Finite Group Databasebeta

← C2×#13081587 #15634663

Subgroups — C2×#13081587 #15634663

Order 2816.

2582 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623084C211yesmaximal, characteristic, complemented
2C2×#10623249C211yesmaximal, characteristic, complemented
3#13081587C2116yesmaximal, direct product factor
4C2×#10622686C211yesmaximal, characteristic, complemented
5C2×#10622764C212yesmaximal, complemented
6C2×#10622456C211yesmaximal, characteristic, complemented
7C2×#10622399C212yesmaximal, complemented
8C2×#10622763C212yesmaximal, complemented
9C2×#10622443C211yesmaximal, characteristic, complemented
10C2×C4×#4323C211yesmaximal, characteristic, complemented
11C2×#10622369C212yesmaximal, complemented
12C2×C11×#459C211yesmaximal, characteristic, complemented
13C22×#4341—21no—
14C22×#4339—21no—
15C22×C11×D8C2212yes—
16C2×C11×#127C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×#66993C2212yes—
19C2×#66993C2212yes—
20C2×#66992—22no—
21C2×#66991—21no—
22C2×D4×Dic11C2212yes—
23C22×#4323C2212yes—
24C22×#4323C2211yescharacteristic
25C22×#4323C2212yes—
26C2×#66983—21no—
27C22×D88C2212yes—
28#10623249—24no—
29#10623249C2218yescomplemented
30#10623084—24no—
31#10623084C2218yescomplemented
32C2×#66946C2212yes—
33C2×#66937—22no—
34C2×#66927C2211yescharacteristic
35C2×C4×D44C2211yescharacteristic
36C2×C4×Dic22C2211yescharacteristic
37C11×#459C2218yescomplemented
38C2×C11×C4⋊C8C2211yescharacteristic
39C2×C11×#102C2212yes—
40C2×#66896C2211yescharacteristic
41#10622764C22116yescomplemented
42#10622763C22116yescomplemented
43C2×#66885C2212yes—
44C2×Dic11⋊C8C2212yes—
45C2×C8×Dic11C2212yes—
46#10622686C2218yescomplemented
47C4×#4323C2218yescomplemented
48C2×#66873C2211yescharacteristic
49C2×#66871C2211yescharacteristic
50C2×C4×C11⋊C8C2211yescharacteristic
51#10622456C2218yescomplemented
52#10622443C2218yescomplemented
53#10622399C22116yescomplemented
54#10622369C22116yescomplemented
55C22×D4×C11—21no—
56C22×D4×C11—21no—
57C22×D4×C11C2312yes—
58C22×D4×C11C2311yescharacteristic
59C23×C4×C11—21no—
60C22×C22⋊D11—22no—
61C22×C22⋊D11—22no—
62C22×C22⋊D11—22no—
63C22×C22⋊D11—22no—
64C23×Dic11—22no—
65C2×#4341—28no—
66C2×#4341—48no—
67C2×#4339—28no—
68C2×#4339—48no—
69C22×D44—21no—
70C22×D44—21no—
71C22×D44C2312yes—
72C22×D44C2311yescharacteristic
73C22×C4×D11—21no—
74C22×C4×D11—22no—
75C22×Dic22D411yescharacteristic
76C2×C11×D8—44no—
77C2×C11×D8C2318yes—
78C22×C8×C11C2312yes—
79C11×#127—22no—
80C11×#127C2314yes—
81C4×D4×C11—22no—
82C4×D4×C11C2314yes—
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C22⋊C4—21no—
85C2×C42×C11C2311yescharacteristic
86C2×C22⋊Dic11—22no—
87#66993—24no—
88#66993—24no—
89#66993C2318yes—
90#66993C2318yes—
91#66992—216no—
92#66991—28no—
93D4×Dic11—24no—
94D4×Dic11C2318yes—
