Finite Group Databasebeta

← C2×#13067170 #14721105

Subgroups — C2×#13067170 #14721105

Order 2816.

1498 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623322C211yesmaximal, characteristic
2C22×C22⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
3#13067170C218yesmaximal, direct product factor
4C2×#10622090C212yesmaximal, complemented
5C2×#10622089C212yesmaximal, complemented
6C2×C11×#381C211yesmaximal, characteristic, complemented
7C24×C4×C11C2211yescharacteristic
8C22×#4339C411yescharacteristic, complemented
9C22×C11×C22⋊C4—21no—
10C2×#67006—21no—
11#10623322—22no—
12#10623322—22no—
13#10623322C414yescomplemented
14#10623322C2214yes—
15C2×#66983C411yescharacteristic, complemented
16C2×#66983C2211yescharacteristic
17C2×#66982—21no—
18C2×C4×C22⋊D11—21no—
19C2×C4×C22⋊D11—21no—
20C2×#66979C411yescharacteristic, complemented
21C2×#66977C411yescharacteristic, complemented
22C2×#66977C2211yescharacteristic
23C23×C11⋊C8—21no—
24C11×#381—22no—
25C11×#381C2214yescomplemented
26C2×C11×#95—21no—
27C2×C11×#95C2212yes—
28C2×C22⋊(C11⋊C8)—22no—
29C2×C22⋊(C11⋊C8)—21no—
30C2×C22⋊(C11⋊C8)C2212yes—
31C2×C22⋊(C11⋊C8)C2214yescomplemented
32#10622090C2218yescomplemented
33#10622089C2218yescomplemented
34C25×C11D411yescharacteristic
35C23×C4×C11—22no—
36C23×C4×C11—44no—
37C23×C4×C11C2×C411yescharacteristic
38C23×C4×C11C2×C411yescharacteristic
39C23×C4×C11C2×C412yes—
40C23×C4×C11D411yescharacteristic
41C23×C4×C11D411yescharacteristic
42C23×C4×C11D412yes—
43C23×C4×C11D411yescharacteristic
44C23×C4×C11D412yes—
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2312yes—
47C22×C22⋊D11—21no—
48C22×C22⋊D11—21no—
49C22×C22⋊D11—21no—
50C2×#4339—22no—
51C2×#4339—44no—
52C2×#4339C2×C414yescomplemented
53C22×D44C2×C411yescharacteristic
54C22×C4×D11—21no—
55C22×Dic22C2×C411yescharacteristic
56C2×C11×C22⋊C4—24no—
57C2×C11×C22⋊C4—44no—
58#67006—24no—
59#67006—24no—
60C2×C22⋊Dic11—21no—
61C2×C22⋊Dic11—21no—
62C2×C22⋊Dic11—21no—
63#66983—22no—
64#66983—21no—
65#66983—21no—
66#66983C2×C412yes—
67#66983C2×C414yescomplemented
68#66983C2312yes—
69#66982—24no—
70#66982—24no—
71C4×C22⋊D11—24no—
72C4×C22⋊D11—24no—
73C4×C22⋊D11—24no—
74C4×C22⋊D11—24no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77#66979—22no—
78#66979C2×C414yescomplemented
79C2×C4⋊Dic11C2×C411yescharacteristic
80C2×C4⋊Dic11C2×C411yescharacteristic
81#66977—22no—
82#66977—21no—
83#66977—21no—
84#66977C2×C412yes—
85#66977C2×C414yescomplemented
86#66977C2312yes—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×C4×Dic11—21no—
90C22×C11⋊C8—22no—
91C22×C11⋊C8—24no—
92C22×C11⋊C8—44no—
93C11×#95—24no—
94C11×#95—22no—
95C11×#95C2314yes—
96C22⋊(C11⋊C8)—22no—
