Finite Group Databasebeta

← #14763568

Subgroups — #14763568

Order 2816.

1022 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623114C211yesmaximal, characteristic
2C2×#10622453C211yesmaximal, characteristic
3#13071237C211yesmaximal, characteristic
4#13069583C211yesmaximal, characteristic, complemented
5#13069579C211yesmaximal, characteristic, complemented
6#13069434C211yesmaximal, characteristic, complemented
7#13069416C211yesmaximal, characteristic, complemented
8#13068927C211yesmaximal, characteristic
9#13068925C211yesmaximal, characteristic
10#13068922C211yesmaximal, characteristic
11#13068920C211yesmaximal, characteristic
12#13068632C211yesmaximal, characteristic, complemented
13#13068631C211yesmaximal, characteristic, complemented
14#13068618C211yesmaximal, characteristic, complemented
15C11×#1803C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C11C2211yescharacteristic
17C2×#66999C2211yescharacteristic
18C2×#66997C2211yescharacteristic
19#10623114—24no—
20#10623114C418yescomplemented
21C2×#66951—21no—
22C2×#66950C2211yescharacteristic
23C2×#66945C2211yescharacteristic
24C2×C4⋊C4×D11C2211yescharacteristic
25C2×#66943C2211yescharacteristic
26C2×#66942—21no—
27C2×#66929—21no—
28C2×#66925C2211yescharacteristic
29C2×#66923—21no—
30C2×C4×Dic22C2211yescharacteristic
31C2×C11×C4⋊C8C2211yescharacteristic
32C2×C11×#103C2211yescharacteristic
33C2×C11×#103C2211yescharacteristic
34C11×#384C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36C2×#66899C2211yescharacteristic
37C2×(C2×D11)⋊C8C2211yescharacteristic
38C2×(C2×D11)⋊C8C2211yescharacteristic
39C2×#66880C2211yescharacteristic
40C2×#66880C2211yescharacteristic
41C2×#66879C2211yescharacteristic
42C2×C8×Dic11C2211yescharacteristic
43#10622602—21no—
44#10622602—21no—
45#10622590C2211yescharacteristic
46#10622589C2211yescharacteristic
47#10622585—21no—
48#10622585—21no—
49C2×#66874C2211yescharacteristic
50C2×#66874C2211yescharacteristic
51#10622549C2211yescharacteristic
52C2×C4⋊(C11⋊C8)C2211yescharacteristic
53#10622453—24no—
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×C4×D11—21no—
64C22×C4×D11C2311yescharacteristic
65C22×Dic22C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C4×Q8×C11—22no—
69C4×Q8×C11C2×C414yescomplemented
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C42×C11—21no—
77C2×C42×C11C2311yescharacteristic
78#66999—22no—
79#66999C2×C414yes—
80#66997—22no—
81#66997C2×C414yescomplemented
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4D411yescharacteristic
86C2×(C2×D11)⋊C4D411yescharacteristic
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4D411yescharacteristic
101C2×Dic11⋊C4D411yescharacteristic
102C2×C4×Dic11—21no—
103C2×C4×Dic11—21no—
104C2×C4×Dic11C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107#66951—28no—
108#66950—22no—
109#66950C2×C414yes—
110#66945—41no—
111#66945—41no—
112C4⋊C4×D11—41no—
113C4⋊C4×D11—41no—
114#66943—22no—
115#66943C2×C414yescomplemented
116#66942—28no—
117#66929—28no—
118#66925C2×C414yes—
119#66925D414yes—
120#66923—28no—
121C4×Dic22—22no—
122C4×Dic22C2×C414yescomplemented
123C11×C4⋊C8—22no—
124C11×#103—41no—
125C11×#103—41no—
126#66899—41no—
127#66899—41no—
128C11⋊#95—21no—
129C11⋊#95—21no—
130C11⋊#95—21no—
131C11⋊#95—21no—
132(C2×D11)⋊C8—22no—
133(C2×D11)⋊C8—22no—
134#66880—41no—
135#66880—41no—
136#66879—22no—
137C8×Dic11—22no—
138#66874—41no—
139#66874—41no—
140C4⋊(C11⋊C8)—22no—
