Finite Group Databasebeta

← C2×#13067616 #14725916

Subgroups — C2×#13067616 #14725916

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×#10623176C211yesmaximal, characteristic
2C2×#10622656C211yesmaximal, characteristic, complemented
3C2×#10622349C211yesmaximal, characteristic
4C2×#10622274C211yesmaximal, characteristic, complemented
5#13067616C218yesmaximal, direct product factor
6C2×#10622089C211yesmaximal, characteristic
7C2×#10622107C211yesmaximal, characteristic, complemented
8C2×C11×#328C211yesmaximal, characteristic, complemented
9C2×C11×C22⋊Q8C2211yescharacteristic
10C2×#66999—21no—
11C2×#66983C2211yescharacteristic
12C22×C4⋊Dic11—21no—
13C22×C4⋊Dic11C2211yescharacteristic
14C22×Dic11⋊C4C2211yescharacteristic
15#10623176—22no—
16#10623176—22no—
17#10623176—22no—
18#10623176C2214yes—
19C2×#66951—21no—
20C2×#66947—21no—
21C2×#66943—21no—
22C2×#66939—21no—
23C2×(C22⋊D11)⋊C4—21no—
24C2×C11×C22⋊C8C2211yescharacteristic
25C2×C11×#95C2211yescharacteristic
26C2×#66899—21no—
27C2×C11⋊#95—21no—
28C2×C22⋊(C11⋊C8)C2211yescharacteristic
29C2×#66885—21no—
30C2×#66882—21no—
31#10622656—22no—
32#10622656C2214yescomplemented
33C2×#66872—21no—
34#10622349—22no—
35#10622349C2214yes—
36#10622274—22no—
37#10622274C2214yescomplemented
38C11×#328C2214yescomplemented
39#10622107C2214yescomplemented
40#10622089C2214yes—
41C22×Q8×C11D411yescharacteristic
42C23×C4×C11—21no—
43C23×C4×C11C2311yescharacteristic
44C22×C22⋊D11—21no—
45C23×Dic11—21no—
46C23×Dic11D411yescharacteristic
47C23×Dic11D411yescharacteristic
48C22×D44D411yescharacteristic
49C22×C4×D11—21no—
50C22×C8×C11—21no—
51C11×C22⋊Q8—21no—
52C11×C22⋊Q8—21no—
53C11×C22⋊Q8D412yes—
54C11×C22⋊Q8C2312yes—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4D411yescharacteristic
57C2×C11×C22⋊C4—21no—
58#66999—24no—
59#66999—24no—
60#66983—21no—
61#66983—21no—
62#66983D412yes—
63#66983C2312yes—
64C2×(C2×D11)⋊C4—21no—
65C2×(C2×D11)⋊C4—21no—
66C2×(C2×D11)⋊C4—21no—
67C2×(C2×D11)⋊C4—21no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11—21no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11—24no—
76C2×C4⋊Dic11—44no—
77C2×C4⋊Dic11D411yescharacteristic
78C2×C4⋊Dic11C2312yes—
79C2×Dic11⋊C4—21no—
80C2×Dic11⋊C4—21no—
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4D412yes—
85C2×Dic11⋊C4C2312yes—
86C2×C4×Dic11—21no—
87C22×C11⋊C8—21no—
88#66951—24no—
89#66951—24no—
90#66947—24no—
91#66947—24no—
92#66943—24no—
93#66943—24no—
94#66939—24no—
95#66939—24no—
96(C22⋊D11)⋊C4—24no—
97(C22⋊D11)⋊C4—24no—
98C11×C22⋊C8—21no—
99C11×C22⋊C8C2312yes—
100C11×#95—21no—
101C11×#95C2312yes—
102#66899—24no—
103C11⋊#95—24no—
104C22⋊(C11⋊C8)—21no—
105C22⋊(C11⋊C8)C2312yes—
106#66885—24no—
107#66882—24no—
108#66872—24no—
109C2×#1609—111nomaximal, Sylow
110C24×C11C2×D411yescharacteristic
111C23×D11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—42no—