97C22⋊(C11⋊C8)—24no—
98C22⋊(C11⋊C8)C2314yes—
99C2×#1516—111nomaximal, Sylow
100C24×C11—24no—
101C24×C11—24no—
102C24×C11—42no—
103C24×C11C22⋊C411yescharacteristic
104C24×C11C22⋊C412yes—
105C24×C11C22⋊C411yescharacteristic
106C24×C11C2×D412yes—
107C24×C11C2×D411yescharacteristic
108C23×D11—21no—
109C22×C4×C11—24no—
110C22×C4×C11—24no—
111C22×C4×C11—24no—
112C22×C4×C11—42no—
113C22×C4×C11—44no—
114C22×C4×C11—42no—
115C22×C4×C11—44no—
116C22×C4×C11—42no—
117C22×C4×C11—44no—
118C22×C4×C11—42no—
119C22×C4×C11—44no—
120C22×C4×C11—44no—
121C22×C4×C11—44no—
122C22×C4×C11—44no—
123C22×C4×C11C22⋊C411yescharacteristic
124C22×C4×C11C22⋊C411yescharacteristic
125C22×C4×C11C22⋊C412yes—
126C22×C4×C11C22⋊C412yes—
127C22×C4×C11C22⋊C412yes—
128C22×C4×C11C22⋊C412yes—
129C22×C4×C11C22⋊C412yes—
130C22×C4×C11C22×C411yescharacteristic
131C22×C4×C11C22×C412yes—
132C22×C4×C11C22×C411yescharacteristic
133C22×C4×C11C22×C412yes—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D412yes—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D412yes—
140C22×C4×C11C2411yescharacteristic
141C2×C22⋊D11—22no—
142C2×C22⋊D11—24no—
143C2×C22⋊D11—24no—
144C2×C22⋊D11—22no—
145C2×C22⋊D11—44no—
146C2×C22⋊D11—44no—
147C2×C22⋊D11—44no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151#4339—48no—
152#4339—48no—
153C2×D44—21no—
154C2×D44—42no—
155C2×D44C22×C412yes—
156C2×C4×D11—24no—
157C2×C4×D11—44no—
158C2×Dic22—21no—
159C2×Dic22—42no—
160C2×Dic22C22×C412yes—
161C11×C22⋊C4—48no—
162C22⋊Dic11—22no—
163C22⋊Dic11—24no—
164C22⋊Dic11—24no—
165C22⋊Dic11—22no—
166(C2×D11)⋊C4—22no—
167(C2×D11)⋊C4—24no—
168(C2×D11)⋊C4—22no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C4⋊Dic11C22×C412yes—
172C4⋊Dic11C22×C412yes—
173Dic11⋊C4—22no—
174Dic11⋊C4—24no—
175Dic11⋊C4—22no—
176C4×Dic11—24no—
177C2×C11⋊C8—24no—
178C2×C11⋊C8—44no—
179C2×C11⋊C8—48no—
180C2×#525—111no—
181C22×C22⋊C8—111no—
182C2×#381D1111yescharacteristic, complemented
183#1516—118no—
184C2×#328—112no—
185C2×#327—112no—
186C23×C11—22no—
187C23×C11—22no—
188C23×C11—22no—
189C23×C11—22no—
190C23×C11—24no—
191C23×C11—24no—
192C23×C11—24no—
193C23×C11—22no—
194C23×C11—24no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11—416no—
200C23×C11#9914yes—
201C23×C11C2×C22⋊C412yes—
202C23×C11C2×C22⋊C412yes—
203C23×C11C2×C22⋊C411yescharacteristic
204C23×C11C2×C22⋊C411yescharacteristic
205C23×C11#13514yes—
206C23×C11C22×D411yescharacteristic
207C22×D11—22no—
208C22×D11—42no—
209C22×D11—42no—
210C22×D11—42no—
211C2×C4×C11—24no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—24no—
216C2×C4×C11—24no—
217C2×C4×C11—24no—
218C2×C4×C11—22no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—41no—
