Finite Group Databasebeta

← C2×#13079786 #15625805

Subgroups — C2×#13079786 #15625805

Order 2816.

1822 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×#10623010C211yesmaximal, characteristic
2C22×#66923C211yesmaximal, characteristic, complemented
3#13079786C2116yesmaximal, direct product factor
4C2×#10622296C212yesmaximal, complemented
5C2×#10622310C212yesmaximal, complemented
6C2×#10622335C211yesmaximal, characteristic, complemented
7C2×#10622348C211yesmaximal, characteristic
8C2×#10622334C211yesmaximal, characteristic, complemented
9C2×#10622349C211yesmaximal, characteristic
10C2×#10622442C212yesmaximal, complemented
11C2×#10622460C212yesmaximal, complemented
12C2×C11×#431C211yesmaximal, characteristic, complemented
13C22×C42×C11C2211yescharacteristic
14C2×#66983C2211yescharacteristic
15C2×#66982—21no—
16C2×C4×C22⋊D11—21no—
17C22×C4⋊Dic11C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C2×#66977C2211yescharacteristic
20C22×Dic11⋊C4—21no—
21C22×Dic11⋊C4—21no—
22#10623010—24no—
23#10623010C2218yes—
24C2×#66929—21no—
25C2×#66928C2211yescharacteristic
26C2×C4×D44C2211yescharacteristic
27C2×#66925—21no—
28C2×#66923—24no—
29C2×#66923—21no—
30C2×#66923—21no—
31C2×#66923C2212yes—
32C2×#66923C2212yes—
33C2×#66923C2211yescharacteristic
34C2×#66923C2218yescomplemented
35C2×C4×Dic22C2211yescharacteristic
36C11×#431C2218yescomplemented
37C2×C11×C4⋊C8C2212yes—
38C2×C11×C22⋊C8C2211yescharacteristic
39C2×C11×C22⋊C8C2211yescharacteristic
40C2×C4×C8×C11C2212yes—
41C2×#66885C2212yes—
42C2×#66885C2212yes—
43C2×#66882C2212yes—
44C2×#66882C2212yes—
45C2×#66881C2212yes—
46C2×#66881C2212yes—
47C2×#66880C2212yes—
48C2×#66880C2212yes—
49#10622460C22116yescomplemented
50#10622442C22116yescomplemented
51#10622349C2218yes—
52#10622348C2218yes—
53#10622335C2218yescomplemented
54#10622334C2218yescomplemented
55#10622310C22116yescomplemented
56#10622296C22116yescomplemented
57C23×C4×C11D411yescharacteristic
58C23×C4×C11D411yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C22×C22⋊D11—21no—
61C23×Dic11—21no—
62C23×Dic11—21no—
63C22×D44C2311yescharacteristic
64C22×C4×D11—21no—
65C22×Dic22C2311yescharacteristic
66C22×C8×C11C2312yes—
67C22×C8×C11C2312yes—
68C2×C42×C11D411yescharacteristic
69C2×C42×C11D411yescharacteristic
70C2×C42×C11D414yes—
71C2×C42×C11C2311yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×C42×C11C2314yes—
74C2×C22⋊Dic11—21no—
75#66983—22no—
76#66983C2314yes—
77#66982—28no—
78C4×C22⋊D11—28no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11—22no—
86C2×C4⋊Dic11—22no—
87C2×C4⋊Dic11C2312yes—
88C2×C4⋊Dic11C2312yes—
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2314yes—
92C2×C4⋊Dic11C2314yes—
93#66977—22no—
94#66977C2314yes—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—22no—
97C2×Dic11⋊C4—22no—
98C2×Dic11⋊C4—22no—
99C2×Dic11⋊C4—22no—
100C2×Dic11⋊C4—28no—
101C2×Dic11⋊C4—28no—
102C2×Dic11⋊C4—21no—
103C2×Dic11⋊C4—21no—
104C2×Dic11⋊C4—21no—
105C2×C4×Dic11—21no—
106#66929—28no—
107#66928—22no—
108#66928C2314yes—
109C4×D44—22no—
110C4×D44C2314yes—
111#66925—28no—
112#66923—24no—
113#66923—24no—
114#66923—28no—
115#66923—28no—
116#66923—22no—
117#66923C2318yes—
118#66923C2318yes—
