Finite Group Databasebeta

← C2×#13080261 #15628918

Subgroups — C2×#13080261 #15628918

Order 2816.

2742 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66971C212yesmaximal, complemented
2C2×#10623258C211yesmaximal, characteristic, complemented
3C2×#10623257C211yesmaximal, characteristic
4#13080261C2116yesmaximal, direct product factor
5C2×#10622802C212yesmaximal, complemented
6C2×#10622703C211yesmaximal, characteristic, complemented
7C2×#10622696C211yesmaximal, characteristic, complemented
8C2×#10622800C212yesmaximal, complemented
9C2×#10622799C212yesmaximal, complemented
10C2×C4×#4314C211yesmaximal, characteristic, complemented
11C2×#10622301C211yesmaximal, characteristic, complemented
12C2×C11×#494C211yesmaximal, characteristic, complemented
13C22×#4343C2212yes—
14C22×Q8×D11C2212yes—
15C22×C11×Q16C2212yes—
16C22×C11×Q16C2212yes—
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×C11×C4⋊Q8C2211yescharacteristic
19C2×#66999C2212yes—
20C2×#66999C2212yes—
21C22×#4326C2212yes—
22C22×#4325C2212yes—
23C2×#66971—216no—
24C2×#66971C22116yescomplemented
25C22×#4314C2211yescharacteristic
26C22×#4313C2212yes—
27#10623258—24no—
28#10623258C2218yescomplemented
29#10623257—24no—
30#10623257C2218yes—
31C2×#66949—22no—
32C2×#66948—21no—
33C2×#66947—22no—
34C2×#66946—21no—
35C2×C4⋊C4×D11—21no—
36C2×#66941—21no—
37C2×C4×D44C2211yescharacteristic
38C2×C4×D44C2211yescharacteristic
39C2×C4×Dic22C2211yescharacteristic
40C11×#494C2218yescomplemented
41C2×C4×C8×C11C2211yescharacteristic
42C2×#66899C2212yes—
43C2×#66899C2212yes—
44#10622802C22116yescomplemented
45#10622800C22116yescomplemented
46#10622799C22116yescomplemented
47C2×#66885C2211yescharacteristic
48C2×(C2×D11)⋊C8C2212yes—
49C2×#66881C2211yescharacteristic
50C2×#66880C2211yescharacteristic
51#10622703C2218yescomplemented
52#10622696C2218yescomplemented
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C4×#4314C2218yescomplemented
55#10622301C2218yescomplemented
56C22×Q8×C11C2312yes—
57C22×Q8×C11C2312yes—
58C2×#4343—24no—
59C2×#4343—28no—
60C2×#4343—44no—
61C2×#4343C2318yes—
62C2×Q8×D11—24no—
63C2×Q8×D11—28no—
64C2×Q8×D11—44no—
65C2×Q8×D11C2318yes—
66C22×D44—22no—
67C22×D44D411yescharacteristic
68C22×D44C2311yescharacteristic
69C22×C4×D11—22no—
70C22×C4×D11—21no—
71C22×C4×D11—22no—
72C22×C4×D11C2312yes—
73C22×Dic22—22no—
74C22×Dic22C2311yescharacteristic
75C2×C11×Q16—28no—
76C2×C11×Q16—44no—
77C2×C11×Q16C2318yes—
78C2×C11×Q16C2318yes—
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C11×C4⋊Q8—22no—
82C11×C4⋊Q8—22no—
83C11×C4⋊Q8C2314yes—
84C11×C4⋊Q8C2314yes—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—21no—
89C2×C42×C11C2311yescharacteristic
90#66999—24no—
91#66999—24no—
92#66999C2318yes—
93#66999C2318yes—
