Finite Group Databasebeta

← #14651090

Subgroups — #14651090

Order 2816.

640 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077638C211yesmaximal, characteristic, complemented
2#13073578C211yesmaximal, characteristic
3#13068601C211yesmaximal, characteristic, complemented
4#13067184C211yesmaximal, characteristic, complemented
5#13066496C211yesmaximal, characteristic, complemented
6#13066494C211yesmaximal, characteristic, complemented
7C11×#1519C211yesmaximal, characteristic, complemented
8C2×C11×#121C2211yescharacteristic
9C2×#66992—21no—
10C2×C4×C22⋊D11C2211yescharacteristic
11C2×C11×C22⋊C8C2211yescharacteristic
12C11×#380C2211yescharacteristic
13#10622836C411yescharacteristic, complemented
14#10622835C411yescharacteristic, complemented
15#10622833—21no—
16#10622825C2211yescharacteristic
17C2×C11⋊#95C2211yescharacteristic
18C2×C22⋊(C11⋊C8)C2211yescharacteristic
19C8×C22⋊D11—22no—
20#10622606C411yescharacteristic, complemented
21#10622593C411yescharacteristic, complemented
22#10622569—21no—
23C2×#66870—21no—
24#10622557—21no—
25(C22⋊D11)⋊C8—22no—
26D11×C22⋊C8—21no—
27#10622331—21no—
28C11×#327—22no—
29#10622175—22no—
30#10622165—21no—
31C22×D4×C11—21no—
32C22×D4×C11C2×C411yescharacteristic
33C23×C4×C11C2311yescharacteristic
34C22×C22⋊D11—21no—
35C22×C22⋊D11D411yescharacteristic
36C23×Dic11—21no—
37C22×C4×D11D411yescharacteristic
38C22×C8×C11—21no—
39C11×#121—21no—
40C11×#121—21no—
41C11×#121—21no—
42C11×#121—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4C2×C411yescharacteristic
45C2×C11×C22⋊C4—21no—
46C2×C11×C22⋊C4—21no—
47C2×C22⋊Dic11—21no—
48C2×C22⋊Dic11—21no—
49C2×C22⋊Dic11—21no—
50C2×C22⋊Dic11—21no—
51C2×C22⋊Dic11D411yescharacteristic
52#66992—42no—
53#66992—42no—
54C4×C22⋊D11—21no—
55C4×C22⋊D11—21no—
56C4×C22⋊D11—21no—
57C4×C22⋊D11—21no—
58C2×(C2×D11)⋊C4—21no—
59C2×(C2×D11)⋊C4C2×C411yescharacteristic
60C2×C4⋊Dic11—21no—
61C2×Dic11⋊C4—21no—
62C2×Dic11⋊C4C2×C411yescharacteristic
63C2×C4×Dic11D411yescharacteristic
64C22×C11⋊C8—21no—
65C2×C8×D11—22no—
66C11×C22⋊C8—21no—
67C11×C22⋊C8D412yescomplemented
68C11×#95—21no—
69C11⋊#95—21no—
70C11⋊#95—21no—
71C11⋊#95—21no—
72C11⋊#95—21no—
73C11⋊#95C2×C411yescharacteristic
74C11⋊#95C2×C411yescharacteristic
75C22⋊(C11⋊C8)—21no—
76C22⋊(C11⋊C8)D412yescomplemented
77(C2×D11)⋊C8—22no—
78Dic11⋊C8—22no—
79C8×Dic11—22no—
80#66870—42no—
81#9384—111nomaximal, Sylow
82C24×C11—21no—
83C24×C11C2×D411yescharacteristic
84C23×D11C22⋊C411yescharacteristic
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—41no—
88C2×D4×C11—41no—
89C2×D4×C11—41no—
90C2×D4×C11—41no—
91C2×D4×C11—41no—
92C2×D4×C11—41no—
93C2×D4×C11—81no—
94C22×C4×C11—21no—
95C22×C4×C11—41no—
96C22×C4×C11—81no—
97C22×C4×C11C22×C411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11#4111yescharacteristic
102C22×C4×C11#4111yescharacteristic
103C2×C22⋊D11—21no—
104C2×C22⋊D11—21no—
105C2×C22⋊D11—21no—
106C2×C22⋊D11—21no—
107C2×C22⋊D11—42no—
108C2×C22⋊D11—42no—
109C2×C22⋊D11—81no—
