Finite Group Databasebeta

← C2×#13067794 #14729428

Subgroups — C2×#13067794 #14729428

Order 2816.

1690 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×D44C211yesmaximal, characteristic
2C2×#10622701C211yesmaximal, characteristic, complemented
3C2×#10622696C211yesmaximal, characteristic, complemented
4#13067794C218yesmaximal, direct product factor
5C2×#10622123C211yesmaximal, characteristic, complemented
6C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
7C2×#10622121C211yesmaximal, characteristic, complemented
8C2×C11×#474C211yesmaximal, characteristic, complemented
9C22×D4×D11—21no—
10C23×D44—21no—
11C2×C11×C4⋊Q8C2211yescharacteristic, complemented
12C2×C4×D4×C11C2211yescharacteristic
13C22×#4325—21no—
14C2×#66983—21no—
15D4×D44—22no—
16D4×D44—22no—
17D4×D44—22no—
18D4×D44C2214yes—
19C2×#66948—21no—
20C2×#66935—22no—
21C2×#66927C2211yescharacteristic
22C2×C4×D44C2211yescharacteristic
23C11×#474—22no—
24C11×#474C2214yescomplemented
25C2×C11×#107—21no—
26C2×C11×C4⋊C8C2211yescharacteristic, complemented
27C2×C11×#102—21no—
28C2×#66899—21no—
29#10622701—22no—
30#10622701C2214yescomplemented
31#10622696—22no—
32#10622696C2214yescomplemented
33C2×#66873—22no—
34C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
35C2×C4×C11⋊C8C2211yescharacteristic, complemented
36D4⋊(C11⋊C8)C2214yescomplemented
37#10622123C2214yescomplemented
38#10622121C2214yescomplemented
39C24×D11—22no—
40C22×Q8×C11—21no—
41C22×D4×C11D411yescharacteristic
42C23×C4×C11—21no—
43C22×C22⋊D11—22no—
44C2×D4×D11—24no—
45C2×D4×D11—24no—
46C2×D4×D11—44no—
47C2×D4×D11—44no—
48C22×D44—22no—
49C22×D44—24no—
50C22×D44—21no—
51C22×D44—21no—
52C22×D44—24no—
53C22×D44—44no—
54C22×D44—44no—
55C22×D44D411yescharacteristic
56C22×D44D412yes—
57C22×C4×D11—21no—
58C22×C8×C11—21no—
59C11×C4⋊Q8—21no—
60C11×C4⋊Q8—21no—
61C11×C4⋊Q8—21no—
62C11×C4⋊Q8C2312yescomplemented
63C4×D4×C11—21no—
64C4×D4×C11—21no—
65C4×D4×C11D412yes—
66C4×D4×C11C2312yes—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4D411yescharacteristic
70C2×C11×C22⋊C4—21no—
71C2×C42×C11C2311yescharacteristic
72C2×#4325—24no—
73C2×#4325—44no—
74#66983—24no—
75#66983—24no—
76C2×(C2×D11)⋊C4—22no—
77C2×(C2×D11)⋊C4—21no—
78C2×C4⋊Dic11D411yescharacteristic
79C22×C11⋊C8—21no—
80C22×C11⋊C8—21no—
81#66948—24no—
82#66948—24no—
83#66935—28no—
84#66935—28no—
85#66927—21no—
86#66927—21no—
87#66927D412yes—
88#66927C2312yes—
89C4×D44—21no—
90C4×D44—21no—
91C4×D44D412yes—
92C4×D44C2312yes—
93C11×#107—24no—
94C11×C4⋊C8—21no—
95C11×C4⋊C8C2312yescomplemented
96C11×#102—24no—
97#66899—24no—
98#66873—28no—
99C4⋊(C11⋊C8)—21no—
100C4⋊(C11⋊C8)C2312yescomplemented
101C4×C11⋊C8—21no—
102C4×C11⋊C8C2312yescomplemented
103C2×#1639—111nomaximal, Sylow
104C24×C11—21no—
105C23×D11—21no—
106C23×D11—22no—
107C23×D11—28no—
108C23×D11—48no—
109C23×D11—48no—
110C23×D11—84no—
111C2×Q8×C11—22no—
112C2×Q8×C11—41no—
113C2×Q8×C11—42no—
114C2×Q8×C11—42no—
115C2×D4×C11—21no—
116C2×D4×C11—22no—
117C2×D4×C11SD1614yescomplemented
118C2×D4×C11C2×D412yes—
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—42no—
123C22×C4×C11—42no—
124C22×C4×C11—41no—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C2×C22⋊D11—28no—
