Finite Group Databasebeta

← C2×#13079856 #15625934

Subgroups — C2×#13079856 #15625934

Order 2816.

1790 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
2#13079856C2116yesmaximal, direct product factor
3C2×#10622693C211yesmaximal, characteristic, complemented
4C2×#10622693C211yesmaximal, characteristic, complemented
5C2×#10622702C211yesmaximal, characteristic, complemented
6C2×#10622702C211yesmaximal, characteristic, complemented
7C2×#10622609C212yesmaximal, complemented
8C2×#10622616C212yesmaximal
9C2×#10622676C212yesmaximal, complemented
10C2×#10622679C212yesmaximal, complemented
11C2×#10622539C211yesmaximal, characteristic, complemented
12C2×C11×#533C211yesmaximal, characteristic, complemented
13C11×#533—24no—
14C11×#533C2218yescomplemented
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×#125C2212yes—
18C2×C11×C22⋊Q8—21no—
19C2×C11×C22⋊Q8—21no—
20C2×C4×Q8×C11—21no—
21C2×C4×Q8×C11—21no—
22C2×C11×#117C2212yes—
23C22×C42×C11C2211yescharacteristic
24C2×#66983C2211yescharacteristic
25C2×#66982—21no—
26C2×C4×C22⋊D11—21no—
27C2×#66977C2211yescharacteristic
28#10623010—24no—
29#10623010C2218yes—
30C2×#66929—21no—
31C2×#66928C2211yescharacteristic
32C2×C4×D44C2211yescharacteristic
33C2×#66925—21no—
34C2×#66923C2211yescharacteristic
35C2×C4×Dic22C2211yescharacteristic
36C2×C22⋊(C11⋊C8)C2212yes—
37#10622702C2218yescomplemented
38#10622702C2218yescomplemented
39#10622693C2218yescomplemented
40#10622693C2218yescomplemented
41#10622679C22116yescomplemented
42#10622676C22116yescomplemented
43#10622616C22116yes—
44#10622609C22116yescomplemented
45C2×#66874C2212yes—
46C2×#66874C2212yes—
47C2×#66873C2212yes—
48C2×#66873C2212yes—
49C2×#66872C2212yes—
50C2×#66872C2212yes—
51C2×#66871C2212yes—
52C2×#66871C2212yes—
53#10622539C2218yescomplemented
54C2×C4⋊(C11⋊C8)C2212yes—
55C2×#66867C2211yescharacteristic
56C2×#66867C2211yescharacteristic
57C22×Q8×C11—21no—
58C22×Q8×C11—21no—
59C23×C4×C11D411yescharacteristic
60C23×C4×C11D411yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11—21no—
63C22×D44C2311yescharacteristic
64C22×C4×D11—21no—
65C22×Dic22C2311yescharacteristic
66C11×C4⋊Q8—22no—
67C11×C4⋊Q8—22no—
68C11×C4⋊Q8C2314yes—
69C11×C4⋊Q8C2314yes—
70C11×#125—24no—
71C11×#125C2318yes—
72C11×C22⋊Q8—28no—
73C11×C22⋊Q8—28no—
74C4×Q8×C11—28no—
75C4×Q8×C11—28no—
76C11×#117—24no—
77C11×#117C2318yes—
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C4⋊C4C2312yes—
84C2×C11×C22⋊C4—22no—
85C2×C42×C11—22no—
86C2×C42×C11D411yescharacteristic
87C2×C42×C11D411yescharacteristic
88C2×C42×C11D414yes—
89C2×C42×C11C2311yescharacteristic
90C2×C42×C11C2311yescharacteristic
91C2×C42×C11C2314yes—
92C2×C22⋊Dic11—21no—
93#66983—22no—
94#66983C2314yes—
95#66982—28no—
96C4×C22⋊D11—28no—
97C2×(C2×D11)⋊C4—21no—
98C2×(C2×D11)⋊C4—21no—
99C2×(C2×D11)⋊C4—21no—
100C2×(C2×D11)⋊C4—21no—
101C2×C4⋊Dic11C2311yescharacteristic
102C2×C4⋊Dic11C2311yescharacteristic
103#66977—22no—
104#66977C2314yes—
105C2×Dic11⋊C4—21no—
106C2×Dic11⋊C4—21no—
107C2×Dic11⋊C4—21no—
108C2×Dic11⋊C4—21no—
109C2×C4×Dic11—21no—
110C22×C11⋊C8C2312yes—
111C22×C11⋊C8C2312yes—
