Finite Group Databasebeta

← #14647867

Subgroups — #14647867

Order 2816.

702 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071316C211yesmaximal, characteristic
2#13068933C211yesmaximal, characteristic
3C2×#10622108C211yesmaximal, characteristic
4#13066879C211yesmaximal, characteristic, complemented
5#13066494C211yesmaximal, characteristic, complemented
6#13066458C211yesmaximal, characteristic, complemented
7C11×#1853C211yesmaximal, characteristic, complemented
8C22×C11×C4⋊C4C2211yescharacteristic
9C2×#66983C2211yescharacteristic
10C22×Dic11⋊C4—21no—
11C2×(C22⋊D11)⋊C4—21no—
12C2×C11×#106—21no—
13C2×C11×C22⋊C8C2211yescharacteristic
14C11×#380C2211yescharacteristic
15C2×C11⋊#95—21no—
16C2×C11⋊#95C2211yescharacteristic
17C2×C11⋊#95C2211yescharacteristic
18C2×C22⋊(C11⋊C8)C2211yescharacteristic
19#10622603—21no—
20#10622602—21no—
21C2×#66873—21no—
22#10622571—21no—
23#10622278—21no—
24#10622267—21no—
25C11×#340—21no—
26#10622167—21no—
27#10622108C414yescomplemented
28C23×C4×C11—21no—
29C23×C4×C11C2311yescharacteristic
30C22×C22⋊D11—21no—
31C23×Dic11—21no—
32C23×Dic11D411yescharacteristic
33C23×Dic11D411yescharacteristic
34C22×D44D411yescharacteristic
35C22×C4×D11—21no—
36C22×C8×C11—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—42no—
40C2×C11×C4⋊C4D411yescharacteristic
41C2×C11×C4⋊C4D411yescharacteristic
42C2×C11×C22⋊C4—21no—
43#66983—21no—
44#66983—21no—
45#66983C2×C412yes—
46#66983Q812yes—
47C2×(C2×D11)⋊C4—21no—
48C2×(C2×D11)⋊C4—21no—
49C2×(C2×D11)⋊C4—21no—
50C2×(C2×D11)⋊C4—21no—
51C2×C4⋊Dic11D411yescharacteristic
52C2×Dic11⋊C4—21no—
53C2×Dic11⋊C4—42no—
54C2×Dic11⋊C4—42no—
55C2×Dic11⋊C4—42no—
56C2×C4×Dic11—21no—
57C22×C11⋊C8—21no—
58(C22⋊D11)⋊C4—42no—
59(C22⋊D11)⋊C4—42no—
60C11×#106—42no—
61C11×C22⋊C8—21no—
62C11×C22⋊C8C2×C412yescomplemented
63C11×#95—21no—
64C11⋊#95—21no—
65C11⋊#95—21no—
66C11⋊#95—21no—
67C11⋊#95—21no—
68C11⋊#95—21no—
69C11⋊#95—42no—
70C11⋊#95C2×C412yescomplemented
71C22⋊(C11⋊C8)—21no—
72C22⋊(C11⋊C8)—21no—
73#66873—42no—
74#8873—111nomaximal, Sylow
75C24×C11C2×D411yescharacteristic
76C23×D11—21no—
77C22×C4×C11—22no—
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11—41no—
81C22×C4×C11—41no—
82C22×C4×C11—41no—
83C22×C4×C11—41no—
84C22×C4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11C22×C411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×Q811yescharacteristic
92C22×C4×C11#4111yescharacteristic
93C22×C4×C11#4111yescharacteristic
94C2×C22⋊D11—22no—
95C2×C22⋊D11—22no—
96C2×C22⋊D11—41no—
97C2×C22⋊D11—41no—
98C2×C22⋊D11—41no—
99C2×C22⋊D11—41no—
100C22×Dic11—22no—
101C22×Dic11—22no—
102C22×Dic11—22no—
103C22×Dic11—21no—
104C22×Dic11—21no—
105C22×Dic11—21no—
106C22×Dic11—21no—
107C22×Dic11—21no—
108C22×Dic11—21no—
109C22×Dic11—41no—
110C22×Dic11—41no—
111C22×Dic11—41no—
112C22×Dic11—41no—
113C22×Dic11—41no—
114C22×Dic11—41no—
115C22×Dic11—41no—
116C22×Dic11—41no—
