Finite Group Databasebeta

← C2×#13079943 #15626567

Subgroups — C2×#13079943 #15626567

Order 2816.

2210 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623008C211yesmaximal, characteristic, complemented
2C2×#10623010C211yesmaximal, characteristic, complemented
3#13079943C2116yesmaximal, direct product factor
4C2×#10622463C211yesmaximal, characteristic, complemented
5C2×#10622460C212yesmaximal, complemented
6C2×#10622455C211yesmaximal, characteristic, complemented
7C2×#10622728C212yesmaximal, complemented
8C2×#10622727C212yesmaximal, complemented
9C2×#10622461C211yesmaximal, characteristic, complemented
10C2×#10622457C212yesmaximal, complemented
11C2×#10622456C211yesmaximal, characteristic, complemented
12C22×C11×C4⋊C8C211yesmaximal, characteristic, complemented
13C22×#4339—21no—
14C23×C8×C11C2212yes—
15C22×C42×C11C2211yescharacteristic
16C2×#66983—21no—
17C2×#66983C2211yescharacteristic
18C2×#66983C2212yes—
19C2×#66982—21no—
20C2×C4×C22⋊D11—21no—
21C2×#66977C2211yescharacteristic
22C22×D88C2212yes—
23C22×#4314C2212yes—
24#10623010—24no—
25#10623010C2218yescomplemented
26C2×#66929—21no—
27#10623008—24no—
28#10623008C2218yescomplemented
29C2×#66928—21no—
30C2×#66928C2211yescharacteristic
31C2×#66927C2211yescharacteristic
32C2×C4×D44—21no—
33C2×C4×D44C2211yescharacteristic
34C2×C4×D44C2212yes—
35C2×#66925—21no—
36C2×#66923C2211yescharacteristic
37C2×#66922C2211yescharacteristic
38C2×C4×Dic22C2211yescharacteristic
39C2×C11×C4⋊C8C2211yescharacteristic
40C2×C11×C4⋊C8C2212yes—
41C2×C11×C4⋊C8C2211yescharacteristic
42C2×C11×C4⋊C8C2218yescomplemented
43#10622728C22116yescomplemented
44#10622727C22116yescomplemented
45C2×#66885C2212yes—
46C2×#66885C2212yes—
47C2×#66885C2212yes—
48C2×#66882C2212yes—
49C2×#66881C2212yes—
50C2×#66880C2212yes—
51#10622463C2218yescomplemented
52#10622461C2218yescomplemented
53#10622460C22116yescomplemented
54#10622457C22116yescomplemented
55#10622456C2218yescomplemented
56#10622455C2218yescomplemented
57C23×C4×C11D411yescharacteristic
58C23×C4×C11D411yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C22×C22⋊D11—21no—
61C22×C22⋊D11—22no—
62C2×#4339—28no—
63C2×#4339—48no—
64C22×D44—21no—
65C22×D44—21no—
66C22×D44C2312yes—
67C22×D44C2311yescharacteristic
68C22×C4×D11—21no—
69C22×C4×D11—22no—
70C22×Dic22—21no—
71C22×Dic22C2311yescharacteristic
72C22×C8×C11—44no—
73C22×C8×C11C2312yes—
74C22×C8×C11C2312yes—
75C22×C8×C11C2318yes—
76C2×C42×C11D411yescharacteristic
77C2×C42×C11D411yescharacteristic
78C2×C42×C11D414yes—
79C2×C42×C11C2311yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C2×C42×C11C2314yes—
82C2×C22⋊Dic11—21no—
83#66983—24no—
84#66983—28no—
85#66983—22no—
86#66983C2318yes—
87#66983C2314yes—
88#66982—28no—
89C4×C22⋊D11—28no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—22no—
