Finite Group Databasebeta

← C2×#13079940 #15626564

Subgroups — C2×#13079940 #15626564

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×#10623247C211yesmaximal, characteristic, complemented
2C2×#10623111C211yesmaximal, characteristic, complemented
3#13079940C2116yesmaximal, direct product factor
4C2×#10622634C211yesmaximal, characteristic, complemented
5C2×#10622376C212yesmaximal, complemented
6C2×#10622455C211yesmaximal, characteristic, complemented
7C2×#10622388C212yesmaximal, complemented
8C2×#10622784C212yesmaximal, complemented
9C2×#10622778C212yesmaximal, complemented
10C2×#10622685C211yesmaximal, characteristic, complemented
11C2×D11×C4⋊C8C211yesmaximal, characteristic, complemented
12C2×C11×#460C211yesmaximal, characteristic, complemented
13C22×#4341—21no—
14C22×C11×SD16C2212yes—
15C2×C11×#127C2211yescharacteristic
16C2×C4×Q8×C11C2211yescharacteristic
17C2×#67000C2211yescharacteristic
18C2×#66999C2211yescharacteristic
19C2×#66991—21no—
20C2×#66991C2212yes—
21C2×#66989—21no—
22C2×D4×Dic11—21no—
23C2×D4×Dic11C2212yes—
24C22×#4323C2212yes—
25C22×C8×D11C2212yes—
26#10623247—24no—
27#10623247C2218yescomplemented
28#10623111—24no—
29#10623111C2218yescomplemented
30C2×#66951—21no—
31C2×#66948C2211yescharacteristic
32C2×#66947—21no—
33C2×#66943C2211yescharacteristic
34C2×C4×D44—21no—
35C2×C4×D44C2211yescharacteristic
36C2×#66925—21no—
37C2×C42×D11C2211yescharacteristic
38C2×#66922C2211yescharacteristic
39C11×#460C2218yescomplemented
40C2×C11×C4⋊C8C2211yescharacteristic
41C2×C11×#102C2212yes—
42C2×#66899C2212yes—
43C2×#66896C2212yes—
44#10622784C22116yescomplemented
45#10622778C22116yescomplemented
46C2×#66885C2212yes—
47C2×#66881C2212yes—
48C2×Dic11⋊C8C2212yes—
49#10622685C2218yescomplemented
50#10622634C2218yescomplemented
51C2×#66871C2212yes—
52C2×C4⋊(C11⋊C8)C2211yescharacteristic
53#10622455C2218yescomplemented
54D11×C4⋊C8C2218yescomplemented
55#10622388C22116yescomplemented
56#10622376C22116yescomplemented
57C22×Q8×C11C2311yescharacteristic
58C22×D4×C11—21no—
59C22×D4×C11—21no—
60C22×D4×C11C2312yes—
61C22×C22⋊D11—22no—
62C23×Dic11—22no—
63C2×#4341—28no—
64C2×#4341—48no—
65C22×D44—21no—
66C22×D44C2311yescharacteristic
67C22×C4×D11—21no—
68C22×C4×D11D411yescharacteristic
69C22×C4×D11D411yescharacteristic
70C22×C4×D11C2311yescharacteristic
71C22×Dic22—21no—
72C2×C11×SD16—44no—
73C2×C11×SD16C2318yes—
74C22×C8×C11C2312yes—
75C11×#127—22no—
76C11×#127C2314yes—
77C4×Q8×C11—22no—
78C4×Q8×C11C2314yes—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C42×C11—21no—
82C2×C42×C11C2311yescharacteristic
83C2×C22⋊Dic11—22no—
84C2×C22⋊Dic11—22no—
85#67000—22no—
86#67000C2314yes—
87#66999—22no—
88#66999C2314yes—
89#66991—24no—
90#66991—28no—
91#66991C2318yes—
92#66989—28no—
93D4×Dic11—24no—
94D4×Dic11—28no—
