Finite Group Databasebeta

← C2×#13078154 #15620697

Subgroups — C2×#13078154 #15620697

Order 2816.

2934 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66961C211yesmaximal, characteristic, complemented
2C22×#67003C211yesmaximal, characteristic, complemented
3C2×#10623361C211yesmaximal, characteristic, complemented
4C2×#10623035C211yesmaximal, characteristic, complemented
5#13078154C2116yesmaximal, direct product factor
6C2×#10622411C212yesmaximal, complemented
7C2×#10622375C212yesmaximal, complemented
8C2×#10622432C212yesmaximal, complemented
9C2×#10622399C212yesmaximal, complemented
10C2×#10622732C211yesmaximal, characteristic, complemented
11C22×#66873C211yesmaximal, characteristic, complemented
12C2×C11×#417C211yesmaximal, characteristic, complemented
13C22×C11×#41C2211yescharacteristic
14C22×#4339C2211yescharacteristic
15C23×D44C2211yescharacteristic
16C22×C11×M16C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18#10623361—24no—
19#10623361C2218yescomplemented
20C2×#67003—28no—
21C2×#67003C2218yescomplemented
22C2×#67000C2212yes—
23C22×#4326C2211yescharacteristic, complemented
24C22×#4325C2211yescharacteristic, complemented
25C2×#66993C2212yes—
26C2×#66990—22no—
27C22×#4324C2211yescharacteristic, complemented
28C22×#4323C2211yescharacteristic, complemented
29C2×#66983—21no—
30C2×#66983—21no—
31C2×C4×C22⋊D11—22no—
32C2×#66979C2211yescharacteristic
33C23×C11⋊C8C2211yescharacteristic
34C2×#66961—28no—
35C2×#66961C2218yescomplemented
36C22×D88C2212yes—
37C22×#4314C2212yes—
38#10623035—24no—
39#10623035C2218yescomplemented
40C2×#66946C2212yescomplemented
41C2×#66945—21no—
42C2×C4⋊C4×D11—21no—
43C2×#66940C2212yescomplemented
44C11×#417C2218yescomplemented
45C2×C11×#103C2212yescomplemented
46C2×C11×#102C2212yescomplemented
47#10622732C2218yescomplemented
48C2×Dic11⋊C8C2212yescomplemented
49C2×Dic11⋊C8C2212yescomplemented
50C2×#66873C2212yes—
51C2×#66873C2212yes—
52C2×#66873C2218yescomplemented
53#10622432C22116yescomplemented
54#10622411C22116yescomplemented
55#10622399C22116yescomplemented
56#10622375C22116yescomplemented
57C24×D11—21no—
58C2×C11×#41—22no—
59C2×C11×#41—24no—
60C2×C11×#41—24no—
61C2×C11×#41C2314yes—
62C22×Q8×C11C2311yescharacteristic
63C22×D4×C11—21no—
64C22×D4×C11C2311yescharacteristic
65C23×C4×C11—21no—
66C23×C4×C11—21no—
67C23×C4×C11C2311yescharacteristic
68C22×C22⋊D11—21no—
69C22×C22⋊D11—22no—
70C22×C22⋊D11—22no—
71C2×#4339—22no—
72C2×#4339—24no—
73C2×#4339D418yescomplemented
74C2×#4339C2314yes—
75C22×D44—24no—
76C22×D44—24no—
77C22×D44—21no—
78C22×D44—22no—
79C22×D44C2312yes—
80C22×D44C2314yes—
81C22×D44C2311yescharacteristic
82C22×C4×D11—21no—