114C2×Q8×C11C2×D412yes—
115C22×C4×C11—24no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—22no—
119C22×C4×C11—42no—
120C22×C4×C11—42no—
121C22×C4×C11—42no—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2411yescharacteristic
128C2×C22⋊D11—22no—
129C2×C22⋊D11—22no—
130C2×C22⋊D11—42no—
131C2×C22⋊D11—42no—
132C22×Dic11—21no—
133C22×Dic11—21no—
134C22×Dic11—21no—
135C22×Dic11—21no—
136C22×Dic11—21no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—42no—
141C22×Dic11—41no—
142C22×Dic11—41no—
143C22×Dic11—42no—
144C22×Dic11—42no—
145C22×Dic11C2×D412yes—
146C22×Dic11C2×D412yes—
147C2×D44—21no—
148C2×D44—42no—
149C2×D44C2×D412yes—
150C2×C4×D11—24no—
151C2×C4×D11—82no—
152C2×C8×C11—22no—
153C2×C8×C11—42no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4C2×D412yes—
158C11×C22⋊C4—22no—
159C11×C22⋊C4—22no—
160(C2×D11)⋊C4—24no—
161(C2×D11)⋊C4—24no—
162(C2×D11)⋊C4—24no—
163(C2×D11)⋊C4—22no—
164(C2×D11)⋊C4—22no—
165C4⋊Dic11—24no—
166C4⋊Dic11—24no—
167C4⋊Dic11—21no—
168C4⋊Dic11—22no—
169C4⋊Dic11—22no—
170C4⋊Dic11—48no—
171C4⋊Dic11—41no—
172C4⋊Dic11—41no—
173C4⋊Dic11C2×D412yes—
174Dic11⋊C4—24no—
175Dic11⋊C4—22no—
176Dic11⋊C4—22no—
177Dic11⋊C4—22no—
178Dic11⋊C4—22no—
179C4×Dic11—24no—
180C2×C11⋊C8—22no—
181C2×C11⋊C8—42no—
182C2×#539—111no—
183C2×#483—111no—
184C2×#480—111no—
185C2×#398—111no—
186#1609—118no—
187C2×#328D1111yescharacteristic, complemented
188C2×#327—111no—
189C2×#324—111no—
190C23×C11—22no—
191C23×C11—22no—
192C23×C11#12011yescharacteristic
193C23×C11#12011yescharacteristic
194C23×C11#13512yes—
195C23×C11AGL(1,ℤ/8)12yes—
196C23×C11C22×D411yescharacteristic
197C22×D11—22no—
198C22×D11—42no—
199C22×D11—42no—
200C22×D11—42no—
201Q8×C11—42no—
202Q8×C11—81no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—24no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—48no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11#12011yescharacteristic
218C2×C4×C11#12011yescharacteristic
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C22×D411yescharacteristic
221C22⋊D11—42no—
222C22⋊D11—42no—
223C22⋊D11—44no—
224C2×Dic11—22no—
225C2×Dic11—22no—
226C2×Dic11—22no—
227C2×Dic11—22no—
228C2×Dic11—22no—
229C2×Dic11—42no—
230C2×Dic11—42no—
231C2×Dic11—42no—
232C2×Dic11—42no—
233C2×Dic11—42no—
234C2×Dic11—42no—
235C2×Dic11—42no—
236C2×Dic11—42no—
237C2×Dic11—81no—
238C2×Dic11—82no—
239C2×Dic11—82no—
240D44—42no—
241D44—81no—
242C4×D11—84no—
243C8×C11—42no—
244C11⋊C8—42no—
245#539—114no—
246#539—222no—
247#539—222no—
248#539—222no—
249C2×#126—221no—
250C2×#125—221no—
251C2×#123—221no—
252C2×#123—221no—
253C2×C22⋊Q8—221no—
254C2×C22⋊Q8C2×D1111yescharacteristic
255C2×#121—111no—
256C2×C4×D4—221no—
257C22×C4⋊C4—111no—
258C22×C4⋊C4—111no—
259C22×C4⋊C4—221no—
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⋊C8C2×D1111yescharacteristic
270#398—114no—
271#398—222no—
272C2×#95—221no—
