Finite Group Databasebeta

← #14648939

Subgroups — #14648939

Order 2816.

678 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622348C211yesmaximal, characteristic
2#13071316C211yesmaximal, characteristic
3#13068704C211yesmaximal, characteristic, complemented
4C2×#10622089C211yesmaximal, characteristic
5#13066883C211yesmaximal, characteristic, complemented
6#13066458C211yesmaximal, characteristic, complemented
7C11×#1294C211yesmaximal, characteristic, complemented
8C2×#66983C2211yescharacteristic
9C22×C4⋊Dic11C2211yescharacteristic
10C2×(C22⋊D11)⋊C4—21no—
11C2×C11×C22⋊C8C2211yescharacteristic
12C11×#380C2211yescharacteristic
13C2×C11×#95C2211yescharacteristic
14C2×C11⋊#95—21no—
15C2×C11⋊#95—21no—
16C2×C11⋊#95C2211yescharacteristic
17C2×C22⋊(C11⋊C8)C2211yescharacteristic
18C2×#66885—21no—
19C2×#66881—21no—
20#10622603—21no—
21#10622602—21no—
22#10622571—21no—
23#10622348—22no—
24#10622348C414yescomplemented
25#10622278—21no—
26#10622267—21no—
27#10622167—21no—
28#10622167—21no—
29#10622089—22no—
30C23×C4×C11—21no—
31C23×C4×C11C2311yescharacteristic
32C22×C22⋊D11—21no—
33C23×Dic11—21no—
34C23×Dic11D411yescharacteristic
35C23×Dic11D411yescharacteristic
36C22×D44D411yescharacteristic
37C22×C4×D11—21no—
38C22×C8×C11—21no—
39C2×C11×C4⋊C4D411yescharacteristic
40C2×C11×C4⋊C4D411yescharacteristic
41C2×C11×C22⋊C4—21no—
42#66983—21no—
43#66983—21no—
44#66983C2×C412yes—
45#66983D412yes—
46C2×(C2×D11)⋊C4—21no—
47C2×(C2×D11)⋊C4—21no—
48C2×(C2×D11)⋊C4—21no—
49C2×(C2×D11)⋊C4—21no—
50C2×C4⋊Dic11—21no—
51C2×C4⋊Dic11—21no—
52C2×C4⋊Dic11—21no—
53C2×C4⋊Dic11—21no—
54C2×C4⋊Dic11—21no—
55C2×C4⋊Dic11C2×C412yescomplemented
56C2×C4⋊Dic11D411yescharacteristic
57C2×Dic11⋊C4—21no—
58C2×C4×Dic11—21no—
59C22×C11⋊C8—21no—
60(C22⋊D11)⋊C4—42no—
61(C22⋊D11)⋊C4—42no—
62C11×C22⋊C8—21no—
63C11×C22⋊C8C2×C412yescomplemented
64C11×#95—21no—
65C11×#95—21no—
66C11×#95—21no—
67C11⋊#95—21no—
68C11⋊#95—21no—
69C11⋊#95—21no—
70C11⋊#95—21no—
71C11⋊#95—42no—
72C11⋊#95—42no—
73C22⋊(C11⋊C8)—21no—
74C22⋊(C11⋊C8)—21no—
75#66885—24no—
76#66881—24no—
77#9045—111nomaximal, Sylow
78C24×C11C2×D411yescharacteristic
79C23×D11—21no—
80C22×C4×C11—22no—
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11—41no—
84C22×C4×C11—41no—
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×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
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—21no—
105C22×Dic11—21no—
106C22×Dic11—21no—
107C22×Dic11—21no—
108C22×Dic11—21no—
109C22×Dic11—21no—
110C22×Dic11—41no—
111C22×Dic11—41no—
112C22×Dic11—41no—
113C22×Dic11—41no—
114C22×Dic11—41no—
115C22×Dic11—41no—
116C22×Dic11—41no—
117C22×Dic11—41no—
118C22×Dic11—41no—
119C22×Dic11—41no—
120C22×Dic11SD1612yes—
121C2×D44—21no—
122C2×D44—41no—
123C2×D44—41no—
124C2×D44C22⋊C412yes—
125C2×C4×D11—42no—
