Finite Group Databasebeta

← C2×#13078958 #15622996

Subgroups — C2×#13078958 #15622996

Order 2816.

2182 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623259C211yesmaximal, characteristic, complemented
2C2×#10623199C211yesmaximal, characteristic
3#13078958C2116yesmaximal, direct product factor
4C2×#10622410C212yesmaximal, complemented
5C2×#10622377C212yesmaximal, complemented
6C2×#10622702C211yesmaximal, characteristic, complemented
7C2×#10622327C211yesmaximal, characteristic, complemented
8C2×#10622668C211yesmaximal, characteristic, complemented
9C2×#10622417C212yesmaximal, complemented
10C2×#10622385C212yesmaximal, complemented
11C2×D11×#97C211yesmaximal, characteristic, complemented
12C2×C11×#489C211yesmaximal, characteristic, complemented
13C22×#4343C2211yescharacteristic
14C22×#4341C2211yescharacteristic
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#124C2211yescharacteristic
17C2×#66999—21no—
18C2×Q8×Dic11—21no—
19C2×#66997C2211yescharacteristic
20C2×#66993C2211yescharacteristic
21C22×C8×D11C2212yes—
22#10623259—24no—
23#10623259C2218yescomplemented
24#10623199—24no—
25#10623199C2218yes—
26C2×#66950—21no—
27C2×#66945C2212yes—
28C2×#66943C2212yes—
29C2×#66940—21no—
30C2×#66937—21no—
31C2×#66937—21no—
32C2×(C22⋊D11)⋊C4—21no—
33C2×(C22⋊D11)⋊C4—21no—
34C2×#66928C2211yescharacteristic
35C2×C42×D11C2211yescharacteristic
36C2×#66922C2211yescharacteristic
37C11×#489C2218yescomplemented
38C2×C11×#103C2212yes—
39C2×C11×#102C2212yes—
40C2×C11×#97C2211yescharacteristic
41C2×#66899C2212yes—
42C2×#66896C2212yes—
43C2×#66885C2212yes—
44C2×#66880C2212yes—
45C2×#66879C2212yes—
46#10622702C2218yescomplemented
47#10622668C2218yescomplemented
48C2×#66874C2212yes—
49C2×#66873C2212yes—
50C2×#66867C2211yescharacteristic
51#10622417C22116yescomplemented
52#10622410C22116yescomplemented
53#10622385C22116yescomplemented
54#10622377C22116yescomplemented
55#10622327C2218yescomplemented
56D11×#97C2218yescomplemented
57C22×Q8×C11—21no—
58C22×Q8×C11C2311yescharacteristic
59C22×D4×C11C2311yescharacteristic
60C22×C22⋊D11—21no—
61C22×C22⋊D11—21no—
62C22×C22⋊D11—21no—
63C23×Dic11—21no—
64C2×#4343—22no—
65C2×#4343—28no—
66C2×#4343C2314yes—
67C2×#4341—22no—
68C2×#4341—28no—
69C2×#4341C2314yes—
70C22×D44—21no—
71C22×D44C2311yescharacteristic
72C22×C4×D11—21no—
73C22×C4×D11D411yescharacteristic
74C22×C4×D11D411yescharacteristic
75C22×C4×D11C2311yescharacteristic
76C22×Dic22—21no—
77C22×Dic22C2311yescharacteristic
78C22×C8×C11C2312yes—
79C11×C4⋊Q8—22no—
80C11×C4⋊Q8C2314yes—
81C11×#124—22no—
82C11×#124C2314yes—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4C2312yes—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C42×C11C2311yescharacteristic
88#66999—28no—
89Q8×Dic11—28no—
90#66997—22no—
91#66997C2314yes—
