Finite Group Databasebeta

← #14722221

Subgroups — #14722221

Order 2816.

1172 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082396C211yesmaximal, characteristic
2#13077724C211yesmaximal, characteristic, complemented
3#13077181C211yesmaximal, characteristic, complemented
4#13067293C211yesmaximal, characteristic, complemented
5#13067290C212yesmaximal, complemented
6#13067287C211yesmaximal, characteristic, complemented
7#13067286C212yesmaximal, complemented
8#13067262C212yesmaximal, complemented
9C2×#10622120C211yesmaximal, characteristic, complemented
10D11×#332C212yesmaximal, complemented
11C11×#1540C211yesmaximal, characteristic, complemented
12C2×#67043—21no—
13C11×#532C2211yescharacteristic
14#10623356—21no—
15C2×#66954—21no—
16D11×C4⋊Q8C2212yes—
17#10623247C2212yes—
18#10623206—22no—
19#10623142—22no—
20#10623142C414yes—
21#10623082—21no—
22#10623082C412yes—
23D4×Dic22—21no—
24D4×Dic22C412yes—
25C4×#4339C2211yescharacteristic
26C2×#66922C2211yescharacteristic
27C11×#431C2211yescharacteristic
28C2×C11×C4⋊C8C2211yescharacteristic
29#10622715—21no—
30#10622537C2211yescharacteristic
31C2×C4⋊(C11⋊C8)C2211yescharacteristic
32#10622452—22no—
33#10622450C2212yes—
34#10622446C2212yes—
35D11×C4⋊C8C2212yes—
36D11×C4⋊C8C2212yes—
37(C22⋊D11)⋊C8—22no—
38C8×D44—21no—
39C8×Dic22—21no—
40C11×#332C2211yescharacteristic
41C11×#332C2211yescharacteristic
42C11×#331C2211yescharacteristic
43C11×#331C2211yescharacteristic
44#10622185C2212yes—
45#10622182C2212yes—
46#10622124C2212yes—
47#10622124C2212yes—
48#10622120C2212yes—
49#10622120C2212yes—
50C2×C11×#41—21no—
51#67043—44no—
52#67043—44no—
53C2×Q8×D11—22no—
54C2×#4341—24no—
55C2×#4341—22no—
56C2×#4339—22no—
57C2×#4339D411yescharacteristic
58C22×Dic22—21no—
59C22×Dic22—22no—
60C22×C8×C11—21no—
61C11×C4⋊Q8C2311yescharacteristic
62C11×#127C2311yescharacteristic
63C11×#124—21no—
64C11×#121—21no—
65C11×#121C2×C412yes—
66C4×D4×C11—21no—
67C4×D4×C11C2×C412yes—
68C2×C42×C11C2311yescharacteristic
69#66997—22no—
70#66991—22no—
71#66991C2×C414yes—
72#66989—22no—
73#66988—24no—
74D4×Dic11—22no—
75D4×Dic11C2×C414yes—
76C4×C22⋊D11C2×C412yes—
77C4×C22⋊D11D412yes—
78#66979D411yescharacteristic
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11C2×C412yes—
81#66977—22no—
82#66977—22no—
83C2×#4318—21no—
84C22×C11⋊C8—21no—
85#66954—44no—
86C2×#4313—22no—
87C2×C8×D11—22no—
88C2×C8×D11—22no—
89C4⋊C4×D11—22no—
90C4⋊C4×D11C2×C414yes—
91#66941—22no—
92#66941C2×C414yes—
93#66936—24no—
94#66936—24no—
95#66931—24no—
96#66931—24no—
97C4×D44C2×C411yescharacteristic
98C4×D44D411yescharacteristic
99#66925D412yes—
100C42×D11C2312yes—
101#66922—21no—
102#66922—21no—
103#66922C2×C412yes—
104#66922C2312yes—
105C4×Dic22C2×C411yescharacteristic
106C4×Dic22D411yescharacteristic
107C11×C4⋊C8—21no—
108C11×C4⋊C8C2311yescharacteristic
109C11×C4⋊C8C2311yescharacteristic
110C11×C4⋊C8C2311yescharacteristic
111C11×C4⋊C8C2311yescharacteristic
112C11×C22⋊C8—21no—
113C4×C8×C11—21no—
114(C2×D11)⋊C8—22no—
115Dic11⋊C8—22no—
116Dic11⋊C8—22no—
117Dic11⋊C8—22no—
118C8×Dic11—22no—
119C4⋊(C11⋊C8)—21no—
120C4⋊(C11⋊C8)—21no—
