Finite Group Databasebeta

← #14770521

Subgroups — #14770521

Order 2816.

1412 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623083C211yesmaximal, characteristic
2C22⋊C4×Dic22C212yesmaximal, complemented
3#13069452C212yesmaximal, complemented
4#13069450C214yesmaximal, complemented
5#13068604C211yesmaximal, characteristic, complemented
6#13068603C212yesmaximal, complemented
7#13068403C212yesmaximal, complemented
8C4×C11×#99C211yesmaximal, characteristic, complemented
9C22×#4339C411yescharacteristic, complemented
10C23×Dic22C2211yescharacteristic
11C2×C4×D4×C11C2211yescharacteristic
12C2×#66992C2212yes—
13C2×#66983C2211yescharacteristic
14C2×#66977C411yescharacteristic, complemented
15#10623083—22no—
16#10623083—24no—
17#10623083—22no—
18C2×#66949C412yescomplemented
19C2×#66938C412yescomplemented
20C2×(C22⋊D11)⋊C4C2212yes—
21C2×#66928C411yescharacteristic, complemented
22C2×C4×Dic22—22no—
23C2×C4×Dic22C411yescharacteristic, complemented
24C2×C11×#99C2212yes—
25C4×C11×C22⋊C4C2212yes—
26C2×#66898C2212yes—
27#10622825C2212yes—
28C2×#66870C2214yes—
29C2×#66870C2214yes—
30#10622555C2214yes—
31C22⋊C4×Dic11C2214yes—
32#10622542—22no—
33#10622259—24no—
34C11×#342C2211yescharacteristic
35C11×#342C2211yescharacteristic
36#10622164C2212yes—
37C22×D4×C11C2311yescharacteristic
38C23×C4×C11C2×C411yescharacteristic
39C23×C4×C11C2311yescharacteristic
40C22×C22⋊D11C2×C412yes—
41C22×C22⋊D11C2312yes—
42C23×Dic11C2312yes—
43C2×#4339—22no—
44C2×#4339—21no—
45C2×#4339—21no—
46C2×#4339—44no—
47C22×D44C2×C411yescharacteristic
48C22×C4×D11C2×C412yes—
49C22×Dic22—44no—
50C22×Dic22C2×C411yescharacteristic
51C22×Dic22C2×C411yescharacteristic
52C22×Dic22C2×C412yes—
53C22×Dic22D412yes—
54C22×Dic22D414yes—
55C22×Dic22D412yes—
56C4×D4×C11—22no—
57C4×D4×C11—22no—
58C2×C11×C4⋊C4C2×C411yescharacteristic
59C2×C11×C22⋊C4C2×C411yescharacteristic
60C2×C11×C22⋊C4C2312yes—
61C2×C11×C22⋊C4C2311yescharacteristic
62C2×C11×C22⋊C4C2312yes—
63C2×C42×C11—22no—
64C2×C42×C11C2×C411yescharacteristic
65C2×C22⋊Dic11C2×C412yes—
66C2×C22⋊Dic11C2314yes—
67#66992—24no—
68#66992—24no—
69#66983—22no—
70#66983—22no—
71C2×(C2×D11)⋊C4C2×C412yes—
72C2×(C2×D11)⋊C4C2×C412yes—
73C2×(C2×D11)⋊C4C2×C412yes—
74C2×C4⋊Dic11—22no—
75C2×C4⋊Dic11C2×C411yescharacteristic
76#66977—22no—
77#66977—22no—
78C2×Dic11⋊C4—24no—
79C2×Dic11⋊C4C2×C412yes—
80C2×Dic11⋊C4C2×C412yes—
81C2×C4×Dic11—24no—
82C2×C4×Dic11C2×C412yes—
83#66949—24no—
84#66949—24no—
85#66938—24no—
86#66938—24no—
87(C22⋊D11)⋊C4—24no—
88(C22⋊D11)⋊C4—24no—
89#66928—22no—
90#66928—22no—
91C4×Dic22—21no—
92C4×Dic22—22no—
93C4×Dic22—21no—
94C4×Dic22—48no—
95C11×#99—24no—
96C11×#95—22no—
97#66898—42no—
98C11⋊#95—22no—
99C11⋊#95—24no—
100C11⋊#95—24no—
101#66870—28no—
102#66870—44no—
103#22534—111nomaximal, Sylow
104C24×C11C22×C411yescharacteristic
105C24×C11C2411yescharacteristic
106C23×D11C22×C412yes—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11—21no—
110C2×D4×C11—21no—
111C22×C4×C11—22no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—22no—
115C22×C4×C11—42no—
116C22×C4×C11—42no—
117C22×C4×C11C22×C411yescharacteristic
118C22×C4×C11C22×C411yescharacteristic
119C22×C4×C11C22×C411yescharacteristic