110C2×C22⋊D11D812yes—
111C2×C22⋊D11SD1612yes—
112C22×Dic11—21no—
113C22×Dic11—21no—
114C22×Dic11—42no—
115C22×Dic11—41no—
116C22×Dic11—41no—
117C22×Dic11—41no—
118C22×Dic11—81no—
119C22×Dic11C22⋊C411yescharacteristic
120C22×Dic11C22⋊C411yescharacteristic
121C22×Dic11C22⋊C411yescharacteristic
122C2×C4×D11—21no—
123C2×C4×D11—21no—
124C2×C4×D11—81no—
125C2×C8×C11—22no—
126C2×C8×C11—81no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—81no—
130C11×C22⋊C4—41no—
131C11×C22⋊C4—41no—
132C11×C22⋊C4—41no—
133C11×C22⋊C4—41no—
134C22⋊Dic11—21no—
135C22⋊Dic11—21no—
136C22⋊Dic11—42no—
137C22⋊Dic11—42no—
138C22⋊Dic11—41no—
139C22⋊Dic11—41no—
140C22⋊Dic11—81no—
141(C2×D11)⋊C4—21no—
142(C2×D11)⋊C4—21no—
143(C2×D11)⋊C4—42no—
144C4⋊Dic11—81no—
145Dic11⋊C4—21no—
146Dic11⋊C4—21no—
147Dic11⋊C4—42no—
148C4×Dic11—21no—
149C4×Dic11—21no—
150C2×C11⋊C8—22no—
151C2×C11⋊C8—81no—
152C8×D11—82no—
153#2972—111no—
154#2543—111no—
155#1799—111no—
156#1519—111no—
157#1519D1111yescharacteristic, complemented
158#1294—111no—
159#1294—111no—
160C23×C11—41no—
161C23×C11—41no—
162C23×C11—41no—
163C23×C11—41no—
164C23×C11—41no—
165C23×C11—41no—
166C23×C11—41no—
167C23×C11—41no—
168C23×C11—41no—
169C23×C11C2×C22⋊C411yescharacteristic
170C23×C11#12111yescharacteristic
171C23×C11#12111yescharacteristic
172C23×C11C2×D811yescharacteristic
173C23×C11C2×SD1611yescharacteristic
174C23×C11#13511yescharacteristic
175C23×C11#13511yescharacteristic
176C22×D11—21no—
177C22×D11—21no—
178C22×D11—41no—
179C22×D11—41no—
180C22×D11#10212yes—
181D4×C11—81no—
182D4×C11—81no—
183D4×C11—81no—
184D4×C11—81no—
185D4×C11—81no—
186D4×C11—81no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—81no—
197C2×C4×C11—81no—
198C2×C4×C11—81no—
199C2×C4×C11C4×D411yescharacteristic
200C2×C4×C11C4×D411yescharacteristic
201C2×C4×C11#12011yescharacteristic
202C2×C4×C11#12311yescharacteristic
203C22⋊D11—22no—
204C22⋊D11—22no—
205C22⋊D11—22no—
206C22⋊D11—22no—
207C22⋊D11—84no—
208C2×Dic11—21no—
209C2×Dic11—21no—
210C2×Dic11—22no—
211C2×Dic11—21no—
212C2×Dic11—21no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11—41no—
219C2×Dic11—41no—
220C2×Dic11—82no—
221C2×Dic11—82no—
222C2×Dic11—81no—
223C2×Dic11—81no—
224C2×Dic11—81no—
225C2×Dic11#10212yes—
226C4×D11—42no—
227C4×D11—81no—
228C8×C11—42no—
229C11⋊C8—42no—
230C2×#121—221no—
231C2×#121C2×D1111yescharacteristic
232C2×C4×D4—111no—
233C8×D4—222no—
234C8×D4—222no—
235#431—221no—
236C2×#99—221no—
237C2×C22⋊C8—111no—
238C2×C22⋊C8—221no—
239C2×C22⋊C8C2×D1111yescharacteristic
240#398—111no—
241#397—111no—
242#394—111no—
243#392—111no—
244#388—221no—
245#386—221no—
246#386—221no—
247#380—111no—
248#380C2×D1111yescharacteristic
249C2×#95—111no—
250#342—221no—
251#327—22no—
252#327—222no—
253C22×C11—21no—
254C22×C11—21no—
255C22×C11—21no—
256C22×C11—21no—
257C22×C11—21no—
258C22×C11—21no—
259C22×C11—41no—
260C22×C11—41no—
261C22×C11—41no—
262C22×C11—41no—
263C22×C11—81no—
264C22×C11—81no—
265C22×C11—81no—
