Finite Group Databasebeta

← C2×#13081029 #15632257

Subgroups — C2×#13081029 #15632257

Order 2816.

1918 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623073C211yesmaximal, characteristic, complemented
2#13081029C2116yesmaximal, direct product factor
3C2×#10622692C211yesmaximal, characteristic, complemented
4C2×#10622609C212yesmaximal, complemented
5C2×#10622648C212yesmaximal, complemented
6C2×#10622704C211yesmaximal, characteristic, complemented
7C2×#10622620C211yesmaximal, characteristic, complemented
8C2×#10622654C212yesmaximal, complemented
9C2×C4×#4324C211yesmaximal, characteristic, complemented
10C2×D4×C11⋊C8C211yesmaximal, characteristic, complemented
11C2×#10622611C212yesmaximal, complemented
12C2×C11×#555C211yesmaximal, characteristic
13C11×#555—24no—
14C11×#555C2218yes—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#124—22no—
17C2×C11×#121—21no—
18C2×C11×#121C2212yes—
19C2×C4×D4×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×C11×#117—21no—
22C2×C11×#117C2212yes—
23C2×#66989—21no—
24C22×#4324C2211yescharacteristic
25C2×#66979C2212yes—
26C2×#66977C2212yes—
27C23×C11⋊C8C2212yes—
28#10623073—24no—
29#10623073C2218yescomplemented
30C2×#66940—21no—
31C2×#66932—22no—
32C2×#66922C2211yescharacteristic
33C2×C4×Dic22C2211yescharacteristic
34C2×#66896C2212yes—
35C2×#66896C2211yescharacteristic
36C2×C22⋊(C11⋊C8)C2212yes—
37#10622704C2218yescomplemented
38#10622692C2218yescomplemented
39#10622654C22116yescomplemented
40#10622648C22116yescomplemented
41C4×#4324C2218yescomplemented
42D4×C11⋊C8C2218yescomplemented
43#10622620C2218yescomplemented
44#10622611C22116yescomplemented
45#10622609C22116yescomplemented
46C2×#66874C2212yes—
47C2×#66874C2211yescharacteristic
48C2×#66872C2212yes—
49C2×#66872C2212yes—
50C2×#66872C2211yescharacteristic
51C2×#66871C2212yes—
52C2×#66871C2212yes—
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C2×C4×C11⋊C8C2211yescharacteristic
55C22×Q8×C11—21no—
56C22×D4×C11—22no—
57C22×D4×C11D411yescharacteristic
58C22×D4×C11C2311yescharacteristic
59C23×C4×C11—21no—
60C23×C4×C11C2312yes—
61C22×Dic22—21no—
62C22×Dic22C2311yescharacteristic
63C11×C4⋊Q8—22no—
64C11×C4⋊Q8C2314yes—
65C11×#124—216no—
66C11×#121—28no—
67C11×#121—24no—
68C11×#121C2318yes—
69C4×D4×C11—22no—
70C4×D4×C11D414yes—
71C4×D4×C11C2314yes—
72C4×D4×C11C2314yes—
73C11×#117—24no—
74C11×#117—28no—
75C11×#117C2318yes—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4D411yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2312yes—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4D412yes—
84C2×C42×C11—22no—
85C2×C42×C11C2311yescharacteristic
86C2×C22⋊Dic11—22no—
87C2×C22⋊Dic11—22no—
88#66989—28no—
89C2×#4324—24no—
90C2×#4324C2314yes—
91#66979—24no—
92#66979C2318yes—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2312yes—
96#66977—24no—
97#66977C2318yes—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—22no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11—22no—
102C22×C11⋊C8—28no—
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2312yes—
105C22×C11⋊C8C2318yes—
106C22×C11⋊C8C2311yescharacteristic
107#66940—28no—
108#66932—216no—