93C2×(C2×D11)⋊C4—22no—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4—21no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2312yes—
100#66977—22no—
101#66977C2314yes—
102C2×Dic11⋊C4—21no—
103C2×Dic11⋊C4—21no—
104C2×Dic11⋊C4—21no—
105C2×Dic11⋊C4—21no—
106C2×C4×Dic11—21no—
107C2×D88—44no—
108C2×D88C2318yes—
109C2×#4314—44no—
110C2×#4314C2318yes—
111#66929—28no—
112#66928—28no—
113#66928—22no—
114#66928C2314yes—
115#66927—22no—
116#66927C2314yes—
117C4×D44—28no—
118C4×D44—24no—
119C4×D44—22no—
120C4×D44C2318yes—
121C4×D44C2314yes—
122#66925—28no—
123#66923—22no—
124#66923C2314yes—
125#66922—22no—
126#66922C2314yes—
127C4×Dic22—22no—
128C4×Dic22C2314yes—
129C11×C4⋊C8C2314yes—
130C11×C4⋊C8C2314yes—
131C11×C4⋊C8C2318yes—
132#66885C2318yes—
133#66885C2318yes—
134#66885C2318yes—
135#66882C2318yes—
136#66881C2318yes—
137#66880C2318yes—
138C2×#3247—111nomaximal, Sylow
139C24×C11C2×D411yescharacteristic
140C23×D11—21no—
141C23×D11—22no—
142C22×C4×C11—24no—
143C22×C4×C11—24no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2×D414yes—
152C22×C4×C11C2×D414yes—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2412yes—
155C22×C4×C11C2411yescharacteristic
156C2×C22⋊D11—24no—
157C2×C22⋊D11—28no—
158C2×C22⋊D11—48no—
159C2×C22⋊D11—44no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—22no—
164#4339—432no—
165C2×D44—22no—
166C2×D44—24no—
167C2×D44—21no—
168C2×D44—24no—
169C2×D44—24no—
170C2×D44—22no—
171C2×D44—24no—
172C2×D44—22no—
173C2×D44—44no—
174C2×D44—44no—
175C2×D44C2414yes—
176C2×D44C2412yes—
177C2×C4×D11—24no—
178C2×C4×D11—28no—
179C2×C4×D11—48no—
180C2×C4×D11—44no—
181C2×Dic22—21no—
182C2×Dic22—24no—
183C2×Dic22—22no—
184C2×Dic22—22no—
185C2×Dic22—44no—
186C2×Dic22C2412yes—
187C2×C8×C11—24no—
188C2×C8×C11—24no—
189C2×C8×C11—48no—
190C2×C8×C11C2414yes—
191C2×C8×C11C2414yes—
192C42×C11C2×D412yes—
193C42×C11C2×D412yes—
194C42×C11C2×D414yes—
195C42×C11C2×D414yes—
196C42×C11C2412yes—
197C42×C11C2412yes—
198C22⋊Dic11—24no—
199(C2×D11)⋊C4—24no—
200(C2×D11)⋊C4—24no—
201(C2×D11)⋊C4—28no—
202(C2×D11)⋊C4—28no—
203(C2×D11)⋊C4—24no—
204(C2×D11)⋊C4—24no—
205C4⋊Dic11—21no—
206C4⋊Dic11—22no—
207C4⋊Dic11—24no—
208C4⋊Dic11—21no—
209C4⋊Dic11C2414yes—
210C4⋊Dic11C2412yes—
211C4⋊Dic11C2412yes—
212Dic11⋊C4—24no—
213Dic11⋊C4—24no—
214Dic11⋊C4—24no—
215Dic11⋊C4—24no—
216C4×Dic11—24no—
217D88—48no—
218#4314—48no—
219C2×#532—111no—
220C2×#529—111no—
221#3247—1116no—
222C2×#477—111no—
223C2×#478—112no—
224C2×#476—111no—
225C2×#466—112no—
226C2×#465—112no—
227C2×#460—111no—
228C2×#463—112no—
229C2×#459—111no—
230C22×C4⋊C8D1111yescharacteristic, complemented
231C23×C11—22no—
232C23×C11—22no—
233C23×C11AGL(1,ℤ/8)14yes—
234C23×C11C22×D412yes—
235C23×C11C22×D411yescharacteristic
236C22×D11—22no—
237C22×D11—24no—
238C22×D11—44no—
239C22×D11—42no—
240C22×D11—42no—
