Finite Group Databasebeta

← #14726443

Subgroups — #14726443

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
1#13077874C212yesmaximal, complemented
2#13071831C211yesmaximal, characteristic
3#13067590C212yesmaximal, complemented
4#13067573C212yesmaximal, complemented
5#13067556C212yesmaximal, complemented
6#13067539C212yesmaximal, complemented
7#13067136C212yesmaximal, complemented
8#13066954C211yesmaximal, characteristic, complemented
9C11×#3501C211yesmaximal, characteristic, complemented
10C22×#4339C2211yescharacteristic
11C11×#554—24no—
12C11×#554—22no—
13D4×Q8×C11—22no—
14C11×#544C2212yes—
15C11×#543—21no—
16C11×#543C2212yes—
17C11×#533—21no—
18C2×C11×C22⋊Q8—21no—
19C2×C11×C22⋊Q8C2212yes—
20C11×#518—21no—
21C2×C4×D4×C11C2211yescharacteristic
22C2×#66995—22no—
23C2×C4×C22⋊D11—21no—
24#10622836—21no—
25C4×C22⋊Dic11C2211yescharacteristic
26#10622820C2212yes—
27#10622663C2214yes—
28#10622660—24no—
29#10622659C2214yes—
30#10622604C2211yescharacteristic
31#10622592C2211yescharacteristic
32#10622579—22no—
33#10622573C2211yescharacteristic
34#10622572—21no—
35#10622560C2211yescharacteristic
36C4×(C2×D11)⋊C4—21no—
37#10622176C2214yes—
38#10622176C2214yes—
39#10622166C2212yes—
40#10622163C2212yes—
41C22×Q8×C11—21no—
42C22×Q8×C11D412yescomplemented
43C22×D4×C11D411yescharacteristic
44C23×C4×C11D411yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C22×C22⋊D11—21no—
47C22×C22⋊D11—21no—
48C2×#4339—22no—
49C2×#4339—22no—
50C2×#4339—44no—
51C22×D44C2311yescharacteristic
52C22×C4×D11—21no—
53C22×Dic22C2311yescharacteristic
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8—24no—
57C11×#125—22no—
58C11×#125—24no—
59C11×C22⋊Q8—22no—
60C11×C22⋊Q8—22no—
61C11×C22⋊Q8—24no—
62C11×C22⋊Q8—24no—
63C11×C22⋊Q8—24no—
64C11×C22⋊Q8—22no—
65C11×C22⋊Q8—22no—
66C11×C22⋊Q8—22no—
67C11×C22⋊Q8—22no—
68C11×C22⋊Q8—24no—
69C11×C22⋊Q8D414yescomplemented
70C11×C22⋊Q8C2314yes—
71C4×Q8×C11—22no—
72C4×Q8×C11—22no—
73C4×D4×C11—24no—
74C4×D4×C11—24no—
75C4×D4×C11—22no—
76C4×D4×C11—22no—
77C11×#117—22no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4D412yescomplemented
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4D411yescharacteristic
86C2×C11×C22⋊C4C2311yescharacteristic
87C2×C42×C11D411yescharacteristic
88C2×C22⋊Dic11—21no—
89C2×C22⋊Dic11—21no—
90C2×#4326—24no—
91#66995—48no—
92C2×#4325—24no—
93C4×C22⋊D11—44no—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4—21no—
96C2×(C2×D11)⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×C4×Dic11—21no—
99C2×#4318—22no—
100C11⋊#95—21no—
101C11⋊#95—21no—
102C11⋊#95C2311yescharacteristic
103C11⋊#95C2311yescharacteristic
104C22⋊(C11⋊C8)—22no—
105C22⋊(C11⋊C8)C2314yes—
106#66874—24no—
107#66873—24no—
108#18167—111nomaximal, Sylow
109C24×C11C2×D411yescharacteristic
110C24×C11C2×D411yescharacteristic
111C23×D11—21no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11—22no—
115C2×Q8×C11—44no—
116C2×Q8×C11—82no—
117C2×Q8×C11C2×D414yes—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—42no—
128C22×C4×C11—42no—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D412yes—