126C2×C4×D11—81no—
127C2×C4×D11—81no—
128C2×C8×C11—22no—
129C2×C8×C11—41no—
130C2×C8×C11—41no—
131C11×C4⋊C4—41no—
132C11×C4⋊C4—41no—
133C11×C22⋊C4—41no—
134C11×C22⋊C4—41no—
135(C2×D11)⋊C4—22no—
136(C2×D11)⋊C4—22no—
137(C2×D11)⋊C4—42no—
138(C2×D11)⋊C4—81no—
139(C2×D11)⋊C4—81no—
140C4⋊Dic11—22no—
141C4⋊Dic11—22no—
142C4⋊Dic11—21no—
143C4⋊Dic11—41no—
144C4⋊Dic11—41no—
145C4⋊Dic11C22⋊C412yes—
146Dic11⋊C4—42no—
147C4×Dic11—42no—
148C2×C11⋊C8—41no—
149C2×C11⋊C8—41no—
150C2×C11⋊C8—41no—
151C2×#481—111no—
152#2325—111no—
153#1824—111no—
154C2×#327—111no—
155#1445—111no—
156#1294D1111yescharacteristic, complemented
157#1280—111no—
158C23×C11—21no—
159C23×C11—21no—
160C23×C11—21no—
161C23×C11—21no—
162C23×C11C4×D411yescharacteristic
163C23×C11#12011yescharacteristic
164C23×C11#12111yescharacteristic
165C23×C11C2×SD1611yescharacteristic
166C23×C11#13511yescharacteristic
167C23×C11AGL(1,ℤ/8)11yescharacteristic
168C23×C11#13711yescharacteristic
169C22×D11—22no—
170C22×D11—41no—
171C22×D11—41no—
172C22×D11—41no—
173C22×D11—41no—
174C22×D11—41no—
175C22×D11—41no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
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—41no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—81no—
194C2×C4×C11—81no—
195C2×C4×C11—81no—
196C2×C4×C11—81no—
197C2×C4×C11C2×C22⋊C411yescharacteristic
198C2×C4×C11C4×D411yescharacteristic
199C2×C4×C11#12111yescharacteristic
200C2×C4×C11#12311yescharacteristic
201C22⋊D11—42no—
202C22⋊D11—42no—
203C22⋊D11—42no—
204C22⋊D11—42no—
205C2×Dic11—22no—
206C2×Dic11—22no—
207C2×Dic11—41no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—42no—
212C2×Dic11—42no—
213C2×Dic11—42no—
214C2×Dic11—42no—
215C2×Dic11—42no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11—41no—
219C2×Dic11—81no—
220C2×Dic11—81no—
221C2×Dic11—81no—
222C2×Dic11—81no—
223C2×Dic11—81no—
224C2×Dic11—81no—
225D44—42no—
226D44—81no—
227C4×D11—84no—
228C8×C11—42no—
229C11⋊C8—81no—
230C2×#121—111no—
231C2×C4×D4—221no—
232C22×C4⋊C4—111no—
233#481—114no—
234#481—222no—
235C2×#106—221no—
236C2×#102—221no—
237C2×C22⋊C8—111no—
238C2×C22⋊C8C2×D1111yescharacteristic
239#388—221no—
240#387—221no—
241#386—221no—
242#386—221no—
243#385—221no—
244#380C2×D1111yescharacteristic
245C2×#95—111no—
246C2×#95—221no—
247C2×#95—221no—
248C2×#95C2×D1111yescharacteristic
249#340—221no—
250#340—221no—
251#327—222no—
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—21no—
261C22×C11—21no—
262C22×C11—21no—
263C22×C11—21no—
264C22×C11#38611yescharacteristic
265C22×C11C4×SD1611yescharacteristic
266C22×C11#44011yescharacteristic
267C22×C11#45011yescharacteristic
268C22×C11#45211yescharacteristic
269C22×C11#45311yescharacteristic
270C22×C11#45411yescharacteristic
271C22×C11#45811yescharacteristic
272C22×C11#45811yescharacteristic
