Finite Group Databasebeta

← C2×#13078308 #15621021

Subgroups — C2×#13078308 #15621021

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
2C22×#66960C211yesmaximal, characteristic, complemented
3C2×#10623041C211yesmaximal, characteristic
4C2×#10623057C211yesmaximal, characteristic, complemented
5#13078308C2116yesmaximal, direct product factor
6C2×#10622481C212yesmaximal, complemented
7C2×#10622499C212yesmaximal, complemented
8C2×#10622500C212yesmaximal, complemented
9C2×#10622477C212yesmaximal, complemented
10C2×#10622615C211yesmaximal, characteristic, complemented
11C22×#66874C211yesmaximal, characteristic, complemented
12C2×C11×#428C211yesmaximal, characteristic, complemented
13C22×#4339C2211yescharacteristic
14C22×#4339C2211yescharacteristic
15C23×Dic22C2211yescharacteristic
16C22×C11×M16C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C2×#66983—22no—
20C23×C11⋊C8C2211yescharacteristic
21C2×#66962—28no—
22C2×#66962C2218yescomplemented
23C2×#66960—28no—
24C2×#66960C2218yescomplemented
25C22×Dic44C2212yes—
26C22×#4314C2212yes—
27C22×#4313C2212yes—
28C22×C8×D11C2212yes—
29#10623057—24no—
30#10623057C2218yescomplemented
31#10623041—24no—
32#10623041C2218yes—
33C2×#66950—21no—
34C2×#66950C2212yes—
35C2×#66950C2212yes—
36C2×#66950C2212yes—
37C2×#66948—21no—
38C2×#66948C2212yes—
39C2×#66939—22no—
40C2×#66928—21no—
41C2×#66922—21no—
42C11×#428C2218yescomplemented
43C2×C11×#107C2212yes—
44C2×C11×#106C2212yes—
45#10622615C2218yescomplemented
46C2×#66874C2212yes—
47C2×#66874C2212yes—
48C2×#66874C2211yescharacteristic
49C2×#66874C2211yescharacteristic
50C2×#66874C2218yescomplemented
51C2×#66873C2211yescharacteristic
52C2×#66873C2211yescharacteristic
53#10622500C22116yescomplemented
54#10622499C22116yescomplemented
55#10622481C22116yescomplemented
56#10622477C22116yescomplemented
57C23×C4×C11—21no—
58C23×C4×C11C2311yescharacteristic
59C22×C22⋊D11—21no—
60C22×C22⋊D11D412yes—
61C23×Dic11—21no—
62C2×#4339—24no—
63C2×#4339—24no—
64C2×#4339—22no—
65C2×#4339—24no—
66C2×#4339—24no—
67C2×#4339D414yes—
68C2×#4339C2314yes—
69C2×#4339C2314yes—
70C22×D44—22no—
71C22×D44D411yescharacteristic
72C22×D44C2311yescharacteristic
73C22×C4×D11—21no—
74C22×C4×D11C2312yes—
75C22×Dic22—24no—
76C22×Dic22—24no—
77C22×Dic22—21no—
78C22×Dic22—22no—
79C22×Dic22D411yescharacteristic
80C22×Dic22C2312yes—
81C22×Dic22C2311yescharacteristic
82C22×Dic22C2314yes—
83C2×C11×M16D418yescomplemented
84C2×C11×M16C2314yes—
85C22×C8×C11C2312yes—
86C11×#117—22no—
87C11×#117C2314yes—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—22no—
90C2×C11×C4⋊C4C2312yes—
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C4⋊C4C2314yes—