112#66929—28no—
113#66928—22no—
114#66928C2314yes—
115C4×D44—22no—
116C4×D44C2314yes—
117#66925—28no—
118#66923—22no—
119#66923C2314yes—
120C4×Dic22—22no—
121C4×Dic22C2314yes—
122C22⋊(C11⋊C8)C2318yes—
123#66874C2318yes—
124#66874C2318yes—
125#66873C2318yes—
126#66873C2318yes—
127#66872C2318yes—
128#66872C2318yes—
129#66871C2318yes—
130#66871C2318yes—
131C4⋊(C11⋊C8)C2318yes—
132#66867C2314yes—
133#66867C2314yes—
134C2×#3240—111nomaximal, Sylow
135C24×C11C2×D411yescharacteristic
136C23×D11—21no—
137C2×Q8×C11—24no—
138C2×Q8×C11—24no—
139C2×Q8×C11—44no—
140C2×Q8×C11—44no—
141C22×C4×C11—24no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—42no—
145C22×C4×C11—42no—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2×D414yes—
153C22×C4×C11C2×D414yes—
154C22×C4×C11C2412yes—
155C22×C4×C11C2411yescharacteristic
156C2×C22⋊D11—24no—
157C2×C22⋊D11—44no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C2×D44—21no—
162C2×D44—24no—
163C2×D44C2412yes—
164C2×C4×D11—24no—
165C2×C4×D11—44no—
166C2×Dic22—21no—
167C2×Dic22—24no—
168C2×Dic22C2412yes—
169C11×C4⋊C4—28no—
170C11×C4⋊C4—28no—
171C11×C4⋊C4—24no—
172C11×C4⋊C4—24no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4C2414yes—
176C11×C4⋊C4C2414yes—
177C11×C22⋊C4—28no—
178C42×C11—28no—
179C42×C11C2×D412yes—
180C42×C11C2×D412yes—
181C42×C11C2×D414yes—
182C42×C11C2×D414yes—
183C42×C11C2412yes—
184C42×C11C2412yes—
185C22⋊Dic11—24no—
186(C2×D11)⋊C4—24no—
187(C2×D11)⋊C4—24no—
188(C2×D11)⋊C4—24no—
189(C2×D11)⋊C4—24no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11C2412yes—
193C4⋊Dic11C2412yes—
194Dic11⋊C4—24no—
195Dic11⋊C4—24no—
196Dic11⋊C4—24no—
197Dic11⋊C4—24no—
198C4×Dic11—24no—
199C2×C11⋊C8—24no—
200C2×C11⋊C8—24no—
201C2×C11⋊C8C2414yes—
202C2×C11⋊C8C2414yes—
203C2×#533D1111yescharacteristic, complemented
204C2×#529—111no—
205#3240—1116no—
206C2×#501—111no—
207C2×#501—111no—
208C2×#489—111no—
209C2×#489—111no—
210C2×#485—112no—
211C2×#482—112no—
212C2×#479—112no—
213C2×#478—112no—
214C2×#432—111no—
215C23×C11—22no—
216C23×C11—22no—
217C23×C11—22no—
218C23×C11C22×D412yes—
219C23×C11C22×D411yescharacteristic
220C22×D11—22no—
221C22×D11—42no—
222C22×D11—42no—
223C22×D11—42no—
224Q8×C11—48no—
225Q8×C11—48no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—44no—
236C2×C4×C11—44no—
237C2×C4×C11—44no—
238C2×C4×C11—44no—
239C2×C4×C11C22×D412yes—
240C2×C4×C11C22×D412yes—
241C2×C4×C11C22×D412yes—
242C2×C4×C11C22×D412yes—
243C2×C4×C11C22×D412yes—
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C112−1+414yes—
246C2×C4×C11C2511yescharacteristic
247C22⋊D11—48no—
248C2×Dic11—22no—
249C2×Dic11—22no—
250C2×Dic11—22no—
251C2×Dic11—42no—
252C2×Dic11—42no—
253C2×Dic11—42no—
254D44—24no—
255D44—42no—
256C4×D11—48no—
257Dic22—24no—
258Dic22—42no—
259C11⋊C8—24no—
260C11⋊C8—24no—
261#533—24no—
262#533C2×D1118yescomplemented
263C2×C4⋊Q8C2×D1111yescharacteristic
264C2×C4⋊Q8C2×D1111yescharacteristic
265#529—118no—
266#529—224no—
267C2×#126—221no—
268C2×#125—111no—
269C2×#125C2×D1112yes—
270C2×#124—111no—
271C2×#123—221no—
272C2×C22⋊Q8—21no—
273C2×C22⋊Q8—21no—
