Finite Group Databasebeta

← C2×#13078275 #15620973

Subgroups — C2×#13078275 #15620973

Order 2816.

2806 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67003C211yesmaximal, characteristic, complemented
2C22×#67001C211yesmaximal, characteristic, complemented
3C2×#10623364C211yesmaximal, characteristic, complemented
4#13078275C2116yesmaximal, direct product factor
5C2×#10622665C212yesmaximal, complemented
6C2×#10622652C212yesmaximal, complemented
7C2×#10622661C212yesmaximal, complemented
8C2×#10622654C212yesmaximal, complemented
9C22×#66872C211yesmaximal, characteristic, complemented
10C2×#10622845C211yesmaximal, characteristic, complemented
11C2×#10622579C211yesmaximal, characteristic, complemented
12C2×C11×#537C211yesmaximal, characteristic, complemented
13C22×C11×#41C2211yescharacteristic
14C22×C11×#41C2211yescharacteristic
15C22×#4339C2211yescharacteristic
16C11×#537—24no—
17C11×#537C2218yescomplemented
18C2×C11×C22⋊Q8—21no—
19C2×C11×C22⋊Q8C2212yes—
20C2×C11×#121—21no—
21C2×C11×#121—22no—
22C2×C11×#121C2212yes—
23C22×C11×C4⋊C4C2211yescharacteristic
24#10623364—24no—
25#10623364C2218yescomplemented
26C2×#67003—28no—
27C2×#67003C2218yescomplemented
28C2×#67001—28no—
29C2×#67001C2218yescomplemented
30C2×#66999—21no—
31C22×#4326C2211yescharacteristic
32C22×#4325C2211yescharacteristic
33C2×#66992—22no—
34C2×#66991—21no—
35C22×#4324C2211yescharacteristic
36C22×#4323C2211yescharacteristic
37C2×#66983C2212yes—
38C22×C4⋊Dic11C2211yescharacteristic
39C2×#66977C2212yes—
40C22×#4318C2211yescharacteristic
41C22×#4318C2212yes—
42C23×C11⋊C8C2212yes—
43C23×C11⋊C8C2211yescharacteristic
44#10622845C2218yescomplemented
45C2×#66899C2212yes—
46C2×#66896C2212yes—
47#10622665C22116yescomplemented
48#10622661C22116yescomplemented
49#10622654C22116yescomplemented
50#10622652C22116yescomplemented
51C2×#66874C2212yes—
52#10622579C2218yescomplemented
53C2×#66873C2212yes—
54C2×#66872C2212yes—
55C2×#66872C2212yes—
56C2×#66872C2218yescomplemented
57C2×C11×#41—24no—
58C2×C11×#41—22no—
59C2×C11×#41—24no—
60C2×C11×#41—24no—
61C2×C11×#41—24no—
62C2×C11×#41D414yes—
63C2×C11×#41C2314yes—
64C2×C11×#41C2314yes—
65C22×Q8×C11D411yescharacteristic
66C22×Q8×C11C2311yescharacteristic
67C22×D4×C11—21no—
68C22×D4×C11—22no—
69C22×D4×C11D411yescharacteristic
70C22×D4×C11D412yes—
71C22×D4×C11C2311yescharacteristic
72C23×C4×C11—21no—
73C23×C4×C11—21no—
74C23×C4×C11C2312yes—
75C23×C4×C11C2311yescharacteristic
76C22×C22⋊D11—21no—
77C22×C22⋊D11—22no—
78C23×Dic11—21no—
79C2×#4339—22no—
