Finite Group Databasebeta

← #14647869

Subgroups — #14647869

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#13071319C211yesmaximal, characteristic
2#13068933C211yesmaximal, characteristic
3#13068809C211yesmaximal, characteristic, complemented
4C2×#10622089C211yesmaximal, characteristic
5#13066495C211yesmaximal, characteristic, complemented
6#13066459C211yesmaximal, characteristic, complemented
7C11×#1444C211yesmaximal, characteristic, complemented
8C22×C11×C4⋊C4—21no—
9C22×C11×C4⋊C4C2211yescharacteristic
10C2×#66983C2211yescharacteristic
11C2×C4×C22⋊D11—21no—
12C2×C11×#95—21no—
13C2×C11×#95C2211yescharacteristic
14C2×C11×#95C2211yescharacteristic
15#10622826—21no—
16#10622825C2211yescharacteristic
17C2×C22⋊(C11⋊C8)C2211yescharacteristic
18C2×C22⋊(C11⋊C8)C2211yescharacteristic
19C2×#66873—21no—
20C2×#66872—21no—
21#10622283—21no—
22#10622281—21no—
23#10622278—21no—
24#10622266—21no—
25#10622167—21no—
26#10622167—21no—
27#10622089C414yescomplemented
28C23×C4×C11—21no—
29C23×C4×C11—21no—
30C23×C4×C11D411yescharacteristic
31C23×C4×C11D411yescharacteristic
32C23×C4×C11C2311yescharacteristic
33C22×C22⋊D11—21no—
34C22×D44D411yescharacteristic
35C22×C4×D11—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—42no—
39C2×C11×C4⋊C4—42no—
40C2×C11×C4⋊C4—42no—
41C2×C11×C4⋊C4—42no—
42C2×C22⋊Dic11—21no—
43#66983—21no—
44#66983—21no—
45#66983C2×C412yes—
46#66983Q812yes—
47C4×C22⋊D11—42no—
48C4×C22⋊D11—42no—
49C2×(C2×D11)⋊C4—21no—
50C2×(C2×D11)⋊C4—21no—
51C2×(C2×D11)⋊C4—21no—
52C2×(C2×D11)⋊C4—21no—
53C2×C4⋊Dic11D411yescharacteristic
54C2×C4⋊Dic11D411yescharacteristic
55C2×C4⋊Dic11D411yescharacteristic
56C2×Dic11⋊C4—21no—
57C2×C4×Dic11—21no—
58C22×C11⋊C8—21no—
59C22×C11⋊C8—21no—
60C11×#95—21no—
61C11×#95—21no—
62C11×#95—21no—
63C11×#95—42no—
64C11×#95C2×C412yescomplemented
65C11⋊#95—21no—
66C11⋊#95—21no—
67C11⋊#95—21no—
68C22⋊(C11⋊C8)—21no—
69C22⋊(C11⋊C8)—21no—
70C22⋊(C11⋊C8)—21no—
71C22⋊(C11⋊C8)C2×C412yescomplemented
72#66873—42no—
73#66872—42no—
74#8873—111nomaximal, Sylow
75C24×C11C2×D411yescharacteristic
76C23×D11—21no—
77C22×C4×C11—22no—
78C22×C4×C11—22no—
79C22×C4×C11—22no—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11—22no—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11—41no—
89C22×C4×C11—41no—
90C22×C4×C11—41no—
91C22×C4×C11—41no—
92C22×C4×C11—41no—
93C22×C4×C11—41no—
94C22×C4×C11—41no—
95C22×C4×C11—41no—
96C22×C4×C11—41no—
97C22×C4×C11—41no—
98C22×C4×C11—41no—
99C22×C4×C11—41no—
100C22×C4×C11—41no—
101C22×C4×C11—41no—
102C22×C4×C11SD1612yes—
103C22×C4×C11C22×C411yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×Q811yescharacteristic
107C22×C4×C11#4111yescharacteristic
108C22×C4×C11#4111yescharacteristic
109C2×C22⋊D11—22no—
110C2×C22⋊D11—22no—
111C2×C22⋊D11—41no—
112C2×C22⋊D11—41no—
113C2×C22⋊D11—41no—
114C2×C22⋊D11—41no—
115C22×Dic11—21no—
116C22×Dic11—21no—
117C22×Dic11—21no—
118C2×D44—21no—
119C2×D44—41no—
120C2×D44—41no—
121C2×D44C4⋊C412yescomplemented
122C2×C4×D11—42no—
123C2×C4×D11—81no—
124C2×C4×D11—81no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—41no—
128C11×C4⋊C4—41no—