119#66923C2314yes—
120C4×Dic22—22no—
121C4×Dic22C2314yes—
122C11×C4⋊C8C2318yes—
123C11×C22⋊C8C2314yes—
124C11×C22⋊C8C2314yes—
125C4×C8×C11C2318yes—
126#66885C2318yes—
127#66885C2318yes—
128#66882C2318yes—
129#66882C2318yes—
130#66881C2318yes—
131#66881C2318yes—
132#66880C2318yes—
133#66880C2318yes—
134C2×#3232—111nomaximal, Sylow
135C24×C11C2×D411yescharacteristic
136C23×D11—21no—
137C22×C4×C11—24no—
138C22×C4×C11—24no—
139C22×C4×C11—42no—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D414yes—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D412yes—
147C22×C4×C11C2×D414yes—
148C22×C4×C11C2412yes—
149C22×C4×C11C2411yescharacteristic
150C2×C22⋊D11—24no—
151C2×C22⋊D11—44no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—24no—
155C22×Dic11—24no—
156C22×Dic11—22no—
157C22×Dic11—22no—
158C22×Dic11—21no—
159C22×Dic11—44no—
160C22×Dic11—44no—
161C2×D44—21no—
162C2×D44—24no—
163C2×D44C2412yes—
164C2×C4×D11—24no—
165C2×C4×D11—44no—
166C2×Dic22—21no—
167C2×Dic22—24no—
168C2×Dic22C2412yes—
169C2×C8×C11—24no—
170C2×C8×C11—24no—
171C2×C8×C11C2414yes—
172C2×C8×C11C2414yes—
173C42×C11C2×D412yes—
174C42×C11C2×D412yes—
175C42×C11C2×D414yes—
176C42×C11C2×D414yes—
177C42×C11C2412yes—
178C42×C11C2412yes—
179C22⋊Dic11—24no—
180(C2×D11)⋊C4—24no—
181(C2×D11)⋊C4—24no—
182(C2×D11)⋊C4—24no—
183(C2×D11)⋊C4—24no—
184C4⋊Dic11—21no—
185C4⋊Dic11—24no—
186C4⋊Dic11—24no—
187C4⋊Dic11—22no—
188C4⋊Dic11—22no—
189C4⋊Dic11—21no—
190C4⋊Dic11C2414yes—
191C4⋊Dic11C2414yes—
192C4⋊Dic11C2412yes—
193C4⋊Dic11C2412yes—
194Dic11⋊C4—24no—
195Dic11⋊C4—28no—
196Dic11⋊C4—28no—
197Dic11⋊C4—28no—
198Dic11⋊C4—28no—
199Dic11⋊C4—24no—
200Dic11⋊C4—24no—
201Dic11⋊C4—24no—
202C4×Dic11—24no—
203C2×#529—111no—
204C22×#125—111no—
205#3232—1116no—
206C2×#499—112no—
207C2×#488—112no—
208C2×#484—111no—
209C2×#481—111no—
210C2×#483—111no—
211C2×#480—111no—
212C2×#479—112no—
213C2×#478—112no—
214C2×#431D1111yescharacteristic, complemented
215C23×C11—22no—
216C23×C11—22no—
217C23×C11#13514yes—
218C23×C11C22×D412yes—
219C23×C11C22×D411yescharacteristic
220C22×D11—22no—
221C22×D11—42no—
222C22×D11—42no—
223C22×D11—42no—
224C2×C4×C11—22no—
225C2×C4×C11—28no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—44no—
233C2×C4×C11C22×D412yes—
234C2×C4×C11C22×D412yes—
235C2×C4×C11C22×D412yes—
236C2×C4×C11C22×D412yes—
237C2×C4×C11C22×D412yes—
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C112−1+414yes—
240C2×C4×C11C2511yescharacteristic
241C22⋊D11—48no—
242C2×Dic11—22no—
243C2×Dic11—22no—
244C2×Dic11—24no—
245C2×Dic11—24no—
246C2×Dic11—22no—
247C2×Dic11—48no—
248C2×Dic11—42no—
249C2×Dic11—48no—
250C2×Dic11—44no—
251C2×Dic11—42no—
252C2×Dic11—42no—
253C2×Dic11—44no—
254D44—24no—
255D44—42no—
256C4×D11—48no—
257Dic22—24no—
258Dic22—42no—
259C8×C11—24no—
260C8×C11—24no—
261#529—118no—
262#529—224no—
263C2×#126—221no—
264C2×#125—112no—
265C2×#125—112no—
266C2×#125—111no—
267C2×#125—118no—
268C2×#125—221no—
269C2×#125—221no—
270C2×#125—224no—
271C2×#124—111no—
272C2×#123—221no—
273C2×C22⋊Q8—111no—
274C2×#121—111no—
275C2×C4×Q8—111no—
276C2×C4×D4—111no—
277C2×C4×D4—221no—
278C2×#117—221no—
279C22×C4⋊C4—111no—
280C22×C4⋊C4—111no—
281C22×C4⋊C4—221no—
