Finite Group Databasebeta

← C2×#13078550 #15621563

Subgroups — C2×#13078550 #15621563

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×#10623055C211yesmaximal, characteristic
2C22×#66945C211yesmaximal, characteristic, complemented
3#13078550C2116yesmaximal, direct product factor
4C2×#10622480C212yesmaximal, complemented
5C2×#10622501C212yesmaximal, complemented
6C2×#10622498C212yesmaximal, complemented
7C2×#10622479C212yesmaximal, complemented
8C2×#10622608C211yesmaximal, characteristic, complemented
9C2×#10622746C211yesmaximal, characteristic, complemented
10C2×#10622579C211yesmaximal, characteristic, complemented
11C2×#10622739C211yesmaximal, characteristic, complemented
12C2×C11×#428C211yesmaximal, characteristic, complemented
13C22×#4339C2211yescharacteristic
14C23×C4×D11C2211yescharacteristic
15C22×C11×M16C2211yescharacteristic
16C2×C11×#117C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×(C2×D11)⋊C4—21no—
19C22×C4⋊Dic11C2211yescharacteristic
20C22×C4×Dic11—21no—
21C22×#4318C2211yescharacteristic
22#10623055—24no—
23#10623055C2218yes—
24C2×#66950C2211yescharacteristic
25C2×#66950C2211yescharacteristic
26C2×#66948C2211yescharacteristic
27C2×#66948C2211yescharacteristic
28C2×#66945—24no—
29C2×#66945—21no—
30C2×#66945—21no—
31C2×#66945C2212yes—
32C2×#66945C2212yes—
33C2×#66945C2218yescomplemented
34C2×#66939—21no—
35C2×#66935—21no—
36C2×C4×D44—21no—
37C2×C4×D44—21no—
38C11×#428C2218yescomplemented
39C2×C11×#107C2212yescomplemented
40C2×C11×#106C2212yescomplemented
41#10622746C2218yescomplemented
42#10622739C2218yescomplemented
43C2×#66885C2212yescomplemented
44C2×(C2×D11)⋊C8C2212yes—
45C2×(C2×D11)⋊C8C2212yes—
46C2×#66880C2212yescomplemented
47#10622608C2218yescomplemented
48C2×#66874C2212yescomplemented
49#10622579C2218yescomplemented
50C2×#66873C2212yescomplemented
51C2×#66872C2212yescomplemented
52C2×#66871C2212yescomplemented
53#10622501C22116yescomplemented
54#10622498C22116yescomplemented
55#10622480C22116yescomplemented
56#10622479C22116yescomplemented
57C24×D11D411yescharacteristic
58C23×C4×C11—21no—
59C23×C4×C11C2311yescharacteristic
60C22×C22⋊D11—21no—
61C23×Dic11—21no—
62C23×Dic11D411yescharacteristic
63C2×#4339—22no—
64C2×#4339—24no—
65C2×#4339—24no—
66C2×#4339C2314yes—
67C22×D44—21no—
68C22×D44—21no—
69C22×D44C2311yescharacteristic
70C22×C4×D11—24no—
71C22×C4×D11—24no—
72C22×C4×D11—21no—
73C22×C4×D11D411yescharacteristic
74C22×C4×D11D411yescharacteristic
75C22×C4×D11D414yes—
76C22×C4×D11C2311yescharacteristic
77C22×C4×D11C2311yescharacteristic
78C22×C4×D11C2314yes—
79C22×Dic22C2311yescharacteristic
80C2×C11×M16—24no—
81C2×C11×M16C2314yes—
82C22×C8×C11C2312yes—
83C11×#117—22no—
84C11×#117C2314yes—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—22no—
87C2×C11×C4⋊C4C2312yes—
88C2×C11×C4⋊C4C2314yes—
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C22⋊C4—21no—
92C2×C42×C11—21no—
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4—22no—