94C2×C11×C22⋊C4—21no—
95C2×C42×C11—21no—
96#66983—216no—
97C2×(C2×D11)⋊C4—22no—
98C2×(C2×D11)⋊C4—22no—
99C2×(C2×D11)⋊C4—22no—
100C2×(C2×D11)⋊C4—22no—
101C2×C4⋊Dic11—22no—
102C2×C4⋊Dic11—22no—
103C2×C4⋊Dic11—22no—
104C22×C11⋊C8—24no—
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2314yes—
108#66962—232no—
109#66960—232no—
110C2×Dic44—28no—
111C2×Dic44C2318yes—
112C2×#4314—28no—
113C2×#4314C2318yes—
114C2×#4313—28no—
115C2×#4313C2318yes—
116C2×C8×D11—28no—
117C2×C8×D11C2318yes—
118#66950—24no—
119#66950—24no—
120#66950—24no—
121#66950—28no—
122#66950C2318yes—
123#66950C2318yes—
124#66950C2318yes—
125#66948—28no—
126#66948—24no—
127#66948C2318yes—
128#66939—216no—
129#66928—28no—
130#66922—28no—
131C11×#107C2318yes—
132C11×#106C2318yes—
133#66874C2318yes—
134#66874C2314yes—
135#66874C2318yes—
136#66874C2314yes—
137#66873C2314yes—
138#66873C2314yes—
139C2×#3063—111nomaximal, Sylow
140C24×C11C2×D411yescharacteristic
141C23×D11—21no—
142C23×D11C2×D412yes—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—22no—
146C22×C4×C11—24no—
147C22×C4×C11—82no—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D412yes—
150C22×C4×C11C2×D414yes—
151C22×C4×C11#4114yes—
152C22×C4×C11C2411yescharacteristic
153C22×C4×C11C2412yes—
154C2×C22⋊D11—28no—
155C2×C22⋊D11—24no—
156C2×C22⋊D11—44no—
157C2×C22⋊D11C2×D418yes—
158C22×Dic11—24no—
159C22×Dic11—22no—
160C22×Dic11—21no—
161C22×Dic11—44no—
162C22×Dic11C2×D412yes—
163#4339—216no—
164#4339—28no—
165#4339—28no—
166#4339—28no—
167#4339—28no—
168#4339—48no—
169C2×D44—28no—
170C2×D44—24no—
171C2×D44—21no—
172C2×D44—22no—
173C2×D44—22no—
174C2×D44—84no—
175C2×D44C2×D414yes—
176C2×D44C2412yes—
177C2×C4×D11—24no—
178C2×C4×D11—24no—
179C2×C4×D11—24no—
180C2×C4×D11—44no—
181C2×C4×D11C2×D414yes—
182C2×C4×D11C2414yes—
183C2×Dic22—24no—
184C2×Dic22—24no—
185C2×Dic22—22no—
186C2×Dic22—28no—
187C2×Dic22—24no—
188C2×Dic22—22no—
189C2×Dic22—21no—
190C2×Dic22—24no—
191C2×Dic22—28no—
192C2×Dic22—22no—
193C2×Dic22—44no—
194C2×Dic22—48no—
195C2×Dic22C2×D414yes—
196C2×Dic22C2414yes—
197C2×Dic22C2412yes—
198C11×M16C2×D4116yescomplemented
199C2×C8×C11C2×D418yes—
200C2×C8×C11C2414yes—
201C11×C4⋊C4—24no—
202C11×C4⋊C4—22no—
203C11×C4⋊C4—21no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4C2412yes—
206C11×C4⋊C4C2412yes—
207C11×C4⋊C4C2414yes—
208C11×C22⋊C4—24no—
209C42×C11—24no—
210(C2×D11)⋊C4—28no—
211(C2×D11)⋊C4—28no—
212(C2×D11)⋊C4—28no—
213(C2×D11)⋊C4—28no—
214C4⋊Dic11—28no—
215C4⋊Dic11—28no—
216C4⋊Dic11—28no—
217C2×C11⋊C8—22no—
218C2×C11⋊C8—22no—
219C2×C11⋊C8—28no—
220C2×C11⋊C8C2412yes—
221C2×C11⋊C8C2412yes—
222Dic44—216no—
223#4314—216no—
224#4313—216no—
225C8×D11—216no—
