Finite Group Databasebeta

← C2×#13078309 #15621022

Subgroups — C2×#13078309 #15621022

Order 2816.

2742 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67004C211yesmaximal, characteristic, complemented
2C22×#67001C211yesmaximal, characteristic, complemented
3C2×#10623356C211yesmaximal, characteristic, complemented
4#13078309C2116yesmaximal, direct product factor
5C2×#10622665C212yesmaximal, complemented
6C2×#10622655C212yesmaximal, complemented
7C2×#10622664C212yesmaximal, complemented
8C2×#10622654C212yesmaximal, complemented
9C2×#10622577C211yesmaximal, characteristic, complemented
10C2×#10622846C211yesmaximal, characteristic, complemented
11C22×#66874C211yesmaximal, characteristic, complemented
12C2×C11×#537C211yesmaximal, characteristic
13C22×C11×#41C2211yescharacteristic
14C22×C11×#41C2211yescharacteristic
15C23×Dic22C2211yescharacteristic
16C11×#537—24no—
17C11×#537C2218yes—
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#10623356—24no—
25#10623356C2218yescomplemented
26C2×#67004—28no—
27C2×#67004C2218yescomplemented
28C2×#67001—28no—
29C2×#67001C2218yescomplemented
30C2×#66997—21no—
31C22×#4326C2212yes—
32C2×#66989—21no—
33C2×#66988—22no—
34C22×#4324C2212yes—
35C2×#66979C2211yescharacteristic
36C2×#66977C2212yes—
37C2×#66977C2212yes—
38C22×#4318C2212yes—
39C22×#4318C2211yescharacteristic
40C23×C11⋊C8C2211yescharacteristic
41C23×C11⋊C8C2212yes—
42#10622846C2218yescomplemented
43C2×#66899C2211yescharacteristic
44C2×#66899C2211yescharacteristic
45C2×#66896C2211yescharacteristic
46C2×#66896C2211yescharacteristic
47#10622665C22116yescomplemented
48#10622664C22116yescomplemented
49#10622655C22116yescomplemented
50#10622654C22116yescomplemented
51C2×#66874C2212yes—
52C2×#66874C2212yes—
53C2×#66874C2218yescomplemented
54#10622577C2218yescomplemented
55C2×#66872C2212yes—
56C2×#66871C2212yes—
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×C11D412yes—
70C22×D4×C11D411yescharacteristic
71C22×D4×C11C2311yescharacteristic
72C23×C4×C11—21no—
73C23×C4×C11—21no—
74C23×C4×C11C2312yes—
75C23×C4×C11C2311yescharacteristic
76C23×Dic11—21no—
77C22×Dic22—24no—
78C22×Dic22—24no—
79C22×Dic22—21no—
80C22×Dic22—22no—
81C22×Dic22C2312yes—
82C22×Dic22C2314yes—
83C11×C22⋊Q8—28no—
84C11×C22⋊Q8—24no—
85C11×C22⋊Q8C2318yes—
86C11×#121—28no—
87C11×#121—216no—
88C11×#121—24no—
89C11×#121C2318yes—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—22no—
92C2×C11×C4⋊C4—22no—
93C2×C11×C4⋊C4C2312yes—
94C2×C11×C4⋊C4C2314yes—
95C2×C11×C22⋊C4—22no—
96C2×C11×C22⋊C4—22no—
97C2×C22⋊Dic11—22no—
98C2×C22⋊Dic11—22no—
99C2×C22⋊Dic11—21no—
100#67004—232no—
101#67001—232no—
102#66997—28no—
103C2×#4326—28no—
104C2×#4326C2318yes—
105#66989—28no—
106#66988—216no—
107C2×#4324—28no—
108C2×#4324C2318yes—
109#66979—22no—
110#66979C2314yes—
