Finite Group Databasebeta

← C2×#13078301 #15621014

Subgroups — C2×#13078301 #15621014

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×#66960C211yesmaximal, characteristic, complemented
2C2×#10623364C211yesmaximal, characteristic
3C2×#10623347C211yesmaximal, characteristic, complemented
4#13078301C2116yesmaximal, direct product factor
5C2×#10622802C212yesmaximal, complemented
6C2×#10622787C212yesmaximal, complemented
7C2×#10622801C212yesmaximal, complemented
8C2×#10622784C212yesmaximal, complemented
9C2×#10622734C211yesmaximal, characteristic, complemented
10C2×#10622846C211yesmaximal, characteristic, complemented
11C22×#66899C211yesmaximal, characteristic, complemented
12C22×C11×#137C211yesmaximal, characteristic, complemented
13C22×C11×#41C2211yescharacteristic
14C23×Q8×C11C2211yescharacteristic
15C22×#4339C2211yescharacteristic
16C2×C11×#137—28no—
17C2×C11×#137C2218yescomplemented
18C22×C11×Q16C2212yes—
19C22×C11×SD16C2212yes—
20C22×C11×M16C2211yescharacteristic
21#10623364—24no—
22#10623364C2218yes—
23#10623347—24no—
24#10623347C2218yescomplemented
25C2×#67000—21no—
26C2×#66999C2212yes—
27C2×#66999C2212yes—
28C2×#66999C2212yes—
29C2×#66997—21no—
30C2×#66992—22no—
31C2×#66991C2212yes—
32C2×#66983—21no—
33C2×#66982—22no—
34C2×#66979C2211yescharacteristic
35C22×C4⋊Dic11C2211yescharacteristic
36C2×#66977—21no—
37C23×C11⋊C8C2211yescharacteristic
38C2×#66960—28no—
39C2×#66960C2218yescomplemented
40C22×#4313C2212yes—
41C22×C8×D11C2212yes—
42#10622846C2218yescomplemented
43C2×#66899C2212yes—
44C2×#66899C2212yes—
45C2×#66899C2211yescharacteristic
46C2×#66899C2211yescharacteristic
47C2×#66899C2218yescomplemented
48C2×#66896C2211yescharacteristic
49C2×#66896C2211yescharacteristic
50#10622802C22116yescomplemented
51#10622801C22116yescomplemented
52#10622787C22116yescomplemented
53#10622784C22116yescomplemented
54#10622734C2218yescomplemented
55C2×#66882C2212yes—
56C2×#66881C2212yes—
57C2×C11×#41—22no—
58C2×C11×#41—24no—
59C2×C11×#41—24no—
60C2×C11×#41C2314yes—
61C22×Q8×C11—21no—
62C22×Q8×C11—22no—
63C22×Q8×C11—24no—
64C22×Q8×C11—24no—
65C22×Q8×C11C2312yes—
66C22×Q8×C11C2311yescharacteristic
67C22×Q8×C11C2314yes—
68C22×D4×C11—21no—
69C22×D4×C11C2311yescharacteristic
70C23×C4×C11—21no—
71C23×C4×C11—21no—
72C23×C4×C11C2311yescharacteristic
73C22×C22⋊D11—22no—
74C22×C22⋊D11D412yes—
75C23×Dic11—21no—
76C2×#4339—24no—
77C2×#4339—24no—
78C2×#4339D414yes—
79C2×#4339C2314yes—
80C22×D44D411yescharacteristic
81C22×C4×D11C2312yes—
82C22×Dic22D411yescharacteristic
83C11×#137—232no—
84C2×C11×Q16—28no—
85C2×C11×Q16C2318yes—
86C2×C11×SD16—28no—
87C2×C11×SD16C2318yes—
88C2×C11×M16D418yescomplemented
89C2×C11×M16C2314yes—
90C22×C8×C11C2312yes—
91C2×C22⋊Dic11—21no—
92C2×C22⋊Dic11—22no—
93#67000—28no—
94#66999—24no—
95#66999—24no—
96#66999—24no—
97#66999C2318yes—
98#66999C2318yes—
99#66999C2318yes—