109#66922—22no—
110#66922C2314yes—
111C4×Dic22—22no—
112C4×Dic22C2314yes—
113#66896C2318yes—
114#66896C2314yes—
115C22⋊(C11⋊C8)C2318yes—
116#66874C2314yes—
117#66874C2318yes—
118#66872C2318yes—
119#66872C2314yes—
120#66872C2318yes—
121#66871C2318yes—
122#66871C2318yes—
123C4⋊(C11⋊C8)C2314yes—
124C4×C11⋊C8C2314yes—
125C2×#3340—111nomaximal, Sylow
126C24×C11—21no—
127C24×C11C2×D412yes—
128C2×Q8×C11—24no—
129C2×Q8×C11—82no—
130C2×D4×C11—28no—
131C2×D4×C11—24no—
132C2×D4×C11—21no—
133C2×D4×C11—22no—
134C2×D4×C11—22no—
135C2×D4×C11—84no—
136C2×D4×C11C2×D414yes—
137C2×D4×C11C2412yes—
138C22×C4×C11—24no—
139C22×C4×C11—24no—
140C22×C4×C11—21no—
141C22×C4×C11—22no—
142C22×C4×C11—24no—
143C22×C4×C11—44no—
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D414yes—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2414yes—
149C22×C4×C11C2411yescharacteristic
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—22no—
153C2×Dic22—21no—
154C2×Dic22—24no—
155C2×Dic22—22no—
156C2×Dic22—22no—
157C2×Dic22—44no—
158C2×Dic22C2412yes—
159C11×C4⋊C4—24no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4C2×D414yes—
163C11×C4⋊C4C2412yes—
164C11×C4⋊C4C2414yes—
165C11×C22⋊C4—28no—
166C11×C22⋊C4—28no—
167C11×C22⋊C4—24no—
168C11×C22⋊C4C2×D418yes—
169C42×C11—28no—
170C42×C11C2×D412yes—
171C42×C11C2412yes—
172C22⋊Dic11—28no—
173C22⋊Dic11—28no—
174#4324—28no—
175C4⋊Dic11—21no—
176C4⋊Dic11—22no—
177C4⋊Dic11—24no—
178C4⋊Dic11C2412yes—
179C4⋊Dic11C2414yes—
180Dic11⋊C4—24no—
181Dic11⋊C4—28no—
182C4×Dic11—24no—
183C4×Dic11—28no—
184C2×C11⋊C8—216no—
185C2×C11⋊C8—24no—
186C2×C11⋊C8—22no—
187C2×C11⋊C8#4114yes—
188C2×C11⋊C8C2412yes—
189C2×C11⋊C8C2414yes—
190C2×C11⋊C8C2412yes—
191C2×#556—111no—
192C2×#555D1111yescharacteristic
193#3340—1116no—
194C2×#498—111no—
195C2×#485—112no—
196C2×#482—112no—
197C2×#477—111no—
198C2×#474—111no—
199C2×#465—112no—
200C2×C4×SD16—111no—
201C2×C8×D4—111no—
202C2×#427—112no—
203C23×C11—24no—
204C23×C11—24no—
205C23×C11—24no—
206C23×C11—22no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11C22×D414yes—
211C23×C11C22×D411yescharacteristic
212Q8×C11—84no—
213D4×C11—28no—
214D4×C11—22no—
215D4×C11—22no—
216D4×C11—42no—
217D4×C11—88no—
218C2×C4×C11—24no—
219C2×C4×C11—22no—
220C2×C4×C11—28no—
221C2×C4×C11—24no—
222C2×C4×C11—24no—
223C2×C4×C11—22no—
224C2×C4×C11—24no—
225C2×C4×C11—42no—
226C2×C4×C11—44no—
227C2×C4×C11—48no—
228C2×C4×C11#13514yes—
229C2×C4×C11C22×D414yes—
230C2×C4×C11C22×D412yes—
231C2×C4×C11C22×D411yescharacteristic
232C2×C4×C11C22×D412yes—
233C2×C4×C11C2×#4112yes—
234C2×C4×C112−1+412yes—
235C2×C4×C11C2511yescharacteristic
236C2×Dic11—22no—
237C2×Dic11—22no—
238C2×Dic11—24no—
239C2×Dic11—42no—
240C2×Dic11—44no—
241C2×Dic11—42no—
242Dic22—22no—
243Dic22—22no—
244Dic22—42no—
245Dic22—48no—
246C11⋊C8—24no—
247C11⋊C8—22no—
248C11⋊C8C2×#4114yes—
249C22×SD16—111no—
250C23×C8—112no—
251#556—118no—
252#556—224no—
253#555—24no—
254#555C2×D1118yes—
255C2×C4⋊Q8—111no—
256C2×C4⋊Q8C2×D1111yescharacteristic
257C2×#126—222no—
258C2×#124—22no—
259C2×#124—221no—
260C2×C22⋊Q8—112no—
261C2×#121—21no—
262C2×#121C2×D1112yes—
263C2×C4×Q8—111no—