96C2×(C2×D11)⋊C4—22no—
97C2×(C2×D11)⋊C4—28no—
98C2×(C2×D11)⋊C4—21no—
99C2×(C2×D11)⋊C4—21no—
100C2×C4⋊Dic11—21no—
101C2×C4⋊Dic11—22no—
102C2×C4⋊Dic11—21no—
103C2×C4⋊Dic11—21no—
104C2×C4⋊Dic11C2312yes—
105C2×C4⋊Dic11C2314yes—
106C2×C4×Dic11—22no—
107C2×C4×Dic11—22no—
108C2×C4×Dic11—28no—
109C2×#4318—24no—
110C2×#4318C2314yes—
111C22×C11⋊C8C2312yes—
112#66950—22no—
113#66950—22no—
114#66950C2314yes—
115#66950C2314yes—
116#66948—22no—
117#66948—22no—
118#66948C2314yes—
119#66948C2314yes—
120#66945—24no—
121#66945—24no—
122#66945—28no—
123#66945—28no—
124#66945C2318yes—
125#66945C2318yes—
126#66939—28no—
127#66935—28no—
128C4×D44—28no—
129C4×D44—28no—
130C11×#107C2318yescomplemented
131C11×#106C2318yescomplemented
132#66885C2318yescomplemented
133(C2×D11)⋊C8C2318yes—
134(C2×D11)⋊C8C2318yes—
135#66880C2318yescomplemented
136#66874C2318yescomplemented
137#66873C2318yescomplemented
138#66872C2318yescomplemented
139#66871C2318yescomplemented
140C2×#3093—111nomaximal, Sylow
141C24×C11C2×D411yescharacteristic
142C23×D11—24no—
143C23×D11—21no—
144C23×D11—42no—
145C23×D11—42no—
146C23×D11C2×D411yescharacteristic
147C23×D11C2×D411yescharacteristic
148C23×D11C2×D414yes—
149C22×C4×C11—24no—
150C22×C4×C11—22no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—44no—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D412yes—
156C22×C4×C11#4114yes—
157C22×C4×C11#4114yes—
158C22×C4×C11C2411yescharacteristic
159C22×C4×C11C2412yes—
160C2×C22⋊D11—24no—
161C2×C22⋊D11—44no—
162C22×Dic11—24no—
163C22×Dic11—24no—
164C22×Dic11—22no—
165C22×Dic11—21no—
166C22×Dic11—44no—
167C22×Dic11C2×D414yes—
168C22×Dic11C2×D411yescharacteristic
169C22×Dic11C2×D411yescharacteristic
170#4339—28no—
171#4339—28no—
172#4339—48no—
173C2×D44—24no—
174C2×D44—24no—
175C2×D44—21no—
176C2×D44—22no—
177C2×D44—22no—
178C2×D44—44no—
179C2×D44—44no—
180C2×D44C2412yes—
181C2×C4×D11—24no—
182C2×C4×D11—24no—
183C2×C4×D11—216no—
184C2×C4×D11—24no—
185C2×C4×D11—22no—
186C2×C4×D11—22no—
187C2×C4×D11—28no—
188C2×C4×D11—22no—
189C2×C4×D11—22no—
190C2×C4×D11—28no—
191C2×C4×D11—44no—
192C2×C4×D11C2×D414yes—
193C2×C4×D11C2×D414yes—
194C2×C4×D11C2×D412yes—
195C2×C4×D11C2×D412yes—
196C2×C4×D11C2412yes—
197C2×C4×D11C2412yes—
198C2×Dic22—21no—
199C2×Dic22—22no—
200C2×Dic22—22no—
201C2×Dic22C2412yes—
202C11×M16—28no—
203C2×C8×C11—24no—
204C2×C8×C11C2414yes—
205C11×C4⋊C4—24no—
206C11×C4⋊C4—22no—
207C11×C4⋊C4—21no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4C2412yes—
210C11×C4⋊C4C2412yes—
211C11×C4⋊C4C2414yes—
212C11×C22⋊C4—24no—
213C42×C11—24no—
214(C2×D11)⋊C4—24no—
215(C2×D11)⋊C4—24no—
216(C2×D11)⋊C4—24no—
217(C2×D11)⋊C4—24no—
218(C2×D11)⋊C4—28no—
219(C2×D11)⋊C4—28no—
220C4⋊Dic11—24no—
221C4⋊Dic11—24no—
222C4⋊Dic11—24no—
223C4⋊Dic11—22no—
224C4⋊Dic11C2414yes—
225C4×Dic11—28no—
226C4×Dic11—28no—
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×#428D1111yescharacteristic, complemented
239C2×#417—111no—
240C2×#417—111no—
241C2×#407—111no—
