Finite Group Databasebeta

← C2×#13069283 #14756352

Subgroups — C2×#13069283 #14756352

Order 2816.

1046 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622737C211yesmaximal, characteristic, complemented
2C2×#10622618C211yesmaximal, characteristic
3C22×#66889C211yesmaximal, characteristic
4C2×#10622745C211yesmaximal, characteristic
5C2×M16×Dic11C211yesmaximal, characteristic, complemented
6#13069283C218yesmaximal, direct product factor
7C2×#10622170C211yesmaximal, characteristic, complemented
8C2×C11×#344C211yesmaximal, characteristic, complemented
9C22×#4339C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13C22×C4×Dic11C2211yescharacteristic
14C22×#4318C2211yescharacteristic
15C22×#4318C2211yescharacteristic
16C2×#66889—22no—
17C2×#66889—21no—
18C2×#66889—21no—
19C2×#66889C2214yes—
20C2×#66888C412yescomplemented
21#10622745C414yescomplemented
22#10622745C2214yes—
23C2×#66887C412yescomplemented
24#10622737—22no—
25#10622737C2214yescomplemented
26C2×#66886—22no—
27M16×Dic11—22no—
28M16×Dic11C2214yescomplemented
29C2×#66879—21no—
30C2×C8×Dic11—21no—
31#10622618—22no—
32#10622618C2214yes—
33C2×#66869—22no—
34C11×#344C2214yescomplemented
35#10622170C2214yescomplemented
36C23×C4×C11C2311yescharacteristic
37C22×C22⋊D11—21no—
38C23×Dic11—21no—
39C2×#4339—21no—
40C2×#4339—21no—
41C2×#4339—21no—
42C2×#4339—21no—
43C2×#4339—21no—
44C2×#4339—21no—
45C2×#4339—21no—
46C2×#4339—21no—
47C2×#4339—21no—
48C2×#4339—21no—
49C2×#4339C2×C412yes—
50C2×#4339C2312yes—
51C22×D44C2×C411yescharacteristic
52C22×C4×D11—21no—
53C22×Dic22C2×C411yescharacteristic
54C2×C11×M16—21no—
55C2×C11×M16—21no—
56C2×C11×M16—21no—
57C2×C11×M16—21no—
58C2×C11×M16—21no—
59C2×C11×M16—21no—
60C2×C11×M16—21no—
61C2×C11×M16—21no—
62C2×C11×M16C2×C412yes—
63C2×C11×M16C2×C412yes—
64C2×C11×M16C2312yes—
65C2×C11×M16C2312yes—
66C22×C8×C11—21no—
67C22×C8×C11—21no—
68C11×#117—21no—
69C11×#117—21no—
70C11×#117—21no—
71C11×#117C2312yes—
72C2×C11×C4⋊C4—21no—
73C2×C11×C22⋊C4—21no—
74C2×C42×C11—21no—
75C2×C4×Dic11—21no—
76C2×C4×Dic11—21no—
77C2×C4×Dic11—21no—
78C2×C4×Dic11D412yes—
79C2×C4×Dic11D411yescharacteristic
80C2×C4×Dic11D411yescharacteristic
81C2×C4×Dic11C2312yes—
82C2×#4318—21no—
83C2×#4318—21no—
84C2×#4318—21no—
85C2×#4318—21no—
86C2×#4318—21no—
87C2×#4318—21no—
88C2×#4318C2×C412yes—
89C2×#4318C2×C412yes—
90C2×#4318D412yes—
91C2×#4318D412yes—
92C2×#4318C2312yes—
93C2×#4318C2312yes—
94C22×C11⋊C8—21no—
95C22×C11⋊C8—21no—
96#66889—24no—
97#66889—24no—
98#66888C2×C418yescomplemented
99#66887C2×C418yescomplemented
100#66886—28no—
101#66879—24no—
102C8×Dic11—24no—
103#66869—28no—
104C2×#1932—111nomaximal, Sylow
105C24×C11#4111yescharacteristic
106C23×D11—21no—
107C22×C4×C11—41no—
108C22×C4×C11C22×C411yescharacteristic
109C22×C4×C11C22×C411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11#4111yescharacteristic
115C22×C4×C11#4111yescharacteristic
116C22×C4×C11#4111yescharacteristic
117C22×C4×C11#4111yescharacteristic
