Finite Group Databasebeta

← C2×#13081042 #15632272

Subgroups — C2×#13081042 #15632272

Order 2816.

1854 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623073C211yesmaximal, characteristic
2#13081042C2116yesmaximal, direct product factor
3C2×#10622691C211yesmaximal, characteristic, complemented
4C2×#10622609C212yesmaximal, complemented
5C2×#10622658C212yesmaximal, complemented
6C2×#10622633C211yesmaximal, characteristic, complemented
7C2×#10622707C211yesmaximal, characteristic, complemented
8C2×#10622664C212yesmaximal, complemented
9C2×C4×#4326C211yesmaximal, characteristic, complemented
10C2×D4×C11⋊C8C211yesmaximal, characteristic
11C2×#10622611C212yesmaximal, complemented
12C2×C11×#556C211yesmaximal, characteristic
13C11×#556—24no—
14C11×#556C2218yes—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#126—22no—
17C2×C11×#124—21no—
18C2×C11×C22⋊Q8C2212yes—
19C2×C4×Q8×C11—21no—
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×C11×#117C2212yes—
23C22×#4326C2211yescharacteristic
24C2×#66989—21no—
25C2×#66979C2212yes—
26C2×#66977C2212yes—
27C23×C11⋊C8C2212yes—
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#10622707C2218yescomplemented
38#10622691C2218yescomplemented
39#10622664C22116yescomplemented
40#10622658C22116yescomplemented
41C4×#4326C2218yescomplemented
42#10622633C2218yescomplemented
43D4×C11⋊C8C2218yes—
44#10622611C22116yescomplemented
45#10622609C22116yescomplemented
46C2×#66874C2212yes—
47C2×#66874C2211yescharacteristic
48C2×#66872C2212yes—
49C2×#66872C2212yes—
50C2×#66871C2212yes—
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×C11C2312yes—
59C22×Dic22—21no—
60C22×Dic22C2311yescharacteristic
61C11×C4⋊Q8—22no—
62C11×C4⋊Q8C2314yes—
63C11×#126—216no—
64C11×#124—28no—
65C11×C22⋊Q8—24no—
66C11×C22⋊Q8C2318yes—
67C4×Q8×C11—28no—
68C4×Q8×C11—22no—
69C4×Q8×C11C2314yes—
70C4×D4×C11D414yes—
71C4×D4×C11C2314yes—
72C11×#117—24no—
73C11×#117C2318yes—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4D411yescharacteristic
78C2×C11×C4⋊C4C2312yes—
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4D412yes—
83C2×C42×C11—22no—
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—
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#66899C2318yes—
114#66899C2314yes—
115C22⋊(C11⋊C8)C2318yes—
116#66874C2314yes—
117#66874C2318yes—
118#66872C2318yes—
119#66872C2318yes—
120#66871C2318yes—
121#66871C2314yes—
122#66871C2318yes—
123C4⋊(C11⋊C8)C2314yes—
124C4×C11⋊C8C2314yes—
125C2×#3342—111nomaximal, Sylow
126C24×C11C2×D412yes—
127C2×Q8×C11—21no—
128C2×Q8×C11—24no—
129C2×Q8×C11—22no—
130C2×Q8×C11—22no—
131C2×Q8×C11—44no—
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×C11C2×D412yes—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D414yes—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2414yes—
