Finite Group Databasebeta

← #14807111

Subgroups — #14807111

Order 2816.

1190 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623096C211yesmaximal, characteristic
2C2×#10622695C211yesmaximal, characteristic, complemented
3C2×#10622696C211yesmaximal, characteristic, complemented
4#13069617C212yesmaximal, complemented
5#13069617C212yesmaximal, complemented
6#13069573C211yesmaximal, characteristic, complemented
7#13069415C211yesmaximal, characteristic, complemented
8#13068929C212yesmaximal, complemented
9#13068924C212yesmaximal, complemented
10#13068444C211yesmaximal, characteristic, complemented
11C11×#2542C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C11×C22⋊Q8C2212yes—
14C2×C11×C22⋊Q8C2212yes—
15C2×C4×D4×C11C2211yescharacteristic
16C22×#4325C2212yes—
17C2×#66992—21no—
18C2×#66983C2211yescharacteristic
19C2×#66983C2211yescharacteristic
20C2×#66979C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22#10623096—24no—
23#10623096—24no—
24C2×#66951—21no—
25C2×#66936—21no—
26C2×(C22⋊D11)⋊C4—21no—
27C2×C4×D44C2211yescharacteristic
28C2×#66923C2211yescharacteristic
29C11×#399—21no—
30C11×#399—21no—
31C11×#390—21no—
32C11×#384—21no—
33C4×C11×C4⋊C4C2211yescharacteristic
34C2×#66899C2212yes—
35C2×#66899C2212yes—
36C2×#66899C2212yes—
37C2×C22⋊(C11⋊C8)C2212yes—
38C2×C22⋊(C11⋊C8)C2212yes—
39#10622696—24no—
40#10622695—24no—
41C2×#66873C2212yes—
42C2×C4⋊(C11⋊C8)C2211yescharacteristic
43C2×#66867C2211yescharacteristic
44#10622167C2212yes—
45#10622167C2212yes—
46#10622167C2212yes—
47C22×Q8×C11C2312yes—
48C22×D4×C11D411yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C22×C22⋊D11—21no—
52C22×C22⋊D11—21no—
53C23×Dic11—21no—
54C22×D44C2311yescharacteristic
55C22×C4×D11—21no—
56C11×C4⋊Q8—22no—
57C11×C4⋊Q8—22no—
58C11×C22⋊Q8—24no—
59C11×C22⋊Q8—24no—
60C11×C22⋊Q8—42no—
61C11×C22⋊Q8—42no—
62C4×D4×C11—22no—
63C4×D4×C11—22no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4D411yescharacteristic
69C2×C11×C4⋊C4C2312yes—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4D411yescharacteristic
73C2×C11×C22⋊C4D411yescharacteristic
74C2×C42×C11—21no—
75C2×C42×C11C2311yescharacteristic
76C2×C22⋊Dic11—21no—
77C2×#4325—24no—
78C2×#4325—42no—
79C2×#4325—42no—
80#66992—28no—
81#66983—22no—
82#66983—22no—
83#66983—22no—
84#66983—22no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88#66979—22no—
89#66979—22no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—22no—
92C2×C4⋊Dic11—22no—
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×C4×Dic11—21no—
99C22×C11⋊C8C2312yes—
100C22×C11⋊C8C2312yes—
101#66951—28no—
102#66936—28no—
103(C22⋊D11)⋊C4—28no—
104C4×D44—22no—
105C4×D44D414yes—
106#66923—22no—
107#66923D414yes—
108C11×#95—21no—
109#66899—24no—
110#66899—24no—
111#66899—24no—
112C22⋊(C11⋊C8)—42no—
113C22⋊(C11⋊C8)—42no—
114#66873—24no—
115C4⋊(C11⋊C8)—22no—
116#66867—22no—
117#25582—111nomaximal, Sylow
118C24×C11C2×D411yescharacteristic
119C24×C11C2×D411yescharacteristic
120C23×D11—21no—
121C2×Q8×C11—22no—
