Finite Group Databasebeta

← C2×#13079766 #15625821

Subgroups — C2×#13079766 #15625821

Order 2816.

2006 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623109C211yesmaximal, characteristic
2C2×D11×C4⋊Q8C211yesmaximal, characteristic
3#13079766C2116yesmaximal, direct product factor
4C2×#10622487C212yesmaximal, complemented
5C2×#10622405C212yesmaximal, complemented
6C2×#10622497C212yesmaximal
7C2×#10622422C212yesmaximal
8C2×#10622463C211yesmaximal, characteristic, complemented
9C2×#10622634C211yesmaximal, characteristic, complemented
10C2×#10622704C211yesmaximal, characteristic, complemented
11C2×#10622446C211yesmaximal, characteristic
12C2×C11×#477C211yesmaximal, characteristic, complemented
13C22×Q8×D11—21no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C4×Q8×C11C2211yescharacteristic
16C2×#66999C2211yescharacteristic
17C2×#66997—21no—
18C2×#66997C2211yescharacteristic
19D11×C4⋊Q8—24no—
20D11×C4⋊Q8C2218yes—
21#10623109—24no—
22#10623109C2218yes—
23C2×#66950C2211yescharacteristic
24C2×#66949—21no—
25C2×C4⋊C4×D11—21no—
26C2×C4⋊C4×D11C2212yes—
27C2×#66942—21no—
28C2×#66941—21no—
29C2×#66941C2212yes—
30C2×#66941C2211yescharacteristic
31C2×#66925—21no—
32C2×C42×D11C2211yescharacteristic
33C2×#66922C2211yescharacteristic
34C2×C4×Dic22—21no—
35C2×C4×Dic22C2211yescharacteristic
36C11×#477C2218yescomplemented
37C2×C11×#107C2212yes—
38C2×C11×C4⋊C8C2211yescharacteristic
39C2×C11×#103C2212yes—
40C2×#66899C2212yes—
41C2×(C2×D11)⋊C8C2212yes—
42C2×#66882C2212yes—
43C2×#66880C2212yes—
44C2×C8×Dic11C2212yes—
45#10622704C2218yescomplemented
46#10622634C2218yescomplemented
47C2×#66874C2212yes—
48C2×#66871C2212yes—
49C2×#66871C2212yes—
50C2×C4⋊(C11⋊C8)C2211yescharacteristic
51#10622497C22116yes—
52#10622487C22116yescomplemented
53#10622463C2218yescomplemented
54#10622446C2218yes—
55#10622422C22116yes—
56#10622405C22116yescomplemented
57C22×Q8×C11—21no—
58C22×Q8×C11C2311yescharacteristic
59C2×Q8×D11—28no—
60C2×Q8×D11—48no—
61C22×C4×D11—22no—
62C22×C4×D11D411yescharacteristic
63C22×C4×D11D411yescharacteristic
64C22×C4×D11C2311yescharacteristic
65C22×Dic22—21no—
66C22×Dic22—21no—
67C22×Dic22—22no—
68C22×Dic22C2311yescharacteristic
69C22×C8×C11C2312yes—
70C11×C4⋊Q8—22no—
71C11×C4⋊Q8C2314yes—
72C4×Q8×C11—22no—
73C4×Q8×C11C2314yes—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4C2312yes—
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C42×C11—21no—
79C2×C42×C11C2311yescharacteristic
80#66999—22no—
81#66999C2314yes—
82#66997—28no—
83#66997—22no—