145C22×C4×C11C2411yescharacteristic
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—22no—
149C2×Dic22—21no—
150C2×Dic22—24no—
151C2×Dic22—22no—
152C2×Dic22—22no—
153C2×Dic22—44no—
154C2×Dic22C2412yes—
155C11×C4⋊C4—28no—
156C11×C4⋊C4—24no—
157C11×C4⋊C4—24no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4C2×D414yes—
161C11×C4⋊C4C2414yes—
162C11×C4⋊C4C2412yes—
163C11×C22⋊C4—28no—
164C11×C22⋊C4—28no—
165C11×C22⋊C4C2×D418yes—
166C42×C11—28no—
167C42×C11—24no—
168C42×C11C2×D412yes—
169C42×C11C2412yes—
170C22⋊Dic11—28no—
171C22⋊Dic11—28no—
172#4326—28no—
173C4⋊Dic11—21no—
174C4⋊Dic11—22no—
175C4⋊Dic11—24no—
176C4⋊Dic11C2414yes—
177C4⋊Dic11C2412yes—
178Dic11⋊C4—24no—
179Dic11⋊C4—28no—
180C4×Dic11—24no—
181C4×Dic11—28no—
182C2×C11⋊C8—216no—
183C2×C11⋊C8—24no—
184C2×C11⋊C8—22no—
185C2×C11⋊C8#4114yes—
186C2×C11⋊C8C2412yes—
187C2×C11⋊C8C2414yes—
188C2×C11⋊C8C2412yes—
189C2×#556—111no—
190C2×#556D1111yescharacteristic
191#3342—1116no—
192C2×#500—111no—
193C2×#485—112no—
194C2×#485—112no—
195C2×#475—111no—
196C2×#475—111no—
197C2×#467—112no—
198C2×C4×Q16—111no—
199C2×C8×D4—111no—
200C2×#427—112no—
201C23×C11—24no—
202C23×C11—24no—
203C23×C11—24no—
204C23×C11C22×D414yes—
205C23×C11C22×D411yescharacteristic
206Q8×C11—22no—
207Q8×C11—22no—
208Q8×C11—42no—
209Q8×C11—48no—
210D4×C11—28no—
211C2×C4×C11—24no—
212C2×C4×C11—22no—
213C2×C4×C11—28no—
214C2×C4×C11—24no—
215C2×C4×C11—24no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—24no—
219C2×C4×C11—42no—
220C2×C4×C11—44no—
221C2×C4×C11—42no—
222C2×C4×C11#13514yes—
223C2×C4×C11C22×D414yes—
224C2×C4×C11C22×D412yes—
225C2×C4×C11C22×D411yescharacteristic
226C2×C4×C11C22×D412yes—
227C2×C4×C11C2×#4112yes—
228C2×C4×C112−1+412yes—
229C2×C4×C11C2511yescharacteristic
230C2×Dic11—22no—
231C2×Dic11—22no—
232C2×Dic11—24no—
233C2×Dic11—42no—
234C2×Dic11—44no—
235C2×Dic11—42no—
236Dic22—22no—
237Dic22—22no—
238Dic22—42no—
239Dic22—48no—
240C11⋊C8—24no—
241C11⋊C8—22no—
242C11⋊C8C2×#4114yes—
243C22×Q16—111no—
244C23×C8—112no—
245#556—24no—
246#556—118no—
247#556—224no—
248#556C2×D1118yes—
249C2×C4⋊Q8—111no—
250C2×C4⋊Q8C2×D1111yescharacteristic
251C2×#126—22no—
252C2×#126—222no—
253C2×#124—21no—
254C2×#124—221no—
255C2×C22⋊Q8—112no—
256C2×C22⋊Q8C2×D1112yes—
257C2×C4×Q8—21no—
258C2×C4×Q8—111no—
259C2×C4×Q8—221no—
260C2×C4×Q8C2×D1111yescharacteristic
261C2×C4×D4C2×D1111yescharacteristic
262C2×#117—112no—
263C2×#117C2×D1112yes—
264#500—118no—
265#485—1116no—
266#485—1116no—
267#475—118no—
268#475—118no—
269#467—1116no—
270C4×Q16—118no—
271C8×D4—118no—
272#427—1116no—
273C2×#107—112no—
274C2×#107—112no—
275C2×#107—111no—
276C2×#106—112no—
277C2×#106—112no—
278C2×C4⋊C8—111no—