92#66993—22no—
93#66993C2314yes—
94C2×(C2×D11)⋊C4—22no—
95C2×(C2×D11)⋊C4—21no—
96C2×(C2×D11)⋊C4—21no—
97C2×C4⋊Dic11—21no—
98C2×C4⋊Dic11—22no—
99C2×C4⋊Dic11C2312yes—
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4—22no—
103C2×C4×Dic11—22no—
104C2×C4×Dic11D411yescharacteristic
105C2×C4×Dic11D411yescharacteristic
106C2×C4×Dic11C2311yescharacteristic
107C22×C11⋊C8C2312yes—
108C2×C8×D11—28no—
109C2×C8×D11C2318yes—
110#66950—28no—
111#66945—24no—
112#66945C2318yes—
113#66943—24no—
114#66943C2318yes—
115#66940—28no—
116#66937—28no—
117#66937—28no—
118(C22⋊D11)⋊C4—28no—
119(C22⋊D11)⋊C4—28no—
120#66928—22no—
121#66928C2314yes—
122C42×D11D414yes—
123C42×D11C2314yes—
124#66922—22no—
125#66922C2314yes—
126C11×#103C2318yes—
127C11×#102C2318yes—
128C11×#97C2314yes—
129#66899C2318yes—
130#66896C2318yes—
131#66885C2318yes—
132#66880C2318yes—
133#66879C2318yes—
134#66874C2318yes—
135#66873C2318yes—
136#66867C2314yes—
137C2×#3135—111nomaximal, Sylow
138C24×C11—21no—
139C23×D11—21no—
140C23×D11C2×D411yescharacteristic
141C2×Q8×C11—21no—
142C2×Q8×C11—24no—
143C2×Q8×C11—24no—
144C2×Q8×C11—44no—
145C2×Q8×C11C2412yes—
146C2×D4×C11—21no—
147C2×D4×C11—24no—
148C2×D4×C11C2412yes—
149C22×C4×C11—22no—
150C22×C4×C11—21no—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2411yescharacteristic
154C2×C22⋊D11—24no—
155C2×C22⋊D11—24no—
156C2×C22⋊D11—24no—
157C2×C22⋊D11—44no—
158C2×C22⋊D11—44no—
159C2×C22⋊D11—44no—
160C22×Dic11—24no—
161C22×Dic11—22no—
162C22×Dic11—21no—
163C22×Dic11—44no—
164C22×Dic11C2×D411yescharacteristic
165C22×Dic11C2×D411yescharacteristic
166C22×Dic11C2×D411yescharacteristic
167#4343—216no—
168#4343—48no—
169#4341—216no—
170#4341—48no—
171C2×D44—24no—
172C2×D44—21no—
173C2×D44—24no—
174C2×D44—44no—
175C2×D44C2412yes—
176C2×C4×D11—24no—
177C2×C4×D11—42no—
178C2×C4×D11—42no—
179C2×C4×D11—44no—
180C2×C4×D11C2×D414yes—
181C2×C4×D11C2×D414yes—
182C2×C4×D11C2×D412yes—
183C2×C4×D11#4118yes—
184C2×C4×D11C2412yes—
185C2×Dic22—24no—
186C2×Dic22—21no—
187C2×Dic22—24no—
188C2×Dic22—44no—
189C2×Dic22C2412yes—
190C2×C8×C11—24no—
191C2×C8×C11C2414yes—
192C11×C4⋊C4—24no—
193C11×C4⋊C4—22no—
194C11×C4⋊C4C2414yes—
195C11×C22⋊C4—24no—
196C11×C22⋊C4—24no—
197C42×C11C2×D412yes—
198C42×C11C2412yes—
199(C2×D11)⋊C4—28no—
200(C2×D11)⋊C4—24no—
201(C2×D11)⋊C4—24no—
202C4⋊Dic11—28no—
203C4⋊Dic11—22no—
204C4⋊Dic11—24no—
205C4⋊Dic11C2414yes—
206Dic11⋊C4—24no—
207Dic11⋊C4—24no—
208Dic11⋊C4—28no—
209C4×Dic11—28no—
210C4×Dic11C2×D412yes—
211C4×Dic11C2×D414yes—
212C4×Dic11C2×D414yes—
213C4×Dic11C2412yes—
214C2×C11⋊C8—24no—
215C2×C11⋊C8C2414yes—
216C8×D11—216no—
217C2×#533—111no—
218C2×#532—111no—
219#3135—1116no—
220C2×#491—112no—
221C2×#490—112no—
222C2×#489—111no—
223C2×#489—111no—
224C2×#489—111no—
225C2×#489D1111yescharacteristic, complemented
