Finite Group Databasebeta

← #14781765

Subgroups — #14781765

Order 2816.

1410 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67004C211yesmaximal, characteristic
2C2×#10622715C211yesmaximal, characteristic, complemented
3C22×#66880C211yesmaximal, characteristic, complemented
4#13071208C211yesmaximal, characteristic
5#13071200C211yesmaximal, characteristic, complemented
6#13069937C214yesmaximal, complemented
7#13069932C214yesmaximal, complemented
8#13068337C211yesmaximal, characteristic, complemented
9C2×C11×#416C211yesmaximal, characteristic
10C22×C11×#41C2211yescharacteristic
11C23×Dic22C2211yescharacteristic
12C23×C8×C11C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C2×#67004—24no—
15C2×#67004—24no—
16C2×#67004—24no—
17C22×#4326C2212yes—
18C22×#4324C2212yes—
19C2×#66979C2211yescharacteristic
20C22×C4⋊Dic11C2211yescharacteristic
21C22×#4318C2211yescharacteristic
22C11×#416—24no—
23C2×C11×#103C2212yes—
24C2×C11×#102C2212yes—
25#10622843C2212yes—
26#10622834C2212yes—
27#10622833—22no—
28#10622825—22no—
29C2×#66880—24no—
30C2×#66880C2214yes—
31#10622715—24no—
32C2×Dic11⋊C8C2214yes—
33#10622587C2214yes—
34#10622556—22no—
35#10622542—22no—
36#10622167C2214yes—
37C2×C11×#41—22no—
38C2×C11×#41—22no—
39C2×C11×#41—22no—
40C2×C11×#41—22no—
41C2×C11×#41—22no—
42C2×C11×#41D414yes—
43C22×Q8×C11C2311yescharacteristic
44C22×D4×C11—21no—
45C22×D4×C11C2311yescharacteristic
46C23×C4×C11—21no—
47C23×C4×C11C2311yescharacteristic
48C23×Dic11—21no—
49C23×Dic11—21no—
50C22×Dic22—22no—
51C22×Dic22—22no—
52C22×Dic22—22no—
53C22×Dic22—22no—
54C22×Dic22—21no—
55C22×Dic22—22no—
56C22×Dic22D414yes—
57C22×Dic22C2312yes—
58C22×C8×C11—22no—
59C22×C8×C11—22no—
60C22×C8×C11—22no—
61C22×C8×C11C2312yes—
62C11×#117—22no—
63C11×#117—22no—
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C22⋊C4—21no—
66C2×C42×C11—21no—
67C2×C22⋊Dic11—24no—
68C2×C22⋊Dic11D412yes—
69#67004—232no—
70C2×#4326—24no—
71C2×#4326—24no—
72C2×#4326—24no—
73C2×#4324—24no—
74C2×#4324—24no—
75C2×#4324—24no—
76#66979—22no—
77#66979—22no—
78C2×C4⋊Dic11—22no—
79C2×C4⋊Dic11—22no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11D412yes—
82C2×C4⋊Dic11C2312yes—
83C2×C4×Dic11C2312yes—
84C2×#4318—22no—
85C2×#4318—22no—
86C2×#4318D414yes—
87C22×C11⋊C8C2312yes—
88C11×#103—24no—
89C11×#102—24no—
90C11⋊#95—28no—
91C11⋊#95—24no—
92#66880—28no—
93Dic11⋊C8—28no—
94#23545—111nomaximal, Sylow
95C24×C11—21no—
96C24×C11C2×D411yescharacteristic
97C11×#41—28no—
98C11×#41—28no—
99C11×#41—44no—
100C11×#41—44no—
101C2×Q8×C11—21no—
102C2×Q8×C11—21no—
103C2×Q8×C11—21no—
104C2×Q8×C11—21no—
105C2×Q8×C11—21no—
106C2×Q8×C11C2×D412yes—
107C2×D4×C11—24no—
108C2×D4×C11—21no—
109C2×D4×C11—21no—
110C2×D4×C11—21no—
111C2×D4×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11—42no—
114C2×D4×C11—42no—
115C2×D4×C11C2×D412yes—