279C2×#103—112no—
280C2×#103—111no—
281C2×#103—112no—
282C2×#103—111no—
283C2×C22⋊C8—112no—
284C2×C4×C8—111no—
285C22×C11—24no—
286C22×C11—24no—
287C22×C11—24no—
288C22×C11—48no—
289C22×C11#54712yes—
290C22×C11C2×#13512yes—
291C22×C11#57812yes—
292C22×C11C23×D411yescharacteristic
293C4×C11—24no—
294C4×C11—22no—
295C4×C11—42no—
296C4×C11—44no—
297C4×C11—42no—
298C4×C11#54712yes—
299C4×C11C2×#13514yes—
300C4×C11C22×#4111yescharacteristic
301C4×C11C2×2−1+411yescharacteristic
302Dic11—42no—
303Dic11—44no—
304Dic11—42no—
305C22×Q8—21no—
306C22×Q8—111no—
307C22×Q8—221no—
308C22×Q8C22×D1111yescharacteristic
309C22×D4C22⋊D1111yescharacteristic
310C23×C4C22×D1112yes—
311C2×Q16—114no—
312C2×Q16—224no—
313C22×C8—111no—
314C22×C8—112no—
315C22×C8—118no—
316C22×C8—111no—
317C22×C8—228no—
318C4⋊Q8—22no—
319C4⋊Q8—114no—
320C4⋊Q8—222no—
321C4⋊Q8C22×D1114yes—
322#126—216no—
323#126—2216no—
324#124—28no—
325#124—228no—
326C22⋊Q8—24no—
327C22⋊Q8—118no—
328C22⋊Q8—224no—
329C22⋊Q8C22×D1118yes—
330C4×Q8—28no—
331C4×Q8—22no—
332C4×Q8—114no—
333C4×Q8—228no—
334C4×Q8—222no—
335C4×Q8C22×D1114yes—
336C4×D4C22⋊D1114yes—
337C4×D4C22×D1114yes—
338#117—24no—
339#117—118no—
340#117—224no—
341#117C22×D1118yes—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—111no—
346C2×C4⋊C4—112no—
347C2×C4⋊C4—221no—
348C2×C4⋊C4—222no—
349C2×C4⋊C4—221no—
350C2×C4⋊C4C22⋊D1111yescharacteristic
351C2×C4⋊C4C22×D1111yescharacteristic
352C2×C4⋊C4C22×D1112yes—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—222no—
356C2×C22⋊C4—222no—
357C2×C22⋊C4C22⋊D1112yes—
358C2×C42—22no—
359C2×C42—21no—
360C2×C42—222no—
361C2×C42—221no—
362C2×C42C22×D1111yescharacteristic
363#107—114no—
364#107—118no—
365#107—118no—
366#106—118no—
367#106—118no—
368C4⋊C8—114no—
369#103—114no—
370#103—118no—
371#103—114no—
372#103—118no—
373C22⋊C8—118no—
374C4×C8—114no—
375C2×C11—44no—
376C2×C11#334214yescomplemented
377C2×C11C2×#54711yescharacteristic
378C2×C11C22×#13511yescharacteristic
379C2×C11C2×#57811yescharacteristic
380C24C2×C22⋊D1112yes—
381C2×Q8—21no—
382C2×Q8—24no—
383C2×Q8—22no—
384C2×Q8—22no—
385C2×Q8—44no—
386C2×Q8—112no—
387C2×Q8—221no—
388C2×Q8—224no—
389C2×Q8—222no—
390C2×Q8—222no—
391C2×Q8—444no—
392C2×Q8C23×D1112yes—
393C2×D4—24no—
394C2×D4C2×C22⋊D1114yes—
395C22×C4—24no—
396C22×C4—24no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—22no—
400C22×C4—221no—
401C22×C4—222no—
402C22×C4—221no—
403C22×C4C2×C22⋊D1114yes—
404C22×C4C2×C22⋊D1112yes—
405C22×C4C2×C22⋊D1111yescharacteristic
406C22×C4C2×C22⋊D1111yescharacteristic
407C22×C4C23×D1114yes—
408C22×C4C23×D1111yescharacteristic
409Q16—228no—
410C2×C8—114no—
411C2×C8—112no—
412C2×C8—112no—
413C2×C8—114no—
414C2×C8—2216no—
415C2×C8—224no—
416C2×C8—222no—
417C4⋊C4—28no—