241C22×D11—44no—
242C22×D11—44no—
243C22×D11—42no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—28no—
249C2×C4×C11—24no—
250C2×C4×C11—28no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11#13514yes—
254C2×C4×C11C22×D412yes—
255C2×C4×C11C22×D412yes—
256C2×C4×C11C22×D412yes—
257C2×C4×C11C22×D412yes—
258C2×C4×C11C22×D411yescharacteristic
259C2×C4×C11C22×D412yes—
260C2×C4×C11H(5,𝔽2)12yes—
261C2×C4×C112−1+412yes—
262C2×C4×C11C2511yescharacteristic
263C22⋊D11—416no—
264C22⋊D11—48no—
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—24no—
269C2×Dic11—42no—
270C2×Dic11—42no—
271C2×Dic11—44no—
272C2×Dic11—42no—
273D44—24no—
274D44—22no—
275D44—24no—
276D44—22no—
277D44—48no—
278D44—44no—
279D44—42no—
280D44—48no—
281C4×D11—416no—
282C4×D11—48no—
283Dic22—22no—
284Dic22—22no—
285Dic22—48no—
286Dic22—42no—
287C8×C11—24no—
288C8×C11—24no—
289C22×#41—221no—
290C22×SD16—112no—
291C22×D8—112no—
292C23×C8C2×D1112yes—
293#532—118no—
294#532—224no—
295C2×C4⋊Q8—111no—
296C2×#127—111no—
297#529—118no—
298#529—224no—
299C2×#126—221no—
300C2×#125—111no—
301C2×#124—111no—
302C2×#124—221no—
303C2×#123—221no—
304C2×C22⋊Q8—111no—
305C2×#121—111no—
306C2×#121—112no—
307C2×#121—221no—
308C2×C4×Q8—111no—
309C2×C4×D4—112no—
310C2×C4×D4—111no—
311C2×C4×D4—221no—
312C2×C4×D4—221no—
313C2×#117—221no—
314C22×C42C2×D1111yescharacteristic
315#478—1116no—
316#477—118no—
317#476—118no—
318#466—1116no—
319#465—1116no—
320#463—1116no—
321#460—118no—
322#459—118no—
323C2×#107—112no—
324C2×#106—112no—
325C2×C4⋊C8C2×D1112yes—
326C2×C4⋊C8C2×D1111yescharacteristic
327C2×C4⋊C8C2×D1111yescharacteristic
328C2×C4⋊C8C2×D1118yescomplemented
329C2×#103—112no—
330C2×#102—112no—
331C2×#102—112no—
332C2×#102—112no—
333C22×C11—22no—
334C22×C11—28no—
335C22×C11—22no—
336C22×C11#53712yes—
337C22×C11C2×#13512yes—
338C22×C11C2×AGL(1,ℤ/8)14yes—
339C22×C11C2×AGL(1,ℤ/8)12yes—
340C22×C11C23×D411yescharacteristic
341C2×D11—42no—
342C2×D11—44no—
343C2×D11—42no—
344C2×D11—44no—
345C2×D11—44no—
346C2×D11—42no—
347C2×D11—84no—
348C2×D11—88no—
349C4×C11—22no—
350C4×C11—22no—
351C4×C11—22no—
352C4×C11—22no—
353C4×C11#53712yes—
354C4×C11C2×#13514yes—
355C4×C11C2×H(5,𝔽2)11yescharacteristic
356C4×C11C2×2−1+411yescharacteristic
357Dic11—42no—
358Dic11—42no—
359Dic11—44no—
360Dic11—42no—
361C2×#41—228no—
362C2×#41—448no—
363C22×Q8—111no—
364C22×Q8—221no—
365C22×D4—111no—
366C22×D4—112no—
367C22×D4—221no—
368C22×D4—222no—
369C22×D4—221no—
370C22×D4—221no—
371C23×C4—221no—
372C23×C4—222no—
373C23×C4D4411yescharacteristic
374C23×C4D4411yescharacteristic
375C23×C4C22×D1111yescharacteristic
376C2×SD16—118no—
377C2×SD16—444no—
378C2×D8—118no—
379C2×D8—444no—
380C22×C8—44no—
381C22×C8C22×D1112yes—
382C22×C8C22×D1112yes—
383C22×C8C22×D1118yes—
384C4⋊Q8—114no—
385C4⋊Q8—222no—
386#127—114no—
387#127—222no—