83C22×C4×D11—22no—
84C22×Dic22C2311yescharacteristic
85C2×C11×M16—24no—
86C2×C11×M16C2314yes—
87C22×C8×C11C2312yes—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—22no—
90C2×C11×C4⋊C4C2312yes—
91C2×C11×C4⋊C4C2314yes—
92C2×C22⋊Dic11D412yes—
93#67003—232no—
94#67000—24no—
95#67000C2318yes—
96C2×#4326—24no—
97C2×#4326C2314yescomplemented
98C2×#4325—24no—
99C2×#4325C2314yescomplemented
100#66993—24no—
101#66993C2318yes—
102#66990—216no—
103C2×#4324—24no—
104C2×#4324C2314yescomplemented
105C2×#4323—24no—
106C2×#4323C2314yescomplemented
107#66983—28no—
108#66983—28no—
109C4×C22⋊D11—216no—
110C2×(C2×D11)⋊C4—22no—
111C2×(C2×D11)⋊C4—22no—
112C2×(C2×D11)⋊C4—22no—
113#66979D414yes—
114#66979C2314yes—
115C2×C4⋊Dic11D411yescharacteristic
116C2×C4⋊Dic11D411yescharacteristic
117C2×Dic11⋊C4—22no—
118C2×C4×Dic11—22no—
119C2×C4×Dic11C2312yes—
120C22×C11⋊C8—24no—
121C22×C11⋊C8C2314yes—
122C22×C11⋊C8C2311yescharacteristic
123C22×C11⋊C8C2311yescharacteristic
124#66961—232no—
125C2×D88—28no—
126C2×D88C2318yes—
127C2×#4314—28no—
128C2×#4314C2318yes—
129#66946—24no—
130#66946C2318yescomplemented
131#66945—28no—
132C4⋊C4×D11—28no—
133#66940—24no—
134#66940C2318yescomplemented
135C11×#103C2318yescomplemented
136C11×#102C2318yescomplemented
137Dic11⋊C8C2318yescomplemented
138Dic11⋊C8C2318yescomplemented
139#66873C2318yes—
140#66873C2318yes—
141C2×#3045—111nomaximal, Sylow
142C24×C11—21no—
143C24×C11C2×D411yescharacteristic
144C23×D11—21no—
145C23×D11—22no—
146C23×D11—24no—
147C23×D11—44no—
148C23×D11—82no—
149C23×D11—82no—
150C11×#41—28no—
151C11×#41—28no—
152C11×#41—48no—
153C2×Q8×C11—21no—
154C2×Q8×C11—22no—
155C2×Q8×C11—22no—
156C2×Q8×C11C2412yes—
157C2×D4×C11—24no—
158C2×D4×C11—22no—
159C2×D4×C11—21no—
160C2×D4×C11—22no—
161C2×D4×C11—44no—
162C2×D4×C11C2412yes—
163C22×C4×C11—22no—
164C22×C4×C11—21no—
165C22×C4×C11—24no—
166C22×C4×C11—24no—
167C22×C4×C11—44no—
168C22×C4×C11—82no—
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D412yes—
171C22×C4×C11C2×D414yes—
172C22×C4×C11#4114yes—
173C22×C4×C11C2411yescharacteristic
174C22×C4×C11C2412yes—
175C2×C22⋊D11—28no—
176C2×C22⋊D11—28no—
177C2×C22⋊D11—28no—
178C2×C22⋊D11—24no—
179C2×C22⋊D11—84no—
180C2×C22⋊D11—84no—
181C22×Dic11—21no—
182C22×Dic11C2×D412yes—
183C22×Dic11C2×D412yes—
184#4339—216no—
185#4339—28no—
186#4339C2×D4116yescomplemented
187C2×D44—21no—
188C2×D44—24no—
189C2×D44—22no—
190C2×D44—24no—
191C2×D44—28no—
192C2×D44—22no—
193C2×D44—24no—
194C2×D44—28no—
195C2×D44—44no—
196C2×D44—48no—
197C2×D44C2×D414yes—
198C2×D44C2414yes—
199C2×D44C2412yes—
200C2×C4×D11—28no—
201C2×C4×D11—28no—
202C2×C4×D11—24no—
203C2×C4×D11—84no—
204C2×Dic22—21no—