118C22×C4×C11#4111yescharacteristic
119C22×C4×C11#4111yescharacteristic
120C22×C4×C11#4111yescharacteristic
121C22×C4×C11C2411yescharacteristic
122C2×C22⋊D11—22no—
123C2×C22⋊D11—22no—
124C2×C22⋊D11—41no—
125C2×C22⋊D11—41no—
126C2×C22⋊D11—41no—
127C2×C22⋊D11—41no—
128C22×Dic11—21no—
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—44no—
134#4339—22no—
135#4339—22no—
136#4339—22no—
137#4339—22no—
138#4339—22no—
139#4339—22no—
140#4339—22no—
141#4339—22no—
142#4339—41no—
143#4339—41no—
144#4339—41no—
145#4339—41no—
146#4339—41no—
147#4339—41no—
148#4339—41no—
149#4339—41no—
150C2×D44—21no—
151C2×D44—21no—
152C2×D44—21no—
153C2×D44—21no—
154C2×D44—21no—
155C2×D44C22×C412yes—
156C2×C4×D11—22no—
157C2×C4×D11—22no—
158C2×C4×D11—41no—
159C2×C4×D11—41no—
160C2×C4×D11—41no—
161C2×C4×D11—41no—
162C2×Dic22—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22—21no—
167C2×Dic22C22×C412yes—
168C11×M16—22no—
169C11×M16—22no—
170C11×M16—22no—
171C11×M16—22no—
172C11×M16—22no—
173C11×M16—41no—
174C11×M16—41no—
175C11×M16C22×C414yes—
176C2×C8×C11—22no—
177C2×C8×C11—22no—
178C2×C8×C11—22no—
179C2×C8×C11—22no—
180C2×C8×C11—41no—
181C2×C8×C11—41no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—41no—
184C11×C22⋊C4—22no—
185C11×C22⋊C4—41no—
186C42×C11—22no—
187C42×C11—41no—
188C4×Dic11—21no—
189C4×Dic11—22no—
190C4×Dic11—21no—
191C4×Dic11—22no—
192C4×Dic11C2×D412yes—
193C4×Dic11C2×D412yes—
194#4318—22no—
195#4318—22no—
196#4318—22no—
197#4318—22no—
198#4318—22no—
199#4318—22no—
200#4318C22×C414yes—
201#4318C2×D414yes—
202C2×C11⋊C8—22no—
203C2×C11⋊C8—22no—
204C2×C11⋊C8—22no—
205C2×C11⋊C8—22no—
206C2×C11⋊C8—22no—
207C2×C11⋊C8—22no—
208C2×#430—111no—
209C2×#421—111no—
210C22×#104—111no—
211C2×#413—111no—
212C2×C4×M16—111no—
213#1932—118no—
214C2×#344D1111yescharacteristic, complemented
215C2×#339—111no—
216C23×C11—42no—
217C23×C11#11711yescharacteristic
218C23×C11#11711yescharacteristic
219C23×C11#12311yescharacteristic
220C23×C11#12311yescharacteristic
221C23×C11#12411yescharacteristic
222C23×C11#12411yescharacteristic
223C23×C11C2×#4111yescharacteristic
224C22×D11—22no—
225C22×D11—41no—
226C22×D11—41no—
227C22×D11—82no—
228C2×C4×C11—42no—
229C2×C4×C11—82no—
230C2×C4×C11#11711yescharacteristic
231C2×C4×C11#11711yescharacteristic
232C2×C4×C11C4×D411yescharacteristic
233C2×C4×C11C4×D411yescharacteristic
234C2×C4×C11C4×D411yescharacteristic
235C2×C4×C11C4×D411yescharacteristic
236C2×C4×C11C4×D411yescharacteristic
237C2×C4×C11C4×D411yescharacteristic
238C2×C4×C11C4×D411yescharacteristic
239C2×C4×C11C4×D411yescharacteristic
240C2×C4×C11#12111yescharacteristic
241C2×C4×C11#12111yescharacteristic
242C2×C4×C11#12111yescharacteristic
243C2×C4×C11#12111yescharacteristic
244C2×C4×C11#12311yescharacteristic
245C2×C4×C11#12311yescharacteristic
246C2×C4×C11#12411yescharacteristic
247C2×C4×C11#12411yescharacteristic
248C2×C4×C11#12611yescharacteristic
249C2×C4×C11#12611yescharacteristic