100#66997—28no—
101#66992—216no—
102#66991—24no—
103#66991C2318yes—
104#66983—28no—
105#66982—216no—
106C2×(C2×D11)⋊C4—22no—
107C2×(C2×D11)⋊C4—22no—
108C2×(C2×D11)⋊C4—22no—
109#66979—22no—
110#66979C2314yes—
111C2×C4⋊Dic11—21no—
112C2×C4⋊Dic11—22no—
113C2×C4⋊Dic11C2314yes—
114C2×C4⋊Dic11C2312yes—
115C2×C4⋊Dic11C2311yescharacteristic
116C2×C4⋊Dic11C2311yescharacteristic
117#66977—28no—
118C2×Dic11⋊C4—22no—
119C2×Dic11⋊C4—22no—
120C2×Dic11⋊C4—22no—
121C2×C4×Dic11—21no—
122C22×C11⋊C8—24no—
123C22×C11⋊C8C2311yescharacteristic
124C22×C11⋊C8C2311yescharacteristic
125C22×C11⋊C8C2314yes—
126#66960—232no—
127C2×#4313—28no—
128C2×#4313C2318yes—
129C2×C8×D11—28no—
130C2×C8×D11C2318yes—
131#66899C2318yes—
132#66899C2318yes—
133#66899C2314yes—
134#66899C2314yes—
135#66896C2314yes—
136#66896C2314yes—
137#66882C2318yes—
138#66881C2318yes—
139C2×#3063—111nomaximal, Sylow
140C24×C11—21no—
141C24×C11C2×D411yescharacteristic
142C23×D11C2×D412yes—
143C11×#41—28no—
144C11×#41—28no—
145C11×#41—48no—
146C2×Q8×C11—24no—
147C2×Q8×C11—22no—
148C2×Q8×C11—21no—
149C2×Q8×C11—24no—
150C2×Q8×C11—22no—
151C2×Q8×C11—28no—
152C2×Q8×C11—24no—
153C2×Q8×C11—28no—
154C2×Q8×C11—22no—
155C2×Q8×C11—44no—
156C2×Q8×C11—48no—
157C2×Q8×C11C2414yes—
158C2×Q8×C11C2412yes—
159C2×D4×C11—24no—
160C2×D4×C11—22no—
161C2×D4×C11—21no—
162C2×D4×C11—22no—
163C2×D4×C11—44no—
164C2×D4×C11C2412yes—
165C22×C4×C11—21no—
166C22×C4×C11—22no—
167C22×C4×C11—24no—
168C22×C4×C11—24no—
169C22×C4×C11—44no—
170C22×C4×C11—44no—
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2×D412yes—
173C22×C4×C11C2×D414yes—
174C22×C4×C11#4114yes—
175C22×C4×C11C2411yescharacteristic
176C22×C4×C11C2412yes—
177C2×C22⋊D11—28no—
178C2×C22⋊D11—28no—
179C2×C22⋊D11—84no—
180C2×C22⋊D11C2×D418yes—
181C22×Dic11—21no—
182C22×Dic11—21no—
183C22×Dic11—22no—
184C22×Dic11—24no—
185C22×Dic11—82no—
186C22×Dic11C2×D412yes—
187#4339—216no—
188#4339—28no—
189#4339—28no—
190C2×D44—24no—
191C2×D44C2×D414yes—
192C2×C4×D11—24no—
193C2×C4×D11—24no—
194C2×C4×D11C2×D414yes—
195C2×C4×D11C2414yes—
196C2×Dic22—24no—
197C2×Dic22C2×D414yes—
198C11×Q16—216no—
199C11×SD16—216no—
200C11×M16C2×D4116yescomplemented
201C2×C8×C11C2×D418yes—
202C2×C8×C11C2414yes—
203C22⋊Dic11—28no—
204C22⋊Dic11—24no—
205(C2×D11)⋊C4—28no—
206(C2×D11)⋊C4—28no—
207(C2×D11)⋊C4—28no—
208C4⋊Dic11—24no—
209C4⋊Dic11—22no—
210C4⋊Dic11—21no—
211C4⋊Dic11—21no—
212C4⋊Dic11C2412yes—
213C4⋊Dic11C2414yes—
214C4⋊Dic11C2412yes—
215Dic11⋊C4—28no—
216Dic11⋊C4—28no—
217Dic11⋊C4—28no—
218C4×Dic11—24no—
219C2×C11⋊C8—22no—
220C2×C11⋊C8—22no—
221C2×C11⋊C8—28no—
222C2×C11⋊C8C2412yes—
223C2×C11⋊C8C2412yes—
224#4313—216no—
225C8×D11—216no—
226C22×#137D1111yescharacteristic, complemented
227C22×#131—111no—
228C2×#537—111no—
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—22no—
241C23×C11—42no—
242C23×C11—42no—
243C23×C11—42no—