205C2×Dic22—22no—
206C2×Dic22C2×D414yes—
207C2×Dic22C2412yes—
208C11×M16—28no—
209C2×C8×C11—24no—
210C2×C8×C11C2414yes—
211C11×C4⋊C4—22no—
212C11×C4⋊C4—24no—
213C11×C4⋊C4C2414yes—
214C22⋊Dic11C2×D418yes—
215#4326—28no—
216#4325—28no—
217#4324—28no—
218#4323—28no—
219(C2×D11)⋊C4—28no—
220(C2×D11)⋊C4—28no—
221(C2×D11)⋊C4—28no—
222C4⋊Dic11C2×D414yes—
223C4⋊Dic11C2×D414yes—
224Dic11⋊C4—28no—
225C4×Dic11—28no—
226C4×Dic11C2×D414yes—
227C4×Dic11C2414yes—
228C2×C11⋊C8—22no—
229C2×C11⋊C8—22no—
230C2×C11⋊C8—28no—
231C2×C11⋊C8C2412yes—
232C2×C11⋊C8C2412yes—
233D88—216no—
234#4314—216no—
235C22×AGL(1,ℤ/8)—111no—
236C22×#135—111no—
237C2×#535—111no—
238C2×#520—111no—
239#3045—1116no—
240C2×#464—112no—
241C2×#460—112no—
242C2×#463—112no—
243C2×#459—112no—
244C2×#424—111no—
245C2×#417D1111yescharacteristic, complemented
246C22×#102—111no—
247C23×C11—22no—
248C23×C11—22no—
249C23×C11—22no—
250C23×C11—42no—
251C23×C11—42no—
252C23×C11—42no—
253C23×C11#12114yes—
254C23×C11C22×D412yes—
255C23×C11C22×D411yescharacteristic
256C22×D11—24no—
257C22×D11—22no—
258C22×D11—24no—
259C22×D11—42no—
260C22×D11—42no—
261C22×D11—48no—
262C22×D11—44no—
263C22×D11—44no—
264C22×D11—44no—
265C22×D11—84no—
266C22×D11—84no—
267C22×D11—816no—
268Q8×C11—22no—
269Q8×C11—22no—
270Q8×C11—42no—
271D4×C11—22no—
272D4×C11—22no—
273D4×C11—48no—
274D4×C11—42no—
275C2×C4×C11—24no—
276C2×C4×C11—22no—
277C2×C4×C11—42no—
278C2×C4×C11—44no—
279C2×C4×C11—48no—
280C2×C4×C11—84no—
281C2×C4×C11#12114yes—
282C2×C4×C11#12118yes—
283C2×C4×C11C22×D411yescharacteristic
284C2×C4×C11C22×D412yes—
285C2×C4×C11C22×D412yes—
286C2×C4×C11C22×D414yes—
287C2×C4×C11C2×#4112yes—
288C2×C4×C11C2×#4114yes—
289C2×C4×C11C2511yescharacteristic
290C22⋊D11—216no—
291C22⋊D11—88no—
292C22⋊D11—88no—
293C2×Dic11—24no—
294C2×Dic11—24no—
295C2×Dic11—24no—
296C2×Dic11—22no—
297C2×Dic11C22×D414yes—
298C2×Dic11C22×D414yes—
299D44—24no—
300D44—24no—
301D44—22no—
302D44—24no—
303D44—48no—
304D44—44no—
305D44C22×D414yes—
306C4×D11—216no—
307C4×D11—88no—
308Dic22—24no—
309Dic22—22no—
310Dic22C22×D414yes—
311C8×C11—24no—
312C11⋊C8—22no—
313C11⋊C8—22no—
314C22×#41—111no—
315C22×#41C2×D1111yescharacteristic
316C23×D4—111no—
317C2×AGL(1,ℤ/8)—118no—
318C2×AGL(1,ℤ/8)—228no—
319C2×#135—118no—
320C2×#135—228no—
321C22×Q16—111no—
322C22×SD16—111no—
323C22×SD16—111no—
324C22×SD16—112no—
325C22×D8—111no—
326C22×D8—112no—
327C22×M16C2×D1111yescharacteristic
328C23×C8—111no—
329#535—118no—
330#535—224no—
331C2×#127—112no—
332C2×#124—112no—
333C2×#121—221no—
334C2×#121—221no—
335C2×#120—222no—
336#520—118no—
337#520—224no—
338C2×C4×Q8—112no—
339C2×C4×D4—112no—
340C2×C4×D4—222no—
341C2×#117—111no—