242C23×C11—22no—
243C23×C11—22no—
244C23×C11#12314yes—
245C23×C11C22×D412yes—
246C23×C11C22×D411yescharacteristic
247C22×D11—28no—
248C22×D11—22no—
249C22×D11—22no—
250C22×D11—22no—
251C22×D11—22no—
252C22×D11—22no—
253C22×D11—22no—
254C22×D11—22no—
255C22×D11—44no—
256C22×D11—44no—
257C22×D11—416no—
258C22×D11—42no—
259C22×D11—42no—
260C22×D11—42no—
261C22×D11C22×D412yes—
262C22×D11C22×D412yes—
263C2×C4×C11—24no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—48no—
267C2×C4×C11—42no—
268C2×C4×C11—42no—
269C2×C4×C11—44no—
270C2×C4×C11#12314yes—
271C2×C4×C11#12318yes—
272C2×C4×C11C22×D412yes—
273C2×C4×C11C22×D411yescharacteristic
274C2×C4×C11C2×#4112yes—
275C2×C4×C11C2×#4114yes—
276C2×C4×C11C2×#4112yes—
277C2×C4×C11C2×#4114yes—
278C2×C4×C11C2511yescharacteristic
279C22⋊D11—48no—
280C2×Dic11—28no—
281C2×Dic11—22no—
282C2×Dic11—22no—
283C2×Dic11—24no—
284C2×Dic11—22no—
285C2×Dic11—48no—
286C2×Dic11—42no—
287C2×Dic11—44no—
288C2×Dic11C22×D412yes—
289C2×Dic11C22×D412yes—
290D44—22no—
291D44—22no—
292D44—48no—
293D44—48no—
294D44—42no—
295C4×D11—24no—
296C4×D11—24no—
297C4×D11—28no—
298C4×D11—28no—
299C4×D11—22no—
300C4×D11—22no—
301C4×D11—22no—
302C4×D11—22no—
303C4×D11—48no—
304Dic22—22no—
305Dic22—22no—
306Dic22—42no—
307C8×C11—24no—
308C11⋊C8—24no—
309C22×#41—111no—
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—112no—
324C2×#117—112no—
325C2×#117—118no—
326C2×#117—221no—
327C2×#117—221no—
328C2×#117—224no—
329C2×#117C2×D1111yescharacteristic
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#428C2×D1118yescomplemented
340C2×#107—112no—
341C2×#107C2×D1112yescomplemented
342C2×#106—112no—
343C2×#106C2×D1112yescomplemented
344#417—118no—
345#417—118no—
346C2×#103—112no—
347C2×#103—112no—
348C2×#102—112no—
349C2×#102—112no—
350#407—118no—
351C2×C22⋊C8—112no—
352C2×C22⋊C8—112no—
353C22×C11—28no—
354C22×C11—22no—
355C22×C11—22no—
356C22×C11C2×#12314yes—
357C22×C11C2×#12312yes—
358C22×C11#57512yes—
359C22×C11#57512yes—
360C22×C11C23×D411yescharacteristic
361C2×D11—22no—
362C2×D11—22no—
363C2×D11—22no—
364C2×D11—22no—
365C2×D11—22no—
366C2×D11—22no—
367C2×D11—416no—
368C2×D11—44no—
369C2×D11—44no—
370C2×D11—42no—
371C2×D11—42no—
372C2×D11—42no—
373C2×D11—84no—
374C4×C11—44no—
375C4×C11—42no—
376C4×C11—42no—
377C4×C11C2×#12312yes—
378C4×C11C2×#12314yes—
379C4×C11C22×#4111yescharacteristic
380C4×C11C22×#4111yescharacteristic
381Dic11—22no—
382Dic11—22no—
383Dic11—42no—
384Dic11—44no—
385C25—111no—
386C2×#41—114no—
387C2×#41—222no—
388C2×#41—224no—
389C2×#41—224no—
390C22×Q8—111no—
391C22×D4—111no—
392C22×D4—221no—
393C22×D4—221no—
394C22×D4—221no—
395C23×C4—21no—
396C23×C4—111no—
397C23×C4—111no—
398C23×C4—111no—
399C23×C4—114no—
400C23×C4—111no—
401C23×C4—111no—
402C23×C4—114no—
403C23×C4—224no—
404C23×C4—224no—
405C23×C4—221no—
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—22no—
427#117—118no—
428#117—118no—
429#117—228no—
430#117—228no—
431#117—224no—
432#117—224no—
