Finite Group Databasebeta

← C2×#13078160 #15620703

Subgroups — C2×#13078160 #15620703

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×#66985C211yesmaximal, characteristic, complemented
2C22×#66957C211yesmaximal, characteristic, complemented
3C2×#10623336C211yesmaximal, characteristic, complemented
4C2×#10623035C211yesmaximal, characteristic, complemented
5#13078160C2116yesmaximal, direct product factor
6C2×#10622380C212yesmaximal, complemented
7C2×#10622375C212yesmaximal, complemented
8C2×#10622400C212yesmaximal, complemented
9C2×#10622399C212yesmaximal, complemented
10C2×#10622715C211yesmaximal, characteristic, complemented
11C2×#10622579C211yesmaximal, characteristic, complemented
12C22×C11×#102C211yesmaximal, characteristic, complemented
13C23×D4×C11C2211yescharacteristic
14C22×#4339C2211yescharacteristic
15C22×#4339C2211yescharacteristic
16C23×C8×C11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C2×#67006—22no—
19#10623336—24no—
20#10623336C2218yescomplemented
21C2×#66993C2212yes—
22C2×#66991—21no—
23C2×#66991—21no—
24C2×#66989C2212yes—
25C22×#4324C2212yes—
26C2×#66985—28no—
27C2×#66985C2218yescomplemented
28C22×#4323C2212yes—
29C2×C4×C22⋊D11—22no—
30C2×#66979C2211yescharacteristic
31C22×#4318C2211yescharacteristic
32C22×Dic44C2211yescharacteristic, complemented
33C2×#66957—28no—
34C2×#66957C2218yescomplemented
35C22×D88C2211yescharacteristic, complemented
36C22×#4314C2211yescharacteristic, complemented
37C22×#4314C2211yescharacteristic, complemented
38#10623035—24no—
39#10623035C2218yescomplemented
40C2×#66946C2212yescomplemented
41C2×#66945—21no—
42C2×C4⋊C4×D11—21no—
43C2×#66940C2212yescomplemented
44C2×C11×#102C2212yes—
45C2×C11×#102C2212yes—
46C2×C11×#102C2218yescomplemented
47#10622715C2218yescomplemented
48C2×Dic11⋊C8C2212yescomplemented
49C2×Dic11⋊C8C2212yescomplemented
50C2×#66874C2212yescomplemented
51#10622579C2218yescomplemented
52C2×#66873C2212yescomplemented
53#10622400C22116yescomplemented
54#10622399C22116yescomplemented
55#10622380C22116yescomplemented
56#10622375C22116yescomplemented
57C25×C11—21no—
58C22×D4×C11—24no—
59C22×D4×C11—21no—
60C22×D4×C11—22no—
61C22×D4×C11—24no—
62C22×D4×C11C2312yes—
63C22×D4×C11C2314yes—
64C23×C4×C11—21no—
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11—21no—
67C22×C22⋊D11—21no—
68C22×C22⋊D11—22no—
69C22×C22⋊D11—22no—
70C2×#4339—22no—
71C2×#4339—24no—
72C2×#4339—22no—
73C2×#4339—24no—
74C2×#4339—24no—
75C2×#4339D418yescomplemented
76C2×#4339C2314yes—
77C2×#4339C2314yes—
78C22×D44C2311yescharacteristic
79C22×D44C2311yescharacteristic
80C22×C4×D11—21no—
81C22×C4×D11—21no—
82C22×C4×D11—22no—
83C22×Dic22C2311yescharacteristic
84C22×Dic22C2311yescharacteristic
85C22×C8×C11—24no—
86C22×C8×C11C2311yescharacteristic
87C22×C8×C11C2311yescharacteristic
88C22×C8×C11C2314yes—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—22no—
