Finite Group Databasebeta

← C2×#13078546 #15621559

Subgroups — C2×#13078546 #15621559

Order 2816.

2346 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623359C211yesmaximal, characteristic
2C22×#66945C211yesmaximal, characteristic, complemented
3#13078546C2116yesmaximal, direct product factor
4C2×#10622427C212yesmaximal, complemented
5C2×#10622428C212yesmaximal, complemented
6C2×#10622392C212yesmaximal, complemented
7C2×#10622397C212yesmaximal, complemented
8C2×#10622734C211yesmaximal, characteristic, complemented
9C2×#10622577C211yesmaximal, characteristic, complemented
10C2×#10622845C211yesmaximal, characteristic, complemented
11C2×#10622739C211yesmaximal, characteristic, complemented
12C2×C11×#417C211yesmaximal, characteristic, complemented
13C22×C11×#41C2211yescharacteristic
14C23×C4×D11C2211yescharacteristic
15C22×C11×M16C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17#10623359—24no—
18#10623359C2218yes—
19C2×#66999C2211yescharacteristic
20C2×#66999C2211yescharacteristic
21C2×#66991C2211yescharacteristic
22C2×#66991C2211yescharacteristic
23C2×#66990—21no—
24C2×#66988—21no—
25C2×C4×C22⋊D11—21no—
26C2×C4×C22⋊D11—21no—
27C22×(C2×D11)⋊C4—21no—
28C2×#66979C2211yescharacteristic
29C22×C4⋊Dic11C2211yescharacteristic
30C22×C4×Dic11—21no—
31C22×#4318C2211yescharacteristic
32C2×#66945—24no—
33C2×#66945—21no—
34C2×#66945—21no—
35C2×#66945C2212yes—
36C2×#66945C2212yes—
37C2×#66945C2218yescomplemented
38C11×#417C2218yescomplemented
39C2×C11×#103C2212yescomplemented
40C2×C11×#102C2212yescomplemented
41#10622845C2218yescomplemented
42C2×#66899C2212yescomplemented
43C2×#66896C2212yescomplemented
44#10622739C2218yescomplemented
45#10622734C2218yescomplemented
46C2×(C2×D11)⋊C8C2212yes—
47C2×(C2×D11)⋊C8C2212yes—
48C2×#66882C2212yescomplemented
49C2×#66881C2212yescomplemented
50#10622577C2218yescomplemented
51C2×#66872C2212yescomplemented
52C2×#66871C2212yescomplemented
53#10622428C22116yescomplemented
54#10622427C22116yescomplemented
55#10622397C22116yescomplemented
56#10622392C22116yescomplemented
57C24×D11D411yescharacteristic
58C2×C11×#41—22no—
59C2×C11×#41—24no—
60C2×C11×#41—24no—
61C2×C11×#41C2314yes—
62C22×Q8×C11C2311yescharacteristic
63C22×D4×C11—21no—
64C22×D4×C11C2311yescharacteristic
65C23×C4×C11—21no—
66C23×C4×C11—21no—
67C23×C4×C11C2311yescharacteristic
68C22×C22⋊D11—21no—
69C22×C22⋊D11—21no—
70C23×Dic11—21no—
71C23×Dic11D411yescharacteristic
72C22×C4×D11—24no—
73C22×C4×D11—24no—
74C22×C4×D11D411yescharacteristic
75C22×C4×D11D411yescharacteristic
76C22×C4×D11D414yes—
77C22×C4×D11C2311yescharacteristic
78C22×C4×D11C2311yescharacteristic
79C22×C4×D11C2314yes—
