Finite Group Databasebeta

← C2×#13078307 #15621020

Subgroups — C2×#13078307 #15621020

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×#66962C211yesmaximal, characteristic, complemented
2C2×#10623364C211yesmaximal, characteristic
3C2×#10623356C211yesmaximal, characteristic, complemented
4#13078307C2116yesmaximal, direct product factor
5C2×#10622750C212yesmaximal, complemented
6C2×#10622747C212yesmaximal, complemented
7C2×#10622729C212yesmaximal, complemented
8C2×#10622727C212yesmaximal, complemented
9C2×#10622734C211yesmaximal, characteristic, complemented
10C2×#10622726C211yesmaximal, characteristic, complemented
11C22×#66880C211yesmaximal, characteristic, complemented
12C22×C11×#131C211yesmaximal, characteristic, complemented
13C22×C11×#41C2211yescharacteristic
14C22×#4339C2211yescharacteristic
15C23×Dic22C2211yescharacteristic
16C2×C11×#131—28no—
17C2×C11×#131C2218yescomplemented
18C22×C11×M16C2212yes—
19C22×C11×M16C2211yescharacteristic
20C23×C8×C11C2211yescharacteristic
21C23×C8×C11C2212yes—
22#10623364—24no—
23#10623364C2218yes—
24#10623356—24no—
25#10623356C2218yescomplemented
26C2×#66999—21no—
27C2×#66997—21no—
28C2×#66992—22no—
29C2×#66991—21no—
30C2×#66989—21no—
31C2×#66988—22no—
32C2×#66983C2212yes—
33C2×#66979C2211yescharacteristic
34C22×C4⋊Dic11C2211yescharacteristic
35C2×#66977C2212yes—
36C2×#66977C2212yes—
37C2×#66977C2212yes—
38C2×#66962—28no—
39C2×#66962C2218yescomplemented
40C22×Dic44C2212yes—
41C22×#4314C2212yes—
42#10622750C22116yescomplemented
43#10622747C22116yescomplemented
44#10622734C2218yescomplemented
45#10622729C22116yescomplemented
46#10622727C22116yescomplemented
47#10622726C2218yescomplemented
48C2×#66885C2211yescharacteristic
49C2×#66885C2211yescharacteristic
50C2×#66882C2212yes—
51C2×#66881C2212yes—
52C2×#66880C2212yes—
53C2×#66880C2212yes—
54C2×#66880C2211yescharacteristic
55C2×#66880C2211yescharacteristic
56C2×#66880C2218yescomplemented
57C2×C11×#41—24no—
58C2×C11×#41—24no—
59C2×C11×#41D414yes—
60C2×C11×#41C2314yes—
61C22×Q8×C11D411yescharacteristic
62C22×D4×C11D412yes—
63C22×D4×C11D411yescharacteristic
64C23×C4×C11C2312yes—
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11—21no—
67C22×C22⋊D11—22no—
68C23×Dic11—21no—
69C23×Dic11—21no—
70C2×#4339—22no—
71C2×#4339—24no—
72C2×#4339—24no—
73C2×#4339C2314yes—
74C22×D44C2311yescharacteristic
75C22×C4×D11—21no—
76C22×Dic22—24no—
77C22×Dic22—24no—
78C22×Dic22—21no—
79C22×Dic22—22no—
80C22×Dic22C2312yes—
81C22×Dic22C2311yescharacteristic
82C22×Dic22C2314yes—
83C11×#131—232no—
84C2×C11×M16—28no—
85C2×C11×M16D418yescomplemented
86C2×C11×M16C2318yes—
87C2×C11×M16C2314yes—
88C22×C8×C11—24no—
89C22×C8×C11—28no—
