Finite Group Databasebeta

← #14757478

Subgroups — #14757478

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×#10622845C211yesmaximal, characteristic
2C2×#10622838C211yesmaximal, characteristic, complemented
3C2×#10622846C211yesmaximal, characteristic
4C22×#66899C211yesmaximal, characteristic, complemented
5C2×#10622610C211yesmaximal, characteristic, complemented
6#13071239C211yesmaximal, characteristic, complemented
7#13069437C212yesmaximal, complemented
8#13069433C212yesmaximal, complemented
9#13069428C212yesmaximal, complemented
10#13069419C212yesmaximal, complemented
11C2×C11×#536C211yesmaximal, characteristic
12C22×C11×#41C2211yescharacteristic
13C23×Q8×C11C2211yescharacteristic
14C11×#536—24no—
15C11×#536C418yescomplemented
16C2×C11×C4⋊Q8C2212yes—
17C2×C11×#124C2212yes—
18C2×C11×#123—22no—
19C2×C11×C22⋊Q8—22no—
20C2×C11×#117C2211yescharacteristic
21C2×#66979C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C22×#4318C2211yescharacteristic
24C23×C11⋊C8C2211yescharacteristic
25#10622846—24no—
26#10622845—24no—
27#10622838—24no—
28C2×#66899—24no—
29C2×#66899C2211yescharacteristic
30C2×#66899C2212yes—
31C2×#66899C2212yes—
32C2×#66899C2212yes—
33C2×#66899C2212yes—
34C2×#66899C2212yes—
35C2×#66899C2211yescharacteristic
36C2×#66896C2211yescharacteristic
37C2×#66896C2212yes—
38C2×#66896C2211yescharacteristic
39#10622610—24no—
40#10622598—22no—
41#10622563—22no—
42#10622549C2212yes—
43#10622548C2212yes—
44C2×#66867C2212yes—
45C2×C4×C11⋊C8C2212yes—
46C2×C11×#41—22no—
47C2×C11×#41—22no—
48C2×C11×#41—22no—
49C2×C11×#41—22no—
50C2×C11×#41—22no—
51C2×C11×#41C2×C414yes—
52C22×Q8×C11—21no—
53C22×Q8×C11—22no—
54C22×Q8×C11—22no—
55C22×Q8×C11—22no—
56C22×Q8×C11—22no—
57C22×Q8×C11—22no—
58C22×Q8×C11C2×C414yes—
59C22×Q8×C11C2312yes—
60C22×Q8×C11C2311yescharacteristic
61C22×D4×C11—21no—
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C23×C4×C11—21no—
65C23×C4×C11C2311yescharacteristic
66C23×Dic11—21no—
67C11×C4⋊Q8—24no—
68C11×C4⋊Q8C2×C418yescomplemented
69C11×#124—24no—
70C11×#124C2×C418yescomplemented
71C11×#123—216no—
72C11×C22⋊Q8—216no—
73C11×#117C2×C414yes—
74C11×#117D414yes—
75C2×C11×C4⋊C4—24no—
76C2×C11×C4⋊C4D412yes—
77C2×C11×C22⋊C4—24no—
78C2×C11×C22⋊C4D412yes—
79C2×C42×C11C2312yes—
80C2×C22⋊Dic11—21no—
81#66979—22no—
82#66979—22no—
83C2×C4⋊Dic11—22no—
84C2×C4⋊Dic11—22no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11—24no—
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2312yes—
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4×Dic11—21no—
91C2×#4318—22no—
92C2×#4318—22no—
93C2×#4318D414yes—
94C22×C11⋊C8—22no—
95C22×C11⋊C8—22no—
96C22×C11⋊C8D414yes—
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2312yes—
99C22×C11⋊C8C2311yescharacteristic
100#66899—24no—
101#66899—24no—
102#66899—24no—
103#66899—24no—
104#66899—24no—
105#66899—22no—
106#66899—22no—
107#66896—24no—
108#66896—22no—
109#66896—22no—
110C11⋊#95—24no—
111#66867—24no—
112C4×C11⋊C8—24no—
113#21205—111nomaximal, Sylow
114C24×C11—21no—
115C24×C11C2×D411yescharacteristic
116C11×#41—28no—