282C22×C4⋊C4—221no—
283C22×C42C2×D1111yescharacteristic
284#499—1116no—
285#488—1116no—
286#484—118no—
287#483—118no—
288#481—118no—
289#480—118no—
290#479—1116no—
291#478—1116no—
292#431C2×D1118yescomplemented
293C2×#107—112no—
294C2×#107—112no—
295C2×#106—112no—
296C2×#106—112no—
297C2×C4⋊C8C2×D1112yes—
298C2×#103—112no—
299C2×#103—112no—
300C2×#102—112no—
301C2×#102—112no—
302C2×C22⋊C8C2×D1111yescharacteristic
303C2×C22⋊C8C2×D1111yescharacteristic
304C2×C4×C8C2×D1112yes—
305C22×C11—22no—
306C22×C11—28no—
307C22×C11—22no—
308C22×C11#53612yes—
309C22×C11C2×#13514yes—
310C22×C11C2×#13512yes—
311C22×C11#57512yes—
312C22×C11C23×D411yescharacteristic
313C2×D11—42no—
314C2×D11—42no—
315C2×D11—42no—
316C2×D11—84no—
317C4×C11—22no—
318C4×C11—22no—
319C4×C11—22no—
320C4×C11—22no—
321C4×C11—22no—
322C4×C11#53612yes—
323C4×C11C2×2−1+412yes—
324Dic11—42no—
325Dic11—44no—
326Dic11—42no—
327Dic11—42no—
328Dic11—44no—
329C22×Q8—111no—
330C22×D4—111no—
331C22×D4—221no—
332C23×C4—221no—
333C23×C4—221no—
334C23×C4—221no—
335C23×C4D4411yescharacteristic
336C23×C4D4411yescharacteristic
337C23×C4C22×D1111yescharacteristic
338C22×C8C22×D1112yes—
339C22×C8C22×D1112yes—
340#126—228no—
341#125—118no—
342#125—118no—
343#125—114no—
344#125—228no—
345#125—224no—
346#125—224no—
347#125—228no—
348#125—222no—
349#124—114no—
350#124—222no—
351#123—228no—
352C22⋊Q8—114no—
353C22⋊Q8—222no—
354#121—114no—
355#121—222no—
356C4×Q8—114no—
357C4×Q8—222no—
358C4×D4—114no—
359C4×D4—228no—
360C4×D4—222no—
361#117—228no—
362C2×C4⋊C4—112no—
363C2×C4⋊C4—112no—
364C2×C4⋊C4—114no—
365C2×C4⋊C4—114no—
366C2×C4⋊C4—111no—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—222no—
369C2×C4⋊C4—222no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4—221no—
372C2×C4⋊C4—228no—
373C2×C4⋊C4—228no—
374C2×C4⋊C4—222no—
375C2×C4⋊C4—222no—
376C2×C4⋊C4—222no—
377C2×C4⋊C4—222no—
378C2×C4⋊C4—221no—
379C2×C4⋊C4—221no—
380C2×C4⋊C4—221no—
381C2×C4⋊C4—221no—
382C2×C22⋊C4—221no—
383C2×C22⋊C4—221no—
384C2×C22⋊C4—221no—
385C2×C22⋊C4—221no—
386C2×C22⋊C4—221no—
387C2×C42—221no—
388C2×C42D4411yescharacteristic
389C2×C42D4411yescharacteristic
390C2×C42D4414yes—
391C2×C42C22×D1111yescharacteristic
392C2×C42C22×D1111yescharacteristic
393C2×C42C22×D1114yes—
394#107—118no—
395#107—118no—
396#106—118no—
397#106—118no—
398C4⋊C8C22×D1118yes—
399#103—118no—
400#103—118no—
401#102—118no—
402#102—118no—
403C22⋊C8C22×D1114yes—
404C22⋊C8C22×D1114yes—
405C4×C8C22×D1118yes—
406C2×C11—24no—
407C2×C11#323214yescomplemented
408C2×C11C2×#53611yescharacteristic
409C2×C11C22×#13511yescharacteristic
410C2×C11C2×#57511yescharacteristic
411D11—82no—
412C24—221no—
413C24C2×D4411yescharacteristic
414C2×Q8—112no—
415C2×Q8—221no—
416C2×Q8—224no—
417C2×D4—112no—
418C2×D4—224no—
419C2×D4—221no—
420C2×D4—224no—
421C2×D4—444no—
422C22×C4—24no—
423C22×C4—24no—
424C22×C4—42no—
425C22×C4—224no—
426C22×C4—224no—
427C22×C4—221no—
428C22×C4—221no—
429C22×C4—221no—
430C22×C4—222no—
431C22×C4—222no—
432C22×C4—224no—
433C22×C4—444no—
434C22×C4—444no—
435C22×C4—444no—
436C22×C4C2×D4414yes—
437C22×C4C2×D4412yes—
438C22×C4C2×D4411yescharacteristic
439C22×C4C2×D4411yescharacteristic
440C22×C4C2×D4411yescharacteristic