94C2×#4326—28no—
95C2×#4326C2318yes—
96C2×#4325—28no—
97C2×#4325C2318yes—
98C2×(C2×D11)⋊C4—22no—
99C2×(C2×D11)⋊C4—22no—
100C2×(C2×D11)⋊C4—21no—
101C2×(C2×D11)⋊C4D412yes—
102C2×C4⋊Dic11D411yescharacteristic
103C2×C4⋊Dic11C2311yescharacteristic
104C2×C4⋊Dic11C2311yescharacteristic
105C2×Dic11⋊C4—21no—
106C2×Dic11⋊C4—22no—
107C2×Dic11⋊C4—22no—
108C2×C4×Dic11—21no—
109C22×C11⋊C8C2312yes—
110#66971—264no—
111C2×#4314D418yescomplemented
112C2×#4314C2314yes—
113C2×#4313—28no—
114C2×#4313C2318yes—
115#66949—216no—
116#66948—28no—
117#66947—216no—
118#66946—28no—
119C4⋊C4×D11—28no—
120#66941—28no—
121C4×D44—22no—
122C4×D44D414yes—
123C4×D44C2314yes—
124C4×D44C2314yes—
125C4×Dic22—22no—
126C4×Dic22C2314yes—
127C4×C8×C11C2314yes—
128#66899C2318yes—
129#66899C2318yes—
130#66885C2314yes—
131(C2×D11)⋊C8C2318yes—
132#66881C2314yes—
133#66880C2314yes—
134C4⋊(C11⋊C8)C2314yes—
135C2×#3276—111nomaximal, Sylow
136C23×D11—21no—
137C23×D11C2×D412yes—
138C2×Q8×C11—22no—
139C2×Q8×C11—22no—
140C2×Q8×C11—24no—
141C2×Q8×C11—24no—
142C2×Q8×C11—24no—
143C2×Q8×C11—24no—
144C2×Q8×C11C2414yes—
145C2×Q8×C11C2414yes—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2411yescharacteristic
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11C2×D412yes—
155#4343—216no—
156#4343—48no—
157#4343—416no—
158Q8×D11—216no—
159Q8×D11—48no—
160Q8×D11—416no—
161C2×D44—28no—
162C2×D44—24no—
163C2×D44—21no—
164C2×D44—22no—
165C2×D44—48no—
166C2×D44C2×D414yes—
167C2×D44C2×D414yes—
168C2×D44C2412yes—
169C2×C4×D11—28no—
170C2×C4×D11—28no—
171C2×C4×D11—24no—
172C2×C4×D11—24no—
173C2×C4×D11—24no—
174C2×C4×D11—48no—
175C2×C4×D11—48no—
176C2×C4×D11—44no—
177C2×C4×D11C2×D414yes—
178C2×C4×D11C2414yes—
179C2×Dic22—28no—
180C2×Dic22—21no—
181C2×Dic22—22no—
182C2×Dic22—48no—
183C2×Dic22C2×D414yes—
184C2×Dic22C2412yes—
185C11×Q16—216no—
186C11×Q16—48no—
187C2×C8×C11—22no—
188C2×C8×C11C2×D414yes—
189C2×C8×C11C2412yes—
190C2×C8×C11C2412yes—
191C11×C4⋊C4—24no—
192C11×C4⋊C4—24no—
193C11×C4⋊C4—24no—
194C11×C4⋊C4—24no—
195C42×C11C2×D412yes—
196C42×C11C2412yes—
197#4326—216no—
198#4325—216no—
199(C2×D11)⋊C4—28no—
200(C2×D11)⋊C4—28no—
201(C2×D11)⋊C4—24no—
202(C2×D11)⋊C4C2×D418yes—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11C2×D414yes—
206C4⋊Dic11C2412yes—
207C4⋊Dic11C2412yes—
208Dic11⋊C4—28no—
209Dic11⋊C4—28no—
210Dic11⋊C4—24no—
211C4×Dic11—24no—
212C2×C11⋊C8—24no—
213C2×C11⋊C8C2414yes—
214#4314C2×D4116yescomplemented
215#4313—216no—
216C22×#137—112no—
217C2×D4×Q8—111no—
218C2×#547—111no—
219#3276—1116no—
220C2×#494D1111yescharacteristic, complemented
221C2×#470—112no—
222C2×#462—111no—
223C2×#461—111no—
224C2×#452—112no—
225C2×#451—112no—
226C2×C4×SD16—111no—
227C2×#436—111no—
228C23×C11C22×D411yescharacteristic
