Finite Group Databasebeta

← #14719813

Subgroups — #14719813

Order 2816.

976 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623171C211yesmaximal, characteristic
2#13077655C211yesmaximal, characteristic, complemented
3#13077638C211yesmaximal, characteristic, complemented
4#13066980C211yesmaximal, characteristic, complemented
5#13066978C212yesmaximal, complemented
6#13066965C211yesmaximal, characteristic, complemented
7#13066963C212yesmaximal, complemented
8#13066962C211yesmaximal, characteristic, complemented
9#13066938C212yesmaximal, complemented
10#13066929C212yesmaximal, complemented
11C11×#1472C211yesmaximal, characteristic, complemented
12C2×C11×C22⋊Q8C2211yescharacteristic
13C2×#67000C411yescharacteristic
14C2×#66997C411yescharacteristic
15C2×#66982C2211yescharacteristic
16C2×C4×C22⋊D11C2211yescharacteristic
17#10623171—22no—
18#10623171—22no—
19#10623171—22no—
20#10623171—22no—
21C2×#66951C411yescharacteristic
22C2×#66949C411yescharacteristic
23C2×#66949C2211yescharacteristic
24C2×#66947C2211yescharacteristic
25C2×#66945C2211yescharacteristic
26C2×#66940C2211yescharacteristic
27C2×#66938C411yescharacteristic
28C2×#66938C411yescharacteristic
29C2×#66937C411yescharacteristic
30C2×#66932C411yescharacteristic
31C11×#407C2211yescharacteristic
32C2×C11×C22⋊C8C2211yescharacteristic
33#10622820C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35#10622741—22no—
36C8×C22⋊D11—22no—
37#10622342—22no—
38#10622339C2212yes—
39(C22⋊D11)⋊C8—22no—
40D11×C22⋊C8C2212yes—
41#10622331C2212yes—
42#10622331C2212yes—
43C11×#324C2212yes—
44C11×#324C2212yes—
45#10622166C2212yes—
46#10622166C2212yes—
47#10622107C2212yes—
48#10622107C2212yes—
49#10622106C2212yes—
50#10622106C2212yes—
51C22×Q8×C11C2×C411yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C22×C22⋊D11C2×C411yescharacteristic
54C22×C22⋊D11C2×C411yescharacteristic
55C22×D44C2×C411yescharacteristic
56C22×C4×D11C2×C411yescharacteristic
57C22×C4×D11C2311yescharacteristic
58C22×Dic22C2×C411yescharacteristic
59C22×Dic22C2×C411yescharacteristic
60C2×C11×M16—21no—
61C22×C8×C11—21no—
62C11×C22⋊Q8—21no—
63C11×C22⋊Q8—21no—
64C11×C22⋊Q8—21no—
65C11×C22⋊Q8—21no—
66C2×C11×C4⋊C4C2×C411yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C22⋊C4C2×C411yescharacteristic
70C2×C11×C22⋊C4C2×C411yescharacteristic
71C2×C22⋊Dic11C2×C411yescharacteristic
72C2×C22⋊Dic11C2×C411yescharacteristic
73#67000—22no—
74#67000—22no—
75#66997—22no—
76#66997—22no—
77#66982—21no—
78#66982—21no—
79#66982—21no—
80#66982—21no—
81C4×C22⋊D11D412yes—
82C4×C22⋊D11D412yes—
83C4×C22⋊D11D412yes—
84C4×C22⋊D11D412yes—
85C2×(C2×D11)⋊C4C2×C411yescharacteristic
86C2×(C2×D11)⋊C4C2×C411yescharacteristic
87C2×(C2×D11)⋊C4C2×C411yescharacteristic
88C2×(C2×D11)⋊C4C2×C411yescharacteristic
89C2×(C2×D11)⋊C4C2×C411yescharacteristic
90C2×(C2×D11)⋊C4C2×C411yescharacteristic
91C2×(C2×D11)⋊C4C2×C411yescharacteristic