90C22×C8×C11C2311yescharacteristic
91C22×C8×C11C2311yescharacteristic
92C22×C8×C11C2314yes—
93C22×C8×C11C2318yes—
94C22×C8×C11C2312yes—
95C2×C22⋊Dic11—22no—
96C2×C22⋊Dic11—22no—
97C2×C22⋊Dic11—22no—
98C2×C22⋊Dic11—21no—
99#66999—28no—
100#66997—28no—
101#66992—216no—
102#66991—28no—
103#66989—28no—
104#66988—216no—
105#66983—24no—
106#66983C2318yes—
107C2×(C2×D11)⋊C4—22no—
108#66979—22no—
109#66979C2314yes—
110C2×C4⋊Dic11—21no—
111C2×C4⋊Dic11—22no—
112C2×C4⋊Dic11C2311yescharacteristic
113C2×C4⋊Dic11C2311yescharacteristic
114C2×C4⋊Dic11C2314yes—
115C2×C4⋊Dic11C2312yes—
116#66977—24no—
117#66977—24no—
118#66977—24no—
119#66977C2318yes—
120#66977C2318yes—
121#66977C2318yes—
122C2×Dic11⋊C4—22no—
123C2×Dic11⋊C4—22no—
124C2×Dic11⋊C4—22no—
125C2×C4×Dic11—21no—
126#66962—232no—
127C2×Dic44—28no—
128C2×Dic44C2318yes—
129C2×#4314—28no—
130C2×#4314C2318yes—
131#66885C2314yes—
132#66885C2314yes—
133#66882C2318yes—
134#66881C2318yes—
135#66880C2314yes—
136#66880C2314yes—
137#66880C2318yes—
138#66880C2318yes—
139C2×#3063—111nomaximal, Sylow
140C24×C11C2×D412yes—
141C24×C11C2×D411yescharacteristic
142C23×D11—21no—
143C11×#41—216no—
144C11×#41—28no—
145C11×#41—28no—
146C2×Q8×C11—24no—
147C2×Q8×C11C2×D414yes—
148C2×D4×C11—28no—
149C2×D4×C11—24no—
150C2×D4×C11C2×D418yes—
151C2×D4×C11C2×D414yes—
152C22×C4×C11—24no—
153C22×C4×C11—24no—
154C22×C4×C11C2×D412yes—
155C22×C4×C11C2×D414yes—
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D412yes—
158C22×C4×C11C2×D414yes—
159C22×C4×C11#4114yes—
160C22×C4×C11C2414yes—
161C22×C4×C11C2411yescharacteristic
162C22×C4×C11C2412yes—
163C2×C22⋊D11—24no—
164C2×C22⋊D11—28no—
165C2×C22⋊D11—44no—
166C2×C22⋊D11—84no—
167C22×Dic11—21no—
168C22×Dic11—21no—
169C22×Dic11—22no—
170C22×Dic11—21no—
171C22×Dic11—22no—
172C22×Dic11—24no—
173C22×Dic11—24no—
174C22×Dic11—44no—
175C22×Dic11—82no—
176#4339—28no—
177#4339—28no—
178#4339—48no—
179C2×D44—21no—
180C2×D44—22no—
181C2×D44—22no—
182C2×D44C2412yes—
183C2×C4×D11—24no—
184C2×C4×D11—44no—
185C2×Dic22—24no—
186C2×Dic22—22no—
187C2×Dic22—28no—
188C2×Dic22—22no—
189C2×Dic22—21no—
190C2×Dic22—24no—
191C2×Dic22—24no—
192C2×Dic22—28no—
193C2×Dic22—22no—
194C2×Dic22—44no—
195C2×Dic22—48no—
196C2×Dic22C2414yes—
197C2×Dic22C2412yes—
198C11×M16—216no—
199C11×M16C2×D4116yescomplemented
200C2×C8×C11—216no—
201C2×C8×C11—22no—
202C2×C8×C11—22no—
203C2×C8×C11—28no—
204C2×C8×C11C2×D418yes—
205C2×C8×C11C2412yes—
206C2×C8×C11C2412yes—
207C2×C8×C11C2414yes—
208C22⋊Dic11—28no—
209C22⋊Dic11—28no—
210C22⋊Dic11—28no—
211C22⋊Dic11—24no—
212(C2×D11)⋊C4—28no—
213C4⋊Dic11—21no—
214C4⋊Dic11—21no—
215C4⋊Dic11—22no—
216C4⋊Dic11—24no—
217C4⋊Dic11C2414yes—
218C4⋊Dic11C2412yes—
219C4⋊Dic11C2412yes—