388#126—228no—
389#125—114no—
390#125—222no—
391#124—114no—
392#124—222no—
393#124—228no—
394#123—228no—
395C22⋊Q8—114no—
396C22⋊Q8—222no—
397#121—114no—
398#121—118no—
399#121—222no—
400#121—224no—
401#121—228no—
402C4×Q8—114no—
403C4×Q8—222no—
404C4×D4—114no—
405C4×D4—118no—
406C4×D4—228no—
407C4×D4—222no—
408C4×D4—224no—
409C4×D4—228no—
410#117—228no—
411C2×C4⋊C4—112no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4—221no—
415C2×C4⋊C4—221no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4—221no—
419C2×C22⋊C4—221no—
420C2×C22⋊C4—221no—
421C2×C22⋊C4—221no—
422C2×C22⋊C4—222no—
423C2×C22⋊C4—221no—
424C2×C22⋊C4—222no—
425C2×C22⋊C4—221no—
426C2×C42—221no—
427C2×C42D4411yescharacteristic
428C2×C42D4411yescharacteristic
429C2×C42D4414yes—
430C2×C42C22×D1111yescharacteristic
431C2×C42C22×D1111yescharacteristic
432C2×C42C22×D1114yes—
433#107—118no—
434#106—118no—
435C4⋊C8C22×D1114yes—
436C4⋊C8C22×D1114yes—
437C4⋊C8C22×D1118yes—
438#103—118no—
439#102—118no—
440#102—118no—
441#102—118no—
442C2×C11—24no—
443C2×C11#324714yescomplemented
444C2×C11C2×#53711yescharacteristic
445C2×C11C22×#13511yescharacteristic
446C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
447D11—82no—
448D11—84no—
449C24—221no—
450C24—222no—
451C24C2×D4411yescharacteristic
452#41—4432no—
453C2×Q8—112no—
454C2×Q8—221no—
455C2×Q8—224no—
456C2×Q8—222no—
457C2×Q8—222no—
458C2×Q8—444no—
459C2×D4—112no—
460C2×D4—114no—
461C2×D4—224no—
462C2×D4—228no—
463C2×D4—221no—
464C2×D4—224no—
465C2×D4—222no—
466C2×D4—224no—
467C2×D4—222no—
468C2×D4—224no—
469C2×D4—222no—
470C2×D4—224no—
471C2×D4—444no—
472C2×D4—448no—
473C2×D4—444no—
474C2×D4—444no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—221no—
480C22×C4—221no—
481C22×C4—221no—
482C22×C4—222no—
483C22×C4—224no—
484C22×C4—228no—
485C22×C4—448no—
486C22×C4—444no—
487C22×C4C2×D4414yes—
488C22×C4C2×D4414yes—
489C22×C4C2×D4412yes—
490C22×C4C2×D4411yescharacteristic
491C22×C4C2×D4411yescharacteristic
492C22×C4C2×D4411yescharacteristic
493C22×C4C2×D4411yescharacteristic
494C22×C4C2×D4411yescharacteristic
495C22×C4C23×D1112yes—
496C22×C4C23×D1111yescharacteristic
497SD16—448no—
498D8—448no—
499C2×C8—24no—
500C2×C8—24no—
501C2×C8—48no—
502C2×C8C23×D1114yes—
503C2×C8C23×D1114yes—
504C4⋊C4—112no—
505C4⋊C4—112no—
506C4⋊C4—114no—
507C4⋊C4—222no—
508C4⋊C4—221no—
509C4⋊C4—221no—
510C4⋊C4—224no—
511C4⋊C4—224no—
512C4⋊C4—224no—
513C4⋊C4—224no—
514C4⋊C4—224no—
515C22⋊C4—224no—
516C22⋊C4—224no—
517C22⋊C4—224no—
518C22⋊C4—228no—
519C22⋊C4—224no—
520C22⋊C4—228no—
521C22⋊C4—224no—
522C42—224no—
523C42C2×D4414yes—
524C42C2×D4412yes—
525C42C2×D4412yes—
526C42C2×D4414yes—
527C42C23×D1112yes—
528C42C23×D1112yes—
529C11C2×#324711yescharacteristic, complemented, Sylow
530C23—22no—
531C23—22no—
532C23—222no—
533C23—224no—
534C23—442no—