80C2×C11×M16—24no—
81C2×C11×M16C2314yes—
82C22×C8×C11C2312yes—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—22no—
85C2×C11×C4⋊C4C2312yes—
86C2×C11×C4⋊C4C2314yes—
87C2×C22⋊Dic11—21no—
88C2×C22⋊Dic11—21no—
89C2×C22⋊Dic11—21no—
90#66999—22no—
91#66999—22no—
92#66999C2314yes—
93#66999C2314yes—
94#66991—22no—
95#66991—22no—
96#66991C2314yes—
97#66991C2314yes—
98#66990—28no—
99#66988—28no—
100C4×C22⋊D11—28no—
101C4×C22⋊D11—28no—
102C2×(C2×D11)⋊C4—22no—
103C2×(C2×D11)⋊C4—22no—
104C2×(C2×D11)⋊C4—28no—
105C2×(C2×D11)⋊C4—21no—
106C2×(C2×D11)⋊C4—21no—
107#66979—22no—
108#66979C2314yes—
109C2×C4⋊Dic11—21no—
110C2×C4⋊Dic11—22no—
111C2×C4⋊Dic11C2314yes—
112C2×C4⋊Dic11C2312yes—
113C2×C4⋊Dic11C2311yescharacteristic
114C2×C4⋊Dic11C2311yescharacteristic
115C2×Dic11⋊C4—21no—
116C2×Dic11⋊C4—21no—
117C2×C4×Dic11—21no—
118C2×C4×Dic11—22no—
119C2×C4×Dic11—22no—
120C2×C4×Dic11—28no—
121C2×#4318—24no—
122C2×#4318C2314yes—
123C22×C11⋊C8C2312yes—
124#66945—24no—
125#66945—24no—
126#66945—28no—
127#66945—28no—
128#66945C2318yes—
129#66945C2318yes—
130C11×#103C2318yescomplemented
131C11×#102C2318yescomplemented
132#66899C2318yescomplemented
133#66896C2318yescomplemented
134(C2×D11)⋊C8C2318yes—
135(C2×D11)⋊C8C2318yes—
136#66882C2318yescomplemented
137#66881C2318yescomplemented
138#66872C2318yescomplemented
139#66871C2318yescomplemented
140C2×#3093—111nomaximal, Sylow
141C24×C11—21no—
142C24×C11C2×D411yescharacteristic
143C23×D11—24no—
144C23×D11—42no—
145C23×D11—42no—
146C23×D11C2×D411yescharacteristic
147C23×D11C2×D411yescharacteristic
148C23×D11C2×D414yes—
149C11×#41—28no—
150C11×#41—28no—
151C11×#41—48no—
152C2×Q8×C11—21no—
153C2×Q8×C11—22no—
154C2×Q8×C11—22no—
155C2×Q8×C11C2412yes—
156C2×D4×C11—24no—
157C2×D4×C11—21no—
158C2×D4×C11—22no—
159C2×D4×C11—22no—
160C2×D4×C11—44no—
161C2×D4×C11C2412yes—
162C22×C4×C11—24no—
163C22×C4×C11—22no—
164C22×C4×C11—21no—
165C22×C4×C11—24no—
166C22×C4×C11—44no—
167C22×C4×C11—44no—
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D412yes—
170C22×C4×C11#4114yes—
171C22×C4×C11#4114yes—
172C22×C4×C11C2411yescharacteristic
173C22×C4×C11C2412yes—
174C2×C22⋊D11—24no—
175C2×C22⋊D11—24no—
176C2×C22⋊D11—44no—
177C2×C22⋊D11—44no—
178C22×Dic11—24no—
179C22×Dic11—24no—
180C22×Dic11—22no—
181C22×Dic11—21no—
182C22×Dic11—21no—
183C22×Dic11—44no—
184C22×Dic11C2×D411yescharacteristic
185C22×Dic11C2×D411yescharacteristic
186C22×Dic11C2×D414yes—
187C2×C4×D11—24no—
188C2×C4×D11—24no—
189C2×C4×D11—216no—
190C2×C4×D11—22no—
191C2×C4×D11—22no—
192C2×C4×D11—28no—
193C2×C4×D11—22no—
194C2×C4×D11—22no—
195C2×C4×D11—28no—
196C2×C4×D11C2×D414yes—
197C2×C4×D11C2×D414yes—
