Finite Group Databasebeta

← #14650349

Subgroups — #14650349

Order 2816.

648 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079364C211yesmaximal, characteristic
2#13071666C211yesmaximal, characteristic, complemented
3#13067183C211yesmaximal, characteristic, complemented
4C2×#10622175C211yesmaximal, characteristic, complemented
5#13066494C211yesmaximal, characteristic, complemented
6#13066464C211yesmaximal, characteristic, complemented
7C11×#1964C211yesmaximal, characteristic, complemented
8C2×C11×#121C2211yescharacteristic
9C2×#66983C2211yescharacteristic
10C2×(C22⋊D11)⋊C4—21no—
11C2×C11×#99—21no—
12C2×C11×#99—21no—
13C11×#380C2211yescharacteristic
14C4×C11×C22⋊C4C2211yescharacteristic
15#10622830C412yescomplemented
16C2×C11⋊#95C2211yescharacteristic
17C2×C22⋊(C11⋊C8)C2211yescharacteristic
18C2×C22⋊(C11⋊C8)C2211yescharacteristic
19#10622651—22no—
20#10622649—21no—
21#10622646—21no—
22#10622580C412yescomplemented
23#10622571—21no—
24#10622553—21no—
25C4×(C2×D11)⋊C4—21no—
26#10622278—21no—
27#10622266—21no—
28#10622175—21no—
29#10622175—21no—
30#10622089—22no—
31C22×D4×C11—21no—
32C22×D4×C11C2×C411yescharacteristic, complemented
33C23×C4×C11C2311yescharacteristic
34C22×C22⋊D11—21no—
35C23×Dic11—21no—
36C22×D44D411yescharacteristic
37C22×C4×D11—21no—
38C11×#121—21no—
39C11×#121—21no—
40C11×#121—21no—
41C11×#121—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4C2×C411yescharacteristic, complemented
44C2×C11×C22⋊C4—21no—
45C2×C11×C22⋊C4—21no—
46C2×C11×C22⋊C4D411yescharacteristic
47C2×C11×C22⋊C4D411yescharacteristic
48C2×C42×C11—21no—
49C2×#4323—22no—
50#66983—21no—
51#66983—21no—
52#66983C2×C412yes—
53#66983D412yes—
54C2×(C2×D11)⋊C4—21no—
55C2×(C2×D11)⋊C4—21no—
56C2×(C2×D11)⋊C4—21no—
57C2×(C2×D11)⋊C4—21no—
58C2×C4⋊Dic11D411yescharacteristic
59C2×Dic11⋊C4—21no—
60C2×C4×Dic11—21no—
61C22×C11⋊C8—21no—
62C22×C11⋊C8—21no—
63(C22⋊D11)⋊C4—42no—
64(C22⋊D11)⋊C4—42no—
65C11×#99—42no—
66C11×#99—42no—
67C11×#95—21no—
68C11×#95—21no—
69#66896—22no—
70C11⋊#95—21no—
71C11⋊#95—21no—
72C11⋊#95—21no—
73C11⋊#95D411yescharacteristic
74C11⋊#95D411yescharacteristic
75C22⋊(C11⋊C8)—21no—
76C22⋊(C11⋊C8)—21no—
77C22⋊(C11⋊C8)—21no—
78C22⋊(C11⋊C8)C2×C412yescomplemented
79#66873—22no—
80#66871—22no—
81#9277—111nomaximal, Sylow
82C24×C11—21no—
83C24×C11C2×D411yescharacteristic
84C23×D11—21no—
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—21no—
96C22×C4×C11—21no—
97C22×C4×C11—41no—
98C22×C4×C11—81no—
99C22×C4×C11C22×C411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11#4111yescharacteristic
104C22×C4×C11#4111yescharacteristic
105C2×C22⋊D11—22no—
106C2×C22⋊D11—22no—
107C2×C22⋊D11—41no—
108C2×C22⋊D11—41no—
109C2×C22⋊D11—41no—
110C2×C22⋊D11—41no—
111C22×Dic11—21no—
112C22×Dic11—21no—
113C22×Dic11—21no—
114C22×Dic11—42no—
115C22×Dic11—41no—
116C22×Dic11—41no—
117C22×Dic11—81no—
118C2×D44—21no—
119C2×D44—81no—