273C22×C11#46111yescharacteristic
274C22×C11#46311yescharacteristic
275C2×D11—42no—
276C2×D11—42no—
277C2×D11—42no—
278C2×D11—81no—
279C2×D11—81no—
280C2×D11—81no—
281C2×D11—81no—
282C4×C11—21no—
283C4×C11—21no—
284C4×C11—21no—
285C4×C11—21no—
286C4×C11—82no—
287C4×C11—81no—
288C4×C11—81no—
289Dic11—42no—
290Dic11—42no—
291Dic11—81no—
292Dic11—82no—
293C22×D4—111no—
294C22×D4—221no—
295C23×C4—21no—
296C23×C4—111no—
297C23×C4—111no—
298C23×C4—221no—
299C23×C4—221no—
300C23×C4C22×D1111yescharacteristic
301C22×C8—21no—
302C22×C8—221no—
303#121—112no—
304#121—112no—
305#121—221no—
306#121—221no—
307C4×D4—442no—
308C4×D4—442no—
309C2×C4⋊C4—111no—
310C2×C4⋊C4—112no—
311C2×C4⋊C4—221no—
312C2×C4⋊C4—221no—
313C2×C4⋊C4—221no—
314C2×C4⋊C4—221no—
315C2×C4⋊C4—221no—
316C2×C4⋊C4—221no—
317C2×C4⋊C4D4411yescharacteristic
318C2×C4⋊C4D4411yescharacteristic
319C2×C22⋊C4—21no—
320C2×C22⋊C4—221no—
321C2×C22⋊C4—221no—
322C2×C22⋊C4—221no—
323C2×C22⋊C4—221no—
324C2×C42—221no—
325#106—224no—
326#102—224no—
327C22⋊C8—21no—
328C22⋊C8—221no—
329C22⋊C8—221no—
330C22⋊C8C4×D1112yescomplemented
331#95—21no—
332#95—21no—
333#95—21no—
334#95—221no—
335#95—221no—
336#95—221no—
337#95—221no—
338#95—442no—
339#95—442no—
340C2×C11—21no—
341C2×C11—21no—
342C2×C11—21no—
343C2×C11—21no—
344C2×C11#161311yescharacteristic
345C2×C11#161511yescharacteristic
346C2×C11#161611yescharacteristic
347C2×C11#161811yescharacteristic
348C2×C11#187711yescharacteristic
349C2×C11#188311yescharacteristic
350C2×C11#189011yescharacteristic
351D11—82no—
352C24—221no—
353C24D4×D1111yescharacteristic
354C2×D4—112no—
355C2×D4—222no—
356C2×D4—222no—
357C2×D4—221no—
358C2×D4—441no—
359C2×D4—441no—
360C2×D4—441no—
361C2×D4—441no—
362C2×D4—441no—
363C2×D4—441no—
364C22×C4—22no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—41no—
368C22×C4—41no—
369C22×C4—41no—
370C22×C4—41no—
371C22×C4—41no—
372C22×C4—41no—
373C22×C4—41no—
374C22×C4—41no—
375C22×C4—112no—
376C22×C4—221no—
377C22×C4—221no—
378C22×C4—221no—
379C22×C4—221no—
380C22×C4—222no—
381C22×C4—221no—
382C22×C4—221no—
383C22×C4—442no—
384C22×C4—441no—
385C22×C4—441no—
386C22×C4—441no—
387C22×C4—441no—
388C22×C4—441no—
389C22×C4—441no—
390C22×C4—441no—
391C22×C4—441no—
392C22×C4—441no—
393C22×C4—441no—
394C22×C4—881no—
395C22×C4—881no—
396C22×C4C2×C4×D1111yescharacteristic
397C22×C4C2×D4411yescharacteristic
398C22×C4#433911yescharacteristic
399C22×C4D4×D1111yescharacteristic
400C22×C4D4×D1111yescharacteristic
401C22×C4#434311yescharacteristic
402C2×C8—22no—
403C2×C8—41no—
404C2×C8—41no—
405C2×C8—441no—
406C2×C8—441no—
407C2×C8—441no—
408C4⋊C4—41no—
409C4⋊C4—41no—
410C4⋊C4—112no—
411C4⋊C4—221no—
412C4⋊C4—222no—
413C4⋊C4—222no—
414C4⋊C4—442no—
415C4⋊C4—441no—
416C4⋊C4—441no—
417C22⋊C4—41no—
418C22⋊C4—41no—
419C22⋊C4—222no—