418C4⋊C4—24no—
419C4⋊C4—24no—
420C4⋊C4—21no—
421C4⋊C4—22no—
422C4⋊C4—112no—
423C4⋊C4—114no—
424C4⋊C4—221no—
425C4⋊C4—222no—
426C4⋊C4—224no—
427C4⋊C4—228no—
428C4⋊C4—224no—
429C4⋊C4C2×C22⋊D1114yes—
430C4⋊C4C23×D1112yes—
431C4⋊C4C23×D1114yes—
432C22⋊C4—28no—
433C22⋊C4—28no—
434C22⋊C4—228no—
435C22⋊C4—228no—
436C22⋊C4C2×C22⋊D1118yes—
437C42—28no—
438C42—24no—
439C42—228no—
440C42—224no—
441C42C2×C22⋊D1112yes—
442C42C23×D1112yes—
443C11C2×#334211yescharacteristic, complemented, Sylow
444C23—24no—
445C23—24no—
446C23—24no—
447C23C22×C22⋊D1114yes—
448C23C22×C22⋊D1111yescharacteristic
449Q8—22no—
450Q8—22no—
451Q8—48no—
452Q8—42no—
453Q8—222no—
454Q8—222no—
455Q8—448no—
456Q8—442no—
457D4—28no—
458C2×C4—24no—
459C2×C4—22no—
460C2×C4—28no—
461C2×C4—24no—
462C2×C4—24no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—24no—
466C2×C4—44no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—222no—
470C2×C4—224no—
471C2×C4—222no—
472C2×C4—444no—
473C2×C4—442no—
474C2×C4—442no—
475C2×C4#6700314yes—
476C2×C4#41×D1112yes—
477C2×C4#6704312yes—
478C2×C4C22×C22⋊D1114yes—
479C2×C4C22×C22⋊D1112yes—
480C2×C4C22×C22⋊D1112yes—
481C2×C4C22×C22⋊D1111yescharacteristic
482C2×C4C24×D1111yescharacteristic
483C8—114no—
484C8—224no—
485C8—222no—
486C22—24no—
487C22—24no—
488C22—24no—
489C22—48no—
490C22C2×#6700312yes—
491C22#1062335512yes—
492C22#1062336912yes—
493C22C23×C22⋊D1111yescharacteristic
494C4—24no—
495C4—22no—
496C4—44no—
497C4—42no—
498C4—42no—
499C4—444no—
500C4—442no—
501C4—442no—
502C4C2×#6700314yes—
503C4#1062335512yes—
504C4C2×#41×D1111yescharacteristic
505C4C2×#6704311yescharacteristic
506C2—44no—
507C2#1308104214yesdirect product factor
508C2C2×#1062335511yescharacteristic
509C2C22×#6700311yescharacteristic
510C2C2×#1062336911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#556C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
hypercenterC2×#556D11
hypocenterC11C2×#3342
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
2. #13081042C2direct (N × H)
3. C2×#10622691C2semidirect
4. C2×#10622609C2semidirect
5. C2×#10622658C2semidirect
6. C2×#10622633C2semidirect
7. C2×#10622707C2semidirect
8. C2×#10622664C2semidirect
9. C2×C4×#4326C2semidirect
11. C2×#10622611C2semidirect
37. #10622707C22semidirect
38. #10622691C22semidirect
39. #10622664C22semidirect
40. #10622658C22semidirect
41. C4×#4326C22semidirect
42. #10622633C22semidirect
44. #10622611C22semidirect
45. #10622609C22semidirect
376. C2×C11#3342semidirect
443. C11C2×#3342semidirect
507. C2#13081042direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230732
#130810422
C2×#106226912
C2×#106226092
C2×#106226582
C2×#106226332
C2×#106227072
C2×#106226642
C2×C4×#43262
C2×D4×C11⋊C82
C2×#106226112
C2×C11×#5562
C2×#334211