120C22×C4×C11C22×C411yescharacteristic
121C22×C4×C11C22×C411yescharacteristic
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2×D412yes—
124C2×C22⋊D11—22no—
125C2×C22⋊D11—22no—
126C2×C22⋊D11—24no—
127C2×C22⋊D11—24no—
128C2×C22⋊D11—22no—
129C2×C22⋊D11—22no—
130C2×C22⋊D11—44no—
131C22×Dic11—24no—
132C22×Dic11—44no—
133C22×Dic11C22×C412yes—
134C22×Dic11C22×C412yes—
135C22×Dic11C22×C412yes—
136C22×Dic11C2×D414yes—
137C22×Dic11C2×D414yes—
138#4339—48no—
139#4339—44no—
140#4339—44no—
141C2×D44—21no—
142C2×D44—21no—
143C2×D44—42no—
144C2×C4×D11—22no—
145C2×C4×D11—22no—
146C2×C4×D11—44no—
147C2×Dic22—28no—
148C2×Dic22—24no—
149C2×Dic22—42no—
150C2×Dic22—44no—
151C2×Dic22—44no—
152C2×Dic22—48no—
153C2×Dic22C22⋊C412yes—
154C2×Dic22C22⋊C411yescharacteristic
155C2×Dic22C22⋊C412yes—
156C2×Dic22C22⋊C414yes—
157C2×Dic22C22⋊C412yes—
158C2×Dic22C22⋊C414yes—
159C2×Dic22C22⋊C411yescharacteristic
160C11×C4⋊C4—22no—
161C11×C22⋊C4—22no—
162C11×C22⋊C4—22no—
163C11×C22⋊C4—22no—
164C11×C22⋊C4—22no—
165C11×C22⋊C4—22no—
166C11×C22⋊C4#4114yescomplemented
167C42×C11—21no—
168C42×C11—21no—
169C42×C11—44no—
170C22⋊Dic11—24no—
171C22⋊Dic11—24no—
172C22⋊Dic11—24no—
173(C2×D11)⋊C4—24no—
174(C2×D11)⋊C4—24no—
175(C2×D11)⋊C4—24no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—44no—
179Dic11⋊C4—22no—
180Dic11⋊C4—22no—
181Dic11⋊C4—24no—
182Dic11⋊C4—48no—
183C4×Dic11—22no—
184C4×Dic11—22no—
185C4×Dic11—48no—
186C2×#548—111no—
187Q8×C22⋊C4—112no—
188#1964—114no—
189#1964—112no—
190#1799—112no—
191#1799—111no—
192C4×#99—112no—
193C4×#99D1111yescharacteristic, complemented
194C23×C11—21no—
195C23×C11—21no—
196C23×C11—21no—
197C23×C11—41no—
198C23×C11—41no—
199C23×C11—41no—
200C23×C11—41no—
201C23×C11C23×C411yescharacteristic
202C23×C11C22×D412yes—
203C23×C11C2×#4112yes—
204C23×C11H(5,𝔽2)11yescharacteristic
205C23×C112−1+411yescharacteristic
206C22×D11—22no—
207C22×D11—22no—
208C22×D11—22no—
209C22×D11—42no—
210C22×D11—42no—
211D4×C11—42no—
212D4×C11—42no—
213C2×C4×C11—24no—
214C2×C4×C11—22no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—24no—
221C2×C4×C11—41no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11C2×C22⋊C411yescharacteristic
233C2×C4×C11C2×C22⋊C412yes—
234C2×C4×C11C2×C22⋊C411yescharacteristic
235C22⋊D11—44no—
236C22⋊D11—44no—
237C22⋊D11—44no—
238C22⋊D11—44no—
239C2×Dic11—28no—
240C2×Dic11—24no—
241C2×Dic11—22no—
242C2×Dic11—22no—
243C2×Dic11—22no—
244C2×Dic11—42no—
245C2×Dic11—44no—
246C2×Dic11—44no—
247C2×Dic11—44no—
248C2×Dic11—44no—
249C2×Dic11C2×C22⋊C412yes—
250C2×Dic11C2×C22⋊C414yes—
251C2×Dic11C2×C22⋊C412yes—
252D44—42no—
253D44—42no—
254C4×D11—44no—
255C4×D11—44no—
256Dic22—24no—
257Dic22—22no—
258Dic22—28no—
259Dic22—24no—
260Dic22—44no—
261Dic22—42no—
262Dic22#9914yescomplemented
263C22×#41—111no—
264C23×Q8—111no—
265#548—222no—
266#548—222no—
267#548—224no—
268C2×#124—112no—
269C2×#124—111no—
270C2×C22⋊Q8—111no—
271C2×C22⋊Q8—112no—
272C2×#121—112no—
273C2×#121—111no—
274C2×C4×Q8—111no—
275C2×C4×Q8—222no—
276C2×C4×D4—112no—
277C2×C4×D4C2×D1111yescharacteristic
278C2×#99—114no—
279C2×#99—112no—
280C2×#99—114no—
281C2×#99C2×D1112yes—
282#391—224no—
283#391—222no—
