Finite Group Databasebeta

← C2×#13079008 #15623061

Subgroups — C2×#13079008 #15623061

Order 2816.

2398 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623199C211yesmaximal, characteristic
2C2×D11×C4⋊Q8C211yesmaximal, characteristic, complemented
3#13079008C2116yesmaximal, direct product factor
4C2×#10622702C211yesmaximal, characteristic, complemented
5C2×#10622327C211yesmaximal, characteristic, complemented
6C2×#10622668C211yesmaximal, characteristic, complemented
7C2×#10622405C212yesmaximal, complemented
8C2×#10622373C212yesmaximal, complemented
9C2×#10622416C212yesmaximal, complemented
10C2×#10622384C212yesmaximal, complemented
11C2×#10622320C211yesmaximal, characteristic, complemented
12C2×C11×#489C211yesmaximal, characteristic, complemented
13C22×#4343C2211yescharacteristic
14C22×Q8×D11—21no—
15C22×#4341C2211yescharacteristic
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×#124C2211yescharacteristic
18C2×#66997—21no—
19C2×#66997C2211yescharacteristic
20C2×#66993C2211yescharacteristic
21C22×#4313C2212yes—
22D11×C4⋊Q8—24no—
23D11×C4⋊Q8C2218yescomplemented
24#10623199—24no—
25#10623199C2218yes—
26C2×C4⋊C4×D11—21no—
27C2×C4⋊C4×D11C2212yes—
28C2×#66941—21no—
29C2×#66941C2212yes—
30C2×#66937—21no—
31C2×#66937—21no—
32C2×(C22⋊D11)⋊C4—21no—
33C2×(C22⋊D11)⋊C4—21no—
34C2×#66928C2211yescharacteristic
35C2×C42×D11C2211yescharacteristic
36C2×#66922C2211yescharacteristic
37C11×#489C2218yescomplemented
38C2×C11×#103C2212yes—
39C2×C11×#102C2212yes—
40C2×C11×#97C2211yescharacteristic
41C2×#66899C2212yes—
42C2×#66896C2212yes—
43C2×#66885C2212yes—
44C2×#66880C2212yes—
45C2×C8×Dic11C2212yes—
46#10622702C2218yescomplemented
47#10622668C2218yescomplemented
48C2×#66874C2212yes—
49C2×#66873C2212yes—
50C2×#66867C2211yescharacteristic
51#10622416C22116yescomplemented
52#10622405C22116yescomplemented
53#10622384C22116yescomplemented
54#10622373C22116yescomplemented
55#10622327C2218yescomplemented
56#10622320C2218yescomplemented
57C22×Q8×C11—21no—
58C22×Q8×C11C2311yescharacteristic
59C22×D4×C11C2311yescharacteristic
60C22×C22⋊D11—21no—
61C22×C22⋊D11—21no—
62C22×C22⋊D11—21no—
63C23×Dic11—21no—
64C2×#4343—22no—
65C2×#4343—28no—
66C2×#4343C2314yes—
67C2×Q8×D11—28no—
68C2×Q8×D11—48no—
69C2×#4341—22no—
70C2×#4341—28no—
71C2×#4341C2314yes—
72C22×D44—21no—
73C22×D44C2311yescharacteristic
74C22×C4×D11—22no—
75C22×C4×D11—21no—
76C22×C4×D11D411yescharacteristic
77C22×C4×D11D411yescharacteristic
78C22×C4×D11C2311yescharacteristic
79C22×Dic22—21no—
80C22×Dic22—22no—
81C22×Dic22C2311yescharacteristic
82C22×C8×C11C2312yes—
83C11×C4⋊Q8—22no—
84C11×C4⋊Q8C2314yes—
85C11×#124—22no—
86C11×#124C2314yes—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4C2312yes—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C42×C11C2311yescharacteristic
92#66997—28no—
93#66997—22no—
94#66997C2314yes—
