Finite Group Databasebeta

← C2×#13067613 #14725913

Subgroups — C2×#13067613 #14725913

Order 2816.

1060 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622656C211yesmaximal, characteristic, complemented
2C2×#10622646C211yesmaximal, characteristic
3C2×#10622596C211yesmaximal, characteristic, complemented
4#13067613C218yesmaximal, direct product factor
5C2×#10622176C211yesmaximal, characteristic, complemented
6C2×#10622175C211yesmaximal, characteristic
7C2×#10622166C211yesmaximal, characteristic, complemented
8C2×C11×#539C211yesmaximal, characteristic
9C11×#539—22no—
10C11×#539—22no—
11C11×#539—22no—
12C11×#539C2214yes—
13C2×C11×#126—21no—
14C2×C11×#125—21no—
15C2×C11×#123—21no—
16C2×C11×#123—21no—
17C2×C11×C22⋊Q8—21no—
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C2×C4×D4×C11—21no—
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C22×Dic11⋊C4—21no—
24C2×#66899—21no—
25C2×#66896—21no—
26C2×C11⋊#95—21no—
27C2×C11⋊#95C2211yescharacteristic
28C2×C22⋊(C11⋊C8)C2211yescharacteristic
29C2×C22⋊(C11⋊C8)C2211yescharacteristic
30#10622656—22no—
31#10622656C2214yescomplemented
32#10622646—22no—
33#10622646C2214yes—
34#10622596—22no—
35#10622596C2214yescomplemented
36C2×#66872—21no—
37C2×#66871—21no—
38#10622176C2214yescomplemented
39#10622175C2214yes—
40#10622166C2214yescomplemented
41C22×Q8×C11D411yescharacteristic
42C22×D4×C11—21no—
43C22×D4×C11D411yescharacteristic
44C23×C4×C11—21no—
45C23×C4×C11D411yescharacteristic
46C23×C4×C11D411yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C23×Dic11—21no—
49C23×Dic11—21no—
50C11×#126—24no—
51C11×#126—24no—
52C11×#125—24no—
53C11×#125—24no—
54C11×#123—24no—
55C11×#123—24no—
56C11×#123—24no—
57C11×#123—24no—
58C11×C22⋊Q8—24no—
59C11×C22⋊Q8—24no—
60C11×C22⋊Q8—21no—
61C11×C22⋊Q8—21no—
62C11×C22⋊Q8D412yes—
63C11×C22⋊Q8C2312yes—
64C11×#121—21no—
65C11×#121—21no—
66C11×#121D412yes—
67C11×#121C2312yes—
68C4×D4×C11—24no—
69C4×D4×C11—24no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4D412yes—
79C2×C11×C4⋊C4D411yescharacteristic
80C2×C11×C4⋊C4D411yescharacteristic
81C2×C11×C4⋊C4C2312yes—
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C42×C11—21no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11C2312yes—
94C2×Dic11⋊C4—24no—
95C2×Dic11⋊C4—44no—
96C22×C11⋊C8—21no—
97C22×C11⋊C8—21no—
98#66899—24no—
99#66896—24no—
100C11⋊#95—24no—
101C11⋊#95—21no—
102C11⋊#95C2312yes—
103C22⋊(C11⋊C8)—21no—
104C22⋊(C11⋊C8)—21no—
105C22⋊(C11⋊C8)C2312yes—
106C22⋊(C11⋊C8)C2312yes—
107#66872—24no—
108#66871—24no—
109C2×#1609—111nomaximal, Sylow
110C24×C11—21no—
111C24×C11C2×D411yescharacteristic
112C2×Q8×C11—21no—
113C2×Q8×C11—42no—
114C2×Q8×C11C2×D412yes—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11—21no—
118C2×D4×C11—42no—
119C2×D4×C11—42no—
120C2×D4×C11—42no—
121C2×D4×C11C2×D412yes—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—24no—
131C22×C4×C11—21no—
132C22×C4×C11—42no—
133C22×C4×C11—42no—
134C22×C4×C11—82no—
135C22×C4×C11C2×D412yes—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D412yes—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2411yescharacteristic
143C22×Dic11—24no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—42no—
147C22×Dic11—41no—
148C22×Dic11—41no—
149C22×Dic11—42no—
150C22×Dic11—42no—
151C22×Dic11—42no—
152C11×C4⋊C4—24no—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—24no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4C2×D412yes—
164C11×C4⋊C4C2×D412yes—
165C11×C22⋊C4—24no—
166C11×C22⋊C4—24no—
167C11×C22⋊C4—24no—
168C11×C22⋊C4—22no—
169C11×C22⋊C4—22no—
170C11×C22⋊C4—22no—
171C11×C22⋊C4—22no—
