Finite Group Databasebeta

← C2×#13067702 #14729467

Subgroups — C2×#13067702 #14729467

Order 2816.

1322 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623257C211yesmaximal, characteristic, complemented
2C2×#10622685C211yesmaximal, characteristic, complemented
3C2×#10622685C211yesmaximal, characteristic, complemented
4#13067702C218yesmaximal, direct product factor
5C2×#10622185C211yesmaximal, characteristic, complemented
6C2×#10622097C211yesmaximal, characteristic, complemented
7C2×#10622097C211yesmaximal, characteristic, complemented
8C2×C11×#486C211yesmaximal, characteristic, complemented
9C22×#4343—21no—
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C11×#127C2211yescharacteristic
12C2×#66999—21no—
13C22×#4323—21no—
14C22×#4323—21no—
15#10623257—22no—
16#10623257—22no—
17#10623257—22no—
18#10623257C2214yescomplemented
19C2×#66948—21no—
20C2×#66947—22no—
21C2×C4⋊C4×D11—21no—
22C2×C4×D44C2211yescharacteristic
23C2×C4×D44C2211yescharacteristic
24C11×#486—22no—
25C11×#486C2214yescomplemented
26C2×C11×#102—22no—
27C2×C4×C8×C11C2211yescharacteristic
28C2×#66896—21no—
29C2×#66896—21no—
30#10622685—22no—
31#10622685—22no—
32#10622685C2214yescomplemented
33#10622685C2214yescomplemented
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36#10622185C2214yescomplemented
37#10622097C2214yescomplemented
38#10622097C2214yescomplemented
39C22×Q8×C11—21no—
40C22×D4×C11—21no—
41C22×D4×C11—21no—
42C22×D4×C11—21no—
43C2×#4343—24no—
44C2×#4343—24no—
45C2×#4343—44no—
46C2×#4343—44no—
47C22×D44—22no—
48C22×D44D411yescharacteristic
49C22×D44D411yescharacteristic
50C22×C4×D11—22no—
51C22×C4×D11—21no—
52C22×C4×D11—21no—
53C22×C8×C11—21no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8D412yes—
57C11×C4⋊Q8C2312yes—
58C11×#127—21no—
59C11×#127—21no—
60C11×#127—21no—
61C11×#127C2312yes—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4D412yes—
64C2×C42×C11C2311yescharacteristic
65#66999—24no—
66#66999—24no—
67C2×#4323—24no—
68C2×#4323—24no—
69C2×#4323—44no—
70C2×#4323—44no—
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×C4⋊Dic11D411yescharacteristic
75C2×C4⋊Dic11D411yescharacteristic
76C2×Dic11⋊C4—22no—
77C22×C11⋊C8—21no—
78C22×C11⋊C8—21no—
79#66948—24no—
80#66948—24no—
81#66947—28no—
82#66947—28no—
83C4⋊C4×D11—24no—
84C4⋊C4×D11—24no—
85C4×D44—21no—
86C4×D44—21no—
87C4×D44—21no—
88C4×D44—21no—
89C4×D44D412yes—
90C4×D44D412yes—
91C4×D44C2312yes—
92C4×D44C2312yes—
93C11×#102—28no—
94C4×C8×C11—21no—
95C4×C8×C11C2312yes—
96#66896—24no—
97#66896—24no—
98C4⋊(C11⋊C8)—21no—
99C4⋊(C11⋊C8)—21no—
100C4⋊(C11⋊C8)C2312yes—
101C4⋊(C11⋊C8)C2312yes—
102C2×#1625—111nomaximal, Sylow
103C24×C11—41no—
104C23×D11—21no—
105C23×D11—21no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—42no—
109C2×Q8×C11—42no—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11—44no—
114C2×D4×C11—41no—
115C2×D4×C11—41no—
116C2×D4×C11—41no—
117C2×D4×C11—42no—
118C2×D4×C11—42no—
119C2×D4×C11—42no—
120C2×D4×C11—42no—