535C23—444no—
536C23—444no—
537C23—442no—
538C23—442no—
539C23—444no—
540C23#6696114yes—
541C23C22×D4412yes—
542C23C22×D4411yescharacteristic
543Q8—222no—
544Q8—222no—
545Q8—448no—
546Q8—442no—
547D4—222no—
548D4—224no—
549D4—222no—
550D4—224no—
551D4—448no—
552D4—4416no—
553D4—448no—
554D4—448no—
555D4—442no—
556D4—444no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—28no—
561C2×C4—22no—
562C2×C4—28no—
563C2×C4—24no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—222no—
567C2×C4—222no—
568C2×C4—222no—
569C2×C4—224no—
570C2×C4—4416no—
571C2×C4—442no—
572C2×C4—444no—
573C2×C4—442no—
574C2×C4—442no—
575C2×C4—448no—
576C2×C4#6695714yes—
577C2×C4C22×D4412yes—
578C2×C4C22×D4412yes—
579C2×C4C22×D4412yes—
580C2×C4C22×D4412yes—
581C2×C4C22×D4412yes—
582C2×C4C22×D4411yescharacteristic
583C2×C4#6703712yes—
584C2×C4#6704012yes—
585C2×C4C24×D1111yescharacteristic
586C8—24no—
587C8—24no—
588C22—22no—
589C22—28no—
590C22—22no—
591C22—442no—
592C22—444no—
593C22—442no—
594C22—444no—
595C22—444no—
596C22—442no—
597C22—884no—
598C22—888no—
599C22#1062304112yes—
600C22C2×#6695712yes—
601C22C2×#6696114yes—
602C22C2×#6696112yes—
603C22C23×D4411yescharacteristic
604C4—22no—
605C4—22no—
606C4—22no—
607C4—22no—
608C4—442no—
609C4—442no—
610C4—444no—
611C4—442no—
612C4#1062304112yes—
613C4C2×#6695714yes—
614C4C2×#6703711yescharacteristic
615C4C2×#6704011yescharacteristic
616C2—24no—
617C2—882no—
618C2—884no—
619C2#1307994314yesdirect product factor
620C2C2×#1062304111yescharacteristic
621C2C22×#6695711yescharacteristic
622C2C22×#6696111yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC22×C11×C4⋊C8C2
socleC23×C11C22×D4
hypercenterC22×C4⋊C8D11
hypocenterC11C2×#3247
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×C4⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#10623008C2semidirect
2. C2×#10623010C2semidirect
3. #13079943C2direct (N × H)
4. C2×#10622463C2semidirect
5. C2×#10622460C2semidirect
6. C2×#10622455C2semidirect
7. C2×#10622728C2semidirect
8. C2×#10622727C2semidirect
9. C2×#10622461C2semidirect
10. C2×#10622457C2semidirect
11. C2×#10622456C2semidirect
12. C22×C11×C4⋊C8C2semidirect
25. #10623010C22semidirect
28. #10623008C22semidirect
42. C2×C11×C4⋊C8C22semidirect
43. #10622728C22semidirect
44. #10622727C22semidirect
51. #10622463C22semidirect
52. #10622461C22semidirect
53. #10622460C22semidirect
54. #10622457C22semidirect
55. #10622456C22semidirect
56. #10622455C22semidirect
230. C22×C4⋊C8D11semidirect
328. C2×C4⋊C8C2×D11semidirect
443. C2×C11#3247semidirect
529. C11C2×#3247semidirect
619. C2#13079943direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230082
C2×#106230102
#130799432
C2×#106224632
C2×#106224602
C2×#106224552
C2×#106227282
C2×#106227272
C2×#106224612
C2×#106224572
C2×#106224562
C22×C11×C4⋊C82
C2×#324711