Finite Group Databasebeta

← #14757476

Subgroups — #14757476

Order 2816.

1526 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623057C211yesmaximal, characteristic
2C2×#10622746C211yesmaximal, characteristic
3C2×#10622733C211yesmaximal, characteristic, complemented
4C2×#10622726C211yesmaximal, characteristic
5C22×#66880C211yesmaximal, characteristic, complemented
6#13071239C211yesmaximal, characteristic, complemented
7#13069436C212yesmaximal, complemented
8#13069432C212yesmaximal, complemented
9#13069427C212yesmaximal, complemented
10#13069418C212yesmaximal, complemented
11C2×C11×#405C211yesmaximal, characteristic, complemented
12C22×#4339C2211yescharacteristic
13C23×Dic22C2211yescharacteristic
14C22×C11×M16C2211yescharacteristic
15C23×C8×C11C2211yescharacteristic
16C2×C11×#117C2211yescharacteristic
17C2×#66979C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19#10623057—24no—
20#10623057C418yescomplemented
21C2×#66950—22no—
22C2×#66939—22no—
23C2×#66928C2212yes—
24C2×#66922C2212yes—
25C11×#405—24no—
26C2×C11×#97C2212yes—
27C2×C4×C8×C11C2212yes—
28#10622746—24no—
29#10622733—24no—
30#10622726—24no—
31C2×#66885C2211yescharacteristic
32C2×#66885C2212yes—
33C2×#66885C2211yescharacteristic
34C2×#66880—24no—
35C2×#66880C2211yescharacteristic
36C2×#66880C2212yes—
37C2×#66880C2212yes—
38C2×#66880C2212yes—
39C2×#66880C2212yes—
40C2×#66880C2212yes—
41C2×#66880C2211yescharacteristic
42#10622598—22no—
43#10622563—22no—
44#10622549C2212yes—
45#10622548C2212yes—
46C23×C4×C11C2311yescharacteristic
47C22×C22⋊D11—21no—
48C23×Dic11—21no—
49C23×Dic11—21no—
50C2×#4339—22no—
51C2×#4339—22no—
52C2×#4339—22no—
53C2×#4339—22no—
54C2×#4339—22no—
55C2×#4339C2×C414yes—
56C22×D44C2311yescharacteristic
57C22×C4×D11—21no—
58C22×Dic22—22no—
59C22×Dic22—22no—
60C22×Dic22—22no—
61C22×Dic22—22no—
62C22×Dic22—21no—
63C22×Dic22—22no—
64C22×Dic22C2×C414yes—
65C22×Dic22C2311yescharacteristic
66C22×Dic22C2312yes—
67C2×C11×M16—22no—
68C2×C11×M16—22no—
69C2×C11×M16D414yes—
70C22×C8×C11—22no—
71C22×C8×C11—22no—
72C22×C8×C11D414yes—
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2312yes—
75C22×C8×C11C2311yescharacteristic
76C11×#117C2×C414yes—
77C11×#117D414yes—
78C2×C11×C4⋊C4D412yes—
79C2×C11×C22⋊C4D412yes—
80C2×C42×C11C2312yes—
81C2×C22⋊Dic11—21no—
82C2×(C2×D11)⋊C4—24no—
83#66979—22no—
84#66979—22no—
85C2×C4⋊Dic11—24no—
86C2×C4⋊Dic11—22no—
87C2×C4⋊Dic11—22no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—24no—
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2312yes—
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4×Dic11—21no—
94#66950—216no—
95#66939—216no—
96#66928—24no—
97#66928C2×C418yescomplemented
98#66922—24no—
99#66922C2×C418yescomplemented
100C11×#97—24no—
101C4×C8×C11—24no—
102C11⋊#95—24no—
103#66885—22no—
104#66885—22no—
105#66885—24no—
106#66880—22no—
107#66880—22no—
108#66880—24no—
109#66880—24no—
110#66880—24no—
111#66880—24no—
112#66880—24no—
113#21205—111nomaximal, Sylow
114C24×C11C2×D411yescharacteristic
115C23×D11—21no—
116C22×C4×C11C22×C412yes—
117C22×C4×C11C2×D414yes—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D412yes—
120C22×C4×C11C2×D412yes—
121C22×C4×C11C2×D412yes—
122C22×C4×C11#4112yes—
123C22×C4×C11#4112yes—
124C22×C4×C11C2411yescharacteristic
