Finite Group Databasebeta

← C2×#13067681 #14729628

Subgroups — C2×#13067681 #14729628

Order 2816.

1438 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622686C211yesmaximal, characteristic, complemented
2C2×#10622640C211yesmaximal, characteristic, complemented
3C2×#10622628C211yesmaximal, characteristic, complemented
4#13067681C218yesmaximal, direct product factor
5C2×#10622182C211yesmaximal, characteristic, complemented
6C2×Q8⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
7C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
8C2×C11×#550C211yesmaximal, characteristic, complemented
9C22×C11×#41—21no—
10C11×#550—22no—
11C11×#550—22no—
12C11×#550—22no—
13C11×#550C2214yescomplemented
14C2×C11×#127—21no—
15C2×C11×#127C2211yescharacteristic
16C2×C11×#121—22no—
17C2×C11×#121—21no—
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×D4×C11—21no—
20C2×C4×D4×C11C2211yescharacteristic
21C22×#4325—21no—
22C22×#4323—21no—
23C22×#4323—22no—
24C2×#66927C2211yescharacteristic
25#10622686—22no—
26#10622686C2214yescomplemented
27#10622640—22no—
28#10622640C2214yescomplemented
29#10622628—22no—
30#10622628C2214yescomplemented
31C2×#66873—21no—
32C2×#66873—21no—
33C2×C4⋊(C11⋊C8)C2211yescharacteristic
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C2×C4×C11⋊C8C2211yescharacteristic
36#10622182C2214yescomplemented
37Q8⋊(C11⋊C8)C2214yescomplemented
38D4⋊(C11⋊C8)C2214yescomplemented
39C2×C11×#41—24no—
40C2×C11×#41—24no—
41C2×C11×#41—44no—
42C2×C11×#41—44no—
43C22×Q8×C11D411yescharacteristic
44C22×D4×C11—22no—
45C22×D4×C11—22no—
46C22×D4×C11—21no—
47C22×D4×C11—21no—
48C22×D4×C11D411yescharacteristic
49C22×D4×C11D412yes—
50C23×C4×C11—22no—
51C23×C4×C11—21no—
52C22×D44—21no—
53C22×D44—21no—
54C22×D44—21no—
55C11×#127—24no—
56C11×#127—24no—
57C11×#127—21no—
58C11×#127—21no—
59C11×#127D412yes—
60C11×#127C2312yes—
61C11×#121—24no—
62C11×#121—28no—
63C11×#121—28no—
64C11×#121—24no—
65C4×Q8×C11—21no—
66C4×Q8×C11—21no—
67C4×Q8×C11D412yes—
68C4×Q8×C11C2312yes—
69C4×D4×C11—24no—
70C4×D4×C11—24no—
71C4×D4×C11—21no—
72C4×D4×C11—21no—
73C4×D4×C11D412yes—
74C4×D4×C11C2312yes—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4D411yescharacteristic
77C2×C11×C4⋊C4D411yescharacteristic
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—21no—
80C2×C42×C11—21no—
81C2×C42×C11C2311yescharacteristic
82C2×#4325—24no—
83C2×#4325—44no—
84C2×#4323—24no—
85C2×#4323—28no—
86C2×#4323—48no—
87C2×#4323—44no—
88C22×C11⋊C8—21no—
89C22×C11⋊C8—21no—
90C22×C11⋊C8—21no—
91#66927—21no—
92#66927—21no—
93#66927—21no—
94#66927C2312yes—
95#66873—24no—
96#66873—24no—
97C4⋊(C11⋊C8)—21no—
98C4⋊(C11⋊C8)—21no—
99C4⋊(C11⋊C8)C2312yes—
100C4⋊(C11⋊C8)C2312yes—
101C4×C11⋊C8—21no—
102C4×C11⋊C8C2312yes—
103C2×#1621—111nomaximal, Sylow
104C24×C11—21no—
105C24×C11—22no—
106C23×D11—41no—
107C11×#41—48no—
108C11×#41—416no—
109C11×#41—48no—
110C2×Q8×C11—21no—
111C2×Q8×C11—22no—
112C2×Q8×C11D814yescomplemented
113C2×Q8×C11C2×D412yes—
114C2×D4×C11—28no—
115C2×D4×C11—28no—