120C2×D44C22⋊C412yes—
121C2×C4×D11—42no—
122C2×C4×D11—42no—
123C2×C4×D11—81no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—81no—
127C11×C22⋊C4—21no—
128C11×C22⋊C4—21no—
129C11×C22⋊C4—21no—
130C11×C22⋊C4—41no—
131C11×C22⋊C4—41no—
132C11×C22⋊C4—41no—
133C11×C22⋊C4—41no—
134C11×C22⋊C4D812yescomplemented
135C42×C11—81no—
136#4323—82no—
137(C2×D11)⋊C4—22no—
138(C2×D11)⋊C4—22no—
139(C2×D11)⋊C4—42no—
140(C2×D11)⋊C4—42no—
141(C2×D11)⋊C4—81no—
142C4⋊Dic11—21no—
143C4⋊Dic11C22⋊C412yes—
144Dic11⋊C4—42no—
145C4×Dic11—42no—
146C2×C11⋊C8—22no—
147C2×C11⋊C8—41no—
148C2×C11⋊C8—81no—
149C2×C11⋊C8—81no—
150#3186—111no—
151#2364—111no—
152#1964D1111yescharacteristic, complemented
153#1519—111no—
154C2×#327—111no—
155#1294—111no—
156#1282—111no—
157C23×C11—41no—
158C23×C11—41no—
159C23×C11—41no—
160C23×C11—41no—
161C23×C11—41no—
162C23×C11—81no—
163C23×C11—81no—
164C23×C11C4×D411yescharacteristic
165C23×C11#12011yescharacteristic
166C23×C11#12111yescharacteristic
167C23×C11C2×D811yescharacteristic
168C23×C11#13511yescharacteristic
169C23×C11AGL(1,ℤ/8)11yescharacteristic
170C23×C11AGL(1,ℤ/8)11yescharacteristic
171C22×D11—22no—
172C22×D11—41no—
173C22×D11—41no—
174C22×D11—41no—
175C22×D11—41no—
176C22×D11—41no—
177C22×D11—41no—
178D4×C11—42no—
179D4×C11—81no—
180D4×C11—81no—
181D4×C11—81no—
182D4×C11—81no—
183D4×C11—81no—
184C2×C4×C11—22no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
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—41no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—81no—
200C2×C4×C11—81no—
201C2×C4×C11—81no—
202C2×C4×C11C2×C22⋊C411yescharacteristic
203C2×C4×C11C4×D411yescharacteristic
204C2×C4×C11#12111yescharacteristic
205C2×C4×C11#12311yescharacteristic
206C22⋊D11—42no—
207C22⋊D11—42no—
208C22⋊D11—42no—
209C22⋊D11—42no—
210C2×Dic11—22no—
211C2×Dic11—22no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11—41no—
219C2×Dic11—82no—
220C2×Dic11—82no—
221D44—42no—
222D44—81no—
223C4×D11—84no—
224C11⋊C8—42no—
225C11⋊C8—81no—
226C2×#121—111no—
227C2×#121C2×D1111yescharacteristic
228C2×C4×D4—221no—
229#480—112no—
230#480—221no—
231#466—222no—
232#447—112no—
233#447—221no—
234C2×#99—21no—
235C2×#99—21no—
236C2×C22⋊C8—111no—
237C2×C22⋊C8—111no—
238#388—221no—
239#387—221no—
240#386—221no—
241#386—221no—
242#380C2×D1111yescharacteristic
243C4×C22⋊C4—221no—
244C4×C22⋊C4C2×D1111yescharacteristic
245C2×#95—111no—
246#327—222no—
247#327—221no—
248#327—221no—
249C22×C11—21no—
250C22×C11—21no—
251C22×C11—21no—
252C22×C11—21no—
253C22×C11—21no—
254C22×C11—21no—
255C22×C11—41no—
256C22×C11—41no—
257C22×C11—41no—
258C22×C11—41no—
259C22×C11—81no—
260C22×C11—81no—
261C22×C11—81no—
262C22×C11—161no—
263C22×C11—161no—
264C22×C11#38611yescharacteristic
265C22×C11C4×D811yescharacteristic
266C22×C11#44211yescharacteristic
267C22×C11#44711yescharacteristic
268C22×C11#44911yescharacteristic