95D4×Dic11C2318yes—
96C2×#4323—44no—
97C2×#4323C2318yes—
98C2×(C2×D11)⋊C4—21no—
99C2×(C2×D11)⋊C4—21no—
100C2×(C2×D11)⋊C4—21no—
101C2×(C2×D11)⋊C4—21no—
102C2×(C2×D11)⋊C4—21no—
103C2×C4⋊Dic11—21no—
104C2×C4⋊Dic11—21no—
105C2×C4⋊Dic11C2312yes—
106C2×C4⋊Dic11C2311yescharacteristic
107C2×Dic11⋊C4—21no—
108C2×Dic11⋊C4—21no—
109C2×C4×Dic11D411yescharacteristic
110C2×C4×Dic11D411yescharacteristic
111C2×C4×Dic11C2311yescharacteristic
112C22×C11⋊C8C2312yes—
113C2×C8×D11—44no—
114C2×C8×D11C2318yes—
115#66951—28no—
116#66948—22no—
117#66948C2314yes—
118#66947—28no—
119#66943—22no—
120#66943C2314yes—
121C4×D44—28no—
122C4×D44—22no—
123C4×D44C2314yes—
124#66925—28no—
125C42×D11D414yes—
126C42×D11C2314yes—
127#66922—22no—
128#66922C2314yes—
129C11×C4⋊C8C2314yes—
130C11×#102C2318yes—
131#66899C2318yes—
132#66896C2318yes—
133#66885C2318yes—
134#66881C2318yes—
135Dic11⋊C8C2318yes—
136#66871C2318yes—
137C4⋊(C11⋊C8)C2314yes—
138C2×#3247—111nomaximal, Sylow
139C24×C11—22no—
140C23×D11—21no—
141C23×D11C2×D411yescharacteristic
142C2×Q8×C11—21no—
143C2×Q8×C11—22no—
144C2×Q8×C11—22no—
145C2×Q8×C11C2412yes—
146C2×D4×C11—22no—
147C2×D4×C11—24no—
148C2×D4×C11—24no—
149C2×D4×C11—24no—
150C2×D4×C11—24no—
151C2×D4×C11—44no—
152C2×D4×C11—44no—
153C2×D4×C11C2414yes—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2411yescharacteristic
159C2×C22⋊D11—28no—
160C2×C22⋊D11—48no—
161C22×Dic11—28no—
162C22×Dic11—21no—
163C22×Dic11—22no—
164C22×Dic11—48no—
165C22×Dic11C2×D411yescharacteristic
166C22×Dic11C2×D411yescharacteristic
167C22×Dic11C2×D411yescharacteristic
168#4341—432no—
169C2×D44—24no—
170C2×D44—21no—
171C2×D44—22no—
172C2×D44—22no—
173C2×D44—44no—
174C2×D44C2412yes—
175C2×C4×D11—24no—
176C2×C4×D11—24no—
177C2×C4×D11—24no—
178C2×C4×D11—22no—
179C2×C4×D11—22no—
180C2×C4×D11—44no—
181C2×C4×D11C2×D412yes—
182C2×C4×D11C2×D414yes—
183C2×C4×D11C2×D414yes—
184C2×C4×D11C2412yes—
185C2×Dic22—24no—
186C2×Dic22—44no—
187C11×SD16—48no—
188C2×C8×C11—24no—
189C2×C8×C11C2414yes—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—24no—
192C11×C4⋊C4C2412yes—
193C42×C11—24no—
194C42×C11C2×D412yes—
195C42×C11C2412yes—
196C22⋊Dic11—28no—
197C22⋊Dic11—28no—
198#4323—48no—
199(C2×D11)⋊C4—24no—
200(C2×D11)⋊C4—24no—
201(C2×D11)⋊C4—24no—
202(C2×D11)⋊C4—24no—
203(C2×D11)⋊C4—24no—
204C4⋊Dic11—24no—
205C4⋊Dic11—22no—
206C4⋊Dic11—24no—
207C4⋊Dic11—21no—
208C4⋊Dic11C2414yes—
209C4⋊Dic11C2412yes—
210Dic11⋊C4—24no—
211Dic11⋊C4—24no—
212C4×Dic11C2×D412yes—
213C4×Dic11C2×D414yes—
214C4×Dic11C2×D414yes—
215C4×Dic11C2412yes—
216C2×C11⋊C8—24no—
217C2×C11⋊C8C2414yes—
218C8×D11—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×#460D1111yescharacteristic, complemented
228C2×#463—112no—
229C2×#459—111no—
230C22×C4⋊C8—111no—
231C23×C11—24no—
232C23×C11—44no—