116C2×D4×C11—21no—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C2×D4×C11—22no—
122C2×D4×C11—22no—
123C2×D4×C11—22no—
124C2×D4×C11—48no—
125C2×D4×C11—44no—
126C2×D4×C11—42no—
127C2×D4×C11—42no—
128C2×D4×C11—42no—
129C2×D4×C11—42no—
130C2×D4×C11—84no—
131C2×D4×C11C2×D412yes—
132C2×D4×C11C2×D414yes—
133C22×C4×C11—21no—
134C22×C4×C11—28no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—48no—
140C22×C4×C11—42no—
141C22×C4×C11—42no—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C2×D44—22no—
146C2×D44—22no—
147C2×D44—22no—
148C2×D44—44no—
149C2×D44—41no—
150C2×D44—41no—
151C2×D44—41no—
152C2×D44—42no—
153C2×D44—42no—
154C2×D44—42no—
155C2×D44—42no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4C2×D412yes—
161C11×C4⋊C4C2×D412yes—
162C11×C22⋊C4—28no—
163C11×C22⋊C4—22no—
164C11×C22⋊C4—22no—
165C42×C11—22no—
166C42×C11—22no—
167C42×C11C2×D411yescharacteristic
168C42×C11C2×D411yescharacteristic
169C42×C11C2×D411yescharacteristic
170C42×C11C2411yescharacteristic
171#4325—48no—
172#4323—48no—
173#4323—416no—
174C2×C11⋊C8—24no—
175C2×C11⋊C8—22no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—42no—
179C2×C11⋊C8—42no—
180C2×#550D1111yescharacteristic, complemented
181C2×#493—111no—
182C2×#460—111no—
183C2×#459—111no—
184#1621—118no—
185C2×#331—111no—
186C2×Q8⋊C8—111no—
187C2×D4⋊C8—111no—
188C23×C11—22no—
189C23×C11—24no—
190C23×C11—44no—
191C23×C11—42no—
192C23×C11—42no—
193C23×C11—44no—
194C23×C11—44no—
195C23×C11—42no—
196C23×C11#12011yescharacteristic
197C22×D11—42no—
198C22×D11—82no—
199C22×D11—82no—
200C22×D11—82no—
201Q8×C11—22no—
202Q8×C11—24no—
203Q8×C11C2×D814yescomplemented
204D4×C11—22no—
205D4×C11—22no—
206D4×C11—44no—
207D4×C11—416no—
208D4×C11—42no—
209D4×C11—42no—
210D4×C11—42no—
211D4×C11—42no—
212D4×C11—44no—
213D4×C11—42no—
214D4×C11—44no—
215D4×C11—82no—
216D4×C11—88no—
217C2×C4×C11—22no—
218C2×C4×C11—24no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—416no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—44no—
228C2×C4×C11#12011yescharacteristic
229C2×C4×C11#12011yescharacteristic
230C2×C4×C11#12011yescharacteristic
231C2×C4×C11C2×D812yes—
232C2×C4×C11#13512yes—
233C2×C4×C11AGL(1,ℤ/8)12yes—
234C2×C4×C11AGL(1,ℤ/8)12yes—
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C22×D411yescharacteristic
237C2×C4×C11C22×D411yescharacteristic
238D44—44no—
239D44—42no—
240D44—42no—
241D44—42no—
242D44—42no—
243D44—82no—
244D44—82no—
245D44—82no—
246C11⋊C8—24no—
247C11⋊C8—42no—
248C11⋊C8—42no—
249C22×#41—21no—
250C22×SD16—221no—
251C22×D8—222no—
252C22×D8—221no—
253#550—22no—
254#550—22no—
255#550—22no—
256#550C2×D1114yescomplemented
257C2×#127—21no—
258C2×#127—111no—
259C2×#127C2×D1111yescharacteristic
260C2×#121—22no—
261C2×#121—21no—
262C2×C4×Q8C2×D1111yescharacteristic
263C2×C4×D4—21no—
264C2×C4×D4C2×D1111yescharacteristic
265#493—114no—
266#493—222no—
267#460—114no—
268#460—222no—
269#459—114no—
270#459—222no—
271C2×C4⋊C8—111no—
272C2×C4⋊C8—111no—
273C2×#102—221no—
274C2×#102—221no—
275C2×C4×C8—111no—
276#331—114no—
277Q8⋊C8—114no—
278D4⋊C8—114no—