111C2×C4⋊Dic11C2311yescharacteristic
112C2×C4⋊Dic11C2311yescharacteristic
113#66977—24no—
114#66977—24no—
115#66977C2318yes—
116#66977C2318yes—
117C2×Dic11⋊C4—22no—
118C2×Dic11⋊C4—22no—
119C2×C4×Dic11—21no—
120C2×#4318—28no—
121C2×#4318D418yescomplemented
122C2×#4318C2318yes—
123C2×#4318C2314yes—
124C22×C11⋊C8—24no—
125C22×C11⋊C8—28no—
126C22×C11⋊C8C2311yescharacteristic
127C22×C11⋊C8C2311yescharacteristic
128C22×C11⋊C8C2314yes—
129C22×C11⋊C8C2318yes—
130C22×C11⋊C8C2312yes—
131#66899C2314yes—
132#66899C2314yes—
133#66896C2314yes—
134#66896C2314yes—
135#66874C2318yes—
136#66874C2318yes—
137#66872C2318yes—
138#66871C2318yes—
139C2×#3063—111nomaximal, Sylow
140C24×C11—21no—
141C24×C11C2×D412yes—
142C24×C11C2×D411yescharacteristic
143C11×#41—216no—
144C11×#41—28no—
145C11×#41—28no—
146C11×#41—28no—
147C11×#41—28no—
148C11×#41—48no—
149C2×Q8×C11—24no—
150C2×Q8×C11—21no—
151C2×Q8×C11—22no—
152C2×Q8×C11—22no—
153C2×Q8×C11C2×D414yes—
154C2×Q8×C11C2412yes—
155C2×D4×C11—28no—
156C2×D4×C11—24no—
157C2×D4×C11—28no—
158C2×D4×C11—24no—
159C2×D4×C11—22no—
160C2×D4×C11—21no—
161C2×D4×C11—22no—
162C2×D4×C11—44no—
163C2×D4×C11—84no—
164C2×D4×C11C2×D418yes—
165C2×D4×C11C2×D414yes—
166C2×D4×C11C2412yes—
167C22×C4×C11—24no—
168C22×C4×C11—24no—
169C22×C4×C11—22no—
170C22×C4×C11—21no—
171C22×C4×C11—24no—
172C22×C4×C11—24no—
173C22×C4×C11—44no—
174C22×C4×C11—82no—
175C22×C4×C11C2×D412yes—
176C22×C4×C11C2×D414yes—
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D412yes—
179C22×C4×C11C2×D414yes—
180C22×C4×C11#4114yes—
181C22×C4×C11C2414yes—
182C22×C4×C11C2411yescharacteristic
183C22×C4×C11C2412yes—
184C22×Dic11—21no—
185C22×Dic11—21no—
186C22×Dic11—22no—
187C22×Dic11—24no—
188C22×Dic11—44no—
189C2×Dic22—24no—
190C2×Dic22—28no—
191C2×Dic22—22no—
192C2×Dic22—24no—
193C2×Dic22—24no—
194C2×Dic22—28no—
195C2×Dic22—44no—
196C2×Dic22—48no—
197C2×Dic22C2414yes—
198C11×C4⋊C4—24no—
199C11×C4⋊C4—22no—
200C11×C4⋊C4—28no—
201C11×C4⋊C4C2414yes—
202C11×C22⋊C4—28no—
203C11×C22⋊C4—28no—
204C22⋊Dic11—28no—
205C22⋊Dic11—28no—
206C22⋊Dic11—24no—
207#4326—216no—
208#4324—216no—
209C4⋊Dic11—21no—
210C4⋊Dic11—21no—
211C4⋊Dic11C2412yes—
212C4⋊Dic11C2412yes—
213Dic11⋊C4—28no—
214Dic11⋊C4—28no—
215C4×Dic11—24no—
216#4318—216no—
217#4318C2×D4116yescomplemented
218C2×C11⋊C8—216no—
219C2×C11⋊C8—22no—
220C2×C11⋊C8—22no—
221C2×C11⋊C8—28no—
222C2×C11⋊C8C2×D418yes—
223C2×C11⋊C8C2412yes—
224C2×C11⋊C8C2412yes—
225C2×C11⋊C8C2414yes—
226C22×#137—111no—
227C22×#131—111no—
228C2×#537D1111yescharacteristic
229C2×#536—111no—
230#3063—1116no—
231C2×#470—112no—
232C2×#468—112no—
233C2×#467—112no—
234C2×#465—112no—
235C2×#428—111no—
236C2×#416—111no—
237C22×#103—111no—
238C23×C11—22no—
239C23×C11—22no—
240C23×C11—24no—
241C23×C11—24no—
242C23×C11—24no—
243C23×C11—22no—
244C23×C11—42no—
