Finite Group Databasebeta

← #14660391

Subgroups — #14660391

Order 2816.

1458 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623359C211yesmaximal, characteristic
2#13077061C211yesmaximal, characteristic, complemented
3C2×#10622739C212yesmaximal, complemented
4C2×#10622197C212yesmaximal, complemented
5C2×C11×#413C211yesmaximal, characteristic, complemented
6C22×C11×#41C2211yescharacteristic
7C23×C4×D11C2211yescharacteristic
8C22×C11×M16C2212yes—
9#10623359—24no—
10#10623359—24no—
11C2×#66999—21no—
12C2×#66991—21no—
13C2×#66990C412yes—
14C2×#66988C412yes—
15C2×C4×C22⋊D11—22no—
16C2×#66979C2211yescharacteristic
17C22×#4318C2212yes—
18C11×#413—24no—
19C2×C11×#101—21no—
20C2×C11×#100—21no—
21#10622847—24no—
22#10622820—22no—
23#10622739—24no—
24#10622739—24no—
25C2×(C2×D11)⋊C8—24no—
26#10622197—24no—
27C24×D11C2×C411yescharacteristic
28C2×C11×#41—22no—
29C2×C11×#41—22no—
30C2×C11×#41—22no—
31C2×C11×#41—22no—
32C2×C11×#41—22no—
33C2×C11×#41—22no—
34C22×Q8×C11D411yescharacteristic
35C22×D4×C11C2×C412yes—
36C22×D4×C11D411yescharacteristic
37C23×C4×C11D412yes—
38C23×C4×C11C2311yescharacteristic
39C22×C22⋊D11—22no—
40C23×Dic11C2×C411yescharacteristic
41C22×C4×D11—22no—
42C22×C4×D11—22no—
43C22×C4×D11—21no—
44C22×C4×D11—21no—
45C22×C4×D11—22no—
46C22×C4×D11—22no—
47C22×C4×D11—22no—
48C22×C4×D11D414yes—
49C2×C11×M16—22no—
50C2×C11×M16—22no—
51C2×C11×M16—22no—
52C2×C11×M16—22no—
53C2×C11×M16—22no—
54C2×C11×M16D414yescomplemented
55C22×C8×C11—22no—
56C2×C22⋊Dic11—22no—
57C2×C22⋊Dic11C2×C412yes—
58#66999—28no—
59#66991—28no—
60#66990—24no—
61#66990—24no—
62#66988—24no—
63#66988—24no—
64C4×C22⋊D11—216no—
65C2×(C2×D11)⋊C4—22no—
66#66979—22no—
67#66979D414yes—
68C2×C4⋊Dic11—21no—
69C2×Dic11⋊C4—22no—
70C2×C4×Dic11—21no—
71C2×#4318—22no—
72C2×#4318—22no—
73C2×#4318—22no—
74C2×#4318—22no—
75C2×#4318—22no—
76C2×#4318—22no—
77C22×C11⋊C8D414yescomplemented
78C11×#101—24no—
79C11×#100—24no—
80C22⋊(C11⋊C8)—28no—
81(C2×D11)⋊C8—216no—
82#10993—111nomaximal, Sylow
83C24×C11C22⋊C412yes—
84C24×C11C22×C411yescharacteristic
85C23×D11—21no—
86C23×D11—22no—
87C23×D11—21no—
88C23×D11—22no—
89C23×D11—44no—
90C23×D11C22⋊C412yes—
91C11×#41—42no—
92C11×#41—42no—
93C11×#41—42no—
94C11×#41—42no—
95C11×#41—42no—
96C11×#41—42no—
97C11×#41—42no—
98C11×#41—42no—
99C2×Q8×C11—21no—
100C2×Q8×C11—22no—
101C2×Q8×C11—22no—
102C2×Q8×C11—21no—
103C2×D4×C11—22no—
104C2×D4×C11—22no—
105C2×D4×C11—24no—
106C2×D4×C11—24no—
107C2×D4×C11—21no—
108C2×D4×C11—22no—
109C2×D4×C11—22no—
110C2×D4×C11—21no—
111C22×C4×C11—22no—
112C22×C4×C11—24no—
113C22×C4×C11—24no—
114C22×C4×C11—22no—
115C22×C4×C11C22⋊C412yes—
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D412yes—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D412yes—
120C22×C4×C11C2×D412yes—
121C22×C4×C11C2×D412yes—
122C22×C4×C11#4112yes—