121C4⋊(C11⋊C8)C2312yes—
122C4⋊(C11⋊C8)C2312yes—
123#17721—111nomaximal, Sylow
124C11×#41—42no—
125C11×#41—42no—
126C2×Q8×C11—21no—
127C2×D4×C11—22no—
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11C22×C412yes—
131C22×C4×C11—22no—
132C22×C4×C11C22×C411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C2×C22⋊D11—24no—
136C2×C22⋊D11C22⋊C412yes—
137C22×Dic11—24no—
138C22×Dic11—22no—
139Q8×D11—44no—
140Q8×D11—44no—
141#4341—416no—
142#4341—44no—
143#4341—44no—
144#4339—48no—
145#4339D814yes—
146#4339SD1614yes—
147C2×D44C22⋊C411yescharacteristic
148C2×C4×D11—24no—
149C2×C4×D11C22×C412yes—
150C2×C4×D11C2×D412yes—
151C2×C4×D11C2×D412yes—
152C2×Dic22—24no—
153C2×Dic22—22no—
154C2×Dic22—22no—
155C2×Dic22—48no—
156C2×Dic22—42no—
157C2×Dic22—42no—
158C2×Dic22C22⋊C411yescharacteristic
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—42no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4C22×C412yes—
166C11×C22⋊C4—22no—
167C11×C22⋊C4—22no—
168C42×C11C22×C411yescharacteristic
169C42×C11C2×D411yescharacteristic
170C42×C11C2×D411yescharacteristic
171C42×C11C2411yescharacteristic
172C22⋊Dic11—24no—
173C22⋊Dic11—24no—
174C22⋊Dic11C22⋊C412yes—
175(C2×D11)⋊C4C22⋊C412yes—
176(C2×D11)⋊C4C22⋊C412yes—
177C4⋊Dic11—22no—
178C4⋊Dic11—22no—
179C4⋊Dic11—22no—
180C4⋊Dic11C22⋊C411yescharacteristic
181C4⋊Dic11C22⋊C411yescharacteristic
182C4⋊Dic11C22×C414yes—
183Dic11⋊C4—24no—
184Dic11⋊C4—24no—
185Dic11⋊C4C22⋊C412yes—
186Dic11⋊C4C22⋊C412yes—
187C4×Dic11C22×C412yes—
188C4×Dic11C2×D412yes—
189C4×Dic11C2×D412yes—
190#4318—42no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8—81no—
194#4313—44no—
195C8×D11—44no—
196C8×D11—82no—
197#3499—111no—
198#2988—111no—
199#2906—111no—
200#1547—112no—
201#1547—111no—
202#1546—111no—
203#1546—112no—
204#1540—112no—
205#1540D1111yescharacteristic, complemented
206C2×#332—111no—
207C2×#332—112no—
208C23×C11—22no—
209C23×C11C2×C22⋊C411yescharacteristic
210C22×D11C2×C22⋊C412yes—
211Q8×C11—41no—
212Q8×C11—41no—
213D4×C11—42no—
214D4×C11—44no—
215D4×C11—41no—
216D4×C11—41no—
217D4×C11—41no—
218D4×C11—41no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—22no—
222C2×C4×C11—41no—
223C2×C4×C11—44no—
224C2×C4×C11C2×C22⋊C411yescharacteristic
225C2×C4×C11C2×C22⋊C411yescharacteristic
226C2×C4×C11C2×C22⋊C411yescharacteristic
227C2×C4×C11C2×D812yes—
228C2×C4×C11C2×SD1612yes—
229C2×C4×C11C23×C411yescharacteristic
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C22×D411yescharacteristic
232C22⋊D11—48no—
233C22⋊D11#10218yes—
234C2×Dic11—24no—
235C2×Dic11—44no—
236C2×Dic11—48no—
237C2×Dic11C2×C22⋊C412yes—
238C2×Dic11C2×C22⋊C412yes—
239C2×Dic11C2×C22⋊C412yes—
240D44#10214yes—
241C4×D11—22no—
242C4×D11—22no—
243C4×D11—42no—
244C4×D11—48no—
245C4×D11C2×D814yes—
246C4×D11C2×SD1614yes—
247Dic22—42no—
248Dic22—42no—
249Dic22—44no—
250Dic22—48no—
251Dic22#10214yes—
252C8×C11—41no—
253C8×C11—41no—
254C8×C11—41no—
255C8×C11—41no—
256C11⋊C8—42no—
257C11⋊C8—42no—
258C2×2−1+4—221no—
259C2×#131—221no—
260D4×Q8—112no—
261D4×Q8—221no—
262#547—114no—
263#547—112no—
264#547—221no—
265#547—222no—
266#536—222no—
267#536—221no—