250C2×C4×C11#12611yescharacteristic
251C2×C4×C11#12611yescharacteristic
252C2×C4×C11C23×C411yescharacteristic
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C22⋊D11—42no—
259C22⋊D11—42no—
260C22⋊D11—42no—
261C22⋊D11—42no—
262C2×Dic11—24no—
263C2×Dic11—22no—
264C2×Dic11—22no—
265C2×Dic11—22no—
266C2×Dic11—44no—
267C2×Dic11—44no—
268C2×Dic11—42no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271D44—22no—
272D44—22no—
273D44—41no—
274D44—41no—
275C4×D11—42no—
276C4×D11—42no—
277C4×D11—42no—
278C4×D11—42no—
279Dic22—22no—
280Dic22—22no—
281Dic22—41no—
282Dic22—41no—
283C8×C11—24no—
284C8×C11—42no—
285C11⋊C8—24no—
286C11⋊C8—24no—
287C22×#41—111no—
288C22×M16—111no—
289C22×M16—111no—
290C22×M16C2×D1111yescharacteristic
291C22×M16C2×D1111yescharacteristic
292C2×#117C2×D1111yescharacteristic
293C22×C42—111no—
294#430—114no—
295#430—222no—
296C2×#108—222no—
297#421—114no—
298#421—222no—
299C2×#104—114no—
300C2×#104—222no—
301C2×#104—221no—
302C2×#104—221no—
303C2×#104—222no—
304#413—114no—
305#413—114no—
306C2×#101—112no—
307C2×#100—112no—
308C4×M16—114no—
309C4×M16—222no—
310C2×#97—221no—
311C2×C4×C8—221no—
312#344C2×D1114yescomplemented
313#339—114no—
314C22×C11—22no—
315C22×C11—22no—
316C22×C11—22no—
317C22×C11—41no—
318C22×C11—41no—
319C22×C11—41no—
320C22×C11—41no—
321C22×C11#38811yescharacteristic
322C22×C11#38811yescharacteristic
323C22×C11#38811yescharacteristic
324C22×C11#38811yescharacteristic
325C22×C11C2×#11711yescharacteristic
326C22×C11C2×#12311yescharacteristic
327C22×C11C2×#12411yescharacteristic
328C2×D11—42no—
329C2×D11—82no—
330C2×D11—82no—
331C2×D11—82no—
332C4×C11—82no—
333C4×C11#38811yescharacteristic
334C4×C11#38811yescharacteristic
335C4×C11#38811yescharacteristic
336C4×C11#38811yescharacteristic
337C4×C11C2×C4×D411yescharacteristic
338C4×C11C2×C4×D411yescharacteristic
339C4×C11C2×#12111yescharacteristic
340C4×C11C2×#12611yescharacteristic
341Dic11—24no—
342Dic11—42no—
343Dic11—42no—
344C2×#41—112no—
345C2×#41—112no—
346C2×#41—221no—
347C2×#41—221no—
348C2×#41—221no—
349C2×#41—221no—
350C2×#41—221no—
351C2×#41—221no—
352C2×#41—221no—
353C2×#41—221no—
354C2×#41—221no—
355C2×#41—221no—
356C22×Q8—111no—
357C22×D4—111no—
358C22×D4—221no—
359C23×C4—221no—
360C23×C4—221no—
361C23×C4C22×D1111yescharacteristic
362C2×M16—21no—
363C2×M16—21no—
364C2×M16—21no—
365C2×M16—21no—
366C2×M16—21no—
367C2×M16—21no—
368C2×M16—21no—
369C2×M16—21no—
370C2×M16—112no—
371C2×M16—112no—
372C2×M16—112no—
373C2×M16—112no—
374C2×M16—112no—
375C2×M16—112no—
376C2×M16—221no—
377C2×M16—221no—
378C2×M16—221no—
379C2×M16—221no—
380C2×M16—221no—
381C2×M16—221no—
382C2×M16C4×D1112yes—
383C2×M16C4×D1112yes—
384C2×M16C22×D1112yes—
385C2×M16C22×D1112yes—
386C22×C8—21no—
387C22×C8—21no—
388C22×C8—221no—
389C22×C8—221no—
390#117—21no—
391#117—21no—
392#117—21no—
393#117C22×D1112yes—
394C2×C4⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C42—21no—
397C2×C42—111no—
398C2×C42—111no—