226C2×#416—112no—
227C2×#416—112no—
228C22×#97—111no—
229C23×C11—22no—
230C23×C11—42no—
231C23×C11—42no—
232C23×C11—42no—
233C23×C11C22×D411yescharacteristic
234C22×D11—22no—
235C22×D11—22no—
236C22×D11—22no—
237C22×D11—42no—
238C22×D11—42no—
239C22×D11—42no—
240C22×D11#12414yes—
241C22×D11C22×D412yes—
242Q8×C11—24no—
243Q8×C11—48no—
244Q8×C11—42no—
245D4×C11—24no—
246D4×C11—42no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—24no—
250C2×C4×C11—22no—
251C2×C4×C11—42no—
252C2×C4×C11—44no—
253C2×C4×C11C22×D412yes—
254C2×C4×C11C22×D412yes—
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C2×#4114yes—
257C2×C4×C11C2511yescharacteristic
258C22⋊D11—48no—
259C22⋊D11—48no—
260C22⋊D11—48no—
261C2×Dic11—22no—
262C2×Dic11—22no—
263C2×Dic11—24no—
264C2×Dic11—22no—
265C2×Dic11—42no—
266C2×Dic11—44no—
267C2×Dic11—48no—
268C2×Dic11#12414yes—
269C2×Dic11C22×D412yes—
270C2×Dic11C22×D412yes—
271C2×Dic11C22×D412yes—
272D44—24no—
273D44—48no—
274D44—42no—
275C4×D11—44no—
276C4×D11—44no—
277C4×D11—48no—
278C4×D11#12418yes—
279C4×D11C2×#4118yes—
280Dic22—24no—
281Dic22—48no—
282Dic22—42no—
283C8×C11—24no—
284C11⋊C8—24no—
285C22×#41—111no—
286C22×#41—111no—
287C23×C8—112no—
288#533—118no—
289#533—224no—
290#532—118no—
291#532—224no—
292C2×C4⋊Q8—111no—
293C2×C4⋊Q8—111no—
294C2×C4⋊Q8C2×D1111yescharacteristic
295C2×#127—111no—
296C2×#125—112no—
297C2×#124—111no—
298C2×#124C2×D1111yescharacteristic
299C2×C22⋊Q8—221no—
300C2×C22⋊Q8—221no—
301C2×#121—221no—
302C2×#121—221no—
303C2×C4×Q8—221no—
304C2×C4×Q8—221no—
305C2×C4×D4—221no—
306C2×C4×D4—221no—
307C2×#117—112no—
308C22×C42—111no—
309#491—1116no—
310#490—1116no—
311#489—118no—
312#489—118no—
313#489—118no—
314#489C2×D1118yescomplemented
315#416—1116no—
316#416—1116no—
317C2×#103—112no—
318C2×#103—112no—
319C2×#103—112no—
320C2×#103C2×D1112yes—
321C2×#102—112no—
322C2×#102—112no—
323C2×#102—112no—
324C2×#102C2×D1112yes—
325C2×#97—112no—
326C2×#97—111no—
327C2×#97—118no—
328C2×#97C2×D1111yescharacteristic
329C22×C11—42no—
330C22×C11—42no—
331C22×C11—42no—
332C22×C11—84no—
333C22×C11C2×#12412yes—
334C22×C11#57512yes—
335C22×C11#57512yes—
336C22×C11C23×D411yescharacteristic
337C2×D11—28no—
338C2×D11—22no—
339C2×D11—22no—
340C2×D11—42no—
341C2×D11—42no—
342C2×D11—42no—
343C2×D11—84no—
344C2×D11C2×#12414yes—
345C4×C11—22no—
346C4×C11—22no—
347C4×C11—42no—
348C4×C11—44no—
349C4×C11C2×#12412yes—
350C4×C11C22×#4112yes—
351Dic11—22no—
352Dic11—22no—
353Dic11—42no—
354Dic11—44no—
355Dic11C2×#12414yes—
356C2×#41—114no—
357C2×#41—114no—
358C2×#41—222no—
359C2×#41—222no—
360C2×#41—228no—
361C2×#41—228no—
362C22×Q8—21no—
363C22×Q8—111no—
364C22×Q8—221no—
365C22×Q8C22×D1111yescharacteristic
366C22×D4—111no—
367C22×D4—221no—
368C22×D4—221no—
369C22×D4—221no—