244C23×C11#12114yes—
245C23×C11C22×D412yes—
246C23×C11C22×D411yescharacteristic
247C22×D11—24no—
248C22×D11—24no—
249C22×D11—24no—
250C22×D11C22×D414yes—
251Q8×C11—24no—
252Q8×C11—22no—
253Q8×C11—24no—
254Q8×C11—22no—
255Q8×C11—48no—
256Q8×C11—44no—
257Q8×C11—42no—
258D4×C11—22no—
259D4×C11—22no—
260D4×C11—48no—
261D4×C11—42no—
262C2×C4×C11—22no—
263C2×C4×C11—24no—
264C2×C4×C11—42no—
265C2×C4×C11—48no—
266C2×C4×C11—44no—
267C2×C4×C11—48no—
268C2×C4×C11#12114yes—
269C2×C4×C11#12118yes—
270C2×C4×C11C22×D412yes—
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C22×D412yes—
273C2×C4×C11C22×D414yes—
274C2×C4×C11C2×#4112yes—
275C2×C4×C11C2×#4114yes—
276C2×C4×C11C2511yescharacteristic
277C22⋊D11—216no—
278C22⋊D11—88no—
279C2×Dic11—24no—
280C2×Dic11—22no—
281C2×Dic11—22no—
282C2×Dic11—24no—
283C2×Dic11—42no—
284C2×Dic11—44no—
285C2×Dic11—42no—
286C2×Dic11—84no—
287C2×Dic11C22×D414yes—
288D44—28no—
289C4×D11—28no—
290C4×D11—24no—
291C4×D11—24no—
292Dic22—28no—
293C8×C11C22×D418yes—
294C11⋊C8—22no—
295C11⋊C8—22no—
296C22×#41—111no—
297C22×#41C2×D1111yescharacteristic
298C23×Q8C2×D1111yescharacteristic
299C2×#137—28no—
300C2×#137C2×D1118yescomplemented
301C22×Q16C2×D1112yes—
302C22×SD16C2×D1112yes—
303C2×#131—118no—
304C2×#131—228no—
305C22×M16—112no—
306C22×M16C2×D1111yescharacteristic
307C23×C8—111no—
308C23×C8—112no—
309#537—118no—
310#537—224no—
311#536—118no—
312#536—224no—
313C2×C4⋊Q8—221no—
314C2×#124—221no—
315C2×#123—222no—
316C2×C22⋊Q8—112no—
317C2×C22⋊Q8—112no—
318C2×C22⋊Q8—112no—
319C2×C22⋊Q8—221no—
320C2×#121—112no—
321C2×#121—221no—
322C2×#121—222no—
323C2×#117—111no—
324C22×C4⋊C4—111no—
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—112no—
334C2×#103—112no—
335C2×#103—118no—
336C2×#103—111no—
337C2×#103—111no—
338C2×#102—111no—
339C2×#102—111no—
340C22×C11—28no—
341C22×C11—22no—
342C22×C11—22no—
343C22×C11—42no—
344C22×C11—42no—
345C22×C11—42no—
346C22×C11—84no—
347C22×C11C2×#12114yes—
348C22×C11C2×#12112yes—
349C22×C11#57712yes—
350C22×C11#57812yes—
351C22×C11C23×D411yescharacteristic
352C2×D11—24no—
353C2×D11—24no—
354C2×D11—24no—
355C2×D11—48no—
356C4×C11—42no—
357C4×C11—44no—
358C4×C11C2×#12114yes—
359C4×C11C2×#12112yes—
360C4×C11C23×D411yescharacteristic
361C4×C11C22×#4111yescharacteristic
362Dic11—24no—
363Dic11—42no—
364Dic11—44no—
365Dic11—42no—
366C2×#41—22no—
367C2×#41—24no—
368C2×#41—24no—
369C2×#41—114no—
370C2×#41—114no—
371C2×#41—224no—
372C2×#41—224no—
373C2×#41C22×D1114yes—
374C22×Q8—21no—
375C22×Q8—22no—
376C22×Q8—24no—
377C22×Q8—24no—
378C22×Q8—111no—
379C22×Q8C22×D1112yes—
380C22×Q8C22×D1111yescharacteristic
381C22×Q8C22×D1114yes—
382C22×D4—21no—
383C22×D4—112no—
384C22×D4—111no—
385C22×D4—222no—
386C22×D4C22×D1111yescharacteristic
387C23×C4—21no—
388C23×C4—21no—
389C23×C4—112no—
390C23×C4—221no—
391C23×C4C22×D1111yescharacteristic
392#137—232no—