268#532—112no—
269#532C2×D1111yescharacteristic
270C2×C4⋊Q8—112no—
271C2×C4⋊Q8—111no—
272C4×#41—111no—
273C8×Q8—221no—
274C8×D4—221no—
275C8×D4—222no—
276#431—112no—
277#431C2×D1111yescharacteristic
278#424—222no—
279#424—221no—
280#423—111no—
281#423—112no—
282C2×C4⋊C8—111no—
283C2×C4⋊C8—112no—
284C2×C4⋊C8—112no—
285C2×C4⋊C8C2×D1111yescharacteristic
286#332—112no—
287#332—112no—
288#332—112no—
289#332—112no—
290#332—112no—
291#332C2×D1111yescharacteristic
292#332C2×D1111yescharacteristic
293#331—112no—
294#331C2×D1111yescharacteristic
295#331C2×D1111yescharacteristic
296C22×C11—21no—
297C22×C11—21no—
298C22×C11—42no—
299C22×C11—42no—
300C22×C11—42no—
301C22×C11C2×#10212yes—
302C22×C11C22×C22⋊C411yescharacteristic
303C2×D11—22no—
304C2×D11—22no—
305C2×D11C2×#10214yes—
306C4×C11—21no—
307C4×C11—21no—
308C4×C11—21no—
309C4×C11—42no—
310C4×C11C2×#10212yes—
311C4×C11C22×D811yescharacteristic
312C4×C11C22×SD1611yescharacteristic
313C4×C11#57711yescharacteristic
314C4×C11#57811yescharacteristic
315Dic11—22no—
316Dic11—22no—
317Dic11—44no—
318Dic11C2×#10214yes—
3192−1+4—444no—
3202−1+4—444no—
321C2×#41—21no—
322C2×#41—111no—
323C2×#41—222no—
324C2×#41—222no—
325C2×#41—224no—
326C22×Q8—222no—
327C22×Q8—222no—
328C22×Q8—221no—
329#131—444no—
330C2×M16—222no—
331C2×M16—221no—
332C22×C8—21no—
333C22×C8—222no—
334C22×C8—222no—
335C22×C8—221no—
336C4⋊Q8—114no—
337C4⋊Q8—112no—
338C4⋊Q8—112no—
339C4⋊Q8—222no—
340C4⋊Q8—222no—
341C4⋊Q8—221no—
342C4⋊Q8—221no—
343C4⋊Q8C22×D1111yescharacteristic
344#127C22×D1111yescharacteristic
345#124—21no—
346#124—222no—
347#123—224no—
348#123—224no—
349#123—224no—
350C22⋊Q8—224no—
351C22⋊Q8—224no—
352C22⋊Q8—222no—
353C22⋊Q8—222no—
354#121—21no—
355#121—114no—
356#121—222no—
357#121C4×D1112yes—
358C4×Q8—111no—
359C4×Q8—111no—
360C4×D4—21no—
361C4×D4—112no—
362C4×D4—112no—
363C4×D4—114no—
364C4×D4—111no—
365C4×D4—111no—
366C4×D4—222no—
367C4×D4C4×D1112yes—
368#117—111no—
369#117—112no—
370C2×C4⋊C4—112no—
371C2×C4⋊C4—114no—
372C2×C4⋊C4—222no—
373C2×C4⋊C4—221no—
374C2×C42—112no—
375C2×C42C22×D1111yescharacteristic
376C4⋊C8—21no—
377C4⋊C8—112no—
378C4⋊C8—112no—
379C4⋊C8—222no—
380C4⋊C8—222no—
381C4⋊C8—222no—
382C4⋊C8—221no—
383C4⋊C8—221no—
384C4⋊C8C22×D1111yescharacteristic
385C4⋊C8C22×D1111yescharacteristic
386C4⋊C8C22×D1111yescharacteristic
387C4⋊C8C22×D1111yescharacteristic
388C22⋊C8—21no—
389C22⋊C8—222no—
390C4×C8—21no—
391C4×C8—222no—
392C2×C11—22no—
393C2×C11—82no—
394C2×C11#288911yescharacteristic
395C2×C11C22×#10211yescharacteristic
396C2×C11#289811yescharacteristic
397D11—24no—
398#41—42no—
399#41—42no—
400#41—114no—
401#41—114no—
402#41—448no—
403#41—444no—
404#41—444no—
405#41—4416no—
406C2×Q8—21no—
407C2×Q8—111no—
408C2×Q8—224no—
409C2×Q8—222no—
410C2×Q8—222no—
411C2×Q8—448no—
412C2×Q8—444no—
413C2×Q8—444no—
414C2×Q8—442no—
415C2×Q8—442no—
416C2×D4—22no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—112no—
420C2×D4—111no—
421C2×D4—224no—
422C2×D4C2×C4×D1112yes—
423C22×C4—22no—
424C22×C4—112no—
425C22×C4—112no—
426C22×C4—112no—
427C22×C4—224no—
428C22×C4—224no—
429C22×C4—222no—
