Finite Group Databasebeta

← #14761478

Subgroups — #14761478

Order 2816.

868 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622460C211yesmaximal, characteristic
2#13071355C211yesmaximal, characteristic, complemented
3#13070976C211yesmaximal, characteristic
4#13069573C211yesmaximal, characteristic, complemented
5#13069193C211yesmaximal, characteristic, complemented
6#13069186C211yesmaximal, characteristic, complemented
7#13068874C211yesmaximal, characteristic
8#13068874C211yesmaximal, characteristic
9#13068613C211yesmaximal, characteristic
10#13068516C211yesmaximal, characteristic, complemented
11#106×Dic11C211yesmaximal, characteristic, complemented
12#13068475C211yesmaximal, characteristic, complemented
13#13068440C211yesmaximal, characteristic
14#13068430C211yesmaximal, characteristic
15C11×#1948C211yesmaximal, characteristic, complemented
16C2×#66946C2211yescharacteristic
17C2×#66946C2211yescharacteristic
18C2×C4×D44C2211yescharacteristic
19C2×#66923C2211yescharacteristic
20C2×C11×#106C2211yescharacteristic
21C2×C11×#106C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C11×#384C2211yescharacteristic
24C4×C11×C4⋊C4C2211yescharacteristic
25C2×#66885C2211yescharacteristic
26C2×#66885C2211yescharacteristic
27C2×#66882C2211yescharacteristic
28C2×#66881C2211yescharacteristic
29C2×#66879C2211yescharacteristic
30C2×C8×Dic11C2211yescharacteristic
31#10622591—21no—
32#10622591—21no—
33C4⋊C4×Dic11C2211yescharacteristic
34C4⋊C4×Dic11C2211yescharacteristic
35C4⋊C4×Dic11C2211yescharacteristic
36C4⋊C4×Dic11C2211yescharacteristic
37#10622586C2211yescharacteristic
38#10622586C2211yescharacteristic
39#10622585—21no—
40#10622585—21no—
41C2×#66873C2211yescharacteristic
42C2×#66873C2211yescharacteristic
43C4×(C2×D11)⋊C4—21no—
44C4×(C2×D11)⋊C4—21no—
45#10622545C2211yescharacteristic
46C2×C4⋊(C11⋊C8)C2211yescharacteristic
47#10622460C418yescomplemented
48#10622279—21no—
49D11×#95—21no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C22×D44C2311yescharacteristic
61C22×C4×D11—21no—
62C22×C4×D11—21no—
63C22×C4×D11—21no—
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C42×C11—21no—
73C2×C42×C11C2311yescharacteristic
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×Dic11⋊C4—21no—
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×C4×Dic11—21no—
85C2×C4×Dic11—21no—
86C2×C4×Dic11—21no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11C2311yescharacteristic
89C2×C4×Dic11C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92#66946—22no—
93#66946—22no—
94#66946—22no—
95#66946Q814yes—
96C4×D44—22no—
97C4×D44C2×C414yes—
98#66923—22no—
99#66923C2×C414yescomplemented
100C11×#106—22no—
101C11×#106—22no—
102C11×C4⋊C8C2×C414yescomplemented
103C11×#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95D411yescharacteristic
111C11⋊#95D411yescharacteristic
112C11⋊#95D411yescharacteristic
113C11⋊#95D411yescharacteristic
114#66885C2×C414yes—
115#66885C2×C414yes—
116#66882C2×C414yescomplemented
117#66881C2×C414yescomplemented
118#66879—22no—
119C8×Dic11—22no—
120#66873—22no—
121#66873—22no—
122C4⋊(C11⋊C8)—22no—
123#21619—111nomaximal, Sylow