266C22×C11—81no—
267C22×C11—81no—
268C22×C11—81no—
269C22×C11—81no—
270C22×C11#38611yescharacteristic
271C22×C11C2×#10211yescharacteristic
272C22×C11#41611yescharacteristic
273C22×C11#46511yescharacteristic
274C22×C11#46511yescharacteristic
275C22×C11#46611yescharacteristic
276C22×C11#46611yescharacteristic
277C2×D11—22no—
278C2×D11—41no—
279C2×D11—41no—
280C2×D11—42no—
281C2×D11—81no—
282C4×C11—21no—
283C4×C11—21no—
284C4×C11—21no—
285C4×C11—21no—
286C4×C11—81no—
287C4×C11—161no—
288Dic11—22no—
289Dic11—42no—
290Dic11—41no—
291Dic11—41no—
292Dic11—81no—
293Dic11—161no—
294C22×D4—21no—
295C22×D4—111no—
296C22×D4—221no—
297C22×D4C4×D1111yescharacteristic
298C23×C4—111no—
299C23×C4—221no—
300C23×C4C22×D1111yescharacteristic
301C22×C8—21no—
302C22×C8—222no—
303C22×C8—221no—
304#121—21no—
305#121—21no—
306#121—21no—
307#121—21no—
308#121—442no—
309#121—442no—
310C4×D4—221no—
311C4×D4—221no—
312C4×D4—221no—
313C4×D4—221no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—111no—
316C2×C4⋊C4—221no—
317C2×C4⋊C4—221no—
318C2×C4⋊C4C4×D1111yescharacteristic
319C2×C22⋊C4—21no—
320C2×C22⋊C4—21no—
321C2×C22⋊C4—111no—
322C2×C22⋊C4—111no—
323C2×C22⋊C4—221no—
324C2×C22⋊C4—221no—
325C2×C22⋊C4—221no—
326C2×C22⋊C4—221no—
327C2×C22⋊C4—221no—
328C2×C42—111no—
329C4⋊C8—222no—
330#99—442no—
331C22⋊C8—21no—
332C22⋊C8—112no—
333C22⋊C8—222no—
334C22⋊C8—221no—
335C22⋊C8C22⋊D1112yescomplemented
336C4×C8—222no—
337#95—21no—
338#95—111no—
339#95—111no—
340#95—221no—
341#95—221no—
342#95—221no—
343#95—221no—
344C2×C11—21no—
345C2×C11—21no—
346C2×C11—21no—
347C2×C11—21no—
348C2×C11—21no—
349C2×C11—21no—
350C2×C11—161no—
351C2×C11#188411yescharacteristic
352C2×C11#189311yescharacteristic
353C2×C11#191311yescharacteristic
354D11—42no—
355C24—21no—
356C24—111no—
357C24D4×D1111yescharacteristic
358C2×D4—21no—
359C2×D4—21no—
360C2×D4—41no—
361C2×D4—41no—
362C2×D4—41no—
363C2×D4—41no—
364C2×D4—41no—
365C2×D4—41no—
366C2×D4—81no—
367C2×D4—112no—
368C2×D4—112no—
369C2×D4—221no—
370C2×D4—221no—
371C2×D4—221no—
372C2×D4—221no—
373C2×D4—442no—
374C2×D4—442no—
375C2×D4—881no—
376C22×C4—21no—
377C22×C4—41no—
378C22×C4—81no—
379C22×C4—111no—
380C22×C4—111no—
381C22×C4—111no—
382C22×C4—221no—
383C22×C4—221no—
384C22×C4—221no—
385C22×C4—221no—
386C22×C4—442no—
387C22×C4—441no—
388C22×C4—441no—
389C22×C4—441no—
390C22×C4—881no—
391C22×C4—881no—
392C22×C4C2×C4×D1111yescharacteristic
393C22×C4#433911yescharacteristic
394C22×C4D4×D1111yescharacteristic
395C22×C4D4×D1111yescharacteristic
396C22×C4#434111yescharacteristic
397C22×C4C2×C22⋊D1111yescharacteristic
398C2×C8—22no—
399C2×C8—81no—
400C2×C8—222no—
401C2×C8—882no—
402C2×C8—881no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—81no—
406C4⋊C4—221no—
407C4⋊C4—221no—
408C4⋊C4—442no—
409C4⋊C4—881no—
410C22⋊C4—41no—
411C22⋊C4—41no—
412C22⋊C4—41no—
413C22⋊C4—41no—
414C22⋊C4—221no—
415C22⋊C4—221no—
416C22⋊C4—221no—
417C22⋊C4—221no—
418C22⋊C4—442no—
419C22⋊C4—442no—
420C22⋊C4—442no—