121C22×C4×C11—22no—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×Dic11—21no—
126C22×Dic11—21no—
127#4343—48no—
128#4343—416no—
129#4343—48no—
130C2×D44—28no—
131C2×D44—21no—
132C2×D44—21no—
133C2×D44—22no—
134C2×D44—22no—
135C2×D44—22no—
136C2×D44—48no—
137C2×D44D814yescomplemented
138C2×D44C2×D412yes—
139C2×D44C2×D412yes—
140C2×C4×D11—28no—
141C2×C4×D11—22no—
142C2×C4×D11—22no—
143C2×C4×D11—22no—
144C2×C4×D11—22no—
145C2×C4×D11—48no—
146C2×C4×D11—42no—
147C2×C4×D11—42no—
148C2×C4×D11—42no—
149C2×C4×D11—42no—
150C2×C8×C11—22no—
151C2×C8×C11—42no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4C2×D414yes—
156C42×C11C2×D411yescharacteristic
157C42×C11C2×D411yescharacteristic
158C42×C11C2×D411yescharacteristic
159C42×C11C2411yescharacteristic
160#4323—48no—
161#4323—48no—
162(C2×D11)⋊C4—28no—
163(C2×D11)⋊C4—22no—
164(C2×D11)⋊C4—22no—
165(C2×D11)⋊C4—22no—
166(C2×D11)⋊C4—22no—
167C4⋊Dic11—21no—
168C4⋊Dic11—21no—
169C4⋊Dic11C2×D412yes—
170C4⋊Dic11C2×D412yes—
171Dic11⋊C4—28no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—42no—
175C2×C11⋊C8—42no—
176C2×#547—111no—
177C2×#486D1111yescharacteristic, complemented
178C2×#459—111no—
179C2×#459—111no—
180#1625—118no—
181C2×#332—111no—
182C2×D4⋊C8—111no—
183C2×D4⋊C8—111no—
184C23×C11—42no—
185C23×C11—82no—
186C23×C11—82no—
187C23×C11—82no—
188C23×C11#12011yescharacteristic
189C22×D11—22no—
190C22×D11—24no—
191C22×D11—22no—
192C22×D11—42no—
193C22×D11—42no—
194C22×D11—42no—
195C22×D11—42no—
196C22×D11—42no—
197Q8×C11—42no—
198Q8×C11—42no—
199Q8×C11—44no—
200D4×C11—44no—
201D4×C11—42no—
202D4×C11—42no—
203D4×C11—42no—
204D4×C11—42no—
205D4×C11—82no—
206D4×C11—82no—
207D4×C11—82no—
208C2×C4×C11—22no—
209C2×C4×C11—24no—
210C2×C4×C11—44no—
211C2×C4×C11#12011yescharacteristic
212C2×C4×C11#12011yescharacteristic
213C2×C4×C11#12011yescharacteristic
214C2×C4×C11C2×D812yes—
215C2×C4×C11#13512yes—
216C2×C4×C11AGL(1,ℤ/8)12yes—
217C2×C4×C11AGL(1,ℤ/8)12yes—
218C2×C4×C11C22×D411yescharacteristic
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C22×D411yescharacteristic
221C2×Dic11—22no—
222C2×Dic11—22no—
223C2×Dic11—42no—
224C2×Dic11—42no—
225D44—22no—
226D44—22no—
227D44—22no—
228D44—24no—
229D44—416no—
230D44—42no—
231D44C2×D814yescomplemented
232C4×D11—416no—
233C4×D11—42no—
234C4×D11—42no—
235C4×D11—42no—
236C4×D11—42no—
237C4×D11—44no—
238C4×D11—44no—
239C8×C11—42no—
240C11⋊C8—42no—
241C11⋊C8—42no—
242C22×#41—221no—
243C22×D8—221no—
244C22×D8—221no—
245#547—114no—
246#547—222no—
247#547—222no—
248#547—222no—
249C2×C4⋊Q8C2×D1111yescharacteristic
250C2×#127C2×D1111yescharacteristic
251C2×#123—222no—
252C2×C22⋊Q8—221no—
253C2×#121—221no—
254C2×C4×D4—111no—
255C2×C4×D4—111no—
256C22×C4⋊C4—221no—
257#486—22no—
258#486C2×D1114yescomplemented
259#459—114no—
260#459—114no—
261#459—222no—
262#459—222no—
263C2×C4⋊C8—111no—
264C2×C4⋊C8—111no—
265C2×#102—22no—
266C2×#102—221no—
267C2×#102—221no—
268C2×C4×C8C2×D1111yescharacteristic
269#332—114no—
270D4⋊C8—114no—