80C2×#4339—24no—
81C2×#4339—24no—
82C2×#4339C2314yes—
83C22×D44C2311yescharacteristic
84C22×C4×D11—21no—
85C22×Dic22C2311yescharacteristic
86C11×C22⋊Q8—28no—
87C11×C22⋊Q8—24no—
88C11×C22⋊Q8C2318yes—
89C11×#121—28no—
90C11×#121—216no—
91C11×#121—24no—
92C11×#121C2318yes—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4—22no—
95C2×C11×C4⋊C4—22no—
96C2×C11×C4⋊C4C2312yes—
97C2×C11×C4⋊C4C2314yes—
98C2×C11×C22⋊C4—22no—
99C2×C11×C22⋊C4—22no—
100C2×C22⋊Dic11—22no—
101#67003—232no—
102#67001—232no—
103#66999—28no—
104C2×#4326—24no—
105C2×#4326C2314yes—
106C2×#4325—24no—
107C2×#4325C2314yes—
108#66992—216no—
109#66991—28no—
110C2×#4324—24no—
111C2×#4324C2314yes—
112C2×#4323—24no—
113C2×#4323C2314yes—
114#66983—24no—
115#66983C2318yes—
116C2×(C2×D11)⋊C4—22no—
117C2×C4⋊Dic11—21no—
118C2×C4⋊Dic11—22no—
119C2×C4⋊Dic11C2312yes—
120C2×C4⋊Dic11C2314yes—
121#66977—24no—
122#66977C2318yes—
123C2×Dic11⋊C4—22no—
124C2×#4318—24no—
125C2×#4318—28no—
126C2×#4318C2314yes—
127C2×#4318C2318yes—
128C22×C11⋊C8—28no—
129C22×C11⋊C8D418yescomplemented
130C22×C11⋊C8C2312yes—
131C22×C11⋊C8C2318yes—
132C22×C11⋊C8C2311yescharacteristic
133C22×C11⋊C8C2311yescharacteristic
134C22×C11⋊C8C2314yes—
135#66899C2318yes—
136#66896C2318yes—
137#66874C2318yes—
138#66873C2318yes—
139#66872C2318yes—
140#66872C2318yes—
141C2×#3060—111nomaximal, Sylow
142C24×C11—21no—
143C24×C11C2×D412yes—
144C24×C11C2×D411yescharacteristic
145C23×D11—21no—
146C11×#41—216no—
147C11×#41—28no—
148C11×#41—28no—
149C11×#41—28no—
150C11×#41—28no—
151C11×#41—48no—
152C2×Q8×C11—24no—
153C2×Q8×C11—21no—
154C2×Q8×C11—22no—
155C2×Q8×C11—22no—
156C2×Q8×C11C2×D414yes—
157C2×Q8×C11C2412yes—
158C2×D4×C11—28no—
159C2×D4×C11—24no—
160C2×D4×C11—28no—
161C2×D4×C11—24no—
162C2×D4×C11—22no—
163C2×D4×C11—21no—
164C2×D4×C11—22no—
165C2×D4×C11—44no—
166C2×D4×C11—84no—
167C2×D4×C11C2×D414yes—
168C2×D4×C11C2×D418yes—
169C2×D4×C11C2412yes—
170C22×C4×C11—24no—
171C22×C4×C11—24no—
172C22×C4×C11—22no—
173C22×C4×C11—21no—
174C22×C4×C11—24no—
175C22×C4×C11—24no—
176C22×C4×C11—44no—
177C22×C4×C11—82no—
178C22×C4×C11C2×D412yes—
179C22×C4×C11C2×D414yes—
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D412yes—
182C22×C4×C11C2×D414yes—
183C22×C4×C11#4114yes—
184C22×C4×C11C2414yes—
185C22×C4×C11C2411yescharacteristic
186C22×C4×C11C2412yes—
187C2×C22⋊D11—24no—
188C2×C22⋊D11—28no—
189C2×C22⋊D11—44no—
190C2×C22⋊D11—84no—
191C22×Dic11—21no—
192C22×Dic11—22no—
193C22×Dic11—24no—
194C22×Dic11—82no—
195#4339—28no—
196#4339—28no—