284#380—112no—
285#380—114no—
286C4×C22⋊C4—114no—
287C4×C22⋊C4C2×D1112yes—
288#342—112no—
289#342C2×D1111yescharacteristic
290#342C2×D1111yescharacteristic
291C22×C11—22no—
292C22×C11—21no—
293C22×C11—22no—
294C22×C11—21no—
295C22×C11—42no—
296C22×C11—41no—
297C22×C11—41no—
298C22×C11—41no—
299C22×C11—41no—
300C22×C11—41no—
301C22×C11—81no—
302C22×C11—81no—
303C22×C11C22×C22⋊C411yescharacteristic
304C22×C11C4×#4111yescharacteristic
305C22×C11#52011yescharacteristic
306C22×C11#54812yes—
307C22×C11#55012yes—
308C2×D11—42no—
309C2×D11—42no—
310C2×D11—42no—
311C2×D11—82no—
312C2×D11—82no—
313C4×C11—21no—
314C4×C11—22no—
315C4×C11—44no—
316C4×C11—41no—
317C4×C11—41no—
318C4×C11—41no—
319C4×C11—82no—
320C4×C11C2×#9912yes—
321Dic11—22no—
322Dic11—24no—
323Dic11—42no—
324Dic11—84no—
325Dic11C2×#9914yes—
326C2×#41—221no—
327C2×#41—222no—
328C2×#41—221no—
329C2×#41—444no—
330C22×Q8—111no—
331C22×Q8—112no—
332C22×Q8—111no—
333C22×Q8—112no—
334C22×Q8—114no—
335C22×Q8—112no—
336C22×Q8—444no—
337C22×D4—112no—
338C22×D4—112no—
339C22×D4—111no—
340C22×D4C22×D1111yescharacteristic
341C23×C4—112no—
342C23×C4—112no—
343C23×C4C4×D1111yescharacteristic
344C23×C4C22×D1111yescharacteristic
345#124—222no—
346#124—222no—
347#124—224no—
348#124—224no—
349C22⋊Q8—224no—
350C22⋊Q8—224no—
351C22⋊Q8—222no—
352C22⋊Q8—222no—
353#121—224no—
354#121—224no—
355#121—222no—
356#121—222no—
357C4×Q8—221no—
358C4×Q8—222no—
359C4×Q8—221no—
360C4×Q8—448no—
361C4×D4—22no—
362C4×D4—22no—
363C4×D4—224no—
364C4×D4—224no—
365C2×C4⋊C4—112no—
366C2×C4⋊C4—112no—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—224no—
369C2×C4⋊C4—222no—
370C2×C4⋊C4C4×D1111yescharacteristic
371C2×C22⋊C4—112no—
372C2×C22⋊C4—112no—
373C2×C22⋊C4—112no—
374C2×C22⋊C4—112no—
375C2×C22⋊C4—114no—
376C2×C22⋊C4C4×D1111yescharacteristic
377C2×C22⋊C4C22×D1112yes—
378C2×C22⋊C4C22×D1111yescharacteristic
379C2×C22⋊C4C22×D1112yes—
380C2×C42—22no—
381C2×C42—112no—
382C2×C42—224no—
383C2×C42C4×D1111yescharacteristic
384#99—24no—
385#99—228no—
386#99—444no—
387#99—442no—
388#95—22no—
389#95—224no—
390#95—224no—
391#95—222no—
392C2×C11—22no—
393C2×C11—22no—
394C2×C11—21no—
395C2×C11—21no—
396C2×C11—81no—
397C2×C11#234111yescharacteristic
398C2×C11C22×#9911yescharacteristic
399C2×C11#288411yescharacteristic
400D11—82no—
401C24—112no—
402C24C2×C4×D1111yescharacteristic
403C24C23×D1111yescharacteristic
404#41—444no—
405#41—448no—
406#41—444no—
407C2×Q8—111no—
408C2×Q8—112no—
409C2×Q8—111no—
410C2×Q8—114no—
411C2×Q8—112no—
412C2×Q8—114no—
413C2×Q8—112no—
414C2×Q8—228no—
415C2×Q8—224no—
416C2×Q8—444no—
417C2×Q8—442no—
418C2×Q8—444no—
419C2×Q8—448no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—222no—
425C2×D4—222no—
426C2×D4—224no—
427C2×D4—224no—
428C2×D4—222no—
429C2×D4—222no—
430C2×D4—221no—
431C2×D4—221no—
432C2×D4—442no—
433C2×D4—444no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—112no—
441C22×C4—114no—
442C22×C4—112no—
443C22×C4—114no—
444C22×C4—112no—
445C22×C4—222no—
446C22×C4—222no—
447C22×C4—224no—
448C22×C4—444no—
449C22×C4—444no—
450C22×C4C2×C4×D1111yescharacteristic
451C22×C4C2×C4×D1111yescharacteristic
452C22×C4C2×C4×D1111yescharacteristic