129C11×C4⋊C4—48no—
130C22⋊Dic11—41no—
131C22⋊Dic11—41no—
132(C2×D11)⋊C4—22no—
133(C2×D11)⋊C4—22no—
134(C2×D11)⋊C4—42no—
135(C2×D11)⋊C4—81no—
136(C2×D11)⋊C4—81no—
137C4⋊Dic11—21no—
138C4⋊Dic11—41no—
139C4⋊Dic11—41no—
140C4⋊Dic11C4⋊C412yescomplemented
141Dic11⋊C4—42no—
142C4×Dic11—42no—
143C2×C11⋊C8—22no—
144C2×C11⋊C8—41no—
145C2×C11⋊C8—41no—
146C2×C11⋊C8—41no—
147C2×C11⋊C8—41no—
148C2×C11⋊C8—41no—
149#2325—111no—
150#1874—111no—
151#1853—111no—
152C2×#327—111no—
153#1444D1111yescharacteristic, complemented
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—24no—
179C2×C4×C11—22no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—42no—
200C2×C4×C11—81no—
201C2×C4×C11—81no—
202C2×C4×C11—81no—
203C2×C4×C11—81no—
204C2×C4×C11—81no—
205C2×C4×C11—81no—
206C2×C4×C11C2×C4⋊C411yescharacteristic
207C2×C4×C11C4×D411yescharacteristic
208C2×C4×C11C22⋊Q811yescharacteristic
209C2×C4×C11#12311yescharacteristic
210C22⋊D11—42no—
211C22⋊D11—42no—
212C22⋊D11—42no—
213C22⋊D11—42no—
214C2×Dic11—22no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11—41no—
219C2×Dic11—41no—
220C2×Dic11—41no—
221C2×Dic11—41no—
222C2×Dic11—41no—
223D44—42no—
224D44—81no—
225C4×D11—84no—
226C11⋊C8—42no—
227C11⋊C8—81no—
228C2×#121—111no—
229C2×C4×D4—221no—
230C22×C4⋊C4—21no—
231C22×C4⋊C4C2×D1111yescharacteristic
232C2×#106—221no—
233C2×#102—221no—
234C2×C22⋊C8—111no—
235C2×C22⋊C8—111no—
236#388—221no—
237#387—221no—
238#386—221no—
239#386—221no—
240#385—221no—
241#380—111no—
242C2×#95—21no—
243C2×#95C2×D1111yescharacteristic
244C2×#95C2×D1111yescharacteristic
245#340—221no—
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—44no—
283C4×C11—42no—
284C4×C11—81no—
285C4×C11—82no—
286Dic11—42no—
287Dic11—81no—
288Dic11—81no—
289C22×D4—111no—
290C22×D4—221no—
291C23×C4—21no—
292C23×C4—21no—
293C23×C4—221no—
294C23×C4C22⋊D1111yescharacteristic
295C23×C4C22⋊D1111yescharacteristic
296C23×C4C22×D1111yescharacteristic
297C22×C8—221no—
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—42no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—111no—
312C2×C4⋊C4—111no—
313C2×C4⋊C4—111no—
314C2×C4⋊C4—221no—
315C2×C22⋊C4—221no—
316C2×C22⋊C4—221no—
317C2×C22⋊C4—221no—
318C2×C22⋊C4—221no—
319C2×C22⋊C4—221no—
320C2×C42—221no—
321#106—442no—
322#102—442no—
323C22⋊C8—112no—
324C22⋊C8—221no—
325C22⋊C8—221no—
326C22⋊C8—221no—
327#95—21no—
328#95—21no—
329#95—21no—
330#95—42no—
331#95—221no—
332#95—221no—
333#95—221no—
334#95C4×D1112yescomplemented
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—
348C24C2×C22⋊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—22no—
361C22×C4—22no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—22no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—41no—
369C22×C4—41no—
370C22×C4—41no—
371C22×C4—41no—
372C22×C4—41no—
373C22×C4—41no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4—41no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4—221no—
385C22×C4—221no—
386C22×C4—221no—
387C22×C4—442no—
388C22×C4—881no—
389C22×C4—881no—
390C22×C4#432512yes—
391C22×C4C2×C4×D1111yescharacteristic
392C22×C4#433911yescharacteristic
