Finite Group Databasebeta

← C2×#13079489 #15624449

Subgroups — C2×#13079489 #15624449

Order 2816.

2314 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623356C211yesmaximal, characteristic, complemented
2C2×#10623361C211yesmaximal, characteristic
3#13079489C2116yesmaximal, direct product factor
4C2×#10622336C212yesmaximal, complemented
5C2×#10622350C212yesmaximal, complemented
6C2×#10622747C212yesmaximal, complemented
7C2×#10622727C212yesmaximal, complemented
8C2×#10622351C212yesmaximal, complemented
9C2×#10622344C212yesmaximal, complemented
10C2×C11×#408C211yesmaximal, characteristic, complemented
11C22×C11×#41C2211yescharacteristic
12C23×D44C2211yescharacteristic
13C23×Dic22C2211yescharacteristic, complemented
14C22×C11×M16C2211yescharacteristic, complemented
15C23×C8×C11C2211yescharacteristic, complemented
16#10623361—24no—
17#10623361C2218yes—
18#10623356—24no—
19#10623356C2218yescomplemented
20C2×#67000—21no—
21C2×#66997—21no—
22C2×#66993—21no—
23C2×#66990—21no—
24C2×#66990—21no—
25C2×#66989—21no—
26C2×#66988—21no—
27C2×#66988—21no—
28C2×#66983C2212yes—
29C2×#66983C2212yes—
30C2×#66979C2211yescharacteristic
31C2×#66979C2211yescharacteristic, complemented
32C2×#66977C2212yes—
33C2×#66977C2212yescomplemented
34C22×#4314C2212yes—
35C22×#4314C2212yes—
36C11×#408C2218yescomplemented
37C2×C11×C22⋊C8C2212yes—
38C2×C11×C22⋊C8C2212yescomplemented
39#10622747C22116yescomplemented
40#10622727C22116yescomplemented
41C2×#66885C2212yes—
42C2×#66885C2212yes—
43C2×#66882C2212yescomplemented
44C2×#66881C2212yescomplemented
45C2×#66880C2212yescomplemented
46C2×#66880C2212yescomplemented
47#10622351C22116yescomplemented
48#10622350C22116yescomplemented
49#10622344C22116yescomplemented
50#10622336C22116yescomplemented
51C24×D11—21no—
52C2×C11×#41—42no—
53C2×C11×#41—42no—
54C2×C11×#41D414yes—
55C2×C11×#41C2314yes—
56C22×Q8×C11D411yescharacteristic
57C22×D4×C11D411yescharacteristic
58C22×D4×C11D411yescharacteristic
59C22×D4×C11D411yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C22×C22⋊D11—22no—
64C22×C22⋊D11—22no—
65C23×Dic11—21no—
66C22×D44—21no—
67C22×D44—22no—
68C22×D44—42no—
69C22×D44—42no—
70C22×D44C2312yes—
71C22×D44C2314yes—
72C22×Dic22—21no—
73C22×Dic22—22no—
74C22×Dic22—42no—
75C22×Dic22—42no—
76C22×Dic22C2312yes—
77C22×Dic22C2314yescomplemented
78C2×C11×M16—42no—
79C2×C11×M16C2314yescomplemented
80C22×C8×C11—42no—
81C22×C8×C11C2312yes—
82C22×C8×C11C2312yes—
83C22×C8×C11C2314yescomplemented
84C2×C22⋊Dic11—22no—
85C2×C22⋊Dic11—22no—
86C2×C22⋊Dic11—21no—
87C2×C22⋊Dic11—21no—
88#67000—28no—
89#66997—28no—
90#66993—28no—
91#66990—28no—
92#66990—28no—
93#66989—28no—
94#66988—28no—
95#66988—28no—
96#66983—24no—
97#66983—24no—
98#66983C2318yes—
99#66983C2318yes—
100C2×(C2×D11)⋊C4—22no—
101C2×(C2×D11)⋊C4—22no—