273C2×#95C2×D1111yescharacteristic
274#328C2×D1114yescomplemented
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#44912yes—
284C22×C11#44912yes—
285C22×C11#45612yes—
286C22×C11#45812yes—
287C22×C11C2×#12011yescharacteristic
288C22×C11C2×#13511yescharacteristic
289C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
290C2×D11—42no—
291C2×D11—42no—
292C2×D11—42no—
293C2×D11—84no—
294C4×C11—21no—
295C4×C11—21no—
296C4×C11—21no—
297C4×C11—21no—
298C4×C11—44no—
299C4×C11—42no—
300C4×C11—42no—
301Dic11—42no—
302Dic11—42no—
303Dic11—42no—
304Dic11—82no—
305C22×Q8D4411yescharacteristic
306C22×D4—111no—
307C22×D4—221no—
308C23×C4—21no—
309C23×C4—111no—
310C23×C4—111no—
311C23×C4—221no—
312C23×C4—221no—
313C23×C4C22×D1111yescharacteristic
314C22×C8—21no—
315C22×C8—221no—
316#126—224no—
317#126—224no—
318#125—224no—
319#125—224no—
320#123—224no—
321#123—224no—
322#123—224no—
323#123—224no—
324C22⋊Q8—21no—
325C22⋊Q8—21no—
326C22⋊Q8—224no—
327C22⋊Q8—224no—
328C22⋊Q8D4412yes—
329C22⋊Q8C22×D1112yes—
330#121—112no—
331#121—112no—
332#121—221no—
333#121—221no—
334C4×D4—224no—
335C4×D4—224no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—111no—
338C2×C4⋊C4—112no—
339C2×C4⋊C4—112no—
340C2×C4⋊C4—112no—
341C2×C4⋊C4—221no—
342C2×C4⋊C4—221no—
343C2×C4⋊C4—221no—
344C2×C4⋊C4—221no—
345C2×C4⋊C4—221no—
346C2×C4⋊C4—221no—
347C2×C4⋊C4—221no—
348C2×C4⋊C4—221no—
349C2×C4⋊C4—221no—
350C2×C4⋊C4—221no—
351C2×C4⋊C4—221no—
352C2×C4⋊C4—224no—
353C2×C4⋊C4—221no—
354C2×C4⋊C4—444no—
355C2×C4⋊C4D4411yescharacteristic
356C2×C22⋊C4—21no—
357C2×C22⋊C4—221no—
358C2×C22⋊C4—221no—
359C2×C22⋊C4—221no—
360C2×C22⋊C4—221no—
361C2×C42—221no—
362#107—224no—
363#106—224no—
364#103—224no—
365#102—224no—
366C22⋊C8—21no—
367C22⋊C8—112no—
368C22⋊C8—221no—
369C22⋊C8C22×D1112yes—
370#95—21no—
371#95—224no—
372#95C22×D1112yes—
373C2×C11—21no—
374C2×C11—21no—
375C2×C11—22no—
376C2×C11#160914yescomplemented
377C2×C11C2×#44911yescharacteristic
378C2×C11C2×#45611yescharacteristic
379C2×C11C2×#45811yescharacteristic
380D11—82no—
381C24—221no—
382C24D4×D1111yescharacteristic
383C2×Q8—21no—
384C2×Q8—42no—
385C2×Q8C2×D4412yes—
386C2×D4—112no—
387C2×D4—222no—
388C2×D4—222no—
389C2×D4—221no—
390C2×D4—442no—
391C2×D4—442no—
392C2×D4—442no—
393C22×C4—24no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—42no—
398C22×C4—42no—
399C22×C4—42no—
400C22×C4—112no—
401C22×C4—112no—
402C22×C4—224no—
403C22×C4—221no—
404C22×C4—221no—
405C22×C4—221no—
406C22×C4—221no—
407C22×C4—222no—
408C22×C4—222no—
409C22×C4—221no—
410C22×C4—222no—
411C22×C4—442no—
412C22×C4—441no—
413C22×C4—441no—
414C22×C4—442no—
415C22×C4—442no—
416C22×C4—882no—
417C22×C4C2×D4411yescharacteristic
418C22×C4C2×D4411yescharacteristic
419C22×C4D4×D1111yescharacteristic
420C22×C4D4×D1111yescharacteristic
421C22×C4D4×D1111yescharacteristic
422C22×C4C23×D1111yescharacteristic