95#66993—22no—
96#66993C2314yes—
97C2×(C2×D11)⋊C4—21no—
98C2×(C2×D11)⋊C4—21no—
99C2×C4⋊Dic11—21no—
100C2×C4⋊Dic11C2312yes—
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4—21no—
103C2×Dic11⋊C4—22no—
104C2×Dic11⋊C4—22no—
105C2×C4×Dic11D411yescharacteristic
106C2×C4×Dic11D411yescharacteristic
107C2×C4×Dic11C2311yescharacteristic
108C22×C11⋊C8C2312yes—
109C2×#4313—28no—
110C2×#4313C2318yes—
111C4⋊C4×D11—24no—
112C4⋊C4×D11—28no—
113C4⋊C4×D11C2318yes—
114#66941—24no—
115#66941—28no—
116#66941C2318yes—
117#66937—28no—
118#66937—28no—
119(C22⋊D11)⋊C4—28no—
120(C22⋊D11)⋊C4—28no—
121#66928—22no—
122#66928C2314yes—
123C42×D11D414yes—
124C42×D11C2314yes—
125#66922—22no—
126#66922C2314yes—
127C11×#103C2318yes—
128C11×#102C2318yes—
129C11×#97C2314yes—
130#66899C2318yes—
131#66896C2318yes—
132#66885C2318yes—
133#66880C2318yes—
134C8×Dic11C2318yes—
135#66874C2318yes—
136#66873C2318yes—
137#66867C2314yes—
138C2×#3141—111nomaximal, Sylow
139C24×C11—21no—
140C23×D11—21no—
141C23×D11C2×D411yescharacteristic
142C2×Q8×C11—21no—
143C2×Q8×C11—24no—
144C2×Q8×C11—24no—
145C2×Q8×C11—44no—
146C2×Q8×C11C2412yes—
147C2×D4×C11—21no—
148C2×D4×C11—24no—
149C2×D4×C11C2412yes—
150C22×C4×C11—21no—
151C22×C4×C11—22no—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2411yescharacteristic
155C2×C22⋊D11—24no—
156C2×C22⋊D11—24no—
157C2×C22⋊D11—24no—
158C2×C22⋊D11—44no—
159C2×C22⋊D11—44no—
160C2×C22⋊D11—44no—
161C22×Dic11—24no—
162C22×Dic11—22no—
163C22×Dic11—21no—
164C22×Dic11—44no—
165C22×Dic11C2×D411yescharacteristic
166C22×Dic11C2×D411yescharacteristic
167C22×Dic11C2×D411yescharacteristic
168#4343—216no—
169#4343—48no—
170Q8×D11—432no—
171#4341—216no—
172#4341—48no—
173C2×D44—24no—
174C2×D44—21no—
175C2×D44—24no—
176C2×D44—44no—
177C2×D44C2412yes—
178C2×C4×D11—24no—
179C2×C4×D11—24no—
180C2×C4×D11—24no—
181C2×C4×D11—28no—
182C2×C4×D11—48no—
183C2×C4×D11—44no—
184C2×C4×D11C2×D414yes—
185C2×C4×D11C2×D414yes—
186C2×C4×D11C2×D412yes—
187C2×C4×D11#4118yes—
188C2×C4×D11C2412yes—
189C2×Dic22—28no—
190C2×Dic22—24no—
191C2×Dic22—21no—
192C2×Dic22—24no—
193C2×Dic22—44no—
194C2×Dic22—48no—
195C2×Dic22C2412yes—
196C2×C8×C11—24no—
197C2×C8×C11C2414yes—
198C11×C4⋊C4—24no—
199C11×C4⋊C4—22no—
200C11×C4⋊C4C2414yes—
201C11×C22⋊C4—24no—
202C11×C22⋊C4—24no—
203C42×C11C2×D412yes—
204C42×C11C2412yes—
205(C2×D11)⋊C4—24no—
206(C2×D11)⋊C4—24no—
207C4⋊Dic11—22no—
208C4⋊Dic11—24no—
209C4⋊Dic11C2414yes—
210Dic11⋊C4—24no—
211Dic11⋊C4—24no—
212Dic11⋊C4—28no—
213Dic11⋊C4—28no—
214C4×Dic11C2×D412yes—
215C4×Dic11C2×D414yes—
216C4×Dic11C2×D414yes—
217C4×Dic11C2412yes—
218C2×C11⋊C8—24no—
219C2×C11⋊C8C2414yes—
220#4313—216no—
221C2×#532—111no—
222C22×C4⋊Q8—111no—
223#3141—1116no—
224C2×#489—111no—
225C2×#489—111no—
226C2×#489—111no—
227C2×#489D1111yescharacteristic, complemented
228C2×#487—112no—
229C2×#486—112no—