197#4339—48no—
198C2×D44—21no—
199C2×D44—22no—
200C2×D44—22no—
201C2×D44C2412yes—
202C2×C4×D11—24no—
203C2×C4×D11—44no—
204C2×Dic22—22no—
205C2×Dic22—21no—
206C2×Dic22—22no—
207C2×Dic22C2412yes—
208C11×C4⋊C4—22no—
209C11×C4⋊C4—24no—
210C11×C4⋊C4—28no—
211C11×C4⋊C4C2414yes—
212C11×C22⋊C4—28no—
213C11×C22⋊C4—28no—
214C22⋊Dic11—28no—
215#4326—28no—
216#4325—28no—
217#4324—28no—
218#4323—28no—
219(C2×D11)⋊C4—28no—
220C4⋊Dic11—22no—
221C4⋊Dic11—24no—
222C4⋊Dic11C2414yes—
223Dic11⋊C4—28no—
224#4318—216no—
225#4318—28no—
226C2×C11⋊C8—216no—
227C2×C11⋊C8—24no—
228C2×C11⋊C8C2×D414yes—
229C2×C11⋊C8C2×D414yes—
230C2×C11⋊C8C2×D4116yescomplemented
231C2×C11⋊C8C2414yes—
232C2×C11⋊C8C2412yes—
233C2×C11⋊C8C2412yes—
234C22×#135—111no—
235C22×#131—111no—
236C2×#537—111no—
237C2×#537D1111yescharacteristic, complemented
238#3060—1116no—
239C2×#470—112no—
240C2×#469—112no—
241C2×#465—112no—
242C2×#465—112no—
243C22×#106—111no—
244C2×#417—111no—
245C2×#417—111no—
246C23×C11—22no—
247C23×C11—22no—
248C23×C11—24no—
249C23×C11—24no—
250C23×C11—24no—
251C23×C11—22no—
252C23×C11—42no—
253C23×C11—42no—
254C23×C11—42no—
255C23×C11#12114yes—
256C23×C11C22×D414yes—
257C23×C11C22×D412yes—
258C23×C11C22×D411yescharacteristic
259C22×D11—22no—
260C22×D11—42no—
261C22×D11—42no—
262C22×D11—42no—
263Q8×C11—28no—
264Q8×C11—22no—
265Q8×C11—22no—
266Q8×C11—42no—
267D4×C11—216no—
268D4×C11—28no—
269D4×C11—22no—
270D4×C11—22no—
271D4×C11—48no—
272D4×C11—42no—
273D4×C11—88no—
274C2×C4×C11—24no—
275C2×C4×C11—28no—
276C2×C4×C11—24no—
277C2×C4×C11—24no—
278C2×C4×C11—24no—
279C2×C4×C11—22no—
280C2×C4×C11—42no—
281C2×C4×C11—44no—
282C2×C4×C11—48no—
283C2×C4×C11—84no—
284C2×C4×C11#12114yes—
285C2×C4×C11#12118yes—
286C2×C4×C11C22×D412yes—
287C2×C4×C11C22×D414yes—
288C2×C4×C11C22×D414yes—
289C2×C4×C11C22×D411yescharacteristic
290C2×C4×C11C22×D412yes—
291C2×C4×C11C2×#4112yes—
292C2×C4×C11C2×#4114yes—
293C2×C4×C11C2511yescharacteristic
294C22⋊D11—48no—
295C22⋊D11—88no—
296C2×Dic11—22no—
297C2×Dic11—24no—
298C2×Dic11—42no—
299C2×Dic11—44no—
300C2×Dic11—84no—
301D44—22no—
302D44—22no—
303D44—42no—
304C4×D11—48no—
305Dic22—22no—
306Dic22—22no—
307Dic22—42no—
308C11⋊C8—24no—
309C11⋊C8C22×D414yes—
310C11⋊C8C22×D414yes—
311C22×#41—111no—
312C22×#41C2×D1111yescharacteristic
313C22×#41C2×D1111yescharacteristic
314C2×#135—118no—
315C2×#135—228no—
316C22×Q16—111no—
317C22×SD16—111no—
318C22×SD16—111no—
319C22×D8—111no—
320C2×#131—118no—
321C2×#131—228no—
322C22×M16—111no—
323C22×M16—112no—
324C23×C8—111no—