117C22×Dic11SD1612yes—
118C2×D44—21no—
119C2×D44—41no—
120C2×D44—41no—
121C2×D44C4⋊C412yescomplemented
122C2×C4×D11—42no—
123C2×C4×D11—81no—
124C2×C4×D11—81no—
125C2×C8×C11—22no—
126C2×C8×C11—41no—
127C2×C8×C11—41no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—41no—
131C11×C4⋊C4—41no—
132C11×C4⋊C4—41no—
133C11×C4⋊C4—41no—
134C11×C22⋊C4—41no—
135C11×C22⋊C4—41no—
136(C2×D11)⋊C4—22no—
137(C2×D11)⋊C4—22no—
138(C2×D11)⋊C4—42no—
139(C2×D11)⋊C4—81no—
140(C2×D11)⋊C4—81no—
141C4⋊Dic11—21no—
142C4⋊Dic11C4⋊C412yescomplemented
143Dic11⋊C4—42no—
144Dic11⋊C4—48no—
145C4×Dic11—42no—
146C2×C11⋊C8—41no—
147C2×C11⋊C8—41no—
148C2×C11⋊C8—41no—
149#2325—111no—
150#1874—111no—
151#1853D1111yescharacteristic, complemented
152C2×#327—111no—
153#1444—111no—
154#1294—111no—
155#1280—111no—
156C23×C11—21no—
157C23×C11—21no—
158C23×C11—21no—
159C23×C11—21no—
160C23×C11C4×D411yescharacteristic
161C23×C11#12011yescharacteristic
162C23×C11C22⋊Q811yescharacteristic
163C23×C11C2×SD1611yescharacteristic
164C23×C11#13511yescharacteristic
165C23×C11AGL(1,ℤ/8)11yescharacteristic
166C23×C11AGL(1,ℤ/8)11yescharacteristic
167C22×D11—22no—
168C22×D11—41no—
169C22×D11—41no—
170C22×D11—41no—
171C22×D11—41no—
172C22×D11—41no—
173C22×D11—41no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—42no—
190C2×C4×C11—41no—
191C2×C4×C11—81no—
192C2×C4×C11—81no—
193C2×C4×C11—81no—
194C2×C4×C11—81no—
195C2×C4×C11C2×C4⋊C411yescharacteristic
196C2×C4×C11C4×D411yescharacteristic
197C2×C4×C11C22⋊Q811yescharacteristic
198C2×C4×C11#12311yescharacteristic
199C22⋊D11—42no—
200C22⋊D11—42no—
201C22⋊D11—42no—
202C22⋊D11—42no—
203C2×Dic11—24no—
204C2×Dic11—22no—
205C2×Dic11—22no—
206C2×Dic11—42no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C2×Dic11—42no—
211C2×Dic11—42no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11—42no—
217C2×Dic11—42no—
218C2×Dic11—41no—
219C2×Dic11—41no—
220C2×Dic11—41no—
221C2×Dic11—81no—
222C2×Dic11—81no—
223D44—42no—
224D44—81no—
225C4×D11—84no—
226C8×C11—42no—
227C11⋊C8—81no—
228C2×#121—111no—
229C2×C4×D4—221no—
230C22×C4⋊C4—221no—
231C22×C4⋊C4C2×D1111yescharacteristic
232C2×#106—21no—
233C2×#102—221no—
234C2×C22⋊C8—111no—
235C2×C22⋊C8C2×D1111yescharacteristic
236#388—221no—
237#387—221no—
238#386—221no—
239#386—221no—
240#385—221no—
241#380C2×D1111yescharacteristic
242C2×#95—111no—
243C2×#95—111no—
244C2×#95—221no—
245#340—21no—
246#340—221no—
247#327—114no—
248C22×C11—21no—
249C22×C11—21no—
250C22×C11—21no—
251C22×C11—21no—
252C22×C11—21no—
253C22×C11—21no—
254C22×C11—21no—
255C22×C11—21no—
256C22×C11—21no—
257C22×C11—21no—
258C22×C11—21no—
259C22×C11—21no—
260C22×C11#38511yescharacteristic
261C22×C11C4×SD1611yescharacteristic
262C22×C11#44211yescharacteristic
263C22×C11#44911yescharacteristic
264C22×C11#45011yescharacteristic
265C22×C11#45311yescharacteristic
266C22×C11#45611yescharacteristic