123C22×C4×C11#4112yes—
124C2×C22⋊D11—28no—
125C2×C22⋊D11—48no—
126C22×Dic11—22no—
127C22×Dic11—21no—
128C22×Dic11—21no—
129C22×Dic11—22no—
130C22×Dic11—22no—
131C22×Dic11C22⋊C412yes—
132C2×C4×D11—24no—
133C2×C4×D11—24no—
134C2×C4×D11—24no—
135C2×C4×D11—24no—
136C2×C4×D11—24no—
137C2×C4×D11—24no—
138C2×C4×D11—41no—
139C2×C4×D11—41no—
140C2×C4×D11—42no—
141C2×C4×D11—42no—
142C2×C4×D11—42no—
143C2×C4×D11—42no—
144C2×C4×D11—41no—
145C2×C4×D11—41no—
146C2×C4×D11—42no—
147C2×C4×D11—42no—
148C11×M16—24no—
149C11×M16—24no—
150C11×M16—42no—
151C11×M16—42no—
152C2×C8×C11—24no—
153C2×C8×C11—42no—
154C2×C8×C11—42no—
155C22⋊Dic11—28no—
156C22⋊Dic11—22no—
157C22⋊Dic11C22⋊C414yes—
158(C2×D11)⋊C4—28no—
159C4⋊Dic11—24no—
160Dic11⋊C4—28no—
161C4×Dic11—24no—
162#4318—42no—
163#4318—42no—
164#4318—42no—
165#4318—42no—
166C2×C11⋊C8—24no—
167C2×C11⋊C8—24no—
168C2×C11⋊C8—24no—
169C2×#525—111no—
170C2×#413D1111yescharacteristic, complemented
171#2879—111no—
172C2×#407—112no—
173C2×#344—112no—
174C23×C11—22no—
175C23×C11—22no—
176C23×C11—22no—
177C23×C11—42no—
178C23×C11—44no—
179C23×C11C2×C22⋊C411yescharacteristic
180C23×C11C2×C22⋊C411yescharacteristic
181C23×C11C2×C22⋊C411yescharacteristic
182C23×C11C4×D412yes—
183C23×C11C4×D412yes—
184C22×D11—24no—
185C22×D11—28no—
186C22×D11—22no—
187C22×D11—24no—
188C22×D11—44no—
189C22×D11—48no—
190C22×D11—44no—
191C22×D11—42no—
192C22×D11—44no—
193C22×D11—41no—
194C22×D11—41no—
195C22×D11—42no—
196Q8×C11—42no—
197Q8×C11—42no—
198D4×C11—44no—
199D4×C11—44no—
200D4×C11—42no—
201D4×C11—42no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—44no—
206C2×C4×C11—44no—
207C2×C4×C11#12012yes—
208C2×C4×C11#12011yescharacteristic
209C2×C4×C11#12012yes—
210C2×C4×C11#12012yes—
211C2×C4×C11#12011yescharacteristic
212C2×C4×C11#12112yes—
213C2×C4×C11#12112yes—
214C2×C4×C11#12112yes—
215C2×C4×C11#12112yes—
216C2×C4×C11#12112yes—
217C2×C4×C11#12112yes—
218C2×C4×C11#12312yes—
219C2×C4×C11#12311yescharacteristic
220C2×C4×C11#12311yescharacteristic
221C2×C4×C11#12412yes—
222C2×C4×C11#12712yes—
223C22⋊D11—416no—
224C2×Dic11—24no—
225C2×Dic11—22no—
226C2×Dic11—24no—
227C2×Dic11—44no—
228C2×Dic11—41no—
229C2×Dic11—41no—
230C2×Dic11—42no—
231C4×D11—44no—
232C4×D11—44no—
233C4×D11—44no—
234C4×D11—44no—
235C8×C11—44no—
236C11⋊C8—44no—
237C22×#41C2×D1111yescharacteristic
238C24×C4—111no—
239C22×M16—112no—
240C22×M16C2×D1112yes—
241#525—224no—
242#525—224no—
243C2×#123—112no—
244C2×C22⋊Q8—221no—
245C2×#121—221no—
246C2×#120—112no—
247C2×C4×D4—222no—
248C2×#117—111no—
249#413—24no—
250C2×#101—21no—
251C2×#100—21no—
252#408—224no—
253#407—224no—
254#407—222no—
255#407—224no—
256C2×C22⋊C8—224no—
257#344—224no—
258C22×C11—22no—
259C22×C11—24no—
260C22×C11—41no—
261C22×C11—41no—
262C22×C11—42no—
263C22×C11—44no—
264C22×C11—44no—
265C22×C11—42no—
266C22×C11—82no—