233C23×C11—44no—
234C23×C11—44no—
235C23×C11C22×D411yescharacteristic
236C22×D11—22no—
237C22×D11—22no—
238C22×D11—22no—
239C22×D11—42no—
240C22×D11—42no—
241C22×D11—42no—
242C22×D11AGL(1,ℤ/8)14yes—
243C22×D11C22×D412yes—
244Q8×C11—22no—
245Q8×C11—22no—
246Q8×C11—42no—
247D4×C11—24no—
248D4×C11—24no—
249D4×C11—48no—
250D4×C11—44no—
251D4×C11—48no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—42no—
256C2×C4×C11—42no—
257C2×C4×C11#13514yes—
258C2×C4×C11C22×D412yes—
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C22×D412yes—
261C2×C4×C11H(5,𝔽2)12yes—
262C2×C4×C112−1+412yes—
263C2×C4×C11C2511yescharacteristic
264C22⋊D11—416no—
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—24no—
270C2×Dic11—416no—
271C2×Dic11—42no—
272C2×Dic11—44no—
273C2×Dic11C22×D412yes—
274C2×Dic11C22×D412yes—
275C2×Dic11C22×D412yes—
276D44—22no—
277D44—22no—
278D44—48no—
279D44—42no—
280C4×D11—28no—
281C4×D11—24no—
282C4×D11—28no—
283C4×D11—22no—
284C4×D11—22no—
285C4×D11—48no—
286Dic22—48no—
287C8×C11—24no—
288C11⋊C8—24no—
289C22×#41—221no—
290C22×SD16C2×D1112yes—
291C22×D8—112no—
292C23×C8—112no—
293#532—118no—
294#532—224no—
295C2×C4⋊Q8—111no—
296C2×#127C2×D1111yescharacteristic
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—112no—
306C2×#121—111no—
307C2×#121—221no—
308C2×C4×Q8C2×D1111yescharacteristic
309C2×C4×D4—112no—
310C2×C4×D4—111no—
311C2×C4×D4—221no—
312C2×C4×D4—221no—
313C2×#117—221no—
314C22×C42—111no—
315#478—1116no—
316#477—118no—
317#476—118no—
318#466—1116no—
319#465—1116no—
320#463—1116no—
321#460C2×D1118yescomplemented
322#459—118no—
323C2×#107—112no—
324C2×#106—112no—
325C2×C4⋊C8—112no—
326C2×C4⋊C8—111no—
327C2×C4⋊C8—118no—
328C2×C4⋊C8C2×D1111yescharacteristic
329C2×#103—112no—
330C2×#102—112no—
331C2×#102—112no—
332C2×#102C2×D1112yes—
333C22×C11—44no—
334C22×C11—44no—
335C22×C11—44no—
336C22×C11—88no—
337C22×C11#53712yes—
338C22×C11C2×#13512yes—
339C22×C11C2×AGL(1,ℤ/8)12yes—
340C22×C11C23×D411yescharacteristic
341C2×D11—22no—
342C2×D11—28no—
343C2×D11—22no—
344C2×D11—42no—
345C2×D11—42no—
346C2×D11—42no—
347C2×D11—84no—
348C2×D11C2×AGL(1,ℤ/8)14yes—
349C4×C11—22no—
350C4×C11—42no—
351C4×C11—42no—
352C4×C11#53712yes—
353C4×C11C2×#13514yes—
354C4×C11C2×H(5,𝔽2)11yescharacteristic
355C4×C11C2×2−1+411yescharacteristic
356Dic11—22no—
357Dic11—22no—
358Dic11—22no—
359Dic11—42no—
360Dic11—44no—
361C2×#41—228no—
362C2×#41—448no—
363C22×Q8—221no—
364C22×Q8C22×D1111yescharacteristic
365C22×D4—21no—
366C22×D4—21no—
367C22×D4—111no—
368C22×D4—221no—
369C22×D4—222no—
370C22×D4C22×D1112yes—
371C23×C4—111no—
372C23×C4—111no—
373C23×C4—111no—
374C23×C4—222no—
375C23×C4—221no—
376C2×SD16—44no—
377C2×SD16C22×D1118yes—
378C2×D8—118no—
379C2×D8—444no—
380C22×C8—112no—
381C22×C8—118no—
382C22×C8—444no—