421C22⋊C4—441no—
422C22⋊C4—441no—
423C22⋊C4—881no—
424C42—221no—
425C42—221no—
426C11#938411yescharacteristic, complemented, Sylow
427C23—41no—
428C23—41no—
429C23—41no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—41no—
436C23—112no—
437C23—221no—
438C23—221no—
439C23—441no—
440C23—441no—
441C23C22⋊C4×D1111yescharacteristic
442C23#6693711yescharacteristic
443C23D8×D1111yescharacteristic
444C23#6696511yescharacteristic
445C23SD16×D1111yescharacteristic
446C23#6696911yescharacteristic
447C23#6699111yescharacteristic
448D4—81no—
449D4—81no—
450D4—81no—
451D4—81no—
452D4—81no—
453D4—81no—
454D4—222no—
455D4—222no—
456D4—222no—
457D4—222no—
458D4—884no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—81no—
469C2×C4—81no—
470C2×C4—81no—
471C2×C4—112no—
472C2×C4—221no—
473C2×C4—221no—
474C2×C4—222no—
475C2×C4—221no—
476C2×C4—221no—
477C2×C4—442no—
478C2×C4—441no—
479C2×C4—441no—
480C2×C4—441no—
481C2×C4—441no—
482C2×C4—441no—
483C2×C4—441no—
484C2×C4—441no—
485C2×C4—881no—
486C2×C4—882no—
487C2×C4—882no—
488C2×C4—881no—
489C2×C4—881no—
490C2×C4—881no—
491C2×C4(C22⋊D11)⋊C411yescharacteristic
492C2×C4#6693611yescharacteristic
493C2×C4C4×C22⋊D1111yescharacteristic
494C2×C4#6699011yescharacteristic
495C8—42no—
496C8—442no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—41no—
504C22—41no—
505C22—41no—
506C22—41no—
507C22—81no—
508C22—81no—
509C22—81no—
510C22—81no—
511C22—81no—
512C22—81no—
513C22—81no—
514C22—222no—
515C22—442no—
516C22—441no—
517C22—441no—
518C22—881no—
519C22D11×#10211yescharacteristic
520C22#1062238511yescharacteristic
521C22#1062238811yescharacteristic
522C22#1062239111yescharacteristic
523C22#1062256911yescharacteristic
524C22#1062277011yescharacteristic
525C22#1062278411yescharacteristic
526C4—21no—
527C4—21no—
528C4—21no—
529C4—21no—
530C4—81no—
531C4—161no—
532C4—222no—
533C4—442no—
534C4—441no—
535C4—441no—
536C4—881no—
537C4—1761no—
538C2—21no—
539C2—21no—
540C2—21no—
541C2—21no—
542C2—21no—
543C2—21no—
544C2—161no—
545C2—442no—
546C2#1306899611yescharacteristic
547C2#1306904111yescharacteristic
548C2#1306915511yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1519C2
socleC22×C11#386
prime radical#13073578C2
cosocleC23×C4×C11C23
hypercenter#1519D11
hypocenterC11#9384
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1519

Complements

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

NH ≅ G/Ntype
1. #13077638C2semidirect
3. #13068601C2semidirect
4. #13067184C2semidirect
5. #13066496C2semidirect
6. #13066494C2semidirect
7. C11×#1519C2semidirect
13. #10622836C4semidirect
14. #10622835C4semidirect
20. #10622606C4semidirect
21. #10622593C4semidirect
67. C11×C22⋊C8D4semidirect
76. C22⋊(C11⋊C8)D4semidirect
157. #1519D11semidirect
335. C22⋊C8C22⋊D11semidirect
426. C11#9384semidirect

Maximal subgroups

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

subgroupindex
#130776382
#130735782
#130686012
#130671842
#130664962
#130664942
C11×#15192
#938411