Finite Group Databasebeta

← #14807110

Subgroups — #14807110

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×#10622682C211yesmaximal, characteristic, complemented
2C2×#10622632C211yesmaximal, characteristic, complemented
3#13073569C211yesmaximal, characteristic, complemented
4#13069619C212yesmaximal, complemented
5#13069619C212yesmaximal, complemented
6#13069574C211yesmaximal, characteristic, complemented
7#13069415C211yesmaximal, characteristic, complemented
8#13068928C212yesmaximal, complemented
9#13068923C212yesmaximal, complemented
10#13068441C211yesmaximal, characteristic, complemented
11C2×C11×#553C211yesmaximal, characteristic
12C11×#553—24no—
13C11×#553—24no—
14C2×C11×#126—21no—
15C2×C11×#125C2211yescharacteristic
16C2×C11×#123—21no—
17C2×C11×#121—21no—
18C2×C11×#121C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C2×C4×D4×C11—21no—
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×C11×#117C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic
25C22×#4324C2212yes—
26C2×#66977C2212yes—
27C2×#66977C2212yes—
28C2×#66922C2211yescharacteristic
29#10622834—21no—
30C2×#66896C2212yes—
31C2×C22⋊(C11⋊C8)C2212yes—
32C2×C22⋊(C11⋊C8)C2212yes—
33#10622682—24no—
34#10622632—24no—
35#10622589—21no—
36C2×#66874C2212yes—
37C2×#66874C2212yes—
38C2×#66874C2212yes—
39#10622562—21no—
40#10622562—21no—
41C4×C4⋊Dic11C2211yescharacteristic
42C2×C4⋊(C11⋊C8)C2211yescharacteristic
43C2×#66867C2211yescharacteristic
44#10622167C2212yes—
45#10622167C2212yes—
46#10622167C2212yes—
47C22×D4×C11—21no—
48C22×D4×C11—21no—
49C22×D4×C11D411yescharacteristic
50C22×D4×C11C2311yescharacteristic
51C23×C4×C11—21no—
52C23×C4×C11—21no—
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C22×Dic22C2312yes—
56C11×#126—28no—
57C11×#125—22no—
58C11×#125D414yes—
59C11×#123—28no—
60C11×#121—28no—
61C11×#121—22no—
62C11×#121—22no—
63C11×#121—22no—
64C11×#121—22no—
65C4×D4×C11—28no—
66C4×D4×C11—22no—
67C4×D4×C11—22no—
68C4×D4×C11—22no—
69C4×D4×C11D414yes—
70C11×#117—22no—
71C11×#117—22no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4D411yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4D411yescharacteristic
86C2×C11×C22⋊C4D411yescharacteristic
87C2×C42×C11—21no—
88C2×C42×C11C2311yescharacteristic
89C2×C22⋊Dic11—22no—
90C2×C22⋊Dic11—22no—
91C2×#4324—24no—
92C2×#4324—42no—
93C2×#4324—42no—
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11C2312yes—
97#66977—24no—
98#66977—24no—
99#66977—42no—
100#66977—42no—
101C2×Dic11⋊C4—22no—
102C2×Dic11⋊C4—22no—
103C2×C4×Dic11—21no—
104C22×C11⋊C8C2312yes—
105C22×C11⋊C8C2312yes—
106#66922—22no—
107#66922—22no—
108#66896—24no—
109C11⋊#95—21no—
110C22⋊(C11⋊C8)—42no—
111C22⋊(C11⋊C8)—42no—
112#66874—24no—
113#66874—24no—
114#66874—24no—
115C4⋊(C11⋊C8)—22no—
116#66867—22no—
117#25582—111nomaximal, Sylow
118C24×C11—21no—
119C24×C11C2×D411yescharacteristic
120C24×C11C2×D411yescharacteristic
121C2×D4×C11—24no—
122C2×D4×C11—22no—
123C2×D4×C11—24no—
124C2×D4×C11—22no—
125C2×D4×C11—21no—
126C2×D4×C11—22no—
127C2×D4×C11—22no—
128C2×D4×C11—41no—
129C2×D4×C11—42no—
130C2×D4×C11—42no—
131C2×D4×C11—82no—
132C2×D4×C11C2×D412yes—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—24no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—24no—
146C22×C4×C11—82no—
147C22×C4×C11—82no—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2411yescharacteristic
153C22×Dic11—22no—
154C22×Dic11—22no—
155C2×Dic22—22no—
156C2×Dic22—22no—
157C2×Dic22—22no—
158C2×Dic22—22no—
159C2×Dic22—22no—
160C2×Dic22—22no—
161C11×C4⋊C4—24no—
162C11×C4⋊C4—24no—
163C11×C4⋊C4—24no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4C2×D412yes—
169C11×C4⋊C4C2×D412yes—
170C11×C4⋊C4C2×D412yes—