92C2×(C2×D11)⋊C4C2311yescharacteristic
93C2×C4⋊Dic11C2×C411yescharacteristic
94C2×Dic11⋊C4C2×C411yescharacteristic
95C2×Dic11⋊C4C2×C411yescharacteristic
96C2×Dic11⋊C4C2×C411yescharacteristic
97C2×Dic11⋊C4C2×C411yescharacteristic
98C2×Dic11⋊C4C2×C411yescharacteristic
99C2×Dic11⋊C4C2311yescharacteristic
100C2×C4×Dic11C2×C411yescharacteristic
101C2×C4×Dic11C2×C411yescharacteristic
102C2×C4×Dic11C2×C411yescharacteristic
103C2×C4×Dic11C2311yescharacteristic
104C2×#4318—21no—
105C22×C11⋊C8—21no—
106C2×#4313—22no—
107C2×C8×D11—22no—
108#66951—22no—
109#66951—22no—
110#66949—22no—
111#66949—22no—
112#66949—22no—
113#66949—22no—
114#66947—22no—
115#66947—22no—
116#66945—22no—
117#66945—22no—
118#66940—22no—
119#66940—22no—
120#66938—22no—
121#66938—22no—
122#66938—22no—
123#66938—22no—
124#66937—22no—
125#66937—22no—
126#66932—22no—
127#66932—22no—
128C11×C22⋊C8—21no—
129C11×C22⋊C8—21no—
130C11×C22⋊C8C2312yes—
131C11×C22⋊C8C2312yes—
132C22⋊(C11⋊C8)—21no—
133C22⋊(C11⋊C8)—21no—
134C22⋊(C11⋊C8)C2312yes—
135C22⋊(C11⋊C8)C2312yes—
136(C2×D11)⋊C8—22no—
137(C2×D11)⋊C8—22no—
138Dic11⋊C8—22no—
139Dic11⋊C8—22no—
140C8×Dic11—22no—
141C8×Dic11—22no—
142#17388—111nomaximal, Sylow
143C24×C11C22×C411yescharacteristic
144C23×D11C22×C411yescharacteristic
145C23×D11C22×C411yescharacteristic
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—81no—
149C22×C4×C11—81no—
150C22×C4×C11C22×C411yescharacteristic
151C22×C4×C11C22×C411yescharacteristic
152C22×C4×C11C22×C411yescharacteristic
153C22×C4×C11C22×C411yescharacteristic
154C22×C4×C11C22×C411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2411yescharacteristic
160C2×C22⋊D11—24no—
161C2×C22⋊D11—21no—
162C2×C22⋊D11—21no—
163C2×C22⋊D11—81no—
164C2×C22⋊D11C22⋊C412yes—
165C2×C22⋊D11C22⋊C412yes—
166C22×Dic11C22×C411yescharacteristic
167C22×Dic11C22×C411yescharacteristic
168C22×Dic11C22×C411yescharacteristic
169C22×Dic11C22×C411yescharacteristic
170C22×Dic11C22×C411yescharacteristic
171C22×Dic11C22×C411yescharacteristic
172C2×D44—22no—
173C2×D44—81no—
174C2×C4×D11—22no—
175C2×C4×D11—24no—
176C2×C4×D11—81no—
177C2×C4×D11C2×D412yes—
178C2×C4×D11C2×D412yes—
179C2×Dic22—22no—
180C2×Dic22—24no—
181C2×Dic22—22no—
182C2×Dic22—81no—
183C11×M16—81no—
184C2×C8×C11—22no—
185C2×C8×C11—22no—
186C2×C8×C11—81no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C22⋊C4—21no—
194C11×C22⋊C4—21no—
195C11×C22⋊C4—21no—
196C11×C22⋊C4—21no—
197C22⋊Dic11—21no—
198C22⋊Dic11—21no—
199C22⋊Dic11C22⋊C412yes—
200C22⋊Dic11C22⋊C412yes—
201(C2×D11)⋊C4—22no—
202(C2×D11)⋊C4—22no—
203(C2×D11)⋊C4—22no—
204(C2×D11)⋊C4—22no—
205(C2×D11)⋊C4—22no—
206(C2×D11)⋊C4—21no—
207(C2×D11)⋊C4—21no—
208(C2×D11)⋊C4—21no—
209(C2×D11)⋊C4—21no—
210(C2×D11)⋊C4C22⋊C412yes—
211(C2×D11)⋊C4C22⋊C412yes—
212C4⋊Dic11—22no—
213Dic11⋊C4—22no—
214Dic11⋊C4—22no—
215Dic11⋊C4—22no—
216Dic11⋊C4—21no—
217Dic11⋊C4—21no—
218Dic11⋊C4—21no—
219Dic11⋊C4—21no—