430C22×C4C2×C4×D1111yescharacteristic
431C22×C4D4×D1111yescharacteristic
432C22×C4D4×D1111yescharacteristic
433M16—444no—
434M16—442no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—42no—
440C2×C8—222no—
441C2×C8—222no—
442C2×C8—444no—
443C2×C8—882no—
444C2×C8—881no—
445C4⋊C4—21no—
446C4⋊C4—112no—
447C4⋊C4—112no—
448C4⋊C4—111no—
449C4⋊C4—111no—
450C4⋊C4—114no—
451C4⋊C4—224no—
452C4⋊C4—224no—
453C4⋊C4—222no—
454C4⋊C4—222no—
455C4⋊C4—222no—
456C4⋊C4C2×C4×D1112yes—
457C22⋊C4—22no—
458C22⋊C4—22no—
459C22⋊C4—112no—
460C22⋊C4—112no—
461C22⋊C4—112no—
462C22⋊C4—224no—
463C22⋊C4—224no—
464C42—112no—
465C42—112no—
466C42—112no—
467C42C2×C4×D1111yescharacteristic
468C42D4×D1111yescharacteristic
469C42D4×D1111yescharacteristic
470C42C23×D1111yescharacteristic
471C11#1772111yescharacteristic, complemented, Sylow
472C23—22no—
473C23—112no—
474C23C22⋊C4×D1111yescharacteristic
475Q8—41no—
476Q8—41no—
477Q8—114no—
478Q8—448no—
479Q8—442no—
480Q8—442no—
481Q8—444no—
482D4—42no—
483D4—44no—
484D4—41no—
485D4—41no—
486D4—41no—
487D4—41no—
488D4—118no—
489D4—114no—
490D4—448no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—22no—
494C2×C4—41no—
495C2×C4—44no—
496C2×C4—112no—
497C2×C4—114no—
498C2×C4—114no—
499C2×C4—112no—
500C2×C4—112no—
501C2×C4—222no—
502C2×C4—222no—
503C2×C4—224no—
504C2×C4—442no—
505C2×C4—448no—
506C2×C4—448no—
507C2×C4—444no—
508C2×C4C22⋊C4×D1111yescharacteristic
509C2×C4C22⋊C4×D1111yescharacteristic
510C2×C4C22⋊C4×D1111yescharacteristic
511C2×C4D8×D1112yes—
512C2×C4SD16×D1112yes—
513C2×C4C22×C4×D1111yescharacteristic
514C2×C4C2×D4×D1111yescharacteristic
515C2×C4C2×D4×D1111yescharacteristic
516C8—41no—
517C8—41no—
518C8—41no—
519C8—41no—
520C8—442no—
521C8—442no—
522C22—21no—
523C22—21no—
524C22—42no—
525C22—42no—
526C22—42no—
527C22—114no—
528C22—222no—
529C22—222no—
530C22D11×#10212yes—
531C22C2×C22⋊C4×D1111yescharacteristic
532C4—21no—
533C4—21no—
534C4—21no—
535C4—42no—
536C4—114no—
537C4—222no—
538C4—222no—
539C4—444no—
540C4D11×#10212yes—
541C4C2×D8×D1111yescharacteristic
542C4C2×SD16×D1111yescharacteristic
543C4#1062330111yescharacteristic
544C4#1062330211yescharacteristic
545C2—22no—
546C2—82no—
547C2—224no—
548C2#1307709711yescharacteristic
549C2C2×D11×#10211yescharacteristic
550C2#1307714511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1540C2
socleC22×C11C22×C22⋊C4
prime radical#13082396C2
cosocleC42×C11C24
hypercenter#1540D11
hypocenterC11#17721
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1540

Complements

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

NH ≅ G/Ntype
2. #13077724C2semidirect
3. #13077181C2semidirect
4. #13067293C2semidirect
5. #13067290C2semidirect
6. #13067287C2semidirect
7. #13067286C2semidirect
8. #13067262C2semidirect
9. C2×#10622120C2semidirect
10. D11×#332C2semidirect
11. C11×#1540C2semidirect
205. #1540D11semidirect
471. C11#17721semidirect

Maximal subgroups

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

subgroupindex
#130823962
#130777242
#130771812
#130672932
#130672902
#130672872
#130672862
#130672622
C2×#106221202
D11×#3322
C11×#15402
#1772111