271D4⋊C8—114no—
272C22×C11—82no—
273C22×C11—82no—
274C22×C11—82no—
275C22×C11—164no—
276C22×C11#44712yes—
277C22×C11#44912yes—
278C22×C11#45412yes—
279C22×C11C2×#12011yescharacteristic
280C2×D11—24no—
281C2×D11—48no—
282C2×D11—42no—
283C2×D11—42no—
284C2×D11—42no—
285C2×D11—42no—
286C2×D11—42no—
287C2×D11—84no—
288C4×C11—21no—
289C4×C11—21no—
290C4×C11—44no—
291C4×C11#44712yes—
292C4×C11#44912yes—
293C4×C11C22×D811yescharacteristic
294C4×C11C2×#13511yescharacteristic
295C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
296C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
297Dic11—42no—
298Dic11—42no—
299C2×#41—224no—
300C2×#41—224no—
301C2×#41—444no—
302C2×#41—444no—
303C22×Q8—21no—
304C22×D4—21no—
305C22×D4—21no—
306C22×D4—21no—
307C22×D4—111no—
308C22×D4—111no—
309C22×D4—222no—
310C23×C4—222no—
311C23×C4—221no—
312C23×C4—221no—
313C2×D8—224no—
314C2×D8—224no—
315C2×D8—444no—
316C2×D8—444no—
317C22×C8—21no—
318C22×C8—221no—
319C22×C8—221no—
320C4⋊Q8—21no—
321C4⋊Q8—21no—
322C4⋊Q8C22⋊D1112yes—
323C4⋊Q8C22×D1112yes—
324#127—21no—
325#127—21no—
326#127—21no—
327#127C22×D1112yes—
328#123—228no—
329#123—228no—
330C22⋊Q8—224no—
331C22⋊Q8—224no—
332#121—224no—
333#121—224no—
334C4×D4—112no—
335C4×D4—112no—
336C4×D4—112no—
337C4×D4—112no—
338C4×D4—221no—
339C4×D4—221no—
340C4×D4—221no—
341C4×D4—221no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—111no—
344C2×C4⋊C4—111no—
345C2×C4⋊C4—224no—
346C2×C4⋊C4—224no—
347C2×C4⋊C4—222no—
348C2×C4⋊C4C22⋊D1112yes—
349C2×C22⋊C4—222no—
350C2×C22⋊C4—221no—
351C2×C22⋊C4—221no—
352C2×C42C22×D1111yescharacteristic
353C4⋊C8—112no—
354C4⋊C8—112no—
355C4⋊C8—221no—
356C4⋊C8—221no—
357#102—28no—
358#102—224no—
359#102—224no—
360C4×C8—21no—
361C4×C8C22×D1112yes—
362C2×C11—162no—
363C2×C11#162514yescomplemented
364C2×C11C2×#44711yescharacteristic
365C2×C11C2×#44911yescharacteristic
366C2×C11C2×#45411yescharacteristic
367D11—44no—
368D11—82no—
369C24—41no—
370C24—221no—
371C24—221no—
372#41—448no—
373#41—4416no—
374#41—448no—
375C2×Q8—22no—
376C2×Q8—22no—
377C2×Q8—42no—
378C2×Q8—42no—
379C2×D4—22no—
380C2×D4—22no—
381C2×D4—22no—
382C2×D4—44no—
383C2×D4—42no—
384C2×D4—42no—
385C2×D4—42no—
386C2×D4—42no—
387C2×D4—41no—
388C2×D4—41no—
389C2×D4—41no—
390C2×D4—114no—
391C2×D4—112no—
392C2×D4—112no—
393C2×D4—228no—
394C2×D4—222no—
395C2×D4—222no—
396C2×D4—222no—
397C2×D4—221no—
398C2×D4—221no—
399C2×D4—448no—
400C22×C4—22no—
401C22×C4—228no—
402C22×C4—221no—
403C22×C4—221no—
404C22×C4—222no—
405C22×C4—222no—
406C22×C4—222no—
407C22×C4—222no—
408C22×C4—448no—
409C22×C4—442no—
410C22×C4—442no—
411C22×C4—442no—
412C22×C4—442no—
413C22×C4D4×D1111yescharacteristic
414C22×C4D4×D1111yescharacteristic
415C22×C4C2×C22⋊D1111yescharacteristic
416D8—448no—
417D8—448no—
418C2×C8—22no—
419C2×C8—42no—
420C2×C8—222no—
421C2×C8—222no—
422C2×C8—442no—
423C2×C8—442no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—112no—
428C4⋊C4—112no—
429C4⋊C4—228no—
430C4⋊C4—221no—
431C4⋊C4—221no—