269C22×C11#45911yescharacteristic
270C22×C11#46311yescharacteristic
271C2×D11—42no—
272C2×D11—42no—
273C2×D11—42no—
274C2×D11—81no—
275C2×D11—81no—
276C2×D11—81no—
277C2×D11—81no—
278C4×C11—21no—
279C4×C11—21no—
280C4×C11—21no—
281C4×C11—21no—
282C4×C11—42no—
283C4×C11—81no—
284C4×C11—81no—
285C4×C11—161no—
286Dic11—42no—
287Dic11—42no—
288Dic11—81no—
289C22×D4—21no—
290C22×D4—111no—
291C22×D4—221no—
292C22×D4C4×D1111yescharacteristic, complemented
293C23×C4—221no—
294C23×C4—221no—
295C23×C4C22×D1111yescharacteristic
296C2×D8—222no—
297C22×C8—221no—
298C22×C8—221no—
299#121—21no—
300#121—21no—
301#121—21no—
302#121—21no—
303#121—112no—
304#121—112no—
305#121—221no—
306#121—221no—
307C4×D4—442no—
308C4×D4—442no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—111no—
311C2×C4⋊C4—221no—
312C2×C4⋊C4C4×D1111yescharacteristic, complemented
313C2×C22⋊C4—21no—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—221no—
316C2×C22⋊C4—221no—
317C2×C22⋊C4—221no—
318C2×C22⋊C4—221no—
319C2×C22⋊C4C22⋊D1111yescharacteristic
320C2×C22⋊C4C22⋊D1111yescharacteristic
321C2×C42—21no—
322C2×C42—221no—
323#107—222no—
324#102—222no—
325#102—222no—
326#99—42no—
327#99—42no—
328C22⋊C8—112no—
329C22⋊C8—221no—
330C22⋊C8—221no—
331C22⋊C8—221no—
332#95—21no—
333#95—21no—
334#95—111no—
335#95—111no—
336#95—221no—
337#95—221no—
338#95—221no—
339C2×C11—21no—
340C2×C11—21no—
341C2×C11—21no—
342C2×C11—21no—
343C2×C11—21no—
344C2×C11—21no—
345C2×C11—161no—
346C2×C11#187911yescharacteristic
347C2×C11#190611yescharacteristic
348C2×C11#191311yescharacteristic
349D11—82no—
350C24—21no—
351C24—221no—
352C24C2×C22⋊D1111yescharacteristic
353C2×D4—21no—
354C2×D4—21no—
355C2×D4—41no—
356C2×D4—41no—
357C2×D4—41no—
358C2×D4—41no—
359C2×D4—41no—
360C2×D4—41no—
361C2×D4—81no—
362C2×D4—112no—
363C2×D4—222no—
364C2×D4—222no—
365C2×D4—221no—
366C2×D4—441no—
367C2×D4—441no—
368C2×D4—441no—
369C2×D4—441no—
370C2×D4—881no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—41no—
375C22×C4—81no—
376C22×C4—221no—
377C22×C4—221no—
378C22×C4—221no—
379C22×C4—442no—
380C22×C4—442no—
381C22×C4—442no—
382C22×C4—441no—
383C22×C4—441no—
384C22×C4—881no—
385C22×C4—881no—
386C22×C4C2×C4×D1111yescharacteristic
387C22×C4#433911yescharacteristic
388C22×C4D4×D1111yescharacteristic
389C22×C4D4×D1111yescharacteristic
390C22×C4D4×D1111yescharacteristic
391C22×C4#434111yescharacteristic
392D8—882no—
393C2×C8—222no—
394C2×C8—441no—
395C2×C8—881no—
396C2×C8—881no—
397C4⋊C4—21no—
398C4⋊C4—21no—
399C4⋊C4—81no—
400C4⋊C4—112no—
401C4⋊C4—221no—
402C4⋊C4—442no—
403C22⋊C4—21no—
404C22⋊C4—21no—
405C22⋊C4—21no—
406C22⋊C4—41no—
407C22⋊C4—41no—
408C22⋊C4—41no—
409C22⋊C4—41no—
410C22⋊C4—222no—
411C22⋊C4—222no—
412C22⋊C4—442no—
413C22⋊C4—442no—
414C22⋊C4—881no—
415C22⋊C4#432312yescomplemented
416C42—81no—
417C42—442no—
418C11#927711yescharacteristic, complemented, Sylow
419C23—41no—
