Finite Group Databasebeta

← C2×#13068999 #14755313

Subgroups — C2×#13068999 #14755313

Order 2816.

1794 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623363C211yesmaximal, characteristic
2C2×#10622752C212yesmaximal, complemented
3C2×#10622853C211yesmaximal, characteristic, complemented
4#13068999C218yesmaximal, direct product factor
5C2×#10622193C212yesmaximal, complemented
6C2×C11×#568C211yesmaximal, characteristic, complemented
7C22×C11×#41C2211yescharacteristic
8C22×#4339C2211yescharacteristic
9C11×#568—22no—
10C11×#568—24no—
11C11×#568C2214yescomplemented
12C2×C11×#131—24no—
13C22×C11×M16—22no—
14C22×C11×M16C2212yes—
15#10623363—22no—
16#10623363—22no—
17#10623363C414yescomplemented
18#10623363C2214yes—
19C2×#67000C411yescharacteristic, complemented
20C2×#66997C411yescharacteristic, complemented
21C2×#66993C411yescharacteristic, complemented
22C2×#66992—22no—
23C2×#66989C411yescharacteristic, complemented
24C2×C4×C22⋊D11—22no—
25C2×#66979C2212yes—
26C22×C4×Dic11C2211yescharacteristic
27#10622853—22no—
28#10622853C2214yescomplemented
29C2×#66898—22no—
30#10622752—24no—
31#10622752C2218yescomplemented
32C2×#66889—24no—
33#10622193C2218yescomplemented
34C2×C11×#41—22no—
35C2×C11×#41—22no—
36C2×C11×#41—22no—
37C2×C11×#41—22no—
38C2×C11×#41C2×C412yes—
39C2×C11×#41D412yes—
40C2×C11×#41D412yes—
41C2×C11×#41C2312yes—
42C22×Q8×C11C2×C411yescharacteristic
43C22×D4×C11C2×C411yescharacteristic
44C22×D4×C11D412yes—
45C23×C4×C11D412yes—
46C23×C4×C11C2311yescharacteristic
47C22×C22⋊D11—22no—
48C22×C22⋊D11—21no—
49C23×Dic11—21no—
50C2×#4339—21no—
51C2×#4339—21no—
52C2×#4339—22no—
53C2×#4339—22no—
54C2×#4339—22no—
55C2×#4339—22no—
56C2×#4339C2×C412yes—
57C2×#4339C2312yes—
58C22×D44C2×C411yescharacteristic
59C22×C4×D11—21no—
60C22×Dic22C2×C411yescharacteristic
61C11×#131—216no—
62C11×#131—216no—
63C2×C11×M16—24no—
64C2×C11×M16—28no—
65C2×C11×M16—22no—
66C2×C11×M16—28no—
67C2×C11×M16—22no—
68C2×C11×M16—22no—
69C2×C11×M16D414yescomplemented
70C2×C11×M16D414yescomplemented
71C2×C11×M16C2314yes—
72C22×C8×C11—24no—
73C22×C8×C11—22no—
74C2×C22⋊Dic11—22no—
75C2×C22⋊Dic11—22no—
76#67000—22no—
77#67000C2×C414yescomplemented
78#66997—22no—
79#66997C2×C414yescomplemented
80#66993—22no—
81#66993C2×C414yescomplemented
82#66992—28no—
83#66992—28no—
84#66989—22no—
85#66989C2×C414yescomplemented
86C4×C22⋊D11—28no—
87C4×C22⋊D11—28no—
88C2×(C2×D11)⋊C4—22no—
89#66979—22no—
90#66979—22no—
91#66979—22no—
92#66979C2314yes—
93C2×C4⋊Dic11—22no—
94C2×Dic11⋊C4—22no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11—22no—
99C2×C4×Dic11C2×C411yescharacteristic
100C2×C4×Dic11C2×C411yescharacteristic
101C2×C4×Dic11C2×C412yes—
102C2×C4×Dic11C2312yes—
103#66898—28no—
104#66889—216no—
105C2×#1884—111nomaximal, Sylow
106C24×C11C22⋊C412yes—
107C24×C11C2×D411yescharacteristic