223C2×C4×C11—42no—
224C2×C4×C11—41no—
225C2×C4×C11—42no—
226C2×C4×C11—41no—
227C2×C4×C11—42no—
228C2×C4×C11—41no—
229C2×C4×C11—44no—
230C2×C4×C11—44no—
231C2×C4×C11—44no—
232C2×C4×C11—88no—
233C2×C4×C11C2×C22⋊C412yes—
234C2×C4×C11C2×C22⋊C411yescharacteristic
235C2×C4×C11C2×C22⋊C412yes—
236C2×C4×C11C2×C22⋊C411yescharacteristic
237C2×C4×C11C23×C411yescharacteristic
238C2×C4×C11C22×D411yescharacteristic
239C22⋊D11—48no—
240C22⋊D11—44no—
241C22⋊D11—48no—
242C22⋊D11—44no—
243C2×Dic11—22no—
244C2×Dic11—22no—
245C2×Dic11—22no—
246C2×Dic11—42no—
247C2×Dic11—42no—
248C2×Dic11—42no—
249D44—42no—
250D44—42no—
251C4×D11—48no—
252Dic22—42no—
253Dic22—42no—
254C11⋊C8—44no—
255C22×#41—111no—
256C24×C4C2×D1111yescharacteristic
257C23×C8—221no—
258#525—114no—
259#525—114no—
260#525—222no—
261#525—222no—
262C2×#123—221no—
263C2×C22⋊Q8—111no—
264C2×C22⋊Q8—111no—
265C2×#121—111no—
266C2×#121—111no—
267C2×#120—221no—
268C2×C4×D4—221no—
269C2×C4×D4—221no—
270C2×#117—111no—
271C22×C22⋊C4—21no—
272C2×C22⋊C8—112no—
273C2×C22⋊C8—114no—
274C2×C22⋊C8—221no—
275C2×C22⋊C8—222no—
276#381—22no—
277#381C2×D1114yescomplemented
278C2×#95—21no—
279C2×#95C2×D1112yes—
280#328—118no—
281#327—118no—
282C22×C11—21no—
283C22×C11—21no—
284C22×C11—22no—
285C22×C11—21no—
286C22×C11—22no—
287C22×C11—21no—
288C22×C11—28no—
289C22×C11—28no—
290C22×C11—22no—
291C22×C11—22no—
292C22×C11—22no—
293C22×C11—48no—
294C22×C11—48no—
295C22×C11—44no—
296C22×C11C2×#9914yes—
297C22×C11C2×#9912yes—
298C22×C11#41612yes—
299C22×C11#41612yes—
300C22×C11#42112yes—
301C22×C11C22×C22⋊C411yescharacteristic
302C22×C11C2×#13512yes—
303C2×D11—42no—
304C2×D11—42no—
305C2×D11—42no—
306C2×D11—84no—
307C4×C11—22no—
308C4×C11—21no—
309C4×C11—21no—
310C4×C11—22no—
311C4×C11—21no—
312C4×C11—21no—
313C4×C11—84no—
314Dic11—42no—
315Dic11—42no—
316Dic11—42no—
317C25C22⋊D1111yescharacteristic
318C2×#41—114no—
319C2×#41—222no—
320C2×#41—444no—
321C22×Q8—111no—
322C22×D4—111no—
323C22×D4—221no—
324C22×D4—221no—
325C22×D4—221no—
326C23×C4—22no—
327C23×C4—44no—
328C23×C4—221no—
329C23×C4C4×D1111yescharacteristic
330C23×C4C4×D1111yescharacteristic
331C23×C4C4×D1112yes—
332C23×C4D4411yescharacteristic
333C23×C4D4411yescharacteristic
334C23×C4D4412yes—
335C23×C4C22⋊D1111yescharacteristic
336C23×C4C22⋊D1112yes—
337C23×C4C22×D1111yescharacteristic
338C23×C4C22×D1112yes—
339C22×C8—224no—
340C22×C8—222no—
341C22×C8—444no—
342#123—224no—
343#123—224no—
344C22⋊Q8—112no—
345C22⋊Q8—114no—
346C22⋊Q8—112no—
347C22⋊Q8—222no—
348C22⋊Q8—221no—
349C22⋊Q8—221no—
350#121—112no—
351#121—114no—
352#121—112no—
353#121—222no—
354#121—221no—
355#121—221no—
356#120—224no—
357#120—224no—
358C4×D4—224no—
359C4×D4—224no—