264C2×C4×Q8—221no—
265C2×C4×D4C2×D1111yescharacteristic
266C2×C4×D4C2×D1111yescharacteristic
267C2×#117—21no—
268C2×#117—112no—
269C2×#117C2×D1112yes—
270#498—118no—
271#485—1116no—
272#482—1116no—
273#477—118no—
274#474—118no—
275#465—1116no—
276C4×SD16—118no—
277C8×D4—118no—
278#427—1116no—
279C2×#107—112no—
280C2×#107—112no—
281C2×#106—112no—
282C2×#106—112no—
283C2×#106—111no—
284C2×C4⋊C8—111no—
285C2×#103—112no—
286C2×#103—111no—
287C2×#102—111no—
288C2×#102—112no—
289C2×C22⋊C8—112no—
290C2×C4×C8—111no—
291C22×C11—24no—
292C22×C11—24no—
293C22×C11—24no—
294C22×C11—48no—
295C22×C11—42no—
296C22×C11—42no—
297C22×C11—42no—
298C22×C11—84no—
299C22×C11#54712yes—
300C22×C11C2×#13512yes—
301C22×C11#57712yes—
302C22×C11C23×D411yescharacteristic
303C4×C11—24no—
304C4×C11—22no—
305C4×C11—42no—
306C4×C11—44no—
307C4×C11#54712yes—
308C4×C11C2×#13514yes—
309C4×C11C22×#4111yescharacteristic
310C4×C11C2×2−1+411yescharacteristic
311Dic11—42no—
312Dic11—44no—
313Dic11—42no—
314C22×Q8—21no—
315C22×Q8—111no—
316C22×Q8—221no—
317C22×D4—22no—
318C22×D4C22⋊D1111yescharacteristic
319C22×D4C22×D1111yescharacteristic
320C23×C4—21no—
321C23×C4C22×D1112yes—
322C2×SD16—114no—
323C2×SD16—224no—
324C22×C8—111no—
325C22×C8—112no—
326C22×C8—118no—
327C22×C8—111no—
328C22×C8—228no—
329C4⋊Q8—22no—
330C4⋊Q8—114no—
331C4⋊Q8—222no—
332C4⋊Q8C22×D1114yes—
333#126—2216no—
334#124—216no—
335#124—228no—
336C22⋊Q8—118no—
337C22⋊Q8—224no—
338#121—28no—
339#121—24no—
340#121C22×D1118yes—
341C4×Q8—114no—
342C4×Q8—228no—
343C4×Q8—222no—
344C4×D4—22no—
345C4×D4C22⋊D1114yes—
346C4×D4C22×D1114yes—
347C4×D4C22×D1114yes—
348#117—24no—
349#117—28no—
350#117—118no—
351#117—224no—
352#117C22×D1118yes—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—111no—
355C2×C4⋊C4—112no—
356C2×C4⋊C4—221no—
357C2×C4⋊C4—222no—
358C2×C4⋊C4—221no—
359C2×C4⋊C4C22⋊D1111yescharacteristic
360C2×C4⋊C4C22×D1111yescharacteristic
361C2×C4⋊C4C22×D1112yes—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—222no—
366C2×C22⋊C4—222no—
367C2×C22⋊C4C22⋊D1112yes—
368C2×C42—22no—
369C2×C42—222no—
370C2×C42—221no—
371C2×C42C22×D1111yescharacteristic
372#107—118no—
373#107—118no—
374#106—114no—
375#106—118no—
376#106—118no—
377C4⋊C8—114no—
378#103—114no—
379#103—118no—
380#102—114no—
381#102—118no—
382C22⋊C8—118no—
383C4×C8—114no—
384C2×C11—44no—
385C2×C11—82no—
386C2×C11#334014yescomplemented
387C2×C11C2×#54711yescharacteristic
388C2×C11C22×#13511yescharacteristic
389C2×C11C2×#57711yescharacteristic
390C24—21no—
391C24C2×C22⋊D1112yes—
392C2×Q8—24no—
393C2×Q8—82no—
394C2×Q8—112no—
395C2×Q8—221no—
396C2×Q8—224no—
397C2×Q8—222no—
398C2×Q8—222no—
399C2×Q8—444no—
400C2×D4—28no—
401C2×D4—24no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—21no—
405C2×D4—84no—
406C2×D4C2×C22⋊D1114yes—
407C2×D4C23×D1112yes—
408C22×C4—24no—
409C22×C4—24no—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—24no—
413C22×C4—44no—
414C22×C4—221no—
415C22×C4—222no—
416C22×C4—221no—
417C22×C4C2×C22⋊D1114yes—
418C22×C4C2×C22⋊D1112yes—
419C22×C4C2×C22⋊D1111yescharacteristic
420C22×C4C2×C22⋊D1111yescharacteristic
421C22×C4C23×D1114yes—
422C22×C4C23×D1111yescharacteristic