245C23×C11—42no—
246C23×C11—42no—
247C23×C11#12114yes—
248C23×C11C22×D414yes—
249C23×C11C22×D412yes—
250C23×C11C22×D411yescharacteristic
251Q8×C11—28no—
252Q8×C11—22no—
253Q8×C11—22no—
254Q8×C11—42no—
255D4×C11—216no—
256D4×C11—28no—
257D4×C11—22no—
258D4×C11—22no—
259D4×C11—48no—
260D4×C11—42no—
261D4×C11—88no—
262C2×C4×C11—24no—
263C2×C4×C11—28no—
264C2×C4×C11—24no—
265C2×C4×C11—24no—
266C2×C4×C11—24no—
267C2×C4×C11—22no—
268C2×C4×C11—42no—
269C2×C4×C11—44no—
270C2×C4×C11—48no—
271C2×C4×C11—84no—
272C2×C4×C11#12114yes—
273C2×C4×C11#12118yes—
274C2×C4×C11C22×D412yes—
275C2×C4×C11C22×D414yes—
276C2×C4×C11C22×D414yes—
277C2×C4×C11C22×D412yes—
278C2×C4×C11C22×D411yescharacteristic
279C2×C4×C11C2×#4112yes—
280C2×C4×C11C2×#4114yes—
281C2×C4×C11C2511yescharacteristic
282C2×Dic11—22no—
283C2×Dic11—22no—
284C2×Dic11—24no—
285C2×Dic11—48no—
286C2×Dic11—44no—
287C2×Dic11—42no—
288C2×Dic11—42no—
289Dic22—24no—
290Dic22—24no—
291Dic22—44no—
292Dic22—48no—
293C11⋊C8—22no—
294C11⋊C8—22no—
295C11⋊C8C22×D418yes—
296C22×#41C2×D1111yescharacteristic
297C22×#41C2×D1111yescharacteristic
298C23×Q8—111no—
299C2×#137—118no—
300C2×#137—228no—
301C22×Q16—112no—
302C22×SD16—112no—
303C2×#131—118no—
304C2×#131—228no—
305C22×M16—111no—
306C22×M16—112no—
307C23×C8—111no—
308C23×C8—112no—
309#537—24no—
310#537C2×D1118yes—
311#536—118no—
312#536—224no—
313C2×C4⋊Q8—221no—
314C2×#124—221no—
315C2×#123—222no—
316C2×C22⋊Q8—21no—
317C2×C22⋊Q8—112no—
318C2×C22⋊Q8—112no—
319C2×C22⋊Q8C2×D1112yes—
320C2×#121—21no—
321C2×#121—22no—
322C2×#121C2×D1112yes—
323C2×#117—111no—
324C22×C4⋊C4C2×D1111yescharacteristic
325#470—1116no—
326#468—1116no—
327#467—1116no—
328#465—1116no—
329#428—118no—
330C2×#107—112no—
331C2×#106—112no—
332#416—118no—
333C2×#103—111no—
334C2×#103—111no—
335C2×#103—112no—
336C2×#103—112no—
337C2×#103—118no—
338C2×#102—111no—
339C2×#102—111no—
340C22×C11—28no—
341C22×C11—22no—
342C22×C11—22no—
343C22×C11—24no—
344C22×C11—24no—
345C22×C11—24no—
346C22×C11—48no—
347C22×C11—42no—
348C22×C11—42no—
349C22×C11—42no—
350C22×C11—84no—
351C22×C11C2×#12114yes—
352C22×C11C2×#12112yes—
353C22×C11#57712yes—
354C22×C11#57812yes—
355C22×C11C23×D411yescharacteristic
356C4×C11—24no—
357C4×C11—42no—
358C4×C11—44no—
359C4×C11C2×#12112yes—
360C4×C11C2×#12114yes—
361C4×C11C23×D411yescharacteristic
362C4×C11C22×#4111yescharacteristic
363Dic11—44no—
364Dic11—42no—
365Dic11—42no—
366C2×#41—24no—
367C2×#41—24no—
368C2×#41—22no—
369C2×#41—24no—
370C2×#41—24no—
371C2×#41C22⋊D1114yes—
372C2×#41C22×D1114yes—
373C2×#41C22×D1114yes—
374C22×Q8—112no—
375C22×Q8—114no—
376C22×Q8—221no—
377C22×Q8—222no—
378C22×Q8—224no—
379C22×Q8—224no—
380C22×Q8C22⋊D1111yescharacteristic
381C22×Q8C22×D1111yescharacteristic
382C22×D4—21no—
383C22×D4—22no—
384C22×D4C22⋊D1112yes—
