Finite Group Databasebeta

← #14644666

Subgroups — #14644666

Order 2816.

804 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071122C211yesmaximal, characteristic
2#13068380C211yesmaximal, characteristic, complemented
3C2×#10622108C211yesmaximal, characteristic
4C2×#10622089C211yesmaximal, characteristic
5#95×Dic11C211yesmaximal, characteristic, complemented
6#13066494C211yesmaximal, characteristic, complemented
7C11×#1294C211yesmaximal, characteristic, complemented
8C2×#66983C2211yescharacteristic
9C22×C4×Dic11—21no—
10C22×C4×Dic11C2211yescharacteristic
11C2×#66946C411yescharacteristic, complemented
12C2×(C22⋊D11)⋊C4—21no—
13C2×C11×C22⋊C8C2211yescharacteristic
14C11×#380C2211yescharacteristic
15C2×C11×#95C2211yescharacteristic
16C2×C11⋊#95—21no—
17C2×C11⋊#95C2211yescharacteristic
18C2×C22⋊(C11⋊C8)C2211yescharacteristic
19C2×#66879—21no—
20#10622601C411yescharacteristic, complemented
21C4⋊C4×Dic11C411yescharacteristic, complemented
22#10622586C411yescharacteristic, complemented
23#10622571—21no—
24#10622282—21no—
25#10622279—21no—
26#10622188—21no—
27#10622108C414yescomplemented
28#10622089C414yescomplemented
29C23×C4×C11—21no—
30C23×C4×C11C2311yescharacteristic
31C22×C22⋊D11—21no—
32C23×Dic11—21no—
33C23×Dic11D411yescharacteristic
34C23×Dic11D411yescharacteristic
35C22×D44C2×C411yescharacteristic
36C22×C4×D11—21no—
37C22×C8×C11—21no—
38C2×C11×C4⋊C4C2×C411yescharacteristic
39C2×C11×C4⋊C4C2×C411yescharacteristic
40C2×C11×C22⋊C4—21no—
41#66983—21no—
42#66983—21no—
43#66983C2×C412yes—
44#66983C2×C412yes—
45C2×(C2×D11)⋊C4—21no—
46C2×(C2×D11)⋊C4—21no—
47C2×(C2×D11)⋊C4—21no—
48C2×(C2×D11)⋊C4—21no—
49C2×C4⋊Dic11C2×C411yescharacteristic
50C2×Dic11⋊C4—21no—
51C2×C4×Dic11—24no—
52C2×C4×Dic11—21no—
53C2×C4×Dic11—42no—
54C2×C4×Dic11—42no—
55C2×C4×Dic11—42no—
56C2×C4×Dic11C2×C411yescharacteristic
57C2×C4×Dic11C2×C411yescharacteristic
58C2×C4×Dic11D411yescharacteristic
59C2×C4×Dic11D411yescharacteristic
60C22×C11⋊C8—21no—
61#66946—42no—
62(C22⋊D11)⋊C4—42no—
63(C22⋊D11)⋊C4—42no—
64C11×C22⋊C8—21no—
65C11×C22⋊C8C2×C412yescomplemented
66C11×#95—21no—
67C11×#95—21no—
68C11×#95C2×C412yescomplemented
69C11⋊#95—24no—
70C11⋊#95—21no—
71C11⋊#95—21no—
72C11⋊#95—21no—
73C11⋊#95C2×C412yescomplemented
74C22⋊(C11⋊C8)—21no—
75C22⋊(C11⋊C8)C2×C412yescomplemented
76#66879—42no—
77#8218—111nomaximal, Sylow
78C24×C11C2×D411yescharacteristic
79C23×D11—21no—
80C22×C4×C11—22no—
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—41no—
86C22×C4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11—41no—
89C22×C4×C11—41no—
90C22×C4×C11—41no—
91C22×C4×C11C22×C411yescharacteristic
92C22×C4×C11C22×C411yescharacteristic
93C22×C4×C11C22×C411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11#4111yescharacteristic
96C22×C4×C11#4111yescharacteristic
97C2×C22⋊D11—22no—
98C2×C22⋊D11—22no—
99C2×C22⋊D11—41no—
100C2×C22⋊D11—41no—
101C2×C22⋊D11—41no—
102C2×C22⋊D11—41no—
103C22×Dic11—22no—
104C22×Dic11—22no—
105C22×Dic11—22no—
106C22×Dic11—22no—
107C22×Dic11—22no—
108C22×Dic11—21no—
109C22×Dic11—22no—
110C22×Dic11—21no—
111C22×Dic11—21no—
112C22×Dic11—21no—
113C22×Dic11—21no—
