Finite Group Databasebeta

← #14787682

Subgroups — #14787682

Order 2816.

1218 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622697C211yesmaximal, characteristic, complemented
2C2×C4×#4325C211yesmaximal, characteristic, complemented
3#13073529C211yesmaximal, characteristic
4#13069809C212yesmaximal, complemented
5#13069617C212yesmaximal, complemented
6#13069578C211yesmaximal, characteristic, complemented
7#13069411C211yesmaximal, characteristic, complemented
8#13068933C212yesmaximal, complemented
9#13068809C212yesmaximal, complemented
10#13068621C211yesmaximal, characteristic, complemented
11C2×C11×#554C211yesmaximal, characteristic, complemented
12C11×#554—24no—
13C11×#554—24no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#125—21no—
16C2×C11×C22⋊Q8—22no—
17C2×C11×C22⋊Q8C2212yes—
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×D4×C11—21no—
20C2×C4×D4×C11C2211yescharacteristic
21C22×C11×C4⋊C4C2212yes—
22C22×#4325C2211yescharacteristic
23C2×#66991—21no—
24C2×#66983C2212yes—
25C2×C4×D44C2211yescharacteristic
26C2×#66899C2211yescharacteristic
27C2×#66899C2212yes—
28#10622825C2212yes—
29C2×C22⋊(C11⋊C8)C2212yes—
30C2×C22⋊(C11⋊C8)C2212yes—
31#10622697—24no—
32C4×#4325—24no—
33#10622600—21no—
34C2×#66873C2212yes—
35C2×#66873C2211yescharacteristic
36C2×#66872C2211yescharacteristic
37C2×#66872C2212yes—
38#10622574—22no—
39#10622548C2211yescharacteristic
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×C4×C11⋊C8C2211yescharacteristic
42#10622167C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45C22×Q8×C11—21no—
46C22×Q8×C11C2311yescharacteristic
47C22×D4×C11D411yescharacteristic
48C23×C4×C11—22no—
49C23×C4×C11C2312yes—
50C22×C22⋊D11—22no—
51C22×D44C2311yescharacteristic
52C22×C4×D11—21no—
53C11×C4⋊Q8—22no—
54C11×C4⋊Q8D414yescomplemented
55C11×#125—28no—
56C11×C22⋊Q8—216no—
57C11×C22⋊Q8—24no—
58C11×C22⋊Q8—24no—
59C4×Q8×C11—22no—
60C4×Q8×C11D414yescomplemented
61C4×D4×C11—28no—
62C4×D4×C11—22no—
63C4×D4×C11—22no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—24no—
69C2×C11×C4⋊C4—24no—
70C2×C11×C4⋊C4D411yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2312yes—
73C2×C11×C22⋊C4—22no—
74C2×C11×C22⋊C4D412yes—
75C2×C42×C11—21no—
76C2×C42×C11C2311yescharacteristic
77C2×C22⋊Dic11—22no—
78C2×#4325—22no—
79C2×#4325—22no—
80C2×#4325—22no—
81#66991—44no—
82#66983—24no—
83#66983—42no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—22no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2312yes—
90C22×C11⋊C8C2311yescharacteristic
91C22×C11⋊C8C2312yes—
92C22×C11⋊C8C2311yescharacteristic
93C4×D44—22no—
94C4×D44—22no—
95#66899—22no—
96#66899—42no—
97C11⋊#95—22no—
98C22⋊(C11⋊C8)—24no—
99C22⋊(C11⋊C8)—42no—
100#66873—22no—
101#66873—24no—
102#66872—22no—
103#66872—24no—
104C4⋊(C11⋊C8)—22no—
105C4×C11⋊C8—22no—
106#24118—111nomaximal, Sylow
107C24×C11C2×D412yes—
108C23×D11—21no—
109C2×Q8×C11—24no—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—81no—
116C2×Q8×C11—81no—
117C2×Q8×C11C2×D412yes—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11SD1614yescomplemented
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—22no—