230C2×#417—112no—
231C2×#417—112no—
232C2×C4×M16—111no—
233C23×C11—22no—
234C23×C11—42no—
235C23×C11—42no—
236C23×C11—42no—
237C23×C11C22×D411yescharacteristic
238C22×D11—22no—
239C22×D11—22no—
240C22×D11—22no—
241C22×D11—42no—
242C22×D11—42no—
243C22×D11—42no—
244C22×D11#12414yes—
245C22×D11C22×D412yes—
246Q8×C11—24no—
247Q8×C11—48no—
248Q8×C11—42no—
249D4×C11—24no—
250D4×C11—42no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—24no—
255C2×C4×C11—42no—
256C2×C4×C11—44no—
257C2×C4×C11C22×D412yes—
258C2×C4×C11C22×D412yes—
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C2×#4114yes—
261C2×C4×C11C2511yescharacteristic
262C22⋊D11—48no—
263C22⋊D11—48no—
264C22⋊D11—48no—
265C2×Dic11—24no—
266C2×Dic11—22no—
267C2×Dic11—42no—
268C2×Dic11—44no—
269C2×Dic11—48no—
270C2×Dic11#12414yes—
271C2×Dic11AGL(1,ℤ/8)14yes—
272C2×Dic11#13714yes—
273C2×Dic11C22×D412yes—
274C2×Dic11C22×D412yes—
275C2×Dic11C22×D412yes—
276D44—24no—
277D44—48no—
278D44—42no—
279C4×D11—28no—
280C4×D11—28no—
281C4×D11—416no—
282C4×D11—48no—
283C4×D11#12418yes—
284C4×D11C2×#4118yes—
285Dic22—24no—
286Dic22—48no—
287Dic22—42no—
288Dic22—416no—
289C8×C11—24no—
290C11⋊C8—24no—
291C22×#41—111no—
292C22×#41—111no—
293C23×Q8—221no—
294C22×M16—112no—
295#532—118no—
296#532—224no—
297C2×C4⋊Q8—118no—
298C2×C4⋊Q8—112no—
299C2×C4⋊Q8—111no—
300C2×C4⋊Q8—111no—
301C2×C4⋊Q8—221no—
302C2×C4⋊Q8—224no—
303C2×C4⋊Q8—221no—
304C2×C4⋊Q8C2×D1111yescharacteristic
305C2×#127—111no—
306C2×#124—111no—
307C2×#124C2×D1111yescharacteristic
308C2×#121—221no—
309C2×#121—221no—
310C2×C4×D4—221no—
311C2×C4×D4—221no—
312C22×C4⋊C4—112no—
313C22×C4⋊C4—221no—
314C22×C42—111no—
315#489—118no—
316#489—118no—
317#489—118no—
318#489C2×D1118yescomplemented
319#487—1116no—
320#486—1116no—
321#417—1116no—
322#417—1116no—
323C2×#103—112no—
324C2×#103—112no—
325C2×#103—112no—
326C2×#103C2×D1112yes—
327C2×#102—112no—
328C2×#102—112no—
329C2×#102—112no—
330C2×#102C2×D1112yes—
331C4×M16—118no—
332C2×#97—111no—
333C2×#97C2×D1111yescharacteristic
334C2×C4×C8—112no—
335C22×C11—42no—
336C22×C11—42no—
337C22×C11—42no—
338C22×C11—84no—
339C22×C11C2×#12412yes—
340C22×C11C2×AGL(1,ℤ/8)12yes—
341C22×C11C2×#13712yes—
342C22×C11C23×D411yescharacteristic
343C2×D11—28no—
344C2×D11—22no—
345C2×D11—22no—
346C2×D11—42no—
347C2×D11—42no—
348C2×D11—42no—
349C2×D11—84no—
350C2×D11C2×#12414yes—
351C4×C11—22no—
352C4×C11—22no—
353C4×C11—42no—
354C4×C11—44no—
355C4×C11C2×#12412yes—
356C4×C11C22×#4112yes—
357Dic11—42no—
358Dic11—44no—
359Dic11C2×#12414yes—
360Dic11C2×AGL(1,ℤ/8)14yes—
361Dic11C2×#13714yes—
362C2×#41—114no—
363C2×#41—114no—
364C2×#41—222no—
365C2×#41—222no—
366C2×#41—228no—
367C2×#41—228no—
368C22×Q8—21no—
369C22×Q8—111no—
370C22×Q8—222no—
371C22×Q8—228no—
372C22×Q8—221no—
373C22×Q8—448no—
374C22×Q8C22×D1111yescharacteristic
375C22×D4—111no—
376C22×D4—221no—
