Finite Group Databasebeta

← C2×#13081231 #15632511

Subgroups — C2×#13081231 #15632511

Order 2816.

1866 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623073C211yesmaximal, characteristic
2#13081231C2116yesmaximal, direct product factor
3C2×#10622692C211yesmaximal, characteristic, complemented
4C2×#10622658C212yesmaximal, complemented
5C2×#10622584C212yesmaximal, complemented
6C2×#10622704C211yesmaximal, characteristic, complemented
7C2×#10622633C211yesmaximal, characteristic, complemented
8C2×#10622665C212yesmaximal, complemented
9C2×C4×#4326C211yesmaximal, characteristic, complemented
10C2×#10622625C211yesmaximal, characteristic
11C2×#10622577C212yesmaximal, complemented
12C2×C11×#554C211yesmaximal, characteristic
13C11×#554—24no—
14C11×#554C2218yes—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#125—21no—
17C2×C11×C22⋊Q8—22no—
18C2×C11×C22⋊Q8C2212yes—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11—21no—
21C2×C4×D4×C11C2211yescharacteristic
22C22×C11×C4⋊C4C2212yes—
23C22×#4326C2211yescharacteristic
24C2×#66989—21no—
25C2×#66979C2212yes—
26C2×#66977C2212yes—
27C22×#4318C2212yes—
28#10623073—24no—
29#10623073C2218yes—
30C2×#66940—21no—
31C2×#66932—22no—
32C2×#66922C2211yescharacteristic
33C2×C4×Dic22C2211yescharacteristic
34C2×#66899C2212yes—
35C2×#66899C2211yescharacteristic
36C2×C22⋊(C11⋊C8)C2212yes—
37#10622704C2218yescomplemented
38#10622692C2218yescomplemented
39#10622665C22116yescomplemented
40#10622658C22116yescomplemented
41C4×#4326C2218yescomplemented
42#10622633C2218yescomplemented
43#10622625C2218yes—
44#10622584C22116yescomplemented
45C2×#66874C2212yes—
46C2×#66874C2211yescharacteristic
47#10622577C22116yescomplemented
48C2×#66872C2212yes—
49C2×#66872C2212yes—
50C2×#66872C2212yes—
51C2×#66871C2212yes—
52C2×#66871C2211yescharacteristic
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C2×C4×C11⋊C8C2211yescharacteristic
55C22×Q8×C11—21no—
56C22×Q8×C11C2311yescharacteristic
57C22×D4×C11D411yescharacteristic
58C23×C4×C11—22no—
59C23×C4×C11C2312yes—
60C22×Dic22—21no—
61C22×Dic22C2311yescharacteristic
62C11×C4⋊Q8—22no—
63C11×C4⋊Q8C2314yes—
64C11×#125—28no—
65C11×C22⋊Q8—24no—
66C11×C22⋊Q8—216no—
67C11×C22⋊Q8C2318yes—
68C4×Q8×C11—22no—
69C4×Q8×C11C2314yes—
70C4×D4×C11—28no—
71C4×D4×C11D414yes—
72C4×D4×C11C2314yes—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—24no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4D411yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2312yes—
81C2×C11×C4⋊C4C2318yes—
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4D412yes—
84C2×C42×C11—21no—
85C2×C42×C11C2311yescharacteristic
86C2×C22⋊Dic11—22no—
87C2×C22⋊Dic11—22no—
88C2×#4326—24no—
89C2×#4326C2314yes—
90#66989—28no—
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—
102C2×#4318—28no—
103C2×#4318C2318yes—
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2312yes—
106C22×C11⋊C8C2311yescharacteristic
107#66940—28no—
108#66932—216no—
109#66922—22no—
110#66922C2314yes—