267C22×C11B(4,𝔽2)11yescharacteristic
268C22×C11#45811yescharacteristic
269C22×C11#47611yescharacteristic
270C22×C11#47811yescharacteristic
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—82no—
283C4×C11—81no—
284C4×C11—81no—
285Dic11—44no—
286Dic11—42no—
287Dic11—42no—
288Dic11—81no—
289C22×D4—111no—
290C22×D4—221no—
291C23×C4—21no—
292C23×C4—111no—
293C23×C4—111no—
294C23×C4—221no—
295C23×C4—221no—
296C23×C4C22×D1111yescharacteristic
297C22×C8—21no—
298C22×C8—221no—
299#121—112no—
300#121—112no—
301#121—221no—
302#121—221no—
303C4×D4—442no—
304C4×D4—442no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—111no—
309C2×C4⋊C4—221no—
310C2×C4⋊C4—442no—
311C2×C4⋊C4—442no—
312C2×C4⋊C4—442no—
313C2×C4⋊C4C22⋊D1111yescharacteristic
314C2×C4⋊C4C22⋊D1111yescharacteristic
315C2×C22⋊C4—21no—
316C2×C22⋊C4—221no—
317C2×C22⋊C4—221no—
318C2×C22⋊C4—221no—
319C2×C22⋊C4—221no—
320C2×C42—221no—
321#106—42no—
322#102—442no—
323C22⋊C8—21no—
324C22⋊C8—221no—
325C22⋊C8—221no—
326C22⋊C8C4×D1112yescomplemented
327#95—21no—
328#95—112no—
329#95—221no—
330#95—221no—
331#95—221no—
332#95—221no—
333#95—221no—
334#95—442no—
335C2×C11—21no—
336C2×C11—21no—
337C2×C11—21no—
338C2×C11—21no—
339C2×C11#160011yescharacteristic
340C2×C11#160411yescharacteristic
341C2×C11#160911yescharacteristic
342C2×C11#161311yescharacteristic
343C2×C11#185911yescharacteristic
344C2×C11#186411yescharacteristic
345C2×C11#186711yescharacteristic
346D11—82no—
347C24—221no—
348C24D4×D1111yescharacteristic
349C2×D4—112no—
350C2×D4—222no—
351C2×D4—222no—
352C2×D4—221no—
353C2×D4—441no—
354C2×D4—441no—
355C2×D4—441no—
356C2×D4—441no—
357C2×D4—441no—
358C2×D4—441no—
359C22×C4—22no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—41no—
363C22×C4—41no—
364C22×C4—41no—
365C22×C4—41no—
366C22×C4—41no—
367C22×C4—41no—
368C22×C4—41no—
369C22×C4—41no—
370C22×C4—112no—
371C22×C4—222no—
372C22×C4—222no—
373C22×C4—222no—
374C22×C4—221no—
375C22×C4—221no—
376C22×C4—221no—
377C22×C4—221no—
378C22×C4—221no—
379C22×C4—221no—
380C22×C4—442no—
381C22×C4—441no—
382C22×C4—441no—
383C22×C4—441no—
384C22×C4—441no—
385C22×C4—441no—
386C22×C4—441no—
387C22×C4—441no—
388C22×C4—441no—
389C22×C4—881no—
390C22×C4—881no—
391C22×C4C2×C4×D1111yescharacteristic
392C22×C4#433911yescharacteristic
393C22×C4D4×D1111yescharacteristic
394C22×C4Q8×D1111yescharacteristic
395C22×C4#434311yescharacteristic
396C22×C4C2×C22⋊D1111yescharacteristic
397C2×C8—22no—
398C2×C8—41no—
399C2×C8—41no—
400C2×C8—441no—
401C2×C8—441no—
402C2×C8—441no—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—41no—
406C4⋊C4—41no—
407C4⋊C4—41no—
408C4⋊C4—41no—
409C4⋊C4—112no—
410C4⋊C4—221no—
411C4⋊C4—442no—
412C4⋊C4—448no—
413C22⋊C4—41no—
414C22⋊C4—41no—
415C22⋊C4—222no—
416C22⋊C4—222no—
417C22⋊C4—442no—
418C22⋊C4—881no—
419C22⋊C4—881no—
420C42—442no—
421C11#887311yescharacteristic, complemented, Sylow
422C23—21no—
423C23—21no—
