Finite Group Databasebeta

← C2×#13078592 #15621620

Subgroups — C2×#13078592 #15621620

Order 2816.

2234 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623364C211yesmaximal, characteristic
2C2×#10623054C211yesmaximal, characteristic, complemented
3#13078592C2116yesmaximal, direct product factor
4C2×#10622422C212yesmaximal, complemented
5C2×#10622427C212yesmaximal, complemented
6C2×#10622397C212yesmaximal, complemented
7C2×#10622387C212yesmaximal, complemented
8C2×#10622608C211yesmaximal, characteristic, complemented
9C22×#66882C211yesmaximal, characteristic, complemented
10C2×#10622845C211yesmaximal, characteristic, complemented
11C2×#10622723C211yesmaximal, characteristic, complemented
12C2×C11×#416C211yesmaximal, characteristic, complemented
13C22×C11×#41C2211yescharacteristic
14C22×#4339C2211yescharacteristic
15C23×C8×C11C2211yescharacteristic
16C2×C11×#117C2211yescharacteristic
17#10623364—24no—
18#10623364C2218yes—
19C2×#66999C2212yes—
20C2×#66992—22no—
21C2×#66991C2212yes—
22C2×#66983—21no—
23C22×C4⋊Dic11C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25C2×#66977—21no—
26C22×#4318C2211yescharacteristic
27#10623054—24no—
28#10623054C2218yescomplemented
29C2×#66945C2212yes—
30C2×C4⋊C4×D11C2212yes—
31C2×(C22⋊D11)⋊C4—22no—
32C2×C4×D44—21no—
33C2×C4×Dic22—21no—
34C11×#416C2218yescomplemented
35C2×C11×#103C2211yescharacteristic
36C2×C11×#103C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×C11×#102C2211yescharacteristic
39#10622845C2218yescomplemented
40C2×#66899C2212yes—
41C2×#66896C2212yes—
42#10622723C2218yescomplemented
43C2×(C2×D11)⋊C8C2212yes—
44C2×(C2×D11)⋊C8C2212yes—
45C2×#66882C2212yes—
46C2×#66882C2212yes—
47C2×#66882C2218yescomplemented
48#10622608C2218yescomplemented
49C2×#66872C2212yes—
50C2×#66871C2212yes—
51#10622427C22116yescomplemented
52#10622422C22116yescomplemented
53#10622397C22116yescomplemented
54#10622387C22116yescomplemented
55C2×C11×#41—22no—
56C2×C11×#41—24no—
57C2×C11×#41—24no—
58C2×C11×#41C2314yes—
59C22×Q8×C11C2311yescharacteristic
60C22×D4×C11—21no—
61C22×D4×C11C2311yescharacteristic
62C23×C4×C11—21no—
63C23×C4×C11C2311yescharacteristic
64C22×C22⋊D11—22no—
65C22×C22⋊D11D412yes—
66C23×Dic11—21no—
67C23×Dic11—21no—
68C2×#4339—24no—
69C2×#4339—24no—
70C2×#4339D414yes—
71C2×#4339C2314yes—
72C22×D44D411yescharacteristic
73C22×C4×D11—22no—
74C22×C4×D11C2312yes—
75C22×Dic22D411yescharacteristic
76C22×C8×C11—24no—
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2314yes—
80C11×#117—22no—
81C11×#117C2314yes—
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C22⋊C4—21no—
85C2×C42×C11—21no—
86C2×C22⋊Dic11—22no—
87#66999—24no—
88#66999C2318yes—
89#66992—216no—
90#66991—24no—