325C23×C8—112no—
326#537—24no—
327#537—118no—
328#537—224no—
329#537C2×D1118yescomplemented
330C2×C22⋊Q8—21no—
331C2×C22⋊Q8—112no—
332C2×C22⋊Q8—221no—
333C2×C22⋊Q8C2×D1112yes—
334C2×#121—21no—
335C2×#121—22no—
336C2×#121—112no—
337C2×#121—221no—
338C2×#121—222no—
339C2×#121C2×D1112yes—
340C22×C4⋊C4—111no—
341C22×C4⋊C4C2×D1111yescharacteristic
342#470—1116no—
343#469—1116no—
344#465—1116no—
345#465—1116no—
346C2×#106—112no—
347C2×#106—112no—
348C2×#106—118no—
349#417—118no—
350#417—118no—
351C2×#103—112no—
352C2×#103—112no—
353C2×#102—112no—
354C2×#102—112no—
355C22×C11—28no—
356C22×C11—22no—
357C22×C11—22no—
358C22×C11—24no—
359C22×C11—24no—
360C22×C11—24no—
361C22×C11—48no—
362C22×C11—42no—
363C22×C11—42no—
364C22×C11—42no—
365C22×C11—84no—
366C22×C11C2×#12114yes—
367C22×C11C2×#12112yes—
368C22×C11#57712yes—
369C22×C11#57712yes—
370C22×C11C23×D411yescharacteristic
371C2×D11—42no—
372C2×D11—42no—
373C2×D11—42no—
374C2×D11—84no—
375C4×C11—24no—
376C4×C11—42no—
377C4×C11—44no—
378C4×C11C2×#12112yes—
379C4×C11C2×#12114yes—
380C4×C11C23×D411yescharacteristic
381C4×C11C22×#4111yescharacteristic
382Dic11—42no—
383Dic11—44no—
384C2×#41—24no—
385C2×#41—24no—
386C2×#41—22no—
387C2×#41—24no—
388C2×#41—24no—
389C2×#41—114no—
390C2×#41—222no—
391C2×#41—224no—
392C2×#41—224no—
393C2×#41C22⋊D1114yes—
394C2×#41C22×D1114yes—
395C2×#41C22×D1114yes—
396C22×Q8—111no—
397C22×Q8C22⋊D1111yescharacteristic
398C22×Q8C22×D1111yescharacteristic
399C22×D4—21no—
400C22×D4—22no—
401C22×D4—111no—
402C22×D4—221no—
403C22×D4—222no—
404C22×D4C22⋊D1112yes—
405C22×D4C22⋊D1111yescharacteristic
406C22×D4C22×D1111yescharacteristic
407C23×C4—21no—
408C23×C4—21no—
409C23×C4—221no—
410C23×C4—221no—
411C23×C4C22×D1112yes—
412C23×C4C22×D1111yescharacteristic
413#135—2232no—
414C2×Q16—114no—
415C2×Q16—224no—
416C2×SD16—114no—
417C2×SD16—114no—
418C2×SD16—224no—
419C2×SD16—224no—
420C2×D8—114no—
421C2×D8—224no—
422#131—2232no—
423C2×M16—114no—
424C2×M16—118no—
425C2×M16—228no—
426C2×M16—224no—
427C22×C8—118no—
428C22×C8—111no—
429C22×C8—111no—
430C22×C8—114no—
431C22×C8—112no—
432C22×C8—118no—
433C22×C8—228no—
434C22⋊Q8—28no—
435C22⋊Q8—24no—
436C22⋊Q8—118no—
437C22⋊Q8—228no—
438C22⋊Q8—224no—
439C22⋊Q8C22×D1118yes—
440#121—28no—
441#121—216no—
442#121—24no—
443#121—118no—
444#121—228no—
445#121—2216no—
446#121—224no—
447#121C22×D1118yes—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—112no—
452C2×C4⋊C4—114no—
453C2×C4⋊C4—221no—
454C2×C4⋊C4—222no—
455C2×C4⋊C4—222no—
