Finite Group Databasebeta

← C2×#13078310 #15621023

Subgroups — C2×#13078310 #15621023

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×#66954C211yesmaximal, characteristic, complemented
3C2×#10623364C211yesmaximal, characteristic
4C2×#10623057C211yesmaximal, characteristic, complemented
5#13078310C2116yesmaximal, direct product factor
6C2×#10622429C212yesmaximal, complemented
7C2×#10622393C212yesmaximal, complemented
8C2×#10622426C212yesmaximal, complemented
9C2×#10622391C212yesmaximal, complemented
10C2×#10622608C211yesmaximal, characteristic, complemented
11C22×#66880C211yesmaximal, characteristic, complemented
12C2×C11×#416C211yesmaximal, characteristic, complemented
13C22×C11×#41C2211yescharacteristic
14C22×#4339C2211yescharacteristic
15C23×Dic22C2211yescharacteristic
16C23×C8×C11C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18#10623364—24no—
19#10623364C2218yes—
20C2×#67004—28no—
21C2×#67004C2218yescomplemented
22C2×#66999C2212yes—
23C22×#4326C2212yes—
24C2×#66992—22no—
25C2×#66991C2212yes—
26C22×#4324C2212yes—
27C2×#66983—21no—
28C22×C4⋊Dic11C2211yescharacteristic
29C2×#66977—21no—
30C22×#4318C2211yescharacteristic
31C2×#66954—28no—
32C2×#66954C2218yescomplemented
33C22×#4313C2212yes—
34C22×C8×D11C2212yes—
35#10623057—24no—
36#10623057C2218yescomplemented
37C2×#66950C2212yes—
38C2×#66950C2212yes—
39C2×#66939—22no—
40C2×#66928—21no—
41C2×#66922—21no—
42C11×#416C2218yescomplemented
43C2×C11×#103C2211yescharacteristic
44C2×C11×#103C2211yescharacteristic
45C2×C11×#102C2211yescharacteristic
46C2×C11×#102C2211yescharacteristic
47C2×#66880C2212yes—
48C2×#66880C2212yes—
49C2×#66880C2218yescomplemented
50#10622608C2218yescomplemented
51C2×#66872C2212yes—
52C2×#66871C2212yes—
53#10622429C22116yescomplemented
54#10622426C22116yescomplemented
55#10622393C22116yescomplemented
56#10622391C22116yescomplemented
57C2×C11×#41—22no—
58C2×C11×#41—24no—
59C2×C11×#41—24no—
60C2×C11×#41C2314yes—
61C22×Q8×C11C2311yescharacteristic
62C22×D4×C11—21no—
63C22×D4×C11C2311yescharacteristic
64C23×C4×C11—21no—
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11—22no—
67C22×C22⋊D11D412yes—
68C23×Dic11—21no—
69C23×Dic11—21no—
70C2×#4339—24no—
71C2×#4339—24no—
72C2×#4339D414yes—
73C2×#4339C2314yes—
74C22×D44D411yescharacteristic
75C22×C4×D11C2312yes—
76C22×Dic22—24no—
77C22×Dic22—24no—
78C22×Dic22—21no—
79C22×Dic22—22no—
80C22×Dic22D411yescharacteristic
81C22×Dic22C2312yes—
82C22×Dic22C2314yes—
83C22×C8×C11—24no—
84C22×C8×C11C2311yescharacteristic
85C22×C8×C11C2311yescharacteristic
86C22×C8×C11C2314yes—
87C11×#117—22no—
88C11×#117C2314yes—
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C22⋊C4—21no—
92C2×C42×C11—21no—
93C2×C22⋊Dic11—22no—
94#67004—232no—
95#66999—24no—
96#66999C2318yes—
97C2×#4326—28no—
98C2×#4326C2318yes—
99#66992—216no—
100#66991—24no—
101#66991C2318yes—
102C2×#4324—28no—
103C2×#4324C2318yes—
104#66983—28no—
105C2×(C2×D11)⋊C4—22no—
106C2×(C2×D11)⋊C4—22no—
107C2×(C2×D11)⋊C4—22no—
108C2×C4⋊Dic11—21no—
109C2×C4⋊Dic11—22no—