91#66991C2318yes—
92#66983—28no—
93C2×(C2×D11)⋊C4—22no—
94C2×(C2×D11)⋊C4—22no—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11—22no—
97C2×C4⋊Dic11—21no—
98C2×C4⋊Dic11—22no—
99C2×C4⋊Dic11C2312yes—
100C2×C4⋊Dic11C2314yes—
101C2×C4⋊Dic11C2312yes—
102C2×C4⋊Dic11C2314yes—
103#66977—28no—
104C2×Dic11⋊C4—22no—
105C2×Dic11⋊C4—22no—
106C2×C4×Dic11—22no—
107C2×#4318—24no—
108C2×#4318C2314yes—
109C22×C11⋊C8C2312yes—
110#66945—24no—
111#66945C2318yes—
112C4⋊C4×D11—24no—
113C4⋊C4×D11C2318yes—
114(C22⋊D11)⋊C4—216no—
115C4×D44—28no—
116C4×Dic22—28no—
117C11×#103C2314yes—
118C11×#103C2314yes—
119C11×#102C2314yes—
120C11×#102C2314yes—
121#66899C2318yes—
122#66896C2318yes—
123(C2×D11)⋊C8C2318yes—
124(C2×D11)⋊C8C2318yes—
125#66882C2318yes—
126#66882C2318yes—
127#66872C2318yes—
128#66871C2318yes—
129C2×#3098—111nomaximal, Sylow
130C24×C11—21no—
131C24×C11C2×D411yescharacteristic
132C23×D11C2×D412yes—
133C11×#41—28no—
134C11×#41—28no—
135C11×#41—48no—
136C2×Q8×C11—21no—
137C2×Q8×C11—22no—
138C2×Q8×C11—22no—
139C2×Q8×C11C2412yes—
140C2×D4×C11—24no—
141C2×D4×C11—21no—
142C2×D4×C11—22no—
143C2×D4×C11—22no—
144C2×D4×C11—44no—
145C2×D4×C11C2412yes—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—24no—
150C22×C4×C11—44no—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D412yes—
153C22×C4×C11#4114yes—
154C22×C4×C11#4114yes—
155C22×C4×C11C2411yescharacteristic
156C22×C4×C11C2412yes—
157C2×C22⋊D11—28no—
158C2×C22⋊D11—28no—
159C2×C22⋊D11—84no—
160C2×C22⋊D11C2×D418yes—
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11—24no—
164C22×Dic11—24no—
165C22×Dic11—82no—
166C22×Dic11—82no—
167C22×Dic11C2×D412yes—
168#4339—216no—
169#4339—28no—
170#4339—28no—
171C2×D44—24no—
172C2×D44C2×D414yes—
173C2×C4×D11—28no—
174C2×C4×D11—24no—
175C2×C4×D11—24no—
176C2×C4×D11—84no—
177C2×C4×D11C2×D414yes—
178C2×C4×D11C2414yes—
179C2×Dic22—24no—
180C2×Dic22C2×D414yes—
181C2×C8×C11—22no—
182C2×C8×C11—22no—
183C2×C8×C11—28no—
184C2×C8×C11C2412yes—
185C2×C8×C11C2412yes—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4C2412yes—
189C11×C4⋊C4C2412yes—
190C11×C22⋊C4—24no—
191C42×C11—24no—
192C22⋊Dic11—28no—
193(C2×D11)⋊C4—28no—
194(C2×D11)⋊C4—28no—
195C4⋊Dic11—24no—
196C4⋊Dic11—22no—
197C4⋊Dic11—24no—
198C4⋊Dic11—22no—
199C4⋊Dic11C2414yes—
200C4⋊Dic11C2414yes—
201Dic11⋊C4—28no—
202Dic11⋊C4—28no—
203C4×Dic11—28no—
204#4318—28no—
205C2×C11⋊C8—24no—
206C2×C11⋊C8C2414yes—
207C2×#537—111no—
208C2×#520—111no—
209#3098—1116no—
210C2×#484—112no—
211C2×#485—112no—
212C2×#482—112no—
213C2×#480—112no—
214C2×#428—111no—
215C22×#107—111no—
216C2×#417—111no—
217C2×#416D1111yescharacteristic, complemented
218C2×#408—111no—
219C23×C11—22no—
220C23×C11—22no—
221C23×C11—22no—