135C22×C4×C11C2411yescharacteristic
136C2×C22⋊D11—42no—
137C2×C22⋊D11—42no—
138C2×C22⋊D11—42no—
139C2×C22⋊D11—42no—
140C2×C22⋊D11—42no—
141C2×C22⋊D11—42no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145#4339—28no—
146#4339—44no—
147#4339—44no—
148#4339—44no—
149C2×D44—22no—
150C2×D44—42no—
151C2×C4×D11—24no—
152C2×C4×D11—42no—
153C2×C4×D11—41no—
154C2×C4×D11—41no—
155C2×Dic22—22no—
156C2×Dic22—42no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—24no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—24no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—24no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—24no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4C2×D414yes—
168C11×C22⋊C4—24no—
169C11×C22⋊C4—24no—
170C11×C22⋊C4—22no—
171C11×C22⋊C4—24no—
172C11×C22⋊C4—22no—
173C42×C11—24no—
174C42×C11—21no—
175C42×C11—21no—
176C22⋊Dic11—42no—
177C22⋊Dic11—42no—
178#4326—48no—
179#4325—48no—
180(C2×D11)⋊C4—42no—
181(C2×D11)⋊C4—42no—
182(C2×D11)⋊C4—42no—
183Dic11⋊C4—42no—
184C4×Dic11—42no—
185#4318—44no—
186C2×C11⋊C8—24no—
187#3501D1111yescharacteristic, complemented
188#3007—112no—
189#2388—111no—
190#1605—112no—
191#1602—112no—
192#1599—112no—
193#1596—112no—
194#1508—112no—
195#1465—111no—
196C23×C11—21no—
197C23×C11—21no—
198C23×C11—21no—
199C23×C11—21no—
200C23×C11—41no—
201C23×C11—41no—
202C23×C11—41no—
203C23×C11—41no—
204C23×C11#12012yes—
205C23×C11#13712yescomplemented
206C23×C11C22×D411yescharacteristic
207C22×D11—22no—
208C22×D11—41no—
209C22×D11—41no—
210C22×D11—41no—
211C22×D11—41no—
212C22×D11—41no—
213C22×D11—41no—
214Q8×C11—44no—
215Q8×C11—44no—
216Q8×C11—82no—
217Q8×C11—82no—
218D4×C11—28no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—24no—
222C2×C4×C11—22no—
223C2×C4×C11—21no—
224C2×C4×C11—24no—
225C2×C4×C11—24no—
226C2×C4×C11—21no—
227C2×C4×C11—41no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—81no—
233C2×C4×C11—82no—
234C2×C4×C11—82no—
235C2×C4×C11—82no—
236C2×C4×C11—82no—
237C2×C4×C11#12011yescharacteristic
238C2×C4×C11#12011yescharacteristic
239C2×C4×C11#13712yescomplemented
240C2×C4×C11C22×D412yes—
241C22⋊D11—48no—
242C22⋊D11—48no—
243C2×Dic11—22no—
244C2×Dic11—22no—
245C2×Dic11—41no—
246C2×Dic11—41no—
247C2×Dic11—41no—
248C2×Dic11—41no—
249C2×Dic11—41no—
250C2×Dic11—41no—
251C2×Dic11—41no—
252D44—24no—
253D44—42no—
254C4×D11—44no—
255C4×D11—44no—
256Dic22—24no—
257Dic22—42no—
258C11⋊C8—44no—
259C22×#41—111no—
260C2×#137—222no—
261#554—24no—
262#554—22no—
263D4×Q8—22no—
264#544C2×D1112yes—
265#543—21no—
266#543C2×D1112yes—
267#533—21no—
268C2×C22⋊Q8—21no—
269C2×C22⋊Q8C2×D1112yes—
270#518—21no—
271C2×C4×D4—221no—
272C2×C4×D4C2×D1111yescharacteristic
273#452—224no—
274#451—114no—
275#450—114no—
276#417—222no—
277#407—112no—
278#395—111no—
279#394—111no—
280#394—221no—
281#393—111no—
282#392—111no—
283#392—221no—
284C4×C22⋊C4—111no—
285C4×C22⋊C4—221no—
286#328—114no—
287#328—114no—
288#324—112no—
289#323—112no—
290C22×C11—21no—
291C22×C11—21no—
292C22×C11—22no—
293C22×C11—22no—
294C22×C11—22no—
295C22×C11—22no—