198C2×C4×D11C2×D412yes—
199C2×C4×D11C2×D412yes—
200C2×C4×D11C2412yes—
201C2×C4×D11C2412yes—
202C11×M16—28no—
203C2×C8×C11—24no—
204C2×C8×C11C2414yes—
205C11×C4⋊C4—24no—
206C11×C4⋊C4—22no—
207C11×C4⋊C4C2414yes—
208C22⋊Dic11—24no—
209C22⋊Dic11—24no—
210C22⋊Dic11—24no—
211(C2×D11)⋊C4—28no—
212(C2×D11)⋊C4—28no—
213(C2×D11)⋊C4—24no—
214(C2×D11)⋊C4—24no—
215C4⋊Dic11—24no—
216C4⋊Dic11—22no—
217C4⋊Dic11—21no—
218C4⋊Dic11—21no—
219C4⋊Dic11C2412yes—
220C4⋊Dic11C2412yes—
221C4⋊Dic11C2414yes—
222Dic11⋊C4—24no—
223Dic11⋊C4—24no—
224C4×Dic11—28no—
225C4×Dic11—28no—
226C4×Dic11—24no—
227#4318—28no—
228C2×C11⋊C8—24no—
229C2×C11⋊C8C2414yes—
230C2×#525—111no—
231C22×#117—111no—
232#3093—1116no—
233C2×#485—112no—
234C2×#485—112no—
235C2×#482—112no—
236C2×#482—112no—
237C2×#428—111no—
238C2×#428—111no—
239C2×#417—111no—
240C2×#417D1111yescharacteristic, complemented
241C2×#407—111no—
242C23×C11—22no—
243C23×C11—22no—
244C23×C11—22no—
245C23×C11—42no—
246C23×C11—42no—
247C23×C11—42no—
248C23×C11#12314yes—
249C23×C11C22×D412yes—
250C23×C11C22×D411yescharacteristic
251C22×D11—28no—
252C22×D11—22no—
253C22×D11—22no—
254C22×D11—22no—
255C22×D11—22no—
256C22×D11—22no—
257C22×D11—22no—
258C22×D11—44no—
259C22×D11—44no—
260C22×D11—416no—
261C22×D11C22×D412yes—
262C22×D11C22×D412yes—
263Q8×C11—22no—
264Q8×C11—22no—
265Q8×C11—42no—
266D4×C11—22no—
267D4×C11—22no—
268D4×C11—48no—
269D4×C11—42no—
270C2×C4×C11—24no—
271C2×C4×C11—22no—
272C2×C4×C11—48no—
273C2×C4×C11—42no—
274C2×C4×C11—44no—
275C2×C4×C11—48no—
276C2×C4×C11#12314yes—
277C2×C4×C11#12318yes—
278C2×C4×C11C22×D412yes—
279C2×C4×C11C22×D411yescharacteristic
280C2×C4×C11C2×#4112yes—
281C2×C4×C11C2×#4114yes—
282C2×C4×C11C2×#4112yes—
283C2×C4×C11C2×#4114yes—
284C2×C4×C11C2511yescharacteristic
285C22⋊D11—48no—
286C22⋊D11—48no—
287C2×Dic11—28no—
288C2×Dic11—22no—
289C2×Dic11—22no—
290C2×Dic11—24no—
291C2×Dic11—22no—
292C2×Dic11—22no—
293C2×Dic11—48no—
294C2×Dic11—44no—
295C2×Dic11—42no—
296C2×Dic11—42no—
297C2×Dic11C22×D412yes—
298C2×Dic11C22×D412yes—
299C4×D11—28no—
300C4×D11—28no—
301C4×D11—24no—
302C4×D11—24no—
303C4×D11—22no—
304C4×D11—22no—
305C4×D11—22no—
306C4×D11—22no—
307C8×C11—24no—
308C11⋊C8—24no—
309C22×#41C2×D1111yescharacteristic
310C24×C4—111no—
311C22×M16—111no—
312C22×M16C2×D1111yescharacteristic
313#525—118no—
314#525—224no—
315C2×#123—221no—
316C2×C22⋊Q8—111no—
317C2×C22⋊Q8—111no—
318C2×#121—111no—
319C2×#121—111no—
320C2×#120—221no—
321C2×C4×D4—221no—
322C2×C4×D4—221no—
323C2×#117—111no—
324C2×#117—112no—
325C2×#117—112no—
326C2×#117—118no—
327C2×#117—221no—
328C2×#117—221no—
329C2×#117—224no—
330C22×C4⋊C4—111no—