102#66979—22no—
103#66979—22no—
104#66979C2314yes—
105#66979C2314yescomplemented
106C2×C4⋊Dic11C2312yes—
107C2×C4⋊Dic11C2312yes—
108#66977—24no—
109#66977—24no—
110#66977C2318yes—
111#66977C2318yescomplemented
112C2×Dic11⋊C4—22no—
113C2×Dic11⋊C4—22no—
114C2×C4×Dic11—21no—
115C2×C4×Dic11—21no—
116C2×#4314—44no—
117C2×#4314—44no—
118C2×#4314C2318yes—
119C2×#4314C2318yes—
120C11×C22⋊C8C2318yes—
121C11×C22⋊C8C2318yescomplemented
122#66885C2318yes—
123#66885C2318yes—
124#66882C2318yescomplemented
125#66881C2318yescomplemented
126#66880C2318yescomplemented
127#66880C2318yescomplemented
128C2×#3200—111nomaximal, Sylow
129C24×C11C2×D411yescharacteristic
130C24×C11C2×D411yescharacteristic
131C24×C11C2×D411yescharacteristic
132C23×D11—22no—
133C23×D11—24no—
134C23×D11—44no—
135C23×D11—84no—
136C11×#41—48no—
137C11×#41—44no—
138C11×#41—44no—
139C2×Q8×C11—42no—
140C2×Q8×C11C2×D414yes—
141C2×D4×C11—42no—
142C2×D4×C11—42no—
143C2×D4×C11—42no—
144C2×D4×C11C2×D414yes—
145C2×D4×C11C2×D414yes—
146C2×D4×C11C2×D414yes—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D412yes—
157C22×C4×C11C2×D412yes—
158C22×C4×C11C2×D412yes—
159C22×C4×C11C2412yes—
160C22×C4×C11C2412yes—
161C22×C4×C11C2412yes—
162C22×C4×C11C2411yescharacteristic
163C2×C22⋊D11—28no—
164C2×C22⋊D11—28no—
165C2×C22⋊D11—84no—
166C2×C22⋊D11—84no—
167C22×Dic11—22no—
168C22×Dic11—22no—
169C22×Dic11—22no—
170C22×Dic11—24no—
171C22×Dic11—44no—
172C2×D44—22no—
173C2×D44—24no—
174C2×D44—24no—
175C2×D44—24no—
176C2×D44—44no—
177C2×D44—44no—
178C2×D44—44no—
179C2×D44—48no—
180C2×D44C2414yes—
181C2×Dic22—22no—
182C2×Dic22—24no—
183C2×Dic22—24no—
184C2×Dic22—24no—
185C2×Dic22—44no—
186C2×Dic22—44no—
187C2×Dic22—44no—
188C2×Dic22—48no—
189C2×Dic22C2414yes—
190C11×M16—44no—
191C2×C8×C11—24no—
192C2×C8×C11—24no—
193C2×C8×C11—44no—
194C2×C8×C11C2414yes—
195C2×C8×C11C2414yes—
196C22⋊Dic11—28no—
197C22⋊Dic11—28no—
198C22⋊Dic11—24no—
199C22⋊Dic11—24no—
200(C2×D11)⋊C4—28no—
201(C2×D11)⋊C4—28no—
202C4⋊Dic11—22no—
203C4⋊Dic11—22no—
204C4⋊Dic11C2414yes—
205C4⋊Dic11C2414yes—
206Dic11⋊C4—28no—
207Dic11⋊C4—28no—
208C4×Dic11—24no—
209C4×Dic11—24no—
210#4314—48no—
211#4314—48no—
212C2×#536—111no—
213C2×#535—111no—
214#3200—1116no—
215C2×#485—112no—
216C2×#482—112no—
217C2×#468—112no—
218C2×#465—112no—
219C2×#448—112no—
220C2×#450—112no—
221C2×#408D1111yescharacteristic, complemented
222C23×C11—22no—
223C23×C11—22no—
224C23×C11—22no—
225C23×C11—24no—
226C23×C11—24no—
227C23×C11—24no—
228C23×C11C22×D412yes—
229C23×C11C22×D412yes—
230C23×C11C22×D412yes—
231C23×C11C22×D411yescharacteristic
232C22×D11—24no—
233C22×D11—48no—
234C22×D11—44no—
235C22×D11—44no—
236C22×D11—44no—
237C22×D11—88no—
238C22×D11—816no—
239Q8×C11—44no—
240D4×C11—44no—
241D4×C11—44no—
242D4×C11—44no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—24no—