84#66997C2314yes—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2312yes—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—22no—
97C2×Dic11⋊C4—22no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11D411yescharacteristic
100C2×C4×Dic11D411yescharacteristic
101C2×C4×Dic11C2311yescharacteristic
102C22×C11⋊C8C2312yes—
103#66950—22no—
104#66950C2314yes—
105#66949—28no—
106C4⋊C4×D11—24no—
107C4⋊C4×D11—28no—
108C4⋊C4×D11C2318yes—
109#66942—28no—
110#66941—24no—
111#66941—28no—
112#66941—22no—
113#66941C2318yes—
114#66941C2314yes—
115#66925—28no—
116C42×D11D414yes—
117C42×D11C2314yes—
118#66922—22no—
119#66922C2314yes—
120C4×Dic22—22no—
121C4×Dic22—28no—
122C4×Dic22C2314yes—
123C11×#107C2318yes—
124C11×C4⋊C8C2314yes—
125C11×#103C2318yes—
126#66899C2318yes—
127(C2×D11)⋊C8C2318yes—
128#66882C2318yes—
129#66880C2318yes—
130C8×Dic11C2318yes—
131#66874C2318yes—
132#66871C2318yes—
133#66871C2318yes—
134C4⋊(C11⋊C8)C2314yes—
135C2×#3230—111nomaximal, Sylow
136C23×D11C2×D411yescharacteristic
137C2×Q8×C11—21no—
138C2×Q8×C11—24no—
139C2×Q8×C11—22no—
140C2×Q8×C11—22no—
141C2×Q8×C11—44no—
142C2×Q8×C11C2412yes—
143C22×C4×C11—21no—
144C22×C4×C11—22no—
145C22×C4×C11—21no—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2411yescharacteristic
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—22no—
152C22×Dic11C2×D411yescharacteristic
153C22×Dic11C2×D411yescharacteristic
154C22×Dic11C2×D411yescharacteristic
155Q8×D11—432no—
156C2×C4×D11—24no—
157C2×C4×D11—28no—
158C2×C4×D11—22no—
159C2×C4×D11—22no—
160C2×C4×D11—48no—
161C2×C4×D11Q1618yes—
162C2×C4×D11C2×D412yes—
163C2×C4×D11C2×D414yes—
164C2×C4×D11C2×D414yes—
165C2×C4×D11C2412yes—
166C2×Dic22—24no—
167C2×Dic22—28no—
168C2×Dic22—21no—
169C2×Dic22—24no—
170C2×Dic22—22no—
171C2×Dic22—22no—
172C2×Dic22—44no—
173C2×Dic22—44no—
174C2×Dic22—48no—
175C2×Dic22C2412yes—
176C2×C8×C11—24no—
177C2×C8×C11C2414yes—
178C11×C4⋊C4—24no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—24no—
182C11×C4⋊C4C2412yes—
183C11×C4⋊C4C2414yes—
184C42×C11—24no—
185C42×C11C2×D412yes—
186C42×C11C2412yes—
187(C2×D11)⋊C4—24no—
188(C2×D11)⋊C4—24no—
189C4⋊Dic11—24no—
190C4⋊Dic11—21no—
191C4⋊Dic11—22no—
192C4⋊Dic11—24no—
193C4⋊Dic11C2412yes—
194C4⋊Dic11C2414yes—
195Dic11⋊C4—24no—
196Dic11⋊C4—24no—
197Dic11⋊C4—24no—
198Dic11⋊C4—24no—
199Dic11⋊C4—28no—
200Dic11⋊C4—28no—
201Dic11⋊C4—24no—
202C4×Dic11—24no—
203C4×Dic11C2×D414yes—
204C4×Dic11C2×D412yes—
205C4×Dic11C2×D414yes—
206C4×Dic11C2412yes—
207C2×C11⋊C8—24no—
208C2×C11⋊C8C2414yes—
209C2×#533—111no—
210C22×C4⋊Q8—111no—
211#3230—1116no—
212C2×#500—112no—
213C2×#487—112no—