370C22×D4—221no—
371C22×D4C22×D1111yescharacteristic
372C23×C4—111no—
373C23×C4—111no—
374C23×C4—111no—
375C23×C4—221no—
376C23×C4—221no—
377C22×C8—112no—
378C22×C8—118no—
379C22×C8—228no—
380C22×C8C22×D1112yes—
381C4⋊Q8—22no—
382C4⋊Q8—114no—
383C4⋊Q8—114no—
384C4⋊Q8—222no—
385C4⋊Q8—222no—
386C4⋊Q8C22×D1114yes—
387#127—114no—
388#127—222no—
389#125—118no—
390#125—224no—
391#124—22no—
392#124—114no—
393#124—222no—
394#124C22×D1114yes—
395C22⋊Q8—228no—
396C22⋊Q8—228no—
397#121—228no—
398#121—228no—
399C4×Q8—228no—
400C4×Q8—228no—
401C4×D4—228no—
402C4×D4—228no—
403#117—118no—
404#117—224no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—112no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4—222no—
410C2×C4⋊C4—222no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4C22×D1112yes—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—222no—
416C2×C22⋊C4—221no—
417C2×C22⋊C4—221no—
418C2×C42—111no—
419C2×C42—111no—
420C2×C42—111no—
421C2×C42—114no—
422C2×C42—114no—
423C2×C42—222no—
424C2×C42C22×D1111yescharacteristic
425#103—118no—
426#103—118no—
427#103—118no—
428#103C22×D1118yes—
429#102—118no—
430#102—118no—
431#102—118no—
432#102C22×D1118yes—
433#97—118no—
434#97—114no—
435#97C22×D1114yes—
436C2×C11—82no—
437C2×C11#313514yescomplemented
438C2×C11C22×#12411yescharacteristic
439C2×C11C2×#57511yescharacteristic
440C2×C11C2×#57511yescharacteristic
441D11—24no—
442D11—82no—
443C24—21no—
444C24—111no—
445C24—221no—
446#41—2216no—
447#41—2216no—
448#41—448no—
449#41—448no—
450C2×Q8—24no—
451C2×Q8—21no—
452C2×Q8—24no—
453C2×Q8—44no—
454C2×Q8—112no—
455C2×Q8—224no—
456C2×Q8—221no—
457C2×Q8—224no—
458C2×Q8—444no—
459C2×Q8C23×D1112yes—
460C2×D4—21no—
461C2×D4—24no—
462C2×D4—112no—
463C2×D4—224no—
464C2×D4—224no—
465C2×D4—224no—
466C2×D4—224no—
467C2×D4—221no—
468C2×D4—224no—
469C2×D4—444no—
470C2×D4—444no—
471C2×D4—444no—
472C2×D4—444no—
473C2×D4C23×D1112yes—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—111no—
477C22×C4—112no—
478C22×C4—118no—
479C22×C4—112no—
480C22×C4—111no—
481C22×C4—111no—
482C22×C4—114no—
483C22×C4—114no—
484C22×C4—224no—
485C22×C4—224no—
486C22×C4—222no—
487C22×C4—221no—
488C22×C4—442no—
489C22×C4—442no—
490C22×C4—444no—
491C22×C4—444no—
492C22×C4D4×D1111yescharacteristic
493C22×C4D4×D1111yescharacteristic
494C22×C4C23×D1111yescharacteristic
495C2×C8—24no—
496C2×C8—114no—
497C2×C8—2216no—
498C2×C8—224no—
499C2×C8C23×D1114yes—
500C4⋊C4—24no—
501C4⋊C4—22no—
502C4⋊C4—114no—
503C4⋊C4—224no—
504C4⋊C4—224no—
505C4⋊C4—228no—
506C4⋊C4—228no—
507C4⋊C4—222no—
508C4⋊C4—224no—
509C4⋊C4C23×D1114yes—
510C22⋊C4—24no—
511C22⋊C4—24no—
512C22⋊C4—228no—
513C22⋊C4—224no—
514C22⋊C4—224no—
515C42—114no—
516C42—114no—
517C42—112no—
518C42—112no—
519C42—228no—
520C42D4×D1112yes—
521C42C23×D1112yes—