95C2×#4323—28no—
96C2×#4323—24no—
97C2×#4323—44no—
98C2×#4323C2314yes—
99C2×#4323C2318yes—
100C2×#4323C2318yes—
101#66983—28no—
102C2×(C2×D11)⋊C4—21no—
103C2×(C2×D11)⋊C4—22no—
104C2×C4⋊Dic11D411yescharacteristic
105C2×C4⋊Dic11C2311yescharacteristic
106C2×Dic11⋊C4D412yes—
107C2×C4×Dic11C2312yes—
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C2×D88—44no—
111C2×D88C2318yes—
112#66946—24no—
113#66946C2318yes—
114#66937—216no—
115#66927—22no—
116#66927C2314yes—
117C4×D44—22no—
118C4×D44C2314yes—
119C4×Dic22D414yes—
120C4×Dic22C2314yes—
121C11×C4⋊C8C2314yes—
122C11×#102C2318yes—
123#66896C2314yes—
124#66885C2318yes—
125Dic11⋊C8C2318yes—
126C8×Dic11C2318yes—
127#66873C2314yes—
128#66871C2314yes—
129C4×C11⋊C8C2314yes—
130C2×#3391—111nomaximal, Sylow
131C24×C11—22no—
132C24×C11—21no—
133C23×D11—22no—
134C23×D11—21no—
135C2×D4×C11—22no—
136C2×D4×C11—24no—
137C2×D4×C11—21no—
138C2×D4×C11—24no—
139C2×D4×C11—24no—
140C2×D4×C11—22no—
141C2×D4×C11—24no—
142C2×D4×C11—22no—
143C2×D4×C11—44no—
144C2×D4×C11—82no—
145C2×D4×C11C2412yes—
146C2×D4×C11C2414yes—
147C22×C4×C11—21no—
148C22×C4×C11—24no—
149C22×C4×C11—44no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2411yescharacteristic
153C2×C22⋊D11—28no—
154C2×C22⋊D11—28no—
155C2×C22⋊D11—28no—
156C2×C22⋊D11—28no—
157C2×C22⋊D11—48no—
158C2×C22⋊D11—48no—
159C2×C22⋊D11—84no—
160C2×C22⋊D11—84no—
161C22×Dic11—28no—
162C22×Dic11—21no—
163C22×Dic11—48no—
164C22×Dic11C2×D412yes—
165C22×Dic11C2×D412yes—
166#4341—432no—
167#4339—432no—
168C2×D44—21no—
169C2×D44—22no—
170C2×D44—24no—
171C2×D44—24no—
172C2×D44—24no—
173C2×D44—22no—
174C2×D44—22no—
175C2×D44—24no—
176C2×D44—44no—
177C2×D44—82no—
178C2×D44C2412yes—
179C2×D44C2414yes—
180C2×C4×D11—28no—
181C2×C4×D11—24no—
182C2×C4×D11—48no—
183C2×C4×D11—44no—
184C2×Dic22D818yescomplemented
185C2×Dic22C2×D414yes—
186C11×D8—48no—
187C2×C8×C11—24no—
188C2×C8×C11C2414yes—
189C11×C4⋊C4—21no—
190C11×C4⋊C4C2412yes—
191C11×C22⋊C4—24no—
192C42×C11C2×D412yes—
193C42×C11C2412yes—
194C22⋊Dic11—28no—
195#4323—28no—
196#4323—216no—
197#4323—48no—
198(C2×D11)⋊C4—28no—
199(C2×D11)⋊C4—24no—
200C4⋊Dic11—21no—
201C4⋊Dic11C2×D414yes—
202C4⋊Dic11C2412yes—
203Dic11⋊C4C2×D418yes—
204C4×Dic11C2×D414yes—
205C4×Dic11C2414yes—
206C2×C11⋊C8—22no—
207C2×C11⋊C8#4114yescomplemented
208C2×C11⋊C8C2412yes—
209C2×C11⋊C8C2412yes—
210D88—48no—
211C2×#550—111no—
212C2×#550—111no—
213#3391—1116no—
214C2×#493—112no—
215C2×#493—111no—
216C2×#459—111no—
217C2×#459—112no—
218C2×#459—112no—
219C2×#459D1111yescharacteristic, complemented
220C2×C8×Q8—111no—
221C2×C4×D8—112no—
222C2×C4×D8—111no—
223C23×C11—24no—
224C23×C11—22no—
225C23×C11—44no—
226C23×C11—42no—
227C23×C11—44no—
228C23×C11—42no—
229C23×C11—42no—
230C23×C11—44no—
231C23×C11C22×D411yescharacteristic