456C2×C4⋊C4C22×D1112yes—
457C2×C4⋊C4C22×D1114yes—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—222no—
461C2×C22⋊C4—222no—
462#106—118no—
463#106—118no—
464#103—118no—
465#103—118no—
466#102—118no—
467#102—118no—
468C2×C11—24no—
469C2×C11—44no—
470C2×C11—82no—
471C2×C11#306014yescomplemented
472C2×C11C22×#12111yescharacteristic
473C2×C11C2×#57711yescharacteristic
474C2×C11C2×#57711yescharacteristic
475D11—82no—
476C24—21no—
477C24—221no—
478C24C2×C22⋊D1112yes—
479C24C2×C22⋊D1111yescharacteristic
480#41—216no—
481#41—28no—
482#41—28no—
483#41—28no—
484#41—28no—
485#41—48no—
486#41—228no—
487#41—228no—
488#41—448no—
489C2×Q8—24no—
490C2×Q8—21no—
491C2×Q8—22no—
492C2×Q8—22no—
493C2×Q8—112no—
494C2×Q8—221no—
495C2×Q8—222no—
496C2×Q8—222no—
497C2×Q8C2×C22⋊D1114yes—
498C2×Q8C23×D1112yes—
499C2×D4—28no—
500C2×D4—24no—
501C2×D4—28no—
502C2×D4—24no—
503C2×D4—22no—
504C2×D4—22no—
505C2×D4—21no—
506C2×D4—44no—
507C2×D4—84no—
508C2×D4—112no—
509C2×D4—224no—
510C2×D4—228no—
511C2×D4—222no—
512C2×D4—222no—
513C2×D4—221no—
514C2×D4—444no—
515C2×D4—884no—
516C2×D4C2×C22⋊D1118yes—
517C2×D4C2×C22⋊D1114yes—
518C2×D4C23×D1112yes—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—44no—
526C22×C4—82no—
527C22×C4—222no—
528C22×C4—221no—
529C22×C4—224no—
530C22×C4—224no—
531C22×C4—444no—
532C22×C4—882no—
533C22×C4D4×D1114yes—
534C22×C4#434114yes—
535C22×C4C2×C22⋊D1114yes—
536C22×C4C2×C22⋊D1112yes—
537C22×C4C2×C22⋊D1112yes—
538C22×C4C2×C22⋊D1111yescharacteristic
539C22×C4C23×D1114yes—
540C22×C4C23×D1112yes—
541C22×C4C23×D1111yescharacteristic
542Q16—228no—
543SD16—228no—
544SD16—228no—
545D8—228no—
546M16—2216no—
547M16—228no—
548C2×C8—114no—
549C2×C8—114no—
550C2×C8—1116no—
551C2×C8—112no—
552C2×C8—112no—
553C2×C8—114no—
554C2×C8—2216no—
555C2×C8—224no—
556C4⋊C4—24no—
557C4⋊C4—22no—
558C4⋊C4—28no—
559C4⋊C4—114no—
560C4⋊C4—224no—
561C4⋊C4—222no—
562C4⋊C4—228no—
563C4⋊C4C23×D1114yes—
564C22⋊C4—28no—
565C22⋊C4—28no—
566C22⋊C4—228no—
567C22⋊C4—228no—
568C11C2×#306011yescharacteristic, complemented, Sylow
569C23—22no—
570C23—22no—
571C23—24no—
572C23—24no—
573C23—24no—
574C23—22no—
575C23—42no—
576C23—42no—
577C23—42no—
578C23—222no—
579C23—442no—
580C23—442no—
581C23—442no—
582C23#6699214yes—
583C23C22×C22⋊D1114yes—
584C23C22×C22⋊D1112yes—
585C23C22×C22⋊D1111yescharacteristic
586Q8—28no—
587Q8—22no—
588Q8—22no—
589Q8—42no—
590Q8—222no—
591Q8—222no—
592Q8—442no—
593D4—216no—
594D4—28no—
595D4—22no—
596D4—22no—
597D4—48no—
598D4—42no—
599D4—88no—
600D4—222no—