214C2×#484—112no—
215C2×#484—112no—
216C2×#477—111no—
217C2×#477—111no—
218C2×#477—111no—
219C2×#477D1111yescharacteristic, complemented
220C2×#431—111no—
221C23×C11C22×D411yescharacteristic
222C22×D11—22no—
223C22×D11—22no—
224C22×D11C2×Q1614yes—
225C22×D11C22×D412yes—
226Q8×C11—22no—
227Q8×C11—22no—
228Q8×C11—48no—
229Q8×C11—42no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—24no—
233C2×C4×C11—22no—
234C2×C4×C11—42no—
235C2×C4×C11—44no—
236C2×C4×C11—42no—
237C2×C4×C11C2×Q1614yes—
238C2×C4×C11C22×D412yes—
239C2×C4×C11C22×D411yescharacteristic
240C2×C4×C11C22×D412yes—
241C2×C4×C112−1+412yes—
242C2×C4×C112−1+412yes—
243C2×C4×C11C2511yescharacteristic
244C2×Dic11—22no—
245C2×Dic11—22no—
246C2×Dic11—22no—
247C2×Dic11—24no—
248C2×Dic11—42no—
249C2×Dic11—44no—
250C2×Dic11—42no—
251C2×Dic11C2×Q1614yes—
252C2×Dic11AGL(1,ℤ/8)14yes—
253C2×Dic11C22×D412yes—
254C2×Dic11C22×D412yes—
255C2×Dic11C22×D412yes—
256C4×D11—24no—
257C4×D11—22no—
258C4×D11—22no—
259C4×D11—28no—
260C4×D11—416no—
261C4×D11C2×Q16116yes—
262Dic22—22no—
263Dic22—22no—
264Dic22—48no—
265Dic22—42no—
266Dic22—48no—
267Dic22—416no—
268C8×C11—24no—
269C11⋊C8—24no—
270C23×Q8—221no—
271#533—118no—
272#533—224no—
273C2×C4⋊Q8—118no—
274C2×C4⋊Q8—112no—
275C2×C4⋊Q8—111no—
276C2×C4⋊Q8—111no—
277C2×C4⋊Q8—111no—
278C2×C4⋊Q8—221no—
279C2×C4⋊Q8—224no—
280C2×C4⋊Q8—221no—
281C2×C4⋊Q8C2×D1111yescharacteristic
282C2×#125—221no—
283C2×C22⋊Q8—111no—
284C2×C22⋊Q8—111no—
285C2×C22⋊Q8—221no—
286C2×C4×Q8—111no—
287C2×C4×Q8—221no—
288C2×C4×Q8C2×D1111yescharacteristic
289C2×#117—221no—
290C22×C4⋊C4—112no—
291C22×C4⋊C4—221no—
292C22×C42—111no—
293#500—1116no—
294#487—1116no—
295#484—1116no—
296#484—1116no—
297#477—118no—
298#477—118no—
299#477—118no—
300#477C2×D1118yescomplemented
301#431—118no—
302C2×#107—112no—
303C2×#107—112no—
304C2×#107—112no—
305C2×#107C2×D1112yes—
306C2×C4⋊C8—111no—
307C2×C4⋊C8C2×D1111yescharacteristic
308C2×#103—112no—
309C2×#103—112no—
310C2×#103—112no—
311C2×#103C2×D1112yes—
312C2×C22⋊C8—112no—
313C2×C4×C8—112no—
314C22×C11#53612yes—
315C22×C11C22×Q1612yes—
316C22×C11C2×AGL(1,ℤ/8)12yes—
317C22×C11C23×D411yescharacteristic
318C2×D11—22no—
319C2×D11—28no—
320C2×D11—22no—
321C2×D11C22×Q1614yes—
322C4×C11—22no—
323C4×C11—42no—
324C4×C11—44no—
325C4×C11—42no—
326C4×C11#53612yes—
327C4×C11C22×Q1614yes—
328C4×C11C2×2−1+411yescharacteristic
329C4×C11C2×2−1+411yescharacteristic
330Dic11—22no—
331Dic11—42no—
332Dic11—44no—
333Dic11—42no—
334Dic11C22×Q1614yes—
335Dic11C2×AGL(1,ℤ/8)14yes—
336C22×Q8—21no—
337C22×Q8—111no—
338C22×Q8—221no—