117C11×#41—28no—
118C11×#41—44no—
119C11×#41—44no—
120C2×Q8×C11—24no—
121C2×Q8×C11—22no—
122C2×Q8×C11—21no—
123C2×Q8×C11—28no—
124C2×Q8×C11—28no—
125C2×Q8×C11—22no—
126C2×Q8×C11—22no—
127C2×Q8×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11—22no—
130C2×Q8×C11—22no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—44no—
134C2×Q8×C11—44no—
135C2×Q8×C11—42no—
136C2×Q8×C11—42no—
137C2×Q8×C11C22×C414yes—
138C2×Q8×C11C22×C412yes—
139C2×D4×C11—24no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—42no—
146C2×D4×C11—42no—
147C2×D4×C11C22×C412yes—
148C22×C4×C11—24no—
149C22×C4×C11—22no—
150C22×C4×C11—21no—
151C22×C4×C11—24no—
152C22×C4×C11—42no—
153C22×C4×C11—42no—
154C22×C4×C11—42no—
155C22×C4×C11—42no—
156C22×C4×C11C22×C412yes—
157C22×C4×C11C2×D414yes—
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D412yes—
160C22×C4×C11C2×D412yes—
161C22×C4×C11C2×D412yes—
162C22×C4×C11#4112yes—
163C22×C4×C11#4112yes—
164C22×C4×C11C2411yescharacteristic
165C22×Dic11—21no—
166C22×Dic11—22no—
167C22×Dic11—21no—
168C22×Dic11—42no—
169C22×Dic11—82no—
170C11×C4⋊C4—216no—
171C11×C4⋊C4C22⋊C418yes—
172C11×C22⋊C4—216no—
173C11×C22⋊C4C22⋊C418yes—
174C42×C11C22×C414yes—
175C42×C11C2×D414yes—
176C22⋊Dic11—42no—
177C4⋊Dic11—22no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—22no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—42no—
184C4⋊Dic11—84no—
185C4×Dic11—42no—
186#4318—28no—
187C2×C11⋊C8—28no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—22no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—22no—
194C2×C11⋊C8C2×D412yes—
195C2×C11⋊C8C2×D412yes—
196C2×C11⋊C8C2×D414yes—
197C2×#536D1111yescharacteristic
198C2×#417—111no—
199C2×#419—111no—
200C2×#416—111no—
201C22×#103—111no—
202C2×#405—111no—
203#2317—111no—
204#1960—112no—
205#1959—112no—
206#1958—112no—
207#1956—112no—
208C23×C11—22no—
209C23×C11—22no—
210C23×C11—22no—
211C23×C11—41no—
212C23×C11—41no—
213C23×C11—42no—
214C23×C11—42no—
215C23×C11C2×C22⋊C412yes—
216C23×C11#12412yes—
217C23×C11#12712yes—
218C23×C11C22×D411yescharacteristic
219Q8×C11—24no—
220Q8×C11—24no—
221Q8×C11—22no—
222Q8×C11—22no—
223Q8×C11—42no—
224Q8×C11—42no—
225Q8×C11—41no—
226Q8×C11—41no—
227Q8×C11—48no—
228D4×C11—22no—
229D4×C11—22no—
230D4×C11—48no—
231D4×C11—41no—
232D4×C11—41no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—22no—
237C2×C4×C11—41no—
238C2×C4×C11—42no—
239C2×C4×C11—41no—
240C2×C4×C11—42no—
241C2×C4×C11—48no—
242C2×C4×C11—48no—
243C2×C4×C11C2×C22⋊C418yes—
244C2×C4×C11C2×C22⋊C412yes—
245C2×C4×C11C4×D414yes—
246C2×C4×C11C4×D414yes—
247C2×C4×C11#12114yes—
248C2×C4×C11#12114yes—
249C2×C4×C11#12412yes—
250C2×C4×C11#12712yes—
251C2×C4×C11C23×C411yescharacteristic
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—42no—
260C2×Dic11—42no—
261C2×Dic11—44no—
262C2×Dic11—42no—
263C2×Dic11—84no—
264C11⋊C8—22no—
265C11⋊C8—22no—
266C11⋊C8—24no—
267C22×#41C2×D1111yescharacteristic
268C23×Q8C2×D1111yescharacteristic
269C22×M16—111no—
270C23×C8—111no—
271#536—24no—
272#536Dic1118yescomplemented
273C2×C4⋊Q8C2×D1112yes—
