—81no—
234D44C4×D412yes—
235C4×D11—22no—
236C4×D11—22no—
237C4×D11—42no—
238C4×D11—42no—
239C4×D11—42no—
240C4×D11—81no—
241Dic22—21no—
242Dic22—22no—
243Dic22—22no—
244Dic22C4×D412yes—
245C8×C11—22no—
246C8×C11—22no—
247C8×C11—22no—
248C8×C11—42no—
249C8×C11—41no—
250C11⋊C8—22no—
251C11⋊C8—22no—
252C2×#135—112no—
253C2×#131—112no—
254C2×#131—112no—
255#532—111no—
256C4×#41—111no—
257#464—112no—
258#463—112no—
259#462—111no—
260#461—111no—
261#460—111no—
262#459—111no—
263#444—228no—
264#436—221no—
265#435—222no—
266C8×D4—221no—
267C2×#108C2×D1112yes—
268#424—112no—
269#424—222no—
270#423—221no—
271#423C2×D1111yescharacteristic
272C2×C4⋊C8—111no—
273C2×C4⋊C8—221no—
274C2×C4⋊C8C2×D1111yescharacteristic
275C2×#104—111no—
276C2×#104—111no—
277C2×#104—112no—
278C2×#104—112no—
279#416—112no—
280#408—112no—
281C4×M16C2×D1111yescharacteristic
282C2×#97—112no—
283C43—111no—
284#341C2×D1112yes—
285#339—111no—
286#339—111no—
287#336—112no—
288C22×C11—21no—
289C22×C11—21no—
290C22×C11C2×C4×D411yescharacteristic
291C22×C11#54711yescharacteristic
292C22×C11#55311yescharacteristic
293C2×D11—22no—
294C2×D11—41no—
295C2×D11—41no—
296C2×D11—42no—
297C2×D11—42no—
298C2×D11—42no—
299C4×C11—21no—
300C4×C11—21no—
301C4×C11—21no—
302C4×C11#44412yescomplemented
303C4×C11C2×C4×D411yescharacteristic
304C4×C11#52011yescharacteristic
305C4×C11D4211yescharacteristic
306C4×C11#54811yescharacteristic
307Dic11—22no—
308Dic11—42no—
309Dic11—42no—
310Dic11—42no—
311Dic11—41no—
312Dic11—41no—
313C2×#41—111no—
314C2×#41—112no—
315#135—224no—
316#135—224no—
317C2×Q16—112no—
318C2×SD16—112no—
319C2×SD16—112no—
320C2×D8—112no—
321#131—224no—
322#131—224no—
323#131—442no—
324#131—442no—
325C2×M16—222no—
326C2×M16—222no—
327C2×M16C22×D1112yes—
328C2×M16C22×D1111yescharacteristic
329C2×M16C22×D1111yescharacteristic
330C22×C8—112no—
331C22×C8—222no—
332C22×C8—222no—
333C22×C8C22×D1112yes—
334C4⋊Q8—111no—
335#127—111no—
336#124—112no—
337#121—221no—
338#121—221no—
339C4×Q8—111no—
340C4×Q8—111no—
341C4×D4—111no—
342C4×D4—111no—
343C4×D4—221no—
344C4×D4—221no—
345C4×D4—221no—
346C4×D4—221no—
347#117—111no—
348#117—221no—
349C2×C42—111no—
350C2×C42—111no—
351C2×C42—221no—
352C2×C42—221no—
353C2×C42—221no—
354C2×C42C22×D1111yescharacteristic
355#108—24no—
356C4⋊C8—21no—
357C4⋊C8—21no—
358C4⋊C8—111no—
359C4⋊C8—111no—
360C4⋊C8—112no—
361C4⋊C8—222no—
362C4⋊C8—222no—
363C4⋊C8C4×D1111yescharacteristic
364C4⋊C8C4×D1111yescharacteristic
365C4⋊C8C4×D1112yes—
366#104—114no—
367#104—224no—
368#104—222no—
369#104—442no—
370#103—112no—
371#103—112no—
372#102—112no—
373#102—112no—
374C22⋊C8—222no—
375C22⋊C8—222no—
376#97—21no—
377#97—224no—
378C4×C8—21no—
379C2×C11—21no—
380C2×C11—21no—
381C2×C11#236111yescharacteristic
382C2×C11C2×#44411yescharacteristic
383C2×C11#295611yescharacteristic
384D11—42no—
385D11—82no—
386#41—112no—
387#41—112no—
388#41—221no—
389#41—221no—
390#41—222no—
391#41—222no—
392#41—222no—
393#41—222no—
394C2×Q8—111no—
395C2×Q8—112no—
396C2×D4—111no—
397C2×D4—112no—
398C2×D4—221no—
399C2×D4—222no—
400C2×D4—221no—
401C2×D4—221no—
402C22×C4—221no—
403C22×C4—221no—
404C22×C4—221no—
405C22×C4—221no—
406C22×C4—222no—
407C22×C4—221no—
408C22×C4#434311yescharacteristic
409C22×C4#434311yescharacteristic
410C22×C4C23×D1111yescharacteristic
411Q16—224no—
412SD16—224no—
413SD16—224no—
414D8—224no—
415M16—21no—
416M16—22no—
417M16—21no—
418M16—21no—
419M16—22no—
420M16—444no—
421M16—444no—