110C2×C4⋊Dic11—22no—
111C2×C4⋊Dic11—22no—
112C2×C4⋊Dic11C2312yes—
113C2×C4⋊Dic11C2314yes—
114#66977—28no—
115C2×Dic11⋊C4—22no—
116C2×#4318D418yescomplemented
117C2×#4318C2314yes—
118C22×C11⋊C8C2312yes—
119#66954—232no—
120C2×#4313—28no—
121C2×#4313C2318yes—
122C2×C8×D11—28no—
123C2×C8×D11C2318yes—
124#66950—24no—
125#66950—24no—
126#66950C2318yes—
127#66950C2318yes—
128#66939—216no—
129#66928—28no—
130#66922—28no—
131C11×#103C2314yes—
132C11×#103C2314yes—
133C11×#102C2314yes—
134C11×#102C2314yes—
135#66880C2318yes—
136#66880C2318yes—
137#66872C2318yes—
138#66871C2318yes—
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—21no—
147C2×Q8×C11—22no—
148C2×Q8×C11—22no—
149C2×Q8×C11C2412yes—
150C2×D4×C11—24no—
151C2×D4×C11—22no—
152C2×D4×C11—21no—
153C2×D4×C11—22no—
154C2×D4×C11—44no—
155C2×D4×C11C2412yes—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—24no—
160C22×C4×C11—44no—
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D412yes—
163C22×C4×C11C2×D414yes—
164C22×C4×C11#4114yes—
165C22×C4×C11C2411yescharacteristic
166C22×C4×C11C2412yes—
167C2×C22⋊D11—28no—
168C2×C22⋊D11—28no—
169C2×C22⋊D11—84no—
170C2×C22⋊D11C2×D418yes—
171C22×Dic11—24no—
172C22×Dic11—22no—
173C22×Dic11—22no—
174C22×Dic11—24no—
175C22×Dic11—44no—
176C22×Dic11—82no—
177C22×Dic11C2×D412yes—
178#4339—216no—
179#4339—28no—
180#4339—28no—
181C2×D44—24no—
182C2×D44C2×D414yes—
183C2×C4×D11—24no—
184C2×C4×D11—24no—
185C2×C4×D11C2×D414yes—
186C2×C4×D11C2414yes—
187C2×Dic22—24no—
188C2×Dic22—24no—
189C2×Dic22—28no—
190C2×Dic22—24no—
191C2×Dic22—22no—
192C2×Dic22—24no—
193C2×Dic22—28no—
194C2×Dic22—44no—
195C2×Dic22—48no—
196C2×Dic22C2×D414yes—
197C2×Dic22C2414yes—
198C2×C8×C11—22no—
199C2×C8×C11—22no—
200C2×C8×C11—28no—
201C2×C8×C11C2412yes—
202C2×C8×C11C2412yes—
203C11×C4⋊C4—21no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4C2412yes—
206C11×C4⋊C4C2412yes—
207C11×C22⋊C4—24no—
208C42×C11—24no—
209C22⋊Dic11—28no—
210#4326—216no—
211#4324—216no—
212(C2×D11)⋊C4—28no—
213(C2×D11)⋊C4—28no—
214(C2×D11)⋊C4—28no—
215C4⋊Dic11—28no—
216C4⋊Dic11—28no—
217C4⋊Dic11—24no—
218C4⋊Dic11—22no—
219C4⋊Dic11C2414yes—
220Dic11⋊C4—28no—
221#4318C2×D4116yescomplemented
222C2×C11⋊C8C2×D418yes—
223C2×C11⋊C8C2414yes—
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×#428—111no—
236C2×#416D1111yescharacteristic, complemented
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—22no—
252Q8×C11—22no—
253Q8×C11—42no—
254D4×C11—22no—
255D4×C11—22no—
256D4×C11—48no—
257D4×C11—42no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—42no—
262C2×C4×C11—42no—
263C2×C4×C11—42no—
264C2×C4×C11—48no—
265C2×C4×C11#12114yes—
266C2×C4×C11#12118yes—
267C2×C4×C11C22×D412yes—
268C2×C4×C11C22×D411yescharacteristic
269C2×C4×C11C22×D412yes—
270C2×C4×C11C22×D414yes—
271C2×C4×C11C2×#4112yes—
272C2×C4×C11C2×#4114yes—
273C2×C4×C11C2511yescharacteristic
274C22⋊D11—216no—
275C22⋊D11—88no—
276C2×Dic11—24no—
277C2×Dic11—24no—
278C2×Dic11—24no—
279C2×Dic11—48no—
280C2×Dic11—44no—
281C2×Dic11—44no—
282C2×Dic11—84no—