274C2×#124C2×D1112yes—
275C2×#123—22no—
276C2×C22⋊Q8—22no—
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—224no—
295C2×#97—112no—
296C2×C4×C8—112no—
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—44no—
306C22×C11—42no—
307C22×C11—82no—
308C22×C11—81no—
309C22×C11—81no—
310C22×C11#39014yes—
311C22×C11C22×C22⋊C411yescharacteristic
312C22×C11C2×#12411yescharacteristic
313C22×C11C2×#12711yescharacteristic
314C22×C11#57712yes—
315C22×C11#57812yes—
316C4×C11—28no—
317C4×C11—42no—
318C4×C11—44no—
319C4×C11#39014yes—
320C4×C11C2×C4×D411yescharacteristic
321C4×C11C2×C4×D411yescharacteristic
322C4×C11C2×#12111yescharacteristic
323C4×C11C2×#12111yescharacteristic
324Dic11—81no—
325Dic11—82no—
326Dic11—81no—
327C2×#41—22no—
328C2×#41—22no—
329C2×#41—22no—
330C2×#41—22no—
331C2×#41—22no—
332C2×#41C2×Dic1114yes—
333C22×Q8—21no—
334C22×Q8—22no—
335C22×Q8—22no—
336C22×Q8—22no—
337C22×Q8—22no—
338C22×Q8—22no—
339C22×Q8C2×Dic1114yes—
340C22×Q8C22×D1112yes—
341C22×Q8C22×D1111yescharacteristic
342C22×D4—21no—
343C22×D4C22×D1111yescharacteristic
344C23×C4—21no—
345C23×C4—21no—
346C23×C4—221no—
347C23×C4C22×D1111yescharacteristic
348C2×M16—114no—
349C2×M16—222no—
350C2×M16—222no—
351C22×C8—114no—
352C22×C8—111no—
353C22×C8—111no—
354C22×C8—112no—
355C22×C8—222no—
356C22×C8—222no—
357C4⋊Q8—24no—
358C4⋊Q8C2×Dic1118yescomplemented
359#124—24no—
360#124C2×Dic1118yescomplemented
361#123—216no—
362C22⋊Q8—216no—
363#117—222no—
364#117—222no—
365#117C2×Dic1114yes—
366#117C22⋊D1114yes—
367C2×C4⋊C4—24no—
368C2×C4⋊C4—112no—
369C2×C4⋊C4—111no—
370C2×C4⋊C4—111no—
371C2×C4⋊C4—222no—
372C2×C4⋊C4—222no—
373C2×C4⋊C4—221no—
374C2×C4⋊C4—224no—
375C2×C4⋊C4C22⋊D1112yes—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—221no—
378C2×C22⋊C4C22⋊D1112yes—
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—224no—
392C4×C8—224no—
393#95—224no—
394C2×C11—24no—
395C2×C11—82no—
396C2×C11C2×#39011yescharacteristic
397C2×C11#289812yes—
398C2×C11#313712yes—
399C2×C11#315411yescharacteristic
400C2×C11#315611yescharacteristic
401C24—21no—
402C24C2×C22⋊D1111yescharacteristic
403#41—28no—
404#41—28no—
405#41—44no—
406#41—44no—
407C2×Q8—24no—
408C2×Q8—22no—
409C2×Q8—21no—
410C2×Q8—28no—
411C2×Q8—28no—
412C2×Q8—22no—
413C2×Q8—22no—
414C2×Q8—21no—
415C2×Q8—21no—
416C2×Q8—22no—
417C2×Q8—22no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—42no—
421C2×Q8—44no—
422C2×Q8—44no—
423C2×Q8—42no—
424C2×Q8C22×Dic1114yes—
425C2×Q8C22×Dic1112yes—
426C2×D4—24no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—42no—
433C2×D4—42no—
434C2×D4C22×Dic1112yes—
435C22×C4—24no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—24no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—221no—
444C22×C4—222no—
445C22×C4—221no—
446C22×C4—442no—
447C22×C4—882no—
448C22×C4D4×D1112yes—
449C22×C4D4×D1112yes—
450C22×C4#434112yes—
451C22×C4#434112yes—
452C22×C4C22×Dic1112yes—
453C22×C4C2×C22⋊D1114yes—
454C22×C4C2×C22⋊D1111yescharacteristic
455C22×C4C2×C22⋊D1112yes—
456C22×C4C23×D1111yescharacteristic
457M16—228no—
458C2×C8—112no—