229C22×D11—24no—
230C22×D11—24no—
231C22×D11—24no—
232C22×D11—24no—
233C22×D11—22no—
234C22×D11—42no—
235C22×D11—42no—
236C22×D11C22×D414yes—
237Q8×C11—24no—
238Q8×C11—24no—
239Q8×C11—24no—
240Q8×C11—24no—
241Q8×C11—44no—
242Q8×C11—44no—
243C2×C4×C11—22no—
244C2×C4×C11—24no—
245C2×C4×C11—24no—
246C2×C4×C11—44no—
247C2×C4×C11—44no—
248C2×C4×C11#13714yescomplemented
249C2×C4×C11C22×D412yes—
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C22×D412yes—
252C2×C4×C11C22×D412yes—
253C2×C4×C11H(5,𝔽2)12yes—
254C2×C4×C11C2511yescharacteristic
255C2×Dic11—24no—
256C2×Dic11—24no—
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—22no—
260C2×Dic11—42no—
261C2×Dic11—42no—
262C2×Dic11C22×D414yes—
263D44—24no—
264D44—28no—
265D44—22no—
266D44—416no—
267D44C22×D414yes—
268C4×D11—28no—
269C4×D11—24no—
270C4×D11—24no—
271C4×D11—416no—
272C4×D11—416no—
273C4×D11—48no—
274Dic22—24no—
275Dic22—22no—
276Dic22—416no—
277Dic22C22×D414yes—
278C8×C11—22no—
279C8×C11C22×D414yes—
280C11⋊C8—24no—
281C22×#41—112no—
282C23×Q8—112no—
283C2×#137—1116no—
284C2×#137—2216no—
285C22×Q16—112no—
286C22×Q16C2×D1112yes—
287C22×Q16C2×D1112yes—
288C22×SD16—112no—
289C22×SD16—111no—
290C22×M16—112no—
291D4×Q8—118no—
292D4×Q8—224no—
293#547—118no—
294#547—224no—
295C2×C4⋊Q8—221no—
296C2×C4⋊Q8C2×D1111yescharacteristic
297C2×C4⋊Q8C2×D1111yescharacteristic
298C2×#123—222no—
299C2×C22⋊Q8—112no—
300C2×C22⋊Q8—112no—
301C2×C22⋊Q8—222no—
302C2×#121—221no—
303C2×C4×Q8—111no—
304C2×C4×D4—111no—
305C2×C4×D4—111no—
306C2×C4×D4—221no—
307C22×C4⋊C4—221no—
308#494C2×D1118yescomplemented
309#470—1116no—
310#462—118no—
311#461—118no—
312#452—1116no—
313#451—1116no—
314C4×SD16—118no—
315#436—118no—
316C2×#106—111no—
317C2×C4⋊C8—111no—
318C2×#103—112no—
319C2×#103—112no—
320C2×#103—111no—
321C2×#102—111no—
322C2×C22⋊C8—112no—
323C2×C4×C8C2×D1111yescharacteristic
324C22×C11D4212yes—
325C22×C11C2×#13712yes—
326C22×C11#57812yes—
327C22×C11C23×D411yescharacteristic
328C2×D11—24no—
329C2×D11—24no—
330C2×D11—24no—
331C2×D11—24no—
332C2×D11—48no—
333C2×D11—48no—
334C2×D11—42no—
335C2×D11—42no—
336C4×C11—22no—
337C4×C11—44no—
338C4×C11—44no—
339C4×C11D4212yes—
340C4×C11C2×#13714yescomplemented
341C4×C11C23×D411yescharacteristic
342C4×C11C2×H(5,𝔽2)11yescharacteristic
343Dic11—24no—
344Dic11—24no—
345Dic11—42no—
346Dic11—42no—
347C2×#41—118no—
348C2×#41—224no—
349C2×#41—228no—
350C2×#41—444no—
351C22×Q8—118no—
352C22×Q8—111no—
353C22×Q8—222no—
354C22×Q8—224no—
355C22×Q8—228no—
356C22×Q8—444no—
357C22×Q8C22×D1112yes—
358C22×Q8C22×D1112yes—
359C22×D4—111no—
360C22×D4—111no—
361C22×D4—222no—
362C23×C4—112no—
363C23×C4—222no—
364C23×C4—222no—
365C23×C4—221no—
366#137—2264no—
367C2×Q16—28no—
368C2×Q16—44no—
369C2×Q16—118no—
370C2×Q16—228no—