283C2×Dic11C22×D414yes—
284D44—28no—
285C4×D11—28no—
286C4×D11—24no—
287C4×D11—24no—
288Dic22—28no—
289Dic22—24no—
290Dic22—24no—
291Dic22—48no—
292Dic22—44no—
293C8×C11—22no—
294C8×C11—22no—
295C11⋊C8C22×D418yes—
296C22×#41—111no—
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—112no—
308C23×C8C2×D1111yescharacteristic
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⋊C4—111no—
325#470—1116no—
326#468—1116no—
327#467—1116no—
328#465—1116no—
329#428—118no—
330C2×#107—112no—
331C2×#106—112no—
332#416C2×D1118yescomplemented
333C2×#103—112no—
334C2×#103—112no—
335C2×#103—118no—
336C2×#103C2×D1111yescharacteristic
337C2×#103C2×D1111yescharacteristic
338C2×#102C2×D1111yescharacteristic
339C2×#102C2×D1111yescharacteristic
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—42no—
358C4×C11—42no—
359C4×C11C2×#12114yes—
360C4×C11C2×#12112yes—
361C4×C11C23×D411yescharacteristic
362C4×C11C22×#4111yescharacteristic
363Dic11—24no—
364Dic11—44no—
365Dic11—44no—
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—111no—
375C22×Q8—112no—
376C22×Q8—114no—
377C22×Q8—221no—
378C22×Q8—222no—
379C22×Q8—224no—
380C22×Q8—224no—
381C22×Q8C22×D1111yescharacteristic
382C22×D4—21no—
383C22×D4—112no—
384C22×D4—111no—
385C22×D4—222no—
386C22×D4C22×D1111yescharacteristic
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—114no—
400C2×M16—118no—
401C2×M16—228no—
402C22×C8—24no—
403C22×C8—112no—
404C22×C8—118no—
405C22×C8—228no—
406C22×C8C22×D1111yescharacteristic
407C22×C8C22×D1111yescharacteristic
408C22×C8C22×D1114yes—
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—228no—
418C22⋊Q8—224no—
419#121—118no—
420#121—228no—
421#121—224no—
422#121—2216no—
423#117—22no—
424#117C22×D1114yes—
425C2×C4⋊C4—112no—
426C2×C4⋊C4—114no—
427C2×C4⋊C4—222no—
428C2×C4⋊C4—222no—
429C2×C4⋊C4—222no—
430C2×C4⋊C4—221no—
431C2×C4⋊C4—222no—
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#107—118no—
441#106—118no—
442#103—118no—
443#103—118no—
444#103C22×D1114yes—
445#103C22×D1114yes—
446#102C22×D1114yes—
447#102C22×D1114yes—
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—21no—
465C2×Q8—22no—
466C2×Q8—22no—
467C2×Q8—114no—
468C2×Q8—114no—
469C2×Q8—224no—
470C2×Q8—222no—
471C2×Q8—224no—
472C2×Q8—224no—
473C2×Q8—228no—
474C2×Q8—224no—
475C2×Q8—228no—
476C2×Q8—444no—
477C2×Q8—448no—
478C2×Q8C23×D1112yes—
479C2×D4—24no—
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—21no—
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—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—24no—
495C22×C4—44no—
496C22×C4—112no—
497C22×C4—114no—
498C22×C4—114no—
499C22×C4—224no—
500C22×C4—224no—
501C22×C4—224no—
502C22×C4—222no—
503C22×C4—222no—
504C22×C4—224no—
505C22×C4—444no—
506C22×C4—882no—
507C22×C4#433914yes—
508C22×C4D4×D1112yes—
509C22×C4D4×D1111yescharacteristic
510C22×C4D4×D1114yes—
511C22×C4C23×D1112yes—
512C22×C4C23×D1111yescharacteristic
513Q16—2216no—
514SD16—2216no—
515M16—1116no—
516M16—2216no—
517C2×C8—22no—
518C2×C8—22no—
519C2×C8—28no—