383C22×C8C22×D1112yes—
384C4⋊Q8—114no—
385C4⋊Q8—222no—
386#127—22no—
387#127C22×D1114yes—
388#126—228no—
389#125—114no—
390#125—222no—
391#124—114no—
392#124—228no—
393#124—222no—
394#123—228no—
395C22⋊Q8—114no—
396C22⋊Q8—222no—
397#121—118no—
398#121—114no—
399#121—222no—
400#121—224no—
401#121—228no—
402C4×Q8—22no—
403C4×Q8C22×D1114yes—
404C4×D4—118no—
405C4×D4—114no—
406C4×D4—228no—
407C4×D4—224no—
408C4×D4—228no—
409C4×D4—222no—
410#117—228no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—112no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4—221no—
415C2×C4⋊C4—221no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4C22×D1111yescharacteristic
419C2×C22⋊C4—221no—
420C2×C22⋊C4—221no—
421C2×C22⋊C4—221no—
422C2×C22⋊C4—221no—
423C2×C22⋊C4—222no—
424C2×C22⋊C4—222no—
425C2×C22⋊C4—221no—
426C2×C42—21no—
427C2×C42—111no—
428C2×C42—111no—
429C2×C42—111no—
430C2×C42—114no—
431C2×C42—114no—
432C2×C42C22×D1111yescharacteristic
433#107—118no—
434#106—118no—
435C4⋊C8—118no—
436C4⋊C8—114no—
437C4⋊C8C22×D1114yes—
438#103—118no—
439#102—118no—
440#102—118no—
441#102C22×D1118yes—
442C2×C11—84no—
443C2×C11#324714yescomplemented
444C2×C11C2×#53711yescharacteristic
445C2×C11C22×#13511yescharacteristic
446C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
447D11—24no—
448D11—82no—
449C24—22no—
450C24—111no—
451C24—221no—
452#41—4432no—
453C2×Q8—21no—
454C2×Q8—22no—
455C2×Q8—22no—
456C2×Q8—224no—
457C2×Q8—444no—
458C2×Q8C23×D1112yes—
459C2×D4—22no—
460C2×D4—24no—
461C2×D4—24no—
462C2×D4—24no—
463C2×D4—24no—
464C2×D4—44no—
465C2×D4—44no—
466C2×D4—112no—
467C2×D4—224no—
468C2×D4—228no—
469C2×D4—221no—
470C2×D4—222no—
471C2×D4—222no—
472C2×D4—444no—
473C2×D4—448no—
474C2×D4C23×D1114yes—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—111no—
478C22×C4—111no—
479C22×C4—111no—
480C22×C4—114no—
481C22×C4—112no—
482C22×C4—114no—
483C22×C4—112no—
484C22×C4—224no—
485C22×C4—228no—
486C22×C4—224no—
487C22×C4—222no—
488C22×C4—222no—
489C22×C4—221no—
490C22×C4—222no—
491C22×C4—224no—
492C22×C4—448no—
493C22×C4—444no—
494C22×C4D4×D1111yescharacteristic
495C22×C4D4×D1111yescharacteristic
496C22×C4C23×D1111yescharacteristic
497SD16—48no—
498D8—448no—
499C2×C8—24no—
500C2×C8—114no—
501C2×C8—224no—
502C2×C8—448no—
503C2×C8C23×D1114yes—
504C4⋊C4—24no—
505C4⋊C4—21no—
506C4⋊C4—112no—
507C4⋊C4—114no—
508C4⋊C4—224no—
509C4⋊C4—224no—
510C4⋊C4—224no—
511C4⋊C4—222no—
512C4⋊C4—221no—
513C4⋊C4—224no—
514C4⋊C4C23×D1112yes—
515C22⋊C4—224no—
516C22⋊C4—224no—
517C22⋊C4—224no—
518C22⋊C4—224no—
519C22⋊C4—228no—
520C22⋊C4—228no—
521C22⋊C4—224no—
522C42—24no—
523C42—114no—
524C42—112no—
525C42—114no—
526C42—112no—
527C42D4×D1112yes—
528C42C23×D1112yes—
529C11C2×#324711yescharacteristic, complemented, Sylow
530C23—24no—
531C23—44no—