129C2×C22⋊D11—48no—
130C22×Dic11—21no—
131D4×D11—48no—
132D4×D11—416no—
133D4×D11—48no—
134C2×D44—28no—
135C2×D44—21no—
136C2×D44—22no—
137C2×D44—22no—
138C2×D44—22no—
139C2×D44—22no—
140C2×D44—22no—
141C2×D44—22no—
142C2×D44—44no—
143C2×D44—48no—
144C2×D44—48no—
145C2×D44—416no—
146C2×D44—48no—
147C2×D44—42no—
148C2×D44—42no—
149C2×D44—42no—
150C2×D44—42no—
151C2×D44D814yes—
152C2×D44C2×D412yes—
153C2×D44C2×D414yes—
154C2×C4×D11—22no—
155C2×C4×D11—22no—
156C2×C4×D11—42no—
157C2×C4×D11—42no—
158C2×C8×C11—22no—
159C2×C8×C11—42no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—41no—
164C11×C4⋊C4—41no—
165C11×C4⋊C4C2×D412yes—
166C11×C22⋊C4—22no—
167C11×C22⋊C4—22no—
168C42×C11C2×D411yescharacteristic
169C42×C11C2×D411yescharacteristic
170C42×C11C2×D411yescharacteristic
171C42×C11C2411yescharacteristic
172#4325—48no—
173(C2×D11)⋊C4—28no—
174(C2×D11)⋊C4—22no—
175(C2×D11)⋊C4—22no—
176C4⋊Dic11—21no—
177C4⋊Dic11C2×D412yes—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—22no—
180C2×C11⋊C8—42no—
181C2×C11⋊C8—42no—
182C2×D42—111no—
183C2×#486—111no—
184C2×#474D1111yescharacteristic, complemented
185C2×#461—111no—
186#1639—118no—
187C2×#331—111no—
188C2×D4⋊C8—111no—
189C2×D4⋊C8—111no—
190C23×C11—22no—
191C23×C11—24no—
192C23×C11—42no—
193C23×C11—42no—
194C23×C11#12011yescharacteristic
195C22×D11—22no—
196C22×D11—24no—
197C22×D11—24no—
198C22×D11—416no—
199C22×D11—42no—
200C22×D11—42no—
201C22×D11—416no—
202C22×D11—44no—
203C22×D11—44no—
204C22×D11—44no—
205C22×D11—88no—
206C22×D11—832no—
207Q8×C11—42no—
208Q8×C11—42no—
209Q8×C11—82no—
210D4×C11—22no—
211D4×C11—24no—
212D4×C11C2×SD1614yescomplemented
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—44no—
219C2×C4×C11—42no—
220C2×C4×C11—82no—
221C2×C4×C11#12011yescharacteristic
222C2×C4×C11#12011yescharacteristic
223C2×C4×C11#12011yescharacteristic
224C2×C4×C11C2×D812yes—
225C2×C4×C11C2×SD1612yes—
226C2×C4×C11AGL(1,ℤ/8)12yes—
227C2×C4×C11AGL(1,ℤ/8)12yes—
228C2×C4×C11C22×D411yescharacteristic
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C22×D411yescharacteristic
231C22⋊D11—416no—
232C2×Dic11—22no—
233C2×Dic11—42no—
234D44—22no—
235D44—24no—
236D44—44no—
237D44—416no—
238D44—42no—
239D44—42no—
240D44—42no—
241D44—42no—
242D44—44no—
243D44—44no—
244D44—82no—
245D44C2×D814yes—
246C4×D11—42no—
247C4×D11—42no—
248C4×D11—44no—
249C8×C11—42no—
250C11⋊C8—42no—
251C11⋊C8—42no—
252C23×D4—221no—
253C23×D4—221no—
254C22×SD16—221no—
255D42—114no—
256D42—222no—
257D42—222no—
258D42—222no—
259C2×C4⋊Q8C2×D1111yescharacteristic, complemented
260C2×#127—111no—
261C2×#121—221no—
262C2×#121—221no—
263C2×#120—222no—
264C2×C4×D4—111no—
265C2×C4×D4C2×D1111yescharacteristic
266#486—114no—
267#486—222no—
268#474—22no—
269#474C2×D1114yescomplemented
270#461—114no—
271#461—222no—
272C2×#107—21no—
273C2×C4⋊C8—111no—
274C2×C4⋊C8C2×D1111yescharacteristic, complemented
275C2×#103—221no—
276C2×#102—21no—
277C2×#102—222no—
278C2×C4×C8—111no—
279#331—114no—
280D4⋊C8—114no—
281D4⋊C8—114no—
282C22×C11—24no—
283C22×C11—48no—
284C22×C11—42no—
285C22×C11—42no—
286C22×C11#44712yes—
287C22×C11#45012yes—
288C22×C11#45512yes—
289C22×C11C2×#12011yescharacteristic