267C22×C11#37911yescharacteristic
268C22×C11#38612yes—
269C22×C11#38611yescharacteristic
270C22×C11#38611yescharacteristic
271C22×C11#39012yes—
272C2×D11—28no—
273C2×D11—24no—
274C2×D11—42no—
275C2×D11—44no—
276C2×D11—44no—
277C2×D11—48no—
278C2×D11—44no—
279C2×D11—42no—
280C4×C11—42no—
281C4×C11#39212yes—
282C4×C11#39212yes—
283C4×C11#39412yes—
284C4×C11#39412yes—
285Dic11—44no—
286Dic11—42no—
287C25—111no—
288C2×#41—22no—
289C2×#41—22no—
290C2×#41—22no—
291C2×#41—22no—
292C2×#41—22no—
293C2×#41—22no—
294C22×Q8C22⋊D1111yescharacteristic
295C22×D4—222no—
296C22×D4C4×D1112yes—
297C22×D4C22⋊D1111yescharacteristic
298C23×C4—111no—
299C23×C4—114no—
300C23×C4—221no—
301C23×C4—222no—
302C23×C4—222no—
303C23×C4—222no—
304C23×C4—222no—
305C23×C4—221no—
306C23×C4—222no—
307C23×C4D4412yes—
308C23×C4C22×D1111yescharacteristic
309C2×M16—22no—
310C2×M16—22no—
311C2×M16—22no—
312C2×M16—22no—
313C2×M16—22no—
314C2×M16—222no—
315C2×M16—222no—
316C2×M16—222no—
317C2×M16—222no—
318C2×M16—222no—
319C2×M16—222no—
320C2×M16C22⋊D1114yescomplemented
321C22×C8—22no—
322C22×C8—114no—
323#123—224no—
324#123—224no—
325C22⋊Q8—228no—
326#121—228no—
327#120—224no—
328#120—224no—
329C4×D4—2216no—
330#117—114no—
331#117—222no—
332C2×C4⋊C4—222no—
333C2×C4⋊C4—221no—
334C2×C22⋊C4—112no—
335C2×C22⋊C4—222no—
336C2×C22⋊C4—222no—
337C2×C42—221no—
338#101—24no—
339#100—24no—
340C22⋊C8—2216no—
341C22⋊C8—228no—
342C2×C11—21no—
343C2×C11—22no—
344C2×C11—21no—
345C2×C11—22no—
346C2×C11—82no—
347C2×C11#143811yescharacteristic
348C2×C11#189112yes—
349D11—44no—
350C24—112no—
351C24—222no—
352C24—221no—
353C24—221no—
354C24—222no—
355C24—444no—
356C24(C2×D11)⋊C412yes—
357C24C2×C4×D1111yescharacteristic
358#41—42no—
359#41—42no—
360#41—42no—
361#41—42no—
362#41—42no—
363#41—42no—
364#41—42no—
365#41—42no—
366C2×Q8—21no—
367C2×Q8—22no—
368C2×Q8—22no—
369C2×Q8—21no—
370C2×D4—22no—
371C2×D4—22no—
372C2×D4—24no—
373C2×D4—24no—
374C2×D4—21no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—21no—
378C2×D4—228no—
379C2×D4—448no—
380C22×C4—24no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—24no—
384C22×C4—112no—
385C22×C4—221no—
386C22×C4—222no—
387C22×C4—222no—
388C22×C4—221no—
389C22×C4—222no—
390C22×C4—224no—
391C22×C4—224no—
392C22×C4—224no—
393C22×C4—224no—
394C22×C4—224no—
395C22×C4—224no—
396C22×C4—441no—
397C22×C4—442no—
398C22×C4—442no—
399C22×C4—441no—
400C22×C4—441no—
401C22×C4—442no—
402C22×C4—442no—
403C22×C4—442no—
404C22×C4—442no—
405C22×C4—441no—
406C22×C4(C2×D11)⋊C412yes—
407C22×C4C2×D4411yescharacteristic
408C22×C4#433912yes—
409C22×C4D4×D1112yes—
410C22×C4D4×D1112yes—
411C22×C4D4×D1112yes—
412C22×C4#434112yes—
413C22×C4C2×C22⋊D1111yescharacteristic
414C22×C4C2×C22⋊D1112yes—
415M16—24no—
416M16—24no—
417M16—42no—
418M16—42no—
419M16—442no—
420M16—442no—
421M16—442no—
422M16—442no—