331C22×C4⋊C4C2×D1111yescharacteristic
332C22×C22⋊C4—221no—
333C22×C42—221no—
334#485—1116no—
335#485—1116no—
336#482—1116no—
337#482—1116no—
338#428—118no—
339#428—118no—
340C2×#107—112no—
341C2×#107—112no—
342C2×#106—112no—
343C2×#106—112no—
344#417—118no—
345#417C2×D1118yescomplemented
346C2×#103—112no—
347C2×#103C2×D1112yescomplemented
348C2×#102—112no—
349C2×#102C2×D1112yescomplemented
350#407—118no—
351C2×C22⋊C8—112no—
352C2×C22⋊C8—112no—
353C22×C11—28no—
354C22×C11—22no—
355C22×C11—22no—
356C22×C11—42no—
357C22×C11—42no—
358C22×C11—42no—
359C22×C11—84no—
360C22×C11C2×#12314yes—
361C22×C11C2×#12312yes—
362C22×C11#57512yes—
363C22×C11#57512yes—
364C22×C11C23×D411yescharacteristic
365C2×D11—22no—
366C2×D11—22no—
367C2×D11—22no—
368C2×D11—22no—
369C2×D11—22no—
370C2×D11—22no—
371C2×D11—416no—
372C2×D11—44no—
373C2×D11—44no—
374C4×C11—42no—
375C4×C11—44no—
376C4×C11C2×#12314yes—
377C4×C11C2×#12312yes—
378C4×C11C22×#4111yescharacteristic
379C4×C11C22×#4111yescharacteristic
380Dic11—22no—
381Dic11—22no—
382Dic11—44no—
383Dic11—42no—
384Dic11—42no—
385C25—111no—
386C2×#41—22no—
387C2×#41—24no—
388C2×#41—24no—
389C2×#41C22×D1114yes—
390C22×Q8C22×D1111yescharacteristic
391C22×D4—21no—
392C22×D4—221no—
393C22×D4—221no—
394C22×D4C22×D1111yescharacteristic
395C23×C4—21no—
396C23×C4—21no—
397C23×C4—111no—
398C23×C4—111no—
399C23×C4—111no—
400C23×C4—114no—
401C23×C4—111no—
402C23×C4—111no—
403C23×C4—114no—
404C23×C4—224no—
405C23×C4—224no—
406C23×C4—221no—
407C23×C4C22×D1111yescharacteristic
408C2×M16—24no—
409C2×M16—114no—
410C2×M16—224no—
411C2×M16C22×D1114yes—
412C22×C8—112no—
413C22×C8C22×D1112yes—
414#123—228no—
415C22⋊Q8—114no—
416C22⋊Q8—114no—
417C22⋊Q8—222no—
418C22⋊Q8—222no—
419#121—114no—
420#121—114no—
421#121—222no—
422#121—222no—
423#120—228no—
424C4×D4—228no—
425C4×D4—228no—
426#117—114no—
427#117—118no—
428#117—118no—
429#117—228no—
430#117—228no—
431#117—224no—
432#117—224no—
433#117—222no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—112no—
437C2×C4⋊C4—114no—
438C2×C4⋊C4—111no—
439C2×C4⋊C4—111no—
440C2×C4⋊C4—221no—
441C2×C4⋊C4—221no—
442C2×C4⋊C4—222no—
443C2×C4⋊C4—221no—
444C2×C4⋊C4C22×D1112yes—
445C2×C4⋊C4C22×D1114yes—
446C2×C22⋊C4—228no—
447C2×C22⋊C4—222no—
448C2×C22⋊C4—222no—
449C2×C22⋊C4—221no—
450C2×C22⋊C4—221no—
451C2×C22⋊C4—221no—
452C2×C22⋊C4—221no—
453C2×C22⋊C4—221no—
454C2×C42—228no—
455C2×C42—222no—
456C2×C42—222no—
457C2×C42—221no—
458#107—118no—
459#107—118no—
460#106—118no—
461#106—118no—
462#103—118no—
463#103C22×D1118yescomplemented
464#102—118no—
465#102C22×D1118yescomplemented
466C22⋊C8—118no—
467C22⋊C8—118no—
468C2×C11—24no—
469C2×C11—82no—