226C22×#137—111no—
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×#428D1111yescharacteristic, complemented
236C2×#416—111no—
237C22×#103—111no—
238C23×C11—22no—
239C23×C11—22no—
240C23×C11#12114yes—
241C23×C11C22×D412yes—
242C23×C11C22×D411yescharacteristic
243C22×D11—24no—
244C22×D11—24no—
245C22×D11—24no—
246C22×D11—22no—
247C22×D11—42no—
248C22×D11—42no—
249C22×D11—42no—
250C22×D11C22×D414yes—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—24no—
254C2×C4×C11—44no—
255C2×C4×C11—42no—
256C2×C4×C11—42no—
257C2×C4×C11—84no—
258C2×C4×C11#12114yes—
259C2×C4×C11#12118yes—
260C2×C4×C11C22×D412yes—
261C2×C4×C11C22×D414yes—
262C2×C4×C11C22×D412yes—
263C2×C4×C11C22×D411yescharacteristic
264C2×C4×C11C2×#4112yes—
265C2×C4×C11C2×#4114yes—
266C2×C4×C11C2511yescharacteristic
267C22⋊D11—216no—
268C22⋊D11—48no—
269C2×Dic11—24no—
270C2×Dic11—24no—
271C2×Dic11—22no—
272C2×Dic11—48no—
273C2×Dic11—44no—
274C2×Dic11—42no—
275C2×Dic11C22×D414yes—
276D44—28no—
277D44—22no—
278D44—22no—
279D44—42no—
280D44—88no—
281C4×D11—28no—
282C4×D11—24no—
283C4×D11—24no—
284C4×D11—48no—
285Dic22—28no—
286Dic22—24no—
287Dic22—22no—
288Dic22—24no—
289Dic22—22no—
290Dic22—48no—
291Dic22—44no—
292Dic22—42no—
293C8×C11C22×D418yes—
294C11⋊C8—22no—
295C11⋊C8—22no—
296C22×#41—111no—
297C22×#41—111no—
298C23×Q8—111no—
299C2×#137—118no—
300C2×#137—228no—
301C22×Q16—112no—
302C22×SD16—112no—
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×#117C2×D1111yescharacteristic
324C22×C4⋊C4C2×D1111yescharacteristic
325#470—1116no—
326#468—1116no—
327#467—1116no—
328#465—1116no—
329#428C2×D1118yescomplemented
330C2×#107C2×D1112yes—
331C2×#106C2×D1112yes—
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×C11C2×#12114yes—
344C22×C11C2×#12112yes—
345C22×C11#57712yes—
346C22×C11#57812yes—
347C22×C11C23×D411yescharacteristic
348C2×D11—24no—
349C2×D11—24no—
350C2×D11—24no—
351C2×D11—48no—
352C2×D11—42no—
353C2×D11—42no—
354C2×D11—42no—
355C2×D11—84no—
356C4×C11—42no—
357C4×C11—44no—
358C4×C11—42no—
359C4×C11C2×#12114yes—
360C4×C11C2×#12112yes—
361C4×C11C23×D411yescharacteristic
362C4×C11C22×#4111yescharacteristic
363Dic11—24no—
364Dic11—44no—
365Dic11—42no—
366C2×#41—114no—
367C2×#41—114no—
368C2×#41—114no—
369C2×#41—224no—
370C2×#41—222no—
371C2×#41—224no—
372C2×#41—224no—
373C2×#41—224no—
374C22×Q8—111no—
375C22×Q8—112no—
376C22×Q8—111no—
377C22×Q8—114no—
378C22×Q8—221no—
379C22×Q8—222no—
380C22×Q8—224no—
381C22×Q8—224no—
382C22×D4—112no—
383C22×D4—111no—
384C22×D4—111no—
385C22×D4—222no—
386C22×D4—221no—
387C23×C4—21no—
388C23×C4—112no—
389C23×C4—221no—
390C23×C4—221no—
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—228no—