339C22×Q8—222no—
340C22×Q8—228no—
341C22×Q8—221no—
342C22×Q8—448no—
343C22×Q8C22×D1111yescharacteristic
344C23×C4—111no—
345C23×C4—111no—
346C23×C4—111no—
347C23×C4—222no—
348C22×C8—112no—
349C22×C8C22×D1112yes—
350C4⋊Q8—22no—
351C4⋊Q8—118no—
352C4⋊Q8—114no—
353C4⋊Q8—114no—
354C4⋊Q8—114no—
355C4⋊Q8—228no—
356C4⋊Q8—224no—
357C4⋊Q8—222no—
358C4⋊Q8—228no—
359C4⋊Q8—222no—
360C4⋊Q8—222no—
361C4⋊Q8C22×D1114yes—
362#125—228no—
363C22⋊Q8—114no—
364C22⋊Q8—114no—
365C22⋊Q8—222no—
366C22⋊Q8—228no—
367C22⋊Q8—222no—
368C4×Q8—22no—
369C4×Q8—114no—
370C4×Q8—228no—
371C4×Q8—222no—
372C4×Q8C22×D1114yes—
373#117—228no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—112no—
377C2×C4⋊C4—111no—
378C2×C4⋊C4—118no—
379C2×C4⋊C4—224no—
380C2×C4⋊C4—228no—
381C2×C4⋊C4—222no—
382C2×C4⋊C4—222no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4—221no—
389C2×C4⋊C4—221no—
390C2×C4⋊C4C22×D1112yes—
391C2×C4⋊C4C22×D1111yescharacteristic
392C2×C22⋊C4—221no—
393C2×C22⋊C4—221no—
394C2×C42—21no—
395C2×C42—111no—
396C2×C42—111no—
397C2×C42—111no—
398C2×C42—114no—
399C2×C42—114no—
400C2×C42—221no—
401C2×C42C22×D1111yescharacteristic
402#107—118no—
403#107—118no—
404#107—118no—
405#107C22×D1118yes—
406C4⋊C8—114no—
407C4⋊C8C22×D1114yes—
408#103—118no—
409#103—118no—
410#103—118no—
411#103C22×D1118yes—
412C22⋊C8—118no—
413C4×C8—118no—
414C2×C11#323014yescomplemented
415C2×C11C2×#53611yescharacteristic
416C2×C11C23×Q1611yescharacteristic
417C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
418D11—24no—
419C24—111no—
420C2×Q8—21no—
421C2×Q8—24no—
422C2×Q8—22no—
423C2×Q8—22no—
424C2×Q8—44no—
425C2×Q8—112no—
426C2×Q8—224no—
427C2×Q8—228no—
428C2×Q8—221no—
429C2×Q8—224no—
430C2×Q8—222no—
431C2×Q8—222no—
432C2×Q8—444no—
433C2×Q8—448no—
434C2×Q8—444no—
435C2×Q8—4432no—
436C2×Q8C23×D1112yes—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—111no—
441C22×C4—111no—
442C22×C4—118no—
443C22×C4—114no—
444C22×C4—111no—
445C22×C4—112no—
446C22×C4—114no—
447C22×C4—112no—
448C22×C4—224no—
449C22×C4—228no—
450C22×C4—222no—
451C22×C4—222no—
452C22×C4—221no—
453C22×C4—221no—
454C22×C4—222no—
455C22×C4—448no—
456C22×C4D4×D1111yescharacteristic
457C22×C4D4×D1111yescharacteristic
458C22×C4C23×D1111yescharacteristic
459C2×C8—24no—
460C2×C8—114no—
461C2×C8—224no—
462C2×C8C23×D1114yes—
463C4⋊C4—24no—
464C4⋊C4—24no—
465C4⋊C4—22no—
466C4⋊C4—21no—
467C4⋊C4—114no—
468C4⋊C4—112no—
469C4⋊C4—228no—
470C4⋊C4—228no—
471C4⋊C4—224no—
472C4⋊C4—224no—
473C4⋊C4—224no—
474C4⋊C4—224no—
475C4⋊C4—224no—
476C4⋊C4—222no—
477C4⋊C4—221no—
478C4⋊C4—224no—