222C23×C11—42no—
223C23×C11—42no—
224C23×C11—42no—
225C23×C11#12314yes—
226C23×C11C22×D412yes—
227C23×C11C22×D411yescharacteristic
228C22×D11—24no—
229C22×D11—24no—
230C22×D11—24no—
231C22×D11C22×D414yes—
232Q8×C11—22no—
233Q8×C11—22no—
234Q8×C11—42no—
235D4×C11—22no—
236D4×C11—22no—
237D4×C11—48no—
238D4×C11—42no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11—48no—
246C2×C4×C11#12314yes—
247C2×C4×C11#12318yes—
248C2×C4×C11C22×D412yes—
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11C2×#4112yes—
251C2×C4×C11C2×#4114yes—
252C2×C4×C11C2×#4112yes—
253C2×C4×C11C2×#4114yes—
254C2×C4×C11C2511yescharacteristic
255C22⋊D11—216no—
256C22⋊D11—88no—
257C2×Dic11—24no—
258C2×Dic11—24no—
259C2×Dic11—24no—
260C2×Dic11—44no—
261C2×Dic11—44no—
262C2×Dic11—84no—
263C2×Dic11—84no—
264C2×Dic11C22×D414yes—
265D44—28no—
266C4×D11—28no—
267C4×D11—24no—
268C4×D11—24no—
269C4×D11—88no—
270Dic22—28no—
271C8×C11—22no—
272C8×C11—22no—
273C11⋊C8—24no—
274C22×#41—111no—
275C22×#41C2×D1111yescharacteristic
276C22×M16—111no—
277C23×C8C2×D1111yescharacteristic
278#537—118no—
279#537—224no—
280C2×C22⋊Q8—112no—
281C2×C22⋊Q8—221no—
282C2×#121—112no—
283C2×#121—221no—
284C2×#121—222no—
285#520—118no—
286#520—224no—
287C2×C4×Q8—221no—
288C2×C4×D4—221no—
289C2×C4×D4—222no—
290C2×#117—112no—
291C2×#117C2×D1111yescharacteristic
292C22×C4⋊C4—111no—
293C22×C4⋊C4—111no—
294C22×C4⋊C4—112no—
295#485—1116no—
296#484—1116no—
297#482—1116no—
298#480—1116no—
299#428—118no—
300C2×#107—112no—
301C2×#107—112no—
302C2×#107—118no—
303C2×#107—112no—
304C2×#106—112no—
305#417—118no—
306#416C2×D1118yescomplemented
307C2×#103—112no—
308C2×#103C2×D1111yescharacteristic
309C2×#103C2×D1111yescharacteristic
310C2×#102—112no—
311C2×#102C2×D1111yescharacteristic
312C2×#102C2×D1111yescharacteristic
313#408—118no—
314C2×C22⋊C8—112no—
315C2×C22⋊C8—112no—
316C22×C11—28no—
317C22×C11—22no—
318C22×C11—22no—
319C22×C11—42no—
320C22×C11—42no—
321C22×C11—42no—
322C22×C11—84no—
323C22×C11C2×#12314yes—
324C22×C11C2×#12312yes—
325C22×C11#57612yes—
326C22×C11#57812yes—
327C22×C11C23×D411yescharacteristic
328C2×D11—24no—
329C2×D11—24no—
330C2×D11—24no—
331C2×D11—48no—
332C4×C11—42no—
333C4×C11—42no—
334C4×C11—42no—
335C4×C11C2×#12314yes—
336C4×C11C2×#12312yes—
337C4×C11C22×#4111yescharacteristic
338C4×C11C22×#4111yescharacteristic
339Dic11—24no—
340Dic11—44no—
341Dic11—44no—
342C2×#41—22no—
343C2×#41—24no—
344C2×#41—24no—
345C2×#41—114no—
346C2×#41—114no—
347C2×#41—224no—
348C2×#41—224no—
349C2×#41C22×D1114yes—
350C22×Q8—111no—
351C22×Q8C22×D1111yescharacteristic
352C22×D4—21no—
353C22×D4—112no—
354C22×D4—111no—
355C22×D4—222no—
356C22×D4C22×D1111yescharacteristic
357C23×C4—21no—