532C23—44no—
533C23—44no—
534C23—114no—
535C23—112no—
536C23—222no—
537C23—222no—
538C23—222no—
539C23—442no—
540C23—442no—
541C23—442no—
542C23C2×D4×D1111yescharacteristic
543Q8—22no—
544Q8—22no—
545Q8—42no—
546Q8—448no—
547D4—24no—
548D4—24no—
549D4—48no—
550D4—48no—
551D4—44no—
552D4—222no—
553D4—222no—
554D4—448no—
555D4—4416no—
556D4—442no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—112no—
563C2×C4—112no—
564C2×C4—112no—
565C2×C4—228no—
566C2×C4—222no—
567C2×C4—222no—
568C2×C4—222no—
569C2×C4—228no—
570C2×C4—224no—
571C2×C4—222no—
572C2×C4—222no—
573C2×C4—222no—
574C2×C4—224no—
575C2×C4—4416no—
576C2×C4—442no—
577C2×C4—444no—
578C2×C4—448no—
579C2×C4#6696914yes—
580C2×C4C2×D4×D1112yes—
581C2×C4C2×D4×D1112yes—
582C2×C4C2×D4×D1111yescharacteristic
583C2×C4#6703712yes—
584C2×C4#6704312yes—
585C2×C4C24×D1111yescharacteristic
586C8—24no—
587C8—224no—
588C22—44no—
589C22—44no—
590C22—44no—
591C22—88no—
592C22—114no—
593C22—222no—
594C22—228no—
595C22—222no—
596C22—442no—
597C22—442no—
598C22—442no—
599C22—884no—
600C22#1062313912yes—
601C22C2×#6696912yes—
602C22D11×AGL(1,ℤ/8)12yes—
603C22C22×D4×D1111yescharacteristic
604C4—22no—
605C4—42no—
606C4—42no—
607C4—222no—
608C4—222no—
609C4—222no—
610C4—442no—
611C4—444no—
612C4#1062313912yes—
613C4C2×#6696914yes—
614C4C2×#6703711yescharacteristic
615C4C2×#6704311yescharacteristic
616C2—84no—
617C2—224no—
618C2—882no—
619C2#1307994014yesdirect product factor
620C2C2×#1062313911yescharacteristic
621C2C22×#6696911yescharacteristic
622C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#460C2
socleC23×C11C22×D4
hypercenterC2×#460D11
hypocenterC11C2×#3247
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#460

Complements

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

NH ≅ G/Ntype
1. C2×#10623247C2semidirect
2. C2×#10623111C2semidirect
3. #13079940C2direct (N × H)
4. C2×#10622634C2semidirect
5. C2×#10622376C2semidirect
6. C2×#10622455C2semidirect
7. C2×#10622388C2semidirect
8. C2×#10622784C2semidirect
9. C2×#10622778C2semidirect
10. C2×#10622685C2semidirect
11. C2×D11×C4⋊C8C2semidirect
12. C2×C11×#460C2semidirect
27. #10623247C22semidirect
29. #10623111C22semidirect
39. C11×#460C22semidirect
44. #10622784C22semidirect
45. #10622778C22semidirect
49. #10622685C22semidirect
50. #10622634C22semidirect
53. #10622455C22semidirect
54. D11×C4⋊C8C22semidirect
55. #10622388C22semidirect
56. #10622376C22semidirect
227. C2×#460D11semidirect
321. #460C2×D11semidirect
443. C2×C11#3247semidirect
529. C11C2×#3247semidirect
619. C2#13079940direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232472
C2×#106231112
#130799402
C2×#106226342
C2×#106223762
C2×#106224552
C2×#106223882
C2×#106227842
C2×#106227782
C2×#106226852
C2×D11×C4⋊C82
C2×C11×#4602
C2×#324711