116C22×C4×C11—21no—
117C22×C4×C11—24no—
118C22×C4×C11—22no—
119C22×C4×C11—42no—
120C22×C4×C11—42no—
121C22×C4×C11C2×D412yes—
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11#4112yes—
126C22×C4×C11#4112yes—
127C22×C4×C11#4112yes—
128C22×C4×C11C2411yescharacteristic
129C22×Dic11—24no—
130C22×Dic11—22no—
131C22×Dic11—22no—
132C22×Dic11—42no—
133C22×Dic11—42no—
134C22×Dic11—42no—
135C22×Dic11—82no—
136C22×Dic11C2×D414yes—
137C2×Dic22—28no—
138C2×Dic22—24no—
139C2×Dic22—28no—
140C2×Dic22—22no—
141C2×Dic22—22no—
142C2×Dic22—22no—
143C2×Dic22—22no—
144C2×Dic22—22no—
145C2×Dic22—42no—
146C2×Dic22—42no—
147C2×Dic22—44no—
148C2×Dic22—44no—
149C2×Dic22C2×D414yes—
150C2×C8×C11—22no—
151C2×C8×C11—22no—
152C2×C8×C11—22no—
153C2×C8×C11—44no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C22⋊C4—42no—
157C42×C11—42no—
158C22⋊Dic11—24no—
159C22⋊Dic11—84no—
160#4326—216no—
161#4324—216no—
162C4⋊Dic11—24no—
163C4⋊Dic11—22no—
164C4⋊Dic11—22no—
165C4⋊Dic11—42no—
166C4×Dic11—22no—
167C4×Dic11—22no—
168#4318—28no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8C2×D414yes—
172C22×#137—111no—
173C2×#424—111no—
174C2×#416D1111yescharacteristic
175C22×#103—111no—
176#2311—111no—
177#2310—111no—
178#2056—114no—
179#2055—114no—
180#1736—111no—
181C23×C11—22no—
182C23×C11—22no—
183C23×C11—22no—
184C23×C11—41no—
185C23×C11—41no—
186C23×C11—42no—
187C23×C11—42no—
188C23×C11#12112yes—
189C23×C11#12112yes—
190C23×C11#12112yes—
191C23×C11C22×D411yescharacteristic
192Q8×C11—22no—
193Q8×C11—22no—
194Q8×C11—41no—
195Q8×C11—41no—
196D4×C11—22no—
197D4×C11—22no—
198D4×C11—48no—
199D4×C11—41no—
200D4×C11—41no—
201C2×C4×C11—22no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—48no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11#12014yes—
209C2×C4×C11#12112yes—
210C2×C4×C11#12112yes—
211C2×C4×C11#12112yes—
212C2×C4×C11#12314yes—
213C2×C4×C11#12314yes—
214C2×C4×C11#12414yes—
215C2×C4×C11C22×D411yescharacteristic
216C2×C4×C11C22×D411yescharacteristic
217C2×C4×C11C22×D411yescharacteristic
218C2×C4×C11C2×#4111yescharacteristic
219C2×C4×C11C2×#4111yescharacteristic
220C2×C4×C11C2×#4111yescharacteristic
221C2×Dic11—24no—
222C2×Dic11—24no—
223C2×Dic11—24no—
224C2×Dic11—24no—
225C2×Dic11—42no—
226C2×Dic11—42no—
227C2×Dic11—48no—
228C2×Dic11—42no—
229C2×Dic11—44no—
230C2×Dic11—84no—
231Dic22—24no—
232Dic22—24no—
233Dic22—42no—
234Dic22—42no—
235Dic22—48no—
236C8×C11—42no—
237C11⋊C8—24no—
238C22×#41C2×D1111yescharacteristic
239C23×Q8—111no—
240C2×#137—224no—
241C2×#137—224no—
242C2×#137—224no—
243C22×Q16—112no—
244C22×SD16—112no—
245C22×M16—111no—
246C23×C8C2×D1111yescharacteristic
247C2×#117—111no—
248C2×#117C2×D1111yescharacteristic
249C22×C4⋊C4—111no—
250#424—224no—
251C2×C4⋊C8—114no—
252#416—24no—
253C2×#103—114no—
254C2×#103—224no—
255C2×#103C2×D1112yes—