122C2×Q8×C11—22no—
123C2×Q8×C11—22no—
124C2×Q8×C11—22no—
125C2×Q8×C11—22no—
126C2×Q8×C11—22no—
127C2×D4×C11—22no—
128C2×D4×C11—22no—
129C2×D4×C11—41no—
130C22×C4×C11—22no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2411yescharacteristic
145C2×C22⋊D11—24no—
146C2×C22⋊D11—24no—
147C2×C22⋊D11—42no—
148C2×C22⋊D11—42no—
149C2×C22⋊D11—82no—
150C22×Dic11—24no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—82no—
155C2×D44—21no—
156C2×D44—22no—
157C2×D44—22no—
158C2×D44C2×D412yes—
159C2×C4×D11—24no—
160C2×C4×D11—82no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—44no—
164C11×C4⋊C4—44no—
165C11×C4⋊C4—42no—
166C11×C4⋊C4—42no—
167C11×C4⋊C4#4114yes—
168C11×C22⋊C4—22no—
169C11×C22⋊C4—22no—
170C11×C22⋊C4—44no—
171C11×C22⋊C4—44no—
172C42×C11—42no—
173C42×C11C2×D412yes—
174C42×C11C2×D412yes—
175C22⋊Dic11—24no—
176#4325—48no—
177(C2×D11)⋊C4—24no—
178(C2×D11)⋊C4—24no—
179(C2×D11)⋊C4—24no—
180C4⋊Dic11—24no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11C2×D412yes—
185C4⋊Dic11C2×D412yes—
186C4⋊Dic11C2×D412yes—
187Dic11⋊C4—24no—
188Dic11⋊C4—24no—
189C4×Dic11—24no—
190C2×C11⋊C8—22no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8—22no—
194C2×C11⋊C8—22no—
195C2×C11⋊C8—22no—
196C2×#553—111no—
197C2×#491—111no—
198C2×#461—111no—
199#2542D1111yescharacteristic, complemented
200#2000—112no—
201#2000—112no—
202#1989—111no—
203#1955—111no—
204#1873—112no—
205#1872—112no—
206#1762—111no—
207C23×C11—21no—
208C23×C11—22no—
209C23×C11—21no—
210C23×C11—22no—
211C23×C11—21no—
212C23×C11—22no—
213C23×C11—21no—
214C23×C11—21no—
215C23×C11—22no—
216C23×C11#13712yes—
217C23×C11C22×D411yescharacteristic
218C22×D11—22no—
219C22×D11—42no—
220C22×D11—41no—
221C22×D11—41no—
222C22×D11—42no—
223Q8×C11—42no—
224Q8×C11—42no—
225Q8×C11—42no—
226Q8×C11—42no—
227D4×C11—44no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—22no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—24no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11#12012yes—
248C2×C4×C11#12012yes—
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C2×#4112yes—
252C2×C4×C11H(5,𝔽2)12yes—
253C22⋊D11—48no—
254C22⋊D11—84no—
255C2×Dic11—22no—
256C2×Dic11—22no—
257C2×Dic11—22no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—42no—
261C2×Dic11—42no—
262C2×Dic11—84no—
263D44—22no—
264D44—22no—
265D44—42no—
266C4×D11—84no—
267C11⋊C8—42no—
268C11⋊C8—42no—
269C22×SD16—112no—
270#553—224no—
271#553—224no—
272C2×C4⋊Q8C2×D1111yescharacteristic
273C2×#126—221no—
274C2×#125—111no—
275C2×#123—221no—
276C2×C22⋊Q8C2×D1112yes—
277C2×C22⋊Q8C2×D1112yes—
278C2×#121—111no—
279C2×#121—111no—
280C2×#121—221no—
281C2×C4×D4—111no—
282C2×C4×D4—221no—
283C2×C4×D4C2×D1111yescharacteristic
284C2×#117—111no—
285C22×C4⋊C4—111no—
286#491—224no—
287#461—224no—
288C2×C4⋊C8—111no—
289C2×#103—112no—
290C2×#103—112no—
291C2×#103—112no—
292C2×#102—112no—
293C2×C22⋊C8—112no—
294C2×C22⋊C8—112no—
295C2×#97—111no—
296#399—21no—
297#399—21no—
298#390—21no—
299#384—21no—
300C4×C4⋊C4C2×D1111yescharacteristic