470C2×C11#309314yescomplemented
471C2×C11C22×#12311yescharacteristic
472C2×C11C2×#57511yescharacteristic
473C2×C11C2×#57511yescharacteristic
474D11—42no—
475D11—42no—
476C24—21no—
477C24—111no—
478C24—111no—
479C24—114no—
480C24—224no—
481C24—442no—
482C24—442no—
483C24D4×D1111yescharacteristic
484#41—28no—
485#41—28no—
486#41—48no—
487C2×Q8—21no—
488C2×Q8—22no—
489C2×Q8—22no—
490C2×Q8C23×D1112yes—
491C2×D4—24no—
492C2×D4—22no—
493C2×D4—21no—
494C2×D4—22no—
495C2×D4—44no—
496C2×D4—224no—
497C2×D4—224no—
498C2×D4—444no—
499C2×D4—444no—
500C2×D4C23×D1112yes—
501C22×C4—24no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—24no—
505C22×C4—44no—
506C22×C4—44no—
507C22×C4—114no—
508C22×C4—111no—
509C22×C4—111no—
510C22×C4—114no—
511C22×C4—114no—
512C22×C4—112no—
513C22×C4—112no—
514C22×C4—112no—
515C22×C4—112no—
516C22×C4—224no—
517C22×C4—224no—
518C22×C4—224no—
519C22×C4—2216no—
520C22×C4—222no—
521C22×C4—222no—
522C22×C4—228no—
523C22×C4—222no—
524C22×C4—222no—
525C22×C4—228no—
526C22×C4—224no—
527C22×C4—222no—
528C22×C4—221no—
529C22×C4—221no—
530C22×C4—444no—
531C22×C4#433914yes—
532C22×C4D4×D1112yes—
533C22×C4D4×D1111yescharacteristic
534C22×C4#434114yes—
535C22×C4C23×D1112yes—
536C22×C4C23×D1111yescharacteristic
537M16—28no—
538M16—228no—
539C2×C8—24no—
540C2×C8—114no—
541C2×C8—224no—
542C2×C8C23×D1114yes—
543C4⋊C4—24no—
544C4⋊C4—22no—
545C4⋊C4—114no—
546C4⋊C4—112no—
547C4⋊C4—112no—
548C4⋊C4—224no—
549C4⋊C4—224no—
550C4⋊C4—224no—
551C4⋊C4—222no—
552C4⋊C4—221no—
553C4⋊C4—221no—
554C4⋊C4C23×D1114yes—
555C22⋊C4—228no—
556C22⋊C4—228no—
557C22⋊C4—224no—
558C22⋊C4—224no—
559C22⋊C4—224no—
560C22⋊C4—224no—
561C22⋊C4—224no—
562C42—228no—
563C42—228no—
564C42—224no—
565C11C2×#309311yescharacteristic, complemented, Sylow
566C23—22no—
567C23—22no—
568C23—22no—
569C23—42no—
570C23—42no—
571C23—42no—
572C23—112no—
573C23—112no—
574C23—228no—
575C23—222no—
576C23—222no—
577C23—222no—
578C23—222no—
579C23—222no—
580C23—222no—
581C23—444no—
582C23—444no—
583C23—4416no—
584C23#6693614yes—
585C23C2×D4×D1112yes—
586C23C2×D4×D1111yescharacteristic
587Q8—22no—
588Q8—22no—
589Q8—42no—
590D4—22no—
591D4—22no—
592D4—48no—
593D4—42no—
594D4—448no—
595D4—448no—
596C2×C4—24no—
597C2×C4—22no—
598C2×C4—48no—
599C2×C4—42no—
600C2×C4—44no—
601C2×C4—48no—
602C2×C4—112no—
603C2×C4—112no—
604C2×C4—228no—
605C2×C4—222no—
606C2×C4—222no—
607C2×C4—228no—
608C2×C4—228no—
609C2×C4—224no—
610C2×C4—224no—
611C2×C4—222no—
612C2×C4—222no—
613C2×C4—222no—
614C2×C4—222no—
615C2×C4—224no—
616C2×C4—222no—
617C2×C4—222no—
618C2×C4—448no—
619C2×C4—442no—
620C2×C4—444no—
621C2×C4—442no—
622C2×C4#6693614yes—