279C22×C11—44no—
280C22×C11—42no—
281C22×C11—42no—
282C22×C11—44no—
283C22×C11—44no—
284C22×C11—42no—
285C22×C11—84no—
286C22×C11—88no—
287C22×C11#44712yes—
288C22×C11#44912yes—
289C22×C11#45312yes—
290C22×C11C2×#12011yescharacteristic
291C2×D11—82no—
292C2×D11—82no—
293C2×D11—82no—
294C2×D11—164no—
295C4×C11—24no—
296C4×C11—21no—
297C4×C11—21no—
298C4×C11—42no—
299C4×C11—42no—
300C4×C11#44712yes—
301C4×C11#44912yes—
302C4×C11C22×D811yescharacteristic
303C4×C11C2×#13511yescharacteristic
304C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
305C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
306C2×#41—24no—
307C2×#41—24no—
308C2×#41—44no—
309C2×#41—44no—
310C22×Q8C22⋊D1111yescharacteristic
311C22×D4—22no—
312C22×D4—22no—
313C22×D4—21no—
314C22×D4—21no—
315C22×D4—221no—
316C22×D4—221no—
317C22×D4—221no—
318C22×D4C22⋊D1111yescharacteristic
319C22×D4C22⋊D1112yes—
320C23×C4—22no—
321C23×C4—21no—
322C2×SD16—224no—
323C2×SD16—444no—
324C2×D8—224no—
325C2×D8—228no—
326C2×D8—448no—
327C2×D8—444no—
328C22×C8—221no—
329C22×C8—221no—
330C22×C8—221no—
331#127—24no—
332#127—24no—
333#127—21no—
334#127—21no—
335#127—112no—
336#127—221no—
337#127—221no—
338#127—221no—
339#127C22⋊D1112yes—
340#127C22×D1112yes—
341#121—24no—
342#121—28no—
343#121—28no—
344#121—24no—
345C4×Q8—21no—
346C4×Q8—21no—
347C4×Q8C22⋊D1112yes—
348C4×Q8C22×D1112yes—
349C4×D4—24no—
350C4×D4—24no—
351C4×D4—21no—
352C4×D4—21no—
353C4×D4C22⋊D1112yes—
354C4×D4C22×D1112yes—
355C2×C4⋊C4—21no—
356C2×C4⋊C4C22⋊D1111yescharacteristic
357C2×C4⋊C4C22⋊D1111yescharacteristic
358C2×C22⋊C4—22no—
359C2×C22⋊C4—21no—
360C2×C42—21no—
361C2×C42C22×D1111yescharacteristic
362C4⋊C8—112no—
363C4⋊C8—112no—
364C4⋊C8—221no—
365C4⋊C8—221no—
366#102—224no—
367#102—224no—
368C4×C8—112no—
369C4×C8—221no—
370C2×C11—82no—
371C2×C11—84no—
372C2×C11#162114yescomplemented
373C2×C11C2×#44711yescharacteristic
374C2×C11C2×#44911yescharacteristic
375C2×C11C2×#45311yescharacteristic
376D11—162no—
377C24—21no—
378C24—22no—
379C24—441no—
380#41—48no—
381#41—416no—
382#41—48no—
383C2×Q8—22no—
384C2×Q8—21no—
385C2×Q8#432314yescomplemented
386C2×Q8C2×C22⋊D1112yes—
387C2×D4—28no—
388C2×D4—28no—
389C2×D4—22no—
390C2×D4—22no—
391C2×D4—21no—
392C2×D4—22no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—48no—
398C2×D4—44no—
399C2×D4—42no—
400C2×D4—42no—
401C2×D4—42no—
402C2×D4—42no—
403C2×D4—84no—
404C2×D4—222no—
405C2×D4—222no—
406C2×D4—222no—
407C2×D4—444no—
408C2×D4—442no—
409C2×D4—442no—
410C2×D4—442no—
411C2×D4—442no—
412C2×D4—441no—
413C2×D4—441no—
414C2×D4—441no—
415C2×D4C2×C22⋊D1112yes—
416C2×D4C2×C22⋊D1114yes—
417C22×C4—21no—
418C22×C4—28no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—48no—
424C22×C4—42no—
425C22×C4—42no—
426C22×C4C2×C22⋊D1111yescharacteristic
427C22×C4C2×C22⋊D1111yescharacteristic
428C22×C4C2×C22⋊D1111yescharacteristic
429SD16—448no—
430D8—4416no—
431D8—448no—
432C2×C8—224no—
433C2×C8—222no—
434C2×C8—222no—
435C2×C8—222no—
436C2×C8—442no—
437C2×C8—442no—
438C4⋊C4—22no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—22no—