124C22×C4×C11—28no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—82no—
132C22×C4×C11—82no—
133C22×C4×C11C2×D412yes—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2411yescharacteristic
137C2×C22⋊D11—44no—
138C2×C22⋊D11—44no—
139C2×C22⋊D11—82no—
140C22×Dic11—21no—
141C22×Dic11—22no—
142C2×D44—21no—
143C2×D44—21no—
144C2×D44—21no—
145C2×D44—21no—
146C2×D44—21no—
147C2×D44#4112yes—
148C2×C4×D11—42no—
149C2×C4×D11—42no—
150C2×C4×D11—42no—
151C11×C4⋊C4—28no—
152C11×C4⋊C4—28no—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—24no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4C2×D412yes—
159C11×C4⋊C4C2×D414yes—
160C11×C22⋊C4—28no—
161C11×C22⋊C4—24no—
162C42×C11—24no—
163C42×C11C2×D412yes—
164C42×C11C2×D412yes—
165C22⋊Dic11—44no—
166#4325—28no—
167(C2×D11)⋊C4—44no—
168(C2×D11)⋊C4—42no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C4⋊Dic11—22no—
172C4⋊Dic11—22no—
173C4⋊Dic11—42no—
174C4⋊Dic11—81no—
175C2×C11⋊C8—21no—
176C2×C11⋊C8—21no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—21no—
179C2×C11⋊C8—22no—
180C2×C11⋊C8—21no—
181C2×C11⋊C8—22no—
182C2×C11⋊C8—21no—
183C2×C11⋊C8#4112yes—
184C2×#554D1111yescharacteristic, complemented
185C2×#476—111no—
186C2×C4×SD16—111no—
187#2537—111no—
188#2035—112no—
189#2000—112no—
190#1990—111no—
191#1954—111no—
192#1874—112no—
193#1853—112no—
194#1803—111no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—22no—
201C23×C11C2×SD1614yes—
202C23×C11C22×D411yescharacteristic
203C22×D11—22no—
204C22×D11—41no—
205C22×D11—41no—
206C22×D11—41no—
207C22×D11—41no—
208C22×D11—41no—
209C22×D11—41no—
210Q8×C11—22no—
211Q8×C11—22no—
212Q8×C11—41no—
213Q8×C11—41no—
214Q8×C11—84no—
215D4×C11—28no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—24no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—42no—
228C2×C4×C11—41no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—88no—
235C2×C4×C11#12012yes—
236C2×C4×C11#12012yes—
237C2×C4×C11C2×SD1612yes—
238C2×C4×C11#13712yes—
239C2×C4×C11C22×D411yescharacteristic
240C2×C4×C11C22×D411yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C2×C4×C11C2×#4111yescharacteristic
243C2×C4×C11H(5,𝔽2)11yescharacteristic
244C2×C4×C112−1+411yescharacteristic
245C22⋊D11—88no—
246C2×Dic11—41no—
247C2×Dic11—42no—
248C2×Dic11—42no—
249C2×Dic11—41no—
250C2×Dic11—41no—
251C2×Dic11—42no—
252D44—22no—
253D44—22no—
254D44—41no—
255D44—41no—
256C4×D11—84no—
257C11⋊C8—22no—
258C11⋊C8—41no—
259C11⋊C8—42no—
260C22×SD16—111no—
261#554—24no—
262#554—24no—
263C2×C4⋊Q8C2×D1111yescharacteristic
264C2×#125—21no—
265C2×C22⋊Q8—22no—
266C2×C22⋊Q8C2×D1112yes—
267C2×#121—112no—
268C2×#121—221no—
269C2×C4×Q8C2×D1111yescharacteristic
270C2×C4×D4—21no—
271C2×C4×D4—111no—
272C2×C4×D4C2×D1111yescharacteristic
273C22×C4⋊C4C2×D1112yes—
274#476—224no—
275C4×SD16—224no—
276C2×#106—111no—
277C2×#106—112no—
278C2×C4⋊C8—111no—
279C2×#103—111no—
280C2×#103—112no—
281C2×#102—111no—
282C2×#102—112no—
283C2×C22⋊C8—112no—
284C2×C22⋊C8—112no—
285C2×C4×C8—111no—
286#394—222no—
287#384—111no—
288#380—112no—
289#380—221no—
290#340—112no—
291#340—112no—
292#340—112no—
293C22×C11—24no—
294C22×C11—24no—
295C22×C11—24no—
296C22×C11—42no—
297C22×C11—42no—