124C23×D11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2411yescharacteristic
132C22×Dic11—21no—
133C22×Dic11—21no—
134C22×Dic11—21no—
135C22×Dic11C2×D411yescharacteristic
136C22×Dic11C2×D411yescharacteristic
137C22×Dic11C2×D411yescharacteristic
138C22×Dic11C2×D411yescharacteristic
139C2×D44—21no—
140C2×D44—21no—
141C2×D44—21no—
142C2×D44C22×C412yes—
143C2×D44C2×Q812yes—
144C2×D44#4112yes—
145C2×C4×D11—24no—
146C2×C4×D11—24no—
147C2×C4×D11—24no—
148C2×C4×D11—81no—
149C2×C4×D11—81no—
150C2×C4×D11—81no—
151C2×C4×D11—81no—
152C2×C4×D11—81no—
153C2×C4×D11—81no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11C22×C412yes—
159C2×C8×C11C22×C412yes—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—81no—
167C11×C4⋊C4—81no—
168C11×C4⋊C4C2×Q812yes—
169C11×C4⋊C4#4112yes—
170C42×C11—81no—
171C42×C11C22×C412yes—
172C42×C11#4112yes—
173(C2×D11)⋊C4—24no—
174(C2×D11)⋊C4—24no—
175(C2×D11)⋊C4—24no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11C22×C412yes—
180C4⋊Dic11C22×C412yes—
181C4⋊Dic11C22×C412yes—
182Dic11⋊C4—24no—
183Dic11⋊C4—24no—
184Dic11⋊C4—81no—
185Dic11⋊C4—81no—
186C4×Dic11—21no—
187C4×Dic11—21no—
188C4×Dic11—81no—
189C4×Dic11—81no—
190C4×Dic11—81no—
191C4×Dic11—81no—
192C4×Dic11C2×Q812yes—
193C4×Dic11#4112yes—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×#478—111no—
201#2330—111no—
202#2275—111no—
203#1989—111no—
204#1948D1111yescharacteristic, complemented
205#1919—111no—
206#1918—111no—
207#1864—111no—
208#1864—111no—
209#1802—111no—
210#1776—111no—
211C4×#106—111no—
212#1768—111no—
213#1762—111no—
214C4×#102—111no—
215C23×C11C22×D411yescharacteristic
216C22×D11—22no—
217C22×D11—22no—
218C22×D11—22no—
219C22×D11—41no—
220C22×D11—41no—
221C22×D11—41no—
222C22×D11—41no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11C4×D412yes—
240C2×C4×C11C4×D412yes—
241C2×C4×C11C23×C411yescharacteristic
242C2×C4×C11C22×Q811yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C2×C4×C11C2×#4111yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—22no—
252C2×Dic11—22no—
253C2×Dic11—22no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11C22⋊Q812yes—
267C2×Dic11C22⋊Q812yes—
268D44—22no—
269D44—22no—
270D44—22no—
271D44C4×Q814yes—
272C4×D11—84no—
273C4×D11—84no—
274C4×D11—84no—
275C8×C11—22no—
276C8×C11—22no—
277C11⋊C8—41no—
278C11⋊C8—41no—
279C2×#125—111no—
280C2×C4×D4—111no—
281C2×C4×D4—111no—
282C2×C4×D4—111no—
283#478—118no—
284C2×#107—111no—
285C2×#106—111no—
286C2×#106C2×D1111yescharacteristic
287C2×#106C2×D1111yescharacteristic
288C2×C4⋊C8—111no—
289C2×C4⋊C8C2×D1111yescharacteristic
290C2×#102—111no—
291C2×#102—111no—
292C2×#102—111no—
293C2×#102—111no—
294C2×#97—111no—
295C2×C4×C8—111no—
296#389—111no—
297#389—111no—
298#389—221no—
299#389—221no—
300#387—221no—
301#387—221no—
302#384C2×D1111yescharacteristic
303C4×C4⋊C4—111no—
304C4×C4⋊C4—111no—
305C4×C4⋊C4—111no—
306C4×C4⋊C4—111no—
307C4×C4⋊C4C2×D1111yescharacteristic
308C4×C22⋊C4—221no—
309C4×C22⋊C4—221no—
310C4×C22⋊C4—221no—
311#376—111no—
312C2×#95—221no—
313#340—111no—
314#340—111no—
315#340—111no—
316#340—111no—
317#340—111no—
318#340—111no—