256C2×#102C2×D1112yes—
257#391—112no—
258#391—114no—
259#391—222no—
260#390—112no—
261#386—222no—
262#381—222no—
263#380—222no—
264#340—114no—
265C22×C11—22no—
266C22×C11—22no—
267C22×C11—24no—
268C22×C11—24no—
269C22×C11—42no—
270C22×C11—44no—
271C22×C11—81no—
272C22×C11—81no—
273C22×C11—82no—
274C22×C11#39414yes—
275C22×C11C2×#12111yescharacteristic
276C22×C11C2×#12111yescharacteristic
277C22×C11C2×#12111yescharacteristic
278C22×C11#57712yes—
279C22×C11#57812yes—
280C4×C11—42no—
281C4×C11—82no—
282C4×C11#39414yes—
283C4×C11C2×#12011yescharacteristic
284C4×C11C2×#12311yescharacteristic
285C4×C11C2×#12311yescharacteristic
286C4×C11C2×#12411yescharacteristic
287Dic11—44no—
288Dic11—44no—
289Dic11—82no—
290C2×#41—22no—
291C2×#41—22no—
292C2×#41—22no—
293C2×#41—22no—
294C2×#41—22no—
295C2×#41C22⋊D1114yes—
296C22×Q8—114no—
297C22×Q8—112no—
298C22×Q8—222no—
299C22×Q8—221no—
300C22×Q8—222no—
301C22×Q8—222no—
302C22×Q8—222no—
303C22×Q8—222no—
304C22×Q8C22×D1111yescharacteristic
305C22×D4—21no—
306C22×D4C22×D1111yescharacteristic
307C23×C4—21no—
308C23×C4—221no—
309C23×C4—221no—
310C23×C4C22×D1111yescharacteristic
311#137—2232no—
312C2×Q16—224no—
313C2×Q16—224no—
314C2×Q16—224no—
315C2×SD16—224no—
316C2×SD16—224no—
317C2×SD16—224no—
318C2×M16—114no—
319C2×M16—222no—
320C2×M16—222no—
321C22×C8—22no—
322C22×C8—22no—
323C22×C8—22no—
324C22×C8—112no—
325C22×C8C22×D1112yes—
326#117—22no—
327#117—22no—
328#117—222no—
329#117—222no—
330C2×C4⋊C4—112no—
331C2×C4⋊C4—112no—
332C2×C4⋊C4—222no—
333C2×C4⋊C4—222no—
334C2×C4⋊C4—221no—
335C2×C4⋊C4C22×D1112yes—
336C2×C22⋊C4—21no—
337C2×C22⋊C4—112no—
338C2×C22⋊C4—224no—
339C2×C42—21no—
340C2×C42—112no—
341C4⋊C8—228no—
342#103—24no—
343#103—228no—
344#102—24no—
345#95—224no—
346#95—228no—
347C2×C11—24no—
348C2×C11—82no—
349C2×C11C2×#39411yescharacteristic
350C2×C11#304311yescharacteristic
351C2×C11#304411yescharacteristic
352C2×C11#304612yes—
353C2×C11#306312yes—
354C24—21no—
355C24D4×D1111yescharacteristic
356#41—28no—
357#41—28no—
358#41—44no—
359#41—44no—
360C2×Q8—21no—
361C2×Q8—21no—
362C2×Q8—21no—
363C2×Q8—21no—
364C2×Q8—21no—
365C2×Q8—114no—
366C2×Q8—224no—
367C2×Q8—222no—
368C2×Q8—228no—
369C2×Q8—228no—
370C2×Q8—222no—
371C2×Q8—222no—
372C2×Q8—222no—
373C2×Q8—222no—
374C2×Q8—442no—
375C2×Q8—444no—
376C2×Q8—444no—
377C2×Q8—442no—
378C2×Q8C2×C22⋊D1112yes—
379C2×D4—24no—
380C2×D4—21no—
381C2×D4—21no—
382C2×D4—21no—
383C2×D4—21no—
384C2×D4—21no—
385C2×D4—42no—
386C2×D4—42no—
387C2×D4C2×C22⋊D1112yes—
388C22×C4—21no—
389C22×C4—24no—
390C22×C4—22no—
391C22×C4—42no—
392C22×C4—42no—
393C22×C4—114no—
394C22×C4—224no—
395C22×C4—222no—
396C22×C4—222no—
397C22×C4—442no—
398C22×C4—442no—
399C22×C4—442no—
400C22×C4—882no—
401C22×C4#433912yes—
402C22×C4#433912yes—
403C22×C4D4×D1112yes—
404C22×C4D4×D1111yescharacteristic