342C2×#117—221no—
343C22×C4⋊C4—221no—
344C22×C4⋊C4C2×D1111yescharacteristic
345#464—1116no—
346#463—1116no—
347#460—1116no—
348#459—1116no—
349#424—118no—
350C2×C4⋊C8—112no—
351C2×C4⋊C8—112no—
352#417C2×D1118yescomplemented
353C2×#103C2×D1112yescomplemented
354C2×#102—112no—
355C2×#102—112no—
356C2×#102—118no—
357C2×#102C2×D1112yescomplemented
358C22×C11—28no—
359C22×C11—22no—
360C22×C11—22no—
361C22×C11—42no—
362C22×C11—42no—
363C22×C11—42no—
364C22×C11—84no—
365C22×C11C2×#12114yes—
366C22×C11C2×#12112yes—
367C22×C11#57612yes—
368C22×C11#57712yes—
369C22×C11C23×D411yescharacteristic
370C2×D11—24no—
371C2×D11—48no—
372C2×D11—42no—
373C2×D11—42no—
374C2×D11—44no—
375C2×D11—44no—
376C2×D11—44no—
377C2×D11—816no—
378C2×D11—88no—
379C4×C11—42no—
380C4×C11—44no—
381C4×C11C2×#12114yes—
382C4×C11C2×#12112yes—
383C4×C11C23×D411yescharacteristic
384C4×C11C22×#4111yescharacteristic
385Dic11—24no—
386Dic11—24no—
387Dic11—24no—
388C25—221no—
389C2×#41—22no—
390C2×#41—24no—
391C2×#41—24no—
392C2×#41—118no—
393C2×#41—114no—
394C2×#41—224no—
395C2×#41—222no—
396C2×#41C22×D1114yes—
397C22×Q8—111no—
398C22×Q8C22×D1111yescharacteristic
399C22×D4—21no—
400C22×D4—111no—
401C22×D4—112no—
402C22×D4—114no—
403C22×D4—222no—
404C22×D4—222no—
405C22×D4—221no—
406C22×D4—224no—
407C22×D4—224no—
408C22×D4—221no—
409C22×D4—222no—
410C22×D4C22×D1111yescharacteristic
411C23×C4—21no—
412C23×C4—21no—
413C23×C4—222no—
414C23×C4—221no—
415C23×C4C22×D1111yescharacteristic
416AGL(1,ℤ/8)—2232no—
417#135—2232no—
418C2×Q16—114no—
419C2×Q16—224no—
420C2×SD16—114no—
421C2×SD16—114no—
422C2×SD16—118no—
423C2×SD16—228no—
424C2×SD16—224no—
425C2×SD16—224no—
426C2×D8—114no—
427C2×D8—118no—
428C2×D8—228no—
429C2×D8—224no—
430C2×M16—24no—
431C2×M16C22×D1114yes—
432C22×C8—111no—
433C22×C8—111no—
434C22×C8—114no—
435C22×C8—224no—
436C22×C8C22×D1112yes—
437#127—118no—
438#127—224no—
439#124—118no—
440#124—224no—
441#121—228no—
442#121—228no—
443#120—2216no—
444C4×Q8—118no—
445C4×Q8—224no—
446C4×D4—118no—
447C4×D4—224no—
448C4×D4—2216no—
449#117—114no—
450#117—114no—
451#117—228no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—111no—
455C2×C4⋊C4—111no—
456C2×C4⋊C4—228no—
457C2×C4⋊C4—222no—
458C2×C4⋊C4C22×D1112yes—
459C2×C4⋊C4C22×D1114yes—
460C2×C22⋊C4—112no—
461C2×C22⋊C4—222no—
462C2×C22⋊C4—222no—
463C2×C22⋊C4—222no—
464C2×C42—112no—
465C2×C42—222no—
466C4⋊C8—118no—
467C4⋊C8—118no—
468#103C22×D1118yescomplemented
469#102—118no—
470#102—118no—
471#102C22×D1118yescomplemented
472C2×C11—24no—
473C2×C11—82no—
474C2×C11#304514yescomplemented
475C2×C11C22×#12111yescharacteristic
476C2×C11C2×#57611yescharacteristic