400C2×M16D4418yescomplemented
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—224no—
416C22⋊Q8—224no—
417C22⋊Q8—224no—
418C22⋊Q8—228no—
419#121—118no—
420#121—224no—
421#121—228no—
422#121—2216no—
423#117—22no—
424#117C22×D1114yes—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—222no—
428C2×C4⋊C4—222no—
429C2×C4⋊C4—222no—
430C2×C4⋊C4C22×D1112yes—
431C2×C4⋊C4C22×D1114yes—
432C2×C4⋊C4C22×D1111yescharacteristic
433C2×C4⋊C4C22×D1111yescharacteristic
434C2×C22⋊C4—21no—
435C2×C22⋊C4—222no—
436C2×C22⋊C4—222no—
437C2×C22⋊C4—222no—
438C2×C22⋊C4—222no—
439C2×C42—21no—
440#107C22×D1118yes—
441#106C22×D1118yes—
442#103—118no—
443#103—118no—
444#103—114no—
445#103—114no—
446#102—114no—
447#102—114no—
448C2×C11—24no—
449C2×C11#306314yescomplemented
450C2×C11C22×#12111yescharacteristic
451C2×C11C2×#57711yescharacteristic
452C2×C11C2×#57811yescharacteristic
453D11—44no—
454D11—82no—
455C24—112no—
456C24—221no—
457C24D4×D1111yescharacteristic
458#41—2216no—
459#41—228no—
460#41—228no—
461#41—228no—
462#41—228no—
463#41—448no—
464C2×Q8—114no—
465C2×Q8—114no—
466C2×Q8—112no—
467C2×Q8—224no—
468C2×Q8—222no—
469C2×Q8—221no—
470C2×Q8—224no—
471C2×Q8—224no—
472C2×Q8—222no—
473C2×Q8—228no—
474C2×Q8—224no—
475C2×Q8—228no—
476C2×Q8—222no—
477C2×Q8—444no—
478C2×Q8—448no—
479C2×D4—118no—
480C2×D4—114no—
481C2×D4—112no—
482C2×D4—228no—
483C2×D4—228no—
484C2×D4—224no—
485C2×D4—224no—
486C2×D4—222no—
487C2×D4—221no—
488C2×D4—222no—
489C2×D4—444no—
490C2×D4—884no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—24no—
495C22×C4—82no—
496C22×C4—112no—
497C22×C4—114no—
498C22×C4—114no—
499C22×C4—224no—
500C22×C4—224no—
501C22×C4—224no—
502C22×C4—221no—
503C22×C4—222no—
504C22×C4—224no—
505C22×C4—444no—
506C22×C4—444no—
507C22×C4C2×D4414yes—
508C22×C4D4×D1112yes—
509C22×C4D4×D1111yescharacteristic
510C22×C4#434314yes—
511C22×C4C23×D1112yes—
512C22×C4C23×D1111yescharacteristic
513Q16—2216no—
514SD16—2216no—
515M16—2216no—
516M16C2×D44116yescomplemented
517C2×C8—112no—
518C2×C8—112no—
519C2×C8—222no—
520C2×C8—222no—
521C2×C8—228no—
522C2×C8—2216no—
523C2×C8C2×D4418yes—
524C2×C8C23×D1114yes—
525C4⋊C4—24no—
526C4⋊C4—22no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—228no—
530C4⋊C4—228no—
531C4⋊C4—228no—
532C4⋊C4C23×D1112yes—
533C4⋊C4C23×D1112yes—
534C4⋊C4C23×D1114yes—
535C22⋊C4—24no—
536C22⋊C4—228no—
537C22⋊C4—228no—
538C22⋊C4—228no—
539C22⋊C4—228no—
540C42—24no—
541C11C2×#306311yescharacteristic, complemented, Sylow
542C23—22no—
543C23—22no—
544C23—114no—
545C23—224no—
546C23—224no—
547C23—224no—
548C23—222no—
549C23—442no—
550C23—442no—
551C23—442no—
552C23#6694814yes—
553C23C2×D4×D1112yes—