171C11×C22⋊C4—24no—
172C11×C22⋊C4—24no—
173C11×C22⋊C4—24no—
174C11×C22⋊C4—24no—
175C11×C22⋊C4—22no—
176C11×C22⋊C4—22no—
177C42×C11—24no—
178C42×C11C2×D412yes—
179C42×C11C2×D412yes—
180C22⋊Dic11—44no—
181C22⋊Dic11—44no—
182#4324—48no—
183C4⋊Dic11—22no—
184C4⋊Dic11—42no—
185C4⋊Dic11—42no—
186C4⋊Dic11#4114yes—
187Dic11⋊C4—44no—
188Dic11⋊C4—44no—
189C4×Dic11—42no—
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×#553D1111yescharacteristic
197C2×#491—111no—
198C2×#461—111no—
199#2542—111no—
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—22no—
214C23×C11—21no—
215C23×C11—21no—
216C23×C11—22no—
217C23×C11—42no—
218C23×C11—41no—
219C23×C11—41no—
220C23×C11—42no—
221C23×C11#13712yes—
222C23×C11C22×D411yescharacteristic
223D4×C11—22no—
224D4×C11—22no—
225D4×C11—44no—
226D4×C11—48no—
227D4×C11—42no—
228D4×C11—84no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—22no—
232C2×C4×C11—21no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—21no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—42no—
242C2×C4×C11—42no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—84no—
250C2×C4×C11—84no—
251C2×C4×C11#12012yes—
252C2×C4×C11#12012yes—
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C2×#4112yes—
256C2×C4×C11H(5,𝔽2)12yes—
257C2×Dic11—24no—
258C2×Dic11—42no—
259C2×Dic11—42no—
260C2×Dic11—42no—
261C2×Dic11—42no—
262C2×Dic11—42no—
263Dic22—42no—
264Dic22—42no—
265Dic22—42no—
266Dic22—42no—
267C11⋊C8—42no—
268C11⋊C8—42no—
269C22×SD16—112no—
270#553—24no—
271#553—24no—
272C2×C4⋊Q8—111no—
273C2×#126—21no—
274C2×#125C2×D1111yescharacteristic
275C2×#123—21no—
276C2×C22⋊Q8—112no—
277C2×C22⋊Q8—112no—
278C2×#121—21no—
279C2×#121C2×D1111yescharacteristic
280C2×#121C2×D1111yescharacteristic
281C2×C4×D4—21no—
282C2×C4×D4C2×D1111yescharacteristic
283C2×C4×D4C2×D1111yescharacteristic
284C2×#117C2×D1111yescharacteristic
285C22×C4⋊C4C2×D1111yescharacteristic
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—221no—
297#399—221no—
298#390—221no—
299#384—221no—
300C4×C4⋊C4—111no—
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—42no—
311C22×C11—41no—
312C22×C11—42no—
313C22×C11—42no—
314C22×C11—41no—
315C22×C11—42no—
316C22×C11—42no—
317C22×C11—82no—
318C22×C11—82no—
319C22×C11C2×#12011yescharacteristic
320C22×C11#54612yes—
321C22×C11C2×#13711yescharacteristic
322C22×C11#57511yescharacteristic
323C22×C11#57712yes—
324C4×C11—22no—
325C4×C11—22no—
326C4×C11—41no—
327C4×C11—41no—
328C4×C11—42no—
329C4×C11—42no—
330C4×C11—42no—
331C4×C11#53211yescharacteristic
332C4×C11#53511yescharacteristic
333C4×C11#55012yes—
334Dic11—44no—
335Dic11—82no—
336C22×Q8—112no—
337C22×D4—21no—
338C22×D4—21no—
339C22×D4C22⋊D1111yescharacteristic
340C22×D4C22×D1111yescharacteristic
341C23×C4—21no—
342C23×C4—21no—
343C23×C4C22×D1111yescharacteristic
344C23×C4C22×D1111yescharacteristic
345C2×SD16—224no—
346C2×SD16—442no—
347C2×SD16—442no—
348C22×C8—112no—
349C22×C8—112no—
350C4⋊Q8—222no—
351C4⋊Q8—222no—
352#126—28no—
353#125—22no—
354#125C22⋊D1114yes—
355#123—28no—
356C22⋊Q8—224no—
357C22⋊Q8—224no—
358C22⋊Q8—442no—
359C22⋊Q8—442no—
360#121—28no—
361#121—22no—
362#121—22no—
363#121—22no—
364#121—22no—
365C4×D4—28no—
366C4×D4—22no—
367C4×D4—22no—
368C4×D4—22no—
369C4×D4C22⋊D1114yes—
370#117—22no—
371#117—22no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—112no—
378C2×C4⋊C4—222no—
379C2×C4⋊C4—222no—
380C2×C4⋊C4—221no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4C22⋊D1111yescharacteristic
383C2×C4⋊C4C22×D1111yescharacteristic
384C2×C4⋊C4C22×D1111yescharacteristic
385C2×C4⋊C4C22×D1111yescharacteristic
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—222no—
391C2×C22⋊C4—222no—