385C22×D4C22⋊D1111yescharacteristic
386C22×D4C22×D1111yescharacteristic
387C23×C4—21no—
388C23×C4—21no—
389C23×C4—221no—
390C23×C4C22×D1112yes—
391C23×C4C22×D1111yescharacteristic
392#137—2232no—
393C2×Q16—118no—
394C2×Q16—228no—
395C2×SD16—118no—
396C2×SD16—228no—
397#131—2232no—
398C2×M16—118no—
399C2×M16—114no—
400C2×M16—118no—
401C2×M16—228no—
402C22×C8—112no—
403C22×C8—111no—
404C22×C8—111no—
405C22×C8—114no—
406C22×C8—118no—
407C22×C8—228no—
408C22×C8—224no—
409C4⋊Q8—228no—
410#124—228no—
411#123—2216no—
412C22⋊Q8—28no—
413C22⋊Q8—24no—
414C22⋊Q8—118no—
415C22⋊Q8—118no—
416C22⋊Q8—224no—
417C22⋊Q8—224no—
418C22⋊Q8C22×D1118yes—
419#121—28no—
420#121—216no—
421#121—24no—
422#121C22×D1118yes—
423#117—114no—
424#117—222no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—111no—
429C2×C4⋊C4—111no—
430C2×C4⋊C4—222no—
431C2×C4⋊C4—222no—
432C2×C4⋊C4C22×D1112yes—
433C2×C4⋊C4C22×D1114yes—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—221no—
437C2×C22⋊C4—222no—
438C2×C22⋊C4—222no—
439C2×C42—221no—
440#107—118no—
441#106—118no—
442#103—114no—
443#103—114no—
444#103—118no—
445#103—118no—
446#102—114no—
447#102—114no—
448C2×C11—24no—
449C2×C11—44no—
450C2×C11—82no—
451C2×C11#306314yescomplemented
452C2×C11C22×#12111yescharacteristic
453C2×C11C2×#57711yescharacteristic
454C2×C11C2×#57811yescharacteristic
455C24—21no—
456C24C2×C22⋊D1112yes—
457C24C2×C22⋊D1111yescharacteristic
458#41—216no—
459#41—28no—
460#41—28no—
461#41—28no—
462#41—28no—
463#41—48no—
464C2×Q8—24no—
465C2×Q8—21no—
466C2×Q8—22no—
467C2×Q8—22no—
468C2×Q8—114no—
469C2×Q8—222no—
470C2×Q8—224no—
471C2×Q8—224no—
472C2×Q8—228no—
473C2×Q8—224no—
474C2×Q8—228no—
475C2×Q8—444no—
476C2×Q8—448no—
477C2×Q8C2×C22⋊D1114yes—
478C2×Q8C23×D1112yes—
479C2×D4—28no—
480C2×D4—24no—
481C2×D4—28no—
482C2×D4—24no—
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—21no—
486C2×D4—44no—
487C2×D4—84no—
488C2×D4C2×C22⋊D1118yes—
489C2×D4C2×C22⋊D1114yes—
490C2×D4C23×D1112yes—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—44no—
498C22×C4—82no—
499C22×C4—224no—
500C22×C4—221no—
501C22×C4—221no—
502C22×C4—222no—
503C22×C4—444no—
504C22×C4D4×D1114yes—
505C22×C4#434114yes—
506C22×C4C2×C22⋊D1114yes—
507C22×C4C2×C22⋊D1112yes—
508C22×C4C2×C22⋊D1112yes—
509C22×C4C2×C22⋊D1111yescharacteristic
510C22×C4C23×D1114yes—
511C22×C4C23×D1112yes—
512C22×C4C23×D1111yescharacteristic
513Q16—2216no—
514SD16—2216no—
515M16—1116no—
516M16—2216no—
517C2×C8—118no—
518C2×C8—114no—
519C2×C8—112no—
520C2×C8—112no—
521C2×C8—2216no—
522C2×C8—222no—
523C2×C8—222no—
524C2×C8—228no—
525C4⋊C4—24no—
526C4⋊C4—22no—
527C4⋊C4—28no—
528C4⋊C4—112no—
529C4⋊C4—112no—
530C4⋊C4—221no—
531C4⋊C4—221no—
532C4⋊C4—228no—
533C4⋊C4—228no—
534C4⋊C4C23×D1114yes—
535C22⋊C4—28no—
536C22⋊C4—28no—
537C22⋊C4—224no—
538C22⋊C4—228no—