358C23×C4—112no—
359C23×C4—222no—
360C23×C4—221no—
361C23×C4—221no—
362C23×C4C22×D1111yescharacteristic
363C2×M16—114no—
364C2×M16—224no—
365C22×C8—24no—
366C22×C8—112no—
367C22×C8C22×D1111yescharacteristic
368C22×C8C22×D1111yescharacteristic
369C22×C8C22×D1114yes—
370C22⋊Q8—118no—
371C22⋊Q8—228no—
372C22⋊Q8—224no—
373#121—118no—
374#121—228no—
375#121—224no—
376#121—2216no—
377C4×Q8—228no—
378C4×D4—228no—
379C4×D4—2216no—
380#117—22no—
381#117—118no—
382#117—224no—
383#117C22×D1114yes—
384C2×C4⋊C4—112no—
385C2×C4⋊C4—114no—
386C2×C4⋊C4—112no—
387C2×C4⋊C4—114no—
388C2×C4⋊C4—118no—
389C2×C4⋊C4—224no—
390C2×C4⋊C4—222no—
391C2×C4⋊C4—222no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—222no—
394C2×C4⋊C4—221no—
395C2×C4⋊C4—222no—
396C2×C4⋊C4C22×D1111yescharacteristic
397C2×C4⋊C4C22×D1111yescharacteristic
398C2×C22⋊C4—21no—
399C2×C22⋊C4—222no—
400C2×C22⋊C4—222no—
401C2×C22⋊C4—222no—
402C2×C42—21no—
403C2×C42—222no—
404#107—118no—
405#107—118no—
406#107—118no—
407#106—118no—
408#103—118no—
409#103C22×D1114yes—
410#103C22×D1114yes—
411#102—118no—
412#102C22×D1114yes—
413#102C22×D1114yes—
414C22⋊C8—118no—
415C22⋊C8—118no—
416C2×C11—24no—
417C2×C11—82no—
418C2×C11#309814yescomplemented
419C2×C11C22×#12311yescharacteristic
420C2×C11C2×#57611yescharacteristic
421C2×C11C2×#57811yescharacteristic
422D11—44no—
423C24—21no—
424C24—112no—
425C24D4×D1111yescharacteristic
426#41—28no—
427#41—28no—
428#41—48no—
429#41—2216no—
430#41—228no—
431#41—228no—
432C2×Q8—21no—
433C2×Q8—22no—
434C2×Q8—22no—
435C2×Q8—114no—
436C2×Q8—224no—
437C2×Q8C23×D1112yes—
438C2×D4—24no—
439C2×D4—22no—
440C2×D4—21no—
441C2×D4—22no—
442C2×D4—44no—
443C2×D4—118no—
444C2×D4—114no—
445C2×D4—228no—
446C2×D4—228no—
447C2×D4—224no—
448C2×D4—884no—
449C2×D4C23×D1112yes—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—24no—
454C22×C4—44no—
455C22×C4—112no—
456C22×C4—114no—
457C22×C4—114no—
458C22×C4—228no—
459C22×C4—224no—
460C22×C4—224no—
461C22×C4—222no—
462C22×C4—222no—
463C22×C4—224no—
464C22×C4—224no—
465C22×C4—884no—
466C22×C4—882no—
467C22×C4—882no—
468C22×C4#433914yes—
469C22×C4D4×D1112yes—
470C22×C4D4×D1111yescharacteristic
471C22×C4#434114yes—
472C22×C4C23×D1112yes—
473C22×C4C23×D1111yescharacteristic
474M16—228no—
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—28no—
478C2×C8—114no—
479C2×C8—224no—
480C2×C8C23×D1112yes—
481C2×C8C23×D1112yes—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—114no—
485C4⋊C4—114no—
486C4⋊C4—228no—
487C4⋊C4—228no—
488C4⋊C4—222no—
489C4⋊C4—224no—
490C4⋊C4—224no—
491C4⋊C4—222no—
492C4⋊C4C23×D1112yes—
493C4⋊C4C23×D1112yes—
494C22⋊C4—24no—
495C22⋊C4—228no—
496C22⋊C4—228no—
497C22⋊C4—228no—
498C42—24no—
499C42—228no—