442C4⋊C4C2×C22⋊D1112yes—
443C4⋊C4C2×C22⋊D1112yes—
444C22⋊C4—28no—
445C22⋊C4—22no—
446C22⋊C4—22no—
447C42—22no—
448C42—22no—
449C42C2×C22⋊D1111yescharacteristic
450C42C2×C22⋊D1111yescharacteristic
451C42C2×C22⋊D1111yescharacteristic
452C42C23×D1111yescharacteristic
453C11C2×#162111yescharacteristic, complemented, Sylow
454C23—22no—
455C23—24no—
456C23—44no—
457C23—42no—
458C23—42no—
459C23—44no—
460C23—44no—
461C23—42no—
462C23—442no—
463C23—882no—
464C23—882no—
465C23—882no—
466C23#6700611yescharacteristic
467Q8—22no—
468Q8—24no—
469Q8C2×#432314yescomplemented
470D4—22no—
471D4—22no—
472D4—44no—
473D4—416no—
474D4—42no—
475D4—42no—
476D4—44no—
477D4—42no—
478D4—42no—
479D4—42no—
480D4—44no—
481D4—82no—
482D4—88no—
483D4—444no—
484D4—442no—
485D4—442no—
486D4—442no—
487D4—442no—
488D4—882no—
489D4—882no—
490D4—882no—
491C2×C4—24no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—416no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—44no—
502C2×C4C2×#432312yes—
503C2×C4#6698512yes—
504C2×C4#6700212yes—
505C2×C4#6700312yes—
506C2×C4#6700611yescharacteristic
507C2×C4#6700611yescharacteristic
508C2×C4#6700611yescharacteristic
509C2×C4C22×C22⋊D1111yescharacteristic
510C2×C4C22×C22⋊D1111yescharacteristic
511C2×C4C22×C22⋊D1111yescharacteristic
512C8—224no—
513C8—442no—
514C8—442no—
515C22—44no—
516C22—42no—
517C22—42no—
518C22—44no—
519C22—44no—
520C22—42no—
521C22—84no—
522C22—88no—
523C22—882no—
524C22—882no—
525C22—882no—
526C22—1764no—
527C22#1062283012yes—
528C22#1062285112yes—
529C22#1062285412yes—
530C22C2×#6700611yescharacteristic
531C4—24no—
532C4—21no—
533C4—21no—
534C4—42no—
535C4—42no—
536C4#1062283012yes—
537C4#1062285112yes—
538C4C22×#432311yescharacteristic
539C4C2×#6698511yescharacteristic
540C4C2×#6700211yescharacteristic
541C4C2×#6700311yescharacteristic
542C2—82no—
543C2—84no—
544C2—1762no—
545C2#1306768114yesdirect product factor
546C2C2×#1062283011yescharacteristic
547C2C2×#1062285111yescharacteristic
548C2C2×#1062285411yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#550C2
socleC23×C11#120
hypercenterC2×#550D11
hypocenterC11C2×#1621
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C2×#10622686C2semidirect
2. C2×#10622640C2semidirect
3. C2×#10622628C2semidirect
4. #13067681C2direct (N × H)
5. C2×#10622182C2semidirect
6. C2×Q8⋊(C11⋊C8)C2semidirect
7. C2×D4⋊(C11⋊C8)C2semidirect
8. C2×C11×#550C2semidirect
13. C11×#550C22semidirect
26. #10622686C22semidirect
28. #10622640C22semidirect
30. #10622628C22semidirect
36. #10622182C22semidirect
37. Q8⋊(C11⋊C8)C22semidirect
38. D4⋊(C11⋊C8)C22semidirect
112. C2×Q8×C11D8semidirect
180. C2×#550D11semidirect
203. Q8×C11C2×D8semidirect
256. #550C2×D11semidirect
372. C2×C11#1621semidirect
385. C2×Q8#4323semidirect
453. C11C2×#1621semidirect
469. Q8C2×#4323semidirect
545. C2#13067681direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106226862
C2×#106226402
C2×#106226282
#130676812
C2×#106221822
C2×Q8⋊(C11⋊C8)2
C2×D4⋊(C11⋊C8)2
C2×C11×#5502
C2×#162111