453C22×C4C2×C4×D1111yescharacteristic
454C22×C4C2×C4×D1111yescharacteristic
455C22×C4D4×D1112yes—
456C22×C4D4×D1112yes—
457C4⋊C4—22no—
458C4⋊C4—224no—
459C4⋊C4—222no—
460C4⋊C4—222no—
461C4⋊C4—221no—
462C4⋊C4—221no—
463C4⋊C4—444no—
464C4⋊C4—448no—
465C22⋊C4—22no—
466C22⋊C4—22no—
467C22⋊C4—22no—
468C22⋊C4—22no—
469C22⋊C4—22no—
470C22⋊C4—224no—
471C22⋊C4—224no—
472C22⋊C4—224no—
473C22⋊C4—224no—
474C22⋊C4—224no—
475C22⋊C4—224no—
476C22⋊C4#433914yescomplemented
477C42—21no—
478C42—21no—
479C42—44no—
480C42—222no—
481C42—222no—
482C42—448no—
483C11#2253411yescharacteristic, complemented, Sylow
484C23—21no—
485C23—21no—
486C23—21no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23—222no—
492C23—222no—
493C23—222no—
494C23—442no—
495C23—442no—
496C23C22×C4×D1111yescharacteristic
497C23C2×#433912yes—
498C23C2×D4×D1112yes—
499C23#6704211yescharacteristic
500C23#6704311yescharacteristic
501Q8—114no—
502Q8—224no—
503Q8—228no—
504Q8—222no—
505Q8—224no—
506Q8—442no—
507Q8—444no—
508D4—42no—
509D4—42no—
510D4—442no—
511D4—444no—
512D4—444no—
513D4—444no—
514D4—444no—
515D4—442no—
516C2×C4—24no—
517C2×C4—22no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—24no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—112no—
536C2×C4—112no—
537C2×C4—114no—
538C2×C4—228no—
539C2×C4—224no—
540C2×C4—222no—
541C2×C4—222no—
542C2×C4—222no—
543C2×C4—444no—
544C2×C4—444no—
545C2×C4—444no—
546C2×C4—442no—
547C2×C4—444no—
548C2×C4—444no—
549C2×C4—444no—
550C2×C4C22⋊C4×D1111yescharacteristic
551C2×C4C22⋊C4×D1112yes—
552C2×C4C22⋊C4×D1111yescharacteristic
553C22—22no—
554C22—21no—
555C22—22no—
556C22—21no—
557C22—42no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—81no—
564C22—81no—
565C22—442no—
566C22—442no—
567C22—442no—
568C22—882no—
569C22—882no—
570C22C4×#433911yescharacteristic
571C22C2×C22⋊C4×D1111yescharacteristic
572C22#1062305411yescharacteristic
573C22#1062308312yes—
574C22#1062308412yes—
575C4—21no—
576C4—22no—
577C4—44no—
578C4—41no—
579C4—41no—
580C4—41no—
581C4—82no—
582C4—114no—
583C4—222no—
584C4—224no—
585C4—442no—
586C4—884no—
587C4D11×#9912yes—
588C2—22no—
589C2—22no—
590C2—21no—
591C2—21no—
592C2—81no—
593C2—882no—
594C2#1307145611yescharacteristic
595C2C2×D11×#9911yescharacteristic
596C2#1307707811yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingC4×C11×#99C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#10623083C2
cosocleC24×C11C24
hypercenterC4×#99D11
hypocenterC11#22534
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
2. C22⋊C4×Dic22C2semidirect
3. #13069452C2semidirect
4. #13069450C2semidirect
5. #13068604C2semidirect
6. #13068603C2semidirect
7. #13068403C2semidirect
8. C4×C11×#99C2semidirect
9. C22×#4339C4semidirect
14. C2×#66977C4semidirect
18. C2×#66949C4semidirect
19. C2×#66938C4semidirect
21. C2×#66928C4semidirect
23. C2×C4×Dic22C4semidirect
166. C11×C22⋊C4#41semidirect
193. C4×#99D11semidirect
262. Dic22#99semidirect
476. C22⋊C4#4339semidirect
483. C11#22534semidirect

Maximal subgroups

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

subgroupindex
C2×#106230832
C22⋊C4×Dic222
#130694522
#130694502
#130686042
#130686032
#130684032
C4×C11×#992
#2253411