423C2×C8—22no—
424C2×C8—42no—
425C2×C8—222no—
426C2×C8—442no—
427C4⋊C4—22no—
428C4⋊C4—21no—
429C4⋊C4—22no—
430C4⋊C4—112no—
431C4⋊C4—224no—
432C4⋊C4—224no—
433C4⋊C4—224no—
434C4⋊C4—222no—
435C4⋊C4—222no—
436C4⋊C4—221no—
437C4⋊C4—222no—
438C4⋊C4—222no—
439C4⋊C4—222no—
440C4⋊C4—222no—
441C4⋊C4—448no—
442C4⋊C4—441no—
443C4⋊C4—441no—
444C4⋊C4C2×D4412yes—
445C22⋊C4—22no—
446C22⋊C4—22no—
447C22⋊C4—224no—
448C22⋊C4—224no—
449C22⋊C4—224no—
450C22⋊C4—222no—
451C22⋊C4—222no—
452C42—224no—
453C11C2×#160911yescharacteristic, complemented, Sylow
454C23—22no—
455C23—22no—
456C23—222no—
457C23—442no—
458C23—442no—
459C23—442no—
460C23#6693511yescharacteristic
461C23#6693511yescharacteristic
462C23#6696712yes—
463C23#6697212yes—
464C23C2×D4×D1111yescharacteristic
465Q8—42no—
466Q8—81no—
467D4—442no—
468D4—442no—
469D4—442no—
470D4—444no—
471D4—881no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—24no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—48no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—222no—
487C2×C4—222no—
488C2×C4—222no—
489C2×C4—222no—
490C2×C4—222no—
491C2×C4—442no—
492C2×C4—442no—
493C2×C4—442no—
494C2×C4—442no—
495C2×C4—442no—
496C2×C4—442no—
497C2×C4—442no—
498C2×C4—442no—
499C2×C4—884no—
500C2×C4—881no—
501C2×C4—882no—
502C2×C4—882no—
503C2×C4#6693511yescharacteristic
504C2×C4#6693511yescharacteristic
505C2×C4C22×D4411yescharacteristic
506C2×C4C2×D4×D1111yescharacteristic
507C8—42no—
508C8—442no—
509C22—24no—
510C22—24no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—21no—
515C22—442no—
516C22—442no—
517C22—442no—
518C22—884no—
519C22#1062235512yes—
520C22#1062242412yes—
521C22#1062242412yes—
522C22#1062243912yes—
523C22C2×#6693511yescharacteristic
524C22C2×#6696711yescharacteristic
525C22C2×#6697211yescharacteristic
526C4—21no—
527C4—21no—
528C4—21no—
529C4—21no—
530C4—44no—
531C4—42no—
532C4—42no—
533C4—442no—
534C4—442no—
535C4—442no—
536C4—882no—
537C2—21no—
538C2—21no—
539C2—22no—
540C2—882no—
541C2#1306761614yesdirect product factor
542C2C2×#1062242411yescharacteristic
543C2C2×#1062243911yescharacteristic
544C2C2×#1062235511yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#328C2
socleC23×C11#120
prime radicalC2×#66983C22
hypercenterC2×#328D11
hypocenterC11C2×#1609
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
2. C2×#10622656C2semidirect
4. C2×#10622274C2semidirect
5. #13067616C2direct (N × H)
7. C2×#10622107C2semidirect
8. C2×C11×#328C2semidirect
32. #10622656C22semidirect
37. #10622274C22semidirect
38. C11×#328C22semidirect
39. #10622107C22semidirect
187. C2×#328D11semidirect
274. #328C2×D11semidirect
376. C2×C11#1609semidirect
453. C11C2×#1609semidirect
541. C2#13067616direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231762
C2×#106226562
C2×#106223492
C2×#106222742
#130676162
C2×#106220892
C2×#106221072
C2×C11×#3282
C2×#160911