298C22×C11—42no—
299C22×C11—42no—
300C22×C11C2×#12011yescharacteristic
301C22×C11#54611yescharacteristic
302C22×C11#54711yescharacteristic
303C22×C11C22×SD1611yescharacteristic
304C22×C11C2×#13711yescharacteristic
305C22×C11#57611yescharacteristic
306C22×C11#57711yescharacteristic
307C2×D11—42no—
308C2×D11—42no—
309C2×D11—42no—
310C2×D11—81no—
311C2×D11—81no—
312C2×D11—81no—
313C2×D11—81no—
314C4×C11—22no—
315C4×C11—42no—
316C4×C11—42no—
317C4×C11—42no—
318C4×C11—44no—
319C4×C11#44814yes—
320C4×C11#52511yescharacteristic
321C4×C11#53711yescharacteristic
322C4×C11#54811yescharacteristic
323C4×C11#55011yescharacteristic
324Dic11—81no—
325Dic11—82no—
326C22×Q8—21no—
327C22×Q8C22×D1111yescharacteristic
328C22×D4—111no—
329C22×D4—222no—
330C22×D4C22⋊D1111yescharacteristic
331C23×C4—22no—
332C23×C4—221no—
333C23×C4C22×D1112yes—
334C2×SD16—222no—
335C2×SD16—222no—
336C2×SD16—222no—
337C22×C8—111no—
338C22×C8—111no—
339C22×C8—112no—
340C4⋊Q8—22no—
341C4⋊Q8C22⋊D1114yescomplemented
342#125—28no—
343C22⋊Q8—216no—
344C22⋊Q8—24no—
345C22⋊Q8—24no—
346#121—224no—
347#121—442no—
348#121—444no—
349C4×Q8—22no—
350C4×Q8C22⋊D1114yescomplemented
351C4×D4—28no—
352C4×D4—22no—
353C4×D4—22no—
354C4×D4—222no—
355C4×D4—222no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—112no—
364C2×C4⋊C4—221no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4C22⋊D1111yescharacteristic
367C2×C4⋊C4C22×D1111yescharacteristic
368C2×C4⋊C4C22×D1112yes—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—222no—
371C2×C22⋊C4—221no—
372C2×C22⋊C4—222no—
373C2×C22⋊C4C22⋊D1112yes—
374C2×C42—21no—
375C2×C42C22×D1111yescharacteristic
376#106—222no—
377#106—224no—
378C4⋊C8—222no—
379#103—222no—
380#103—442no—
381#102—222no—
382#102—224no—
383C22⋊C8—224no—
384C22⋊C8—442no—
385C4×C8—222no—
386#95—222no—
387C2×C11—44no—
388C2×C11#240711yescharacteristic
389C2×C11C2×#44811yescharacteristic
390C2×C11#301211yescharacteristic
391C2×C11#329511yescharacteristic
392C2×C11#333111yescharacteristic
393C2×C11#333511yescharacteristic
394C2×C11#335711yescharacteristic
395D11—82no—
396C24—221no—
397C24C2×C22⋊D1112yes—
398C2×Q8—24no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—21no—
402C2×Q8—21no—
403C2×Q8—21no—
404C2×Q8—81no—
405C2×Q8—81no—
406C2×Q8C2×C22⋊D1112yes—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—112no—
410C2×D4—221no—
411C2×D4—221no—
412C2×D4—221no—
413C2×D4—221no—
414C2×D4—221no—
415C2×D4—444no—
416C2×D4—444no—
417C2×D4—882no—
418C2×D4#432514yescomplemented
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—28no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—82no—
430C22×C4—82no—
431C22×C4—221no—
432C22×C4—222no—
433C22×C4—442no—
434C22×C4—442no—
435C22×C4—442no—
436C22×C4C2×C22⋊D1112yes—
437C22×C4C2×C22⋊D1111yescharacteristic
438C22×C4C2×C22⋊D1111yescharacteristic
439C22×C4C23×D1111yescharacteristic
440SD16—228no—
441C2×C8—112no—
442C2×C8—221no—
443C2×C8—221no—
444C2×C8—222no—
445C2×C8—221no—
446C2×C8—222no—
447C2×C8—221no—
448C2×C8—221no—
449C2×C8—222no—
450C4⋊C4—28no—
451C4⋊C4—28no—
452C4⋊C4—24no—
453C4⋊C4—24no—
454C4⋊C4—22no—
455C4⋊C4—21no—
456C4⋊C4—22no—
457C4⋊C4—222no—
458C4⋊C4—222no—
459C4⋊C4—221no—