274C2×C22⋊Q8—111no—
275C2×#121—111no—
276C2×C4×Q8—21no—
277C2×C4×Q8—21no—
278C2×C4×Q8—111no—
279C2×C4×D4—111no—
280C2×C4×D4—221no—
281C2×#117—221no—
282C2×#117C2×D1112yes—
283C22×C42C2×D1111yescharacteristic
284#501—118no—
285#501—118no—
286#489—118no—
287#489—118no—
288#485—1116no—
289#482—1116no—
290#479—1116no—
291#478—1116no—
292#432—118no—
293C2×#107—112no—
294C2×#107—112no—
295C2×#106—112no—
296C2×#106—112no—
297C2×C4⋊C8—112no—
298C2×#103—112no—
299C2×#103—112no—
300C2×#102—112no—
301C2×#102—112no—
302C2×C22⋊C8—112no—
303C2×#97—111no—
304C2×#97—111no—
305C22×C11—22no—
306C22×C11—22no—
307C22×C11—22no—
308C22×C11—44no—
309C22×C11#53612yes—
310C22×C11#57512yes—
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—44no—
323C4×C11—44no—
324C4×C11#53612yes—
325C4×C11C2×2−1+412yes—
326Dic11—42no—
327Dic11—42no—
328Dic11—42no—
329C22×Q8—21no—
330C22×Q8—21no—
331C22×Q8—111no—
332C22×D4—111no—
333C22×D4—221no—
334C23×C4—221no—
335C23×C4C22⋊D1111yescharacteristic
336C23×C4C22⋊D1111yescharacteristic
337C23×C4C22×D1111yescharacteristic
338C22×C8—112no—
339C22×C8—112no—
340C4⋊Q8—22no—
341C4⋊Q8—22no—
342C4⋊Q8C22×D1114yes—
343C4⋊Q8C22×D1114yes—
344#126—228no—
345#125—24no—
346#125—114no—
347#125—222no—
348#125C22×D1118yes—
349#124—114no—
350#124—222no—
351#123—228no—
352C22⋊Q8—28no—
353C22⋊Q8—28no—
354C22⋊Q8—114no—
355C22⋊Q8—222no—
356#121—114no—
357#121—222no—
358C4×Q8—28no—
359C4×Q8—28no—
360C4×Q8—114no—
361C4×Q8—222no—
362C4×D4—114no—
363C4×D4—228no—
364C4×D4—222no—
365#117—24no—
366#117—228no—
367#117C22×D1118yes—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—111no—
373C2×C4⋊C4—111no—
374C2×C4⋊C4—221no—
375C2×C4⋊C4—221no—
376C2×C4⋊C4—221no—
377C2×C4⋊C4—221no—
378C2×C4⋊C4C22×D1112yes—
379C2×C4⋊C4C22×D1112yes—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—221no—
382C2×C22⋊C4—221no—
383C2×C22⋊C4—221no—
384C2×C22⋊C4—221no—
385C2×C22⋊C4—221no—
386C2×C42—22no—
387C2×C42—221no—
388C2×C42C22⋊D1111yescharacteristic
389C2×C42C22⋊D1111yescharacteristic
390C2×C42C22⋊D1114yes—
391C2×C42C22×D1111yescharacteristic
392C2×C42C22×D1111yescharacteristic
393C2×C42C22×D1114yes—
394#107—118no—
395#107—118no—
396#106—118no—
397#106—118no—
398C4⋊C8—118no—
399#103—118no—
400#103—118no—
401#102—118no—
402#102—118no—
403C22⋊C8—118no—
404#97—114no—
405#97—114no—
406C2×C11—42no—
407C2×C11#324014yescomplemented
408C2×C11C2×#53611yescharacteristic
409C2×C11C2×#57511yescharacteristic
410C2×C11C2×#57511yescharacteristic
411D11—82no—
412C24—221no—
413C24C2×C22⋊D1111yescharacteristic
414C2×Q8—24no—
415C2×Q8—24no—
416C2×Q8—44no—
417C2×Q8—44no—
418C2×Q8—112no—
419C2×Q8—221no—
420C2×Q8—224no—
421C2×D4—112no—
422C2×D4—224no—
423C2×D4—224no—
424C2×D4—221no—
425C2×D4—444no—
426C22×C4—24no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4—221no—
432C22×C4—221no—
433C22×C4—221no—
434C22×C4—224no—
435C22×C4—444no—
436C22×C4C2×C22⋊D1112yes—
437C22×C4C2×C22⋊D1111yescharacteristic
438C22×C4C2×C22⋊D1111yescharacteristic
439C22×C4C2×C22⋊D1111yescharacteristic
440C22×C4C2×C22⋊D1111yescharacteristic
441C22×C4C2×C22⋊D1111yescharacteristic