423C2×C8—24no—
424C2×C8—42no—
425C2×C8—42no—
426C2×C8—224no—
427C2×C8—224no—
428C2×C8—224no—
429C4⋊C4—228no—
430C4⋊C4—224no—
431C22⋊C4—114no—
432C22⋊C4—228no—
433C22⋊C4—228no—
434C22⋊C4—222no—
435C42—224no—
436C11#1099311yescharacteristic, complemented, Sylow
437C23—22no—
438C23—22no—
439C23—22no—
440C23—42no—
441C23—44no—
442C23—224no—
443C23—228no—
444C23—222no—
445C23—224no—
446C23—442no—
447C23—444no—
448C23—444no—
449C23—444no—
450C23—448no—
451C23—442no—
452C23—441no—
453C23—441no—
454C23C22⋊C4×D1111yescharacteristic
455C23C22⋊C4×D1111yescharacteristic
456C23(C22⋊D11)⋊C412yes—
457C23C2×(C2×D11)⋊C411yescharacteristic
458C23C4×C22⋊D1112yes—
459Q8—42no—
460Q8—42no—
461D4—44no—
462D4—44no—
463D4—42no—
464D4—42no—
465D4—4416no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—44no—
470C2×C4—44no—
471C2×C4—224no—
472C2×C4—222no—
473C2×C4—224no—
474C2×C4—444no—
475C2×C4—442no—
476C2×C4—441no—
477C2×C4—441no—
478C2×C4—444no—
479C2×C4—444no—
480C2×C4—444no—
481C2×C4—444no—
482C2×C4#6693512yes—
483C2×C4#6693511yescharacteristic
484C2×C4#6693612yes—
485C2×C4#6693712yes—
486C2×C4#6693712yes—
487C2×C4#6693812yes—
488C2×C4#6693911yescharacteristic
489C2×C4#6698211yescharacteristic
490C2×C4#6698312yes—
491C2×C4#6699012yes—
492C2×C4#6699012yes—
493C2×C4#6699112yes—
494C2×C4#6699212yes—
495C2×C4#6699212yes—
496C2×C4#6699312yes—
497C2×C4#6700611yescharacteristic
498C8—44no—
499C8—444no—
500C22—22no—
501C22—24no—
502C22—41no—
503C22—41no—
504C22—42no—
505C22—44no—
506C22—42no—
507C22—44no—
508C22—82no—
509C22—224no—
510C22—228no—
511C22—442no—
512C22—444no—
513C22—444no—
514C22—448no—
515C22—442no—
516C22—444no—
517C22#1062256811yescharacteristic
518C22#1062256912yes—
519C22#1062257012yes—
520C22#1062257111yescharacteristic
521C22#1062282611yescharacteristic
522C4—42no—
523C4—444no—
524C4—442no—
525C4#1062257212yes—
526C4#1062257312yes—
527C4#1062257412yes—
528C4#1062283612yes—
529C2—21no—
530C2—21no—
531C2—22no—
532C2—22no—
533C2—82no—
534C2—444no—
535C2#1306685511yescharacteristic
536C2#1306903212yes—
subgroupG/H
centerC2×C4#66935
commutatorC24×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C11×#413C2
socleC22×C11#386
prime radicalC2×#10623359C2
cosocleC23×C4×C11C23
hypercenterC2×#413D11
hypocenterC11#10993
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#413

Complements

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

NH ≅ G/Ntype
2. #13077061C2semidirect
3. C2×#10622739C2semidirect
4. C2×#10622197C2semidirect
5. C2×C11×#413C2semidirect
54. C2×C11×M16D4semidirect
77. C22×C11⋊C8D4semidirect
170. C2×#413D11semidirect
320. C2×M16C22⋊D11semidirect
436. C11#10993semidirect

Maximal subgroups

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

subgroupindex
C2×#106233592
#130770612
C2×#106227392
C2×#106221972
C2×C11×#4132
#1099311