91C2×C11×C4⋊C4C2312yes—
92C2×C11×C4⋊C4C2314yes—
93#67006—216no—
94C2×C22⋊Dic11—22no—
95C2×C22⋊Dic11—22no—
96C2×C22⋊Dic11D412yes—
97#66993—24no—
98#66993C2318yes—
99#66991—28no—
100#66991—28no—
101#66989—24no—
102#66989C2318yes—
103C2×#4324—28no—
104C2×#4324C2318yes—
105#66985—232no—
106C2×#4323—28no—
107C2×#4323C2318yes—
108C4×C22⋊D11—216no—
109C2×(C2×D11)⋊C4—22no—
110#66979D414yes—
111#66979C2314yes—
112C2×C4⋊Dic11D411yescharacteristic
113C2×C4⋊Dic11D411yescharacteristic
114C2×Dic11⋊C4—22no—
115C2×C4×Dic11—22no—
116C2×C4×Dic11C2312yes—
117C2×#4318—24no—
118C2×#4318C2314yes—
119C22×C11⋊C8C2312yes—
120C2×Dic44—24no—
121C2×Dic44C2314yescomplemented
122#66957—232no—
123C2×D88—24no—
124C2×D88C2314yescomplemented
125C2×#4314—24no—
126C2×#4314—24no—
127C2×#4314C2314yescomplemented
128C2×#4314C2314yescomplemented
129#66946—24no—
130#66946C2318yescomplemented
131#66945—28no—
132C4⋊C4×D11—28no—
133#66940—24no—
134#66940C2318yescomplemented
135C11×#102C2318yes—
136C11×#102C2318yes—
137Dic11⋊C8C2318yescomplemented
138Dic11⋊C8C2318yescomplemented
139#66874C2318yescomplemented
140#66873C2318yescomplemented
141C2×#3045—111nomaximal, Sylow
142C24×C11—22no—
143C24×C11—24no—
144C24×C11—44no—
145C24×C11—82no—
146C24×C11—82no—
147C24×C11C2×D411yescharacteristic
148C23×D11—21no—
149C23×D11—21no—
150C2×D4×C11—24no—
151C2×D4×C11—28no—
152C2×D4×C11—22no—
153C2×D4×C11—24no—
154C2×D4×C11—24no—
155C2×D4×C11—28no—
156C2×D4×C11—44no—
157C2×D4×C11—48no—
158C2×D4×C11C2414yes—
159C22×C4×C11—22no—
160C22×C4×C11—24no—
161C22×C4×C11—82no—
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D412yes—
164C22×C4×C11C2×D414yes—
165C22×C4×C11#4114yes—
166C22×C4×C11C2411yescharacteristic
167C22×C4×C11C2412yes—
168C2×C22⋊D11—28no—
169C2×C22⋊D11—28no—
170C2×C22⋊D11—28no—
171C2×C22⋊D11—24no—
172C2×C22⋊D11—24no—
173C2×C22⋊D11—44no—
174C2×C22⋊D11—84no—
175C2×C22⋊D11—84no—
176C22×Dic11—21no—
177C22×Dic11—21no—
178C22×Dic11C2×D412yes—
179C22×Dic11C2×D412yes—
180#4339—216no—
181#4339—28no—
182#4339—28no—
183#4339—28no—
184#4339—48no—
185#4339C2×D4116yescomplemented
186C2×D44—21no—
187C2×D44—21no—
188C2×D44—22no—
189C2×D44—22no—
190C2×D44—22no—
191C2×D44C2×D414yes—
192C2×D44C2412yes—
193C2×D44C2412yes—
194C2×C4×D11—28no—
195C2×C4×D11—28no—
196C2×C4×D11—24no—
197C2×C4×D11—24no—
198C2×C4×D11—44no—
199C2×C4×D11—84no—
200C2×Dic22—21no—
201C2×Dic22—22no—
202C2×Dic22—21no—
203C2×Dic22—22no—
204C2×Dic22—22no—
205C2×Dic22C2×D414yes—
206C2×Dic22C2412yes—
207C2×Dic22C2412yes—
208C2×C8×C11—22no—
209C2×C8×C11—22no—
210C2×C8×C11—28no—
211C2×C8×C11C2412yes—
212C2×C8×C11C2412yes—
213C11×C4⋊C4—22no—
214C11×C4⋊C4—24no—
215C11×C4⋊C4C2414yes—
216C22⋊Dic11—28no—
217C22⋊Dic11—28no—
218C22⋊Dic11C2×D418yes—
219#4324—216no—
220#4323—216no—
221(C2×D11)⋊C4—28no—
222C4⋊Dic11C2×D414yes—
223C4⋊Dic11C2×D414yes—
224Dic11⋊C4—28no—
225C4×Dic11—28no—
