Finite Group Databasebeta

← #14660332

Subgroups — #14660332

Order 2816.

1382 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623363C211yesmaximal, characteristic
2C2×#10622618C212yesmaximal, complemented
3#13077061C211yesmaximal, characteristic, complemented
4C2×#10622170C212yesmaximal, complemented
5C2×C11×#410C211yesmaximal, characteristic, complemented
6C22×C11×#41C2211yescharacteristic
7C22×#4339C2211yescharacteristic
8C2×C11×#117C2212yes—
9#10623363—24no—
10#10623363—24no—
11C2×#67000C411yescharacteristic, complemented
12C2×#66997C411yescharacteristic, complemented
13C2×#66993C411yescharacteristic, complemented
14C2×#66992—22no—
15C2×#66989C411yescharacteristic, complemented
16C2×C4×C22⋊D11—22no—
17C22×C4×Dic11C2211yescharacteristic
18C22×#4318C2212yes—
19C11×#410—24no—
20C2×C11×#99—22no—
21#10622847—24no—
22#10622820—22no—
23#10622618—24no—
24#10622618—24no—
25C2×#66869—24no—
26#10622170—24no—
27C2×C11×#41—22no—
28C2×C11×#41—22no—
29C2×C11×#41—22no—
30C2×C11×#41—22no—
31C2×C11×#41—22no—
32C2×C11×#41—22no—
33C22×Q8×C11C2×C411yescharacteristic
34C22×D4×C11C2×C411yescharacteristic
35C22×D4×C11D412yes—
36C23×C4×C11D412yes—
37C23×C4×C11C2311yescharacteristic
38C22×C22⋊D11—22no—
39C22×C22⋊D11—21no—
40C23×Dic11—21no—
41C2×#4339—22no—
42C2×#4339—22no—
43C2×#4339—22no—
44C2×#4339—22no—
45C2×#4339—22no—
46C2×#4339D414yes—
47C22×D44C2×C411yescharacteristic
48C22×C4×D11—21no—
49C22×Dic22C2×C411yescharacteristic
50C11×#117—22no—
51C11×#117—22no—
52C11×#117—22no—
53C11×#117D414yescomplemented
54C2×C11×C4⋊C4—22no—
55C2×C11×C22⋊C4—22no—
56C2×C42×C11—22no—
57C2×C22⋊Dic11—22no—
58#67000—22no—
59#67000—22no—
60#66997—22no—
61#66997—22no—
62#66993—22no—
63#66993—22no—
64#66992—216no—
65#66989—22no—
66#66989—22no—
67C4×C22⋊D11—216no—
68C2×(C2×D11)⋊C4—22no—
69C2×Dic11⋊C4—22no—
70C2×C4×Dic11—21no—
71C2×C4×Dic11—22no—
72C2×C4×Dic11C2×C411yescharacteristic
73C2×C4×Dic11C2×C411yescharacteristic
74C2×C4×Dic11D414yes—
75C2×#4318—22no—
76C2×#4318—22no—
77C2×#4318—22no—
78C2×#4318—22no—
79C2×#4318—22no—
80C2×#4318D414yescomplemented
81C22×C11⋊C8—22no—
82C11×#99—28no—
83C22⋊(C11⋊C8)—28no—
84#66869—216no—
85#10979—111nomaximal, Sylow
86C24×C11C22⋊C412yes—
87C24×C11C2×D411yescharacteristic
88C23×D11—21no—
89C11×#41—42no—
90C11×#41—42no—
91C11×#41—42no—
92C11×#41—42no—
93C11×#41—42no—
94C11×#41—42no—
95C11×#41—42no—
96C11×#41—42no—
97C2×Q8×C11—21no—
98C2×Q8×C11—21no—
99C2×Q8×C11—22no—
100C2×Q8×C11—22no—
101C2×D4×C11—22no—
102C2×D4×C11—24no—
103C2×D4×C11—24no—
104C2×D4×C11—22no—
105C2×D4×C11—21no—
106C2×D4×C11—21no—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—24no—
111C22×C4×C11—24no—
112C22×C4×C11—22no—
113C22×C4×C11—42no—
114C22×C4×C11C22⋊C412yes—
115C22×C4×C11C22×C411yescharacteristic
116C22×C4×C11C2×D412yes—
117C22×C4×C11C2×D412yes—
118C22×C4×C11C2×D412yes—