172C42×C11—24no—
173C4⋊Dic11—22no—
174C4⋊Dic11—22no—
175C4⋊Dic11—41no—
176C4⋊Dic11—41no—
177Dic11⋊C4—48no—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—22no—
180C2×C11⋊C8—42no—
181C2×C11⋊C8—42no—
182C2×#539D1111yescharacteristic
183C2×#483—111no—
184C2×#480—111no—
185C2×#398—111no—
186#1609—118no—
187C2×#328—111no—
188C2×#327—111no—
189C2×#324—111no—
190C23×C11—22no—
191C23×C11—22no—
192C23×C11—22no—
193C23×C11—42no—
194C23×C11—42no—
195C23×C11—42no—
196C23×C11#12011yescharacteristic
197C23×C11#12011yescharacteristic
198C23×C11#13512yes—
199C23×C11AGL(1,ℤ/8)12yes—
200C23×C11C22×D411yescharacteristic
201Q8×C11—42no—
202Q8×C11—81no—
203D4×C11—42no—
204D4×C11—42no—
205D4×C11—42no—
206D4×C11—44no—
207D4×C11—81no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—81no—
229C2×C4×C11—84no—
230C2×C4×C11#12011yescharacteristic
231C2×C4×C11#12011yescharacteristic
232C2×C4×C11C22×D411yescharacteristic
233C2×C4×C11C22×D411yescharacteristic
234C2×Dic11—24no—
235C2×Dic11—48no—
236C2×Dic11—42no—
237C2×Dic11—42no—
238C2×Dic11—42no—
239C2×Dic11—42no—
240C2×Dic11—42no—
241C2×Dic11—82no—
242C2×Dic11—82no—
243C11⋊C8—42no—
244C11⋊C8—42no—
245#539—22no—
246#539—22no—
247#539—22no—
248#539C2×D1114yes—
249C2×#126—21no—
250C2×#125—21no—
251C2×#123—21no—
252C2×#123—21no—
253C2×C22⋊Q8—21no—
254C2×C22⋊Q8C2×D1111yescharacteristic
255C2×#121C2×D1111yescharacteristic
256C2×C4×D4—21no—
257C22×C4⋊C4—111no—
258C22×C4⋊C4—221no—
259C22×C4⋊C4C2×D1111yescharacteristic
260#483—114no—
261#483—222no—
262#480—114no—
263#480—222no—
264C2×#107—221no—
265C2×#106—221no—
266C2×#103—221no—
267C2×#102—221no—
268C2×C22⋊C8—111no—
269C2×C22⋊C8—111no—
270#398—114no—
271#398—222no—
272C2×#95—111no—
273C2×#95—221no—
274#328—114no—
275#327—114no—
276#324—114no—
277C22×C11—24no—
278C22×C11—24no—
279C22×C11—21no—
280C22×C11—21no—
281C22×C11—21no—
282C22×C11—21no—
283C22×C11—42no—
284C22×C11—42no—
285C22×C11—42no—
286C22×C11—84no—
287C22×C11#44912yes—
288C22×C11#44912yes—
289C22×C11#45612yes—
290C22×C11#45812yes—
291C22×C11C2×#12011yescharacteristic
292C22×C11C2×#13511yescharacteristic
293C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
294C4×C11—21no—
295C4×C11—21no—
296C4×C11—21no—
297C4×C11—21no—
298C4×C11—42no—
299C4×C11—42no—
300C4×C11—42no—
301C4×C11—42no—
302C4×C11—42no—
303Dic11—44no—
304Dic11—82no—
305C22×Q8C22⋊D1111yescharacteristic
306C22×D4—21no—
307C22×D4C22⋊D1111yescharacteristic
308C23×C4—21no—
309C23×C4—221no—
310C23×C4—221no—
311C23×C4C22⋊D1111yescharacteristic
312C23×C4C22⋊D1111yescharacteristic
313C23×C4C22×D1111yescharacteristic
314C22×C8—221no—
315C22×C8—221no—
316#126—24no—
317#126—24no—
318#125—24no—
319#125—24no—
320#123—24no—
321#123—24no—
322#123—24no—
323#123—24no—
324C22⋊Q8—24no—
325C22⋊Q8—24no—
326C22⋊Q8—21no—
327C22⋊Q8—21no—
328C22⋊Q8C22⋊D1112yes—
329C22⋊Q8C22×D1112yes—
330#121—21no—
331#121—21no—
332#121C22⋊D1112yes—
333#121C22×D1112yes—
334C4×D4—24no—
335C4×D4—24no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—112no—
345C2×C4⋊C4—221no—
346C2×C4⋊C4—221no—
347C2×C4⋊C4—221no—
348C2×C4⋊C4—221no—
349C2×C4⋊C4—221no—
350C2×C4⋊C4—224no—
351C2×C4⋊C4—444no—
352C2×C4⋊C4C22⋊D1112yes—
353C2×C4⋊C4C22⋊D1111yescharacteristic
354C2×C4⋊C4C22⋊D1111yescharacteristic
355C2×C4⋊C4C22×D1112yes—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C42—21no—
362#107—224no—
363#106—224no—
364#103—224no—
365#102—224no—
366C22⋊C8—112no—
367C22⋊C8—112no—
368C22⋊C8—221no—
369C22⋊C8—221no—
370#95—112no—
371#95—221no—
372#95—224no—
373C2×C11—21no—
374C2×C11—21no—
375C2×C11—22no—
376C2×C11—82no—
377C2×C11#160914yescomplemented