226C4×Dic11C2×D414yes—
227C4×Dic11C2414yes—
228#4318—28no—
229C2×C11⋊C8—24no—
230C2×C11⋊C8C2414yes—
231Dic44—28no—
232D88—28no—
233#4314—28no—
234#4314—28no—
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×#417—111no—
246C22×#102D1111yescharacteristic, complemented
247C23×C11—22no—
248C23×C11—22no—
249C23×C11—24no—
250C23×C11—48no—
251C23×C11—44no—
252C23×C11—44no—
253C23×C11—44no—
254C23×C11—84no—
255C23×C11—84no—
256C23×C11—816no—
257C23×C11#12114yes—
258C23×C11C22×D412yes—
259C23×C11C22×D411yescharacteristic
260C22×D11—24no—
261C22×D11—22no—
262C22×D11—22no—
263C22×D11—42no—
264C22×D11—42no—
265C22×D11—42no—
266C22×D11—42no—
267C22×D11—42no—
268D4×C11—24no—
269D4×C11—24no—
270D4×C11—44no—
271D4×C11—48no—
272C2×C4×C11—24no—
273C2×C4×C11—44no—
274C2×C4×C11—84no—
275C2×C4×C11#12114yes—
276C2×C4×C11#12118yes—
277C2×C4×C11C22×D411yescharacteristic
278C2×C4×C11C22×D412yes—
279C2×C4×C11C22×D412yes—
280C2×C4×C11C22×D414yes—
281C2×C4×C11C2×#4112yes—
282C2×C4×C11C2×#4114yes—
283C2×C4×C11C2511yescharacteristic
284C22⋊D11—216no—
285C22⋊D11—48no—
286C22⋊D11—88no—
287C22⋊D11—88no—
288C2×Dic11—24no—
289C2×Dic11—24no—
290C2×Dic11—24no—
291C2×Dic11—22no—
292C2×Dic11—22no—
293C2×Dic11—42no—
294C2×Dic11C22×D414yes—
295C2×Dic11C22×D414yes—
296D44—24no—
297D44—22no—
298D44—22no—
299D44—22no—
300D44—42no—
301D44C22×D414yes—
302C4×D11—216no—
303C4×D11—48no—
304C4×D11—88no—
305Dic22—24no—
306Dic22—22no—
307Dic22—22no—
308Dic22—22no—
309Dic22—42no—
310Dic22C22×D414yes—
311C8×C11—22no—
312C8×C11—22no—
313C11⋊C8—24no—
314C22×#41—111no—
315C22×#41—111no—
316C23×D4C2×D1111yescharacteristic
317C2×AGL(1,ℤ/8)—118no—
318C2×AGL(1,ℤ/8)—228no—
319C2×#135—118no—
320C2×#135—228no—
321C22×Q16—111no—
322C22×SD16—112no—
323C22×SD16—111no—
324C22×SD16—111no—
325C22×D8—112no—
326C22×D8—111no—
327C22×M16—111no—
328C23×C8C2×D1111yescharacteristic
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#417—118no—
353C2×#103—112no—
354C2×#102—112no—
355C2×#102C2×D1112yes—
356C2×#102C2×D1112yes—
357C2×#102C2×D1118yescomplemented
358C22×C11—28no—
359C22×C11—22no—
360C22×C11—22no—
361C22×C11—44no—
362C22×C11—44no—
363C22×C11—44no—
364C22×C11—816no—
365C22×C11—88no—
366C22×C11C2×#12114yes—
367C22×C11C2×#12112yes—
368C22×C11#57612yes—
369C22×C11#57712yes—
370C22×C11C23×D411yescharacteristic
371C2×D11—24no—
372C2×D11—48no—
373C2×D11—42no—
374C2×D11—42no—
375C2×D11—42no—
376C2×D11—42no—
377C2×D11—42no—
378C2×D11—84no—
379C4×C11—44no—
380C4×C11C2×#12112yes—
381C4×C11C2×#12114yes—
382C4×C11C23×D411yescharacteristic
383C4×C11C22×#4111yescharacteristic
384Dic11—24no—
385Dic11—24no—
386Dic11—24no—
387Dic11—42no—
388C25—21no—
389C2×#41—118no—
390C2×#41—114no—
391C2×#41—114no—
392C2×#41—224no—
393C2×#41—222no—
394C2×#41—222no—
395C2×#41—224no—
396C2×#41—224no—
397C22×Q8—111no—
398C22×Q8—111no—
399C22×D4—24no—
400C22×D4—24no—
401C22×D4—21no—