220Dic11⋊C4—28no—
221Dic11⋊C4—28no—
222Dic11⋊C4—28no—
223C4×Dic11—24no—
224Dic44—216no—
225#4314—216no—
226C22×#137—111no—
227C22×#131D1111yescharacteristic, complemented
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—24no—
241C23×C11—24no—
242C23×C11—24no—
243C23×C11#12114yes—
244C23×C11C22×D414yes—
245C23×C11C22×D412yes—
246C23×C11C22×D411yescharacteristic
247C22×D11—22no—
248C22×D11—42no—
249C22×D11—42no—
250C22×D11—42no—
251Q8×C11—28no—
252D4×C11—216no—
253D4×C11—28no—
254C2×C4×C11—24no—
255C2×C4×C11—28no—
256C2×C4×C11—24no—
257C2×C4×C11—24no—
258C2×C4×C11#12114yes—
259C2×C4×C11#12118yes—
260C2×C4×C11C22×D414yes—
261C2×C4×C11C22×D412yes—
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C22×D412yes—
264C2×C4×C11C22×D414yes—
265C2×C4×C11C2×#4112yes—
266C2×C4×C11C2×#4114yes—
267C2×C4×C11C2511yescharacteristic
268C22⋊D11—48no—
269C22⋊D11—88no—
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11—24no—
273C2×Dic11—22no—
274C2×Dic11—24no—
275C2×Dic11—48no—
276C2×Dic11—44no—
277C2×Dic11—42no—
278C2×Dic11—42no—
279C2×Dic11—44no—
280C2×Dic11—42no—
281C2×Dic11—84no—
282D44—22no—
283D44—22no—
284D44—42no—
285C4×D11—48no—
286Dic22—24no—
287Dic22—22no—
288Dic22—24no—
289Dic22—22no—
290Dic22—44no—
291Dic22—48no—
292Dic22—42no—
293C8×C11—22no—
294C8×C11—22no—
295C8×C11C22×D418yes—
296C22×#41—111no—
297C22×#41C2×D1111yescharacteristic
298C23×Q8—111no—
299C2×#137—118no—
300C2×#137—228no—
301C22×Q16—112no—
302C22×SD16—112no—
303C2×#131—28no—
304C2×#131C2×D1118yescomplemented
305C22×M16C2×D1112yes—
306C22×M16C2×D1111yescharacteristic
307C23×C8C2×D1111yescharacteristic
308C23×C8C2×D1112yes—
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—24no—
344C22×C11—24no—
345C22×C11—24no—
346C22×C11—48no—
347C22×C11C2×#12114yes—
348C22×C11C2×#12112yes—
349C22×C11#57712yes—
350C22×C11#57812yes—
351C22×C11C23×D411yescharacteristic
352C2×D11—42no—
353C2×D11—42no—
354C2×D11—42no—
355C2×D11—84no—
356C4×C11—24no—
357C4×C11C2×#12112yes—
358C4×C11C2×#12114yes—
359C4×C11C23×D411yescharacteristic
360C4×C11C22×#4111yescharacteristic
361Dic11—44no—
362Dic11—42no—
363Dic11—42no—
364Dic11—44no—
365Dic11—42no—
366C2×#41—24no—
367C2×#41—24no—
368C2×#41—114no—
369C2×#41—222no—
370C2×#41—224no—
371C2×#41—224no—
372C2×#41D4414yes—
373C2×#41C22×D1114yes—
374C22×Q8—112no—
375C22×Q8—111no—
376C22×Q8—114no—
377C22×Q8—221no—
378C22×Q8—222no—
379C22×Q8—224no—
380C22×Q8—224no—
381C22×Q8D4411yescharacteristic
382C22×D4—111no—
383C22×D4—221no—
384C22×D4—222no—
385C22×D4D4412yes—
386C22×D4D4411yescharacteristic
387C23×C4—221no—
388C23×C4—221no—
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—232no—
398C2×M16—28no—