108C23×D11—21no—
109C11×#41—24no—
110C11×#41—24no—
111C11×#41—24no—
112C11×#41—24no—
113C11×#41—24no—
114C11×#41—24no—
115C11×#41—24no—
116C11×#41—24no—
117C2×Q8×C11—22no—
118C2×Q8×C11—22no—
119C2×Q8×C11C22⋊C412yes—
120C2×Q8×C11C22×C412yes—
121C2×D4×C11—24no—
122C2×D4×C11—24no—
123C2×D4×C11—22no—
124C2×D4×C11—22no—
125C2×D4×C11C22⋊C412yes—
126C2×D4×C11C22⋊C414yes—
127C2×D4×C11C22×C412yes—
128C2×D4×C11C2×D414yes—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11C22⋊C412yes—
134C22×C4×C11C22⋊C414yes—
135C22×C4×C11C22×C411yescharacteristic
136C22×C4×C11C22×C411yescharacteristic
137C22×C4×C11C2×D414yes—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D412yes—
142C22×C4×C11C2×D412yes—
143C22×C4×C11#4112yes—
144C22×C4×C11#4112yes—
145C22×C4×C11C2411yescharacteristic
146C2×C22⋊D11—28no—
147C2×C22⋊D11—22no—
148C2×C22⋊D11—22no—
149C2×C22⋊D11—48no—
150C2×C22⋊D11—42no—
151C2×C22⋊D11—42no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—22no—
155C22×Dic11—21no—
156C22×Dic11—22no—
157C22×Dic11—44no—
158C22×Dic11—42no—
159#4339—24no—
160#4339—24no—
161#4339—24no—
162#4339—24no—
163#4339—42no—
164#4339—42no—
165#4339—42no—
166#4339—42no—
167C2×D44—21no—
168C2×D44—22no—
169C2×D44—22no—
170C2×D44C22×C412yes—
171C2×C4×D11—22no—
172C2×C4×D11—22no—
173C2×C4×D11—41no—
174C2×C4×D11—41no—
175C2×C4×D11—41no—
176C2×C4×D11—41no—
177C2×Dic22—21no—
178C2×Dic22—22no—
179C2×Dic22—22no—
180C2×Dic22C22×C412yes—
181C11×M16—216no—
182C11×M16—24no—
183C11×M16—24no—
184C11×M16—24no—
185C11×M16C2×D418yescomplemented
186C2×C8×C11—216no—
187C2×C8×C11—24no—
188C2×C8×C11—24no—
189C2×C8×C11—24no—
190C22⋊Dic11—28no—
191C22⋊Dic11—24no—
192C22⋊Dic11—42no—
193(C2×D11)⋊C4—28no—
194C4⋊Dic11—24no—
195C4⋊Dic11—42no—
196Dic11⋊C4—28no—
197C4×Dic11—22no—
198C4×Dic11—21no—
199C4×Dic11—21no—
200C4×Dic11—22no—
201C4×Dic11—24no—
202C4×Dic11—42no—
203C4×Dic11C22×C412yes—
204C4×Dic11C22×C412yes—
205C2×#568D1111yescharacteristic, complemented
206C2×#532—111no—
207C2×#421—112no—
208C2×#410—111no—
209#1884—118no—
210C2×#339—112no—
211C23×C11—22no—
212C23×C11—22no—
213C23×C11—42no—
214C23×C11—44no—
215C23×C11C2×C22⋊C411yescharacteristic
216C23×C11C2×C22⋊C414yes—
217C23×C11C2×C22⋊C411yescharacteristic
218C23×C11#12112yes—
219C23×C11#12112yes—
220C23×C11C22×D411yescharacteristic
221C22×D11—22no—
222C22×D11—44no—
223C22×D11—41no—
224C22×D11—41no—
225Q8×C11—24no—
226Q8×C11—24no—
227D4×C11—28no—
228D4×C11—28no—
229D4×C11—24no—
230D4×C11—24no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11C2×C22⋊C414yes—
238C2×C4×C11C2×C22⋊C411yescharacteristic
239C2×C4×C11C2×C22⋊C411yescharacteristic
240C2×C4×C11C4×D412yes—
241C2×C4×C11C4×D412yes—
242C2×C4×C11C4×D412yes—
243C2×C4×C11C4×D412yes—
244C2×C4×C11#12012yes—
245C2×C4×C11#12011yescharacteristic
246C2×C4×C11#12011yescharacteristic
247C2×C4×C11#12112yes—