377C22×D4—221no—
378C22×D4—221no—
379C22×D4—221no—
380C22×D4C22×D1111yescharacteristic
381C23×C4—111no—
382C23×C4—111no—
383C23×C4—111no—
384C23×C4—221no—
385C23×C4—222no—
386C23×C4—221no—
387C2×M16—118no—
388C2×M16—228no—
389C22×C8—112no—
390C22×C8C22×D1112yes—
391C4⋊Q8—22no—
392C4⋊Q8—118no—
393C4⋊Q8—114no—
394C4⋊Q8—114no—
395C4⋊Q8—228no—
396C4⋊Q8—224no—
397C4⋊Q8—228no—
398C4⋊Q8—222no—
399C4⋊Q8—222no—
400C4⋊Q8C22×D1114yes—
401#127—114no—
402#127—222no—
403#124—22no—
404#124—114no—
405#124—222no—
406#124C22×D1114yes—
407#121—228no—
408#121—228no—
409C4×D4—228no—
410C4×D4—228no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—112no—
413C2×C4⋊C4—118no—
414C2×C4⋊C4—224no—
415C2×C4⋊C4—228no—
416C2×C4⋊C4—222no—
417C2×C4⋊C4—222no—
418C2×C4⋊C4—221no—
419C2×C4⋊C4—221no—
420C2×C4⋊C4—221no—
421C2×C4⋊C4C22×D1112yes—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—221no—
425C2×C22⋊C4—221no—
426C2×C42—111no—
427C2×C42—111no—
428C2×C42—111no—
429C2×C42—114no—
430C2×C42—114no—
431C2×C42C22×D1111yescharacteristic
432#103—118no—
433#103—118no—
434#103—118no—
435#103C22×D1118yes—
436#102—118no—
437#102—118no—
438#102—118no—
439#102C22×D1118yes—
440#97—114no—
441#97C22×D1114yes—
442C4×C8—118no—
443C2×C11—82no—
444C2×C11#314114yescomplemented
445C2×C11C22×#12411yescharacteristic
446C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
447C2×C11C22×#13711yescharacteristic
448D11—24no—
449D11—82no—
450C24—21no—
451C24—111no—
452C24—221no—
453#41—2216no—
454#41—2216no—
455#41—448no—
456#41—448no—
457C2×Q8—21no—
458C2×Q8—24no—
459C2×Q8—24no—
460C2×Q8—44no—
461C2×Q8—112no—
462C2×Q8—228no—
463C2×Q8—221no—
464C2×Q8—224no—
465C2×Q8—224no—
466C2×Q8—444no—
467C2×Q8—448no—
468C2×Q8—4432no—
469C2×Q8C23×D1112yes—
470C2×D4—21no—
471C2×D4—24no—
472C2×D4—112no—
473C2×D4—224no—
474C2×D4—224no—
475C2×D4—224no—
476C2×D4—224no—
477C2×D4—221no—
478C2×D4—224no—
479C2×D4—444no—
480C2×D4—444no—
481C2×D4—444no—
482C2×D4—444no—
483C2×D4C23×D1112yes—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—111no—
487C22×C4—111no—
488C22×C4—111no—
489C22×C4—112no—
490C22×C4—118no—
491C22×C4—112no—
492C22×C4—114no—
493C22×C4—114no—
494C22×C4—224no—
495C22×C4—224no—
496C22×C4—224no—
497C22×C4—228no—
498C22×C4—224no—
499C22×C4—221no—
500C22×C4—222no—
501C22×C4—444no—
502C22×C4—448no—
503C22×C4—444no—
504C22×C4D4×D1111yescharacteristic
505C22×C4D4×D1111yescharacteristic
506C22×C4C23×D1111yescharacteristic
507M16—2216no—
508C2×C8—24no—
509C2×C8—114no—
510C2×C8—224no—
511C2×C8C23×D1114yes—
512C4⋊C4—24no—
513C4⋊C4—22no—
514C4⋊C4—114no—
515C4⋊C4—228no—
516C4⋊C4—228no—
517C4⋊C4—224no—
518C4⋊C4—224no—
519C4⋊C4—222no—
520C4⋊C4—224no—
521C4⋊C4C23×D1114yes—
522C22⋊C4—24no—
523C22⋊C4—24no—
524C22⋊C4—224no—
525C22⋊C4—224no—
526C42—114no—
527C42—114no—
528C42—112no—
529C42—112no—
530C42D4×D1112yes—