119C22×C4×C11C2×D412yes—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11#4112yes—
122C22×C4×C11#4112yes—
123C2×C22⋊D11—28no—
124C2×C22⋊D11—24no—
125C2×C22⋊D11—48no—
126C2×C22⋊D11—41no—
127C2×C22⋊D11—42no—
128C2×C22⋊D11—41no—
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11—21no—
132C22×Dic11—24no—
133C22×Dic11—44no—
134#4339—24no—
135#4339—24no—
136#4339—24no—
137#4339—24no—
138#4339—42no—
139#4339—42no—
140#4339—42no—
141#4339—42no—
142C2×D44—21no—
143C2×D44—22no—
144C2×D44—22no—
145C2×D44C22⋊C412yes—
146C2×C4×D11—24no—
147C2×C4×D11—41no—
148C2×C4×D11—42no—
149C2×C4×D11—41no—
150C2×Dic22—21no—
151C2×Dic22—22no—
152C2×Dic22—22no—
153C2×Dic22C22⋊C412yes—
154C11×C4⋊C4—24no—
155C11×C4⋊C4—42no—
156C11×C22⋊C4—24no—
157C11×C22⋊C4—42no—
158C42×C11—24no—
159C42×C11—42no—
160C22⋊Dic11—28no—
161(C2×D11)⋊C4—28no—
162Dic11⋊C4—28no—
163C4×Dic11—21no—
164C4×Dic11—21no—
165C4×Dic11—24no—
166C4×Dic11C22⋊C412yes—
167C4×Dic11C22⋊C412yes—
168#4318—24no—
169#4318—24no—
170#4318—42no—
171#4318—42no—
172C2×C11⋊C8—24no—
173C2×C11⋊C8—42no—
174C2×C11⋊C8—42no—
175C2×#532—111no—
176C2×#421—112no—
177C2×#410D1111yescharacteristic, complemented
178#2879—111no—
179C2×#339—112no—
180C23×C11—22no—
181C23×C11—22no—
182C23×C11—22no—
183C23×C11—42no—
184C23×C11—44no—
185C23×C11C2×C22⋊C411yescharacteristic
186C23×C11#12012yes—
187C23×C11#12011yescharacteristic
188C23×C11#12112yes—
189C23×C11#12311yescharacteristic
190C22×D11—22no—
191C22×D11—44no—
192C22×D11—41no—
193C22×D11—41no—
194Q8×C11—42no—
195Q8×C11—42no—
196D4×C11—44no—
197D4×C11—44no—
198D4×C11—42no—
199D4×C11—42no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—44no—
204C2×C4×C11—44no—
205C2×C4×C11—44no—
206C2×C4×C11—84no—
207C2×C4×C11C2×C22⋊C411yescharacteristic
208C2×C4×C11C2×C22⋊C411yescharacteristic
209C2×C4×C11C4×D412yes—
210C2×C4×C11C4×D412yes—
211C2×C4×C11#12012yes—
212C2×C4×C11#12011yescharacteristic
213C2×C4×C11#12012yes—
214C2×C4×C11#12112yes—
215C2×C4×C11#12112yes—
216C2×C4×C11#12112yes—
217C2×C4×C11#12112yes—
218C2×C4×C11#12112yes—
219C2×C4×C11#12312yes—
220C2×C4×C11#12311yescharacteristic
221C2×C4×C11#12412yes—
222C2×C4×C11#12712yes—
223C22⋊D11—416no—
224C22⋊D11—44no—
225C22⋊D11—44no—
226C2×Dic11—24no—
227C2×Dic11—22no—
228C2×Dic11—22no—
229C2×Dic11—22no—
230C2×Dic11—48no—
231C2×Dic11—42no—
232C2×Dic11—41no—
233C2×Dic11—41no—
234D44—24no—
235D44—42no—
236C4×D11—44no—
237C4×D11—44no—
238Dic22—24no—
239Dic22—42no—
240C11⋊C8—44no—
241C22×#41—111no—
242C22×#41C2×D1111yescharacteristic
243C22×M16—112no—
244#532—224no—
245#532—224no—
246C2×C4⋊Q8—111no—
247C2×#127—111no—
248C2×#124—111no—
249C2×#124—111no—
250C2×#121—222no—
251C2×C4×D4—222no—
252C2×#117C2×D1112yes—
253C22×C42—111no—
254#421—224no—
255#421—224no—
256C2×#104—224no—
257#410—24no—
258C2×#99—22no—
259#408—224no—
260#407—222no—
261#339—224no—
262C22×C11—24no—
263C22×C11—22no—
264C22×C11—41no—
265C22×C11—42no—