111C4×Dic22—22no—
112C4×Dic22C2314yes—
113#66899C2318yes—
114#66899C2314yes—
115C22⋊(C11⋊C8)C2318yes—
116#66874C2314yes—
117#66874C2318yes—
118#66872C2318yes—
119#66872C2318yes—
120#66872C2318yes—
121#66871C2314yes—
122#66871C2318yes—
123C4⋊(C11⋊C8)C2314yes—
124C4×C11⋊C8C2314yes—
125C2×#3356—111nomaximal, Sylow
126C24×C11C2×D412yes—
127C2×Q8×C11—21no—
128C2×Q8×C11—24no—
129C2×Q8×C11—22no—
130C2×Q8×C11—22no—
131C2×Q8×C11—82no—
132C2×Q8×C11C2412yes—
133C2×D4×C11—24no—
134C2×D4×C11C2×D414yes—
135C22×C4×C11—24no—
136C22×C4×C11—24no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—22no—
140C22×C4×C11—28no—
141C22×C4×C11—84no—
142C22×C4×C11C2×D412yes—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D414yes—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2414yes—
147C22×C4×C11C2411yescharacteristic
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—22no—
151C2×Dic22—21no—
152C2×Dic22—24no—
153C2×Dic22—22no—
154C2×Dic22—22no—
155C2×Dic22—44no—
156C2×Dic22C2412yes—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—28no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—24no—
161C11×C4⋊C4—24no—
162C11×C4⋊C4—28no—
163C11×C4⋊C4C2×D414yes—
164C11×C4⋊C4C2412yes—
165C11×C4⋊C4C2414yes—
166C11×C22⋊C4—28no—
167C11×C22⋊C4C2×D418yes—
168C42×C11—24no—
169C42×C11C2×D412yes—
170C42×C11C2412yes—
171C22⋊Dic11—28no—
172C22⋊Dic11—28no—
173#4326—28no—
174C4⋊Dic11—21no—
175C4⋊Dic11—22no—
176C4⋊Dic11—24no—
177C4⋊Dic11C2412yes—
178C4⋊Dic11C2414yes—
179Dic11⋊C4—24no—
180Dic11⋊C4—28no—
181C4×Dic11—24no—
182C4×Dic11—28no—
183#4318—216no—
184C2×C11⋊C8—24no—
185C2×C11⋊C8—22no—
186C2×C11⋊C8#4114yes—
187C2×C11⋊C8C2412yes—
188C2×C11⋊C8C2414yes—
189C2×C11⋊C8C2412yes—
190C2×#556—111no—
191C2×#554D1111yescharacteristic
192#3356—1116no—
193C2×#498—111no—
194C2×#485—112no—
195C2×#483—112no—
196C2×#477—111no—
197C2×#475—111no—
198C2×#470—112no—
199C2×C4×Q16—111no—
200C2×#436—111no—
201C2×#428—112no—
202C23×C11—24no—
203C23×C11—24no—
204C23×C11—24no—
205C23×C11C22×D414yes—
206C23×C11C22×D411yescharacteristic
207Q8×C11—22no—
208Q8×C11—22no—
209Q8×C11—42no—
210Q8×C11—84no—
211D4×C11—28no—
212C2×C4×C11—24no—
213C2×C4×C11—22no—
214C2×C4×C11—28no—
215C2×C4×C11—24no—
216C2×C4×C11—24no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—24no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—44no—
223C2×C4×C11—88no—
224C2×C4×C11#13714yes—
225C2×C4×C11C22×D414yes—
226C2×C4×C11C22×D412yes—
227C2×C4×C11C22×D411yescharacteristic
228C2×C4×C11C22×D412yes—
229C2×C4×C11C2×#4112yes—
230C2×C4×C112−1+412yes—
231C2×C4×C11C2511yescharacteristic
232C2×Dic11—22no—
233C2×Dic11—22no—
234C2×Dic11—24no—
235C2×Dic11—42no—
236C2×Dic11—44no—
237C2×Dic11—42no—
238Dic22—22no—
239Dic22—22no—
240Dic22—42no—
241Dic22—48no—
242C11⋊C8—24no—
243C11⋊C8—22no—
244C11⋊C8C2×#4114yes—
245C22×Q16—111no—
246C22×M16—112no—
247#556—118no—
248#556—224no—
249#554—24no—
250#554C2×D1118yes—
251C2×C4⋊Q8—111no—
252C2×C4⋊Q8C2×D1111yescharacteristic
253C2×#126—222no—
254C2×#125—21no—