393C2×Q16—28no—
394C2×Q16C22×D1118yes—
395C2×SD16—28no—
396C2×SD16C22×D1118yes—
397#131—2232no—
398C2×M16—118no—
399C2×M16—228no—
400C2×M16C22⋊D1118yescomplemented
401C2×M16C22×D1114yes—
402C22×C8—111no—
403C22×C8—111no—
404C22×C8—114no—
405C22×C8—118no—
406C22×C8—224no—
407C22×C8—228no—
408C22×C8C22×D1112yes—
409C4⋊Q8—228no—
410#124—228no—
411#123—2216no—
412C22⋊Q8—118no—
413C22⋊Q8—118no—
414C22⋊Q8—118no—
415C22⋊Q8—228no—
416C22⋊Q8—224no—
417C22⋊Q8—224no—
418C22⋊Q8—224no—
419#121—118no—
420#121—228no—
421#121—224no—
422#121—2216no—
423#117—114no—
424#117—222no—
425C2×C4⋊C4—112no—
426C2×C4⋊C4—114no—
427C2×C4⋊C4—111no—
428C2×C4⋊C4—111no—
429C2×C4⋊C4—222no—
430C2×C4⋊C4—222no—
431C2×C4⋊C4—222no—
432C2×C4⋊C4—221no—
433C2×C4⋊C4—222no—
434C2×C22⋊C4—222no—
435C2×C22⋊C4—222no—
436C2×C22⋊C4—222no—
437C2×C22⋊C4—222no—
438C2×C22⋊C4—221no—
439C2×C42—221no—
440#107—118no—
441#106—118no—
442#103—118no—
443#103—118no—
444#103—114no—
445#103—114no—
446#102—114no—
447#102—114no—
448C2×C11—24no—
449C2×C11—82no—
450C2×C11#306314yescomplemented
451C2×C11C22×#12111yescharacteristic
452C2×C11C2×#57711yescharacteristic
453C2×C11C2×#57811yescharacteristic
454D11—44no—
455C24—21no—
456C24—112no—
457C24D4×D1111yescharacteristic
458#41—28no—
459#41—28no—
460#41—48no—
461#41—2216no—
462#41—228no—
463#41—228no—
464C2×Q8—22no—
465C2×Q8—21no—
466C2×Q8—24no—
467C2×Q8—24no—
468C2×Q8—28no—
469C2×Q8—22no—
470C2×Q8—24no—
471C2×Q8—22no—
472C2×Q8—28no—
473C2×Q8—44no—
474C2×Q8—48no—
475C2×Q8—114no—
476C2×Q8—224no—
477C2×Q8C23×D1114yes—
478C2×Q8C23×D1112yes—
479C2×D4—24no—
480C2×D4—21no—
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—44no—
484C2×D4—118no—
485C2×D4—114no—
486C2×D4—228no—
487C2×D4—228no—
488C2×D4—224no—
489C2×D4—884no—
490C2×D4C23×D1112yes—
491C22×C4—24no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—24no—
495C22×C4—44no—
496C22×C4—44no—
497C22×C4—112no—
498C22×C4—114no—
499C22×C4—114no—
500C22×C4—224no—
501C22×C4—224no—
502C22×C4—221no—
503C22×C4—221no—
504C22×C4—222no—
505C22×C4—224no—
506C22×C4—882no—
507C22×C4D4×D1112yes—
508C22×C4D4×D1111yescharacteristic
509C22×C4#434114yes—
510C22×C4C2×C22⋊D1114yes—
511C22×C4C23×D1112yes—
512C22×C4C23×D1111yescharacteristic
513Q16—216no—
514SD16—216no—
515M16—2216no—
516M16C2×C22⋊D11116yescomplemented
517C2×C8—112no—
518C2×C8—112no—
519C2×C8—222no—
520C2×C8—222no—
521C2×C8—228no—
522C2×C8—2216no—
523C2×C8C2×C22⋊D1118yes—
524C2×C8C23×D1114yes—
525C4⋊C4—112no—
526C4⋊C4—112no—
527C4⋊C4—114no—
528C4⋊C4—228no—
529C4⋊C4—228no—
530C4⋊C4—228no—
531C4⋊C4—224no—
532C4⋊C4—222no—
533C4⋊C4—221no—
534C4⋊C4—221no—
535C22⋊C4—228no—
536C22⋊C4—228no—
537C22⋊C4—228no—
538C22⋊C4—228no—
539C22⋊C4—224no—
540C42—224no—
541C11C2×#306311yescharacteristic, complemented, Sylow
542C23—22no—
543C23—22no—
544C23—22no—
545C23—42no—
546C23—42no—
547C23—42no—
548C23—114no—
549C23—224no—