266C22×C11—41no—
267C22×C11—44no—
268C22×C11—44no—
269C22×C11—42no—
270C22×C11—82no—
271C22×C11#37911yescharacteristic
272C22×C11#38611yescharacteristic
273C22×C11#38611yescharacteristic
274C22×C11#39212yes—
275C22×C11#39412yes—
276C2×D11—44no—
277C2×D11—42no—
278C2×D11—82no—
279C2×D11—82no—
280C4×C11—42no—
281C4×C11—84no—
282C4×C11#38612yes—
283C4×C11#39012yes—
284C4×C11#39212yes—
285C4×C11#39412yes—
286Dic11—24no—
287Dic11—42no—
288Dic11—42no—
289C2×#41—22no—
290C2×#41—22no—
291C2×#41—22no—
292C2×#41—22no—
293C2×#41—22no—
294C2×#41—22no—
295C2×#41—114no—
296C2×#41—222no—
297C2×#41—222no—
298C2×#41—222no—
299C2×#41—222no—
300C2×#41—222no—
301C22×Q8—111no—
302C22×Q8C4×D1111yescharacteristic
303C22×D4—111no—
304C22×D4—222no—
305C22×D4—221no—
306C22×D4C4×D1111yescharacteristic
307C22×D4C22⋊D1112yes—
308C23×C4—221no—
309C23×C4—221no—
310C23×C4D4412yes—
311C23×C4C22×D1111yescharacteristic
312C2×M16—114no—
313C2×M16—222no—
314C2×M16—222no—
315C2×M16—222no—
316C2×M16—222no—
317C2×M16—222no—
318C22×C8—222no—
319C4⋊Q8—222no—
320C4⋊Q8—222no—
321#127—222no—
322#127—222no—
323#124—222no—
324#124—222no—
325#124—222no—
326#124—222no—
327#121—2216no—
328C4×D4—2216no—
329#117—22no—
330#117—22no—
331#117—22no—
332#117C22⋊D1114yescomplemented
333C2×C4⋊C4—22no—
334C2×C4⋊C4—222no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—222no—
337C2×C22⋊C4—222no—
338C2×C42—22no—
339C2×C42—111no—
340C2×C42—111no—
341C2×C42—114no—
342C2×C42—221no—
343C2×C42—222no—
344#104—2216no—
345#99—28no—
346C22⋊C8—228no—
347C2×C11—21no—
348C2×C11—22no—
349C2×C11—21no—
350C2×C11—22no—
351C2×C11—82no—
352C2×C11#143811yescharacteristic
353C2×C11#188412yes—
354D11—82no—
355C24—221no—
356C24(C2×D11)⋊C412yes—
357C24C2×C22⋊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—
366#41—224no—
367#41—224no—
368#41—224no—
369#41—224no—
370#41—442no—
371#41—442no—
372#41—442no—
373#41—442no—
374C2×Q8—21no—
375C2×Q8—21no—
376C2×Q8—22no—
377C2×Q8—22no—
378C2×Q8—112no—
379C2×Q8—221no—
380C2×Q8—222no—
381C2×Q8—222no—
382C2×D4—22no—
383C2×D4—24no—
384C2×D4—24no—
385C2×D4—22no—
386C2×D4—21no—
387C2×D4—21no—
388C2×D4—22no—
389C2×D4—22no—
390C2×D4—112no—
391C2×D4—228no—
392C2×D4—224no—
393C2×D4—221no—
394C2×D4—222no—
395C2×D4—222no—
396C2×D4—448no—
397C2×D4—441no—
398C2×D4—442no—
399C2×D4—441no—
400C22×C4—24no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—24no—
404C22×C4—42no—
405C22×C4—221no—
406C22×C4—221no—
407C22×C4—221no—
408C22×C4—224no—
409C22×C4—224no—
410C22×C4—444no—
411C22×C4—441no—
412C22×C4—441no—
413C22×C4—442no—
414C22×C4(C2×D11)⋊C412yes—
415C22×C4C2×C4×D1111yescharacteristic
416C22×C4C2×D4411yescharacteristic
417C22×C4#433912yes—
418C22×C4D4×D1112yes—
419C22×C4D4×D1112yes—
420C22×C4D4×D1112yes—
421C22×C4#434112yes—
422C22×C4C2×C22⋊D1112yes—
423M16—224no—
424M16—224no—
425M16—442no—
426M16—442no—
427C2×C8—224no—