477C2×C11C2×#57711yescharacteristic
478D11—44no—
479D11—84no—
480C24—21no—
481C24—221no—
482C24—222no—
483C24—224no—
484C24—444no—
485C24—882no—
486C24—882no—
487C24D4×D1111yescharacteristic
488#41—28no—
489#41—28no—
490#41—48no—
491#41—1116no—
492#41—2216no—
493#41—228no—
494C2×Q8—21no—
495C2×Q8—22no—
496C2×Q8—22no—
497C2×Q8—114no—
498C2×Q8—112no—
499C2×Q8—222no—
500C2×Q8—221no—
501C2×Q8C23×D1112yes—
502C2×D4—24no—
503C2×D4—22no—
504C2×D4—22no—
505C2×D4—21no—
506C2×D4—44no—
507C2×D4—114no—
508C2×D4—112no—
509C2×D4—114no—
510C2×D4—228no—
511C2×D4—228no—
512C2×D4—228no—
513C2×D4—224no—
514C2×D4—222no—
515C2×D4—224no—
516C2×D4—228no—
517C2×D4—221no—
518C2×D4—224no—
519C2×D4—228no—
520C2×D4—224no—
521C2×D4—222no—
522C2×D4—444no—
523C2×D4—448no—
524C2×D4—884no—
525C2×D4—884no—
526C2×D4C23×D1112yes—
527C22×C4—22no—
528C22×C4—21no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—44no—
532C22×C4—82no—
533C22×C4—112no—
534C22×C4—112no—
535C22×C4—228no—
536C22×C4—221no—
537C22×C4—228no—
538C22×C4—224no—
539C22×C4—884no—
540C22×C4#433914yes—
541C22×C4D4×D1112yes—
542C22×C4D4×D1111yescharacteristic
543C22×C4D4×D1114yes—
544C22×C4C23×D1112yes—
545C22×C4C23×D1111yescharacteristic
546Q16—228no—
547SD16—2216no—
548SD16—228no—
549SD16—228no—
550D8—2216no—
551D8—228no—
552M16—28no—
553C2×C8—24no—
554C2×C8—112no—
555C2×C8—112no—
556C2×C8—222no—
557C2×C8—222no—
558C2×C8—228no—
559C2×C8C23×D1114yes—
560C4⋊C4—24no—
561C4⋊C4—22no—
562C4⋊C4—114no—
563C4⋊C4—114no—
564C4⋊C4—228no—
565C4⋊C4C23×D1114yes—
566C22⋊C4—118no—
567C22⋊C4—228no—
568C22⋊C4—228no—
569C22⋊C4—228no—
570C42—114no—
571C42—114no—
572C42—228no—
573C11C2×#304511yescharacteristic, complemented, Sylow
574C23—22no—
575C23—22no—
576C23—22no—
577C23—42no—
578C23—42no—
579C23—42no—
580C23—224no—
581C23—222no—
582C23—224no—
583C23—442no—
584C23—442no—
585C23—448no—
586C23—444no—
587C23—444no—
588C23—444no—
589C23—884no—
590C23—884no—
591C23—8816no—
592C23#6693714yes—
593C23C2×D4×D1112yes—
594C23C2×D4×D1111yescharacteristic
595Q8—22no—
596Q8—22no—
597Q8—42no—
598Q8—114no—
599Q8—224no—
600Q8—222no—
601D4—22no—
602D4—22no—
603D4—48no—
604D4—42no—
605D4—114no—
606D4—2216no—
607D4—224no—
608D4—222no—
609D4—224no—
610D4—224no—
611D4—448no—
612D4—444no—
613D4—888no—
614D4—888no—
615C2×C4—24no—
616C2×C4—22no—
617C2×C4—42no—
618C2×C4—44no—
619C2×C4—48no—
620C2×C4—84no—
621C2×C4—114no—
622C2×C4—114no—
623C2×C4—224no—
624C2×C4—224no—
625C2×C4—224no—
626C2×C4—222no—
627C2×C4—2216no—
628C2×C4—888no—
629C2×C4#6693714yes—
630C2×C4#6693718yes—
631C2×C4C2×#433912yes—
632C2×C4C2×#433914yes—
633C2×C4C2×D4×D1111yescharacteristic
634C2×C4C2×D4×D1112yes—
635C2×C4C2×D4×D1112yes—