360C4×D4—224no—
361C4×D4—224no—
362#117—114no—
363#117—222no—
364C2×C4⋊C4—111no—
365C2×C4⋊C4—111no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4—221no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—221no—
371C2×C22⋊C4—221no—
372C2×C22⋊C4—221no—
373C2×C22⋊C4—221no—
374C2×C22⋊C4—221no—
375C2×C42—221no—
376C22⋊C8—114no—
377C22⋊C8—224no—
378C22⋊C8—222no—
379#95—24no—
380#95—22no—
381#95C22×D1114yes—
382C2×C11—22no—
383C2×C11—24no—
384C2×C11—22no—
385C2×C11—42no—
386C2×C11#151614yescomplemented
387C2×C11C22×#9911yescharacteristic
388C2×C11C2×#41611yescharacteristic
389C2×C11C2×#42111yescharacteristic
390D11—82no—
391C24—24no—
392C24—24no—
393C24—42no—
394C24—221no—
395C24(C2×D11)⋊C411yescharacteristic
396C24(C2×D11)⋊C412yes—
397C24(C2×D11)⋊C411yescharacteristic
398C24C2×C22⋊D1112yes—
399C24C2×C22⋊D1111yescharacteristic
400#41—448no—
401#41—448no—
402C2×Q8—112no—
403C2×Q8—221no—
404C2×Q8—442no—
405C2×D4—112no—
406C2×D4—224no—
407C2×D4—222no—
408C2×D4—224no—
409C2×D4—222no—
410C2×D4—221no—
411C2×D4—442no—
412C2×D4—444no—
413C2×D4—444no—
414C2×D4—444no—
415C22×C4—24no—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—42no—
419C22×C4—44no—
420C22×C4—42no—
421C22×C4—44no—
422C22×C4—42no—
423C22×C4—44no—
424C22×C4—42no—
425C22×C4—44no—
426C22×C4—44no—
427C22×C4—44no—
428C22×C4—44no—
429C22×C4—221no—
430C22×C4—221no—
431C22×C4—221no—
432C22×C4—224no—
433C22×C4—444no—
434C22×C4(C2×D11)⋊C412yes—
435C22×C4(C2×D11)⋊C412yes—
436C22×C4(C2×D11)⋊C411yescharacteristic
437C22×C4(C2×D11)⋊C411yescharacteristic
438C22×C4(C2×D11)⋊C412yes—
439C22×C4(C2×D11)⋊C412yes—
440C22×C4(C2×D11)⋊C412yes—
441C22×C4C2×C4×D1112yes—
442C22×C4C2×C4×D1111yescharacteristic
443C22×C4C2×C4×D1112yes—
444C22×C4C2×C4×D1111yescharacteristic
445C22×C4C2×D4412yes—
446C22×C4C2×D4411yescharacteristic
447C22×C4C2×D4412yes—
448C22×C4C2×D4411yescharacteristic
449C22×C4C2×C22⋊D1112yes—
450C22×C4C2×C22⋊D1111yescharacteristic
451C22×C4C23×D1111yescharacteristic
452C2×C8—224no—
453C2×C8—448no—
454C2×C8—444no—
455C4⋊C4—112no—
456C4⋊C4—112no—
457C4⋊C4—221no—
458C4⋊C4—221no—
459C4⋊C4—224no—
460C4⋊C4—222no—
461C4⋊C4—222no—
462C22⋊C4—48no—
463C22⋊C4—224no—
464C22⋊C4—224no—
465C22⋊C4—222no—
466C22⋊C4—222no—
467C22⋊C4—224no—
468C22⋊C4—222no—
469C22⋊C4—222no—
470C42—224no—
471C11C2×#151611yescharacteristic, complemented, Sylow
472C23—22no—
473C23—22no—
474C23—22no—
475C23—22no—
476C23—24no—
477C23—24no—
478C23—22no—
479C23—24no—
480C23—24no—
481C23—22no—
482C23—22no—
483C23—42no—
484C23—42no—
485C23—416no—
486C23—222no—
487C23—442no—
488C23—442no—
489C23—442no—
490C23#6687014yes—
491C23C2×(C2×D11)⋊C412yes—
492C23C2×(C2×D11)⋊C412yes—