460C4⋊C4—221no—
461C4⋊C4—442no—
462C4⋊C4—881no—
463C4⋊C4C2×C22⋊D1112yes—
464C4⋊C4C2×C22⋊D1114yes—
465C22⋊C4—28no—
466C22⋊C4—24no—
467C22⋊C4—444no—
468C22⋊C4—444no—
469C22⋊C4—442no—
470C42—24no—
471C42C2×C22⋊D1112yes—
472C42C2×C22⋊D1112yes—
473C11#2411811yescharacteristic, complemented, Sylow
474C23—22no—
475C23—22no—
476C23—22no—
477C23—22no—
478C23—22no—
479C23—22no—
480C23—222no—
481C23—441no—
482C23—441no—
483C23—441no—
484C23—441no—
485C23—441no—
486C23—441no—
487C23C2×#432514yes—
488C23C22×C22⋊D1111yescharacteristic
489Q8—22no—
490Q8—22no—
491Q8—41no—
492Q8—41no—
493Q8—84no—
494D4—28no—
495D4—222no—
496D4—222no—
497D4—441no—
498D4—441no—
499D4—888no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—24no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—42no—
512C2×C4—41no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—88no—
519C2×C4—441no—
520C2×C4—442no—
521C2×C4—441no—
522C2×C4—442no—
523C2×C4—442no—
524C2×C4—441no—
525C2×C4—884no—
526C2×C4C2×#432512yes—
527C2×C4#6699512yes—
528C2×C4#6700612yes—
529C2×C4#6700612yes—
530C2×C4#41×D1111yescharacteristic
531C2×C4#41×D1111yescharacteristic
532C2×C4#6704211yescharacteristic
533C2×C4#6704311yescharacteristic
534C2×C4C22×C22⋊D1111yescharacteristic
535C2×C4C22×C22⋊D1111yescharacteristic
536C8—222no—
537C8—441no—
538C8—442no—
539C22—24no—
540C22—24no—
541C22—24no—
542C22—42no—
543C22—42no—
544C22—42no—
545C22—42no—
546C22—442no—
547C22—442no—
548C22—442no—
549C22—881no—
550C22—881no—
551C22—881no—
552C22—881no—
553C22C22×#432511yescharacteristic
554C22C2×#6699511yescharacteristic
555C22#1062335511yescharacteristic
556C22#1062336011yescharacteristic
557C22#1062336611yescharacteristic
558C22#1062336711yescharacteristic
559C22C2×#6700611yescharacteristic
560C4—22no—
561C4—42no—
562C4—42no—
563C4—42no—
564C4—44no—
565C4—881no—
566C4—882no—
567C4#1062284014yes—
568C4#1062335911yescharacteristic
569C4#1062336211yescharacteristic
570C4#1062336411yescharacteristic
571C4#1062336511yescharacteristic
572C2—44no—
573C2—882no—
574C2#1307195511yescharacteristic
575C2C2×#1062284011yescharacteristic
576C2#1307792011yescharacteristic
577C2#1308043411yescharacteristic
578C2#1308092611yescharacteristic
579C2#1308096711yescharacteristic
580C2#1308124211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#554C2
socleC23×C11C22×D4
prime radical#13073529C2
hypercenterC2×#554D11
hypocenterC11#24118
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×#10622697C2semidirect
2. C2×C4×#4325C2semidirect
4. #13069809C2semidirect
5. #13069617C2semidirect
6. #13069578C2semidirect
7. #13069411C2semidirect
8. #13068933C2semidirect
9. #13068809C2semidirect
10. #13068621C2semidirect
11. C2×C11×#554C2semidirect
54. C11×C4⋊Q8D4semidirect
60. C4×Q8×C11D4semidirect
120. C2×D4×C11SD16semidirect
184. C2×#554D11semidirect
341. C4⋊Q8C22⋊D11semidirect
350. C4×Q8C22⋊D11semidirect
418. C2×D4#4325semidirect
473. C11#24118semidirect

Maximal subgroups

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

subgroupindex
C2×#106226972
C2×C4×#43252
#130735292
#130698092
#130696172
#130695782
#130694112
#130689332
#130688092
#130686212
C2×C11×#5542
#2411811