405C22×C4D4×D1112yes—
406C22×C4#434112yes—
407C22×C4C2×C22⋊D1112yes—
408C22×C4C23×D1111yescharacteristic
409Q16—2216no—
410SD16—2216no—
411M16—228no—
412C2×C8—22no—
413C2×C8—22no—
414C2×C8—22no—
415C2×C8—44no—
416C2×C8—114no—
417C2×C8—222no—
418C2×C8—222no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—224no—
422C4⋊C4—222no—
423C4⋊C4—222no—
424C4⋊C4—442no—
425C22⋊C4—42no—
426C22⋊C4—224no—
427C22⋊C4—884no—
428C42—42no—
429C42—222no—
430C42—222no—
431C11#2354511yescharacteristic, complemented, Sylow
432C23—22no—
433C23—22no—
434C23—22no—
435C23—41no—
436C23—41no—
437C23—42no—
438C23—42no—
439C23#6693712yes—
440C23#6693712yes—
441C23#6699212yes—
442C23C2×D4×D1111yescharacteristic
443Q8—22no—
444Q8—22no—
445Q8—41no—
446Q8—41no—
447Q8—224no—
448Q8—224no—
449Q8—442no—
450Q8—442no—
451Q8—448no—
452D4—22no—
453D4—22no—
454D4—48no—
455D4—41no—
456D4—41no—
457C2×C4—22no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—48no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—224no—
465C2×C4—224no—
466C2×C4—224no—
467C2×C4—224no—
468C2×C4—442no—
469C2×C4—442no—
470C2×C4—448no—
471C2×C4—442no—
472C2×C4—444no—
473C2×C4—884no—
474C2×C4#6693614yes—
475C2×C4#6693712yes—
476C2×C4#6693712yes—
477C2×C4#6693814yes—
478C2×C4#6698214yes—
479C2×C4#6699014yes—
480C2×C4#6699212yes—
481C2×C4C2×#433911yescharacteristic
482C2×C4C2×#433911yescharacteristic
483C2×C4C2×D4×D1111yescharacteristic
484C2×C4C2×D4×D1111yescharacteristic
485C2×C4C2×#434111yescharacteristic
486C2×C4C22×C22⋊D1111yescharacteristic
487C8—42no—
488C8—224no—
489C22—24no—
490C22—22no—
491C22—22no—
492C22—24no—
493C22—44no—
494C22—42no—
495C22—82no—
496C22—81no—
497C22—81no—
498C22#1062257214yes—
499C22C2×#6693711yescharacteristic
500C22C2×#6693711yescharacteristic
501C22#1062330112yes—
502C22#1062330212yes—
503C22C2×#6699211yescharacteristic
504C4—42no—
505C4—82no—
506C4—444no—
507C4—444no—
508C4—882no—
509C4#1062257214yes—
510C4C2×#6693611yescharacteristic
511C4C2×#6693811yescharacteristic
512C4C2×#6698211yescharacteristic
513C4C2×#6699011yescharacteristic
514C2—24no—
515C2—82no—
516C2C2×#1062257211yescharacteristic
517C2#1307814011yescharacteristic
518C2#1307814911yescharacteristic
519C2#1307816412yes—
520C2#1307831012yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#416C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
hypercenterC2×#416D11
hypocenterC11#23545
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
2. C2×#10622715C2semidirect
3. C22×#66880C2semidirect
5. #13071200C2semidirect
6. #13069937C2semidirect
7. #13069932C2semidirect
8. #13068337C2semidirect
431. C11#23545semidirect

Maximal subgroups

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

subgroupindex
C22×#670042
C2×#106227152
C22×#668802
#130712082
#130712002
#130699372
#130699322
#130683372
C2×C11×#4162
#2354511