433#117C22×D1114yes—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—112no—
437C2×C4⋊C4—114no—
438C2×C4⋊C4—221no—
439C2×C4⋊C4—221no—
440C2×C4⋊C4—222no—
441C2×C4⋊C4—221no—
442C2×C4⋊C4C22×D1112yes—
443C2×C4⋊C4C22×D1114yes—
444C2×C4⋊C4C22×D1111yescharacteristic
445C2×C4⋊C4C22×D1111yescharacteristic
446C2×C22⋊C4—21no—
447C2×C22⋊C4—221no—
448C2×C22⋊C4—221no—
449C2×C22⋊C4—228no—
450C2×C22⋊C4—222no—
451C2×C22⋊C4—222no—
452C2×C22⋊C4—221no—
453C2×C22⋊C4—221no—
454C2×C42—21no—
455C2×C42—228no—
456C2×C42—222no—
457C2×C42—222no—
458#107—118no—
459#107C22×D1118yescomplemented
460#106—118no—
461#106C22×D1118yescomplemented
462#103—118no—
463#103—118no—
464#102—118no—
465#102—118no—
466C22⋊C8—118no—
467C22⋊C8—118no—
468C2×C11—24no—
469C2×C11#309314yescomplemented
470C2×C11C22×#12311yescharacteristic
471C2×C11C2×#57511yescharacteristic
472C2×C11C2×#57511yescharacteristic
473D11—42no—
474D11—42no—
475D11—82no—
476C24—111no—
477C24—111no—
478C24—114no—
479C24—224no—
480C24—221no—
481C24—442no—
482C24—442no—
483C24D4×D1111yescharacteristic
484#41—228no—
485#41—228no—
486#41—448no—
487C2×Q8—112no—
488C2×Q8—221no—
489C2×Q8—222no—
490C2×Q8—222no—
491C2×D4—112no—
492C2×D4—224no—
493C2×D4—224no—
494C2×D4—224no—
495C2×D4—222no—
496C2×D4—221no—
497C2×D4—222no—
498C2×D4—444no—
499C2×D4—444no—
500C2×D4—444no—
501C22×C4—24no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—44no—
506C22×C4—114no—
507C22×C4—111no—
508C22×C4—111no—
509C22×C4—114no—
510C22×C4—114no—
511C22×C4—112no—
512C22×C4—112no—
513C22×C4—112no—
514C22×C4—112no—
515C22×C4—224no—
516C22×C4—224no—
517C22×C4—224no—
518C22×C4—2216no—
519C22×C4—222no—
520C22×C4—222no—
521C22×C4—228no—
522C22×C4—222no—
523C22×C4—222no—
524C22×C4—228no—
525C22×C4—224no—
526C22×C4—222no—
527C22×C4—221no—
528C22×C4—224no—
529C22×C4—444no—
530C22×C4—444no—
531C22×C4#433914yes—
532C22×C4D4×D1112yes—
533C22×C4D4×D1111yescharacteristic
534C22×C4#434314yes—
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—21no—
546C4⋊C4—21no—
547C4⋊C4—114no—
548C4⋊C4—224no—
549C4⋊C4—224no—
550C4⋊C4—224no—
551C4⋊C4—222no—
552C4⋊C4C23×D1114yes—
553C4⋊C4C23×D1112yes—
554C4⋊C4C23×D1112yes—
555C22⋊C4—24no—
556C22⋊C4—224no—
557C22⋊C4—224no—
558C22⋊C4—228no—
559C22⋊C4—228no—
560C22⋊C4—224no—
561C22⋊C4—224no—
562C42—24no—
563C42—228no—
564C42—228no—
565C11C2×#309311yescharacteristic, complemented, Sylow
566C23—22no—
567C23—22no—
568C23—112no—
569C23—112no—
570C23—228no—
571C23—222no—
572C23—222no—
573C23—222no—
574C23—222no—
575C23—222no—
576C23—222no—
577C23—222no—
578C23—444no—
579C23—444no—
580C23—4416no—
581C23—442no—
582C23—442no—
583C23—442no—
584C23#6694714yes—
585C23C2×D4×D1112yes—
586C23C2×D4×D1111yescharacteristic
587Q8—222no—
588Q8—222no—
589Q8—442no—
590D4—222no—
591D4—222no—
592D4—448no—
593D4—448no—
594D4—448no—
595D4—442no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—24no—
599C2×C4—48no—
600C2×C4—44no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—112no—