601D4—222no—
602D4—448no—
603D4—442no—
604D4—888no—
605C2×C4—24no—
606C2×C4—28no—
607C2×C4—24no—
608C2×C4—24no—
609C2×C4—24no—
610C2×C4—22no—
611C2×C4—42no—
612C2×C4—44no—
613C2×C4—48no—
614C2×C4—84no—
615C2×C4—224no—
616C2×C4—222no—
617C2×C4—442no—
618C2×C4—444no—
619C2×C4—448no—
620C2×C4—884no—
621C2×C4#6699214yes—
622C2×C4#6699218yes—
623C2×C4C2×D4×D1112yes—
624C2×C4C2×D4×D1114yes—
625C2×C4C2×#434112yes—
626C2×C4C2×#434114yes—
627C2×C4C22×C22⋊D1114yes—
628C2×C4C22×C22⋊D1112yes—
629C2×C4C22×C22⋊D1111yescharacteristic
630C2×C4C24×D1111yescharacteristic
631C8—114no—
632C8—114no—
633C8—224no—
634C22—28no—
635C22—22no—
636C22—22no—
637C22—24no—
638C22—24no—
639C22—24no—
640C22—48no—
641C22—42no—
642C22—42no—
643C22—42no—
644C22—84no—
645C22—442no—
646C22—442no—
647C22—442no—
648C22—884no—
649C22C2×#6699214yes—
650C22C2×#6699212yes—
651C22#1062336712yes—
652C22#1062336812yes—
653C22C23×C22⋊D1111yescharacteristic
654C4—24no—
655C4—42no—
656C4—44no—
657C4—442no—
658C4—444no—
659C4C2×#6699212yes—
660C4C2×#6699214yes—
661C4C22×D4×D1111yescharacteristic
662C4C22×#434111yescharacteristic
663C2—24no—
664C2—44no—
665C2—82no—
666C2—882no—
667C2#1307827514yesdirect product factor
668C2C22×#6699211yescharacteristic
669C2C2×#1062336811yescharacteristic
670C2C2×#1062336711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#537C2
socleC23×C11C22×D4
hypercenterC2×#537D11
hypocenterC11C2×#3060
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. C22×#67003C2semidirect
2. C22×#67001C2semidirect
3. C2×#10623364C2semidirect
4. #13078275C2direct (N × H)
5. C2×#10622665C2semidirect
6. C2×#10622652C2semidirect
7. C2×#10622661C2semidirect
8. C2×#10622654C2semidirect
9. C22×#66872C2semidirect
10. C2×#10622845C2semidirect
11. C2×#10622579C2semidirect
12. C2×C11×#537C2semidirect
17. C11×#537C22semidirect
25. #10623364C22semidirect
27. C2×#67003C22semidirect
29. C2×#67001C22semidirect
44. #10622845C22semidirect
47. #10622665C22semidirect
48. #10622661C22semidirect
49. #10622654C22semidirect
50. #10622652C22semidirect
52. #10622579C22semidirect
56. C2×#66872C22semidirect
129. C22×C11⋊C8D4semidirect
230. C2×C11⋊C8C2×D4semidirect
237. C2×#537D11semidirect
329. #537C2×D11semidirect
471. C2×C11#3060semidirect
568. C11C2×#3060semidirect
667. C2#13078275direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670032
C22×#670012
C2×#106233642
#130782752
C2×#106226652
C2×#106226522
C2×#106226612
C2×#106226542
C22×#668722
C2×#106228452
C2×#106225792
C2×C11×#5372
C2×#306011