422M16D4×D1112yes—
423C2×C8—22no—
424C2×C8—21no—
425C2×C8—22no—
426C2×C8—21no—
427C2×C8—22no—
428C2×C8—112no—
429C2×C8—112no—
430C2×C8—222no—
431C2×C8—222no—
432C2×C8—444no—
433C2×C8—444no—
434C2×C8C2×C4×D1112yes—
435C2×C8C2×C4×D1112yes—
436C4⋊C4—111no—
437C4⋊C4—111no—
438C4⋊C4—221no—
439C4⋊C4—221no—
440C4⋊C4—221no—
441C4⋊C4—221no—
442C22⋊C4—221no—
443C22⋊C4—221no—
444C22⋊C4—221no—
445C22⋊C4—222no—
446C22⋊C4—222no—
447C42—112no—
448C42—221no—
449C42—221no—
450C42—221no—
451C42—221no—
452C42—221no—
453C42—221no—
454C42—442no—
455C42—442no—
456C42C2×C4×D1111yescharacteristic
457C42C2×C4×D1111yescharacteristic
458C42D4×D1111yescharacteristic
459C42D4×D1111yescharacteristic
460C11#2301611yescharacteristic, complemented, Sylow
461C23—221no—
462C23—222no—
463C23C2×#434311yescharacteristic
464Q8—112no—
465Q8—221no—
466Q8—222no—
467Q8—222no—
468D4—112no—
469D4—222no—
470D4—222no—
471D4—222no—
472D4—221no—
473D4—222no—
474D4—442no—
475D4—442no—
476D4—442no—
477D4—881no—
478C2×C4—22no—
479C2×C4—41no—
480C2×C4—221no—
481C2×C4—222no—
482C2×C4—222no—
483C2×C4—222no—
484C2×C4—222no—
485C2×C4—221no—
486C2×C4—221no—
487C2×C4—222no—
488C2×C4—441no—
489C2×C4—441no—
490C2×C4—441no—
491C2×C4—441no—
492C2×C4—442no—
493C2×C4—442no—
494C2×C4—442no—
495C2×C4—881no—
496C2×C4#6694611yescharacteristic
497C2×C4#6694611yescharacteristic
498C2×C4#6694611yescharacteristic
499C2×C4#6694611yescharacteristic
500C2×C4C22×C4×D1111yescharacteristic
501C2×C4C2×D4×D1111yescharacteristic
502C2×C4C2×D4×D1111yescharacteristic
503C2×C4#6704011yescharacteristic
504C2×C4#41×D1111yescharacteristic
505C2×C4#6704211yescharacteristic
506C8—22no—
507C8—22no—
508C8—22no—
509C8—42no—
510C8—41no—
511C8—222no—
512C8—222no—
513C22—21no—
514C22—21no—
515C22—222no—
516C22—441no—
517C22—441no—
518C22—442no—
519C22—442no—
520C22—442no—
521C22C2×#6694611yescharacteristic
522C22#1062322611yescharacteristic
523C22#1062325711yescharacteristic
524C4—21no—
525C4—21no—
526C4—21no—
527C4—222no—
528C4—442no—
529C4—442no—
530C4—441no—
531C4—442no—
532C4—441no—
533C4#1062250712yescomplemented
534C4C4×D4×D1111yescharacteristic
535C4#1062310511yescharacteristic
536C4#1062314011yescharacteristic
537C4#1062316411yescharacteristic
538C2—21no—
539C2—21no—
540C2—442no—
541C2—882no—
542C2#1307163111yescharacteristic
543C2C2×#1062250711yescharacteristic
544C2#1307752511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1950C2
socleC22×C11C2×C4×D4
prime radical#13078073C2
cosocleC22×C4×C11C24
hypercenter#1950D11
hypocenterC11#23016
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1950

Complements

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

NH ≅ G/Ntype
2. C2×#10622507C2semidirect
3. #13077362C2semidirect
4. #13077185C2semidirect
5. #13069443C2semidirect
6. #13069325C2semidirect
7. #13068944C2semidirect
8. #13068888C2semidirect
9. #13068471C2semidirect
10. C4×#66889C2semidirect
11. C11×#1950C2semidirect
32. #10622462C4semidirect
33. #10622461C4semidirect
34. #10622458C4semidirect
35. #10622457C4semidirect
36. #10622456C4semidirect
37. #10622454C4semidirect
101. #66889D4semidirect
194. #1950D11semidirect
302. C4×C11#444semidirect
460. C11#23016semidirect
533. C4#10622507semidirect

Maximal subgroups

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

subgroupindex
#130780732
C2×#106225072
#130773622
#130771852
#130694432
#130693252
#130689442
#130688882
#130684712
C4×#668892
C11×#19502
#2301611