420C23—41no—
421C23—41no—
422C23—41no—
423C23—41no—
424C23—81no—
425C23—81no—
426C23—222no—
427C23—441no—
428C23—441no—
429C23—441no—
430C23—441no—
431C23—441no—
432C23—441no—
433C23C4×C22⋊D1111yescharacteristic
434C23C2×#432311yescharacteristic
435C23#6698511yescharacteristic
436C23#6699011yescharacteristic
437C23#6699111yescharacteristic
438C23#6700211yescharacteristic
439C23#6700311yescharacteristic
440D4—42no—
441D4—81no—
442D4—81no—
443D4—81no—
444D4—81no—
445D4—81no—
446D4—442no—
447D4—442no—
448D4—442no—
449D4—442no—
450D4—442no—
451D4—881no—
452C2×C4—22no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
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—81no—
468C2×C4—81no—
469C2×C4—81no—
470C2×C4—222no—
471C2×C4—222no—
472C2×C4—441no—
473C2×C4—441no—
474C2×C4—441no—
475C2×C4—441no—
476C2×C4—441no—
477C2×C4—441no—
478C2×C4—441no—
479C2×C4—884no—
480C2×C4—882no—
481C2×C4—882no—
482C2×C4C22⋊C4×D1111yescharacteristic
483C2×C4(C22⋊D11)⋊C411yescharacteristic
484C2×C4#6693611yescharacteristic
485C2×C4#6693711yescharacteristic
486C8—442no—
487C8—881no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—41no—
495C22—41no—
496C22—41no—
497C22—41no—
498C22—81no—
499C22—81no—
500C22—81no—
501C22—161no—
502C22—161no—
503C22—442no—
504C22—442no—
505C22—442no—
506C22—881no—
507C22—881no—
508C22—881no—
509C22—881no—
510C22#1062256911yescharacteristic
511C22C4×#432311yescharacteristic
512C22#1062262711yescharacteristic
513C22#1062264911yescharacteristic
514C22#1062265011yescharacteristic
515C22#1062267011yescharacteristic
516C22#1062268511yescharacteristic
517C4—21no—
518C4—21no—
519C4—21no—
520C4—21no—
521C4—42no—
522C4—81no—
523C4—81no—
524C4—161no—
525C4—442no—
526C4—442no—
527C4—881no—
528C2—21no—
529C2—21no—
530C2—21no—
531C2—21no—
532C2—21no—
533C2—21no—
534C2—161no—
535C2—882no—
536C2#1306896711yescharacteristic
537C2#1306911411yescharacteristic
538C2#1306915511yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1964C2
socleC22×C11#386
prime radical#13079364C2
cosocleC23×C4×C11C23
hypercenter#1964D11
hypocenterC11#9277
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1964

Complements

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

NH ≅ G/Ntype
2. #13071666C2semidirect
3. #13067183C2semidirect
4. C2×#10622175C2semidirect
5. #13066494C2semidirect
6. #13066464C2semidirect
7. C11×#1964C2semidirect
15. #10622830C4semidirect
22. #10622580C4semidirect
32. C22×D4×C11C2×C4semidirect
43. C2×C11×C4⋊C4C2×C4semidirect
78. C22⋊(C11⋊C8)C2×C4semidirect
134. C11×C22⋊C4D8semidirect
152. #1964D11semidirect
292. C22×D4C4×D11semidirect
312. C2×C4⋊C4C4×D11semidirect
415. C22⋊C4#4323semidirect
418. C11#9277semidirect

Maximal subgroups

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

subgroupindex
#130793642
#130716662
#130671832
C2×#106221752
#130664942
#130664642
C11×#19642
#927711