290C2×D11—24no—
291C2×D11—48no—
292C2×D11—42no—
293C2×D11—42no—
294C2×D11—44no—
295C2×D11—44no—
296C2×D11—44no—
297C2×D11—832no—
298C2×D11—88no—
299C4×C11—21no—
300C4×C11—21no—
301C4×C11—42no—
302C4×C11—82no—
303C4×C11#44712yes—
304C4×C11#45012yes—
305C4×C11C22×D811yescharacteristic
306C4×C11C22×SD1611yescharacteristic
307C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
308C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
309Dic11—42no—
310C25—222no—
311C22×Q8—21no—
312C22×D4—111no—
313C22×D4—112no—
314C22×D4—224no—
315C22×D4—222no—
316C22×D4—224no—
317C22×D4—224no—
318C22×D4—222no—
319C22×D4—224no—
320C22×D4—221no—
321C22×D4—221no—
322C22×D4—444no—
323C22×D4—444no—
324C22×D4—444no—
325C22×D4—444no—
326C22×D4C22⋊D1111yescharacteristic
327C23×C4—21no—
328C23×C4—221no—
329C2×SD16—224no—
330C2×SD16—444no—
331C22×C8—21no—
332C22×C8—221no—
333C22×C8—221no—
334C4⋊Q8—21no—
335C4⋊Q8—21no—
336C4⋊Q8—21no—
337C4⋊Q8C22×D1112yescomplemented
338#127—112no—
339#127—112no—
340#127—221no—
341#127—221no—
342#121—224no—
343#121—224no—
344#121—224no—
345#121—224no—
346#120—228no—
347#120—228no—
348C4×D4—21no—
349C4×D4—21no—
350C4×D4—112no—
351C4×D4—112no—
352C4×D4—221no—
353C4×D4—221no—
354C4×D4C22⋊D1112yes—
355C4×D4C22×D1112yes—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—111no—
359C2×C4⋊C4C22⋊D1111yescharacteristic
360C2×C22⋊C4—21no—
361C2×C22⋊C4—222no—
362C2×C22⋊C4—221no—
363C2×C42C22×D1111yescharacteristic
364#107—24no—
365C4⋊C8—21no—
366C4⋊C8—112no—
367C4⋊C8—221no—
368C4⋊C8C22×D1112yescomplemented
369#103—224no—
370#102—24no—
371#102—228no—
372C4×C8—112no—
373C4×C8—221no—
374C2×C11—44no—
375C2×C11#163914yescomplemented
376C2×C11C2×#44711yescharacteristic
377C2×C11C2×#45011yescharacteristic
378C2×C11C2×#45511yescharacteristic
379D11—44no—
380D11—84no—
381C24—21no—
382C24—228no—
383C24—221no—
384C24—222no—
385C24—448no—
386C24—448no—
387C24—884no—
388C2×Q8—22no—
389C2×Q8—41no—
390C2×Q8—42no—
391C2×Q8—42no—
392C2×D4—21no—
393C2×D4—22no—
394C2×D4—114no—
395C2×D4—112no—
396C2×D4—114no—
397C2×D4—228no—
398C2×D4—228no—
399C2×D4—222no—
400C2×D4—221no—
401C2×D4—222no—
402C2×D4—222no—
403C2×D4—222no—
404C2×D4—222no—
405C2×D4—222no—
406C2×D4—444no—
407C2×D4—448no—
408C2×D4—4416no—
409C2×D4—448no—
410C2×D4—448no—
411C2×D4—448no—
412C2×D4—4416no—
413C2×D4—448no—
414C2×D4—448no—
415C2×D4—442no—
416C2×D4—442no—
417C2×D4—442no—
418C2×D4—442no—
419C2×D4#432514yescomplemented
420C2×D4C2×C22⋊D1112yes—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—42no—
425C22×C4—42no—
426C22×C4—41no—
427C22×C4—221no—
428C22×C4—222no—
429C22×C4—222no—
430C22×C4—442no—
431C22×C4—442no—
432C22×C4D4×D1111yescharacteristic
433C22×C4D4×D1111yescharacteristic
434C22×C4C2×C22⋊D1111yescharacteristic
435SD16—448no—
436C2×C8—22no—
437C2×C8—42no—
438C2×C8—222no—
439C2×C8—222no—
440C2×C8—442no—
441C2×C8—442no—
442C4⋊C4—21no—
443C4⋊C4—22no—
444C4⋊C4—22no—
445C4⋊C4—41no—
446C4⋊C4—41no—
447C4⋊C4—112no—
448C4⋊C4—221no—
449C4⋊C4C2×C22⋊D1112yes—
450C22⋊C4—22no—
451C22⋊C4—22no—
452C22⋊C4—228no—
453C22⋊C4—222no—
454C22⋊C4—222no—
455C42D4×D1111yescharacteristic
456C42D4×D1111yescharacteristic
457C42C2×C22⋊D1111yescharacteristic