399C2×M16C22⋊D1118yescomplemented
400C2×M16C22×D1118yes—
401C2×M16C22×D1114yes—
402C22×C8—24no—
403C22×C8—28no—
404C22×C8C22×D1111yescharacteristic
405C22×C8C22×D1111yescharacteristic
406C22×C8C22×D1114yes—
407C22×C8C22×D1118yes—
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—2216no—
422#121—224no—
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—221no—
430C2×C4⋊C4—222no—
431C2×C4⋊C4—222no—
432C2×C4⋊C4—222no—
433C2×C4⋊C4—222no—
434C2×C22⋊C4—221no—
435C2×C22⋊C4—222no—
436C2×C22⋊C4—222no—
437C2×C22⋊C4—222no—
438C2×C22⋊C4—222no—
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—44no—
450C2×C11#306314yescomplemented
451C2×C11C22×#12111yescharacteristic
452C2×C11C2×#57711yescharacteristic
453C2×C11C2×#57811yescharacteristic
454D11—82no—
455C24—221no—
456C24C2×D4412yes—
457C24C2×D4411yescharacteristic
458#41—216no—
459#41—28no—
460#41—28no—
461#41—228no—
462#41—228no—
463#41—448no—
464C2×Q8—24no—
465C2×Q8—114no—
466C2×Q8—112no—
467C2×Q8—222no—
468C2×Q8—221no—
469C2×Q8—224no—
470C2×Q8—224no—
471C2×Q8—228no—
472C2×Q8—222no—
473C2×Q8—224no—
474C2×Q8—222no—
475C2×Q8—228no—
476C2×Q8—444no—
477C2×Q8—448no—
478C2×Q8C2×D4414yes—
479C2×D4—28no—
480C2×D4—24no—
481C2×D4—112no—
482C2×D4—224no—
483C2×D4—228no—
484C2×D4—221no—
485C2×D4—222no—
486C2×D4—222no—
487C2×D4—444no—
488C2×D4—884no—
489C2×D4C2×D4418yes—
490C2×D4C2×D4414yes—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—224no—
494C22×C4—221no—
495C22×C4—221no—
496C22×C4—222no—
497C22×C4—221no—
498C22×C4—222no—
499C22×C4—224no—
500C22×C4—224no—
501C22×C4—444no—
502C22×C4—444no—
503C22×C4—882no—
504C22×C4C2×D4414yes—
505C22×C4C2×D4412yes—
506C22×C4C2×D4412yes—
507C22×C4C2×D4411yescharacteristic
508C22×C4#433914yes—
509C22×C4C2×C22⋊D1114yes—
510C22×C4C23×D1114yes—
511C22×C4C23×D1112yes—
512C22×C4C23×D1111yescharacteristic
513Q16—2216no—
514SD16—2216no—
515M16—216no—
516M16C2×C22⋊D11116yescomplemented
517C2×C8—22no—
518C2×C8—22no—
519C2×C8—28no—
520C2×C8—216no—
521C2×C8C2×C22⋊D1118yes—
522C2×C8C23×D1112yes—
523C2×C8C23×D1112yes—
524C2×C8C23×D1114yes—
525C4⋊C4—112no—
526C4⋊C4—112no—
527C4⋊C4—114no—
528C4⋊C4—224no—
529C4⋊C4—222no—
530C4⋊C4—221no—
531C4⋊C4—221no—
532C4⋊C4—228no—
533C4⋊C4—228no—
534C4⋊C4—228no—
535C22⋊C4—224no—
536C22⋊C4—228no—
537C22⋊C4—228no—
538C22⋊C4—228no—
539C22⋊C4—228no—
540C42—224no—
541C11C2×#306311yescharacteristic, complemented, Sylow
542C23—22no—
543C23—22no—
544C23—24no—
545C23—24no—
546C23—24no—
547C23—222no—
548C23—442no—
549C23—442no—
550C23—442no—
551C23#6698314yes—
552C23C22×D4414yes—
553C23C22×D4412yes—
554C23C22×D4411yescharacteristic
555Q8—28no—
556Q8—224no—
557Q8—222no—
558Q8—224no—
559Q8—222no—
560Q8—444no—
561Q8—448no—
562Q8—442no—