402C22×D4—22no—
403C22×D4—111no—
404C22×D4—111no—
405C22×D4—222no—
406C22×D4—222no—
407C22×D4—221no—
408C22×D4—221no—
409C22×D4C22×D1112yes—
410C22×D4C22×D1114yes—
411C23×C4—21no—
412C23×C4—222no—
413C23×C4—221no—
414C23×C4—221no—
415C23×C4C22×D1111yescharacteristic
416AGL(1,ℤ/8)—2232no—
417#135—2232no—
418C2×Q16—114no—
419C2×Q16—224no—
420C2×SD16—118no—
421C2×SD16—114no—
422C2×SD16—114no—
423C2×SD16—224no—
424C2×SD16—224no—
425C2×SD16—228no—
426C2×D8—118no—
427C2×D8—114no—
428C2×D8—224no—
429C2×D8—228no—
430C2×M16—114no—
431C2×M16—224no—
432C22×C8—24no—
433C22×C8—112no—
434C22×C8C22×D1111yescharacteristic
435C22×C8C22×D1111yescharacteristic
436C22×C8C22×D1114yes—
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#103—118no—
469#102—118no—
470#102C22×D1118yes—
471#102C22×D1118yes—
472C2×C11—24no—
473C2×C11—84no—
474C2×C11#304514yescomplemented
475C2×C11C22×#12111yescharacteristic
476C2×C11C2×#57611yescharacteristic
477C2×C11C2×#57711yescharacteristic
478D11—44no—
479D11—82no—
480C24—22no—
481C24—24no—
482C24—44no—
483C24—82no—
484C24—82no—
485C24—221no—
486C24—221no—
487C24D4×D1111yescharacteristic
488#41—1116no—
489#41—2216no—
490#41—228no—
491#41—228no—
492#41—228no—
493#41—448no—
494C2×Q8—114no—
495C2×Q8—112no—
496C2×Q8—112no—
497C2×Q8—222no—
498C2×Q8—221no—
499C2×Q8—221no—
500C2×Q8—222no—
501C2×Q8—222no—
502C2×D4—24no—
503C2×D4—28no—
504C2×D4—24no—
505C2×D4—28no—
506C2×D4—24no—
507C2×D4—22no—
508C2×D4—44no—
509C2×D4—48no—
510C2×D4—114no—
511C2×D4—112no—
512C2×D4—112no—
513C2×D4—228no—
514C2×D4—228no—
515C2×D4—228no—
516C2×D4—224no—
517C2×D4—224no—
518C2×D4—222no—
519C2×D4—222no—
520C2×D4—221no—
521C2×D4—222no—
522C2×D4—221no—
523C2×D4—444no—
524C2×D4—884no—
525C2×D4—884no—
526C2×D4C23×D1114yes—
527C22×C4—22no—
528C22×C4—24no—
529C22×C4—82no—
530C22×C4—112no—
531C22×C4—112no—
532C22×C4—228no—
533C22×C4—221no—
534C22×C4—228no—
535C22×C4—224no—
536C22×C4—221no—
537C22×C4—224no—
538C22×C4—444no—
539C22×C4—884no—
540C22×C4#433914yes—
541C22×C4D4×D1112yes—
542C22×C4D4×D1111yescharacteristic
543C22×C4D4×D1114yes—
544C22×C4C23×D1112yes—
545C22×C4C23×D1111yescharacteristic
546Q16—228no—
547SD16—228no—
548SD16—228no—
549SD16—2216no—
550D8—228no—
551D8—2216no—
552M16—228no—
553C2×C8—22no—
554C2×C8—22no—
555C2×C8—28no—
556C2×C8—114no—
557C2×C8—224no—
558C2×C8C23×D1112yes—
559C2×C8C23×D1112yes—
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—24no—
577C23—48no—
578C23—44no—
579C23—44no—
580C23—44no—
581C23—84no—
582C23—84no—
583C23—816no—
584C23—224no—
585C23—222no—
586C23—222no—
587C23—442no—
588C23—442no—
589C23—442no—
590C23—442no—
591C23—442no—
592C23#6693714yes—
593C23C2×D4×D1112yes—
594C23C2×D4×D1111yescharacteristic
595Q8—114no—
596Q8—224no—
597Q8—222no—
598Q8—222no—
599Q8—222no—
600Q8—442no—
601D4—24no—
602D4—24no—
603D4—48no—
604D4—44no—
605D4—114no—
606D4—2216no—
607D4—224no—