114C22×Dic11—41no—
115C22×Dic11—41no—
116C22×Dic11—41no—
117C22×Dic11—41no—
118C22×Dic11—41no—
119C22×Dic11C22⋊C411yescharacteristic
120C22×Dic11C22⋊C411yescharacteristic
121C22×Dic11C22⋊C411yescharacteristic
122C22×Dic11C22⋊C411yescharacteristic
123C2×D44—21no—
124C2×D44—41no—
125C2×D44—41no—
126C2×D44C4212yescomplemented
127C2×C4×D11—42no—
128C2×C4×D11—42no—
129C2×C4×D11—42no—
130C2×C8×C11—22no—
131C2×C8×C11—41no—
132C2×C8×C11—41no—
133C11×C4⋊C4—41no—
134C11×C4⋊C4—41no—
135C11×C22⋊C4—41no—
136C11×C22⋊C4—41no—
137(C2×D11)⋊C4—22no—
138(C2×D11)⋊C4—22no—
139(C2×D11)⋊C4—42no—
140(C2×D11)⋊C4—42no—
141(C2×D11)⋊C4—42no—
142C4⋊Dic11—21no—
143C4⋊Dic11C4212yescomplemented
144Dic11⋊C4—42no—
145C4×Dic11—22no—
146C4×Dic11—22no—
147C4×Dic11—41no—
148C4×Dic11—41no—
149C4×Dic11—42no—
150C4×Dic11—48no—
151C2×C11⋊C8—22no—
152C2×C11⋊C8—41no—
153C2×C11⋊C8—41no—
154C4×#121—111no—
155#1749—111no—
156C2×#327—111no—
157C2×#327—111no—
158C4×#95—111no—
159#1294—111no—
160#1294D1111yescharacteristic, complemented
161C23×C11—21no—
162C23×C11—21no—
163C23×C11—21no—
164C23×C11—21no—
165C23×C11C2×C22⋊C411yescharacteristic
166C23×C11C4×D411yescharacteristic
167C23×C11C4×D411yescharacteristic
168C23×C11AGL(1,ℤ/8)11yescharacteristic
169C23×C11AGL(1,ℤ/8)11yescharacteristic
170C23×C11AGL(1,ℤ/8)11yescharacteristic
171C23×C11#13711yescharacteristic
172C22×D11—22no—
173C22×D11—41no—
174C22×D11—41no—
175C22×D11—41no—
176C22×D11—41no—
177C22×D11—41no—
178C22×D11—41no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—24no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11C2×C4211yescharacteristic
201C2×C4×C11#11711yescharacteristic
202C2×C4×C11C4×D411yescharacteristic
203C2×C4×C11C4×D411yescharacteristic
204C22⋊D11—42no—
205C22⋊D11—42no—
206C22⋊D11—42no—
207C22⋊D11—42no—
208C2×Dic11—24no—
209C2×Dic11—24no—
210C2×Dic11—21no—
211C2×Dic11—21no—
212C2×Dic11—21no—
213C2×Dic11—21no—
214C2×Dic11—21no—
215C2×Dic11—21no—
216C2×Dic11—24no—
217C2×Dic11—22no—
218C2×Dic11—21no—
219C2×Dic11—21no—
220C2×Dic11—21no—
221C2×Dic11—42no—
222C2×Dic11—42no—
223C2×Dic11—42no—
224C2×Dic11—42no—
225C2×Dic11—42no—
226C2×Dic11—42no—
227C2×Dic11—42no—
228C2×Dic11—41no—
229C2×Dic11—41no—
230C2×Dic11—42no—
231C2×Dic11#9912yes—
232C2×Dic11#10412yes—
233C2×Dic11#10412yes—
234D44—42no—
235D44—42no—
236C4×D11—84no—
237C8×C11—42no—
238C11⋊C8—42no—
239C2×#121—111no—
240C2×C4×D4—111no—
241C2×C4×D4—221no—
242C22×C42—111no—
243C22×C42—221no—
244C2×C22⋊C8—111no—
245C2×C22⋊C8C2×D1111yescharacteristic
246C2×#97—221no—
247#390—111no—
248#389—111no—
249#388—221no—
250#386—221no—
251#380C2×D1111yescharacteristic
252C4×C4⋊C4—111no—
253C4×C22⋊C4—221no—
254C2×#95—111no—
255C2×#95—221no—
256C2×#95C2×D1111yescharacteristic
257#336—221no—
258#327—114no—
259#327—114no—
260C22×C11—21no—
261C22×C11—21no—
262C22×C11—21no—
263C22×C11—21no—
264C22×C11—21no—
265C22×C11—21no—
266C22×C11—21no—
267C22×C11—21no—
268C22×C11—21no—
269C22×C11—21no—
270C22×C11—21no—
271C22×C11—21no—
272C22×C11C4×C22⋊C411yescharacteristic
273C22×C11C2×#9911yescharacteristic
274C22×C11#41011yescharacteristic
275C22×C11#41711yescharacteristic
276C22×C11#41811yescharacteristic