520C2×C8—118no—
521C2×C8—114no—
522C2×C8—2216no—
523C2×C8C23×D1112yes—
524C2×C8C23×D1112yes—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—114no—
528C4⋊C4—228no—
529C4⋊C4—228no—
530C4⋊C4—228no—
531C4⋊C4—224no—
532C4⋊C4—222no—
533C4⋊C4C23×D1112yes—
534C4⋊C4C23×D1112yes—
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—22no—
545C23—42no—
546C23—42no—
547C23—42no—
548C23—114no—
549C23—224no—
550C23—224no—
551C23—224no—
552C23#6693714yes—
553C23C2×D4×D1112yes—
554C23C2×D4×D1111yescharacteristic
555Q8—22no—
556Q8—22no—
557Q8—42no—
558Q8—228no—
559Q8—224no—
560Q8—224no—
561Q8—448no—
562Q8—444no—
563D4—22no—
564D4—22no—
565D4—48no—
566D4—42no—
567D4—2216no—
568D4—228no—
569D4—888no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—48no—
577C2×C4—114no—
578C2×C4—224no—
579C2×C4—228no—
580C2×C4—224no—
581C2×C4—224no—
582C2×C4—224no—
583C2×C4—224no—
584C2×C4—448no—
585C2×C4—444no—
586C2×C4—444no—
587C2×C4—884no—
588C2×C4#6693714yes—
589C2×C4#6693718yes—
590C2×C4C2×#433912yes—
591C2×C4C2×#433914yes—
592C2×C4C2×D4×D1112yes—
593C2×C4C2×D4×D1111yescharacteristic
594C2×C4C2×D4×D1112yes—
595C2×C4C2×D4×D1114yes—
596C2×C4C24×D1111yescharacteristic
597C8—22no—
598C8—22no—
599C8—118no—
600C22—28no—
601C22—22no—
602C22—22no—
603C22—42no—
604C22—42no—
605C22—42no—
606C22—84no—
607C22—224no—
608C22—224no—
609C22—224no—
610C22—448no—
611C22C2×#6693714yes—
612C22C2×#6693712yes—
613C22#1062330112yes—
614C22#1062330212yes—
615C22C22×D4×D1111yescharacteristic
616C4—42no—
617C4—42no—
618C4—42no—
619C4—224no—
620C4—444no—
621C4—444no—
622C4C2×#6693714yes—
623C4C2×#6693712yes—
624C4C22×#433911yescharacteristic
625C4C22×D4×D1111yescharacteristic
626C2—24no—
627C2—82no—
628C2—444no—
629C2#1307831014yesdirect product factor
630C2C22×#6693711yescharacteristic
631C2C2×#1062330111yescharacteristic
632C2C2×#1062330211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#416C2
socleC23×C11C22×D4
prime radicalC2×#10623364C2
hypercenterC2×#416D11
hypocenterC11C2×#3063
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
1. C22×#67004C2semidirect
2. C22×#66954C2semidirect
4. C2×#10623057C2semidirect
5. #13078310C2direct (N × H)
6. C2×#10622429C2semidirect
7. C2×#10622393C2semidirect
8. C2×#10622426C2semidirect
9. C2×#10622391C2semidirect
10. C2×#10622608C2semidirect
11. C22×#66880C2semidirect
12. C2×C11×#416C2semidirect
21. C2×#67004C22semidirect
32. C2×#66954C22semidirect
36. #10623057C22semidirect
42. C11×#416C22semidirect
49. C2×#66880C22semidirect
50. #10622608C22semidirect
53. #10622429C22semidirect
54. #10622426C22semidirect
55. #10622393C22semidirect
56. #10622391C22semidirect
116. C2×#4318D4semidirect
221. #4318C2×D4semidirect
236. C2×#416D11semidirect
332. #416C2×D11semidirect
450. C2×C11#3063semidirect
541. C11C2×#3063semidirect
629. C2#13078310direct (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×#669542
C2×#106233642
C2×#106230572
#130783102
C2×#106224292
C2×#106223932
C2×#106224262
C2×#106223912
C2×#106226082
C22×#668802
C2×C11×#4162
C2×#306311