458C42C23×D1111yescharacteristic
459C11C2×#163911yescharacteristic, complemented, Sylow
460C23—22no—
461C23—24no—
462C23—42no—
463C23—42no—
464C23—224no—
465C23—222no—
466C23—224no—
467C23—4416no—
468C23—4416no—
469C23—442no—
470C23—442no—
471C23—444no—
472C23—444no—
473C23—444no—
474C23—888no—
475C23—8832no—
476C23#6699011yescharacteristic
477Q8—42no—
478Q8—42no—
479Q8—82no—
480D4—22no—
481D4—24no—
482D4—114no—
483D4—224no—
484D4—222no—
485D4—444no—
486D4—4416no—
487D4—4416no—
488D4—444no—
489D4—442no—
490D4—442no—
491D4—442no—
492D4—442no—
493D4—444no—
494D4—882no—
495D4C2×#432514yescomplemented
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—42no—
499C2×C4—44no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—82no—
504C2×C4—222no—
505C2×C4—442no—
506C2×C4—442no—
507C2×C4—442no—
508C2×C4—444no—
509C2×C4D8×D1112yes—
510C2×C4#6696412yes—
511C2×C4#6699011yescharacteristic
512C2×C4#6699011yescharacteristic
513C2×C4#6699011yescharacteristic
514C2×C4C2×#432512yes—
515C2×C4#6700212yes—
516C2×C4C2×D4×D1111yescharacteristic
517C2×C4C2×D4×D1111yescharacteristic
518C2×C4C22×C22⋊D1111yescharacteristic
519C8—42no—
520C8—442no—
521C8—442no—
522C22—24no—
523C22—48no—
524C22—42no—
525C22—42no—
526C22—224no—
527C22—448no—
528C22—442no—
529C22—442no—
530C22—444no—
531C22—444no—
532C22—444no—
533C22—8832no—
534C22—888no—
535C22#1062265912yes—
536C22#1062276912yes—
537C22#1062281512yes—
538C22C2×#6699011yescharacteristic
539C4—21no—
540C4—21no—
541C4—42no—
542C4—82no—
543C4—442no—
544C4#1062265912yes—
545C4#1062276912yes—
546C4C2×D8×D1111yescharacteristic
547C4C2×#6696411yescharacteristic
548C4C22×#432511yescharacteristic
549C4C2×#6700211yescharacteristic
550C2—44no—
551C2—444no—
552C2—884no—
553C2#1306779414yesdirect product factor
554C2C2×#1062276911yescharacteristic
555C2C2×#1062265911yescharacteristic
556C2C2×#1062281511yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#474C2
socleC23×C11#120
prime radicalC2×D4×D44C2
hypercenterC2×#474D11
hypocenterC11C2×#1639
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
2. C2×#10622701C2semidirect
3. C2×#10622696C2semidirect
4. #13067794C2direct (N × H)
5. C2×#10622123C2semidirect
6. C2×D4⋊(C11⋊C8)C2semidirect
7. C2×#10622121C2semidirect
8. C2×C11×#474C2semidirect
11. C2×C11×C4⋊Q8C22semidirect
24. C11×#474C22semidirect
26. C2×C11×C4⋊C8C22semidirect
30. #10622701C22semidirect
32. #10622696C22semidirect
34. C2×C4⋊(C11⋊C8)C22semidirect
35. C2×C4×C11⋊C8C22semidirect
36. D4⋊(C11⋊C8)C22semidirect
37. #10622123C22semidirect
38. #10622121C22semidirect
62. C11×C4⋊Q8C23semidirect
95. C11×C4⋊C8C23semidirect
100. C4⋊(C11⋊C8)C23semidirect
102. C4×C11⋊C8C23semidirect
117. C2×D4×C11SD16semidirect
184. C2×#474D11semidirect
212. D4×C11C2×SD16semidirect
259. C2×C4⋊Q8C2×D11semidirect
269. #474C2×D11semidirect
274. C2×C4⋊C8C2×D11semidirect
337. C4⋊Q8C22×D11semidirect
368. C4⋊C8C22×D11semidirect
375. C2×C11#1639semidirect
419. C2×D4#4325semidirect
459. C11C2×#1639semidirect
495. D4C2×#4325semidirect
553. C2#13067794direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×D442
C2×#106227012
C2×#106226962
#130677942
C2×#106221232
C2×D4⋊(C11⋊C8)2
C2×#106221212
C2×C11×#4742
C2×#163911