232C22×D11—24no—
233C22×D11—22no—
234C22×D11—42no—
235C22×D11—44no—
236C22×D11—44no—
237C22×D11—42no—
238C22×D11—44no—
239C22×D11—42no—
240D4×C11—22no—
241D4×C11—24no—
242D4×C11—24no—
243D4×C11—22no—
244D4×C11—44no—
245D4×C11—42no—
246D4×C11—48no—
247D4×C11—84no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—42no—
251C2×C4×C11—48no—
252C2×C4×C11C2×D814yes—
253C2×C4×C11C22×D412yes—
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C22×D412yes—
256C2×C4×C11C2×#4112yes—
257C2×C4×C11H(5,𝔽2)12yes—
258C2×C4×C11C2511yescharacteristic
259C22⋊D11—416no—
260C22⋊D11—416no—
261C22⋊D11—88no—
262C22⋊D11—88no—
263C2×Dic11—24no—
264C2×Dic11—22no—
265C2×Dic11—42no—
266C2×Dic11—416no—
267C2×Dic11C2×D818yes—
268C2×Dic11C22×D414yes—
269C2×Dic11C22×D414yes—
270D44—22no—
271D44—24no—
272D44—22no—
273D44—24no—
274D44—42no—
275D44—44no—
276D44—48no—
277D44—84no—
278C4×D11—48no—
279C4×D11—416no—
280Dic22C2×D8116yescomplemented
281C8×C11—24no—
282C11⋊C8—22no—
283C11⋊C8C2×#4114yescomplemented
284C22×#41—221no—
285C22×#41—221no—
286C22×D8—112no—
287C22×D8—111no—
288C22×D8—112no—
289C22×D8—112no—
290C22×D8C2×D1112yes—
291#550—118no—
292#550—118no—
293#550—224no—
294#550—224no—
295C2×#127—112no—
296C2×#127—112no—
297C2×#127—111no—
298C2×#127C2×D1111yescharacteristic
299C2×#121—222no—
300C2×#121—221no—
301C2×#121—221no—
302C2×#121—222no—
303C2×C4×Q8—111no—
304C2×C4×D4—112no—
305C2×C4×D4—112no—
306C2×C4×D4—111no—
307C2×C4×D4C2×D1111yescharacteristic
308#493—1116no—
309#493—118no—
310#459—1116no—
311#459—118no—
312#459—1116no—
313#459C2×D1118yescomplemented
314C8×Q8—118no—
315C4×D8—118no—
316C4×D8—1116no—
317C2×#107—111no—
318C2×C4⋊C8—112no—
319C2×C4⋊C8C2×D1111yescharacteristic
320C2×#102—111no—
321C2×#102—112no—
322C2×#102—111no—
323C2×#102C2×D1112yes—
324C2×C4×C8—112no—
325C2×C4×C8—111no—
326C22×C11—44no—
327C22×C11—42no—
328C22×C11—42no—
329C22×C11—44no—
330C22×C11—44no—
331C22×C11—42no—
332C22×C11—88no—
333C22×C11—84no—
334C22×C11#55012yes—
335C22×C11C22×D812yes—
336C22×C11#57612yes—
337C22×C11C23×D411yescharacteristic
338C2×D11—44no—
339C2×D11—42no—
340C2×D11—44no—
341C2×D11—42no—
342C2×D11—44no—
343C2×D11—42no—
344C2×D11—88no—
345C2×D11—84no—
346C4×C11—22no—
347C4×C11—42no—
348C4×C11#55012yes—
349C4×C11C22×D814yes—
350C4×C11C22×#4111yescharacteristic
351C4×C11C2×H(5,𝔽2)11yescharacteristic
352Dic11—24no—
353Dic11—42no—
354Dic11C22×D818yes—
355C2×#41—228no—
356C2×#41—228no—
357C2×#41—448no—
358C2×#41—448no—
359C22×Q8—111no—
360C22×D4—21no—
361C22×D4—21no—
362C22×D4—112no—
363C22×D4—111no—
364C22×D4—222no—
365C22×D4—222no—
366C22×D4—222no—
367C22×D4—222no—
368C22×D4—221no—
369C22×D4—221no—
370C22×D4C22×D1112yes—
371C22×D4C22×D1111yescharacteristic
372C23×C4—21no—
373C23×C4—222no—
374C23×C4—222no—