220Dic11⋊C4C22⋊C412yes—
221Dic11⋊C4C22⋊C412yes—
222C4×Dic11—22no—
223C4×Dic11—22no—
224C4×Dic11—22no—
225C4×Dic11C2×D412yes—
226C4×Dic11C2×D412yes—
227#4318—81no—
228C2×C11⋊C8—22no—
229C2×C11⋊C8—22no—
230C2×C11⋊C8—81no—
231#4313—82no—
232C8×D11—82no—
233C2×#542—111no—
234#2975—111no—
235#2972—111no—
236#1472—112no—
237#1472—111no—
238#1472D1111yescharacteristic, complemented
239#1468—111no—
240#1468—111no—
241#1468—112no—
242#1461—112no—
243#1458—112no—
244C23×C11—22no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11C2×C22⋊C411yescharacteristic
248C23×C11C2×C22⋊C411yescharacteristic
249C23×C11C23×C411yescharacteristic
250C22×D11—22no—
251C22×D11—21no—
252C22×D11—22no—
253C22×D11—41no—
254C22×D11—41no—
255C22×D11—41no—
256C22×D11—41no—
257C22×D11C2×C22⋊C412yes—
258Q8×C11—81no—
259Q8×C11—81no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11C2×C22⋊C411yescharacteristic
275C2×C4×C11C2×C22⋊C411yescharacteristic
276C2×C4×C11C22×D411yescharacteristic
277C2×C4×C11C22×D411yescharacteristic
278C22⋊D11—24no—
279C22⋊D11—24no—
280C22⋊D11—81no—
281C22⋊D11—81no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—22no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11C2×C22⋊C412yes—
291C2×Dic11C2×C22⋊C412yes—
292C2×Dic11C2×C22⋊C412yes—
293C2×Dic11#13114yes—
294D44—82no—
295C4×D11—42no—
296C4×D11—42no—
297C4×D11—44no—
298Dic22—44no—
299Dic22—82no—
300C8×C11—42no—
301C8×C11—42no—
302C11⋊C8—42no—
303C11⋊C8—42no—
304#542—222no—
305#542—222no—
306#542—222no—
307#542—222no—
308C2×C4⋊Q8—111no—
309C2×#126—111no—
310C2×#126—111no—
311C2×#124—111no—
312C2×#124—111no—
313C2×#124—111no—
314C2×#123—111no—
315C2×#123—111no—
316C2×C22⋊Q8—111no—
317C2×C22⋊Q8—111no—
318C2×C22⋊Q8C2×D1111yescharacteristic
319C2×#121—111no—
320C2×C4×Q8—111no—
321C2×C4×D4—111no—
322C2×#117—111no—
323#436—222no—
324#436—222no—
325C8×D4—222no—
326C8×D4—222no—
327#431—112no—
328#431—112no—
329#407—111no—
330#407—112no—
331#407C2×D1111yescharacteristic
332C2×C22⋊C8—111no—
333C2×C22⋊C8—112no—
334C2×C22⋊C8C2×D1111yescharacteristic
335#324—112no—
336#324—112no—
337#324—112no—
338#324—112no—
339#324C2×D1112yes—
340#324C2×D1112yes—
341#323—112no—
342#323—112no—
343C22×C11—21no—
344C22×C11—21no—
345C22×C11—21no—
346C22×C11—21no—
347C22×C11—21no—
348C22×C11—21no—
349C22×C11—21no—
350C22×C11—21no—
351C22×C11—82no—
352C22×C11C22×C22⋊C411yescharacteristic
353C22×C11C2×#13112yes—
354C2×D11—22no—
355C2×D11—22no—
356C2×D11—22no—
357C2×D11—41no—
358C2×D11—41no—
359C2×D11—41no—
360C2×D11—82no—
361C2×D11—82no—
362C4×C11—21no—
363C4×C11—21no—
364C4×C11—21no—
365C4×C11—21no—
366C4×C11—41no—
367C4×C11—41no—
368C4×C11—41no—
369C4×C11—41no—
370Dic11—22no—
371Dic11—22no—
372Dic11—41no—
373Dic11—41no—
374Dic11—41no—
375Dic11#40814yes—
376C22×Q8—111no—
377C22×Q8—111no—
378C22×Q8C4×D1111yescharacteristic
379C22×D4—111no—
380C22×D4—111no—
381C22×D4—111no—