319#340C2×D1111yescharacteristic
320#340C2×D1111yescharacteristic
321#336—111no—
322#336—111no—
323C22×C11C2×C4×D411yescharacteristic
324C22×C11C2×C22⋊Q811yescharacteristic
325C22×C11#52511yescharacteristic
326C22×C11#57611yescharacteristic
327C22×C11#57711yescharacteristic
328C22×C11#57711yescharacteristic
329C22×C11#57711yescharacteristic
330C2×D11—24no—
331C2×D11—42no—
332C2×D11—42no—
333C2×D11—42no—
334C2×D11—42no—
335C2×D11—42no—
336C2×D11—42no—
337C4×C11—22no—
338C4×C11—22no—
339C4×C11—42no—
340C4×C11—42no—
341C4×C11—81no—
342C4×C11—81no—
343C4×C11C2×C4×Q811yescharacteristic
344C4×C11C4×#4111yescharacteristic
345C4×C11#52911yescharacteristic
346C4×C11#53311yescharacteristic
347Dic11—22no—
348Dic11—22no—
349Dic11—41no—
350Dic11—41no—
351Dic11—42no—
352Dic11—42no—
353Dic11—42no—
354C22×D4—111no—
355C23×C4—221no—
356C23×C4—221no—
357C23×C4—221no—
358C22×C8—111no—
359C22×C8—111no—
360C22×C8C22×D1111yescharacteristic
361C22×C8C22×D1111yescharacteristic
362#125—114no—
363#125—222no—
364C4×D4—114no—
365C4×D4—114no—
366C4×D4—222no—
367C4×D4—222no—
368C4×D4—222no—
369C4×D4—222no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—111no—
373C2×C4⋊C4—111no—
374C2×C4⋊C4—111no—
375C2×C4⋊C4—221no—
376C2×C4⋊C4—221no—
377C2×C4⋊C4—221no—
378C2×C4⋊C4—221no—
379C2×C4⋊C4C22×D1111yescharacteristic
380C2×C4⋊C4C22×D1111yescharacteristic
381C2×C4⋊C4C22×D1111yescharacteristic
382C2×C4⋊C4C22×D1111yescharacteristic
383C2×C22⋊C4—221no—
384C2×C22⋊C4—221no—
385C2×C22⋊C4—221no—
386C2×C42—21no—
387C2×C42—111no—
388C2×C42—111no—
389C2×C42—221no—
390C2×C42—221no—
391C2×C42—221no—
392C2×C42—221no—
393C2×C42C22×D1111yescharacteristic
394#107—114no—
395#106—22no—
396#106—22no—
397#106—114no—
398C4⋊C8—222no—
399C4⋊C8C4×D1114yescomplemented
400#102—114no—
401#102—114no—
402#102—222no—
403#102—222no—
404#97—222no—
405C4×C8—222no—
406#95—21no—
407#95—111no—
408#95—111no—
409#95—111no—
410#95—111no—
411#95—221no—
412#95—221no—
413#95—221no—
414#95—221no—
415#95—221no—
416#95—221no—
417C2×C11C4×C22⋊Q811yescharacteristic
418C2×C11#294611yescharacteristic
419C2×C11#295211yescharacteristic
420C2×C11#308111yescharacteristic
421C2×C11#308411yescharacteristic
422C2×C11#311911yescharacteristic
423C2×C11#312311yescharacteristic
424D11—44no—
425C24—221no—
426C2×D4—112no—
427C2×D4—112no—
428C2×D4—112no—
429C2×D4—221no—
430C2×D4—221no—
431C2×D4—221no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—111no—
437C22×C4—111no—
438C22×C4—111no—
439C22×C4—111no—
440C22×C4—224no—
441C22×C4—224no—
442C22×C4—221no—
443C22×C4—221no—
444C22×C4—221no—
445C22×C4—224no—
446C22×C4—881no—
447C22×C4—881no—
448C22×C4—881no—
449C22×C4—881no—
450C22×C4—881no—
451C22×C4—881no—
452C22×C4D4×D1111yescharacteristic
453C22×C4D4×D1111yescharacteristic
454C22×C4C23×D1111yescharacteristic
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—221no—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8—221no—
465C2×C8C2×C4×D1112yes—
466C2×C8C2×C4×D1112yes—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—81no—
474C4⋊C4—81no—
475C4⋊C4—112no—
476C4⋊C4—112no—
477C4⋊C4—112no—
478C4⋊C4—224no—