301#340—112no—
302#340—112no—
303#340—112no—
304C22×C11—22no—
305C22×C11—24no—
306C22×C11—41no—
307C22×C11—41no—
308C22×C11—42no—
309C22×C11—41no—
310C22×C11—41no—
311C22×C11—41no—
312C22×C11—42no—
313C22×C11—42no—
314C22×C11C2×#12011yescharacteristic
315C22×C11#54612yes—
316C22×C11C2×#13711yescharacteristic
317C22×C11#57511yescharacteristic
318C22×C11#57712yes—
319C2×D11—42no—
320C2×D11—42no—
321C2×D11—42no—
322C2×D11—82no—
323C2×D11—82no—
324C4×C11—22no—
325C4×C11—22no—
326C4×C11—41no—
327C4×C11—41no—
328C4×C11—44no—
329C4×C11—82no—
330C4×C11#53211yescharacteristic
331C4×C11#53511yescharacteristic
332C4×C11#55012yes—
333Dic11—42no—
334Dic11—42no—
335Dic11—42no—
336C22×Q8C22×D1112yes—
337C22×D4—111no—
338C22×D4—221no—
339C22×D4—221no—
340C22×D4C22⋊D1111yescharacteristic
341C23×C4—221no—
342C23×C4—221no—
343C23×C4C22×D1111yescharacteristic
344C23×C4C22×D1111yescharacteristic
345C2×SD16—224no—
346C2×SD16—442no—
347C2×SD16—442no—
348C22×C8—112no—
349C22×C8—112no—
350C4⋊Q8—22no—
351C4⋊Q8—22no—
352#126—228no—
353#125—114no—
354#125—222no—
355#123—228no—
356C22⋊Q8—24no—
357C22⋊Q8—24no—
358C22⋊Q8—42no—
359C22⋊Q8—42no—
360#121—222no—
361#121—222no—
362#121—222no—
363#121—222no—
364#121—228no—
365C4×D4—22no—
366C4×D4—22no—
367C4×D4—114no—
368C4×D4—228no—
369C4×D4—222no—
370#117—222no—
371#117—222no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—111no—
377C2×C4⋊C4—111no—
378C2×C4⋊C4—111no—
379C2×C4⋊C4—222no—
380C2×C4⋊C4—222no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4C22⋊D1111yescharacteristic
385C2×C4⋊C4C22×D1112yes—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—221no—
389C2×C22⋊C4—221no—
390C2×C22⋊C4—221no—
391C2×C22⋊C4—221no—
392C2×C22⋊C4C22⋊D1111yescharacteristic
393C2×C22⋊C4C22⋊D1111yescharacteristic
394C2×C42—21no—
395C2×C42—221no—
396C2×C42C22×D1111yescharacteristic
397C4⋊C8—222no—
398#103—224no—
399#103—224no—
400#103—224no—
401#102—224no—
402C22⋊C8—442no—
403C22⋊C8—442no—
404#97—222no—
405#95—21no—
406C2×C11—42no—
407C2×C11—81no—
408C2×C11#243111yescharacteristic
409C2×C11#300711yescharacteristic
410C2×C11#300911yescharacteristic
411C2×C11#330712yes—
412C2×C11#332012yes—
413D11—82no—
414C24—221no—
415C24C2×C22⋊D1111yescharacteristic
416C24C2×C22⋊D1111yescharacteristic
417C2×Q8—22no—
418C2×Q8—22no—
419C2×Q8—22no—
420C2×Q8—22no—
421C2×Q8—22no—
422C2×Q8—22no—
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—41no—
426C2×D4—112no—
427C2×D4—224no—
428C2×D4—224no—
429C2×D4—221no—
430C2×D4—222no—
431C2×D4—222no—
432C2×D4—442no—
433C2×D4—442no—
434C2×D4—882no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—221no—
446C22×C4—221no—
447C22×C4—221no—
448C22×C4—224no—
449C22×C4—224no—
450C22×C4—882no—
451C22×C4—882no—
452C22×C4C2×C22⋊D1111yescharacteristic
453C22×C4C2×C22⋊D1111yescharacteristic
454C22×C4C2×C22⋊D1111yescharacteristic
455C22×C4C2×C22⋊D1111yescharacteristic
456C22×C4C23×D1111yescharacteristic
457SD16—448no—
458C2×C8—222no—
459C2×C8—222no—
460C2×C8—222no—