382C23×C4—111no—
383C23×C4—111no—
384C23×C4C22×D1111yescharacteristic
385C2×M16—21no—
386C2×M16—222no—
387C2×M16—221no—
388C22×C8—21no—
389C22×C8—222no—
390C22×C8—221no—
391C4⋊Q8—222no—
392C4⋊Q8—222no—
393#126—222no—
394#126—222no—
395#126—222no—
396#126—222no—
397#124—222no—
398#124—222no—
399#124—222no—
400#124—222no—
401#124—222no—
402#124—222no—
403#123—222no—
404#123—222no—
405#123—221no—
406#123—221no—
407#123—221no—
408#123—221no—
409C22⋊Q8—21no—
410C22⋊Q8—21no—
411C22⋊Q8—21no—
412C22⋊Q8—21no—
413C22⋊Q8—222no—
414C22⋊Q8—222no—
415C22⋊Q8—222no—
416C22⋊Q8—222no—
417#121—222no—
418#121—222no—
419C4×Q8—222no—
420C4×Q8—222no—
421C4×D4—112no—
422C4×D4—112no—
423C4×D4—112no—
424C4×D4—112no—
425#117—222no—
426#117—222no—
427C2×C4⋊C4—111no—
428C2×C4⋊C4—111no—
429C2×C4⋊C4—111no—
430C2×C4⋊C4—111no—
431C2×C4⋊C4—111no—
432C2×C4⋊C4—111no—
433C2×C4⋊C4—111no—
434C2×C4⋊C4C4×D1111yescharacteristic
435C2×C4⋊C4C22×D1111yescharacteristic
436C2×C4⋊C4C22×D1111yescharacteristic
437C2×C22⋊C4—111no—
438C2×C22⋊C4—111no—
439C2×C22⋊C4—111no—
440C2×C22⋊C4—111no—
441C2×C22⋊C4—111no—
442C2×C22⋊C4—111no—
443C2×C22⋊C4—111no—
444C2×C22⋊C4—111no—
445C2×C22⋊C4—111no—
446C2×C22⋊C4—111no—
447C2×C22⋊C4C4×D1111yescharacteristic
448C2×C22⋊C4C4×D1111yescharacteristic
449C2×C42—111no—
450C2×C42—111no—
451C2×C42—111no—
452C2×C42—111no—
453C4⋊C8—222no—
454C4⋊C8—222no—
455C22⋊C8—21no—
456C22⋊C8—21no—
457C22⋊C8—112no—
458C22⋊C8—112no—
459C22⋊C8—222no—
460C22⋊C8—222no—
461C22⋊C8—221no—
462C22⋊C8—221no—
463C22⋊C8C22×D1112yes—
464C22⋊C8C22×D1112yes—
465C4×C8—222no—
466C4×C8—222no—
467C2×C11—22no—
468C2×C11—41no—
469C2×C11—41no—
470C2×C11C2×#40811yescharacteristic
471C2×C11#288311yescharacteristic
472C2×C11#288911yescharacteristic
473D11—42no—
474D11—81no—
475C24—111no—
476C24—111no—
477C24C2×C4×D1111yescharacteristic
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—81no—
481C2×Q8—222no—
482C2×Q8—224no—
483C2×Q8—222no—
484C2×Q8—881no—
485C2×D4—112no—
486C2×D4—112no—
487C2×D4—222no—
488C2×D4—224no—
489C2×D4—221no—
490C2×D4—221no—
491C2×D4—881no—
492C2×D4—881no—
493C22×C4—81no—
494C22×C4—111no—
495C22×C4—111no—
496C22×C4—111no—
497C22×C4—112no—
498C22×C4—112no—
499C22×C4—111no—
500C22×C4—111no—
501C22×C4—111no—
502C22×C4—222no—
503C22×C4—224no—
504C22×C4—881no—
505C22×C4C2×C4×D1111yescharacteristic
506C22×C4C2×C4×D1111yescharacteristic
507C22×C4C2×C4×D1111yescharacteristic
508C22×C4C2×C4×D1111yescharacteristic
509C22×C4C2×C4×D1111yescharacteristic
510C22×C4D4×D1111yescharacteristic
511C22×C4D4×D1111yescharacteristic
512C22×C4D4×D1111yescharacteristic
513C22×C4D4×D1111yescharacteristic
514C22×C4C23×D1111yescharacteristic
515M16—81no—
516M16—882no—
517M16—881no—
518C2×C8—22no—
519C2×C8—22no—
520C2×C8—81no—
521C2×C8—222no—
522C2×C8—222no—
523C2×C8—882no—
524C2×C8—881no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—112no—
532C4⋊C4—112no—