428C2×C8—442no—
429C2×C8—442no—
430C4⋊C4—24no—
431C4⋊C4—42no—
432C4⋊C4—228no—
433C22⋊C4—24no—
434C22⋊C4—42no—
435C22⋊C4—228no—
436C22⋊C4—228no—
437C42—24no—
438C42—42no—
439C42—112no—
440C42—112no—
441C42—221no—
442C42—221no—
443C42—224no—
444C11#1097911yescharacteristic, complemented, Sylow
445C23—22no—
446C23—22no—
447C23—22no—
448C23—42no—
449C23—44no—
450C23—222no—
451C23—444no—
452C23—441no—
453C23—441no—
454C23C2×(C2×D11)⋊C411yescharacteristic
455C23#6698211yescharacteristic
456C23#6699012yes—
457C23#6699212yes—
458C23#6700611yescharacteristic
459Q8—42no—
460Q8—42no—
461Q8—224no—
462Q8—442no—
463D4—44no—
464D4—44no—
465D4—42no—
466D4—42no—
467D4—224no—
468D4—4416no—
469D4—444no—
470D4—444no—
471D4—442no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—44no—
476C2×C4—44no—
477C2×C4—44no—
478C2×C4—84no—
479C2×C4—224no—
480C2×C4—222no—
481C2×C4—222no—
482C2×C4—222no—
483C2×C4—448no—
484C2×C4—442no—
485C2×C4—441no—
486C2×C4—441no—
487C2×C4—444no—
488C2×C4—444no—
489C2×C4C22⋊C4×D1111yescharacteristic
490C2×C4C22⋊C4×D1111yescharacteristic
491C2×C4(C22⋊D11)⋊C412yes—
492C2×C4#6693512yes—
493C2×C4#6693511yescharacteristic
494C2×C4#6693612yes—
495C2×C4#6693712yes—
496C2×C4#6693712yes—
497C2×C4#6693812yes—
498C2×C4#6693911yescharacteristic
499C2×C4C4×C22⋊D1112yes—
500C2×C4#6698312yes—
501C2×C4#6699012yes—
502C2×C4#6699112yes—
503C2×C4#6699212yes—
504C2×C4#6699312yes—
505C8—444no—
506C22—24no—
507C22—22no—
508C22—42no—
509C22—41no—
510C22—41no—
511C22—44no—
512C22—42no—
513C22—44no—
514C22—82no—
515C22—444no—
516C22—442no—
517C22—882no—
518C22—882no—
519C22#1062256811yescharacteristic
520C22#1062257111yescharacteristic
521C22#1062257212yes—
522C22#1062282611yescharacteristic
523C22#1062283612yes—
524C4—42no—
525C4—84no—
526C4—224no—
527C4—442no—
528C4—442no—
529C4#1062256912yes—
530C4#1062257012yes—
531C4#1062257312yes—
532C4#1062257412yes—
533C2—22no—
534C2—21no—
535C2—21no—
536C2—22no—
537C2—82no—
538C2—882no—
539C2#1306685511yescharacteristic
540C2#1306899712yes—
subgroupG/H
centerC2×C4#66935
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C11×#410C2
socleC22×C11#386
prime radicalC2×#10623363C2
cosocleC23×C4×C11C23
hypercenterC2×#410D11
hypocenterC11#10979
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#410

Complements

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

NH ≅ G/Ntype
2. C2×#10622618C2semidirect
3. #13077061C2semidirect
4. C2×#10622170C2semidirect
5. C2×C11×#410C2semidirect
11. C2×#67000C4semidirect
12. C2×#66997C4semidirect
13. C2×#66993C4semidirect
15. C2×#66989C4semidirect
53. C11×#117D4semidirect
80. C2×#4318D4semidirect
177. C2×#410D11semidirect
332. #117C22⋊D11semidirect
444. C11#10979semidirect

Maximal subgroups

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

subgroupindex
C2×#106233632
C2×#106226182
#130770612
C2×#106221702
C2×C11×#4102
#1097911