141#21873—111nomaximal, Sylow
142C23×D11C2×D411yescharacteristic
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11C22×C412yes—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2411yescharacteristic
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11C2×D411yescharacteristic
161C22×Dic11C2×D411yescharacteristic
162C22×Dic11C2×D411yescharacteristic
163C2×C4×D11—21no—
164C2×C4×D11—21no—
165C2×C4×D11—21no—
166C2×C4×D11—21no—
167C2×C4×D11—42no—
168C2×C4×D11—81no—
169C2×C4×D11—81no—
170C2×C4×D11C22×C412yes—
171C2×C4×D11C2×D412yes—
172C2×Dic22—21no—
173C2×Dic22—21no—
174C2×Dic22—21no—
175C2×Dic22—21no—
176C2×Dic22—21no—
177C2×Dic22C22×C412yes—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C11×C4⋊C4—24no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—81no—
191C11×C4⋊C4—81no—
192C11×C4⋊C4C22×C412yes—
193C42×C11—24no—
194C42×C11C22×C412yes—
195C42×C11C2×D412yes—
196(C2×D11)⋊C4—24no—
197(C2×D11)⋊C4—24no—
198(C2×D11)⋊C4—42no—
199(C2×D11)⋊C4C22⋊C414yes—
200(C2×D11)⋊C4C22⋊C414yes—
201C4⋊Dic11—24no—
202C4⋊Dic11—24no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11C22×C412yes—
209Dic11⋊C4—24no—
210Dic11⋊C4—24no—
211Dic11⋊C4—24no—
212Dic11⋊C4—24no—
213Dic11⋊C4—24no—
214Dic11⋊C4—42no—
215Dic11⋊C4—81no—
216Dic11⋊C4—81no—
217Dic11⋊C4C22⋊C414yes—
218Dic11⋊C4C22⋊C414yes—
219C4×Dic11—24no—
220C4×Dic11—42no—
221C4×Dic11C22×C412yes—
222C4×Dic11C2×D412yes—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×#541—111no—
230C2×#433—111no—
231#2317—111no—
232#1992—111no—
233#1991—111no—
234#1960—111no—
235#1956—111no—
236#1873—111no—
237#1873—111no—
238#1872—111no—
239#1872—111no—
240#1805—111no—
241#1805—111no—
242#1803—111no—
243#1803D1111yescharacteristic, complemented
244C23×C11C22×D411yescharacteristic
245C22×D11—21no—
246C22×D11—21no—
247C22×D11—21no—
248C22×D11—21no—
249C22×D11—21no—
250C22×D11—21no—
251C22×D11C2×C22⋊C412yes—
252Q8×C11—22no—
253Q8×C11—22no—
254Q8×C11—41no—
255Q8×C11—41no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
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×C11C2×C22⋊C412yes—
273C2×C4×C11C2×C22⋊C412yes—
274C2×C4×C11C23×C411yescharacteristic
275C2×C4×C11C22×D411yescharacteristic
276C2×C4×C11H(5,𝔽2)11yescharacteristic
277C2×C4×C11H(5,𝔽2)11yescharacteristic
278C2×C4×C112−1+411yescharacteristic
279C2×C4×C112−1+411yescharacteristic
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—22no—
287C2×Dic11—22no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11C2×C22⋊C412yes—
299C2×Dic11C2×C22⋊C412yes—
300C2×Dic11C2×C22⋊C412yes—
301C4×D11—22no—
302C4×D11—22no—
303C4×D11—22no—
304C4×D11—22no—
305C4×D11—84no—
306Dic22—22no—
307Dic22—22no—
308Dic22—41no—
309Dic22—41no—
310C8×C11—41no—
311C8×C11—41no—
312C11⋊C8—41no—
313C11⋊C8—41no—
314#541—118no—
315#541—224no—
316C2×C4⋊Q8—111no—
317C2×#126—221no—
318C2×#126—221no—
319C2×#125—111no—
320C2×#125—221no—
321C2×#125—221no—
322C2×C22⋊Q8—111no—
323C2×C22⋊Q8—111no—
324C2×C4×Q8—111no—
325C2×C4×Q8C2×D1111yescharacteristic
326C2×#117—111no—
327C2×#117—111no—
328C22×C4⋊C4—111no—
329#433—224no—
330C2×C4⋊C8—111no—
331C2×C4⋊C8C2×D1111yescharacteristic
332C2×#103—111no—
333C2×#103—111no—
334C2×#103—111no—
335C2×#103—111no—
336C2×#103—111no—
337C2×#103—111no—
338C2×#103C2×D1111yescharacteristic
339C2×#103C2×D1111yescharacteristic
340C2×C22⋊C8—111no—
341C2×C22⋊C8—111no—
342C2×#97—111no—
343C2×C4×C8—111no—
344#389—221no—
345#389—221no—
346#385—221no—