432C4⋊C4C2×C22⋊D1114yes—
433C22⋊C4—228no—
434C22⋊C4—222no—
435C22⋊C4—222no—
436C22⋊C4—222no—
437C22⋊C4—222no—
438C42D4×D1111yescharacteristic
439C42D4×D1111yescharacteristic
440C42C2×C22⋊D1111yescharacteristic
441C42C23×D1111yescharacteristic
442C11C2×#162511yescharacteristic, complemented, Sylow
443C23—42no—
444C23—82no—
445C23—82no—
446C23—82no—
447C23—224no—
448C23—222no—
449C23—222no—
450C23—442no—
451C23—442no—
452C23—442no—
453C23—442no—
454C23—442no—
455C23#6699011yescharacteristic
456Q8—44no—
457Q8—42no—
458Q8—42no—
459D4—44no—
460D4—42no—
461D4—42no—
462D4—42no—
463D4—42no—
464D4—82no—
465D4—82no—
466D4—82no—
467D4—114no—
468D4—224no—
469D4—222no—
470D4—222no—
471D4—222no—
472D4—4416no—
473D4—442no—
474C2×C4—22no—
475C2×C4—24no—
476C2×C4—44no—
477C2×C4—222no—
478C2×C4—222no—
479C2×C4—4416no—
480C2×C4—442no—
481C2×C4—442no—
482C2×C4—444no—
483C2×C4—442no—
484C2×C4—442no—
485C2×C4—442no—
486C2×C4—442no—
487C2×C4—444no—
488C2×C4D8×D1112yes—
489C2×C4#6696412yes—
490C2×C4#6696712yes—
491C2×C4#6696912yes—
492C2×C4#6699011yescharacteristic
493C2×C4#6699011yescharacteristic
494C2×C4#6699011yescharacteristic
495C2×C4C2×D4×D1111yescharacteristic
496C2×C4C2×D4×D1111yescharacteristic
497C2×C4C22×C22⋊D1111yescharacteristic
498C8—42no—
499C8—442no—
500C8—442no—
501C22—82no—
502C22—82no—
503C22—82no—
504C22—164no—
505C22—224no—
506C22—442no—
507C22—448no—
508C22—442no—
509C22—442no—
510C22—442no—
511C22—442no—
512C22—884no—
513C22#1062267512yes—
514C22#1062276912yes—
515C22#1062278512yes—
516C22C2×#6699011yescharacteristic
517C4—21no—
518C4—21no—
519C4—44no—
520C4—442no—
521C4—442no—
522C4#1062276912yes—
523C4#1062278512yes—
524C4C2×D8×D1111yescharacteristic
525C4C2×#6696411yescharacteristic
526C4C2×#6696711yescharacteristic
527C4C2×#6696911yescharacteristic
528C2—162no—
529C2—444no—
530C2—882no—
531C2#1306770214yesdirect product factor
532C2C2×#1062276911yescharacteristic
533C2C2×#1062278511yescharacteristic
534C2C2×#1062267511yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#486C2
socleC23×C11#120
hypercenterC2×#486D11
hypocenterC11C2×#1625
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#486

Complements

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

NH ≅ G/Ntype
1. C2×#10623257C2semidirect
2. C2×#10622685C2semidirect
3. C2×#10622685C2semidirect
4. #13067702C2direct (N × H)
5. C2×#10622185C2semidirect
6. C2×#10622097C2semidirect
7. C2×#10622097C2semidirect
8. C2×C11×#486C2semidirect
18. #10623257C22semidirect
25. C11×#486C22semidirect
32. #10622685C22semidirect
33. #10622685C22semidirect
36. #10622185C22semidirect
37. #10622097C22semidirect
38. #10622097C22semidirect
137. C2×D44D8semidirect
177. C2×#486D11semidirect
231. D44C2×D8semidirect
258. #486C2×D11semidirect
363. C2×C11#1625semidirect
442. C11C2×#1625semidirect
531. C2#13067702direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232572
C2×#106226852
#130677022
C2×#106221852
C2×#106220972
C2×C11×#4862
C2×#162511