531C42C23×D1112yes—
532C11C2×#314111yescharacteristic, complemented, Sylow
533C23—22no—
534C23—42no—
535C23—42no—
536C23—42no—
537C23—112no—
538C23—114no—
539C23—222no—
540C23—222no—
541C23—222no—
542C23—442no—
543C23—442no—
544C23—442no—
545C23C2×D4×D1111yescharacteristic
546Q8—24no—
547Q8—48no—
548Q8—42no—
549Q8—224no—
550Q8—448no—
551Q8—4416no—
552Q8—442no—
553D4—24no—
554D4—42no—
555D4—224no—
556D4—448no—
557D4—448no—
558D4—448no—
559D4—448no—
560D4—442no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—24no—
565C2×C4—44no—
566C2×C4—42no—
567C2×C4—114no—
568C2×C4—114no—
569C2×C4—112no—
570C2×C4—112no—
571C2×C4—112no—
572C2×C4—114no—
573C2×C4—118no—
574C2×C4—118no—
575C2×C4—228no—
576C2×C4—228no—
577C2×C4—222no—
578C2×C4—224no—
579C2×C4—448no—
580C2×C4—4416no—
581C2×C4—448no—
582C2×C4—444no—
583C2×C4—442no—
584C2×C4C2×D4×D1112yes—
585C2×C4C2×D4×D1112yes—
586C2×C4C2×D4×D1111yescharacteristic
587C2×C4#41×D1114yes—
588C2×C4C24×D1111yescharacteristic
589C8—24no—
590C8—224no—
591C22—42no—
592C22—42no—
593C22—42no—
594C22—84no—
595C22—114no—
596C22—222no—
597C22—222no—
598C22—228no—
599C22—442no—
600C22—442no—
601C22—442no—
602C22—884no—
603C22D11×#12412yes—
604C22D11×AGL(1,ℤ/8)12yes—
605C22D11×#13712yes—
606C22C22×D4×D1111yescharacteristic
607C4—22no—
608C4—22no—
609C4—42no—
610C4—44no—
611C4—114no—
612C4—114no—
613C4—114no—
614C4—442no—
615C4—444no—
616C4D11×#12412yes—
617C4C2×#41×D1112yes—
618C2—82no—
619C2—224no—
620C2—882no—
621C2#1307900814yesdirect product factor
622C2C2×D11×#12411yescharacteristic
623C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
624C2C2×D11×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#489C2
socleC23×C11C22×D4
prime radicalC2×#10623199C2
hypercenterC2×#489D11
hypocenterC11C2×#3141
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#489

Complements

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

NH ≅ G/Ntype
2. C2×D11×C4⋊Q8C2semidirect
3. #13079008C2direct (N × H)
4. C2×#10622702C2semidirect
5. C2×#10622327C2semidirect
6. C2×#10622668C2semidirect
7. C2×#10622405C2semidirect
8. C2×#10622373C2semidirect
9. C2×#10622416C2semidirect
10. C2×#10622384C2semidirect
11. C2×#10622320C2semidirect
12. C2×C11×#489C2semidirect
23. D11×C4⋊Q8C22semidirect
37. C11×#489C22semidirect
46. #10622702C22semidirect
47. #10622668C22semidirect
51. #10622416C22semidirect
52. #10622405C22semidirect
53. #10622384C22semidirect
54. #10622373C22semidirect
55. #10622327C22semidirect
56. #10622320C22semidirect
227. C2×#489D11semidirect
318. #489C2×D11semidirect
444. C2×C11#3141semidirect
532. C11C2×#3141semidirect
621. C2#13079008direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231992
C2×D11×C4⋊Q82
#130790082
C2×#106227022
C2×#106223272
C2×#106226682
C2×#106224052
C2×#106223732
C2×#106224162
C2×#106223842
C2×#106223202
C2×C11×#4892
C2×#314111