500C11C2×#309811yescharacteristic, complemented, Sylow
501C23—22no—
502C23—22no—
503C23—22no—
504C23—42no—
505C23—42no—
506C23—42no—
507C23—114no—
508C23—224no—
509C23—224no—
510C23—224no—
511C23#6693614yes—
512C23C2×D4×D1112yes—
513C23C2×D4×D1111yescharacteristic
514Q8—22no—
515Q8—22no—
516Q8—42no—
517Q8—228no—
518D4—22no—
519D4—22no—
520D4—48no—
521D4—42no—
522D4—2216no—
523D4—228no—
524D4—888no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—48no—
532C2×C4—114no—
533C2×C4—224no—
534C2×C4—228no—
535C2×C4—224no—
536C2×C4—224no—
537C2×C4—224no—
538C2×C4—224no—
539C2×C4—444no—
540C2×C4—444no—
541C2×C4—888no—
542C2×C4—884no—
543C2×C4—884no—
544C2×C4#6693614yes—
545C2×C4#6693618yes—
546C2×C4C2×#433912yes—
547C2×C4C2×#433914yes—
548C2×C4C2×D4×D1112yes—
549C2×C4C2×D4×D1111yescharacteristic
550C2×C4C2×#434112yes—
551C2×C4C2×#434114yes—
552C2×C4C24×D1111yescharacteristic
553C8—22no—
554C8—22no—
555C8—224no—
556C22—28no—
557C22—22no—
558C22—22no—
559C22—42no—
560C22—42no—
561C22—42no—
562C22—84no—
563C22—224no—
564C22—224no—
565C22—224no—
566C22—448no—
567C22C2×#6693614yes—
568C22C2×#6693612yes—
569C22#1062330012yes—
570C22#1062330212yes—
571C22C22×D4×D1111yescharacteristic
572C4—42no—
573C4—42no—
574C4—42no—
575C4—224no—
576C4—444no—
577C4—444no—
578C4C2×#6693614yes—
579C4C2×#6693612yes—
580C4C22×#433911yescharacteristic
581C4C22×#434111yescharacteristic
582C2—24no—
583C2—82no—
584C2—444no—
585C2#1307859214yesdirect product factor
586C2C22×#6693611yescharacteristic
587C2C2×#1062330011yescharacteristic
588C2C2×#1062330211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#416C2
socleC23×C11C22×D4
prime radicalC2×#10623364C2
hypercenterC2×#416D11
hypocenterC11C2×#3098
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
2. C2×#10623054C2semidirect
3. #13078592C2direct (N × H)
4. C2×#10622422C2semidirect
5. C2×#10622427C2semidirect
6. C2×#10622397C2semidirect
7. C2×#10622387C2semidirect
8. C2×#10622608C2semidirect
9. C22×#66882C2semidirect
10. C2×#10622845C2semidirect
11. C2×#10622723C2semidirect
12. C2×C11×#416C2semidirect
28. #10623054C22semidirect
34. C11×#416C22semidirect
39. #10622845C22semidirect
42. #10622723C22semidirect
47. C2×#66882C22semidirect
48. #10622608C22semidirect
51. #10622427C22semidirect
52. #10622422C22semidirect
53. #10622397C22semidirect
54. #10622387C22semidirect
217. C2×#416D11semidirect
306. #416C2×D11semidirect
418. C2×C11#3098semidirect
500. C11C2×#3098semidirect
585. C2#13078592direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106233642
C2×#106230542
#130785922
C2×#106224222
C2×#106224272
C2×#106223972
C2×#106223872
C2×#106226082
C22×#668822
C2×#106228452
C2×#106227232
C2×C11×#4162
C2×#309811