423SD16—228no—
424C2×C8—114no—
425C2×C8—112no—
426C2×C8—112no—
427C2×C8—114no—
428C2×C8—2216no—
429C2×C8—224no—
430C2×C8—222no—
431C4⋊C4—24no—
432C4⋊C4—21no—
433C4⋊C4—22no—
434C4⋊C4—114no—
435C4⋊C4—112no—
436C4⋊C4—221no—
437C4⋊C4—222no—
438C4⋊C4—224no—
439C4⋊C4—228no—
440C4⋊C4—224no—
441C4⋊C4C2×C22⋊D1114yes—
442C4⋊C4C23×D1114yes—
443C4⋊C4C23×D1112yes—
444C22⋊C4—28no—
445C22⋊C4—28no—
446C22⋊C4—24no—
447C22⋊C4—228no—
448C22⋊C4—228no—
449C22⋊C4C2×C22⋊D1118yes—
450C42—28no—
451C42—228no—
452C42—224no—
453C42C2×C22⋊D1112yes—
454C42C23×D1112yes—
455C11C2×#334011yescharacteristic, complemented, Sylow
456C23—24no—
457C23—24no—
458C23—24no—
459C23—22no—
460C23—42no—
461C23—42no—
462C23—42no—
463C23C22×C22⋊D1114yes—
464C23C22×C22⋊D1111yescharacteristic
465Q8—84no—
466Q8—222no—
467Q8—222no—
468Q8—448no—
469Q8—442no—
470D4—28no—
471D4—22no—
472D4—22no—
473D4—42no—
474D4—88no—
475C2×C4—24no—
476C2×C4—22no—
477C2×C4—28no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—22no—
481C2×C4—24no—
482C2×C4—42no—
483C2×C4—44no—
484C2×C4—48no—
485C2×C4—222no—
486C2×C4—224no—
487C2×C4—222no—
488C2×C4—444no—
489C2×C4—442no—
490C2×C4—442no—
491C2×C4#6700314yes—
492C2×C4#41×D1112yes—
493C2×C4#6704312yes—
494C2×C4C22×C22⋊D1114yes—
495C2×C4C22×C22⋊D1112yes—
496C2×C4C22×C22⋊D1112yes—
497C2×C4C22×C22⋊D1111yescharacteristic
498C2×C4C24×D1111yescharacteristic
499C8—114no—
500C8—224no—
501C8—222no—
502C22—24no—
503C22—24no—
504C22—24no—
505C22—48no—
506C22—42no—
507C22—42no—
508C22—42no—
509C22—84no—
510C22C2×#6700312yes—
511C22#1062335512yes—
512C22#1062336712yes—
513C22C23×C22⋊D1111yescharacteristic
514C4—24no—
515C4—22no—
516C4—42no—
517C4—44no—
518C4—444no—
519C4—442no—
520C4—442no—
521C4C2×#6700314yes—
522C4#1062335512yes—
523C4C2×#41×D1111yescharacteristic
524C4C2×#6704311yescharacteristic
525C2—44no—
526C2—82no—
527C2#1308102914yesdirect product factor
528C2C2×#1062335511yescharacteristic
529C2C22×#6700311yescharacteristic
530C2C2×#1062336711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC2×C11×#555C2
socleC23×C11C22×D4
hypercenterC2×#555D11
hypocenterC11C2×#3340
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#555

Complements

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

NH ≅ G/Ntype
1. C2×#10623073C2semidirect
2. #13081029C2direct (N × H)
3. C2×#10622692C2semidirect
4. C2×#10622609C2semidirect
5. C2×#10622648C2semidirect
6. C2×#10622704C2semidirect
7. C2×#10622620C2semidirect
8. C2×#10622654C2semidirect
9. C2×C4×#4324C2semidirect
10. C2×D4×C11⋊C8C2semidirect
11. C2×#10622611C2semidirect
29. #10623073C22semidirect
37. #10622704C22semidirect
38. #10622692C22semidirect
39. #10622654C22semidirect
40. #10622648C22semidirect
41. C4×#4324C22semidirect
42. D4×C11⋊C8C22semidirect
43. #10622620C22semidirect
44. #10622611C22semidirect
45. #10622609C22semidirect
386. C2×C11#3340semidirect
455. C11C2×#3340semidirect
527. C2#13081029direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230732
#130810292
C2×#106226922
C2×#106226092
C2×#106226482
C2×#106227042
C2×#106226202
C2×#106226542
C2×C4×#43242
C2×D4×C11⋊C82
C2×#106226112
C2×C11×#5552
C2×#334011