459C2×C8—112no—
460C2×C8—114no—
461C2×C8—228no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8—222no—
465C2×C8—221no—
466C2×C8—222no—
467C2×C8—221no—
468C4⋊C4—216no—
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⋊C4C22⋊Dic1118yes—
478C22⋊C4—216no—
479C22⋊C4—442no—
480C22⋊C4C22⋊Dic1118yes—
481C42—442no—
482C42C22×Dic1114yes—
483C42C2×C22⋊D1114yes—
484C11#2120511yescharacteristic, complemented, Sylow
485C23—22no—
486C23—22no—
487C23—22no—
488C23—41no—
489C23—41no—
490C23—42no—
491C23—42no—
492C23#6698912yes—
493C23#6699312yes—
494C23C2×C22⋊Dic1112yes—
495C23C22×C22⋊D1111yescharacteristic
496Q8—24no—
497Q8—24no—
498Q8—22no—
499Q8—22no—
500Q8—42no—
501Q8—42no—
502Q8—41no—
503Q8—41no—
504Q8—48no—
505D4—22no—
506D4—22no—
507D4—48no—
508D4—41no—
509D4—41no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—22no—
514C2×C4—41no—
515C2×C4—42no—
516C2×C4—41no—
517C2×C4—42no—
518C2×C4—48no—
519C2×C4—48no—
520C2×C4—441no—
521C2×C4—441no—
522C2×C4—442no—
523C2×C4—442no—
524C2×C4—444no—
525C2×C4—442no—
526C2×C4—884no—
527C2×C4D4×Dic1114yes—
528C2×C4D4×Dic1114yes—
529C2×C4#6698912yes—
530C2×C4#6699114yes—
531C2×C4#6699114yes—
532C2×C4#6699312yes—
533C2×C4C2×C22⋊Dic1118yes—
534C2×C4C2×C22⋊Dic1112yes—
535C2×C4C2×D4×D1111yescharacteristic
536C2×C4C2×D4×D1111yescharacteristic
537C2×C4C2×#434111yescharacteristic
538C2×C4C2×#434111yescharacteristic
539C2×C4C23×Dic1111yescharacteristic
540C2×C4C22×C22⋊D1111yescharacteristic
541C8—222no—
542C8—222no—
543C8—224no—
544C22—22no—
545C22—22no—
546C22—24no—
547C22—24no—
548C22—44no—
549C22—42no—
550C22—81no—
551C22—81no—
552C22—82no—
553C22#1062283414yes—
554C22C2×#6698911yescharacteristic
555C22C2×#6699311yescharacteristic
556C22#1062336812yes—
557C22#1062336912yes—
558C22C22×C22⋊Dic1111yescharacteristic
559C4—28no—
560C4—42no—
561C4—44no—
562C4—882no—
563C4—881no—
564C4—881no—
565C4#1062283414yes—
566C4C2×D4×Dic1111yescharacteristic
567C4C2×D4×Dic1111yescharacteristic
568C4C2×#6699111yescharacteristic
569C4C2×#6699111yescharacteristic
570C2—24no—
571C2—82no—
572C2C2×#1062283411yescharacteristic
573C2#1307714912yes—
574C2#1307898112yes—
575C2#1307909411yescharacteristic
576C2#1307910711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#536C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
cosocleC22×C4×C11C24
hypercenterC2×#536D11
hypocenterC11#21205
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
2. C2×#10622838C2semidirect
4. C22×#66899C2semidirect
5. C2×#10622610C2semidirect
6. #13071239C2semidirect
7. #13069437C2semidirect
8. #13069433C2semidirect
9. #13069428C2semidirect
10. #13069419C2semidirect
15. C11×#536C4semidirect
68. C11×C4⋊Q8C2×C4semidirect
70. C11×#124C2×C4semidirect
272. #536Dic11semidirect
358. C4⋊Q8C2×Dic11semidirect
360. #124C2×Dic11semidirect
484. C11#21205semidirect

Maximal subgroups

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

subgroupindex
C2×#106228452
C2×#106228382
C2×#106228462
C22×#668992
C2×#106226102
#130712392
#130694372
#130694332
#130694282
#130694192
C2×C11×#5362
#2120511