347#385—221no—
348#384—111no—
349#384C2×D1111yescharacteristic
350#382—111no—
351#382—111no—
352#340—111no—
353#340—111no—
354#340—111no—
355#340—111no—
356#340—111no—
357#340—111no—
358#340C2×D1111yescharacteristic
359#340C2×D1111yescharacteristic
360C22×C11C22×C22⋊C411yescharacteristic
361C22×C11#53511yescharacteristic
362C22×C11#53611yescharacteristic
363C22×C11#57711yescharacteristic
364C22×C11#57711yescharacteristic
365C22×C11#57811yescharacteristic
366C22×C11#57811yescharacteristic
367C2×D11—22no—
368C2×D11—22no—
369C2×D11—22no—
370C2×D11—41no—
371C2×D11—41no—
372C2×D11—41no—
373C2×D11—41no—
374C4×C11—22no—
375C4×C11—22no—
376C4×C11—42no—
377C4×C11—42no—
378C4×C11—81no—
379C4×C11—81no—
380C4×C11#52011yescharacteristic
381C4×C11#52011yescharacteristic
382C4×C11#53711yescharacteristic
383C4×C11#53711yescharacteristic
384Dic11—22no—
385Dic11—22no—
386Dic11—22no—
387Dic11—42no—
388Dic11—42no—
389Dic11—81no—
390Dic11—81no—
391C22×Q8—111no—
392C22×Q8C22×D1111yescharacteristic
393C23×C4—111no—
394C23×C4—221no—
395C22×C8—111no—
396C22×C8—111no—
397C22×C8C22×D1111yescharacteristic
398C22×C8C22×D1111yescharacteristic
399C4⋊Q8—114no—
400C4⋊Q8—222no—
401#126—228no—
402#126—228no—
403#125—114no—
404#125—228no—
405#125—222no—
406#125—228no—
407C22⋊Q8—114no—
408C22⋊Q8—114no—
409C22⋊Q8—222no—
410C22⋊Q8—222no—
411C4×Q8—22no—
412C4×Q8—114no—
413C4×Q8—222no—
414C4×Q8C4×D1114yescomplemented
415#117—114no—
416#117—114no—
417#117—441no—
418#117—441no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—111no—
423C2×C4⋊C4—111no—
424C2×C4⋊C4—111no—
425C2×C4⋊C4—111no—
426C2×C4⋊C4—111no—
427C2×C4⋊C4—221no—
428C2×C4⋊C4—221no—
429C2×C4⋊C4—221no—
430C2×C4⋊C4—221no—
431C2×C4⋊C4—221no—
432C2×C4⋊C4—221no—
433C2×C4⋊C4—221no—
434C2×C4⋊C4—221no—
435C2×C4⋊C4—221no—
436C2×C4⋊C4—221no—
437C2×C4⋊C4—441no—
438C2×C4⋊C4—441no—
439C2×C4⋊C4C22×D1111yescharacteristic
440C2×C4⋊C4C22×D1111yescharacteristic
441C2×C4⋊C4C22×D1111yescharacteristic
442C2×C22⋊C4—111no—
443C2×C22⋊C4—111no—
444C2×C22⋊C4—221no—
445C2×C22⋊C4—221no—
446C2×C22⋊C4—221no—
447C2×C42—21no—
448C2×C42—111no—
449C2×C42—221no—
450C2×C42—221no—
451C2×C42C22×D1111yescharacteristic
452C4⋊C8—22no—
453C4⋊C8—222no—
454#103—41no—
455#103—41no—
456#103—441no—
457#103—441no—
458#103—441no—
459#103—441no—
460#103—441no—
461#103—441no—
462C22⋊C8—222no—
463C22⋊C8—222no—
464#97—222no—
465C4×C8—222no—
466#95—221no—
467#95—221no—
468#95—221no—
469#95—221no—
470C2×C11#231111yescharacteristic
471C2×C11#289811yescharacteristic
472C2×C11#289811yescharacteristic
473C2×C11#322211yescharacteristic
474C2×C11#322311yescharacteristic
475C2×C11#324211yescharacteristic
476C2×C11#324211yescharacteristic
477D11—42no—
478C24—111no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—112no—
485C2×Q8—221no—
486C2×Q8—221no—
487C2×Q8—221no—
488C2×Q8—221no—
489C2×Q8—221no—
490C2×Q8C2×C4×D1112yes—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—111no—
496C22×C4—111no—
497C22×C4—111no—
498C22×C4—112no—
499C22×C4—112no—
500C22×C4—221no—
501C22×C4—221no—
502C22×C4—221no—
503C22×C4—221no—
504C22×C4—221no—
505C22×C4—221no—
506C22×C4—221no—
507C22×C4—221no—
508C22×C4—442no—
509C22×C4—881no—
510C22×C4—881no—
511C22×C4D4×D1111yescharacteristic
512C22×C4D4×D1111yescharacteristic
513C22×C4C23×D1111yescharacteristic
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—221no—
521C2×C8—221no—
522C2×C8—221no—
523C2×C8—221no—
524C2×C8—221no—