255C2×#124—221no—
256C2×C22⋊Q8—22no—
257C2×C22⋊Q8—112no—
258C2×C22⋊Q8C2×D1112yes—
259C2×C4×Q8—111no—
260C2×C4×Q8—221no—
261C2×C4×Q8C2×D1111yescharacteristic
262C2×C4×D4—21no—
263C2×C4×D4C2×D1111yescharacteristic
264C2×#117—112no—
265C22×C4⋊C4C2×D1112yes—
266#498—118no—
267#485—1116no—
268#483—1116no—
269#477—118no—
270#475—118no—
271#470—1116no—
272C4×Q16—118no—
273#436—118no—
274#428—1116no—
275C2×#107—112no—
276C2×#107—111no—
277C2×#106—112no—
278C2×#106—112no—
279C2×#106—112no—
280C2×C4⋊C8—111no—
281C2×#103—112no—
282C2×#103—111no—
283C2×#103—112no—
284C2×#103—111no—
285C2×C22⋊C8—112no—
286C2×C4×C8—111no—
287C22×C11—24no—
288C22×C11—24no—
289C22×C11—24no—
290C22×C11—48no—
291C22×C11#54712yes—
292C22×C11C2×#13712yes—
293C22×C11#57712yes—
294C22×C11C23×D411yescharacteristic
295C4×C11—24no—
296C4×C11—22no—
297C4×C11—42no—
298C4×C11—42no—
299C4×C11—44no—
300C4×C11#54712yes—
301C4×C11C2×#13714yes—
302C4×C11C22×#4111yescharacteristic
303C4×C11C2×2−1+411yescharacteristic
304Dic11—42no—
305Dic11—44no—
306Dic11—42no—
307C22×Q8—21no—
308C22×Q8—111no—
309C22×Q8—221no—
310C22×Q8C22×D1111yescharacteristic
311C22×D4C22⋊D1111yescharacteristic
312C23×C4—22no—
313C23×C4C22×D1112yes—
314C2×Q16—114no—
315C2×Q16—224no—
316C2×M16—118no—
317C2×M16—228no—
318C22×C8—111no—
319C22×C8—112no—
320C22×C8—111no—
321C4⋊Q8—22no—
322C4⋊Q8—114no—
323C4⋊Q8—222no—
324C4⋊Q8C22×D1114yes—
325#126—2216no—
326#125—28no—
327#124—228no—
328C22⋊Q8—24no—
329C22⋊Q8—216no—
330C22⋊Q8—118no—
331C22⋊Q8—224no—
332C22⋊Q8C22×D1118yes—
333C4×Q8—22no—
334C4×Q8—114no—
335C4×Q8—228no—
336C4×Q8—222no—
337C4×Q8C22×D1114yes—
338C4×D4—28no—
339C4×D4C22⋊D1114yes—
340C4×D4C22×D1114yes—
341#117—118no—
342#117—224no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—111no—
349C2×C4⋊C4—112no—
350C2×C4⋊C4—221no—
351C2×C4⋊C4—222no—
352C2×C4⋊C4—221no—
353C2×C4⋊C4C22⋊D1111yescharacteristic
354C2×C4⋊C4C22×D1111yescharacteristic
355C2×C4⋊C4C22×D1112yes—
356C2×C4⋊C4C22×D1118yes—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—222no—
359C2×C22⋊C4—222no—
360C2×C22⋊C4C22⋊D1112yes—
361C2×C42—21no—
362C2×C42—222no—
363C2×C42—221no—
364C2×C42C22×D1111yescharacteristic
365#107—114no—
366#107—118no—
367#106—118no—
368#106—118no—
369#106—118no—
370C4⋊C8—114no—
371#103—114no—
372#103—118no—
373#103—114no—
374#103—118no—
375C22⋊C8—118no—
376C4×C8—114no—
377C2×C11—44no—
378C2×C11#335614yescomplemented
379C2×C11C2×#54711yescharacteristic
380C2×C11C22×#13711yescharacteristic
381C2×C11C2×#57711yescharacteristic
382C24C2×C22⋊D1112yes—
383C2×Q8—21no—
384C2×Q8—24no—
385C2×Q8—22no—
386C2×Q8—22no—
387C2×Q8—82no—
388C2×Q8—112no—
389C2×Q8—221no—
390C2×Q8—224no—
391C2×Q8—222no—
392C2×Q8—222no—
393C2×Q8—444no—
394C2×Q8C23×D1112yes—
395C2×D4—24no—
396C2×D4C2×C22⋊D1114yes—
397C22×C4—24no—
398C22×C4—24no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—28no—
403C22×C4—84no—
404C22×C4—221no—
405C22×C4—222no—
406C22×C4—221no—
407C22×C4C2×C22⋊D1114yes—
408C22×C4C2×C22⋊D1112yes—