247C2×C4×C11—24no—
248C2×C4×C11—24no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11C22×D412yes—
256C2×C4×C11C22×D412yes—
257C2×C4×C11C22×D412yes—
258C2×C4×C11C22×D411yescharacteristic
259C2×C4×C11H(5,𝔽2)12yes—
260C2×C4×C11H(5,𝔽2)12yes—
261C2×C4×C11C2511yescharacteristic
262C22⋊D11—88no—
263C22⋊D11—88no—
264C2×Dic11—24no—
265C2×Dic11—24no—
266C2×Dic11—24no—
267C2×Dic11—48no—
268C2×Dic11—44no—
269C2×Dic11—44no—
270C2×Dic11—44no—
271D44—24no—
272D44—24no—
273D44—48no—
274D44—44no—
275Dic22—24no—
276Dic22—24no—
277Dic22—48no—
278Dic22—44no—
279C8×C11—24no—
280C8×C11—24no—
281C22×#41C2×D1111yescharacteristic
282C23×Q8—111no—
283C23×D4—111no—
284C22×SD16—112no—
285C22×SD16—112no—
286C22×M16C2×D1111yescharacteristic, complemented
287C23×C8C2×D1111yescharacteristic, complemented
288#536—118no—
289#536—224no—
290#535—118no—
291#535—224no—
292C2×C4⋊Q8—221no—
293C2×#127—221no—
294C2×#124—221no—
295C2×#124—221no—
296C2×#123—221no—
297C2×#123—221no—
298C2×C22⋊Q8—112no—
299C2×C22⋊Q8—112no—
300C2×#121—112no—
301C2×#121—112no—
302C2×#120—221no—
303C2×#120—221no—
304C2×#117—111no—
305C2×#117—111no—
306#485—1116no—
307#482—1116no—
308#468—1116no—
309#465—1116no—
310#450—1116no—
311#448—1116no—
312C2×#107—112no—
313C2×#106—112no—
314C2×#103—112no—
315C2×#103—112no—
316C2×#102—112no—
317C2×#102—112no—
318#408C2×D1118yescomplemented
319C2×C22⋊C8C2×D1112yes—
320C2×C22⋊C8C2×D1112yescomplemented
321C22×C11—22no—
322C22×C11—22no—
323C22×C11—22no—
324C22×C11—24no—
325C22×C11—24no—
326C22×C11—24no—
327C22×C11—44no—
328C22×C11—44no—
329C22×C11—44no—
330C22×C11#53412yes—
331C22×C11#57714yes—
332C22×C11C23×D411yescharacteristic
333C2×D11—44no—
334C2×D11—44no—
335C2×D11—44no—
336C2×D11—816no—
337C2×D11—88no—
338C4×C11—22no—
339C4×C11—22no—
340C4×C11—22no—
341C4×C11#53412yes—
342C4×C11C2×H(5,𝔽2)11yescharacteristic
343C4×C11C2×H(5,𝔽2)11yescharacteristic
344Dic11—44no—
345Dic11—44no—
346Dic11—44no—
347C25—221no—
348C2×#41—42no—
349C2×#41—42no—
350C2×#41D4414yes—
351C2×#41C22×D1114yes—
352C22×Q8—112no—
353C22×Q8—114no—
354C22×Q8—221no—
355C22×Q8—222no—
356C22×Q8—442no—
357C22×Q8—442no—
358C22×Q8D4411yescharacteristic
359C22×D4—112no—
360C22×D4—114no—
361C22×D4—222no—
362C22×D4—222no—
363C22×D4—221no—
364C22×D4—222no—
365C22×D4—442no—
366C22×D4—442no—
367C22×D4D4411yescharacteristic
368C22×D4D4411yescharacteristic
369C22×D4D4411yescharacteristic
370C23×C4—221no—
371C23×C4C22×D1111yescharacteristic
372C23×C4C22×D1111yescharacteristic
373C23×C4C22×D1111yescharacteristic
374C2×SD16—118no—
375C2×SD16—118no—
376C2×SD16—444no—
377C2×SD16—444no—
378C2×M16—42no—
379C2×M16C22×D1114yescomplemented
380C22×C8—42no—
381C22×C8C22×D1112yes—
382C22×C8C22×D1112yes—
383C22×C8C22×D1114yescomplemented
384C4⋊Q8—228no—
385#127—228no—