424C23—21no—
425C23—21no—
426C23—222no—
427C23—441no—
428C23—441no—
429C23—441no—
430C23—441no—
431C23—441no—
432C23—441no—
433C23#6694611yescharacteristic
434C23#6694911yescharacteristic
435C23SD16×D1111yescharacteristic
436C23#6696711yescharacteristic
437C23#6696711yescharacteristic
438C23#6696911yescharacteristic
439C23#6699011yescharacteristic
440D4—442no—
441D4—442no—
442D4—442no—
443D4—442no—
444D4—442no—
445D4—881no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—42no—
462C2×C4—41no—
463C2×C4—81no—
464C2×C4—81no—
465C2×C4—81no—
466C2×C4—81no—
467C2×C4—224no—
468C2×C4—222no—
469C2×C4—222no—
470C2×C4—442no—
471C2×C4—442no—
472C2×C4—442no—
473C2×C4—442no—
474C2×C4—442no—
475C2×C4—442no—
476C2×C4—441no—
477C2×C4—441no—
478C2×C4—441no—
479C2×C4—441no—
480C2×C4—442no—
481C2×C4—442no—
482C2×C4—441no—
483C2×C4—441no—
484C2×C4—441no—
485C2×C4—884no—
486C2×C4—881no—
487C2×C4—881no—
488C2×C4C4⋊C4×D1111yescharacteristic
489C2×C4#6694711yescharacteristic
490C2×C4C4×C22⋊D1111yescharacteristic
491C2×C4#6699911yescharacteristic
492C8—42no—
493C8—881no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—442no—
507C22—442no—
508C22—442no—
509C22—881no—
510C22—881no—
511C22—881no—
512C22—881no—
513C22#1062246511yescharacteristic
514C22#1062248211yescharacteristic
515C22#1062248311yescharacteristic
516C22#1062248411yescharacteristic
517C22#1062260211yescharacteristic
518C22#1062264511yescharacteristic
519C22#1062266611yescharacteristic
520C22#1062278211yescharacteristic
521C22#1062278511yescharacteristic
522C22#1062281111yescharacteristic
523C22#1062281811yescharacteristic
524C4—21no—
525C4—21no—
526C4—21no—
527C4—21no—
528C4—82no—
529C4—81no—
530C4—81no—
531C4—444no—
532C4—442no—
533C4—442no—
534C4—881no—
535C2—21no—
536C2—21no—
537C2—21no—
538C2—21no—
539C2—882no—
540C2#1306756111yescharacteristic
541C2#1306758311yescharacteristic
542C2#1306761211yescharacteristic
543C2#1306763411yescharacteristic
544C2#1306883911yescharacteristic
545C2#1306887411yescharacteristic
546C2#1306889511yescharacteristic
subgroupG/H
centerC23#66990
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1853C2
socleC23×C11#120
prime radicalC2×#66983C22
cosocleC23×C4×C11C23
hypercenter#1853D11
hypocenterC11#8873
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1853

Complements

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

NH ≅ G/Ntype
4. #13066879C2semidirect
5. #13066494C2semidirect
6. #13066458C2semidirect
7. C11×#1853C2semidirect
27. #10622108C4semidirect
62. C11×C22⋊C8C2×C4semidirect
70. C11⋊#95C2×C4semidirect
121. C2×D44C4⋊C4semidirect
142. C4⋊Dic11C4⋊C4semidirect
151. #1853D11semidirect
326. C22⋊C8C4×D11semidirect
421. C11#8873semidirect

Maximal subgroups

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

subgroupindex
#130713162
#130689332
C2×#106221082
#130668792
#130664942
#130664582
C11×#18532
#887311