248C2×C4×C11#12112yes—
249C2×C4×C11#12311yescharacteristic
250C2×C4×C11#12311yescharacteristic
251C2×C4×C11#12312yes—
252C2×C4×C11C23×C411yescharacteristic
253C2×C4×C11C22×D412yes—
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C2×#4112yes—
256C22⋊D11—416no—
257C22⋊D11—44no—
258C22⋊D11—44no—
259C2×Dic11—24no—
260C2×Dic11—22no—
261C2×Dic11—22no—
262C2×Dic11—22no—
263C2×Dic11—44no—
264C2×Dic11—44no—
265C2×Dic11—42no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—44no—
269C2×Dic11—84no—
270D44—24no—
271D44—42no—
272C4×D11—42no—
273C4×D11—42no—
274C4×D11—42no—
275C4×D11—42no—
276Dic22—24no—
277Dic22—42no—
278C8×C11—28no—
279C22×#41—111no—
280C22×#41C2×D1111yescharacteristic
281#568—22no—
282#568—24no—
283#568C2×D1114yescomplemented
284C2×#131—24no—
285C22×M16—22no—
286C22×M16C2×D1112yes—
287#532—114no—
288#532—114no—
289#532—222no—
290#532—222no—
291C2×C4⋊Q8—111no—
292C2×#127—111no—
293C2×#124—111no—
294C2×#124—111no—
295C2×#121—222no—
296C2×C4×D4—222no—
297C2×#117—112no—
298C22×C42—111no—
299#421—118no—
300#421—224no—
301C2×#104—224no—
302#410—114no—
303#410—222no—
304C2×#99—222no—
305#339—118no—
306C22×C11—22no—
307C22×C11—24no—
308C22×C11—24no—
309C22×C11—41no—
310C22×C11—42no—
311C22×C11—41no—
312C22×C11—44no—
313C22×C11—44no—
314C22×C11—82no—
315C22×C11#38611yescharacteristic
316C22×C11#38612yes—
317C22×C11#38611yescharacteristic
318C22×C11C22×C22⋊C411yescharacteristic
319C22×C11C2×#12112yes—
320C2×D11—44no—
321C2×D11—42no—
322C2×D11—82no—
323C2×D11—82no—
324C4×C11—24no—
325C4×C11#38611yescharacteristic
326C4×C11#38611yescharacteristic
327C4×C11#38612yes—
328C4×C11C2×C4×D412yes—
329C4×C11C2×#12011yescharacteristic
330C4×C11C2×#12311yescharacteristic
331Dic11—24no—
332Dic11—42no—
333Dic11—42no—
334Dic11—84no—
335C2×#41—22no—
336C2×#41—22no—
337C2×#41—22no—
338C2×#41—22no—
339C2×#41—112no—
340C2×#41—112no—
341C2×#41—221no—
342C2×#41—221no—
343C2×#41—222no—
344C2×#41—222no—
345C2×#41—222no—
346C2×#41—222no—
347C2×#41C4×D1112yes—
348C2×#41D4412yes—
349C2×#41C22⋊D1112yes—
350C2×#41C22×D1112yes—
351C22×Q8—111no—
352C22×Q8C4×D1111yescharacteristic
353C22×D4—111no—
354C22×D4—222no—
355C22×D4—221no—
356C22×D4C4×D1111yescharacteristic
357C22×D4D4412yes—
358C23×C4—221no—
359C23×C4—221no—
360C23×C4C22⋊D1112yes—
361C23×C4C22×D1111yescharacteristic
362#131—216no—
363#131—216no—
364C2×M16—24no—
365C2×M16—28no—
366C2×M16—22no—
367C2×M16—28no—
368C2×M16—22no—
369C2×M16—22no—
370C2×M16C22⋊D1114yescomplemented
371C2×M16C22⋊D1114yescomplemented
372C2×M16C22×D1114yes—
373C22×C8—24no—
374C22×C8—22no—
375C4⋊Q8—114no—
376C4⋊Q8—222no—
377#127—114no—
378#127—222no—
379#124—114no—
380#124—114no—
381#124—222no—
382#124—222no—
383#121—228no—
384#121—228no—
385C4×D4—228no—
386C4×D4—228no—
387#117—114no—
388#117—222no—
389#117—222no—
390#117—222no—