420C22⋊C4—222no—
421C22⋊C4—442no—
422C22⋊C4—881no—
423C22⋊C4—881no—
424C42—442no—
425C11#904511yescharacteristic, complemented, Sylow
426C23—21no—
427C23—21no—
428C23—21no—
429C23—21no—
430C23—222no—
431C23—441no—
432C23—441no—
433C23—441no—
434C23—441no—
435C23—441no—
436C23—441no—
437C23#6693511yescharacteristic
438C23#6693711yescharacteristic
439C23#6694611yescharacteristic
440C23#6696411yescharacteristic
441C23SD16×D1111yescharacteristic
442C23#6696911yescharacteristic
443C23#6697111yescharacteristic
444D4—442no—
445D4—442no—
446D4—442no—
447D4—442no—
448D4—442no—
449D4—881no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—42no—
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—81no—
471C2×C4—222no—
472C2×C4—222no—
473C2×C4—441no—
474C2×C4—441no—
475C2×C4—441no—
476C2×C4—441no—
477C2×C4—442no—
478C2×C4—442no—
479C2×C4—442no—
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×C4—881no—
489C2×C4—881no—
490C2×C4—881no—
491C2×C4—881no—
492C2×C4C4×D4411yescharacteristic
493C2×C4C22⋊C4×D1111yescharacteristic
494C2×C4#6694711yescharacteristic
495C2×C4#6694811yescharacteristic
496C8—42no—
497C8—881no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—442no—
511C22—442no—
512C22—442no—
513C22—881no—
514C22—881no—
515C22—881no—
516C22—881no—
517C22#1062227811yescharacteristic
518C22#1062235511yescharacteristic
519C22#1062235511yescharacteristic
520C22#1062238911yescharacteristic
521C22#1062240011yescharacteristic
522C22#1062242311yescharacteristic
523C22#1062243111yescharacteristic
524C22#1062243511yescharacteristic
525C22#1062244011yescharacteristic
526C22#1062246511yescharacteristic
527C22#1062250211yescharacteristic
528C4—21no—
529C4—21no—
530C4—21no—
531C4—21no—
532C4—82no—
533C4—81no—
534C4—81no—
535C4—442no—
536C4—442no—
537C4—881no—
538C4—882no—
539C2—21no—
540C2—21no—
541C2—21no—
542C2—21no—
543C2—882no—
544C2#1306763711yescharacteristic
545C2#1306765011yescharacteristic
546C2#1306765411yescharacteristic
547C2#1306766711yescharacteristic
548C2#1306895111yescharacteristic
549C2#1306899311yescharacteristic
550C2#1306902811yescharacteristic
subgroupG/H
centerC23#66935
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1294C2
socleC23×C11#120
prime radicalC2×#66983C22
cosocleC23×C4×C11C23
hypercenter#1294D11
hypocenterC11#9045
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
3. #13068704C2semidirect
5. #13066883C2semidirect
6. #13066458C2semidirect
7. C11×#1294C2semidirect
24. #10622348C4semidirect
55. C2×C4⋊Dic11C2×C4semidirect
63. C11×C22⋊C8C2×C4semidirect
156. #1294D11semidirect
330. C22⋊C8C4×D11semidirect
425. C11#9045semidirect

Maximal subgroups

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

subgroupindex
C2×#106223482
#130713162
#130687042
C2×#106220892
#130668832
#130664582
C11×#12942
#904511