399C2×C42—112no—
400C2×C42—112no—
401C2×C42—221no—
402C2×C42—221no—
403C2×C42—221no—
404#108—228no—
405#104—228no—
406#104—224no—
407#104—224no—
408#101—118no—
409#100—118no—
410#97—224no—
411C4×C8—224no—
412C2×C11—21no—
413C2×C11—21no—
414C2×C11—21no—
415C2×C11—21no—
416C2×C11—21no—
417C2×C11—21no—
418C2×C11#193212yescomplemented
419C2×C11C2×#38811yescharacteristic
420D11—82no—
421C24—221no—
422C24#433911yescharacteristic
423#41—222no—
424#41—222no—
425#41—222no—
426#41—222no—
427#41—222no—
428#41—222no—
429#41—222no—
430#41—222no—
431#41—441no—
432#41—441no—
433#41—441no—
434#41—441no—
435#41—441no—
436#41—441no—
437#41—441no—
438#41—441no—
439C2×Q8—112no—
440C2×Q8—221no—
441C2×Q8—221no—
442C2×Q8—221no—
443C2×Q8—221no—
444C2×Q8—221no—
445C2×D4—112no—
446C2×D4—222no—
447C2×D4—222no—
448C2×D4—221no—
449C2×D4—221no—
450C2×D4—221no—
451C2×D4—221no—
452C2×D4—221no—
453C2×D4—441no—
454C2×D4—441no—
455C2×D4—441no—
456C2×D4—441no—
457C22×C4—41no—
458C22×C4—221no—
459C22×C4—221no—
460C22×C4—222no—
461C22×C4—221no—
462C22×C4—222no—
463C22×C4—222no—
464C22×C4—222no—
465C22×C4—444no—
466C22×C4—441no—
467C22×C4—441no—
468C22×C4—441no—
469C22×C4—441no—
470C22×C4C2×C4×D1111yescharacteristic
471C22×C4C2×C4×D1111yescharacteristic
472C22×C4#433911yescharacteristic
473C22×C4#433911yescharacteristic
474C22×C4#433911yescharacteristic
475C22×C4D4×D1111yescharacteristic
476C22×C4D4×D1111yescharacteristic
477C22×C4D4×D1111yescharacteristic
478C22×C4D4×D1111yescharacteristic
479C22×C4#434111yescharacteristic
480C22×C4#434111yescharacteristic
481C22×C4#434311yescharacteristic
482C22×C4#434311yescharacteristic
483C22×C4C23×D1111yescharacteristic
484M16—22no—
485M16—22no—
486M16—22no—
487M16—22no—
488M16—22no—
489M16—41no—
490M16—41no—
491M16—114no—
492M16—114no—
493M16—222no—
494M16—222no—
495M16—222no—
496M16—222no—
497M16—222no—
498M16—222no—
499M16C2×C4×D1114yes—
500C2×C8—22no—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—22no—
504C2×C8—41no—
505C2×C8—41no—
506C2×C8—222no—
507C2×C8—222no—
508C2×C8—222no—
509C2×C8—222no—
510C2×C8—222no—
511C2×C8—222no—
512C4⋊C4—22no—
513C4⋊C4—41no—
514C22⋊C4—22no—
515C22⋊C4—41no—
516C42—22no—
517C42—41no—
518C42—112no—
519C42—112no—
520C42—221no—
521C42—222no—
522C42—221no—
523C42—222no—
524C11C2×#193211yescharacteristic, complemented, Sylow
525C23—42no—
526C23—222no—
527C23—441no—
528C23—441no—
529C23—882no—
530C23#6692511yescharacteristic
531C23#6692511yescharacteristic
532C23#6693811yescharacteristic
533C23#6693811yescharacteristic
534C23#6694711yescharacteristic
535C23#6694711yescharacteristic
536C23C2×#433911yescharacteristic
537Q8—222no—
538Q8—222no—
539Q8—441no—
540Q8—441no—
541D4—222no—
542D4—222no—
543D4—442no—
544D4—442no—
545D4—442no—
546D4—442no—
547D4—441no—
548D4—441no—
549C2×C4—42no—
550C2×C4—82no—
551C2×C4—224no—
552C2×C4—222no—
553C2×C4—222no—
554C2×C4—222no—
555C2×C4—444no—
556C2×C4—444no—
557C2×C4—442no—
558C2×C4—441no—