441C22×C4C2×D4411yescharacteristic
442C22×C4C2×D4411yescharacteristic
443C22×C4C2×D4414yes—
444C22×C4C23×D1112yes—
445C22×C4C23×D1111yescharacteristic
446C2×C8—24no—
447C2×C8—24no—
448C2×C8C23×D1114yes—
449C2×C8C23×D1114yes—
450C4⋊C4—114no—
451C4⋊C4—114no—
452C4⋊C4—112no—
453C4⋊C4—112no—
454C4⋊C4—224no—
455C4⋊C4—224no—
456C4⋊C4—222no—
457C4⋊C4—222no—
458C4⋊C4—221no—
459C4⋊C4—221no—
460C4⋊C4—228no—
461C4⋊C4—228no—
462C4⋊C4—228no—
463C4⋊C4—228no—
464C4⋊C4—224no—
465C4⋊C4—224no—
466C4⋊C4—224no—
467C4⋊C4—224no—
468C22⋊C4—224no—
469C22⋊C4—224no—
470C22⋊C4—224no—
471C22⋊C4—224no—
472C22⋊C4—224no—
473C42—224no—
474C42C2×D4414yes—
475C42C2×D4412yes—
476C42C2×D4412yes—
477C42C2×D4414yes—
478C42C23×D1112yes—
479C42C23×D1112yes—
480C11C2×#323211yescharacteristic, complemented, Sylow
481C23—22no—
482C23—22no—
483C23—222no—
484C23—442no—
485C23—442no—
486C23—442no—
487C23#6695714yes—
488C23C22×D4412yes—
489C23C22×D4411yescharacteristic
490Q8—224no—
491Q8—442no—
492D4—224no—
493D4—448no—
494D4—442no—
495C2×C4—28no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—44no—
504C2×C4—222no—
505C2×C4—222no—
506C2×C4—222no—
507C2×C4—224no—
508C2×C4—224no—
509C2×C4—448no—
510C2×C4—448no—
511C2×C4—448no—
512C2×C4—444no—
513C2×C4—442no—
514C2×C4—442no—
515C2×C4—444no—
516C2×C4—442no—
517C2×C4C22×D4412yes—
518C2×C4C22×D4412yes—
519C2×C4C22×D4412yes—
520C2×C4C22×D4412yes—
521C2×C4C22×D4412yes—
522C2×C4C22×D4411yescharacteristic
523C2×C4#6704314yes—
524C2×C4C24×D1111yescharacteristic
525C8—24no—
526C8—24no—
527C22—22no—
528C22—22no—
529C22—28no—
530C22—442no—
531C22—442no—
532C22—442no—
533C22—884no—
534C22#1062305712yes—
535C22C2×#6695714yes—
536C22C2×#6695712yes—
537C22#1062327912yes—
538C22C23×D4411yescharacteristic
539C4—22no—
540C4—22no—
541C4—22no—
542C4—22no—
543C4—22no—
544C4—442no—
545C4—444no—
546C4—442no—
547C4—442no—
548C4—444no—
549C4#1062305712yes—
550C4C2×#6704312yes—
551C2—24no—
552C2—882no—
553C2#1307978614yesdirect product factor
554C2C2×#1062305711yescharacteristic
555C2C22×#6695711yescharacteristic
556C2C2×#1062327911yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#431C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenterC2×#431D11
hypocenterC11C2×#3232
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#431

Complements

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

NH ≅ G/Ntype
2. C22×#66923C2semidirect
3. #13079786C2direct (N × H)
4. C2×#10622296C2semidirect
5. C2×#10622310C2semidirect
6. C2×#10622335C2semidirect
8. C2×#10622334C2semidirect
10. C2×#10622442C2semidirect
11. C2×#10622460C2semidirect
12. C2×C11×#431C2semidirect
34. C2×#66923C22semidirect
36. C11×#431C22semidirect
49. #10622460C22semidirect
50. #10622442C22semidirect
53. #10622335C22semidirect
54. #10622334C22semidirect
55. #10622310C22semidirect
56. #10622296C22semidirect
214. C2×#431D11semidirect
292. #431C2×D11semidirect
407. C2×C11#3232semidirect
480. C11C2×#3232semidirect
553. C2#13079786direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230102
C22×#669232
#130797862
C2×#106222962
C2×#106223102
C2×#106223352
C2×#106223482
C2×#106223342
C2×#106223492
C2×#106224422
C2×#106224602
C2×C11×#4312
C2×#323211