296C22×C11—42no—
297C22×C11—41no—
298C22×C11—41no—
299C22×C11—81no—
300C22×C11—81no—
301C22×C11—81no—
302C22×C11C2×#12011yescharacteristic
303C22×C11C2×#13711yescharacteristic
304C22×C11C2×#13711yescharacteristic
305C2×D11—42no—
306C2×D11—42no—
307C2×D11—42no—
308C2×D11—81no—
309C2×D11—81no—
310C2×D11—81no—
311C2×D11—81no—
312C4×C11—22no—
313C4×C11—21no—
314C4×C11—22no—
315C4×C11—41no—
316C4×C11—44no—
317C4×C11—41no—
318C4×C11—44no—
319C4×C11B(4,𝔽2)12yes—
320Dic11—42no—
321Dic11—42no—
322Dic11—81no—
323C2×#41—222no—
324C2×#41—222no—
325C2×#41—444no—
326C22×Q8—21no—
327C22×Q8—111no—
328C22×Q8C22⋊D1112yescomplemented
329C22×D4—111no—
330C22×D4—221no—
331C22×D4—221no—
332C22×D4C22⋊D1111yescharacteristic
333C23×C4—221no—
334C23×C4C22⋊D1111yescharacteristic
335C23×C4C22×D1111yescharacteristic
336#137—448no—
337C2×Q16—224no—
338C2×SD16—224no—
339C2×M16—222no—
340C4⋊Q8—21no—
341C4⋊Q8—21no—
342C4⋊Q8—24no—
343#125—22no—
344#125—24no—
345C22⋊Q8—22no—
346C22⋊Q8—22no—
347C22⋊Q8—24no—
348C22⋊Q8—24no—
349C22⋊Q8—24no—
350C22⋊Q8—22no—
351C22⋊Q8—22no—
352C22⋊Q8—22no—
353C22⋊Q8—22no—
354C22⋊Q8—24no—
355C22⋊Q8C22⋊D1114yescomplemented
356C22⋊Q8C22×D1114yes—
357C4×Q8—22no—
358C4×Q8—22no—
359C4×D4—24no—
360C4×D4—24no—
361C4×D4—22no—
362C4×D4—22no—
363C4×D4—444no—
364#117—22no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—221no—
369C2×C4⋊C4C22⋊D1112yescomplemented
370C2×C4⋊C4C22×D1111yescharacteristic
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—221no—
374C2×C22⋊C4—221no—
375C2×C22⋊C4—221no—
376C2×C22⋊C4—221no—
377C2×C22⋊C4—221no—
378C2×C22⋊C4C22⋊D1111yescharacteristic
379C2×C22⋊C4C22×D1111yescharacteristic
380C2×C42—221no—
381C2×C42C22⋊D1111yescharacteristic
382#103—224no—
383#102—224no—
384C22⋊C8—114no—
385C22⋊C8—222no—
386#95—111no—
387#95—111no—
388#95—221no—
389#95—221no—
390C2×C11—21no—
391C2×C11—21no—
392C2×C11—42no—
393C2×C11—42no—
394C2×C11#300411yescharacteristic
395C2×C11#301811yescharacteristic
396C2×C11C2×B(4,𝔽2)11yescharacteristic
397D11—82no—
398C24—221no—
399C24C2×C22⋊D1111yescharacteristic
400C24C2×C22⋊D1111yescharacteristic
401#41—228no—
402#41—444no—
403#41—444no—
404#41—444no—
405C2×Q8—22no—
406C2×Q8—22no—
407C2×Q8—22no—
408C2×Q8—44no—
409C2×Q8—82no—
410C2×Q8—222no—
411C2×Q8—442no—
412C2×Q8C2×C22⋊D1114yes—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—222no—
417C2×D4—442no—
418C2×D4—442no—
419C2×D4—442no—
420C2×D4—442no—
421C2×D4—442no—
422C2×D4—442no—
423C2×D4—442no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—224no—
433C22×C4—221no—
434C22×C4—221no—
435C22×C4—221no—
436C22×C4—442no—
437C22×C4—441no—
438C22×C4—441no—
439C22×C4C2×C22⋊D1111yescharacteristic
440C22×C4C2×C22⋊D1111yescharacteristic
441C22×C4C2×C22⋊D1112yes—
442C22×C4C2×C22⋊D1111yescharacteristic
443C22×C4C2×C22⋊D1111yescharacteristic
444C22×C4C2×C22⋊D1112yes—
445C22×C4C23×D1111yescharacteristic
446Q16—448no—
447SD16—448no—
448M16—444no—
449C2×C8—224no—
450C4⋊C4—22no—
451C4⋊C4—24no—
452C4⋊C4—22no—
453C4⋊C4—22no—
454C4⋊C4—24no—
455C4⋊C4—22no—
456C4⋊C4—24no—
457C4⋊C4—22no—
458C4⋊C4—24no—
459C4⋊C4—22no—