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—221no—
406C2×C11—42no—
407C2×C11—81no—
408C2×C11—82no—
409C2×C11#243111yescharacteristic
410C2×C11#300711yescharacteristic
411C2×C11#300911yescharacteristic
412C2×C11#330712yes—
413C2×C11#332012yes—
414C24—21no—
415C24C2×C22⋊D1111yescharacteristic
416C24C2×C22⋊D1111yescharacteristic
417C2×Q8—222no—
418C2×Q8—222no—
419C2×Q8—222no—
420C2×Q8—222no—
421C2×Q8—222no—
422C2×Q8—222no—
423C2×D4—24no—
424C2×D4—22no—
425C2×D4—24no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—21no—
430C2×D4—41no—
431C2×D4—42no—
432C2×D4—42no—
433C2×D4—82no—
434C2×D4C2×C22⋊D1112yes—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—24no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—24no—
448C22×C4—82no—
449C22×C4—82no—
450C22×C4—222no—
451C22×C4—222no—
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—24no—
465C4⋊C4—24no—
466C4⋊C4—24no—
467C4⋊C4—22no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—114no—
472C4⋊C4—222no—
473C4⋊C4—444no—
474C4⋊C4—444no—
475C4⋊C4—442no—
476C4⋊C4—442no—
477C4⋊C4C2×C22⋊D1112yes—
478C4⋊C4C2×C22⋊D1112yes—
479C4⋊C4C2×C22⋊D1112yes—
480C22⋊C4—24no—
481C22⋊C4—24no—
482C22⋊C4—24no—
483C22⋊C4—24no—
484C22⋊C4—22no—
485C22⋊C4—22no—
486C22⋊C4—444no—
487C22⋊C4—444no—
488C42—24no—
489C42—442no—
490C42C2×C22⋊D1112yes—
491C42C2×C22⋊D1112yes—
492C11#2558211yescharacteristic, complemented, Sylow
493C23—21no—
494C23—22no—
495C23—22no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—22no—
500C23—22no—
501C23—21no—
502C23—22no—
503C23—41no—
504C23—41no—
505C23—42no—
506C23—42no—
507C23#6700412yes—
508C23C22×C22⋊D1111yescharacteristic
509Q8—442no—
510Q8—442no—
511Q8—442no—
512Q8—442no—
513D4—22no—
514D4—22no—
515D4—44no—
516D4—48no—
517D4—42no—
518D4—84no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—21no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—21no—
528C2×C4—22no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—84no—
540C2×C4—84no—
541C2×C4—224no—
542C2×C4—442no—
543C2×C4—442no—
544C2×C4—442no—
545C2×C4—442no—
546C2×C4—442no—
547C2×C4#6700612yes—
548C2×C4#6700612yes—
549C2×C4#41×D1112yes—
550C2×C4#6704212yes—
551C2×C4C22×C22⋊D1111yescharacteristic
552C2×C4C22×C22⋊D1111yescharacteristic
553C8—442no—
554C8—442no—
555C22—22no—
556C22—24no—
557C22—42no—
558C22—41no—
559C22—41no—
560C22—42no—
561C22—41no—
562C22—42no—
563C22—41no—
564C22—42no—
565C22—42no—
566C22—41no—
567C22—42no—
568C22—82no—
569C22—82no—
570C22#1062335311yescharacteristic
571C22C2×#6700411yescharacteristic
572C22#1062336012yes—
573C22#1062336712yes—
574C22C2×#6700611yescharacteristic
575C4—22no—
576C4—22no—
577C4—41no—
578C4—41no—
579C4—42no—
580C4—42no—
581C4—42no—
582C4—444no—
583C4—882no—
584C4#1062336111yescharacteristic
585C4#1062336311yescharacteristic
586C4#1062336512yes—
587C2—42no—
588C2—81no—
589C2—82no—
590C2#1307223111yescharacteristic
591C2#1307787611yescharacteristic
592C2#1307789311yescharacteristic
593C2#1308058612yes—
594C2#1308078112yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#553C2
socleC23×C11C22×D4
hypercenterC2×#553D11
hypocenterC11#25582
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#10622682C2semidirect
2. C2×#10622632C2semidirect
3. #13073569C2semidirect
4. #13069619C2semidirect
5. #13069619C2semidirect
6. #13069574C2semidirect
7. #13069415C2semidirect
8. #13068928C2semidirect
9. #13068923C2semidirect
10. #13068441C2semidirect
492. C11#25582semidirect

Maximal subgroups

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

subgroupindex
C2×#106226822
C2×#106226322
#130735692
#130696192
#130695742
#130694152
#130689282
#130689232
#130684412
C2×C11×#5532
#2558211