479C4⋊C4—224no—
480C4⋊C4C23×D1114yes—
481C4⋊C4C23×D1112yes—
482C22⋊C4—224no—
483C22⋊C4—224no—
484C42—24no—
485C42—114no—
486C42—114no—
487C42—112no—
488C42—112no—
489C42—224no—
490C42D4×D1112yes—
491C42C23×D1112yes—
492C11C2×#323011yescharacteristic, complemented, Sylow
493C23—114no—
494C23—112no—
495C23—222no—
496C23—222no—
497C23C2×D4×D1111yescharacteristic
498Q8—22no—
499Q8—22no—
500Q8—48no—
501Q8—42no—
502Q8—222no—
503Q8—222no—
504Q8—448no—
505Q8—4416no—
506Q8—448no—
507Q8—442no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—44no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—114no—
516C2×C4—114no—
517C2×C4—112no—
518C2×C4—112no—
519C2×C4—1116no—
520C2×C4—112no—
521C2×C4—228no—
522C2×C4—222no—
523C2×C4—224no—
524C2×C4—222no—
525C2×C4—222no—
526C2×C4—222no—
527C2×C4—222no—
528C2×C4—224no—
529C2×C4—4416no—
530C2×C4—444no—
531C2×C4—442no—
532C2×C4—442no—
533C2×C4Q16×D1114yes—
534C2×C4C2×D4×D1112yes—
535C2×C4C2×D4×D1112yes—
536C2×C4C2×D4×D1111yescharacteristic
537C2×C4#6704012yes—
538C2×C4#6704312yes—
539C2×C4C24×D1111yescharacteristic
540C8—24no—
541C8—224no—
542C22—114no—
543C22—222no—
544C22—222no—
545C22—228no—
546C22#1062315912yes—
547C22C2×Q16×D1112yes—
548C22D11×AGL(1,ℤ/8)12yes—
549C22C22×D4×D1111yescharacteristic
550C4—22no—
551C4—42no—
552C4—44no—
553C4—42no—
554C4—114no—
555C4—114no—
556C4—222no—
557C4—442no—
558C4—444no—
559C4—442no—
560C4#1062315912yes—
561C4C2×Q16×D1114yes—
562C4C2×#6704011yescharacteristic
563C4C2×#6704311yescharacteristic
564C2—224no—
565C2#1307976614yesdirect product factor
566C2C2×#1062315911yescharacteristic
567C2C22×Q16×D1111yescharacteristic
568C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#477C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenterC2×#477D11
hypocenterC11C2×#3230
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
3. #13079766C2direct (N × H)
4. C2×#10622487C2semidirect
5. C2×#10622405C2semidirect
8. C2×#10622463C2semidirect
9. C2×#10622634C2semidirect
10. C2×#10622704C2semidirect
12. C2×C11×#477C2semidirect
36. C11×#477C22semidirect
45. #10622704C22semidirect
46. #10622634C22semidirect
52. #10622487C22semidirect
53. #10622463C22semidirect
56. #10622405C22semidirect
219. C2×#477D11semidirect
300. #477C2×D11semidirect
414. C2×C11#3230semidirect
492. C11C2×#3230semidirect
565. C2#13079766direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231092
C2×D11×C4⋊Q82
#130797662
C2×#106224872
C2×#106224052
C2×#106224972
C2×#106224222
C2×#106224632
C2×#106226342
C2×#106227042
C2×#106224462
C2×C11×#4772
C2×#323011