460C4⋊C4—442no—
461C4⋊C4C2×C22⋊D1114yes—
462C22⋊C4—24no—
463C22⋊C4—24no—
464C22⋊C4—22no—
465C22⋊C4—24no—
466C22⋊C4—22no—
467C22⋊C4—442no—
468C22⋊C4—442no—
469C22⋊C4—442no—
470C22⋊C4—442no—
471C22⋊C4—442no—
472C42—24no—
473C42—21no—
474C42—21no—
475C42—442no—
476C11#1816711yescharacteristic, complemented, Sylow
477C23—21no—
478C23—21no—
479C23—21no—
480C23—21no—
481C23—41no—
482C23—41no—
483C23—41no—
484C23—41no—
485C23—222no—
486C23—441no—
487C23—441no—
488C23—441no—
489C23—441no—
490C23—441no—
491C23—441no—
492C23#6699512yescomplemented
493C23#6700612yes—
494C23C22×C22⋊D1111yescharacteristic
495Q8—44no—
496Q8—44no—
497Q8—82no—
498Q8—82no—
499Q8—224no—
500Q8—442no—
501D4—28no—
502D4—224no—
503D4—442no—
504D4—448no—
505D4—448no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—22no—
509C2×C4—24no—
510C2×C4—21no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—21no—
514C2×C4—42no—
515C2×C4—41no—
516C2×C4—42no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—81no—
520C2×C4—82no—
521C2×C4—82no—
522C2×C4—82no—
523C2×C4—82no—
524C2×C4—222no—
525C2×C4—222no—
526C2×C4—444no—
527C2×C4—441no—
528C2×C4—441no—
529C2×C4—441no—
530C2×C4—441no—
531C2×C4—444no—
532C2×C4—441no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4#6699512yescomplemented
536C2×C4#6700611yescharacteristic
537C2×C4#6700611yescharacteristic
538C2×C4C22×C22⋊D1112yes—
539C8—444no—
540C22—21no—
541C22—21no—
542C22—22no—
543C22—22no—
544C22—22no—
545C22—22no—
546C22—42no—
547C22—41no—
548C22—41no—
549C22—81no—
550C22—81no—
551C22—81no—
552C22—442no—
553C22—442no—
554C22—442no—
555C22—881no—
556C22—881no—
557C22—881no—
558C22—881no—
559C22C2×#6699511yescharacteristic
560C22C2×#6699511yescharacteristic
561C22C2×#6700611yescharacteristic
562C4—22no—
563C4—22no—
564C4—21no—
565C4—41no—
566C4—44no—
567C4—41no—
568C4—44no—
569C4—442no—
570C4—442no—
571C4—881no—
572C4#1062285712yes—
573C2—21no—
574C2—21no—
575C2—42no—
576C2—42no—
577C2—882no—
578C2#1307785011yescharacteristic
579C2#1307796511yescharacteristic
580C2C2×#1062285711yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3501C2
socleC22×C11C2×#120
prime radical#13071831C2
hypercenter#3501D11
hypocenterC11#18167
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3501

Complements

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

NH ≅ G/Ntype
1. #13077874C2semidirect
3. #13067590C2semidirect
4. #13067573C2semidirect
5. #13067556C2semidirect
6. #13067539C2semidirect
7. #13067136C2semidirect
8. #13066954C2semidirect
9. C11×#3501C2semidirect
42. C22×Q8×C11D4semidirect
69. C11×C22⋊Q8D4semidirect
81. C2×C11×C4⋊C4D4semidirect
187. #3501D11semidirect
205. C23×C11#137semidirect
239. C2×C4×C11#137semidirect
328. C22×Q8C22⋊D11semidirect
355. C22⋊Q8C22⋊D11semidirect
369. C2×C4⋊C4C22⋊D11semidirect
476. C11#18167semidirect
492. C23#66995semidirect
535. C2×C4#66995semidirect

Maximal subgroups

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

subgroupindex
#130778742
#130718312
#130675902
#130675732
#130675562
#130675392
#130671362
#130669542
C11×#35012
#1816711