391C2×C4⋊C4—222no—
392C2×C4⋊C4—222no—
393C2×C22⋊C4—222no—
394C2×C22⋊C4—222no—
395C2×C22⋊C4—222no—
396C2×C42—111no—
397C2×C42—111no—
398C2×C42—112no—
399C2×C42—112no—
400C2×C42—221no—
401C2×C42—221no—
402C2×C42—221no—
403C2×C42—222no—
404#104—2216no—
405#99—228no—
406C2×C11—21no—
407C2×C11—22no—
408C2×C11—21no—
409C2×C11—22no—
410C2×C11—44no—
411C2×C11#188412yescomplemented
412C2×C11C2×#38611yescharacteristic
413D11—82no—
414C24—221no—
415C24(C2×D11)⋊C412yes—
416C24C2×D4411yescharacteristic
417#41—24no—
418#41—24no—
419#41—24no—
420#41—24no—
421#41—24no—
422#41—24no—
423#41—24no—
424#41—24no—
425#41—224no—
426#41—224no—
427#41—224no—
428#41—224no—
429#41—442no—
430#41—442no—
431#41—442no—
432#41—442no—
433C2×Q8—22no—
434C2×Q8—22no—
435C2×Q8—112no—
436C2×Q8—221no—
437C2×Q8—222no—
438C2×Q8—222no—
439C2×Q8(C2×D11)⋊C412yes—
440C2×Q8C2×C4×D1112yes—
441C2×D4—24no—
442C2×D4—24no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—112no—
446C2×D4—228no—
447C2×D4—222no—
448C2×D4—222no—
449C2×D4—221no—
450C2×D4—222no—
451C2×D4—222no—
452C2×D4—448no—
453C2×D4—442no—
454C2×D4—442no—
455C2×D4(C2×D11)⋊C414yes—
456C2×D4(C2×D11)⋊C412yes—
457C2×D4C2×C4×D1112yes—
458C2×D4C2×D4414yes—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—221no—
464C22×C4—221no—
465C22×C4—222no—
466C22×C4—221no—
467C22×C4—222no—
468C22×C4—222no—
469C22×C4—222no—
470C22×C4—444no—
471C22×C4—441no—
472C22×C4—441no—
473C22×C4—441no—
474C22×C4—441no—
475C22×C4—442no—
476C22×C4(C2×D11)⋊C412yes—
477C22×C4(C2×D11)⋊C414yes—
478C22×C4C2×C4×D1111yescharacteristic
479C22×C4C2×C4×D1111yescharacteristic
480C22×C4C2×D4411yescharacteristic
481C22×C4#433912yes—
482C22×C4#433912yes—
483C22×C4C2×C22⋊D1114yes—
484C22×C4C2×C22⋊D1111yescharacteristic
485C22×C4C2×C22⋊D1111yescharacteristic
486C22×C4C2×C22⋊D1112yes—
487C22×C4C2×C22⋊D1112yes—
488C22×C4C23×D1111yescharacteristic
489M16—216no—
490M16—24no—
491M16—24no—
492M16—24no—
493M16C2×C22⋊D1118yescomplemented
494C2×C8—216no—
495C2×C8—24no—
496C2×C8—24no—
497C2×C8—24no—
498C4⋊C4—228no—
499C4⋊C4—224no—
500C4⋊C4—442no—
501C22⋊C4—228no—
502C22⋊C4—228no—
503C22⋊C4—224no—
504C22⋊C4—442no—
505C42—112no—
506C42—112no—
507C42—222no—
508C42—221no—
509C42—221no—
510C42—222no—
511C42—224no—
512C42—442no—
513C11C2×#188411yescharacteristic, complemented, Sylow
514C23—22no—
515C23—22no—
516C23—42no—
517C23—44no—
518C23—222no—
519C23—444no—
520C23—441no—
521C23—441no—
522C23C2×(C2×D11)⋊C411yescharacteristic
523C23C2×(C2×D11)⋊C414yes—
524C23C2×(C2×D11)⋊C411yescharacteristic
525C23#6698312yes—
526C23#6698312yes—
527C23C22×D4411yescharacteristic
528Q8—24no—
529Q8—24no—
530Q8—224no—
531Q8—442no—
532D4—28no—
533D4—28no—
534D4—24no—
535D4—24no—
536D4—224no—
537D4—4416no—
538D4—444no—
539D4—444no—
540D4—442no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—224no—