277C22×C11C2×#10411yescharacteristic
278C22×C11C2×#10411yescharacteristic
279C22×C11#44011yescharacteristic
280C22×C11#44011yescharacteristic
281C22×C11#44211yescharacteristic
282C22×C11#44211yescharacteristic
283C2×D11—42no—
284C2×D11—42no—
285C2×D11—42no—
286C2×D11—81no—
287C2×D11—81no—
288C2×D11—81no—
289C2×D11—81no—
290C4×C11—21no—
291C4×C11—21no—
292C4×C11—21no—
293C4×C11—21no—
294C4×C11—44no—
295C4×C11—81no—
296C4×C11—81no—
297Dic11—22no—
298Dic11—22no—
299Dic11—22no—
300Dic11—44no—
301Dic11—42no—
302Dic11—41no—
303C22×D4—111no—
304C22×D4—221no—
305C23×C4—21no—
306C23×C4—111no—
307C23×C4—111no—
308C23×C4—221no—
309C23×C4—221no—
310C23×C4C22×D1111yescharacteristic
311C22×C8—21no—
312C22×C8—221no—
313#121—112no—
314#121—112no—
315#121—221no—
316#121—221no—
317C4×D4—442no—
318C4×D4—442no—
319C4×D4—442no—
320C2×C4⋊C4—111no—
321C2×C4⋊C4—221no—
322C2×C4⋊C4C4×D1111yescharacteristic
323C2×C4⋊C4C4×D1111yescharacteristic
324C2×C22⋊C4—21no—
325C2×C22⋊C4—221no—
326C2×C22⋊C4—221no—
327C2×C22⋊C4—221no—
328C2×C22⋊C4—221no—
329C2×C42—111no—
330C2×C42—111no—
331C2×C42—111no—
332C2×C42—111no—
333C2×C42—221no—
334C2×C42—224no—
335C2×C42—442no—
336C2×C42—442no—
337C2×C42—442no—
338C22⋊C8—21no—
339C22⋊C8—112no—
340C22⋊C8—221no—
341C22⋊C8C4×D1112yescomplemented
342#97—442no—
343#95—21no—
344#95—21no—
345#95—112no—
346#95—221no—
347#95—221no—
348#95—224no—
349#95—221no—
350#95C4×D1112yescomplemented
351C2×C11—21no—
352C2×C11—21no—
353C2×C11—21no—
354C2×C11—21no—
355C2×C11#150411yescharacteristic
356C2×C11#150511yescharacteristic
357C2×C11#150711yescharacteristic
358C2×C11#150911yescharacteristic
359C2×C11C4×#9911yescharacteristic
360C2×C11C4×#10411yescharacteristic
361C2×C11#176211yescharacteristic
362D11—82no—
363C24—221no—
364C24D4×D1111yescharacteristic
365C2×D4—112no—
366C2×D4—222no—
367C2×D4—222no—
368C2×D4—221no—
369C2×D4—441no—
370C2×D4—441no—
371C2×D4—441no—
372C2×D4—441no—
373C2×D4—441no—
374C2×D4—441no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4—41no—
385C22×C4—41no—
386C22×C4—111no—
387C22×C4—111no—
388C22×C4—111no—
389C22×C4—111no—
390C22×C4—222no—
391C22×C4—222no—
392C22×C4—222no—
393C22×C4—221no—
394C22×C4—221no—
395C22×C4—222no—
396C22×C4—222no—
397C22×C4—221no—
398C22×C4—222no—
399C22×C4—221no—
400C22×C4—221no—
401C22×C4—442no—
402C22×C4—442no—
403C22×C4—442no—
404C22×C4—441no—
405C22×C4—441no—
406C22×C4—441no—
407C22×C4—441no—
408C22×C4—441no—
409C22×C4C2×C4×D1111yescharacteristic
410C22×C4C2×C4×D1111yescharacteristic
411C22×C4C2×C4×D1111yescharacteristic
412C22×C4D4×D1111yescharacteristic
413C22×C4#434111yescharacteristic
414C22×C4#434311yescharacteristic
415C2×C8—22no—
416C2×C8—41no—
417C2×C8—41no—
418C2×C8—222no—
419C2×C8—441no—
420C2×C8—441no—
421C4⋊C4—41no—
422C4⋊C4—41no—
423C4⋊C4—112no—
424C4⋊C4—221no—
425C4⋊C4—442no—
426C22⋊C4—41no—
427C22⋊C4—41no—
428C22⋊C4—222no—
429C22⋊C4—222no—
430C22⋊C4—442no—
431C22⋊C4—442no—
432C22⋊C4—442no—
433C42—222no—
434C42—222no—
435C42—441no—
436C42—441no—
437C42—448no—
438C42—442no—
439C11#821811yescharacteristic, complemented, Sylow
440C23—21no—
441C23—21no—
442C23—21no—
443C23—21no—
444C23—222no—