525C2×C8—221no—
526C4⋊C4—24no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—81no—
533C4⋊C4—81no—
534C4⋊C4—114no—
535C4⋊C4—114no—
536C4⋊C4—112no—
537C4⋊C4—224no—
538C4⋊C4—224no—
539C4⋊C4—224no—
540C4⋊C4—224no—
541C4⋊C4—224no—
542C4⋊C4—224no—
543C4⋊C4—224no—
544C4⋊C4—221no—
545C4⋊C4—221no—
546C4⋊C4—221no—
547C4⋊C4—221no—
548C4⋊C4—221no—
549C4⋊C4—442no—
550C4⋊C4—881no—
551C4⋊C4—881no—
552C4⋊C4C2×C4×D1112yes—
553C22⋊C4—114no—
554C22⋊C4—114no—
555C22⋊C4—224no—
556C22⋊C4—224no—
557C22⋊C4—442no—
558C42—24no—
559C42—112no—
560C42—112no—
561C42—224no—
562C42—442no—
563C42C2×C4×D1112yes—
564C42D4×D1112yes—
565C11#2187311yescharacteristic, complemented, Sylow
566C23—112no—
567C23—221no—
568C23—221no—
569C23—221no—
570C23—221no—
571C23—221no—
572C23—221no—
573C23C2×D4×D1111yescharacteristic
574Q8—22no—
575Q8—22no—
576Q8—41no—
577Q8—41no—
578Q8—222no—
579Q8—222no—
580Q8—441no—
581Q8—441no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—112no—
599C2×C4—112no—
600C2×C4—112no—
601C2×C4—221no—
602C2×C4—221no—
603C2×C4—221no—
604C2×C4—221no—
605C2×C4—221no—
606C2×C4—221no—
607C2×C4—222no—
608C2×C4—222no—
609C2×C4—222no—
610C2×C4—222no—
611C2×C4—222no—
612C2×C4—222no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4—441no—
620C2×C4—441no—
621C2×C4—441no—
622C2×C4—441no—
623C2×C4—884no—
624C2×C4C22⋊C4×D1112yes—
625C2×C4C22⋊C4×D1112yes—
626C2×C4C22×C4×D1111yescharacteristic
627C2×C4C2×D4×D1111yescharacteristic
628C2×C4#6703711yescharacteristic
629C2×C4#6704011yescharacteristic
630C2×C4#6704211yescharacteristic
631C2×C4#6704311yescharacteristic
632C8—41no—
633C8—41no—
634C8—441no—
635C8—441no—
636C22—222no—
637C22—222no—
638C22—222no—
639C22—441no—
640C22—441no—
641C22—441no—
642C22—441no—
643C22C2×C22⋊C4×D1111yescharacteristic
644C22#1062313811yescharacteristic
645C22#1062315911yescharacteristic
646C22#1062329311yescharacteristic
647C22#1062329711yescharacteristic
648C22#1062330611yescharacteristic
649C22#1062331011yescharacteristic
650C4—22no—
651C4—22no—
652C4—42no—
653C4—42no—
654C4—81no—
655C4—81no—
656C4—222no—
657C4—222no—
658C4—222no—
659C4—442no—
660C4—442no—
661C4—881no—
662C4—881no—
663C4#1062303511yescharacteristic
664C4#1062305411yescharacteristic
665C4#1062313911yescharacteristic
666C4#1062316011yescharacteristic
667C2—442no—
668C2#1307120511yescharacteristic
669C2#1307714411yescharacteristic
670C2#1307714711yescharacteristic
671C2#1307968711yescharacteristic
672C2#1307969811yescharacteristic
673C2#1307988311yescharacteristic
674C2#1307989111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1803C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1803D11
hypocenterC11#21873
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
4. #13069583C2semidirect
5. #13069579C2semidirect
6. #13069434C2semidirect
7. #13069416C2semidirect
12. #13068632C2semidirect
13. #13068631C2semidirect
14. #13068618C2semidirect
15. C11×#1803C2semidirect
20. #10623114C4semidirect
69. C4×Q8×C11C2×C4semidirect
81. #66997C2×C4semidirect
115. #66943C2×C4semidirect
122. C4×Dic22C2×C4semidirect
243. #1803D11semidirect
414. C4×Q8C4×D11semidirect
565. C11#21873semidirect

Maximal subgroups

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

subgroupindex
C2×#106231142
C2×#106224532
#130712372
#130695832
#130695792
#130694342
#130694162
#130689272
#130689252
#130689222
#130689202
#130686322
#130686312
#130686182
C11×#18032
#2187311