608D4—222no—
609D4—222no—
610D4—222no—
611D4—448no—
612D4—442no—
613D4—888no—
614D4—888no—
615C2×C4—24no—
616C2×C4—44no—
617C2×C4—84no—
618C2×C4—114no—
619C2×C4—114no—
620C2×C4—224no—
621C2×C4—224no—
622C2×C4—224no—
623C2×C4—222no—
624C2×C4—2216no—
625C2×C4—222no—
626C2×C4—442no—
627C2×C4—448no—
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—22no—
639C8—22no—
640C8—224no—
641C22—28no—
642C22—22no—
643C22—22no—
644C22—44no—
645C22—44no—
646C22—44no—
647C22—816no—
648C22—88no—
649C22—224no—
650C22—448no—
651C22—442no—
652C22—442no—
653C22—442no—
654C22—442no—
655C22—442no—
656C22—884no—
657C22C2×#6693714yes—
658C22C2×#6693712yes—
659C22#1062328812yes—
660C22#1062329312yes—
661C22C22×D4×D1111yescharacteristic
662C4—44no—
663C4—224no—
664C4—224no—
665C4—224no—
666C4—442no—
667C4C2×#6693714yes—
668C4C2×#6693712yes—
669C4C22×#433911yescharacteristic
670C4C22×D4×D1111yescharacteristic
671C2—24no—
672C2—84no—
673C2—444no—
674C2—882no—
675C2#1307816014yesdirect product factor
676C2C22×#6693711yescharacteristic
677C2C2×#1062328811yescharacteristic
678C2C2×#1062329311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC22×C11×#102C2
socleC23×C11C22×D4
hypercenterC22×#102D11
hypocenterC11C2×#3045
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
1. C22×#66985C2semidirect
2. C22×#66957C2semidirect
3. C2×#10623336C2semidirect
4. C2×#10623035C2semidirect
5. #13078160C2direct (N × H)
6. C2×#10622380C2semidirect
7. C2×#10622375C2semidirect
8. C2×#10622400C2semidirect
9. C2×#10622399C2semidirect
10. C2×#10622715C2semidirect
11. C2×#10622579C2semidirect
12. C22×C11×#102C2semidirect
20. #10623336C22semidirect
27. C2×#66985C22semidirect
32. C22×Dic44C22semidirect
34. C2×#66957C22semidirect
35. C22×D88C22semidirect
36. C22×#4314C22semidirect
37. C22×#4314C22semidirect
39. #10623035C22semidirect
40. C2×#66946C22semidirect
43. C2×#66940C22semidirect
46. C2×C11×#102C22semidirect
47. #10622715C22semidirect
48. C2×Dic11⋊C8C22semidirect
49. C2×Dic11⋊C8C22semidirect
50. C2×#66874C22semidirect
51. #10622579C22semidirect
52. C2×#66873C22semidirect
53. #10622400C22semidirect
54. #10622399C22semidirect
55. #10622380C22semidirect
56. #10622375C22semidirect
75. C2×#4339D4semidirect
121. C2×Dic44C23semidirect
124. C2×D88C23semidirect
127. C2×#4314C23semidirect
128. C2×#4314C23semidirect
130. #66946C23semidirect
134. #66940C23semidirect
137. Dic11⋊C8C23semidirect
138. Dic11⋊C8C23semidirect
139. #66874C23semidirect
140. #66873C23semidirect
185. #4339C2×D4semidirect
246. C22×#102D11semidirect
357. C2×#102C2×D11semidirect
474. C2×C11#3045semidirect
573. C11C2×#3045semidirect
675. C2#13078160direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669852
C22×#669572
C2×#106233362
C2×#106230352
#130781602
C2×#106223802
C2×#106223752
C2×#106224002
C2×#106223992
C2×#106227152
C2×#106225792
C22×C11×#1022
C2×#304511