125C2×C22⋊D11—24no—
126C2×C22⋊D11—42no—
127C2×C22⋊D11—42no—
128C22×Dic11—24no—
129C22×Dic11—21no—
130C22×Dic11—22no—
131C22×Dic11—21no—
132C22×Dic11—22no—
133C22×Dic11—21no—
134C22×Dic11—42no—
135C22×Dic11—42no—
136C22×Dic11—42no—
137C22×Dic11—82no—
138#4339—28no—
139#4339—28no—
140#4339—44no—
141#4339—44no—
142C2×D44—21no—
143C2×D44—21no—
144C2×D44—21no—
145C2×D44—21no—
146C2×D44—21no—
147C2×D44C22×C412yes—
148C2×C4×D11—24no—
149C2×C4×D11—42no—
150C2×C4×D11—42no—
151C2×Dic22—24no—
152C2×Dic22—28no—
153C2×Dic22—28no—
154C2×Dic22—22no—
155C2×Dic22—22no—
156C2×Dic22—21no—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22—22no—
160C2×Dic22—22no—
161C2×Dic22—22no—
162C2×Dic22—21no—
163C2×Dic22—21no—
164C2×Dic22—44no—
165C2×Dic22—44no—
166C2×Dic22—42no—
167C2×Dic22—42no—
168C2×Dic22C22×C412yes—
169C2×Dic22C22×C414yes—
170C11×M16—28no—
171C2×C8×C11—28no—
172C2×C8×C11—21no—
173C2×C8×C11—22no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—22no—
178C2×C8×C11C2×D412yes—
179C2×C8×C11C2×D412yes—
180C2×C8×C11C2×D414yes—
181C11×C4⋊C4C22⋊C418yes—
182C11×C22⋊C4C22⋊C418yes—
183C42×C11C22×C414yes—
184C42×C11C2×D414yes—
185C22⋊Dic11—42no—
186(C2×D11)⋊C4—216no—
187C4⋊Dic11—216no—
188C4⋊Dic11—22no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—22no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—42no—
195C4⋊Dic11—84no—
196C4×Dic11—42no—
197C2×#536—111no—
198C2×#417—111no—
199C2×#419—111no—
200C2×#416—111no—
201C22×#103—111no—
202C2×#405D1111yescharacteristic, complemented
203#2317—111no—
204#1960—112no—
205#1959—112no—
206#1958—112no—
207#1956—112no—
208C23×C11—22no—
209C23×C11—22no—
210C23×C11C2×C22⋊C412yes—
211C23×C11#12412yes—
212C23×C11#12712yes—
213C23×C11C22×D411yescharacteristic
214C22×D11—22no—
215C22×D11—41no—
216C22×D11—41no—
217C22×D11—42no—
218C22×D11—42no—
219C2×C4×C11—24no—
220C2×C4×C11—24no—
221C2×C4×C11C2×C22⋊C418yes—
222C2×C4×C11C2×C22⋊C412yes—
223C2×C4×C11C4×D414yes—
224C2×C4×C11C4×D414yes—
225C2×C4×C11#12114yes—
226C2×C4×C11#12114yes—
227C2×C4×C11#12412yes—
228C2×C4×C11#12712yes—
229C2×C4×C11C23×C411yescharacteristic
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C22×D411yescharacteristic
232C2×C4×C11C22×D411yescharacteristic
233C2×C4×C11C2×#4111yescharacteristic
234C2×C4×C11C2×#4111yescharacteristic
235C22⋊D11—48no—
236C2×Dic11—22no—
237C2×Dic11—24no—
238C2×Dic11—42no—
239C2×Dic11—41no—
240C2×Dic11—42no—
241C2×Dic11—41no—
242C2×Dic11—48no—
243C2×Dic11—41no—
244C2×Dic11—41no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247C2×Dic11—44no—
248C2×Dic11—42no—
249C2×Dic11—84no—
250D44—22no—
251D44—22no—
252D44—41no—
253D44—41no—
254C4×D11—48no—
255Dic22—24no—
256Dic22—24no—
257Dic22—22no—
258Dic22—22no—
259Dic22—42no—
260Dic22—42no—
261Dic22—41no—
262Dic22—41no—
263Dic22—48no—
264C8×C11—22no—
265C8×C11—22no—
266C8×C11—24no—
267C22×#41—111no—
268C23×Q8—111no—
269C22×M16C2×D1111yescharacteristic
270C23×C8C2×D1111yescharacteristic
271#536—118no—
272#536—224no—
273C2×C4⋊Q8—112no—
274C2×#124—112no—
275C2×#123—222no—
276C2×C22⋊Q8—222no—
277C2×#117—111no—
278C2×#117C2×D1111yescharacteristic
279C22×C4⋊C4—111no—
280#419—224no—
281#417—224no—
282#416—224no—
283C2×#103—112no—
284C2×#103—112no—
285C2×#103—111no—
286C2×#103—111no—