563D4—216no—
564D4—28no—
565D4—222no—
566D4—222no—
567D4—448no—
568D4—442no—
569D4—888no—
570C2×C4—24no—
571C2×C4—28no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—222no—
575C2×C4—222no—
576C2×C4—224no—
577C2×C4—222no—
578C2×C4—224no—
579C2×C4—444no—
580C2×C4—442no—
581C2×C4—442no—
582C2×C4—442no—
583C2×C4—448no—
584C2×C4—444no—
585C2×C4—448no—
586C2×C4—884no—
587C2×C4#6698314yes—
588C2×C4#6698318yes—
589C2×C4C22×D4414yes—
590C2×C4C22×D4412yes—
591C2×C4C22×D4411yescharacteristic
592C2×C4C2×#433912yes—
593C2×C4C2×#433914yes—
594C2×C4C22×C22⋊D1112yes—
595C2×C4C22×C22⋊D1114yes—
596C2×C4C24×D1111yescharacteristic
597C8—22no—
598C8—22no—
599C8C22×C22⋊D1118yes—
600C22—28no—
601C22—22no—
602C22—22no—
603C22—24no—
604C22—24no—
605C22—24no—
606C22—48no—
607C22—442no—
608C22—442no—
609C22—442no—
610C22—884no—
611C22#1062328212yes—
612C22#1062328412yes—
613C22C2×#6698314yes—
614C22C2×#6698312yes—
615C22C23×D4411yescharacteristic
616C4—24no—
617C4—442no—
618C4—444no—
619C4—444no—
620C4—442no—
621C4—442no—
622C4C2×#6698312yes—
623C4C2×#6698314yes—
624C4C22×#433911yescharacteristic
625C4C23×C22⋊D1111yescharacteristic
626C2—24no—
627C2—44no—
628C2—882no—
629C2#1307830714yesdirect product factor
630C2C22×#6698311yescharacteristic
631C2C2×#1062328211yescharacteristic
632C2C2×#1062328411yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC22×C11×#131C2
socleC23×C11C22×D4
prime radicalC2×#10623364C2
hypercenterC22×#131D11
hypocenterC11C2×#3063
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#41 ◁ C22×#131

Complements

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

NH ≅ G/Ntype
1. C22×#66962C2semidirect
3. C2×#10623356C2semidirect
4. #13078307C2direct (N × H)
5. C2×#10622750C2semidirect
6. C2×#10622747C2semidirect
7. C2×#10622729C2semidirect
8. C2×#10622727C2semidirect
9. C2×#10622734C2semidirect
10. C2×#10622726C2semidirect
11. C22×#66880C2semidirect
12. C22×C11×#131C2semidirect
17. C2×C11×#131C22semidirect
25. #10623356C22semidirect
39. C2×#66962C22semidirect
42. #10622750C22semidirect
43. #10622747C22semidirect
44. #10622734C22semidirect
45. #10622729C22semidirect
46. #10622727C22semidirect
47. #10622726C22semidirect
56. C2×#66880C22semidirect
85. C2×C11×M16D4semidirect
199. C11×M16C2×D4semidirect
227. C22×#131D11semidirect
304. C2×#131C2×D11semidirect
399. C2×M16C22⋊D11semidirect
450. C2×C11#3063semidirect
516. M16C2×C22⋊D11semidirect
541. C11C2×#3063semidirect
629. C2#13078307direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669622
C2×#106233642
C2×#106233562
#130783072
C2×#106227502
C2×#106227472
C2×#106227292
C2×#106227272
C2×#106227342
C2×#106227262
C22×#668802
C22×C11×#1312
C2×#306311