386#124—228no—
387#124—228no—
388#123—228no—
389#123—228no—
390C22⋊Q8—118no—
391C22⋊Q8—118no—
392C22⋊Q8—224no—
393C22⋊Q8—224no—
394#121—118no—
395#121—118no—
396#121—224no—
397#121—224no—
398#120—228no—
399#120—228no—
400#117—114no—
401#117—114no—
402#117—222no—
403#117—222no—
404C2×C4⋊C4—112no—
405C2×C4⋊C4—112no—
406C2×C4⋊C4—222no—
407C2×C4⋊C4—222no—
408C2×C22⋊C4—221no—
409C2×C22⋊C4—221no—
410C2×C22⋊C4—222no—
411C2×C22⋊C4—222no—
412C2×C22⋊C4—222no—
413C2×C22⋊C4—222no—
414C2×C42—221no—
415C2×C42—221no—
416#107—118no—
417#106—118no—
418#103—118no—
419#103—118no—
420#102—118no—
421#102—118no—
422C22⋊C8C22×D1118yes—
423C22⋊C8C22×D1118yescomplemented
424C2×C11—42no—
425C2×C11—42no—
426C2×C11—42no—
427C2×C11#320014yescomplemented
428C2×C11C2×#53411yescharacteristic
429C2×C11C2×#57712yes—
430D11—84no—
431C24—222no—
432C24—224no—
433C24—444no—
434C24—884no—
435C24C2×D4411yescharacteristic
436C24C2×D4411yescharacteristic
437C24C2×D4411yescharacteristic
438#41—44no—
439#41—44no—
440#41—48no—
441C2×Q8—42no—
442C2×Q8—114no—
443C2×Q8—222no—
444C2×Q8—224no—
445C2×Q8—224no—
446C2×Q8—224no—
447C2×Q8—444no—
448C2×Q8—444no—
449C2×Q8—444no—
450C2×Q8—448no—
451C2×Q8C2×D4414yes—
452C2×D4—42no—
453C2×D4—42no—
454C2×D4—42no—
455C2×D4—114no—
456C2×D4—228no—
457C2×D4—228no—
458C2×D4—222no—
459C2×D4—224no—
460C2×D4—224no—
461C2×D4—224no—
462C2×D4—444no—
463C2×D4—444no—
464C2×D4—444no—
465C2×D4—448no—
466C2×D4—884no—
467C2×D4—884no—
468C2×D4C2×D4414yes—
469C2×D4C2×D4414yes—
470C2×D4C2×D4414yes—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—224no—
478C22×C4—222no—
479C22×C4—222no—
480C22×C4—222no—
481C22×C4—444no—
482C22×C4C2×D4412yes—
483C22×C4C2×D4412yes—
484C22×C4C2×D4412yes—
485C22×C4C2×D4411yescharacteristic
486C22×C4C2×D4411yescharacteristic
487C22×C4C2×D4411yescharacteristic
488C22×C4C23×D1112yes—
489C22×C4C23×D1112yes—
490C22×C4C23×D1112yes—
491C22×C4C23×D1111yescharacteristic
492SD16—448no—
493SD16—448no—
494M16—44no—
495C2×C8—24no—
496C2×C8—24no—
497C2×C8—44no—
498C2×C8C23×D1114yes—
499C2×C8C23×D1114yes—
500C4⋊C4—114no—
501C4⋊C4—114no—
502C4⋊C4—222no—
503C4⋊C4—222no—
504C4⋊C4—228no—
505C4⋊C4—228no—
506C22⋊C4—224no—
507C22⋊C4—224no—
508C22⋊C4—228no—
509C22⋊C4—228no—
510C22⋊C4—228no—
511C22⋊C4—228no—
512C42—224no—
513C42—224no—
514C11C2×#320011yescharacteristic, complemented, Sylow
515C23—22no—
516C23—22no—
517C23—22no—
518C23—24no—
519C23—24no—
520C23—24no—
521C23—224no—
522C23—448no—
523C23—444no—
524C23—444no—
525C23—444no—
526C23—888no—
527C23—8816no—
528C23C22×D4412yes—
529C23C22×D4412yes—
530C23C22×D4412yes—
531C23C22×D4411yescharacteristic
532Q8—44no—
533Q8—224no—
534Q8—224no—
535Q8—448no—
536Q8—444no—
537D4—44no—
538D4—44no—
539D4—44no—
540D4—224no—
541D4—224no—
542D4—448no—
543D4—444no—
544D4—888no—