375C23×C4—221no—
376C2×D8—44no—
377C2×D8—114no—
378C2×D8—118no—
379C2×D8—118no—
380C2×D8—118no—
381C2×D8—228no—
382C2×D8—224no—
383C2×D8—444no—
384C2×D8—444no—
385C2×D8C22×D1118yes—
386C22×C8—111no—
387C22×C8—111no—
388C22×C8C22×D1112yes—
389#127—22no—
390#127—118no—
391#127—118no—
392#127—114no—
393#127—224no—
394#127—224no—
395#127—222no—
396#127C22×D1114yes—
397#121—2216no—
398#121—228no—
399#121—228no—
400#121—2216no—
401C4×Q8—114no—
402C4×Q8—114no—
403C4×D4—22no—
404C4×D4—118no—
405C4×D4—118no—
406C4×D4—114no—
407C4×D4—224no—
408C4×D4—224no—
409C4×D4—222no—
410C4×D4C22×D1114yes—
411C2×C4⋊C4—112no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4C22×D1111yescharacteristic
415C2×C22⋊C4—21no—
416C2×C22⋊C4—222no—
417C2×C22⋊C4—222no—
418C2×C22⋊C4—221no—
419C2×C42—112no—
420C2×C42C22×D1111yescharacteristic
421#107—114no—
422C4⋊C8—118no—
423C4⋊C8C22×D1114yes—
424#102—114no—
425#102—118no—
426#102—114no—
427#102C22×D1118yes—
428C4×C8—118no—
429C4×C8—114no—
430C2×C11—82no—
431C2×C11—84no—
432C2×C11#339114yescomplemented
433C2×C11C2×#55011yescharacteristic
434C2×C11C23×D811yescharacteristic
435C2×C11C2×#57611yescharacteristic
436D11—84no—
437D11—82no—
438C24—21no—
439C24—22no—
440C24—222no—
441C24—221no—
442#41—4432no—
443#41—4432no—
444C2×Q8—118no—
445C2×Q8—114no—
446C2×D4—21no—
447C2×D4—22no—
448C2×D4—24no—
449C2×D4—24no—
450C2×D4—22no—
451C2×D4—24no—
452C2×D4—24no—
453C2×D4—22no—
454C2×D4—44no—
455C2×D4—82no—
456C2×D4—114no—
457C2×D4—112no—
458C2×D4—228no—
459C2×D4—228no—
460C2×D4—228no—
461C2×D4—228no—
462C2×D4—222no—
463C2×D4—221no—
464C2×D4—224no—
465C2×D4—224no—
466C2×D4—222no—
467C2×D4—224no—
468C2×D4—224no—
469C2×D4—222no—
470C2×D4—448no—
471C2×D4—448no—
472C2×D4—444no—
473C2×D4—882no—
474C2×D4—884no—
475C2×D4—884no—
476C2×D4C23×D1112yes—
477C2×D4C23×D1114yes—
478C22×C4—21no—
479C22×C4—24no—
480C22×C4—44no—
481C22×C4—112no—
482C22×C4—112no—
483C22×C4—228no—
484C22×C4—228no—
485C22×C4—221no—
486C22×C4—224no—
487C22×C4—448no—
488C22×C4—448no—
489C22×C4—444no—
490C22×C4D4×D1111yescharacteristic
491C22×C4D4×D1111yescharacteristic
492C22×C4C23×D1111yescharacteristic
493D8—48no—
494D8—228no—
495D8—2216no—
496D8—448no—
497D8—448no—
498C2×C8—24no—
499C2×C8—114no—
500C2×C8—112no—
501C2×C8—112no—
502C2×C8—222no—
503C2×C8C23×D1114yes—
504C4⋊C4—21no—
505C4⋊C4—118no—
506C4⋊C4—114no—
507C4⋊C4—112no—
508C4⋊C4—221no—
509C4⋊C4C23×D1112yes—
510C22⋊C4—24no—
511C22⋊C4—228no—
512C22⋊C4—228no—
513C22⋊C4—224no—
514C42—114no—
515C42—114no—
516C42D4×D1112yes—
517C42C23×D1112yes—
518C11C2×#339111yescharacteristic, complemented, Sylow
519C23—22no—
520C23—24no—
521C23—42no—
522C23—44no—
523C23—44no—
524C23—42no—
525C23—42no—
526C23—44no—
527C23—224no—
528C23—222no—
529C23—444no—
530C23—442no—