533C4⋊C4—222no—
534C4⋊C4—222no—
535C4⋊C4—222no—
536C4⋊C4—222no—
537C4⋊C4—221no—
538C4⋊C4—221no—
539C4⋊C4—221no—
540C4⋊C4—221no—
541C22⋊C4—21no—
542C22⋊C4—21no—
543C22⋊C4—21no—
544C22⋊C4—21no—
545C22⋊C4—112no—
546C22⋊C4—112no—
547C22⋊C4—112no—
548C22⋊C4—112no—
549C22⋊C4—222no—
550C22⋊C4—222no—
551C22⋊C4—222no—
552C22⋊C4—222no—
553C22⋊C4—222no—
554C22⋊C4—221no—
555C22⋊C4—221no—
556C22⋊C4—221no—
557C22⋊C4—221no—
558C22⋊C4—221no—
559C22⋊C4—221no—
560C42—112no—
561C42—112no—
562C42—222no—
563C42—222no—
564C42—222no—
565C11#1738811yescharacteristic, complemented, Sylow
566C23—22no—
567C23—41no—
568C23—41no—
569C23—112no—
570C23—222no—
571C23—221no—
572C23—222no—
573C23—441no—
574C23—441no—
575C23—441no—
576C23—441no—
577C23C22⋊C4×D1111yescharacteristic
578C23C22⋊C4×D1111yescharacteristic
579C23C22×C4×D1111yescharacteristic
580Q8—81no—
581Q8—81no—
582Q8—444no—
583Q8—882no—
584D4—224no—
585D4—224no—
586D4—882no—
587D4—881no—
588D4—881no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—112no—
604C2×C4—114no—
605C2×C4—112no—
606C2×C4—112no—
607C2×C4—221no—
608C2×C4—221no—
609C2×C4—221no—
610C2×C4—222no—
611C2×C4—442no—
612C2×C4—442no—
613C2×C4—444no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4C22⋊C4×D1111yescharacteristic
619C2×C4C22⋊C4×D1111yescharacteristic
620C2×C4C2×D4×D1111yescharacteristic
621C2×C4C2×D4×D1111yescharacteristic
622C8—42no—
623C8—42no—
624C8—442no—
625C8—442no—
626C22—21no—
627C22—21no—
628C22—21no—
629C22—21no—
630C22—21no—
631C22—21no—
632C22—21no—
633C22—21no—
634C22—82no—
635C22—222no—
636C22—222no—
637C22—222no—
638C22—441no—
639C22—441no—
640C22—441no—
641C22—882no—
642C22—882no—
643C22C2×C22⋊C4×D1111yescharacteristic
644C22D11×#13112yes—
645C4—21no—
646C4—21no—
647C4—21no—
648C4—21no—
649C4—41no—
650C4—41no—
651C4—41no—
652C4—41no—
653C4—114no—
654C4—222no—
655C4—222no—
656C4—441no—
657C4—441no—
658C4—441no—
659C2—22no—
660C2—41no—
661C2—41no—
662C2—442no—
663C2—881no—
664C2D11×#40811yescharacteristic
665C2#1307707411yescharacteristic
666C2#1307709611yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1472C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#66937C4
cosocleC22×C4×C11C24
hypercenter#1472D11
hypocenterC11#17388
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1472

Complements

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

NH ≅ G/Ntype
2. #13077655C2semidirect
3. #13077638C2semidirect
4. #13066980C2semidirect
5. #13066978C2semidirect
6. #13066965C2semidirect
7. #13066963C2semidirect
8. #13066962C2semidirect
9. #13066938C2semidirect
10. #13066929C2semidirect
11. C11×#1472C2semidirect
238. #1472D11semidirect
565. C11#17388semidirect

Maximal subgroups

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

subgroupindex
C2×#106231712
#130776552
#130776382
#130669802
#130669782
#130669652
#130669632
#130669622
#130669382
#130669292
C11×#14722
#1738811