493C23C2×(C2×D11)⋊C411yescharacteristic
494C23C2×(C2×D11)⋊C411yescharacteristic
495C23#6700314yes—
496C23C22×C22⋊D1111yescharacteristic
497Q8—442no—
498Q8—442no—
499D4—442no—
500D4—442no—
501D4—448no—
502D4—448no—
503D4—444no—
504D4—444no—
505C2×C4—24no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—24no—
509C2×C4—22no—
510C2×C4—24no—
511C2×C4—22no—
512C2×C4—24no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—41no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—41no—
520C2×C4—42no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—44no—
524C2×C4—44no—
525C2×C4—44no—
526C2×C4—88no—
527C2×C4—222no—
528C2×C4—222no—
529C2×C4—222no—
530C2×C4—448no—
531C2×C4—442no—
532C2×C4—442no—
533C2×C4—442no—
534C2×C4C2×(C2×D11)⋊C412yes—
535C2×C4C2×(C2×D11)⋊C411yescharacteristic
536C2×C4C2×(C2×D11)⋊C412yes—
537C2×C4C2×(C2×D11)⋊C411yescharacteristic
538C2×C4C22×C4×D1111yescharacteristic
539C2×C4C22×D4411yescharacteristic
540C8—444no—
541C22—21no—
542C22—21no—
543C22—22no—
544C22—28no—
545C22—28no—
546C22—21no—
547C22—22no—
548C22—21no—
549C22—22no—
550C22—22no—
551C22—22no—
552C22—48no—
553C22—48no—
554C22—44no—
555C22—442no—
556C22—442no—
557C22—442no—
558C22—884no—
559C22C2×#6687014yes—
560C22C2×#6687012yes—
561C22#1062261512yes—
562C22#1062261512yes—
563C22#1062261812yes—
564C22C22×(C2×D11)⋊C411yescharacteristic
565C22C2×#6700312yes—
566C4—21no—
567C4—22no—
568C4—21no—
569C4—22no—
570C4—21no—
571C4—21no—
572C4—84no—
573C4—442no—
574C4—442no—
575C4—442no—
576C2—22no—
577C2—24no—
578C2—22no—
579C2—42no—
580C2—882no—
581C2#1306717014yesdirect product factor
582C2C22×#6687011yescharacteristic
583C2C2×#1062261511yescharacteristic
584C2C2×#1062261811yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#381C2
socleC23×C11C2×C22⋊C4
prime radicalC2×#10623322C2
cosocleC22×C4×C11C24
hypercenterC2×#381D11
hypocenterC11C2×#1516
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
2. C22×C22⋊(C11⋊C8)C2semidirect
3. #13067170C2direct (N × H)
4. C2×#10622090C2semidirect
5. C2×#10622089C2semidirect
6. C2×C11×#381C2semidirect
8. C22×#4339C4semidirect
13. #10623322C4semidirect
15. C2×#66983C4semidirect
20. C2×#66979C4semidirect
21. C2×#66977C4semidirect
25. C11×#381C22semidirect
31. C2×C22⋊(C11⋊C8)C22semidirect
32. #10622090C22semidirect
33. #10622089C22semidirect
52. C2×#4339C2×C4semidirect
67. #66983C2×C4semidirect
78. #66979C2×C4semidirect
85. #66977C2×C4semidirect
182. C2×#381D11semidirect
277. #381C2×D11semidirect
386. C2×C11#1516semidirect
471. C11C2×#1516semidirect
581. C2#13067170direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106233222
C22×C22⋊(C11⋊C8)2
#130671702
C2×#106220902
C2×#106220892
C2×C11×#3812
C2×#151611