623C2×C4#6693618yes—
624C2×C4C2×#433912yes—
625C2×C4C2×#433914yes—
626C2×C4C2×D4×D1112yes—
627C2×C4C2×D4×D1111yescharacteristic
628C2×C4C2×#434112yes—
629C2×C4C2×#434114yes—
630C2×C4C24×D1111yescharacteristic
631C8—24no—
632C8—224no—
633C22—28no—
634C22—22no—
635C22—22no—
636C22—42no—
637C22—42no—
638C22—42no—
639C22—84no—
640C22—222no—
641C22—222no—
642C22—222no—
643C22—222no—
644C22—222no—
645C22—222no—
646C22—4416no—
647C22—444no—
648C22—444no—
649C22C2×#6693614yes—
650C22C2×#6693612yes—
651C22#1062330412yes—
652C22#1062330812yes—
653C22C22×D4×D1111yescharacteristic
654C4—44no—
655C4—42no—
656C4—222no—
657C4—222no—
658C4—442no—
659C4—444no—
660C4—442no—
661C4C2×#6693614yes—
662C4C2×#6693612yes—
663C4C22×#433911yescharacteristic
664C4C22×#434111yescharacteristic
665C2—24no—
666C2—82no—
667C2—442no—
668C2—442no—
669C2#1307854614yesdirect product factor
670C2C22×#6693611yescharacteristic
671C2C2×#1062330411yescharacteristic
672C2C2×#1062330811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#417C2
socleC23×C11C22×D4
prime radicalC2×#10623359C2
hypercenterC2×#417D11
hypocenterC11C2×#3093
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
2. C22×#66945C2semidirect
3. #13078546C2direct (N × H)
4. C2×#10622427C2semidirect
5. C2×#10622428C2semidirect
6. C2×#10622392C2semidirect
7. C2×#10622397C2semidirect
8. C2×#10622734C2semidirect
9. C2×#10622577C2semidirect
10. C2×#10622845C2semidirect
11. C2×#10622739C2semidirect
12. C2×C11×#417C2semidirect
37. C2×#66945C22semidirect
38. C11×#417C22semidirect
39. C2×C11×#103C22semidirect
40. C2×C11×#102C22semidirect
41. #10622845C22semidirect
42. C2×#66899C22semidirect
43. C2×#66896C22semidirect
44. #10622739C22semidirect
45. #10622734C22semidirect
48. C2×#66882C22semidirect
49. C2×#66881C22semidirect
50. #10622577C22semidirect
51. C2×#66872C22semidirect
52. C2×#66871C22semidirect
53. #10622428C22semidirect
54. #10622427C22semidirect
55. #10622397C22semidirect
56. #10622392C22semidirect
130. C11×#103C23semidirect
131. C11×#102C23semidirect
132. #66899C23semidirect
133. #66896C23semidirect
136. #66882C23semidirect
137. #66881C23semidirect
138. #66872C23semidirect
139. #66871C23semidirect
240. C2×#417D11semidirect
345. #417C2×D11semidirect
347. C2×#103C2×D11semidirect
349. C2×#102C2×D11semidirect
463. #103C22×D11semidirect
465. #102C22×D11semidirect
470. C2×C11#3093semidirect
565. C11C2×#3093semidirect
669. C2#13078546direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106233592
C22×#669452
#130785462
C2×#106224272
C2×#106224282
C2×#106223922
C2×#106223972
C2×#106227342
C2×#106225772
C2×#106228452
C2×#106227392
C2×C11×#4172
C2×#309311