479C4⋊C4—224no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4—881no—
484C4⋊C4—881no—
485C4⋊C4#434112yes—
486C4⋊C4Q8×D1112yes—
487C22⋊C4—224no—
488C22⋊C4—224no—
489C22⋊C4—224no—
490C42—81no—
491C42—112no—
492C42—112no—
493C42—221no—
494C42—221no—
495C42—881no—
496C42—881no—
497C42—881no—
498C42—881no—
499C42C2×C4×D1112yes—
500C42#434312yes—
501C11#2161911yescharacteristic, complemented, Sylow
502C23—222no—
503C23—222no—
504C23—222no—
505C23—441no—
506C23—441no—
507C23—441no—
508C23—441no—
509C23C2×D4×D1111yescharacteristic
510D4—114no—
511D4—222no—
512D4—222no—
513D4—222no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—112no—
531C2×C4—112no—
532C2×C4—221no—
533C2×C4—221no—
534C2×C4—221no—
535C2×C4—221no—
536C2×C4—222no—
537C2×C4—222no—
538C2×C4—222no—
539C2×C4—221no—
540C2×C4—221no—
541C2×C4—221no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—221no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—884no—
552C2×C4—884no—
553C2×C4—884no—
554C2×C4#6694612yes—
555C2×C4#6694612yes—
556C2×C4C22×C4×D1111yescharacteristic
557C2×C4C2×#434111yescharacteristic
558C2×C4C2×Q8×D1111yescharacteristic
559C2×C4C2×#434311yescharacteristic
560C2×C4#41×D1111yescharacteristic
561C2×C4#41×D1111yescharacteristic
562C8—22no—
563C8—22no—
564C8—441no—
565C8—441no—
566C22—224no—
567C22—442no—
568C22—442no—
569C22—442no—
570C22—442no—
571C22—442no—
572C22—442no—
573C22C2×#6694611yescharacteristic
574C22#1062313711yescharacteristic
575C22D11×C22⋊Q811yescharacteristic
576C22#1062329311yescharacteristic
577C22#1062329311yescharacteristic
578C22#1062330511yescharacteristic
579C22#1062330911yescharacteristic
580C4—22no—
581C4—22no—
582C4—42no—
583C4—42no—
584C4—81no—
585C4—81no—
586C4—222no—
587C4—222no—
588C4—441no—
589C4—441no—
590C4—442no—
591C4—442no—
592C4—442no—
593C4C4×#434111yescharacteristic
594C4C4×Q8×D1111yescharacteristic
595C4#1062322211yescharacteristic
596C4#1062325911yescharacteristic
597C2—444no—
598C2#1307114611yescharacteristic
599C2#1307744611yescharacteristic
600C2#1307749911yescharacteristic
601C2#1307844211yescharacteristic
602C2#1307847511yescharacteristic
603C2#1307881411yescharacteristic
604C2#1307886611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1948C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#1948D11
hypocenterC11#21619
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1948

Complements

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

NH ≅ G/Ntype
2. #13071355C2semidirect
4. #13069573C2semidirect
5. #13069193C2semidirect
6. #13069186C2semidirect
10. #13068516C2semidirect
11. #106×Dic11C2semidirect
12. #13068475C2semidirect
15. C11×#1948C2semidirect
47. #10622460C4semidirect
99. #66923C2×C4semidirect
102. C11×C4⋊C8C2×C4semidirect
116. #66882C2×C4semidirect
117. #66881C2×C4semidirect
204. #1948D11semidirect
399. C4⋊C8C4×D11semidirect
501. C11#21619semidirect

Maximal subgroups

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

subgroupindex
C2×#106224602
#130713552
#130709762
#130695732
#130691932
#130691862
#130688742
#130686132
#130685162
#106×Dic112
#130684752
#130684402
#130684302
C11×#19482
#2161911