371C2×Q16C22×D1118yes—
372C2×Q16C22×D1118yes—
373C2×SD16—118no—
374C2×SD16—118no—
375C2×SD16—114no—
376C2×SD16—228no—
377C2×M16—118no—
378C2×M16—228no—
379C22×C8—112no—
380C22×C8C22×D1111yescharacteristic
381C22×C8C22×D1111yescharacteristic
382C4⋊Q8—22no—
383C4⋊Q8—22no—
384C4⋊Q8—228no—
385C4⋊Q8C22×D1114yes—
386C4⋊Q8C22×D1114yes—
387#123—2216no—
388C22⋊Q8—118no—
389C22⋊Q8—118no—
390C22⋊Q8—2216no—
391C22⋊Q8—224no—
392C22⋊Q8—224no—
393#121—228no—
394C4×Q8—114no—
395C4×Q8—222no—
396C4×D4—114no—
397C4×D4—114no—
398C4×D4—114no—
399C4×D4—228no—
400C4×D4—222no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—111no—
407C2×C4⋊C4—111no—
408C2×C4⋊C4—228no—
409C2×C4⋊C4—222no—
410C2×C4⋊C4—222no—
411C2×C4⋊C4—221no—
412C2×C22⋊C4—112no—
413C2×C22⋊C4—222no—
414C2×C22⋊C4—222no—
415C2×C22⋊C4—221no—
416C2×C42—221no—
417C2×C42C22×D1111yescharacteristic
418#106—114no—
419C4⋊C8—114no—
420#103—118no—
421#103—118no—
422#103—114no—
423#102—114no—
424C22⋊C8—118no—
425C4×C8C22×D1114yes—
426C2×C11#327614yescomplemented
427C2×C11C2×D4211yescharacteristic
428C2×C11C22×#13711yescharacteristic
429C2×C11C2×#57811yescharacteristic
430D11—44no—
431D11—44no—
432C24—112no—
433C24—221no—
434#41—2216no—
435#41—448no—
436#41—4416no—
437C2×Q8—22no—
438C2×Q8—22no—
439C2×Q8—24no—
440C2×Q8—24no—
441C2×Q8—24no—
442C2×Q8—24no—
443C2×Q8—114no—
444C2×Q8—112no—
445C2×Q8—228no—
446C2×Q8—221no—
447C2×Q8—222no—
448C2×Q8—2216no—
449C2×Q8—448no—
450C2×Q8—448no—
451C2×Q8—4416no—
452C2×Q8C23×D1114yes—
453C2×Q8C23×D1114yes—
454C2×D4—114no—
455C2×D4—114no—
456C2×D4—112no—
457C2×D4—228no—
458C2×D4—224no—
459C2×D4—221no—
460C2×D4—222no—
461C2×D4—448no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—112no—
465C22×C4—114no—
466C22×C4—114no—
467C22×C4—228no—
468C22×C4—228no—
469C22×C4—221no—
470C22×C4—224no—
471C22×C4—224no—
472C22×C4—221no—
473C22×C4—221no—
474C22×C4—224no—
475C22×C4—448no—
476C22×C4—448no—
477C22×C4—444no—
478C22×C4D4×D1111yescharacteristic
479C22×C4D4×D1111yescharacteristic
480C22×C4C23×D1111yescharacteristic
481Q16—216no—
482Q16—48no—
483Q16—2216no—
484SD16—1116no—
485SD16—2216no—
486M16—2216no—
487C2×C8—22no—
488C2×C8—114no—
489C2×C8—224no—
490C2×C8D4×D1114yes—
491C2×C8C23×D1112yes—
492C2×C8C23×D1112yes—
493C4⋊C4—24no—
494C4⋊C4—24no—
495C4⋊C4—24no—
496C4⋊C4—24no—
497C4⋊C4—114no—
498C4⋊C4—112no—
499C4⋊C4—112no—
500C4⋊C4—228no—
501C4⋊C4—228no—
502C4⋊C4—221no—
503C4⋊C4—221no—
504C4⋊C4—224no—
505C22⋊C4—118no—
506C22⋊C4—228no—
507C22⋊C4—228no—
508C22⋊C4—224no—
509C42—224no—
510C42D4×D1112yes—
511C42C23×D1112yes—
512C11C2×#327611yescharacteristic, complemented, Sylow
513C23—114no—
514C23—224no—
515C23—224no—
516C23—224no—
517C23—224no—
518C23—222no—
519C23—442no—
520C23—442no—
521C23C2×D4×D1111yescharacteristic