445C23—441no—
446C23—441no—
447C23—441no—
448C23—441no—
449C23—441no—
450C23—441no—
451C23C22⋊C4×D1111yescharacteristic
452C23(C22⋊D11)⋊C411yescharacteristic
453C23#6694611yescharacteristic
454C23#6696411yescharacteristic
455C23#6696711yescharacteristic
456C23#6696711yescharacteristic
457C23#6697111yescharacteristic
458D4—442no—
459D4—442no—
460D4—442no—
461D4—442no—
462D4—442no—
463D4—442no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—24no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—112no—
486C2×C4—112no—
487C2×C4—112no—
488C2×C4—224no—
489C2×C4—224no—
490C2×C4—221no—
491C2×C4—221no—
492C2×C4—221no—
493C2×C4—221no—
494C2×C4—221no—
495C2×C4—221no—
496C2×C4—224no—
497C2×C4—222no—
498C2×C4—221no—
499C2×C4—221no—
500C2×C4—221no—
501C2×C4—442no—
502C2×C4—442no—
503C2×C4—442no—
504C2×C4—442no—
505C2×C4—442no—
506C2×C4—442no—
507C2×C4—442no—
508C2×C4—442no—
509C2×C4—441no—
510C2×C4—441no—
511C2×C4—884no—
512C2×C4C42×D1111yescharacteristic
513C2×C4(C22⋊D11)⋊C411yescharacteristic
514C2×C4#6694511yescharacteristic
515C2×C4#6694611yescharacteristic
516C8—42no—
517C8—442no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22—21no—
527C22—21no—
528C22—21no—
529C22—21no—
530C22—442no—
531C22—442no—
532C22—442no—
533C22—881no—
534C22—881no—
535C22—881no—
536C22—881no—
537C22#1062227911yescharacteristic
538C22#1062235311yescharacteristic
539C22D11×#9911yescharacteristic
540C22#1062238311yescharacteristic
541C22#1062239811yescharacteristic
542C22#1062241611yescharacteristic
543C22#1062243011yescharacteristic
544C22D11×#10411yescharacteristic
545C22D11×#10411yescharacteristic
546C22#1062248211yescharacteristic
547C22#1062250211yescharacteristic
548C4—21no—
549C4—21no—
550C4—21no—
551C4—21no—
552C4—44no—
553C4—81no—
554C4—81no—
555C4—222no—
556C4—222no—
557C4—222no—
558C4—444no—
559C4—441no—
560C4—442no—
561C2—21no—
562C2—21no—
563C2—21no—
564C2—21no—
565C2—882no—
566C2#1306711911yescharacteristic
567C2#1306712211yescharacteristic
568C2#1306713011yescharacteristic
569C2#1306714011yescharacteristic
570C2#1306840311yescharacteristic
571C2#1306842011yescharacteristic
572C2#1306844011yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC2×C4×C11C2×C42
FrattiniC23×C4C22×D11
FittingC11×#1294C2
socleC23×C11C2×C22⋊C4
prime radicalC2×#66983C22
cosocleC23×C4×C11C23
hypercenter#1294D11
hypocenterC11#8218
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
2. #13068380C2semidirect
5. #95×Dic11C2semidirect
6. #13066494C2semidirect
7. C11×#1294C2semidirect
11. C2×#66946C4semidirect
20. #10622601C4semidirect
21. C4⋊C4×Dic11C4semidirect
22. #10622586C4semidirect
27. #10622108C4semidirect
28. #10622089C4semidirect
65. C11×C22⋊C8C2×C4semidirect
68. C11×#95C2×C4semidirect
73. C11⋊#95C2×C4semidirect
75. C22⋊(C11⋊C8)C2×C4semidirect
126. C2×D44C42semidirect
143. C4⋊Dic11C42semidirect
160. #1294D11semidirect
341. C22⋊C8C4×D11semidirect
350. #95C4×D11semidirect
439. C11#8218semidirect

Maximal subgroups

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

subgroupindex
#130711222
#130683802
C2×#106221082
C2×#106220892
#95×Dic112
#130664942
C11×#12942
#821811