545D4—888no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—224no—
559C2×C4—224no—
560C2×C4—224no—
561C2×C4—448no—
562C2×C4—444no—
563C2×C4—444no—
564C2×C4—444no—
565C2×C4C22×D4412yes—
566C2×C4C22×D4412yes—
567C2×C4C22×D4412yes—
568C2×C4C22×D4411yescharacteristic
569C2×C4#6703712yes—
570C2×C4#6703712yes—
571C2×C4C24×D1111yescharacteristic
572C8—24no—
573C8—24no—
574C22—22no—
575C22—22no—
576C22—22no—
577C22—24no—
578C22—24no—
579C22—24no—
580C22—44no—
581C22—44no—
582C22—44no—
583C22—444no—
584C22—444no—
585C22—444no—
586C22—8816no—
587C22—888no—
588C22#1062302412yes—
589C22#1062328214yes—
590C22C23×D4411yescharacteristic
591C4—22no—
592C4—22no—
593C4—22no—
594C4—444no—
595C4—444no—
596C4—444no—
597C4#1062302412yes—
598C4C2×#6703711yescharacteristic
599C4C2×#6703711yescharacteristic
600C2—42no—
601C2—42no—
602C2—42no—
603C2—884no—
604C2#1307948914yesdirect product factor
605C2C2×#1062302411yescharacteristic
606C2C2×#1062328212yes—
subgroupG/H
centerC23C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#408C2
socleC23×C11C22×D4
prime radicalC2×#10623361C2
hypercenterC2×#408D11
hypocenterC11C2×#3200
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#408

Complements

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

NH ≅ G/Ntype
1. C2×#10623356C2semidirect
3. #13079489C2direct (N × H)
4. C2×#10622336C2semidirect
5. C2×#10622350C2semidirect
6. C2×#10622747C2semidirect
7. C2×#10622727C2semidirect
8. C2×#10622351C2semidirect
9. C2×#10622344C2semidirect
10. C2×C11×#408C2semidirect
13. C23×Dic22C22semidirect
14. C22×C11×M16C22semidirect
15. C23×C8×C11C22semidirect
19. #10623356C22semidirect
31. C2×#66979C22semidirect
33. C2×#66977C22semidirect
36. C11×#408C22semidirect
38. C2×C11×C22⋊C8C22semidirect
39. #10622747C22semidirect
40. #10622727C22semidirect
43. C2×#66882C22semidirect
44. C2×#66881C22semidirect
45. C2×#66880C22semidirect
46. C2×#66880C22semidirect
47. #10622351C22semidirect
48. #10622350C22semidirect
49. #10622344C22semidirect
50. #10622336C22semidirect
77. C22×Dic22C23semidirect
79. C2×C11×M16C23semidirect
83. C22×C8×C11C23semidirect
105. #66979C23semidirect
111. #66977C23semidirect
121. C11×C22⋊C8C23semidirect
124. #66882C23semidirect
125. #66881C23semidirect
126. #66880C23semidirect
127. #66880C23semidirect
221. C2×#408D11semidirect
286. C22×M16C2×D11semidirect
287. C23×C8C2×D11semidirect
318. #408C2×D11semidirect
320. C2×C22⋊C8C2×D11semidirect
379. C2×M16C22×D11semidirect
383. C22×C8C22×D11semidirect
423. C22⋊C8C22×D11semidirect
427. C2×C11#3200semidirect
514. C11C2×#3200semidirect
604. C2#13079489direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106233562
C2×#106233612
#130794892
C2×#106223362
C2×#106223502
C2×#106227472
C2×#106227272
C2×#106223512
C2×#106223442
C2×C11×#4082
C2×#320011