442C22×C4C2×C22⋊D1114yes—
443C22×C4C2×C22⋊D1114yes—
444C22×C4C23×D1112yes—
445C22×C4C23×D1111yescharacteristic
446C2×C8—114no—
447C2×C8—114no—
448C2×C8—224no—
449C2×C8—224no—
450C4⋊C4—28no—
451C4⋊C4—28no—
452C4⋊C4—24no—
453C4⋊C4—24no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—112no—
457C4⋊C4—112no—
458C4⋊C4—221no—
459C4⋊C4—221no—
460C4⋊C4—224no—
461C4⋊C4—224no—
462C4⋊C4—224no—
463C4⋊C4—224no—
464C4⋊C4C23×D1114yes—
465C4⋊C4C23×D1114yes—
466C22⋊C4—28no—
467C22⋊C4—224no—
468C22⋊C4—224no—
469C22⋊C4—224no—
470C22⋊C4—224no—
471C22⋊C4—224no—
472C42—28no—
473C42—224no—
474C42C2×C22⋊D1114yes—
475C42C2×C22⋊D1112yes—
476C42C2×C22⋊D1114yes—
477C42C2×C22⋊D1112yes—
478C42C23×D1112yes—
479C42C23×D1112yes—
480C11C2×#324011yescharacteristic, complemented, Sylow
481C23—22no—
482C23—22no—
483C23—22no—
484C23—222no—
485C23—442no—
486C23—442no—
487C23—442no—
488C23C22×C22⋊D1112yes—
489C23C22×C22⋊D1111yescharacteristic
490Q8—48no—
491Q8—48no—
492Q8—224no—
493Q8—442no—
494D4—224no—
495D4—448no—
496D4—442no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—44no—
507C2×C4—44no—
508C2×C4—44no—
509C2×C4—44no—
510C2×C4—222no—
511C2×C4—222no—
512C2×C4—222no—
513C2×C4—448no—
514C2×C4—442no—
515C2×C4—442no—
516C2×C4—442no—
517C2×C4#6704014yes—
518C2×C4C22×C22⋊D1112yes—
519C2×C4C22×C22⋊D1112yes—
520C2×C4C22×C22⋊D1112yes—
521C2×C4C22×C22⋊D1112yes—
522C2×C4C22×C22⋊D1112yes—
523C2×C4C22×C22⋊D1111yescharacteristic
524C2×C4C24×D1111yescharacteristic
525C8—224no—
526C8—224no—
527C22—22no—
528C22—22no—
529C22—22no—
530C22—44no—
531C22—442no—
532C22—442no—
533C22—442no—
534C22—884no—
535C22#1062334712yes—
536C22#1062335312yes—
537C22#1062335312yes—
538C22C23×C22⋊D1111yescharacteristic
539C4—22no—
540C4—22no—
541C4—22no—
542C4—22no—
543C4—22no—
544C4—44no—
545C4—44no—
546C4—442no—
547C4—442no—
548C4—442no—
549C4#1062334712yes—
550C4C2×#6704012yes—
551C2—42no—
552C2—882no—
553C2#1307985614yesdirect product factor
554C2C2×#1062334711yescharacteristic
555C2C2×#1062335311yescharacteristic
556C2C2×#1062335311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#533C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenterC2×#533D11
hypocenterC11C2×#3240
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
2. #13079856C2direct (N × H)
3. C2×#10622693C2semidirect
4. C2×#10622693C2semidirect
5. C2×#10622702C2semidirect
6. C2×#10622702C2semidirect
7. C2×#10622609C2semidirect
9. C2×#10622676C2semidirect
10. C2×#10622679C2semidirect
11. C2×#10622539C2semidirect
12. C2×C11×#533C2semidirect
14. C11×#533C22semidirect
37. #10622702C22semidirect
38. #10622702C22semidirect
39. #10622693C22semidirect
40. #10622693C22semidirect
41. #10622679C22semidirect
42. #10622676C22semidirect
44. #10622609C22semidirect
53. #10622539C22semidirect
203. C2×#533D11semidirect
262. #533C2×D11semidirect
407. C2×C11#3240semidirect
480. C11C2×#3240semidirect
553. C2#13079856direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230102
#130798562
C2×#106226932
C2×#106227022
C2×#106226092
C2×#106226162
C2×#106226762
C2×#106226792
C2×#106225392
C2×C11×#5332
C2×#324011