522C11C2×#313511yescharacteristic, complemented, Sylow
523C23—22no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—112no—
528C23—114no—
529C23—222no—
530C23—222no—
531C23—222no—
532C23—442no—
533C23—442no—
534C23—442no—
535C23C2×D4×D1111yescharacteristic
536Q8—24no—
537Q8—48no—
538Q8—42no—
539Q8—224no—
540Q8—448no—
541Q8—442no—
542D4—24no—
543D4—42no—
544D4—224no—
545D4—448no—
546D4—448no—
547D4—448no—
548D4—448no—
549D4—442no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—22no—
554C2×C4—44no—
555C2×C4—42no—
556C2×C4—112no—
557C2×C4—114no—
558C2×C4—118no—
559C2×C4—118no—
560C2×C4—112no—
561C2×C4—112no—
562C2×C4—222no—
563C2×C4—222no—
564C2×C4—224no—
565C2×C4—222no—
566C2×C4—444no—
567C2×C4—444no—
568C2×C4—448no—
569C2×C4—448no—
570C2×C4—444no—
571C2×C4—442no—
572C2×C4C2×D4×D1112yes—
573C2×C4C2×D4×D1112yes—
574C2×C4C2×D4×D1111yescharacteristic
575C2×C4#41×D1114yes—
576C2×C4C24×D1111yescharacteristic
577C8—24no—
578C8—224no—
579C22—42no—
580C22—42no—
581C22—42no—
582C22—84no—
583C22—114no—
584C22—228no—
585C22—222no—
586C22—222no—
587C22—442no—
588C22—442no—
589C22—442no—
590C22—884no—
591C22D11×#12412yes—
592C22#1062330412yes—
593C22#1062330812yes—
594C22C22×D4×D1111yescharacteristic
595C4—22no—
596C4—22no—
597C4—42no—
598C4—44no—
599C4—114no—
600C4—222no—
601C4—222no—
602C4—442no—
603C4—444no—
604C4D11×#12412yes—
605C4C2×#41×D1112yes—
606C2—82no—
607C2—224no—
608C2—882no—
609C2#1307895814yesdirect product factor
610C2C2×D11×#12411yescharacteristic
611C2C2×#1062330411yescharacteristic
612C2C2×#1062330811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#489C2
socleC23×C11C22×D4
prime radicalC2×#10623199C2
hypercenterC2×#489D11
hypocenterC11C2×#3135
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#489

Complements

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

NH ≅ G/Ntype
1. C2×#10623259C2semidirect
3. #13078958C2direct (N × H)
4. C2×#10622410C2semidirect
5. C2×#10622377C2semidirect
6. C2×#10622702C2semidirect
7. C2×#10622327C2semidirect
8. C2×#10622668C2semidirect
9. C2×#10622417C2semidirect
10. C2×#10622385C2semidirect
11. C2×D11×#97C2semidirect
12. C2×C11×#489C2semidirect
23. #10623259C22semidirect
37. C11×#489C22semidirect
46. #10622702C22semidirect
47. #10622668C22semidirect
51. #10622417C22semidirect
52. #10622410C22semidirect
53. #10622385C22semidirect
54. #10622377C22semidirect
55. #10622327C22semidirect
56. D11×#97C22semidirect
225. C2×#489D11semidirect
314. #489C2×D11semidirect
437. C2×C11#3135semidirect
522. C11C2×#3135semidirect
609. C2#13078958direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232592
C2×#106231992
#130789582
C2×#106224102
C2×#106223772
C2×#106227022
C2×#106223272
C2×#106226682
C2×#106224172
C2×#106223852
C2×D11×#972
C2×C11×#4892
C2×#313511