550C23—224no—
551C23—224no—
552C23#6699114yes—
553C23C2×D4×D1112yes—
554C23C2×D4×D1111yescharacteristic
555Q8—24no—
556Q8—22no—
557Q8—24no—
558Q8—22no—
559Q8—48no—
560Q8—44no—
561Q8—42no—
562Q8—228no—
563D4—22no—
564D4—22no—
565D4—48no—
566D4—42no—
567D4—2216no—
568D4—228no—
569D4—888no—
570C2×C4—22no—
571C2×C4—24no—
572C2×C4—42no—
573C2×C4—48no—
574C2×C4—44no—
575C2×C4—48no—
576C2×C4—114no—
577C2×C4—224no—
578C2×C4—228no—
579C2×C4—224no—
580C2×C4—224no—
581C2×C4—222no—
582C2×C4—222no—
583C2×C4—224no—
584C2×C4—444no—
585C2×C4—442no—
586C2×C4—442no—
587C2×C4—884no—
588C2×C4#6699114yes—
589C2×C4#6699118yes—
590C2×C4C2×D4×D1112yes—
591C2×C4C2×D4×D1111yescharacteristic
592C2×C4C2×#434112yes—
593C2×C4C2×#434114yes—
594C2×C4C22×C22⋊D1112yes—
595C2×C4C22×C22⋊D1114yes—
596C2×C4C24×D1111yescharacteristic
597C8—222no—
598C8—222no—
599C8C22×C22⋊D1118yes—
600C22—28no—
601C22—22no—
602C22—22no—
603C22—42no—
604C22—42no—
605C22—42no—
606C22—84no—
607C22—224no—
608C22—224no—
609C22—224no—
610C22—448no—
611C22#1062330912yes—
612C22#1062331012yes—
613C22C2×#6699114yes—
614C22C2×#6699112yes—
615C22C22×D4×D1111yescharacteristic
616C4—42no—
617C4—44no—
618C4—224no—
619C4—444no—
620C4—442no—
621C4—442no—
622C4C2×#6699114yes—
623C4C2×#6699112yes—
624C4C22×#434111yescharacteristic
625C4C23×C22⋊D1111yescharacteristic
626C2—24no—
627C2—82no—
628C2—444no—
629C2#1307830114yesdirect product factor
630C2C22×#6699111yescharacteristic
631C2C2×#1062330911yescharacteristic
632C2C2×#1062331011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC22×C11×#137C2
socleC23×C11C22×D4
prime radicalC2×#10623364C2
hypercenterC22×#137D11
hypocenterC11C2×#3063
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#137

Complements

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

NH ≅ G/Ntype
1. C22×#66960C2semidirect
3. C2×#10623347C2semidirect
4. #13078301C2direct (N × H)
5. C2×#10622802C2semidirect
6. C2×#10622787C2semidirect
7. C2×#10622801C2semidirect
8. C2×#10622784C2semidirect
9. C2×#10622734C2semidirect
10. C2×#10622846C2semidirect
11. C22×#66899C2semidirect
12. C22×C11×#137C2semidirect
17. C2×C11×#137C22semidirect
24. #10623347C22semidirect
39. C2×#66960C22semidirect
42. #10622846C22semidirect
47. C2×#66899C22semidirect
50. #10622802C22semidirect
51. #10622801C22semidirect
52. #10622787C22semidirect
53. #10622784C22semidirect
54. #10622734C22semidirect
88. C2×C11×M16D4semidirect
200. C11×M16C2×D4semidirect
226. C22×#137D11semidirect
300. C2×#137C2×D11semidirect
400. C2×M16C22⋊D11semidirect
450. C2×C11#3063semidirect
516. M16C2×C22⋊D11semidirect
541. C11C2×#3063semidirect
629. C2#13078301direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669602
C2×#106233642
C2×#106233472
#130783012
C2×#106228022
C2×#106227872
C2×#106228012
C2×#106227842
C2×#106227342
C2×#106228462
C22×#668992
C22×C11×#1372
C2×#306311