604C2×C4—112no—
605C2×C4—228no—
606C2×C4—222no—
607C2×C4—222no—
608C2×C4—228no—
609C2×C4—228no—
610C2×C4—224no—
611C2×C4—224no—
612C2×C4—222no—
613C2×C4—222no—
614C2×C4—222no—
615C2×C4—222no—
616C2×C4—224no—
617C2×C4—222no—
618C2×C4—448no—
619C2×C4—442no—
620C2×C4—444no—
621C2×C4—448no—
622C2×C4#6694714yes—
623C2×C4#6694718yes—
624C2×C4C2×#433912yes—
625C2×C4C2×#433914yes—
626C2×C4C2×D4×D1112yes—
627C2×C4C2×D4×D1111yescharacteristic
628C2×C4C2×#434312yes—
629C2×C4C2×#434314yes—
630C2×C4C24×D1111yescharacteristic
631C8—24no—
632C8—224no—
633C22—28no—
634C22—22no—
635C22—22no—
636C22—222no—
637C22—222no—
638C22—222no—
639C22—222no—
640C22—222no—
641C22—222no—
642C22—4416no—
643C22—444no—
644C22—444no—
645C22—442no—
646C22—442no—
647C22—442no—
648C22—884no—
649C22C2×#6694714yes—
650C22C2×#6694712yes—
651C22#1062330412yes—
652C22#1062330812yes—
653C22C22×D4×D1111yescharacteristic
654C4—44no—
655C4—42no—
656C4—42no—
657C4—222no—
658C4—222no—
659C4—444no—
660C4—442no—
661C4C2×#6694714yes—
662C4C2×#6694712yes—
663C4C22×#433911yescharacteristic
664C4C22×#434311yescharacteristic
665C2—24no—
666C2—442no—
667C2—442no—
668C2—882no—
669C2#1307855014yesdirect product factor
670C2C22×#6694711yescharacteristic
671C2C2×#1062330411yescharacteristic
672C2C2×#1062330811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#428C2
socleC23×C11C22×D4
prime radicalC2×#10623055C2
hypercenterC2×#428D11
hypocenterC11C2×#3093
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
2. C22×#66945C2semidirect
3. #13078550C2direct (N × H)
4. C2×#10622480C2semidirect
5. C2×#10622501C2semidirect
6. C2×#10622498C2semidirect
7. C2×#10622479C2semidirect
8. C2×#10622608C2semidirect
9. C2×#10622746C2semidirect
10. C2×#10622579C2semidirect
11. C2×#10622739C2semidirect
12. C2×C11×#428C2semidirect
33. C2×#66945C22semidirect
38. C11×#428C22semidirect
39. C2×C11×#107C22semidirect
40. C2×C11×#106C22semidirect
41. #10622746C22semidirect
42. #10622739C22semidirect
43. C2×#66885C22semidirect
46. C2×#66880C22semidirect
47. #10622608C22semidirect
48. C2×#66874C22semidirect
49. #10622579C22semidirect
50. C2×#66873C22semidirect
51. C2×#66872C22semidirect
52. C2×#66871C22semidirect
53. #10622501C22semidirect
54. #10622498C22semidirect
55. #10622480C22semidirect
56. #10622479C22semidirect
130. C11×#107C23semidirect
131. C11×#106C23semidirect
132. #66885C23semidirect
135. #66880C23semidirect
136. #66874C23semidirect
137. #66873C23semidirect
138. #66872C23semidirect
139. #66871C23semidirect
238. C2×#428D11semidirect
339. #428C2×D11semidirect
341. C2×#107C2×D11semidirect
343. C2×#106C2×D11semidirect
459. #107C22×D11semidirect
461. #106C22×D11semidirect
469. C2×C11#3093semidirect
565. C11C2×#3093semidirect
669. C2#13078550direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230552
C22×#669452
#130785502
C2×#106224802
C2×#106225012
C2×#106224982
C2×#106224792
C2×#106226082
C2×#106227462
C2×#106225792
C2×#106227392
C2×C11×#4282
C2×#309311