539C22⋊C4—228no—
540C42—224no—
541C11C2×#306311yescharacteristic, complemented, Sylow
542C23—22no—
543C23—22no—
544C23—24no—
545C23—24no—
546C23—24no—
547C23—22no—
548C23—42no—
549C23—42no—
550C23—42no—
551C23#6699214yes—
552C23C22×C22⋊D1114yes—
553C23C22×C22⋊D1112yes—
554C23C22×C22⋊D1111yescharacteristic
555Q8—28no—
556Q8—22no—
557Q8—22no—
558Q8—42no—
559Q8—224no—
560Q8—224no—
561Q8—444no—
562Q8—448no—
563D4—216no—
564D4—28no—
565D4—22no—
566D4—22no—
567D4—48no—
568D4—42no—
569D4—88no—
570C2×C4—24no—
571C2×C4—28no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—22no—
576C2×C4—42no—
577C2×C4—44no—
578C2×C4—48no—
579C2×C4—84no—
580C2×C4—222no—
581C2×C4—222no—
582C2×C4—224no—
583C2×C4—448no—
584C2×C4—444no—
585C2×C4—442no—
586C2×C4—442no—
587C2×C4#6699214yes—
588C2×C4#6699218yes—
589C2×C4C2×D4×D1112yes—
590C2×C4C2×D4×D1114yes—
591C2×C4C2×#434112yes—
592C2×C4C2×#434114yes—
593C2×C4C22×C22⋊D1114yes—
594C2×C4C22×C22⋊D1112yes—
595C2×C4C22×C22⋊D1111yescharacteristic
596C2×C4C24×D1111yescharacteristic
597C8—118no—
598C8—222no—
599C8—222no—
600C22—28no—
601C22—22no—
602C22—22no—
603C22—24no—
604C22—24no—
605C22—24no—
606C22—48no—
607C22—42no—
608C22—42no—
609C22—42no—
610C22—84no—
611C22C2×#6699214yes—
612C22C2×#6699212yes—
613C22#1062336712yes—
614C22#1062336912yes—
615C22C23×C22⋊D1111yescharacteristic
616C4—24no—
617C4—42no—
618C4—44no—
619C4—444no—
620C4—442no—
621C4—442no—
622C4C2×#6699212yes—
623C4C2×#6699214yes—
624C4C22×D4×D1111yescharacteristic
625C4C22×#434111yescharacteristic
626C2—24no—
627C2—44no—
628C2—82no—
629C2#1307830914yesdirect product factor
630C2C22×#6699211yescharacteristic
631C2C2×#1062336711yescharacteristic
632C2C2×#1062336911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC2×C11×#537C2
socleC23×C11C22×D4
hypercenterC2×#537D11
hypocenterC11C2×#3063
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×#67004C2semidirect
2. C22×#67001C2semidirect
3. C2×#10623356C2semidirect
4. #13078309C2direct (N × H)
5. C2×#10622665C2semidirect
6. C2×#10622655C2semidirect
7. C2×#10622664C2semidirect
8. C2×#10622654C2semidirect
9. C2×#10622577C2semidirect
10. C2×#10622846C2semidirect
11. C22×#66874C2semidirect
25. #10623356C22semidirect
27. C2×#67004C22semidirect
29. C2×#67001C22semidirect
42. #10622846C22semidirect
47. #10622665C22semidirect
48. #10622664C22semidirect
49. #10622655C22semidirect
50. #10622654C22semidirect
53. C2×#66874C22semidirect
54. #10622577C22semidirect
121. C2×#4318D4semidirect
217. #4318C2×D4semidirect
451. C2×C11#3063semidirect
541. C11C2×#3063semidirect
629. C2#13078309direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670042
C22×#670012
C2×#106233562
#130783092
C2×#106226652
C2×#106226552
C2×#106226642
C2×#106226542
C2×#106225772
C2×#106228462
C22×#668742
C2×C11×#5372
C2×#306311