522Q8—24no—
523Q8—24no—
524Q8—24no—
525Q8—24no—
526Q8—44no—
527Q8—44no—
528Q8—114no—
529Q8—224no—
530Q8—222no—
531Q8—4416no—
532D4—114no—
533D4—224no—
534D4—228no—
535D4—222no—
536D4—4416no—
537C2×C4—22no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—44no—
541C2×C4—44no—
542C2×C4—114no—
543C2×C4—224no—
544C2×C4—224no—
545C2×C4—222no—
546C2×C4—228no—
547C2×C4—224no—
548C2×C4—224no—
549C2×C4—222no—
550C2×C4—222no—
551C2×C4—4416no—
552C2×C4—4416no—
553C2×C4—442no—
554C2×C4—442no—
555C2×C4—448no—
556C2×C4#6697114yescomplemented
557C2×C4C2×D4×D1112yes—
558C2×C4C2×D4×D1111yescharacteristic
559C2×C4C2×D4×D1112yes—
560C2×C4C2×D4×D1112yes—
561C2×C4#6703712yes—
562C2×C4C24×D1111yescharacteristic
563C8—22no—
564C8—224no—
565C8C2×D4×D1114yes—
566C22—224no—
567C22—224no—
568C22—224no—
569C22—224no—
570C22—448no—
571C22—448no—
572C22—442no—
573C22—442no—
574C22#1062324812yes—
575C22C2×#6697112yes—
576C22#1062329712yes—
577C22C22×D4×D1111yescharacteristic
578C4—22no—
579C4—44no—
580C4—44no—
581C4—224no—
582C4—224no—
583C4—442no—
584C4—442no—
585C4#1062324812yes—
586C4C2×#6697114yescomplemented
587C4C22×D4×D1111yescharacteristic
588C4C2×#6703711yescharacteristic
589C2—444no—
590C2—444no—
591C2#1308026114yesdirect product factor
592C2C2×#1062324811yescharacteristic
593C2C22×#6697111yescharacteristic
594C2C2×#1062329711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#494C2
socleC23×C11C22×D4
prime radicalC2×#10623257C2
hypercenterC2×#494D11
hypocenterC11C2×#3276
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#494

Complements

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

NH ≅ G/Ntype
1. C22×#66971C2semidirect
2. C2×#10623258C2semidirect
4. #13080261C2direct (N × H)
5. C2×#10622802C2semidirect
6. C2×#10622703C2semidirect
7. C2×#10622696C2semidirect
8. C2×#10622800C2semidirect
9. C2×#10622799C2semidirect
10. C2×C4×#4314C2semidirect
11. C2×#10622301C2semidirect
12. C2×C11×#494C2semidirect
24. C2×#66971C22semidirect
28. #10623258C22semidirect
40. C11×#494C22semidirect
44. #10622802C22semidirect
45. #10622800C22semidirect
46. #10622799C22semidirect
51. #10622703C22semidirect
52. #10622696C22semidirect
54. C4×#4314C22semidirect
55. #10622301C22semidirect
111. C2×#4314D4semidirect
214. #4314C2×D4semidirect
220. C2×#494D11semidirect
248. C2×C4×C11#137semidirect
308. #494C2×D11semidirect
340. C4×C11C2×#137semidirect
426. C2×C11#3276semidirect
512. C11C2×#3276semidirect
556. C2×C4#66971semidirect
586. C4C2×#66971semidirect
591. C2#13080261direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669712
C2×#106232582
C2×#106232572
#130802612
C2×#106228022
C2×#106227032
C2×#106226962
C2×#106228002
C2×#106227992
C2×C4×#43142
C2×#106223012
C2×C11×#4942
C2×#327611