559C2×C4—441no—
560C2×C4—442no—
561C2×C4—442no—
562C2×C4—442no—
563C2×C4—442no—
564C2×C4#6692511yescharacteristic
565C2×C4#6692511yescharacteristic
566C2×C4(C22⋊D11)⋊C411yescharacteristic
567C2×C4(C22⋊D11)⋊C411yescharacteristic
568C2×C4(C22⋊D11)⋊C411yescharacteristic
569C2×C4(C22⋊D11)⋊C411yescharacteristic
570C2×C4#6693711yescharacteristic
571C2×C4#6693711yescharacteristic
572C2×C4#6693711yescharacteristic
573C2×C4#6693711yescharacteristic
574C2×C4#6693811yescharacteristic
575C2×C4#6693811yescharacteristic
576C2×C4#6694611yescharacteristic
577C2×C4#6694611yescharacteristic
578C2×C4#6694611yescharacteristic
579C2×C4#6694611yescharacteristic
580C2×C4#6694711yescharacteristic
581C2×C4#6694711yescharacteristic
582C2×C4#6695111yescharacteristic
583C2×C4#6695111yescharacteristic
584C2×C4#6695111yescharacteristic
585C2×C4#6695111yescharacteristic
586C2×C4C22×C4×D1111yescharacteristic
587C2×C4C2×#433911yescharacteristic
588C2×C4C2×D4×D1111yescharacteristic
589C2×C4C2×D4×D1111yescharacteristic
590C2×C4C2×#434111yescharacteristic
591C2×C4C2×#434311yescharacteristic
592C8—24no—
593C8—42no—
594C8—224no—
595C8—224no—
596C22—22no—
597C22—22no—
598C22—22no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—442no—
604C22—882no—
605C22—882no—
606C22—882no—
607C22#1062228211yescharacteristic
608C22#1062228211yescharacteristic
609C22#1062228211yescharacteristic
610C22#1062228211yescharacteristic
611C22C2×#6692511yescharacteristic
612C22C2×#6693811yescharacteristic
613C22C2×#6694711yescharacteristic
614C4—82no—
615C4—224no—
616C4—442no—
617C4—442no—
618C4#1062228211yescharacteristic
619C4#1062228211yescharacteristic
620C4#1062228211yescharacteristic
621C4#1062228211yescharacteristic
622C4C2×(C22⋊D11)⋊C411yescharacteristic
623C4C2×#6693711yescharacteristic
624C4C2×#6694611yescharacteristic
625C4C2×#6695111yescharacteristic
626C2—21no—
627C2—21no—
628C2—21no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—882no—
633C2#1306928312yesdirect product factor
634C2C2×#1062228211yescharacteristic
subgroupG/H
centerC2×C4#66937
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#344C2
socleC22×C11#388
prime radicalC22×#4339C22
cosocleC22×C4×C11C24
hypercenterC2×#344D11
hypocenterC11C2×#1932
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
1. C2×#10622737C2semidirect
5. C2×M16×Dic11C2semidirect
6. #13069283C2direct (N × H)
7. C2×#10622170C2semidirect
8. C2×C11×#344C2semidirect
20. C2×#66888C4semidirect
21. #10622745C4semidirect
23. C2×#66887C4semidirect
25. #10622737C22semidirect
28. M16×Dic11C22semidirect
34. C11×#344C22semidirect
35. #10622170C22semidirect
98. #66888C2×C4semidirect
99. #66887C2×C4semidirect
214. C2×#344D11semidirect
312. #344C2×D11semidirect
418. C2×C11#1932semidirect
524. C11C2×#1932semidirect
633. C2#13069283direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106227372
C2×#106226182
C22×#668892
C2×#106227452
C2×M16×Dic112
#130692832
C2×#106221702
C2×C11×#3442
C2×#193211