531C23—444no—
532C23—442no—
533C23—442no—
534C23—444no—
535C23C2×D4×D1111yescharacteristic
536Q8—1116no—
537D4—22no—
538D4—24no—
539D4—22no—
540D4—24no—
541D4—48no—
542D4—42no—
543D4—44no—
544D4—84no—
545D4—222no—
546D4—224no—
547D4—224no—
548D4—222no—
549D4—4416no—
550D4—4416no—
551D4—448no—
552D4—444no—
553D4—442no—
554D4—884no—
555D4—888no—
556D4—888no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—42no—
560C2×C4—48no—
561C2×C4—118no—
562C2×C4—114no—
563C2×C4—114no—
564C2×C4—224no—
565C2×C4—222no—
566C2×C4—4416no—
567C2×C4—4416no—
568C2×C4—442no—
569C2×C4—448no—
570C2×C4D8×D1114yes—
571C2×C4C2×D4×D1112yes—
572C2×C4C2×D4×D1112yes—
573C2×C4C2×D4×D1111yescharacteristic
574C2×C4#6703712yes—
575C2×C4#41×D1112yes—
576C2×C4C24×D1111yescharacteristic
577C8—24no—
578C8—114no—
579C8—222no—
580C22—42no—
581C22—44no—
582C22—44no—
583C22—42no—
584C22—42no—
585C22—44no—
586C22—84no—
587C22—88no—
588C22—444no—
589C22—442no—
590C22—444no—
591C22—442no—
592C22—442no—
593C22—444no—
594C22—888no—
595C22—884no—
596C22#1062313012yes—
597C22C2×D8×D1112yes—
598C22#1062330512yes—
599C22C22×D4×D1111yescharacteristic
600C4—22no—
601C4—42no—
602C4—118no—
603C4—224no—
604C4—442no—
605C4#1062313012yes—
606C4C2×D8×D1114yes—
607C4C2×#6703711yescharacteristic
608C4C2×#41×D1111yescharacteristic
609C2—82no—
610C2—84no—
611C2—884no—
612C2—882no—
613C2#1308158714yesdirect product factor
614C2C2×#1062313011yescharacteristic
615C2C22×D8×D1111yescharacteristic
616C2C2×#1062330511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#459C2
socleC23×C11C22×D4
hypercenterC2×#459D11
hypocenterC11C2×#3391
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. C2×#10623084C2semidirect
2. C2×#10623249C2semidirect
3. #13081587C2direct (N × H)
4. C2×#10622686C2semidirect
5. C2×#10622764C2semidirect
6. C2×#10622456C2semidirect
7. C2×#10622399C2semidirect
8. C2×#10622763C2semidirect
9. C2×#10622443C2semidirect
10. C2×C4×#4323C2semidirect
11. C2×#10622369C2semidirect
12. C2×C11×#459C2semidirect
29. #10623249C22semidirect
31. #10623084C22semidirect
37. C11×#459C22semidirect
41. #10622764C22semidirect
42. #10622763C22semidirect
46. #10622686C22semidirect
47. C4×#4323C22semidirect
51. #10622456C22semidirect
52. #10622443C22semidirect
53. #10622399C22semidirect
54. #10622369C22semidirect
184. C2×Dic22D8semidirect
207. C2×C11⋊C8#41semidirect
219. C2×#459D11semidirect
280. Dic22C2×D8semidirect
283. C11⋊C8C2×#41semidirect
313. #459C2×D11semidirect
432. C2×C11#3391semidirect
518. C11C2×#3391semidirect
613. C2#13081587direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230842
C2×#106232492
#130815872
C2×#106226862
C2×#106227642
C2×#106224562
C2×#106223992
C2×#106227632
C2×#106224432
C2×C4×#43232
C2×#106223692
C2×C11×#4592
C2×#339111