287C2×#103—112no—
288C2×#103—112no—
289C2×#103—112no—
290C2×#103—224no—
291C2×#102—111no—
292C2×#102—111no—
293C2×#102—112no—
294#405—24no—
295C2×#97C2×D1112yes—
296C2×C4×C8C2×D1112yes—
297#389—222no—
298#385—222no—
299#384—112no—
300#382—112no—
301C22×C11—24no—
302C22×C11—24no—
303C22×C11—22no—
304C22×C11—22no—
305C22×C11#39014yes—
306C22×C11C22×C22⋊C411yescharacteristic
307C22×C11C2×#12411yescharacteristic
308C22×C11C2×#12711yescharacteristic
309C22×C11#57712yes—
310C22×C11#57812yes—
311C2×D11—44no—
312C2×D11—42no—
313C2×D11—82no—
314C2×D11—81no—
315C2×D11—81no—
316C4×C11—28no—
317C4×C11#39014yes—
318C4×C11C2×C4×D411yescharacteristic
319C4×C11C2×C4×D411yescharacteristic
320C4×C11C2×#12111yescharacteristic
321C4×C11C2×#12111yescharacteristic
322Dic11—44no—
323Dic11—42no—
324Dic11—81no—
325Dic11—82no—
326Dic11—81no—
327C2×#41—114no—
328C2×#41—222no—
329C2×#41—222no—
330C2×#41—222no—
331C2×#41—222no—
332C2×#41—222no—
333C22×Q8—114no—
334C22×Q8—112no—
335C22×Q8—111no—
336C22×Q8—221no—
337C22×Q8—222no—
338C22×Q8—222no—
339C22×Q8—222no—
340C22×Q8—222no—
341C22×Q8—222no—
342C22×D4—111no—
343C22×D4—221no—
344C23×C4—221no—
345C23×C4—221no—
346C23×C4—221no—
347C23×C4C22×D1111yescharacteristic
348C2×M16—22no—
349C2×M16—22no—
350C2×M16D4414yes—
351C22×C8—22no—
352C22×C8—22no—
353C22×C8D4414yes—
354C22×C8C22×D1111yescharacteristic
355C22×C8C22×D1111yescharacteristic
356C22×C8C22×D1112yes—
357C4⋊Q8—118no—
358C4⋊Q8—224no—
359#124—118no—
360#124—224no—
361#123—2216no—
362C22⋊Q8—2216no—
363#117—222no—
364#117—222no—
365#117C4×D1114yes—
366#117C22⋊D1114yes—
367C2×C4⋊C4—112no—
368C2×C4⋊C4—111no—
369C2×C4⋊C4—111no—
370C2×C4⋊C4—224no—
371C2×C4⋊C4—222no—
372C2×C4⋊C4—222no—
373C2×C4⋊C4—221no—
374C2×C4⋊C4—224no—
375C2×C4⋊C4D4412yes—
376C2×C22⋊C4—224no—
377C2×C22⋊C4—221no—
378C2×C22⋊C4D4412yes—
379C2×C42—221no—
380C2×C42C22×D1112yes—
381#103—224no—
382#103—224no—
383#103—222no—
384#103—222no—
385#103—224no—
386#103—224no—
387#103—224no—
388#102—222no—
389#102—222no—
390#102—224no—
391#97—24no—
392C4×C8—24no—
393#95—224no—
394C2×C11—24no—
395C2×C11C2×#39011yescharacteristic
396C2×C11#289812yes—
397C2×C11#313712yes—
398C2×C11#315411yescharacteristic
399C2×C11#315611yescharacteristic
400D11—82no—
401C24—221no—
402C24C2×D4411yescharacteristic
403#41—228no—
404#41—228no—
405#41—444no—
406#41—444no—
407C2×Q8—114no—
408C2×Q8—112no—
409C2×Q8—224no—
410C2×Q8—222no—
411C2×Q8—221no—
412C2×Q8—228no—
413C2×Q8—228no—
414C2×Q8—222no—
415C2×Q8—222no—
416C2×Q8—221no—
417C2×Q8—221no—
418C2×Q8—222no—
419C2×Q8—222no—
420C2×Q8—221no—
421C2×Q8—221no—
422C2×Q8—442no—
423C2×Q8—442no—
424C2×Q8—444no—
425C2×Q8—444no—
426C2×D4—112no—
427C2×D4—224no—
428C2×D4—221no—
429C2×D4—221no—
430C2×D4—221no—
431C2×D4—221no—
432C2×D4—221no—
433C2×D4—442no—
434C2×D4—442no—
435C22×C4—224no—
436C22×C4—222no—
437C22×C4—221no—
438C22×C4—224no—
439C22×C4—221no—
440C22×C4—222no—
441C22×C4—221no—
442C22×C4—442no—
443C22×C4—442no—
444C22×C4—442no—
445C22×C4—442no—
446C22×C4—442no—
447C22×C4—882no—
448C22×C4C2×C4×D1112yes—
449C22×C4C2×D4414yes—
450C22×C4C2×D4412yes—
451C22×C4C2×D4412yes—
452C22×C4C2×D4411yescharacteristic
453C22×C4#433912yes—
454C22×C4#433912yes—
455C22×C4C2×C22⋊D1112yes—
456C22×C4C23×D1111yescharacteristic
457M16—28no—