548C2×C4—222no—
549C2×C4—222no—
550C2×C4—222no—
551C2×C4—444no—
552C2×C4—444no—
553C2×C4—442no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—442no—
557C2×C4—442no—
558C2×C4—442no—
559C2×C4—442no—
560C2×C4—444no—
561C2×C4—884no—
562C2×C4C2×(C2×D11)⋊C414yes—
563C2×C4C2×(C2×D11)⋊C411yescharacteristic
564C2×C4C2×(C2×D11)⋊C411yescharacteristic
565C2×C4C4×C22⋊D1112yes—
566C2×C4C4×C22⋊D1112yes—
567C2×C4C4×C22⋊D1112yes—
568C2×C4C4×C22⋊D1112yes—
569C2×C4#6698211yescharacteristic
570C2×C4#6698211yescharacteristic
571C2×C4#6698212yes—
572C2×C4#6698312yes—
573C2×C4#6698312yes—
574C2×C4#6700612yes—
575C2×C4#6700611yescharacteristic
576C2×C4#6700611yescharacteristic
577C2×C4C22×C4×D1111yescharacteristic
578C2×C4C2×#433912yes—
579C2×C4C22×C22⋊D1112yes—
580C2×C4C22×C22⋊D1111yescharacteristic
581C8—28no—
582C22—22no—
583C22—24no—
584C22—24no—
585C22—41no—
586C22—41no—
587C22—42no—
588C22—44no—
589C22—44no—
590C22—82no—
591C22—444no—
592C22—442no—
593C22—882no—
594C22—882no—
595C22#1062282611yescharacteristic
596C22#1062282612yes—
597C22#1062282611yescharacteristic
598C22C22×(C2×D11)⋊C411yescharacteristic
599C22C2×#6698312yes—
600C4—24no—
601C4—224no—
602C4—442no—
603C4—442no—
604C4—884no—
605C4#1062282611yescharacteristic
606C4#1062282611yescharacteristic
607C4#1062282612yes—
608C4C2×C4×C22⋊D1112yes—
609C4C2×#6698211yescharacteristic
610C4C2×#6700611yescharacteristic
611C2—21no—
612C2—22no—
613C2—21no—
614C2—22no—
615C2—44no—
616C2—882no—
617C2#1306899912yesdirect product factor
618C2C2×#1062282611yescharacteristic
subgroupG/H
centerC2×C4#67006
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#568C2
socleC22×C11#386
prime radicalC2×#10623363C2
cosocleC22×C4×C11C24
hypercenterC2×#568D11
hypocenterC11C2×#1884
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#568

Complements

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

NH ≅ G/Ntype
2. C2×#10622752C2semidirect
3. C2×#10622853C2semidirect
4. #13068999C2direct (N × H)
5. C2×#10622193C2semidirect
6. C2×C11×#568C2semidirect
11. C11×#568C22semidirect
17. #10623363C4semidirect
19. C2×#67000C4semidirect
20. C2×#66997C4semidirect
21. C2×#66993C4semidirect
23. C2×#66989C4semidirect
28. #10622853C22semidirect
31. #10622752C22semidirect
33. #10622193C22semidirect
69. C2×C11×M16D4semidirect
70. C2×C11×M16D4semidirect
77. #67000C2×C4semidirect
79. #66997C2×C4semidirect
81. #66993C2×C4semidirect
85. #66989C2×C4semidirect
185. C11×M16C2×D4semidirect
205. C2×#568D11semidirect
283. #568C2×D11semidirect
370. C2×M16C22⋊D11semidirect
371. C2×M16C22⋊D11semidirect
411. C2×C11#1884semidirect
493. M16C2×C22⋊D11semidirect
513. C11C2×#1884semidirect
617. C2#13068999direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106233632
C2×#106227522
C2×#106228532
#130689992
C2×#106221932
C2×C11×#5682
C2×#188411