378C2×C11C2×#44911yescharacteristic
379C2×C11C2×#45611yescharacteristic
380C2×C11C2×#45811yescharacteristic
381C24—21no—
382C24C2×C22⋊D1111yescharacteristic
383C2×Q8—21no—
384C2×Q8—42no—
385C2×Q8C2×C22⋊D1112yes—
386C2×D4—22no—
387C2×D4—22no—
388C2×D4—21no—
389C2×D4—42no—
390C2×D4—42no—
391C2×D4—42no—
392C2×D4C2×C22⋊D1112yes—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—24no—
402C22×C4—21no—
403C22×C4—42no—
404C22×C4—42no—
405C22×C4—82no—
406C22×C4—224no—
407C22×C4—222no—
408C22×C4—222no—
409C22×C4—442no—
410C22×C4—442no—
411C22×C4—442no—
412C22×C4—442no—
413C22×C4—441no—
414C22×C4—441no—
415C22×C4C2×C22⋊D1112yes—
416C22×C4C2×C22⋊D1111yescharacteristic
417C22×C4C2×C22⋊D1111yescharacteristic
418C22×C4C2×C22⋊D1112yes—
419C22×C4C2×C22⋊D1111yescharacteristic
420C22×C4C2×C22⋊D1111yescharacteristic
421C22×C4C2×C22⋊D1111yescharacteristic
422C22×C4C23×D1111yescharacteristic
423C2×C8—222no—
424C2×C8—222no—
425C2×C8—442no—
426C2×C8—442no—
427C4⋊C4—24no—
428C4⋊C4—24no—
429C4⋊C4—24no—
430C4⋊C4—22no—
431C4⋊C4—22no—
432C4⋊C4—22no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—22no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—222no—
439C4⋊C4—222no—
440C4⋊C4—448no—
441C4⋊C4—441no—
442C4⋊C4—441no—
443C4⋊C4C2×C22⋊D1112yes—
444C4⋊C4C2×C22⋊D1112yes—
445C22⋊C4—24no—
446C22⋊C4—24no—
447C22⋊C4—24no—
448C22⋊C4—22no—
449C22⋊C4—22no—
450C22⋊C4—22no—
451C22⋊C4—22no—
452C42—24no—
453C11C2×#160911yescharacteristic, complemented, Sylow
454C23—22no—
455C23—22no—
456C23—22no—
457C23—42no—
458C23—42no—
459C23—42no—
460C23#6700212yes—
461C23#6700312yes—
462C23#6700611yescharacteristic
463C23#6700611yescharacteristic
464C23C22×C22⋊D1111yescharacteristic
465Q8—42no—
466Q8—81no—
467D4—42no—
468D4—42no—
469D4—42no—
470D4—44no—
471D4—81no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—81no—
493C2×C4—84no—
494C2×C4—224no—
495C2×C4—448no—
496C2×C4—442no—
497C2×C4—442no—
498C2×C4—442no—
499C2×C4—442no—
500C2×C4—442no—
501C2×C4—882no—
502C2×C4—882no—
503C2×C4#6700611yescharacteristic
504C2×C4#6700611yescharacteristic
505C2×C4C22×C22⋊D1111yescharacteristic
506C2×C4C22×C22⋊D1111yescharacteristic
507C8—442no—
508C8—442no—
509C22—24no—
510C22—24no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—21no—
515C22—42no—
516C22—42no—
517C22—42no—
518C22—84no—
519C22#1062285112yes—
520C22#1062285112yes—
521C22#1062285612yes—
522C22#1062285912yes—
523C22C2×#6700211yescharacteristic
524C22C2×#6700311yescharacteristic
525C22C2×#6700611yescharacteristic
526C4—21no—
527C4—21no—
528C4—21no—
529C4—21no—
530C4—42no—
531C4—42no—
532C4—42no—
533C4—42no—
534C4—42no—
535C4—444no—
536C4—882no—
537C2—21no—
538C2—21no—
539C2—22no—
540C2—82no—
541C2#1306761314yesdirect product factor
542C2C2×#1062285111yescharacteristic
543C2C2×#1062285911yescharacteristic
544C2C2×#1062285611yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#539C2
socleC23×C11#120
prime radicalC2×C11×#121C22
hypercenterC2×#539D11
hypocenterC11C2×#1609
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#539

Complements

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

NH ≅ G/Ntype
1. C2×#10622656C2semidirect
3. C2×#10622596C2semidirect
4. #13067613C2direct (N × H)
5. C2×#10622176C2semidirect
7. C2×#10622166C2semidirect
31. #10622656C22semidirect
35. #10622596C22semidirect
38. #10622176C22semidirect
40. #10622166C22semidirect
377. C2×C11#1609semidirect
453. C11C2×#1609semidirect
541. C2#13067613direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106226562
C2×#106226462
C2×#106225962
#130676132
C2×#106221762
C2×#106221752
C2×#106221662
C2×C11×#5392
C2×#160911