636C2×C4C2×D4×D1114yes—
637C2×C4C24×D1111yescharacteristic
638C8—24no—
639C8—222no—
640C8—222no—
641C22—28no—
642C22—22no—
643C22—22no—
644C22—42no—
645C22—42no—
646C22—42no—
647C22—84no—
648C22—224no—
649C22—448no—
650C22—442no—
651C22—442no—
652C22—444no—
653C22—444no—
654C22—444no—
655C22—8816no—
656C22—888no—
657C22C2×#6693714yes—
658C22C2×#6693712yes—
659C22#1062330512yes—
660C22#1062330912yes—
661C22C22×D4×D1111yescharacteristic
662C4—44no—
663C4—42no—
664C4—224no—
665C4—224no—
666C4—224no—
667C4C2×#6693714yes—
668C4C2×#6693712yes—
669C4C22×#433911yescharacteristic
670C4C22×D4×D1111yescharacteristic
671C2—24no—
672C2—82no—
673C2—444no—
674C2—884no—
675C2#1307815414yesdirect product factor
676C2C22×#6693711yescharacteristic
677C2C2×#1062330511yescharacteristic
678C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#417C2
socleC23×C11C22×D4
hypercenterC2×#417D11
hypocenterC11C2×#3045
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
1. C22×#66961C2semidirect
2. C22×#67003C2semidirect
3. C2×#10623361C2semidirect
4. C2×#10623035C2semidirect
5. #13078154C2direct (N × H)
6. C2×#10622411C2semidirect
7. C2×#10622375C2semidirect
8. C2×#10622432C2semidirect
9. C2×#10622399C2semidirect
10. C2×#10622732C2semidirect
11. C22×#66873C2semidirect
12. C2×C11×#417C2semidirect
19. #10623361C22semidirect
21. C2×#67003C22semidirect
23. C22×#4326C22semidirect
24. C22×#4325C22semidirect
27. C22×#4324C22semidirect
28. C22×#4323C22semidirect
35. C2×#66961C22semidirect
39. #10623035C22semidirect
40. C2×#66946C22semidirect
43. C2×#66940C22semidirect
44. C11×#417C22semidirect
45. C2×C11×#103C22semidirect
46. C2×C11×#102C22semidirect
47. #10622732C22semidirect
48. C2×Dic11⋊C8C22semidirect
49. C2×Dic11⋊C8C22semidirect
52. C2×#66873C22semidirect
53. #10622432C22semidirect
54. #10622411C22semidirect
55. #10622399C22semidirect
56. #10622375C22semidirect
73. C2×#4339D4semidirect
97. C2×#4326C23semidirect
99. C2×#4325C23semidirect
104. C2×#4324C23semidirect
106. C2×#4323C23semidirect
130. #66946C23semidirect
134. #66940C23semidirect
135. C11×#103C23semidirect
136. C11×#102C23semidirect
137. Dic11⋊C8C23semidirect
138. Dic11⋊C8C23semidirect
186. #4339C2×D4semidirect
245. C2×#417D11semidirect
352. #417C2×D11semidirect
353. C2×#103C2×D11semidirect
357. C2×#102C2×D11semidirect
468. #103C22×D11semidirect
471. #102C22×D11semidirect
474. C2×C11#3045semidirect
573. C11C2×#3045semidirect
675. C2#13078154direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669612
C22×#670032
C2×#106233612
C2×#106230352
#130781542
C2×#106224112
C2×#106223752
C2×#106224322
C2×#106223992
C2×#106227322
C22×#668732
C2×C11×#4172
C2×#304511