409C22×C4C2×C22⋊D1111yescharacteristic
410C22×C4C2×C22⋊D1111yescharacteristic
411C22×C4C23×D1114yes—
412C22×C4C23×D1111yescharacteristic
413Q16—228no—
414M16—2216no—
415C2×C8—114no—
416C2×C8—112no—
417C2×C8—112no—
418C2×C8—114no—
419C2×C8—224no—
420C2×C8—222no—
421C4⋊C4—21no—
422C4⋊C4—28no—
423C4⋊C4—22no—
424C4⋊C4—24no—
425C4⋊C4—24no—
426C4⋊C4—28no—
427C4⋊C4—114no—
428C4⋊C4—112no—
429C4⋊C4—221no—
430C4⋊C4—222no—
431C4⋊C4—224no—
432C4⋊C4—228no—
433C4⋊C4—224no—
434C4⋊C4C2×C22⋊D1114yes—
435C4⋊C4C23×D1112yes—
436C4⋊C4C23×D1114yes—
437C22⋊C4—28no—
438C22⋊C4—228no—
439C22⋊C4—228no—
440C22⋊C4C2×C22⋊D1118yes—
441C42—24no—
442C42—228no—
443C42—224no—
444C42C2×C22⋊D1112yes—
445C42C23×D1112yes—
446C11C2×#335611yescharacteristic, complemented, Sylow
447C23—24no—
448C23—24no—
449C23—24no—
450C23C22×C22⋊D1114yes—
451C23C22×C22⋊D1111yescharacteristic
452Q8—22no—
453Q8—22no—
454Q8—42no—
455Q8—84no—
456Q8—222no—
457Q8—222no—
458Q8—448no—
459Q8—442no—
460D4—28no—
461C2×C4—24no—
462C2×C4—22no—
463C2×C4—28no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—24no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—44no—
472C2×C4—88no—
473C2×C4—222no—
474C2×C4—224no—
475C2×C4—222no—
476C2×C4—444no—
477C2×C4—442no—
478C2×C4—442no—
479C2×C4#6699514yes—
480C2×C4#41×D1112yes—
481C2×C4#6704312yes—
482C2×C4C22×C22⋊D1114yes—
483C2×C4C22×C22⋊D1112yes—
484C2×C4C22×C22⋊D1112yes—
485C2×C4C22×C22⋊D1111yescharacteristic
486C2×C4C24×D1111yescharacteristic
487C8—114no—
488C8—224no—
489C8—222no—
490C22—24no—
491C22—24no—
492C22—24no—
493C22—48no—
494C22C2×#6699512yes—
495C22#1062335512yes—
496C22#1062336712yes—
497C22C23×C22⋊D1111yescharacteristic
498C4—24no—
499C4—22no—
500C4—42no—
501C4—42no—
502C4—44no—
503C4—442no—
504C4—444no—
505C4—442no—
506C4C2×#6699514yes—
507C4#1062335512yes—
508C4C2×#41×D1111yescharacteristic
509C4C2×#6704311yescharacteristic
510C2—44no—
511C2#1308123114yesdirect product factor
512C2C2×#1062335511yescharacteristic
513C2C22×#6699511yescharacteristic
514C2C2×#1062336711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#554C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
hypercenterC2×#554D11
hypocenterC11C2×#3356
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
2. #13081231C2direct (N × H)
3. C2×#10622692C2semidirect
4. C2×#10622658C2semidirect
5. C2×#10622584C2semidirect
6. C2×#10622704C2semidirect
7. C2×#10622633C2semidirect
8. C2×#10622665C2semidirect
9. C2×C4×#4326C2semidirect
11. C2×#10622577C2semidirect
37. #10622704C22semidirect
38. #10622692C22semidirect
39. #10622665C22semidirect
40. #10622658C22semidirect
41. C4×#4326C22semidirect
42. #10622633C22semidirect
44. #10622584C22semidirect
47. #10622577C22semidirect
378. C2×C11#3356semidirect
446. C11C2×#3356semidirect
511. C2#13081231direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230732
#130812312
C2×#106226922
C2×#106226582
C2×#106225842
C2×#106227042
C2×#106226332
C2×#106226652
C2×C4×#43262
C2×#106226252
C2×#106225772
C2×C11×#5542
C2×#335611