554C23C2×D4×D1111yescharacteristic
555Q8—228no—
556Q8—224no—
557Q8—222no—
558Q8—224no—
559Q8—222no—
560Q8—444no—
561Q8—448no—
562Q8—442no—
563D4—2216no—
564D4—228no—
565D4—222no—
566D4—222no—
567D4—448no—
568D4—442no—
569D4—888no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—24no—
573C2×C4—42no—
574C2×C4—44no—
575C2×C4—42no—
576C2×C4—84no—
577C2×C4—114no—
578C2×C4—224no—
579C2×C4—228no—
580C2×C4—224no—
581C2×C4—224no—
582C2×C4—222no—
583C2×C4—224no—
584C2×C4—442no—
585C2×C4—448no—
586C2×C4—444no—
587C2×C4—448no—
588C2×C4#6694814yes—
589C2×C4#6694818yes—
590C2×C4C22×D4412yes—
591C2×C4C22×D4414yes—
592C2×C4C2×D4×D1112yes—
593C2×C4C2×D4×D1111yescharacteristic
594C2×C4C2×#434312yes—
595C2×C4C2×#434314yes—
596C2×C4C24×D1111yescharacteristic
597C8—222no—
598C8—222no—
599C8C22×D4418yes—
600C22—28no—
601C22—22no—
602C22—22no—
603C22—224no—
604C22—224no—
605C22—224no—
606C22—448no—
607C22—442no—
608C22—442no—
609C22—442no—
610C22—884no—
611C22C2×#6694814yes—
612C22C2×#6694812yes—
613C22#1062330612yes—
614C22#1062331012yes—
615C22C22×D4×D1111yescharacteristic
616C4—44no—
617C4—42no—
618C4—42no—
619C4—224no—
620C4—442no—
621C4—444no—
622C4C2×#6694812yes—
623C4C2×#6694814yes—
624C4C23×D4411yescharacteristic
625C4C22×#434311yescharacteristic
626C2—24no—
627C2—444no—
628C2—882no—
629C2#1307830814yesdirect product factor
630C2C22×#6694811yescharacteristic
631C2C2×#1062330611yescharacteristic
632C2C2×#1062331011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#428C2
socleC23×C11C22×D4
prime radicalC2×#10623041C2
hypercenterC2×#428D11
hypocenterC11C2×#3063
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
1. C22×#66962C2semidirect
2. C22×#66960C2semidirect
4. C2×#10623057C2semidirect
5. #13078308C2direct (N × H)
6. C2×#10622481C2semidirect
7. C2×#10622499C2semidirect
8. C2×#10622500C2semidirect
9. C2×#10622477C2semidirect
10. C2×#10622615C2semidirect
11. C22×#66874C2semidirect
12. C2×C11×#428C2semidirect
22. C2×#66962C22semidirect
24. C2×#66960C22semidirect
30. #10623057C22semidirect
42. C11×#428C22semidirect
45. #10622615C22semidirect
50. C2×#66874C22semidirect
53. #10622500C22semidirect
54. #10622499C22semidirect
55. #10622481C22semidirect
56. #10622477C22semidirect
83. C2×C11×M16D4semidirect
198. C11×M16C2×D4semidirect
235. C2×#428D11semidirect
329. #428C2×D11semidirect
400. C2×M16D44semidirect
449. C2×C11#3063semidirect
516. M16C2×D44semidirect
541. C11C2×#3063semidirect
629. C2#13078308direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669622
C22×#669602
C2×#106230412
C2×#106230572
#130783082
C2×#106224812
C2×#106224992
C2×#106225002
C2×#106224772
C2×#106226152
C22×#668742
C2×C11×#4282
C2×#306311