458C2×C8—28no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—22no—
462C2×C8—21no—
463C2×C8—22no—
464C2×C8—21no—
465C2×C8C2×D4412yes—
466C2×C8C2×D4412yes—
467C2×C8C2×D4414yes—
468C4⋊C4—2216no—
469C4⋊C4—222no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4—222no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4—442no—
476C4⋊C4—884no—
477C4⋊C4(C2×D11)⋊C418yes—
478C22⋊C4—2216no—
479C22⋊C4—442no—
480C22⋊C4(C2×D11)⋊C418yes—
481C42—442no—
482C42C2×C4×D1114yes—
483C42C2×C22⋊D1114yes—
484C11#2120511yescharacteristic, complemented, Sylow
485C23—22no—
486C23—22no—
487C23—222no—
488C23—441no—
489C23—441no—
490C23—442no—
491C23—442no—
492C23#6692712yes—
493C23#6692812yes—
494C23C2×(C2×D11)⋊C412yes—
495C23C22×D4411yescharacteristic
496Q8—224no—
497Q8—224no—
498Q8—222no—
499Q8—222no—
500Q8—448no—
501Q8—442no—
502Q8—442no—
503Q8—441no—
504Q8—441no—
505D4—222no—
506D4—222no—
507D4—448no—
508D4—441no—
509D4—441no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—224no—
513C2×C4—222no—
514C2×C4—441no—
515C2×C4—442no—
516C2×C4—441no—
517C2×C4—442no—
518C2×C4—448no—
519C2×C4—448no—
520C2×C4—441no—
521C2×C4—441no—
522C2×C4—442no—
523C2×C4—442no—
524C2×C4—444no—
525C2×C4—442no—
526C2×C4—884no—
527C2×C4C4×D4414yes—
528C2×C4C4×D4414yes—
529C2×C4#6692712yes—
530C2×C4#6692812yes—
531C2×C4C2×(C2×D11)⋊C418yes—
532C2×C4C2×(C2×D11)⋊C412yes—
533C2×C4#6698314yes—
534C2×C4#6698314yes—
535C2×C4C22×C4×D1111yescharacteristic
536C2×C4C22×D4411yescharacteristic
537C2×C4C22×D4411yescharacteristic
538C2×C4C2×#433911yescharacteristic
539C2×C4C2×#433911yescharacteristic
540C2×C4C22×C22⋊D1111yescharacteristic
541C8—22no—
542C8—22no—
543C8—24no—
544C22—22no—
545C22—22no—
546C22—24no—
547C22—24no—
548C22—444no—
549C22—442no—
550C22—881no—
551C22—881no—
552C22—882no—
553C22#1062255214yes—
554C22C2×#6692711yescharacteristic
555C22C2×#6692811yescharacteristic
556C22#1062328212yes—
557C22#1062328412yes—
558C22C22×(C2×D11)⋊C411yescharacteristic
559C4—28no—
560C4—442no—
561C4—444no—
562C4—882no—
563C4—881no—
564C4—881no—
565C4#1062255214yes—
566C4C2×C4×D4411yescharacteristic
567C4C2×C4×D4411yescharacteristic
568C4C2×#6698311yescharacteristic
569C4C2×#6698311yescharacteristic
570C2—24no—
571C2—882no—
572C2C2×#1062255211yescharacteristic
573C2#1307715012yes—
574C2#1307898312yes—
575C2#1307909211yescharacteristic
576C2#1307911011yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#405C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
cosocleC22×C4×C11C24
hypercenterC2×#405D11
hypocenterC11#21205
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#405

Complements

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

NH ≅ G/Ntype
3. C2×#10622733C2semidirect
5. C22×#66880C2semidirect
6. #13071239C2semidirect
7. #13069436C2semidirect
8. #13069432C2semidirect
9. #13069427C2semidirect
10. #13069418C2semidirect
11. C2×C11×#405C2semidirect
20. #10623057C4semidirect
97. #66928C2×C4semidirect
99. #66922C2×C4semidirect
202. C2×#405D11semidirect
484. C11#21205semidirect

Maximal subgroups

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

subgroupindex
C2×#106230572
C2×#106227462
C2×#106227332
C2×#106227262
C22×#668802
#130712392
#130694362
#130694322
#130694272
#130694182
C2×C11×#4052
#2120511