393C22×C4D4×D1111yescharacteristic
394C22×C4D4×D1111yescharacteristic
395C22×C4Q8×D1111yescharacteristic
396C22×C4#434311yescharacteristic
397C2×C8—222no—
398C2×C8—441no—
399C2×C8—441no—
400C2×C8—441no—
401C2×C8—441no—
402C2×C8—441no—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—41no—
406C4⋊C4—41no—
407C4⋊C4—48no—
408C4⋊C4—112no—
409C4⋊C4—221no—
410C4⋊C4—441no—
411C4⋊C4—441no—
412C4⋊C4—442no—
413C22⋊C4—222no—
414C22⋊C4—222no—
415C22⋊C4—442no—
416C22⋊C4—441no—
417C22⋊C4—441no—
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—
433C23C4×C22⋊D1111yescharacteristic
434C23#6698511yescharacteristic
435C23#6699011yescharacteristic
436C23C2×#432511yescharacteristic
437C23#6699911yescharacteristic
438C23#6700211yescharacteristic
439C23#6700311yescharacteristic
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—24no—
451C2×C4—22no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—41no—
469C2×C4—42no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—81no—
473C2×C4—81no—
474C2×C4—81no—
475C2×C4—81no—
476C2×C4—81no—
477C2×C4—81no—
478C2×C4—222no—
479C2×C4—441no—
480C2×C4—441no—
481C2×C4—441no—
482C2×C4—441no—
483C2×C4—441no—
484C2×C4—441no—
485C2×C4—441no—
486C2×C4—441no—
487C2×C4—884no—
488C2×C4C4⋊C4×D1111yescharacteristic
489C2×C4#6694611yescharacteristic
490C2×C4#6694711yescharacteristic
491C2×C4#6694911yescharacteristic
492C8—442no—
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#1062260211yescharacteristic
514C22#1062262711yescharacteristic
515C22C4×#432511yescharacteristic
516C22#1062264511yescharacteristic
517C22#1062265011yescharacteristic
518C22#1062265911yescharacteristic
519C22#1062266611yescharacteristic
520C22#1062267911yescharacteristic
521C22#1062269011yescharacteristic
522C22#1062269711yescharacteristic
523C22#1062270811yescharacteristic
524C4—21no—
525C4—21no—
526C4—21no—
527C4—21no—
528C4—44no—
529C4—42no—
530C4—81no—
531C4—82no—
532C4—442no—
533C4—881no—
534C4—881no—
535C2—21no—
536C2—21no—
537C2—21no—
538C2—21no—
539C2—882no—
540C2#1306756011yescharacteristic
541C2#1306758411yescharacteristic
542C2#1306761111yescharacteristic
543C2#1306763511yescharacteristic
544C2#1306884111yescharacteristic
545C2#1306887611yescharacteristic
546C2#1306889511yescharacteristic
subgroupG/H
centerC23#66990
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1444C2
socleC23×C11#120
prime radicalC2×#66983C22
cosocleC23×C4×C11C23
hypercenter#1444D11
hypocenterC11#8873
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1444

Complements

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

NH ≅ G/Ntype
3. #13068809C2semidirect
5. #13066495C2semidirect
6. #13066459C2semidirect
7. C11×#1444C2semidirect
27. #10622089C4semidirect
64. C11×#95C2×C4semidirect
71. C22⋊(C11⋊C8)C2×C4semidirect
121. C2×D44C4⋊C4semidirect
140. C4⋊Dic11C4⋊C4semidirect
153. #1444D11semidirect
334. #95C4×D11semidirect
421. C11#8873semidirect

Maximal subgroups

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

subgroupindex
#130713192
#130689332
#130688092
C2×#106220892
#130664952
#130664592
C11×#14442
#887311