461C2×C8—222no—
462C2×C8—222no—
463C2×C8—222no—
464C4⋊C4—22no—
465C4⋊C4—22no—
466C4⋊C4—44no—
467C4⋊C4—44no—
468C4⋊C4—42no—
469C4⋊C4—42no—
470C4⋊C4—112no—
471C4⋊C4—112no—
472C4⋊C4—112no—
473C4⋊C4—224no—
474C4⋊C4—224no—
475C4⋊C4—224no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4—221no—
479C4⋊C4#434114yes—
480C22⋊C4—22no—
481C22⋊C4—22no—
482C22⋊C4—44no—
483C22⋊C4—44no—
484C22⋊C4—224no—
485C22⋊C4—224no—
486C22⋊C4—224no—
487C22⋊C4—224no—
488C42—42no—
489C42—224no—
490C42D4×D1112yes—
491C42D4×D1112yes—
492C11#2558211yescharacteristic, complemented, Sylow
493C23—21no—
494C23—22no—
495C23—21no—
496C23—22no—
497C23—21no—
498C23—22no—
499C23—21no—
500C23—21no—
501C23—22no—
502C23—222no—
503C23—442no—
504C23—441no—
505C23—441no—
506C23—442no—
507C23#6699512yes—
508C23C22×C22⋊D1111yescharacteristic
509Q8—42no—
510Q8—42no—
511Q8—42no—
512Q8—42no—
513D4—44no—
514D4—222no—
515D4—222no—
516D4—448no—
517D4—442no—
518D4—884no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—22no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—24no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—222no—
539C2×C4—222no—
540C2×C4—222no—
541C2×C4—441no—
542C2×C4—441no—
543C2×C4—442no—
544C2×C4—442no—
545C2×C4—884no—
546C2×C4—884no—
547C2×C4#6699012yes—
548C2×C4#6699012yes—
549C2×C4C2×D4×D1111yescharacteristic
550C2×C4C2×D4×D1111yescharacteristic
551C2×C4C2×#434112yes—
552C2×C4#6703712yes—
553C8—442no—
554C8—442no—
555C22—22no—
556C22—24no—
557C22—42no—
558C22—41no—
559C22—41no—
560C22—42no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—42no—
565C22—442no—
566C22—442no—
567C22—442no—
568C22—882no—
569C22—882no—
570C22C2×#6699011yescharacteristic
571C22#1062333712yes—
572C22C2×#6699511yescharacteristic
573C22#1062335311yescharacteristic
574C22#1062336812yes—
575C4—22no—
576C4—22no—
577C4—44no—
578C4—41no—
579C4—41no—
580C4—82no—
581C4—442no—
582C4—442no—
583C4—442no—
584C4#1062324611yescharacteristic
585C4#1062324711yescharacteristic
586C4#1062324912yes—
587C2—42no—
588C2—81no—
589C2—882no—
590C2#1307223211yescharacteristic
591C2#1307787411yescharacteristic
592C2#1307789111yescharacteristic
593C2#1308059212yes—
594C2#1308078712yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2542C2
socleC23×C11C22×D4
prime radicalC2×#10623096C2
hypercenter#2542D11
hypocenterC11#25582
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2542

Complements

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

NH ≅ G/Ntype
2. C2×#10622695C2semidirect
3. C2×#10622696C2semidirect
4. #13069617C2semidirect
5. #13069617C2semidirect
6. #13069573C2semidirect
7. #13069415C2semidirect
8. #13068929C2semidirect
9. #13068924C2semidirect
10. #13068444C2semidirect
11. C11×#2542C2semidirect
199. #2542D11semidirect
492. C11#25582semidirect

Maximal subgroups

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

subgroupindex
C2×#106230962
C2×#106226952
C2×#106226962
#130696172
#130695732
#130694152
#130689292
#130689242
#130684442
C11×#25422
#2558211